La première personne que je souhaiterais remercier est, bien sûr, mon tuteur/directeur de thèse Cyril Poupon, sans qui mon expérience à Neurospin n'aurait pas été si bénéfique. Premièrement merci de m'avoir fait confiance, en premier lieu pour le stage, car je n'avais pas forcément un parcours très cohérent avec le domaine de la recherche. Merci de ne pas m'avoir cantonnée à ce que je pouvais a priori savoir faire, et de m'avoir laissée explorer l'anatomie du cerveau humain à mon grés. Merci pour ton soutien et la confiance répétée lors de mon souhait de poursuivre en thèse sur ce sujet passionnant. Ton investissement et ta disponibilité m'ont plus d'une fois rassurés, en particulier à l'approche d'échéances importantes. Tes prochains thésards ont beaucoup de chance! I would like to thank Dr Tim Dyrby and Dr Gary Zhang for doing me the honor of being my reviewers. Your work was very inspirational for me and all the team that I am part of, and I am very proud to have you in my thesis committee. Merci également à Eric Bardinet, Josselin Houenou et Luc Darrasse, d'avoir accepté de faire partie de mon jury de thèse, ainsi qu'à Christophe Destrieux et Jean-Franc ¸ois Mangin, pour leurs conseils et leur accompagnement tout au long de ma thèse et pour s'être rendu disponibles pour ma soutenance.

Au cours de cette thèse, j'ai eu la chance de collaborer avec différentes équipes. Je souhaiterais donc remercier l'équipe de Katrin Amunts, à Jülich, en particulier Nicola Palomero-Gallagher, pour ses conseils inestimables sur l'anatomie de l'hippocampe humain, ainsi que Markus Axer, pour son accueil au Forschungszentrum de Jülich. Un grand merci également à l'équipe de Christophe Destrieux : Christophe, Franc ¸ois, Frédéric, Laurent, Scott,

 [START_REF] Azmitia | Changing views of cajal's neuron: Introduction[END_REF]. Si de nombreuses avancées ont été réalisées au cours du siècle dernier, la majorité des grandes questions reste encore en suspens.

Ces axes de recherche concernent notamment des maladies neurologiques (sclérose en plaque, maladie d'Alzheimer ou de Parkinson) ou psychiatriques (schizophrénie, autisme, ou TOC). Il s'agit également d'approcher la nature et le fonctionnement du cerveau et de l'esprit, avec, au coeur de cela, la question de la conscience. Comprendre le fonctionnement du cerveau humain, c'est à la fois connaître son anatomie, être en mesure de ségréguer ses diverses aires fonctionnelles, et comprendre comment ces aires sont interconnectées.

Jusqu'à l'avènement de l'imagerie médicale moderne, cette quête passait essentiellement par la dissection de pièces anatomiques. Au cours du siècle dernier, les techniques de neuroimagerie telles que la tomodensitométrie (CT), la tomographie par émission de positons (TEP), l'éléctroencéphalographie (EEG), la magnétoencéphalographie (MEG), et enfin l'imagerie par résonance magnétique (IRM), ont révolutionné l'étude du cerveau humain en permettant aux neuroscientifiques d'observer le cerveau humain in vivo. L'IRM est rapidement devenue la modalité de choix, et ce pour plusieurs raisons.

Premièrement, l'IRM est non invasive, contrairement au scanner CT et à la TEP, ce qui rend possible l'étude de sujets sains. Par ailleurs, l'IRM produit un très bon contraste pour les tissus mous et permet d'obtenir des images cérébrales de haute qualité. Enfin, cette modalité donne accès à l'étude de différents aspects du cerveau. L'IRM fonctionnelle renseigne sur les principaux réseau fonctionnels, tandis que l'IRM de diffusion donne accès à la connectivité structurelle du tissu cérébral ainsi qu'à des caractéristiques de sa microstructure, telle que la densité axonale. Cependant, la résolution spatiale accessible in vivo reste limitée. Avec une résolution de l'ordre de 1-3 mm, l'IRM de diffusion ne permet de reconstruire que les principaux réseaux de communication, et la résolution anatomique, de l'ordre de 1 mm, n'est pas suffisante pour accéder aux structures les plus fine telles que les noyaux du tronc cérébral.

L'ambition des très hauts champs magnétiques (≥ 7 T) associés à des systèmes de gradients très xvii puissants (≥ 300 mT/m) est de dépasser la résolution millimétrique et d'atteindre ainsi l'échelle mésoscopique en neuroimagerie. Etudier le cerveau à cette échelle permettrait d'avoir accès aux couches corticales et de pouvoir parcelliser le cortex à sa surface, ce qui est fondamental pour mieux comprendre le lien entre une fonction cérébrale et son substrat anatomique. Etre en mesure de cartographier des structures submillimétriques inexplorables à plus bas champ, à l'instar des noyaux du tronc cérébral ou des structures internes de l'hippocampe, et étudier comment ces structures sont interconnectées est également essentiel pour affiner la compréhension des mécanismes en jeu dans nombre de pathologies cérébrales (neurologiques, psychologies, ou développementales).

Pour atteindre de telles résolutions, il est nécessaire de combiner un champ magnétique très élevé et un système de gradients très puissant. L'augmentation du champ magnétique augmente le niveau de signal et améliore ainsi la résolution spatiale. Des systèmes de gradients plus performants permettent d'une part de répondre au besoin d'accélération des acquisitions lié à la réduction du temps de relaxation transversale provoquée par l'augmentation du champ magnétique, et d'autre part d'augmenter la sensibilité de l'IRM au processus de diffusion, technique essentielle pour sonder la microstructure du tissu cérébral. Malheureusement, les contraintes mécaniques très fortes subies par les gradients à très hauts champs lors de la commutation d'impulsions de très fortes amplitudes ne permettent pas aujourd'hui de bénéficier des deux progrès à la fois sur un IRM clinique. De surcroît, dans l'hypothèse où ces technologies seraient disponibles, la durée des acquisitions nécessaire à l'obtention de résolutions mésoscopiques dépasserait les limites acceptables dans un cadre d'études in vivo.

Cette thèse vise à répondre au besoin de cartographie du cerveau humain à une échelle mésoscopique via l'étude d'échantillons post mortem. Ces échantillons sont étudiés à l'aide d'une IRM préclinique associant très hauts champs magnétiques (7T et 11.7T) et gradients de forte amplitude (780mT/m), ce qui permet l'obtention d'une cartographie des structures anatomiques, de la cytoarchitecture et de la connectivité du tissu cérébral à une résolution de quelques centaines de micromètres.

Ces travaux de thèse ont été menés dans le cadre de deux projets:

• le projet FibrAtlasII-III visant à valider les méthodes d'inférence de la connectvité anatomique sur une base de données issue de volontaires ayant fait don de leur corps à la science et ayant été scannés in vivo et ex vivo. Ce projet se déroule sous la coordination du Pr Destrieux (Bretonneau University Hospital, Tours, UMR930),

• le Human Brain Project (HBP) visant à élaborer une cartographie multiéchelle (de micro à macro) du cerveau humain. Dans ce cadre, l'objectif est ici de fournir des données mésoscopiques ex vivo du cerveau humain, et d'étudier la connectivité fine ainsi que la microstructure de la substance blanche. Ce projet se déroule en collaboration avec l'équipe des Pr K. Amunts et K. Zilles (INM1,Forschungszentrum Jülich), sous la double coordination du Pr K. Amunts et de Dr Jean-Franc ¸ois Mangin L'objectif principal de cette thèse était l'étalissement d'un atlas IRM post mortem du cerveau humain à une résolution mésoscopique (quelques centaines de micromètres). Cet objectif étant un objectif à long terme, sa réalisation fut échelonnée par l'étude de structures clé du cerveau humain (l'hippocampe, le tronc cérébral et le cortex visuel) permettant de valider la méthodologie mise en oeuvre. Chacune des ces études constitue un chapitre de ce manuscrit, le dernier chapitre étant consacré à l'établissement d'un nouvel atlas IMR post mortem à très haut champ et hautes résolutions.

L'hippocampe: étude de ses sous-champs, de leur connectivité et de leur microstructure L'étude d'un hippocampe humain post mortem a permis la mise au point d'un protocole d'acquisition à 11.7 T. Ce protocole incluait des images anatomiques pondérées en T2 à 200 µm ainsi que des images pondérées en diffusion à une résolution de 300 µm combinant un jeu de données HARDI (b = 4500 s/mm 2 , 500 directions) pour l'analyse de la connectivité, et un jeu de données HYDI (b = 4500, 7500, 10000 s/mm 2 , 60 directions chacun) permettant l'utilisation de modèles avancés de la microstructure. L'analyse de ces images a conduit à l'élaboration d'un protocole de segmentation des sous-champs de l'hippocampe humain combinant les contrastes anatomiques pondérés en T2 et les contrastes obtenus avec les images pondérées en diffusion (Fig. 1). L'analyse de la connectivité (Fig.

2

) et des cartes de microstructure a révélé une connectivité accrue dans la zone de l'uncus quelle que soit la méthode de tractographie appliquée, ainsi qu'une plus grande densité neuritique. Cette observation est cohérente avec la spécialisation de l'hippocampe selon son axe longitudinal observée dans d'autres études. Par ailleurs, la structure laminaire de l'hippocampe en trois couches principales a été mise en évidence grâce à l'exploitation des cartes de densité neuritique (Fig. 3), ce qui présume du rôle croissant que pourraient jouer les contrastes apportés par les cartes de caractéristiques microstructurelles dans l'établissement de protocole de segmentation des structures cérébrales. Cette première étude a été conclue par une publication dans la revue scientifique Brain Structure And Function (voir appendix A). Le tronc cérébral: étude de ses noyaux, de leur connectivité et de leur microstructure

Les acquisitions réalisées à 11.7 T sur un échantillon de tronc cérébral humain post mortem ont conduit à l'obtention d'un jeu de données unique à haute résolution spatio-angulaire: 100 et 185 µm isotrope pour les images anatomiques pondérées en T2, et 300 µm pour les images pondérées en diffusion, avec l'acquisition de dix valeurs de b allant jusqu'à 10000 s/mm 2 , et le long de 400 directions à b = 4500 s/mm 2 . Un protocole de segmentation manuelle de 51 des 73 structures recensées dans le tronc a été mis au point par Dr F. Lechanoine (Université de Tours, hopital Bretonneau), ce qui en fait à ce jour l'atlas IRM le plus complet du tronc cérébral humain (Fig. 4). Les principaux faisceaux de matière blanche ont été reconstruits, incluant le faisceau cortico-spinal et les pédoncules cérebelleux, ainsi que les projections du locus coeruleus, une structure connue pour être impactée dans la maladie de Parkinson (Fig. 5). L'utilisation du modèle NODDI a permis de mettre en évidence de nouveaux contrastes qui pourraient être mis à profit pour l'amélioration des méthodes de segmentation actuelles. Ce travail fait actuellement l'objet de la rédaction d'une publication scientifique.

Le cortex visuel: mise en évidence des couches corticales par l'étude conjointe de contrastes sensibles à la myelo-et à la cyto-architecture

Ce travail propose une nouvelle méthode de segmentation automatique des couches corticales en intégrant des informations de nature myéloarchitecturales révélées par la mesure quantitative du temps de relaxation T1 et des informations de nature cytoarchitecturale apportées par des modèles avancés du processus de diffusion en IRM. Un échantillon de cerveau humain contenant une partie du cortex visuel primaire et secondaire a été scanné à 11.7 T et à 7 T. Le jeu de données produit incluait des cartes anatomiques à haute résolution (100 et 150 µm), des images pondérées en diffusion = 1500, 4500, 8000 s/mm 2 , acquis le long de 25, 60, 90 directions). Le champ de vue de l'antenne étant limité, l'acquisition de chaque bloc de 20 cm était divisée en quatre acquisitions durant chacune 107h, chaque session d'imagerie permettant l'acquisition d'un champ de vue de 5.6 cm de long et de section carrée de 4×4 cm (Fig. 7).

L'automatisation de la phase de prétraitement des images acquises à 11.7 T, de l'étape de reconstruction à l'application d'un filtre de débruitage pour les images de diffusion, a été mise en place au court

Principales contributions et perspectives

Le "Human Brain Project" (HBP) est un projet européen lancé en 2013 pour une durée de 10 ans. Il présente trois objectifs principaux. Le premier est de s'attaquer à des questions d'ordre fondamental sur la spécificité de l'Homme par rapport aux autres espèces animales. Le second est de contribuer à la compréhension des pathologies cérébrales et de développer de nouvelles approches thérapeutiques.

Enfin, ce projet doit mener à une nouvelle génération de systèmes informatiques neuromorphiques.

Ce projet de thèse s'inscrit dans le cadre du projet HBP, et plus particulièrement du sous-projet SP2

Context and motivations

The human brain is an incredibly complex system and its understanding represents one of the greatest challenge of the 21st century. At the turn of the 20th century, Santiago Ramon y Cajal argued that the brain was made up of neurons woven together in a highly specific way [START_REF] Azmitia | Changing views of cajal's neuron: Introduction[END_REF]. Great advances have been made since then. In the 1950s, the hippocampus was identified as the place where memories are formed, and fifty years after, its plasticity was demonstrated by E. Maguire through the study of London's drivers brains. Functions have been progressively associated to brain areas and links between abnormal brain anatomy and diseases have been established (e.g. a decreased volume of the hippocampus in the case of Alzheimer's disease). Nonetheless, the majority of the major questions remain. Neurological diseases (multiple sclerosis, Alzeihmer's or Parkinson's diseases) and psychiatric diseases (schizophrenia, autism and bipolar disorders) are currently receiving considerable attention, as well as questions such as the general nature and workings of the brain and mind and how phenomena such as consciousness evolve.

Understanding how the human brain works requires to have knowledge about its anatomy, to segregate its functional areas, and to understand how these areas are interconnected. Over the last century, neuroimaging tools such as computed tomography (CT), positron-emission tomography (PET), electroencephalography (EEG), magnetoencephalography (MEG), and magnetic resonance imaging (MRI) have revolutionized the study of the human brain by allowing neuroscientists to look at the brain in vivo. MRI rapidly became the key imaging modality to explore the brain anatomy. The reasons are twofold. First, MRI does not use ionizing radiation, contrary to CT or PET, which makes possible the deep investigation of healthy subjects neuroanatomy. Then, MRI shows much greater soft tissue contrast and provides anatomical images with resolutions that are constantly improving.

MRI has proven to be a highly versatile imaging technique. Functional MRI (fMRI) provides information about the major functional networks, while diffusion MRI (dMRI) gives access to the structural connectivity of the tissue as well as key features about its microstructure such as the mean 1 Chapter 1. Introduction 2 neurite density or the fiber orientation dispersion. However, the spatial resolution accessible in vivo remains limited. The typical voxel size for in vivo dMRI is in the range 1-3 mm, which only gives access to the major and large bundles, and anatomical images are usually acquired with a resolution of 1 mm, which is not sufficient to study the finer structures such as the brainstem nuclei.

The aim of ultra high magnetic fields (≥ 7 T) and ultra-strong gradient magnitudes (≥ 300 mT/m) is to go beyond the millimeter resolution imposed at lower field and to reach the mesoscopic scale in neuroimaging, in order to explore the human brain at spatial resolutions of a few hundred micrometers. The ability to map and differentiate cortical layers, or even to parcellate the cortex, is fundamental to better understand the relationships between a brain function and its anatomical substrate. Submillimeter structures such as brainstem nuclei, hippocampal subfields or cortical layers remain difficult to probe at low or moderate fields. Similarly, exploring the subcortical connectivity turns to be challenging with weak gradients. Being able to map all these structures and study connections could play a crucial role to decipher the structural and functional organization of the human brain. This would also help understanding the mechanisms involved in neurological, psychological, or developmental diseases, while exploring subcortical connectivity could highlight the human connectome.

To reach such resolutions, clinical MRI systems require both high static field and strong gradient systems. Increasing the field strength improves the signal level and consequently increases the achievable spatial resolution. High-performance gradient systems enable to accelerate acquisition sequences, which is required at higher field due to the reduction of transverse relaxation time, and also improve the sensitivity to the diffusion process. However, this is not yet possible to benefit from both progress at the same time on a clinical MRI system, because of the mechanical constraints experienced by ultra high field gradients when switching pulses of high amplitudes. Moreover, in the hypothesis of a system combining ultra-high field and strong gradients, the duration of acquisitions that would be conducted to obtain a mesoscopic resolution in vivo would greatly exceed the acceptable limits for a living subject.

This thesis aims at answering the needs for mapping the human brain at a mesoscopic scale through the study of post mortem samples. An alternative approach has been adopted, based on the use of preclinical systems equipped with ultra-high magnetic fields (7T/11.7 T) and strong gradients (780 mT/m).

This thesis work was carried out within the framework of two projects:

• the FibrAtlasII-III project, which aimed at validating methods used to infer the anatomical connectivity, through the acquisition of a unique database established from volunteers who gave their body to science and who have been scanned in vivo and ex vivo. This project was conducted in collaboration with Pr Destrieux's team (Bretonneau University Hospital, Tours, UMR930),

• the Human Brain Project (HBP), which purpose was to develop a multi-scale (micro to macro) mapping of the human brain, focusing here on obtaining ex vivo mesoscopic data of the human brain by studying the fine connectivity and microstructure of the white matter. This project was carried out in collaboration with Pr Amunts and Pr Zilles' team (INM1,Forschungszentrum Jülich).

The overall objective of this thesis work was the establishment of a mesoscopic post mortem human brain MRI atlas. This objective being a long-term work, it was guided by the study of key structures of the human brain that helped to define the methodology: the hippocampus, the brainstem, and the visual cortex.

Organization of this thesis

This thesis is organized into three parts. The background part describes the cerebral anatomy, the principles of dMRI, and the prerequisites to perform post mortem imaging. Then, the second part presents the first contributions of this thesis with the study of three key structures, the hippocampus, the brainstem and the visual cortex. Finally, the last part depicts the Chenonceau project, which is the name given to the post mortem human brain MRI atlas resulting from the work achieved during this thesis.

Part I -Background

Chapter 2: Human brain anatomy

This chapter presents a background on the key aspects of the human brain anatomy. First of all, the gross anatomy is presented, including a description of the principal structures of the encephalon. The second section explains how the folded appearance of the cerebrum surface inspired neuroanatomists to divide it into lobes, each of them assumed to be associated with distinct cognitive functions. Structure and role of cortical areas and deep nuclei are reviewed, as well as the structural connectivity of the brain supported by white matter fiber bundles. Last, the cellular composition of brain tissue (e.g.

the laminar structure of the cortex) is presented in order to highlight its potential to further segregate brain areas.

Chapter 3: Diffusion MRI: a powerful tool to probe the brain architecture

This chapter presents the principles of magnetic resonance imaging (MRI), a key non-invasive tool to probe the human brain anatomy and functions. The chapter is divided into two sections. The first section gives a short introduction to Nuclear Magnetic Resonance (NMR) principles and key components of the hardware. Basic acquisition sequences are explained as well as image generation mechanisms. The second section discusses in detail diffusion-weighted MRI, a key modality of interest for this thesis work. The basis of diffusion contrast and acquisition schemes are introduced, before explaining why and how the water molecules diffusion may be exploited to investigate the human brain microstructure and the structural connectome.

Chapter 4: Post mortem imaging

The purpose of this chapter is to discuss the specifics of ex vivo imaging, and to go into more details regarding MRI acquisition techniques required to understand the choices made during the design of the acquisition protocols developed in the frame of this thesis. The first section presents the main reasons motivating the use of post mortem imaging. The second section highlights the specific properties of fixed tissues, the challenges arising from it, and details some "good-practice" to follow to obtain high quality ex vivo MR acquisitions. The third section details some criteria required for the evaluation of image quality as well as acquisition time, and presents the common artifacts met with post mortem ultra-high field (UHF) MRI. Finally, the last part of this chapter explains useful MR acquisition techniques which were successfully used during this thesis work.

Part II -Preliminary studies

Chapter 5: Investigation of the internal connectivity and microstructure of two major structures of the human brain: the hippocampus and the brainstem

In this chapter, we establish preliminary proofs of concept to assess the feasibility of the Chenonceau project, which aims to provide a mesoscopic resolution MRI atlas of the human brain connectivity and microstructure. The motivation is therefore to define an acquisition protocol and an analysis pipeline that could be applied later to the entire brain. In order to do so, we focused our analysis on two brain structures known to play a key role in neurodegenerative diseases: the hippocampus and the brainstem. The first section presents the contributions regarding the human hippocampus. After a brief review of the existing knowledge on the anatomical structure and functions of the hippocampus, the section describes the acquisition protocol set up to collect high spatial resolution MRI datasets, the manual segmentation method used to delineate the hippocampus subfields, the inference of its structural connectivity and finally the investigation of its laminar structure. The second section investigates the human brainstem, following a similar approach. The last section discusses the prospects and limitations of the work presented in this chapter. The purpose of this chapter is to create a unique mesoscopic MRI atlas of the human brain, including anatomical and diffusion-weighted images. The idea is to provide a high spatio-angular resolution dataset suitable to apply recent advanced signal and biophysical models such as NODDI [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF] and the 3D MAP-MRI model [ Özarslan et al., 2013a[ Özarslan et al., , Fick et al., 2015]]. The first section presents the studied specimen as well as the chosen methodology for its cutting and its storage. Then, the set up of the designed protocol is detailed. Acquired images are registered for the reconstruction of the entire left hemisphere, and the first images are discussed with regards to the anatomical knowledge. Finally, future studies that could be conducted based on this unique dataset are discussed.

Chapter 8: Conclusion, discussion and perspectives

This chapter summarizes the contributions of this thesis and discusses future work on this topic.

Part I

Background

Chapter 2

Human brain anatomy

This chapter presents a background on the key aspects of the human brain anatomy. First of all, the gross anatomy is presented, including a description of the principal structures of the encephalon. The second section explains how the folded appearance of the cerebrum surface inspired neuroanatomists to divide it into lobes, each of them assumed to be associated with distinct cognitive functions. Brain tissue is separated into two types: gray and white matter. Both are detailed in sections 2.3 and 2.4.

Section 2.3 describes the structure and role of cortical areas and deep nuclei, whereas section 2.4 provides a review of the structural connectivity of the brain supported by white matter fiber bundles.

Last, the cellular composition of brain tissues is presented in order to highlight its potential to further segregate brain areas, such as the laminar structure of the cortex. Overall, this chapter is inspired from atlases, review articles and thesis chapters from [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF], [START_REF] Gray | Anatomy of the human body[END_REF], [START_REF] Lebois | Brain microstructure mapping using quantitative and diffsusion MRI[END_REF], [START_REF] Teillac | Tractographie globale sous contraintes anatomiques[END_REF], Alexander et al. [2017].

Gross anatomy

In vertebrates, the nervous system consists of two main parts: the central nervous system (CNS), comprised of the brain and the spinal cord, and the peripheral nervous system (PNS), that consists of the nerves and ganglia outside the CNS. This thesis focuses on the human brain or encephalon.

Encephalon, from ancient Greek enképhalos, literally means "within the head", and includes: the cerebrum, the cerebellum, the diencephalon and the brainstem (see Figure 2.1.a.).

The brain is protected by the skull, and surrounded by three membranes called meninges. The pia mater covers the entire surface of the central nervous system. Then comes the arachnoid mater and the dura mater, which is thicker and closer to the bone. In addition to this protection, a hydraulic shock absorber lies between the pia and the arachnoid mater: the cerebrospinal fluid (CSF). This fluid also occupies the ventricular system around and inside the brain and serves several other purposes such as clearing waste produced by the brain or supplying nutrients to nervous system tissues (Figure The encephalon can be divided into four structures. The cerebrum, consisting of the cerebral hemispheres, forms the largest part of the brain. The diencephalon is located deep within the brain, between the cerebrum and the brainstem. The brainstem connects the cerebrum via the diencephalon, the cerebellum and the spinal cord. It includes the midbrain, the pons, and the medulla oblongata (image adapted from [Marieb, 2009]). (b) Intracranial cerebrospinal fluid distribution highlighting the brain's ventricular system (image adapted from [START_REF] Blausen | Medical gallery of blausen medical[END_REF]).

2.1.b.). The adult human brain weighs typically 1.2-1.5 kg. Suspended in CSF, its mass is then equivalent to 50g [START_REF] Ben Lc Wright | Cerebrospinal fluid and lumbar puncture: a practical review[END_REF].

The primary components of the nervous system are neurons. A neuron is a specialized type of cell that consists of a cell body (soma), dendrites, and an axon. The term neurite is used to describe either a dendrite or an axon (Figure 2.2.a.). Neuronal cell bodies constitute much of the brain's gray matter, in particular the outer layer of the cerebrum called the cerebral cortex. Myelinated axons, also called tracts, make up the white matter, which is named for its appearance resulting from the lipid content of myelin. White matter is composed of bundles of axons, which connect various gray matter areas of the brain to each other, and carry nerve impulses between neurons (Figure 2.2.b.).

The cerebral cortex (surface of the cerebrum) is folded into ridges (gyri) and grooves (sulci). Many of which are named, usually according to their position, such as the frontal gyrus or the central sulcus.

The main sulci define recognizable lobes that are presented in the next section.

Brain lobes

The human cerebral cortex is highly folded, providing a greater surface area in the confined volume of the cranium. Each hemisphere is typically divided into four external lobes: frontal, parietal, occipital and temporal (Figure 2.3.a. and 2.3.c.). Two internal lobes can be added: the insula ( • The frontal lobe can be functionally divided into different areas. The prefrontal cortex is involved in reasoning skills and decision-making. The premotor cortex is responsible for planning and organization of movements while the primary motor cortex sends orders to execute movements. Finally, another noticeable region is called the Broca's area, which plays a key role in speech production.

• The parietal lobe plays an important role in integrating sensory information from various parts of the body and processes information relating to the sense of touch. It includes the primary and secondary somatosensory cortex [START_REF] Penfield | The cerebral cortex of man; a clinical study of localization of function[END_REF]].

• The occipital lobe is the visual processing center of the brain, receiving visual information from the retina. This information is then sent to the temporal or parietal lobe for analysis.

• The temporal lobe is involved in numerous cognitive processes and plays a key role in the formation of explicit long-term memory. This lobe also contains the auditory cortex that analyzes auditory information, and the Wernicke's area, which plays a key role in speech comprehension.

• The insular cortex is believed to be involved in consciousness or empathy, but its role is still little understood. • The limbic lobe plays a role in memory management and emotional life, the two being highly interconnected.

In the early twentieth century, the brain division into lobes has been extended. Korbinian Brodmann [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF] delineated 43 areas defined by their histological structure. Many of these areas have since been correlated closely to diverse cortical functions. This parcellation and other specificities of the gray matter are presented in the following section.

Gray matter

Gray matter contains most of the brain's neuronal cell bodies. The latter constitutes the outer layer of the cerebrum and the cerebellum, respectively called the cerebral and cerebellar cortex, but is also found deeper in the brain, in the form of nuclei, that are internal clusters of neurons usually sharing similar connections and functions.

In the cerebrum

Cytoarchitectonic parcellation of the cortex

Gray matter that composes the surface of the brain is called the cortical mantel or cortex. Its thickness varies according to the location. For instance, [START_REF] Zilles | Anatomical basis for functional specialization[END_REF] reported a thickness of 4.2-5.7mm in the primary motor cortex, while the primary somatosensory cortex depicts a thickness of only 2.4-2.7mm.

There are two types of cortex in the human brain: the neocortex and the allocortex. The neocortex, made up of six layers, is the largest part of the cerebral cortex. The allocortex, depicting only three layers, is found in the olfactory system and the hippocampus. Further information about the cellular organization of the cortex can be found in section 2.5.3.

The cellular organization of the cortex differs not only between the two types of cortex, but also between different regions of the brain. The cytoarchitecture reveals variations in cell shape, size, and density; characteristics which are used as anatomical landmarks to divide the cortex into distinct areas. These cytoarchitectural differences have led [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF] to delineate numerous cortical regions, or areas, based on a cell body staining technique called Nissl staining (see section 2.5.1.1). 43 areas were thus defined, as depicted in Figure 2.5. Many of the areas defined by K.Brodmann, based solely on their neuronal organization, have since been correlated closely to diverse cortical functions (see Figure 2.5). For example, the area number 17 corresponds to the primary visual cortex. Despite controversy, Brodmann areas remain the most widely known and frequently cited cytoarchitectural organization of the human cortex [START_REF] Zilles | Anatomical basis for functional specialization[END_REF], 2010[START_REF] Geyer | Microstructural parcellation of the human cerebral cortex-from brodmann's post-mortem map to in vivo mapping with high-field magnetic resonance imaging[END_REF][START_REF] Šimic | In search of the definitive brodmann's map of cortical areas in human[END_REF].

Basal ganglia

In addition to the cortical mantel, the cerebrum also contains a group of subcortical nuclei, i.e. clusters of neurons, referred to as basal ganglia. In fact, the term basal ganglia in the strictest sense refers to nuclei embedded deep in the brain hemispheres forming the striatum [START_REF] José L Lanciego | Functional neuroanatomy of the basal ganglia[END_REF]. This structure contains in its dorsal part the caudate nucleus and the lentiform nucleus that comprises the putamen and the globus pallidus. The ventral striatum includes the nucleus accumbens. One white matter fiber bundle, the internal capsule, located in the dorsal striatum, separates the caudate nucleus and the putamen. The striatum derived its name from the striated appearance of the region, which is caused by small fascicules belonging to the internal capsule passing through it.

Although the basal ganglia were considered to be exclusively concerned with motor control for a very long time, these structures are also involved in cognitive functions such as procedural learning and working memory tasks. From a functional point of view, basal ganglia have related nuclei in the diencephalon (subthalamic nucleus) and the mesencephalon (substantia nigra) that form the basal ganglia control system. By extension, these nuclei can also be referred to as part of the basal ganglia.

The diencephalon

The diencephalon is a large gray matter mass located at the rostral end of the brainstem. The diencephalon consists of four structures: the thalamus, the hypothalamus, the epithalamus and the subthalamus. The thalamus comprises the majority parts of the diencephalon (80%) and plays a role of relay for sensory signals, including motor signals, to the cerebral cortex (see Figure 2.7.a.).

Regarding the subthalamus, its most prominent structure is the subthalamic nucleus (STN) that lies dorsal to the substantia nigra of the mesencephalon and is part of the basal ganglia control system.

In the brainstem

The cranial nerves innervate regions of the head and the neck. Humans are considered to have twelve

In the cerebellum

The cerebellum is structured in a similar manner as the cerebrum. Its surface is made of a tightly folded and crumpled layer of gray matter called cerebellar cortex, with white matter underneath.

Embedded within the white matter are four deep cerebellar nuclei: the dentate, emboliform, globose, and fastigii (see Figure 2.8). In summary, gray matter is found in all the regions of the human brain, either in the surface (cerebral or cerebellar cortex), or deep inside the structures, forming nuclei such as the basal ganglia in the cerebrum, or the cranial nerves nuclei in the brainstem. Bear in mind that gray matter mainly consists of neuronal bodies, that are connected to each other by their axons. These axons, when myelinated, form the white matter, a real communication network between the various regions of the brain. The following section presents the major white matter pathways that can be found within the human brain.

White matter

White matter mostly consists of myelinated axons through which messages pass between different areas of gray matter. Axons that connect the same regions tend to bundle together and form tracts.

White matter fibers are classified into three categories: projection, association and commissural fibers. The next subsections define these three classes of connections.

Projection fibers

Projection fibers are tracts connecting the cortex with other areas of the CNS, such as the deep nuclei, the brainstem, the cerebellum or the spinal cord. These tracts may be efferent, i.e. conducting information outwards from the cortex or afferent, i.e. conducting information inwards the cortex.

Essentially, efferent (descending) tracts are motor tracts, whereas ascending pathways form sensory tracts. Major projection fibers include the corticospinal tract (CST) and the medial lemniscus (ML).

Tracts' names often consist of two components: the first term is the origin ("cortico" for the cortex)

and the second term is the termination ("spinal" for the spinal cord).

Descending motor tracts

Motor tracts can be functionally divided into two major groups:

• Pyramidal tracts -These tracts originate in the cerebral cortex, carrying motor fibers to the spinal cord and the brainstem. They are responsible for voluntary movements of the face and of the body. The pyramidal tract contains the corticospial tract (CST), controlling the body, and the corticobulbar tract, controlling the head and the neck. CST mainly originate from motor and premotor areas as well as the primary somatosensory cortex. Corticobulbar tracts arise from the lateral aspect of the primary motor cortex and receive the same inputs as the corticospinal tracts. After originating from the cortex, the neurons converge, descend through the internal capsule, the crus cerebri of the midbrain, the pons and the medulla. Corticobulbar tracts synapse with cranial nerves nuclei and other sensory nuclei including gracile nucleus, cuneate nucleus, solitary nucleus, and all trigeminal nuclei, whereas CST continue to descend.

In the most inferior part of the medulla, 80% of the CST fibers decussate (cross over to the other side of the CNS). All the CST fibers descend into the spinal cord and finally synapse a lower motor neuron (see Figure 2.9.a.).

• Extrapyramidal tracts -These tracts originate in the brainstem, carrying motor fibers to the spinal cord. They are responsible for the involuntary and automatic control of all musculature, such as muscle tone, balance, posture and locomotion. There are four extrapyramidal tracts:

the vestibulospinal (arising from the vestibular nuclei), the reticulospinal (from the reticular formation), the rubrospinal (from the red nuclei) and the tectospinal (from the superior colliculus of the midbrain also called tectum) tracts.

Ascending sensory tracts

The ascending tracts refer to the neural pathways by which sensory information from the peripheral nerves is transmitted to the cerebral cortex. Functionally, these tracts can be divided according to the type of information they transmit: conscious or unconscious. Conscious tracts are comprised of the dorsal column-medial lemniscal pathway and the anterolateral system, whereas unconscious tracts are comprised of the spinocerebellar tracts. In this section, only the medial lemniscus (ML) is described in details.

The medial lemniscus is a large ascending bundle of heavily myelinated axons that decussates in the brainstem. This is a three-neurons tract. The first neurons synapse with neurons in the gracile nuclei (medulla) if they are lower body axons, or with the cuneate nuclei (medulla) if they are upper body axons. The second axons travel up the rest of the brainstem, and synapse at the thalamus that is a relay for sensory information. Then third axons synapse in the primary somatosensory cortex (see Figure 2.9.b.).

Association fibers

Association fibers connect cortical areas within the same cerebral hemisphere. There are two kinds of association fibers: short association fibers, also called arcuate or "U"-fibers, located under the cerebral mantel and connecting adjacent gyri, and long association fibers connecting more distant areas. The most studied association fibers in the literature include:

• the uncinate fasciculus that connects parts of the limbic system such as the hippocampus and amygdala in the temporal lobe with the frontal cortex,

• the cingulum connecting the cingulate gyrus to the entorhinal cortex and thus allowing communication between components of the limbic system,

• the inferior longitudinal fasciculus connecting the temporal and occipital lobes. 2). Corticospinal tracts conduct impulses from the brain to the spinal cord whereas the corticobulbar tract conducts impulses from the brain to the medulla (part of the brainstem) in particular to the cranial nerves and also to the sensory nuclei including gracile nucleus, cuneate nucleus, solitary nucleus, and all trigeminal nuclei. 80% of the CST decussate in the most inferior part of the medulla. b. The medial lemniscus is a large ascending (sensory) bundle of heavily myelinated axons that decussate in the brainstem, specifically in the medulla oblongata. The first neurons synapse with neurons in the gracile nuclei (medulla) if they are lower body axons, or with the cuneate nuclei (medulla) if they are upper body axons. The second axons travel up the rest of the brainstem, and synapse at the thalamus that is a relay for sensory information. Then, third axons synapse in the primary somatosensory cortex (image adapted from [START_REF] Gray | Anatomy of the human body[END_REF])

Commissural fibers

Commissural fibers or transverse fibers are axons that connect the two hemispheres of the brain. The three main commissures are: the corpus callosum, and the anterior and posterior commissures (see Figure 2.10.b.). The corpus callosum is the wider commissure, and even the largest white matter structure in the human brain. The anterior commissure is a tract connecting the two temporal lobes, placed in front of the columns of the fornix. Finally, the posterior commissure connects the pretectal nuclei (in the midbrain), mediating the pupillary light reflex. Other commissures exist like the hippocampal commissure enabling the communication between the right and left hippocampi.

The previous sections gave an overview of the human brain subdivisions at a macroscopic scale.

First split into six lobes delineated by cortical sulci, the cortex has been further divided according to its local cytoarchitecture. Looking deeper in the brain, the cerebral tissue can be divided into two categories: the gray matter, mainly containing the neuronal bodies, and the white matter, containing myelinated axons. The following section aims at describing the brain tissue at a cellular level. This is a crucial step in the frame of this thesis, as a major work is to implement microstructural models aiming at inferring the microstructural composition of each voxel. This is done using diffusion-weighted magnetic resonance imaging (dMRI) and advanced multicompartmental biophysical models of the diffusion process of water molecules in brain tissues. Having a clear understanding of the brain's microscopic organization is therefore essential to design the most adapted model depending on the observed structure.

Brain microanatomy

Whereas brain macroanatomy corresponds to the scale studied by neuroanatomists, brain microstructure corresponds more to the scale investigated by biologists. This scale turns to be extremely complex due to the diversity of cells constituting the brain tissue. In this section, we propose a short and descriptive review of existing cells in brain tissues and provide details about their dimensions, density, shape, and functional role.

Neuronal cells

Microstructure of a neuron

Responsible for the transmission of the nerve signals, neurons are the main cellular corpus found in the brain. The principal neuronal components are: the cell body, or soma, the signal receivers called dendrites, and the projections, the axons (the main part of the white matter), conducting the nerve impulse (see Figure 2.2).

Soma

The nucleus is a key feature of the soma as it encloses the DNA. Surrounding the nucleus, the cytoplasm contains many organelles, including granules called Nissl corpus (granular endoplasmic reticulum) and free ribosomes, synthesizing proteins. As Nissl bodies are located in the soma as well as in dendrites but not in the axon, the Nissl staining method that colors Nissl bodies in blue can be used to identify cell bodies. This staining method was successfully used by Brodmann to delineate 43 areas in the cerebral cortex, based on the variation of cell body shape and density in the cortical layers (see section 2.3.1.1).

Dendrites If axons may extend to targets a meter or more away from the cell body (e.g. corticospinal neurons), dendrites are rarely longer than 1 to 2 µm. Their diameter range from 0.2 to 3 µm for dendrites both proximal (close) and distal (far) to the soma. For neurons in the cerebral cortex, the dendritic trees are mostly isotropic, whereas elsewhere, e.g. in the layers of the hippocampus, the trees can be highly anisotropic [START_REF] John C Fiala | Dendrite structure[END_REF]. The dendritic complexity reflects the number of connections received by the neuron.

Axons Axons may extend from a few millimeters ("U"-fibers) to over one meter (e.g. corticospinal neurons in humans) [START_REF] Schüz | The human cortical white matter: quantitative aspects of cortico-cortical longrange connectivity[END_REF]. The diameter of axons can differ by a factor of more than 100 within the mammalian nervous system. Fiber inner diameters are reported to range from 0.16 to 9 µm in human brain [START_REF] Aboitiz | Fiber composition of the human corpus callosum[END_REF][START_REF] Liewald | Distribution of axon diameters in cortical white matter: an electron-microscopic study on three human brains and a macaque[END_REF], and are up to 15 µm in the human spinal cord [START_REF] Häggqvist | Analyse der faserverteilung in einem rückenmarkquerschnitt (th 3)[END_REF]. Most of the average values are below 1 µm and only a small population is much thicker. Interestingly, previous studies in mammals showed that the bulk of axons in the corpus callosum has similar diameters in large and small species. Large brains differ from small ones mainly by a small population of thick fibers [START_REF] Schüz | Basic connectivity of the cerebral cortex and some considerations on the corpus callosum[END_REF][START_REF] Olivares | Species differences and similarities in the fine structure of the mammalian corpus callosum[END_REF][START_REF] Samuel | Functional trade-offs in white matter axonal scaling[END_REF].

Fiber diameter is related to conduction velocity: in myelinated axons, conduction velocity increases approximately linearly with axon diameter [START_REF] Herbert | Axon diameters in relation to the spike dimensions and the conduction velocity in mammalian a fibers[END_REF]. Consequently, one might expect the axon diameters to follow the growth of the brain in order to maintain the conduction times, from a mouse to a human. However, making conduction times as short in human brains as in small brains would lead to an impossibly large brain volume. Furthermore, the increase in conduction times may be related to the improvement of cognitive abilities [Roberts andRobinson, 2008, Bojak and[START_REF] Bojak | Axonal velocity distributions in neural field equations[END_REF].

Myelin

The myelin sheath consists of 80% lipids and 20% proteins and wraps around the axon in layers about 10nm thick, as illustrated in with a soma having a size around 20 µm. These neurons are found in areas including the cerebral cortex and the hippocampus. In the primary motor cortex, giant pyramidal cells, called Betz cells, send their axons down to the spinal cord via the corticospinal tract. Granular neurons are very small neurons that can be found in areas including the dentate gyrus of the hippocampus and the cerebral cortex. Spiny stellate cells receive inputs from thalamus and have excitatory outputs. They have mostly vertical axonal fibers which can communicate with all the other cells along a cerebral column.

Some neurons have excitatory outputs (pyramidal, spiny stellate cells) and others have inhibitory outputs (basket or chandelier cells).

Glial cells or neuroglia

Besides neurons, the central nervous system also contains glial cells that maintain homeostasis, create myelin sheath, and provide support and protection for neurons. In contrast to neurons, glial cells have no axon and retain the ability to undergo cell division in adulthood. In adult human neocortex, the proportion of glial cells were found to be 76.6% oligodendrocytes, 17.3% astrocytes and 6.5%

microglia [START_REF] Dp Pelvig | Neocortical glial cell numbers in human brains[END_REF][START_REF] Salvesen | Neocortical neuronal loss in patients with multiple system atrophy: a stereological study[END_REF], and the glia/neuron ratio is 1.32 and 1.40 for males and females respectively. Aquaporin-4 (AQP-4) water channels in the cell membrane make the membrane highly permeable to water and are a key feature characterizing glial cells [START_REF] Manley | New insights into water transport and edema in the central nervous system from phenotype analysis of aquaporin-4 null mice[END_REF]]. In the central nervous system, glial cells include oligodendrocytes, astrocytes, ependymal cells, and microglia.

Astrocytes are the most abundant type of macroglial cell in the CNS and have the shape of a star.

Their somas are about 10-15 µm in diameter, with an overall diameter of about 15 µm [START_REF] Nancy | Uniquely hominid features of adult human astrocytes[END_REF]. They have a role in tissue repair and scarring, as well as in maintenance of extracellular ion balance.

Oligodendrocytes are mainly responsible for the production of myelin. These cells are present in the gray matter, where they play a metabolic role, and in the white matter, where they product the myelin sheath, as shown in Figure 2.11.b. They are located only in the central nervous system and their soma, ellipsoïdal or oval, is about 13 µm in diameter in the corpus callosum and 4 µm in the hippocampus [START_REF] Bakiri | Morphological and electrical properties of oligodendrocytes in the white matter of the corpus callosum and cerebellum[END_REF][START_REF] Gagyi | Decreased oligodendrocyte nuclear diameter in alzheimer's disease and lewy body dementia[END_REF]. A single oligodendrocyte can extend its processes up to 50 axons [START_REF] Baumann | Biology of oligodendrocyte and myelin in the mammalian central nervous system[END_REF], wrapping approximately 1 µm of myelin sheath around each axon.

Ependymal cells form the ependyma, the lining of the ventricular system of the brain and the central canal of the spinal cord. These cells play an important role in the production of CSF, their cilia helping for its circulation.

Microglia are macrophages that provide the first reaction for many CNS injuries [START_REF] Gehrmann | Microglia: intrinsic immuneffector cell of the brain[END_REF]. Their soma is 10 µm in diameter, and total coverage (with processes) is about 15-30 µm. The human cerebral cortex has a laminar structure presenting distinct cell organization and myelination. After the work of [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF], the neocortex (section 2.3.1.1) has been divided into six main layers, from outside (pial surface) to inside (white matter), as illustrated in Figure 2.12:

Cortex histology

• Layer I: the molecular layer, with few neurons. This layer is mainly composed of glial cells, apical dendrites and axons parallel to the pial surface.

• Layer II: the external granular layer, mainly constituted of small granular cells, receives afferents from and sends efferents to other cortical areas. Layers I and II are hardly distinguishable and are thus often grouped together.

• Layer III: the external pyramidal layer, contains predominantly small pyramidal neurons.

Layers I-III are referred to as supragranular layers and constitute the primary origin and termination of intracortical connections, which are either associational or commissural.

• Layer IV: the internal granular layer, includes dense packing of granular cells and spiny stellate cells. This layer is the main target of thalamocortical afferences and sends signals to the rest of the column. This is the most prominent layer in the primary sensory cortices and the main receiving layer of the cortex.

• Layer V: the internal pyramidal layer, contains large pyramidal neurons which give rise to axons leaving the cortex and running down to subcortical structures. Layers V and VI are referred to as infragranular layers and are most developed in motor cortical areas. In the primary motor cortex of the frontal lobe, layer V contains Betz cells, whose axons travel through the internal capsule, the brainstem and the spinal cord forming the corticospinal tract, which is the main pathway for voluntary motor control.

• Layer VI: the polymorphic layer, contains few large pyramidal neurons and many small multiform neurons. Layer VI sends outputs to thalamus, for both excitatory and inhibitory actions.

Conclusion

This first background chapter introduced the human brain anatomy from the macroscopic to the cellular level. This step is essential since this thesis aims at improving knowledge about the human brain, in particular regarding short and ultra-short connections and their microstructure. The human brain connectivity is extremely complex and the principal long range bundles described in section 2.4 only represent a small part of the whole brain connectivity. Much remains to be learned about short connections in the brain, that are hardly observable with a clinical MRI, due to their limited spatioangular resolution: to date, only U-fibers have been specifically described in healthy subject [START_REF] Guevara | Creation of a whole brain short association bundle atlas using a hybrid approach[END_REF]. The idea of this work is then to study the internal connectivity of key structures of the brain, such as the hippocampus or the brainstem, and to extract parameters able to characterize the microstructure, such as the axonal density for each voxel. To achieve this, specific MRI acquisitions will be done on a human ex-vivo brain and the information contained in diffusion MRI signal will be analyzed. The next chapter thus introduces the foundations of diffusion MRI, that constitutes a powerful non-invasive mean to investigate the architecture of the human brain tissue.

Chapter 3

Diffusion MRI: a powerful tool to probe the brain architecture

This chapter is divided into two sections. The first section gives a short introduction to NMR principles and key components of the hardware. Basic acquisition sequences are explained as well as image generation mechanisms. The second section discusses in detail diffusion-weighted MRI, which is the modality of interest for this research. First, the basis of diffusion contrast and acquisition schemes are introduced. The second part of the section focuses on explaining how the water molecules diffusion may be exploited to investigate the human brain microstructure and the structural connectome.

Basic principles of MRI

The hardware

The aim of this section is to detail the main components of a MR scanner based on Fig. 3.1, in order to get a better understanding of their interaction during an acquisition sequence.

A superconducting electromagnet The magnet is the main component of the scanner as it creates the static field B 0 . This is a supraconducting coil, presenting a zero electrical resistance when cooled by liquid helium cryostat to 4 Kelvin, allowing ultra-high static field to be reached with a low energy consumption.

The strength of the magnet is measured in tesla (T). Clinical magnets generally have a field strength in the range 1.5-3.0 T, with advanced research systems reaching 7T, 9.4T, 10.5T and, soon, 11.7T.

Regarding preclinical MRI, as it is easier to design magnets with a homogeneous magnetic field on a reduced field of view (a few centimeters), the standard field is noticeably higher (7T), and advanced systems can reach 9.4T, 11.7T, or 17T. Shim coils Inhomogeneities in the main magnetic field are corrected by adjusting currents in the shim coils, which generates harmonics fields counteracting the main field inhomogeneities.

Gradient coils Gradient coils are used to modify the magnetic field linearly along the X, Y, and Z directions. These variations allow the spatial encoding of the MR signal, and are also used to tag the positions of water molecules in diffusion MRI.

Antennas Radiofrequency (RF) coils are LC resonant circuits made up of copper coil surrounding the sample in the scanner. The coils transmit the RF impulses and receive the RF signal. RF coils for MRI can be grouped into two different classes: volume and surface coils. Volume coils provide a more homogeneous RF excitation but also a lower SNR compared to surface coils. Regarding the large volume of the samples we studied in this thesis, volume coils have been preferred to ensure a better signal homogeneity, crucial for diffusion MRI.

Basic physical principles

Magnetic properties of the hydrogen nucleus

The underlying principle of MRI is the magnetic nuclear resonance, or NMR, which is a consequence of the magnetic properties of the nuclei. The atomic nuclei are made of nucleons (protons and neutrons), all rotating around an axis. The rotation of a particle induces an angular moment aligned to the rotational axis, named spin S in the case of elementary particles. Protons being electrically Chapter 3. diffusion MRI: a powerful tool to probe the brain architecture 29 charged body, their rotation also induces a magnetic moment µ, linked to S by the relation µ = γ S, with γ the gyromagnetic ratio, specific to each nucleus.

The value of γ varies according to the chemical specie. Hydrogen is the element with the largest gyromagnetic ratio, and its abundance in tissues makes it the privileged element in MRI. Hydrogen nuclei, often referred to as protons, can be likened to small magnets with a north pole and a south pole. They are characterized by two energy levels, a level of high and low energy.

Magnetic resonance phenomenon

The magnetic resonance phenomenon used in MRI can be divided into three stages: polarization, resonance, and relaxation.

Polarization In the absence of a magnetic field B 0 , the microscopic magnetic moment µ of each proton is randomly oriented (∑ µ = 0). When a magnetic field B 0 is applied, each proton will be either aligned with or against B 0 . A slight majority of the nuclei are aligned with B 0 , which results in a non-zero macroscopic magnetization, or net magnetization vector M: this is the polarization phenomenon (see Figure 3.2.a.).

This vector can be decomposed into a longitudinal component M z , parallel to B 0 , and a transverse component M xy . At equilibrium, M is oriented with the applied B 0 field (traditionally set along the +Z-direction) and there is no net magnetization in the transverse XY plane. The maximal longitudinal magnetization depends on the proton density and the strength of B 0 . Spins precess around B 0 at the Larmor precession frequency ω 0 = γB 0 with γ equal to 42 mHz/T for the hydrogen. The net magnetization is not observable at equilibrium because its strength is infinitely small compared to B 0 . In order to measure M, the spins have thus to be tilted down to the transverse plane.

Resonance: spins excitation Spins can be flipped by the application of a rotating magnetic field, denoted B 1 , which is applied for a short time in the plane perpendicular to B 0 (Figure 3.2.b.). The transfer of energy requires that the rotation frequency ω r of B 1 equals to the Larmor frequency ω 0 =γB 0 of the spins. The absorption and exchange of energy between two oscillating systems with the same frequency constitute the resonance phenomenon. In this case, this phenomenon is called Nuclear Magnetic Resonance (NMR). In practice, the Larmor frequency lies in the range of radio waves, which is why these pulses are denoted as RF pulses. During the magnetic resonance process, the RF pulse gives energy to the spin system which restores it as soon as the application of the pulse is stopped. These two phases correspond to two consecutive processes of excitation and relaxation.

During the excitation process, the spins are all or partly tilted in the transverse plane, resulting in a decrease of longitudinal magnetization and a non-zero net transverse magnetization M xy .

Relaxation The relaxation phase is the return to equilibrium of the net magnetization, i.e. aligned with B 0 . Electromagnetic energy is then retransmitted, and the resulting RF emission stemming from individual spins provides the NMR signal that can be probed using a reception antenna. In 1946, [START_REF] Bloch | Nuclear induction[END_REF] published an analysis of the nuclear induction phenomenon, providing a set of equations explaining the origin and properties of the NMR signal. Two relaxation time constants, T1 and T2, were phenomenologically defined to account for the return to equilibrium of the net magnetization. Bloch equations describe the temporal evolution of M. When considering a 90°RF pulse, the equations of motion for M are:

       M x (t) = M 0 e -t T 2 sin(ωt) M y (t) = M 0 e -t T 2 cos(ωt) M z (t) = M 0 (1 -e -t T 1 ) (3.1)
with M 0 the original maximum value of M z .

Relaxation thus combines two mechanisms:

• Longitudinal relaxation, which corresponds to longitudinal magnetization recovery, follows an exponential curve with a time constant T1 (Figure 3.2.g. and h.).

• Transverse relaxation corresponds to transverse magnetization decay. This decay is described by an exponential curve with a time constant T2 (Figure 3.2.e. and f.).

Due to local variations of the applied magnetic field B 0 , the Larmor frequency slightly varies between different locations. This causes a dephasing between the spins so that, in practice, the signal decays more rapidly. The combined effect of T2 relaxation and magnetic field non-uniformities is referred to as T2* relaxation (Figure 3.2.c. and d.). A sequence called spin echo, introduced in § 3.1.3.3, eliminates the added relaxation caused by magnetic field inhomogeneities and therefore gives access to the T2 value. T1 and T2 vary from one tissue to another, and this difference in relaxation times is responsible for the creation of contrast in MRI images. The reception coil, placed in the transverse plane of the MRI system, receives the signal coming from the transverse magnetization, called Free Induction Decay (FID).

Image encoding and construction

3.1.3.1 Magnetic field gradients for 2D spatial encoding Slice selection The application of a RF pulse at ω r = ω 0 leads to the excitation of the entire volume.

The first step of spatial encoding consists in selecting the slice plane. A magnetic field gradient, the Slice Selection Gradient (GSS), is applied perpendicular to the desired slice plane, using the gradient coils. If the gradient is applied along the Z direction, ω 0 becomes ω z = γ(B 0 + G z ) with G z the e., f. The additional decay caused by field inhomogeneities can be reversed by the application of a 180°refocusing pulse. Both T2 and T 2 * are exponential processes with times constants T2 and T 2 * respectively. The resultant decaying signal is known as the Free Induction Decay (FID); g., h. The longitudinal magnetization recovers gradually back to its equilibrium value. The recovery of M z is an exponential process with a time constant T1.

gradient value at position z. The RF wave is simultaneously applied, with the same frequency as that of the protons in the desired slice plane. For instance, a pulse at ω r = ω 6 is applied to select the red slice P6 in the Figure 3.3.

Phase and frequency encoding Once the slice is selected, the phase encoding gradient G φ encodes the line and the frequency encoding gradient G ω (or readout gradient) encodes the column. Applied for a given time period, G φ modifies the spin resonance frequencies, inducing dephasing, which persists after the gradient is interrupted. The protons in the same row all have the same phase. G ω is applied in the last direction and modifies the Larmor frequencies. The protons in the same column all have the same frequency. G ω is applied during the signal reception and is therefore called readout gradient.

Filling k-space It can be demonstrated that this dual phase/frequency encoding of the MRI signal corresponds to a Fourier encoding of the NMR signal with two spatial frequencies k x and k y (see Figure 3.4). Therefore, a simple filling of the Fourier space (also called the k-space) with a classical spin-echo sequence as depicted in Fig. 3.5 gives access to the original image by simply applying an inverse Fourier transform. Alternative methods can be used to fill the k-space, like the Echo Planar Imaging (EPI), where all the k-space is filled using a unique excitation, which considerably speed up the acquisition.

Image contrast mechanisms

The measured transverse magnetization amplitude M xy is converted into grayscale. The contrast thus provides evidence of the different relaxation times T1 and T2 between tissues. In order to adjust the sensitivity of the signal intensity and highlight one tissue rather than another, two new parameters should be introduced :

• the echo time TE, corresponding to the time from middle of first RF pulse to middle of the NMR echo. This time conditions the T2 weighting, increasing with TE.

• the repetition time TR, corresponding to the cycle time between two consecutive excitations.

This time conditions the T1 weighting, decreasing with TR.

These times are adjustable settings allowing the user to tune the sensitivity of the signal intensity to T1, T2 or the proton density ρ. The signal is proportional to ρe -T E T 2 (1-e -T R T 1 ) with ρ the proton density. Therefore, short TE and long TR imply ρ e -T E T 2 (1-e -T R T 1 ) ≈ ρ, i.e. a proton density contrast. A long TE and TR will result to a high T2 contrast, and a short TR and TE to a high T1 contrast. Note that this is valid for spin echo sequences. In the case of gradient echo sequences, i.e. without a 180°R F rephasing pulse, the contrast is not T2-weighted but T 2 * -weighted (see the following paragraph).

MRI sequences

Any MRI sequence is the result for a particular setting of radiofrequency pulses and gradients, resulting in a particular image contrast. The user can tune various sequence parameters such as TR, TE, or the flip angle, in order to find the best compromise between contrast, spatial resolution, signalto-noise (SNR) ratio and total scan time. There exists two historical sequence families: spin echo and gradient echo sequences. Introduced by [START_REF] Erwin L Hahn | Spin echoes[END_REF], the spin echo sequence is made up of the following series of events: a 90°RF pulse that flips net magnetization in the transverse plane, a 180°R F pulse applied at t = TE/2 to rephase the spins (see figure 3.2 and 3.6.a.), and the signal reading at TE. This scheme is repeated at each time interval TR, as many times as there are lines in the image Chapter 3. diffusion MRI: a powerful tool to probe the brain architecture 34 matrix. The gradient echo (GRE) sequence differs from the spin echo by the use of a flip angle below 90°and the absence of any 180°refocussing pulse. One of the main interest of this sequence is the acquisition time: the longitudinal magnetization regrowing faster for lower flip angles, TR and TE can be shortened. GRE sequences also provide a T 2 * contrast, revealing structures containing iron like the substantia nigra in the brainstem. However, the sequence is very sensitive to susceptibility artifacts that occur in the presence of air bubbles. This explains why spin echo sequences have been preferred during this thesis.

Diffusion MRI

Principle

Diffusion MRI (dMRI) makes MR images sensitive to the displacement of water molecules in brain tissues. The diffusion process of a molecule is characterized by a random movement, also called Brownian motion, resulting from the thermal energy of the latter. This physical process is intrinsic to tissues, independent of acquisition sequences and applied magnetic field, which is not the case for other quantitative parameters accessible by this imaging technique such as magnetic properties like T1 or T2 relaxation times.

Apparent diffusion coefficient (ADC)

In a free medium, the diffusion process is not restricted by any physical barrier. Therefore, this process is isotropic and characterized by a diffusion coefficient D. At 37°C, this value results in a displacement of about 10 µm for a duration of 50 ms [Le Bihan et al., 2001].

Practically, in the human body, there does not exist unrestricted media. That is why the experimental measure of the absolute diffusion coefficient is not possible. Only the apparent diffusion coefficient (ADC) can be estimated, always lower than the real diffusion coefficient.

Diffusion anisotropy

In biological tissues, the membranes behave like obstacles, hindering or restricting the path of molecules, making the diffusion process anisotropic. There is therefore a decrease of their mobility in a direction perpendicular to the obstacles. In white matter, myelinated axonal fibers are almost impermeable and organized into bundles, which enhances this anisotropy. The displacement of water molecules is then drastically reduced in any direction that do not correspond to the main direction of fibers. This phenomenon is the core principle used to investigate the local orientation of white matter bundles with diffusion MRI data, this principal orientation being assumed to correspond to the direction of maximum diffusivity.

Introduction to the diffusion tensor model (DT)

In order to fully account for the anisotropy of the diffusion process, [START_REF] Peter | Mr diffusion tensor spectroscopy and imaging[END_REF] proposed to use the diffusion tensor to model the intrinsic diffusion properties of biological tissues. The diffusion tensor (DT) is the extension of the scalar diffusion coefficient introduced in section 3.2.2. D is a 3x3 matrix, symmetric and positive definite, that can be mathematically written as :

D =     D xx D xy D xz D xy D yy D yz D xz D xy D zz     (3.2) • In the case of isotropic diffusion: D xx =D yy =D zz =D and D xy =D yz =D zx =0.
• In the case of non-isotropic diffusion, D is a real, symmetric matrix. The spectral theorem is thus applicable and D can be diagonalized by means of an orthogonal change of coordinates.

The eigenvalues of the matrix λ 1 ≥ λ 2 ≥ λ 3 inform on the diffusivity along the eigenvetor directions (e 1 , e 2 , e 3 ). The largest value λ 1 is associated with the diffusivity in the principal direction and therefore with the fiber orientation. In the case of white matter, this value is three to six times greater than that of the diffusivities in the orthogonal plane λ 2 and λ 3 . This information can be visualized as an ellipsoid whose semi-axes are equal to the eigenvalues and directed along their corresponding eigenvectors (see Figure 3.7). The ellipsoid represents the average diffusion distance in each direction during the diffusion time τ. The principal axis of the ellipsoid gives the principal fiber orientation in the voxel. The eccentricity informs on the degree of anisotropy and its symmetry (Figure 3.7).

√

2λ τ is the mean displacement of water molecules during a given diffusion time τ, according to Einstein's equation [START_REF] Einstein | Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen[END_REF] 3.2.5 Encoding the MR signal for diffusion MRI can be sensitized to the diffusion process of water molecules using a specific MRI sequence, including a pair of strong diffusion gradients to "tag" the position of spins. The simpler and far more prevalent sequence was introduced in 1965 by [START_REF] Edward | Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient[END_REF] and is called Pulsed Gradient Spin Echo (PGSE) (see Figure 3.8 for its simplified sequence diagram). In addition of the classical spin echo sequence, two linear gradients are applied before and after the 180°pulse.

These gradients give the protons a phase shift of precession depending on their position. Thus, the first applied gradient gives a phase advance proportional to the position along the gradient axis. The second gradient, exactly opposite to the first one, gives a delay of the same angle. Consequently, a proton that has remained immobile will have a zero phase shift and those who have moved will have a phase shift proportional to their displacement. The principle is shown in Figure 3.9.

In the case of a perfectly rectangular diffusion gradients, the diffusion time τ di f f can be expressed as:

τ di f f = ∆ -δ /3 (3.3)
The effect of the diffusion on the received NMR signal is then an exponential attenuation:

S ∝ S 0 e -bD (3.4)
with b the shorthand notation that characterizes this degree of diffusion sensitization and S 0 the initial signal without any diffusion gradient. For the PGSE experiment and assuming a perfect rectangular diffusion-gradient shape, b is linked to the gradients characteristics by the relation: where G=[G x ,G y ,G z ] is the vector of the gradients amplitudes along the three axis, ∆ the time interval between two gradients, δ the gradients duration, γ the proton gyromagnetic ratio, and q the wave vector such as q=γδ G (see Figure 3.8). However, for real clinical or preclinical systems, the diffusion-gradient shape is not a perfect rectangle since the rise time r, that is the time taken to reach the strength G, is non-zero. When this rise-time is taken into account, equation 3.5 becomes :

b = (Gγ) 2 (δ 2 (∆ - δ 3 ) + r 3 30 -δ r 6 ) (3.6)
By assuming the pulses to be infinitely narrow (narrow pulse approximation), i.e. if the gradient pulse duration δ is short enough for the diffusion of the water molecule to be negligible during that time, the signal attenuation S(q,τ) is expressed as the 3-dimensional (3D) Fourier transform of the diffusion propagator p [Callaghan, 1993] (equation 3.7).

S(q, τ)

S 0 = R 3 p(r, τ)e -i2πq T r dr = F[p(r, τ)] (3.7)
The propagator p represents the probability that a water molecule initially located at the position r 0 FIGURE 3.9: The schematic diagram explains the relationship between water motion and the observed signal attenuation. Each circle represents a water molecule in an imaged pixel and the dark arrow inside is the phase of the spin. After the excitation pulse, all the spins have the same phase. The first diffusion gradient introduces a gradient of signal phase across the sample. After a diffusion time typically between 10 and 100 ms, a second diffusion gradient is applied to rephase the spins. If water molecules move in between the two gradient applications, the second gradient cannot perfectly refocus the phases, which leads to signal loss. In this example, horizontal motion (indicated by yellow arrow) leads to the signal loss, but vertical motion (green arrow) does not affect the signal intensity; adapted from [START_REF] Mori | Principles of diffusion tensor imaging and its applications to basic neuroscience research[END_REF] moves to r with R=r-r 0 the displacement. Also called diffusion Probability Density Function (PDF)

or diffusion propagator, p is ultimately the function one is looking to reconstruct in diffusion MRI.

Hence, multiple measures are needed with different q. The space of all possible 3D q vectors is called q-space.

If p is assumed to be Gaussian, the signal intensity S(q,τ) is expressed as :

S(q, τ) = S 0 e -τq T Dq (3.8)
In practice, the narrow pulse assumption is not verified, and the previous relationships only give access to the ensemble average propagator (EAP), that can still provide significant angular and radial information on the diffusion process.

Information given by the diffusion tensor

DTI needs at least six diffusion-weighted images and one nul b-value image S 0 to determine the six unknown coefficients of D. Once D is diagonalized, several rotationaly invariant features can be computed from the eigenvalues λ 1 , λ 2 , λ 3 , where λ 1 ≥ λ 2 ≥ λ 3 , and corresponding eigenvectors e 1 , e 2 , e 3 :

• the mean diffusivity (MD), characterizing the mean displacement of water molecules inside the voxel, is obtained by taking the third of the trace (Fig. 3.10.f.):

λ = λ 1 + λ 2 + λ 3 3 (3.9)
• the fractional anisotropy (FA), describing the degree of anisotropy of a diffusion process, correlates with the presence of oriented structures in the tissue (Fig. 3.10.e.). The fraction is defined by:

FA = 3 2 (λ 1 -λ ) 2 + (λ 2 -λ ) 2 + (λ 3 -λ ) 2 λ 1 + λ 2 + λ 3 (3.10)
• the preferred diffusion direction given by e 1 , corresponds to the principal orientation of the fibers inside the voxel.

In practice, DTs are commonly visualized with a Red-Green-Blue (RGB) colormap, that encodes the x-y-z coordinates of the principal eigenvector e 1 (Fig. 3.10.d.).

DT is a powerful tool which has earned success in many clinical applications because of the simplicity of the model, with very few parameters, as well as the relatively small number of data required.

However, this model is intrinsically limited. First, due to the constraints of the tensor model, DTI can only resolve a single fiber orientation within each imaging voxel. This is an important limitation, since resolution of DTI acquisition obtained with clinical MRI is currently between 1-3mm 3 , while the physical diameter of fibers can vary between 0.1µm and 10µm [START_REF] Liewald | Distribution of axon diameters in cortical white matter: an electron-microscopic study on three human brains and a macaque[END_REF] (see paragraph 2.5.1.1). In fact, fiber bundle crossings are thought to occur in more than one-third of imaging voxels in white-matter [START_REF] Behrens | Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?[END_REF]. Second, even though DTI gives considerable quantitative information, diffusion tensor features like FA and MD are inherently non-specific, and a reduction in their value can be associated with different types of microstructural changes. For instance, a reduction in FA can be due to demyelination, edema, increased neurite dispersion, or other microstructural changes [START_REF] Takahashi | Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord[END_REF][START_REF] Beaulieu | The biological basis of diffusion anisotropy[END_REF][START_REF] De Santis | Why diffusion tensor MRI does well only some of the time: variance and covariance of white matter tissue microstructure attributes in the living human brain[END_REF].

Therefore, higher order models than DTI and new reconstruction techniques are needed to describe non-Gaussian diffusion signals. This has led to the development of High Angular Resolution Diffusion Imaging (HARDI) techniques that are presented in the next section.

HARDI to go beyond DTI

The discrimination of multiple fiber crossings would theoretically requires to drastically increase the spatial resolution, which cannot be achieved due to severe hardware limitations. An alternative The information obtained highly depends on the performed acquisition scheme. There are three acquisition strategies to cover the q-space :

1. Sampling of the whole q-space on a dense 3D Cartesian grid. This sampling scheme is generally associated with diffusion spectrum imaging (DSI) [wed],

2. Spherical sampling of the q-space for a single or multiple b-value(s). This is then respectively called single-shell/multi-shell HARDI [START_REF] David S Tuch | High angular resolution diffusion imaging of the human brain[END_REF],

3. Hybrid sampling of the q-space using samples that can be along radial lines (varying the diffusion times) or other more sophisticated distributions. These schemes are generally called HYDI (HYbrid Diffusion Imaging) [START_REF] Wu | Hybrid diffusion imaging[END_REF].

In the first case, a large number of q-space points are taken over the discrete grid (N ≥ 200) and the inverse Fourier transform of the measured DWI signal is taken to obtain an estimate of the diffusion probability density function (PDF). This method requires very high b-values (500 ≤ b ≤ 20000 s/mm 2 ) and a long acquisition time, which is not always compatible with clinical applications. Many improvements have been performed to take benefit from the parsimony of the q-space in order to reduce the scan time to 15-30 minutes [START_REF] Gramfort | Sparse dsi: Learning dsi structure for denoising and fast imaging[END_REF].

In many situations, for instance to perform fiber tracking, the full PDF information is not required and the knowledge of its angular part, the Orientation Distribution Function (ODF), is sufficient. The ODF is defined as the radial projection of the diffusion PDF:

ψ(θ , φ ) = ∞ 0 p(r, θ , φ )dr (3.11) where (θ , φ ) such as (θ ∈ [0,π], φ ∈ [0, 2π]).
The ODF has its maximum(a) aligned with the underlying population(s) of fiber(s) and is therefore an interesting function to perform tractography.

This function only needs a single-shell HARDI acquisition to be reconstructed (sheme 2). In practice, at least 60 measurements are desirable and medium gradient strengths are acceptable although strong gradients give better diffusion ODF reconstructions. Typically, 60 ≤ N ≤ 200 and b ≥ 1500 s/mm 2 is used for clinical acquisition (equivalent to a b-value of 4500 for preclinical acquisitions due to the drop of the ADC).

A plethora of methods have been developed to analyze the DW-MRI data and estimate diffusion features. The most common models can be separated into two classes:

• "signal models" expand the free/isotropic diffusion model (section 3.2.2) to increase the agreement with the measured data,

• "biophysical models" generate a geometrical model of the underlying tissue and calculate the corresponding MR signal.

One cannot exhaustively cover all these techniques, and only modeling approaches that are directly relevant to this work are detailed in the next sections.

Signal models

Model-based techniques The first two models that have been introduced are the ADC and the DT models, (see sections 3.2.2 and 3.2.4. When the community realized that DTI model was enable to recover fiber crossings, the natural extension was to try more than one tensor per voxel. Tuch et al.

[ 2002] proposed to model the HARDI signal as a finite mixture of N tensors with volume fractions p i , giving a new Multi-Gaussian (Tensor) model leading to equation 3.8:

S(q, τ) = S 0 N ∑ i=1
p i e -τq T D i q (3.12)

From this work, numerous models have been proposed using alternative orthogonal basis functions such as Wisharts, Bingham, Watson or von Mises-Fisher functions to replace the basic assumption of Gaussian distributions behind the tensor model [McGraw et al., 2006, Jian and[START_REF] Jian | Multi-fiber reconstruction from diffusion MRI using mixture of wisharts and sparse deconvolution[END_REF].

Whether considering the ADC, DT, Multi-Gaussian or even models using more complex functions to describe the diffusion process, all these techniques are "model dependent". They are indeed based on assumptions about how the water molecules diffuse in their environment (following respectively a Gaussian, Whishart or Watson distribution). However, modeling water diffusion in biological tissue is not straightforward, which motivated the introduction of "model-free" techniques in parallel.

Model-free techniques Model-free techniques do not make any physical assumption about tissue properties. A summary of the major model-free techniques developed during the last two decades is listed below :

• Diffusion Spectrum Imaging, presented in section 3.2.7 [wed],

• Q-Ball Imaging (QBI) [START_REF] Ds Tuch | Diffusion MRI of complex tissue structure phd thesis massachusetts institute of technology[END_REF], introducing a spherical sampling of the Q-space. This sampling reduces the acquisition time of the DSI technique despite the decrease in angular resolution. QBI gives access to the dODF from equation 3.7 using the Funk-Radon Transform,

• Analytical QBall Imaging (aQBI) [START_REF] Descoteaux | Regularized, fast, and robust analytical q-ball imaging[END_REF], using the same acquisition scheme as QBI but decomposing the signal into a modified spherical harmonics basis,

• Kurtosis Imaging technique (DKI) [START_REF] Jensen | Diffusional kurtosis imaging: The quantification of non-gaussian water diffusion by means of magnetic resonance imaging[END_REF], quantifying the degree of non Gaussianity of the diffusion process,

• Mean Average Propagator (MAP-MRI) [ Özarslan et al., 2013a], based on the idea of expressing the signal and the propagator using the same harmonics basis of Hermite functions.

In the frame of this thesis, aQBI model was chosen to reconstruct ODFs with a single-shell HARDI acquisition. MAP-MRI was also applied when multi-shell acquisitions with a constant diffusion time were available. Both have the advantage of being model-independent. A short introduction to these models is given in the next two paragraphs. Supplementary details can be found in Özarslan et al.

[2013a], [START_REF] Descoteaux | High angular resolution diffusion MRI: from local estimation to segmentation and tractography[END_REF].

Analytical Q-Ball Imaging (aQBI) In 2007, Descoteaux et al. exploited the fact that any function on the sphere can be decomposed on a set of orthogonal functions, defined as spherical harmonics Y m l , of order l and degree m. Due to the nature of the diffusion, the induced signal is real and symmetric.

Hence, a real and symmetric modified orthonormal spherical harmonics basis was defined, with only even order terms in order to respect the symmetric property. Therefore, the HARDI signal S can be approximated using a truncated spherical series of order l max , with (l max +1)(l max +2) 2 terms. The reader is referred to [START_REF] Descoteaux | High angular resolution diffusion MRI: from local estimation to segmentation and tractography[END_REF] for more information about the analytical QBI equations.

The capability of aQBI to differentiate crossing fibers depends on the q-sphere encoding points and the wave vector q. Moreover, as ∆r ∝ 1 |q| with ∆r the radial resolution, one can recall that the higher the b-value, the higher the angular resolution of the ODF [START_REF] David S Tuch | Q-ball imaging[END_REF].

While ODFs obtained with HARDI enable a more robust fiber populations estimation than DTI, they only rely on the angular profile and miss valuable information embedded in the radial part of the PDF. With the improvements of hardware, in particular regarding the gradients, new models have been developed to take advantage of this radial information to obtain in fine EAP instead of simple ODFs.

The latest diffusion propagator models: SHORE and MAP-MRI In 2013, Özarslan proposed a framework for expressing the diffusion q-space signal in terms of Hermite functions, well-known in quantum mechanics. The acquisition relies on a multiple-shell HYDI sampling scheme with multiple b-values obtained by varying the gradient magnitudes, with all other parameters (δ , ∆) remaining constant. This model, first introduced in 1D with SHORE [ Özarslan et al., 2013b], was then generalized in 3D with MAP-MRI [ Özarslan et al., 2013a[ Özarslan et al., , Fick et al., 2015]]. Because Fourier transform of these functions are Hermite functions themselves, this basis possesses the ability to represent both the signal and its Fourier transform, i.e. the average propagator. This method thus gives a fast estimation of the PDF as well as its features such as the Return To Axis Probability (RTAP). These features constitutes a more comprehensive tissue characterization than DTI parameters. For instance, when axons are modeled as parallel cylinders, RTAP can be related to the mean cross-sectional area of the axons, from which we can then compute the mean axon radius. However, this relation holds only if the intra-axonal signal is the only one considered, if δ ≈ 0 and if δ ∆, conditions that are rarely met in practice on clinical MRI systems, but that can become feasible on preclinical systems equipped with strong gradients.

Biophysical models

Biophysical models rely on a geometrical representation of the underlying tissue, described with several components. With the assumption of impermeability of the compartments, these models express the measured diffusion-weighted signal attenuation as the integration of individual contributions stemming from each compartment, weighted by their specific volume fractions. Then, the resolution of the inverse problem gives tissue features from the measured data. Biophysical models are also called "model-dependent", as they make biophysical assumptions about the microstructure of the tissue and how water molecules propagate in this environment. Numerous models have emerged during the last decades. Only the most relevant models will be presented in this manuscript, in a roughly chronological order.

Ball-and-Stick model [START_REF] Behrens | Characterization and propagation of uncertainty in diffusion-weighted mr imaging[END_REF] This model, considering two compartments, assumes that water molecules in an imaging voxel belong to one of two populations. The first compartment is a free population that is not affected by fiber structure barriers, with a fully isotropic Gaussian diffusion process. Including the extracellular space as well as the CSF, this is referred as "ball". The second compartment is a restricted population within or near fiber structures, considered as "sticks", with a Gaussian and highly anisotropic diffusion process (Figure 3.11.A.).

While simplicity is a key when having a limited amount of data, this model cannot represent microstructural tissue features such as axon diameter. Numerous techniques were derived, further refining the model, and using cylinder or a distribution of cylinder for the restricted compartments, and ball, tensor or zeppelin for the extra-cellular part, where an additional isotropically restricted compartment can sometimes be inserted [START_REF] Panagiotaki | Compartment models of the diffusion mr signal in brain white matter: a taxonomy and comparison[END_REF].

Composite hindered and restricted model of diffusion (CHARMED) [START_REF] Assaf | New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter[END_REF][START_REF] Assaf | Composite hindered and restricted model of diffusion (charmed) mr imaging of the human brain[END_REF] CHARMED has been extended in two major frameworks, developed simultaneously by two teams, and giving access to the axon diameter: the AxCaliber framework developed by [START_REF] Assaf | Axcaliber: a method for measuring axon diameter distribution from diffusion MRI[END_REF] and the ActiveAx framework developed by Alexander [2008].

AxCaliber [START_REF] Assaf | Axcaliber: a method for measuring axon diameter distribution from diffusion MRI[END_REF] Developed by the same research group as CHARMED, this extension estimates the distribution of axon diameters, assuming a known fiber direction. Thus, target regions are typically nerves or the corpus callosum, because of their high level of anisotropy. Based on previous histological work by [START_REF] Aboitiz | Fiber composition of the human corpus callosum[END_REF], the axon diameters are assumed to follow a Gamma distribution (Figure 3.11.B.2.). The correspondence between histology and MR measurements of axon diameter in sciatic and optic nerve tissue specimens was found to be very satisfying.

Nonetheless, this approach is not designed for clinical applications as it requires many measurements perpendicular to the studied bundle and, above all assumes prior knowledge of the fiber orientation.

ActiveAx [START_REF] Daniel | A general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features[END_REF] To overcome these limitations, Alexander [2008] developed a framework making axon diameter estimation compatible with a clinical scan duration. In order to increase the robustness of the parameter estimates, the tissue model was simplified and white matter was defined as a collection of axons with the same diameter (corresponding to the average diameter of the real distribution). The extra-cellular compartment remained unchanged. In the latest work derived from ActiveAx [Alexander et al., 2010], two other compartments were added. First, in order to account for partial volume effects from the CSF, one new compartment features isotropic free diffusion.

Then, from ex vivo studies performed on monkey brains, Alexander et al. observed that an additional fully restricted water compartment was needed to model changes of tissue properties occurring after the fixation of post mortem tissues (Figure 3.11.B.3.).

In summary, each compartment contributes to the global diffusion attenuation A resulting from a linear combination of the individual signal attenuations associated to each compartment:

1. A ic , the signal attenuation stemming from the compartment of highly restricted water molecules trapped within axons and characterized by a volume fraction f ic , 2. A ec , the signal attenuation stemming from the extra-cellular compartment of water molecules surrounding the axons, characterized by a volume fraction f ec , 3. A iso , the signal attenuation stemming from the CSF compartment containing free molecules with an isotropic displacement probability and characterized by a volume fraction f iso , 4. A stat , the signal attenuation stemming from the compartment of stationary water molecules trapped within glial cells modeled as spheres of zero diameter (i.e. points) and characterized by a volume fraction f stat . This additional compartment results from the process of fixation, in particular with the 4% formaldehyde, that reduces the membrane permeability of glial cells due to an interaction with aquaporin channels [START_REF] Peter E Thelwall | Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model[END_REF].

The net diffusion signal attenuation A corresponds to the following linear combination:

A = f ic .A ic + f ec .A ec + f iso .A iso + f stat .A stat (3.13) with f ic + f ec + f stat + f iso = 1.
The signal from the stationary population remains unattenuated by diffusion weighting, yielding A stat = 1. Eq.3.13 can therefore be written as:

A = f ic .A ic + f ec .A ec + f iso .A iso + f stat (3.14)
Although the model reduces the characterization of the axon diameter distribution to a single volumeweighted diameter index, it still requires high quality data and large gradient strengths in order to estimate small axon diameters. As the gradient strength increases, smaller sizes can be detected

and measured [START_REF] Daniel | A general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features[END_REF]. The diameter estimation could then be significantly improved by the use of post-mortem data on preclinical MRI, which have gradients up to 750 mT/m, i.e. ten times more than classical clinical MRI (70 mT/m) (see the following paragraph entitled What is the resolution limit for axon diameter estimation?).

Beyond strictly parallel cylinders Previous models assume fiber populations with strictly parallel axons in each voxels, which is only acceptable in highly isotropic regions like nerves or the corpus callosum.

In [START_REF] David R Riddle | Brain aging: models, methods, and mechanisms[END_REF][START_REF] Sune N Jespersen | Modeling dendrite density from magnetic resonance diffusion measurements[END_REF] approximated an arbitrary orientation distribution of dendrites and axons using a truncated spherical harmonic series, to model both gray and white matter. ). Due to its simple acquisition scheme, NODDI has become very popular and used in various studies to characterize healthy and pathological brain tissues [START_REF] Kunz | Assessing white matter microstructure of the newborn with multishell diffusion MRI and biophysical compartment models[END_REF], Schneider et al., 2014[START_REF] Colgan | Application of neurite orientation dispersion and density imaging (noddi) to a tau pathology model of alzheimer's disease[END_REF].

The Watson's distribution is symmetrical around the main fiber direction and cannot recover fiber crossings. Thus, more complex distributions can be used, such as Bingham, a spherical analogue of the 2D Gaussian distribution. [START_REF] Tariq | Bingham-noddi: mapping anisotropic orientation dispersion of neurites using diffusion MRI[END_REF] used the Bingham distribution to extend NODDI and created the Bingham-NODDI model. More recently, [START_REF] Zucchelli | NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI[END_REF] also introduced NODDI-SH, robust to multiple fiber crossings. However, these models are far from being as commonly used as NODDI, the addition of parameters making the fit more complex to achieve. What is the resolution limit for axon diameter estimation? The sensitivity to small-diameter axons estimation is mainly limited by the gradient strength and by the type of pulse sequence [Dyrby et al., 2013]. [START_REF] Drobnjak | OGSE, and sensitivity to axon diameter in diffusion MRI: insight from a simulation study[END_REF] compared the resolution limit obtained using Pulsed Gradient Spin Echo (PGSE) and Oscillating Gradient Spin Echo (OGSE) sequences and showed that in the idealized case where gradients are perpendicular to straight, parallel, impermeable cylinders, the standard PGSE experiment gives the greatest sensitivity with a resolution limit of 4.5-7 µm (depending on the SNR) with 60 mT/m, but reduces to 2-3 µm with 300 mT/m. In a more realistic case including fiber dispersion, the resolution limit increases, and the sensitivity using OGSE sequences becomes higher than with PGSE. [START_REF] Nilsson | Investigating tissue microstructure using diffusion MRI: how does the resolution limit of the axon diameter relate to the maximal gradient strength[END_REF] showed that, for the idealized case described above, the resolution limit obtained with a PGSE sequence was proportional to G -1/2 max , SNR -1/4 , and δ -1/4 , whence comes the interest in using preclinical MRI equipped with strong gradients. This resolution limit raises the question of whether diffusion MRI can really access the axon diameter, since histological measurements of most axons are below 1 µm (see paragraph 2.5.1.1). However, histological preparations usually induce tissue shrinkage, and in vivo axons may have a diameter somewhat larger. Then, even if large axons are a tiny minority in terms of number of axons, they are much more significant in terms of signal they contribute. Thus, diffusion MRI may at least provide strong sensitivity to the existence and size of large axons, enabling for instance the investigation of pathologies effects (e.g. multiple sclerosis) on large motor tracts.

Future directions of research Now more than ever, the community works on the improvement of tissue microstructure inference. These improvements focus on the following points :

• improving the model realism. This involves, in particular, the modeling of the myelin sheath surrounding most of the axons membranes, the Ranvier nodes, or the micro-vasculature. Moreover, none of the models discussed above account for membrane permeability when modeling restriction. Axon wall permeability allows exchange of particles between the intra and extra cellular compartments, which can be modeled by coupled differential equations [Nilsson et al., 2013b]. A way around the analytical problem can be the use of machine learning based compartment models with permeability [START_REF] Nedjati-Gilani | Machine learning based compartment models with permeability for white matter microstructure imaging[END_REF].

• improving the optimization process. The idea is to reduce the fitting time and improve the stability of parameter estimates. This stability is affected by the non-linear parameter fitting procedure employed. The objective functions often have local minima, rendering the determination of the global minimum challenging and time consuming. For instance in 2015, [START_REF] Daducci | Accelerated microstructure imaging via convex optimization (amico) from diffusion MRI data[END_REF] proposed a framework for accelerated microstructure imaging via complex optimization (AMICO), which linearizes the fitting procedure. This results in a reduction of the computation time and also a higher stability of diameter estimations, avoiding local minima.

Other frameworks were developed since then, like the one of [START_REF] Sepehrband | Towards higher sensitivity and stability of axon diameter estimation with diffusion-weighted MRI[END_REF], or [START_REF] Harms | Robust and fast nonlinear optimization of diffusion MRI microstructure models[END_REF] • developing new acquisition sequences. The sequence presented in section 3.2.5 is a classical PGSE. However, sequences with Double Diffusion Encoding [START_REF] Shemesh | Conventions and nomenclature for double diffusion encoding NMR and MRI[END_REF], or arbitrary gradients waveforms [START_REF] Drobnjak | Optimizing gradient waveforms for microstructure sensitivity in diffusion-weighted mr[END_REF], in particular the use of Oscillating Gradient Spin Echo (OGSE), have been shown to improve the signal sensibility to the microstructure features. In particular, there is a growing interest in trapezoid OGSE that became usable on the latest Connectome MRI systems, such as the Prisma 3T MRI (Siemens, Erlangen).

• introducing a BigData approach. Research groups have recently started to apply deep learning techniques to the field of dMRI, particularly for the compartment modeling or the addition of the tissue permeability [START_REF] Nedjati-Gilani | Machine learning based compartment models with permeability for white matter microstructure imaging[END_REF]. The quest for a complete analytical model actually seems to be doomed to fail, because of the necessary trade-off between the model complexity to mirror the reality, and the reasonable number of parameters that can be fitted.

That is why deep learning techniques appear to be the next step for microstructure inference, the drawback being the need for a tremendous dictionary for the training part. This sections presented the major local models used for diffusion MRI, whether for signal or biophysical modeling. These models can be model-dependent (depending on assumptions about how the water molecules diffuse, following a Gaussian or even more complex distribution, or assumptions about the geometrical representation for the underlying tissue), or model-free. The next section exposes the two main application of diffusion MRI, that are based on these local models.

Applications of diffusion MRI

Diffusion MRI is a powerful tool to infer structural information in the human brain. The first major clinical application of dMRI is the diagnosis and management of acute brain ischemia (stroke).

Another major application is the in vivo inference of the brain connectivity, by following the major pathways defined by the mobility of water molecules. Finally, the last application is the microscopic diffusion MRI to extract structural parameters such as axon diameter and density in the white matter.

Diagnosis of stroke and cancer

The diagnosis of stroke is probably the most prevalent application of dMRI in clinical routine. In 1990, [START_REF] Moseley | Early detection of regional cerebral ischemia in cats: comparison of diffusion-and T2-weighted MRI and spectroscopy[END_REF] discovered that water diffusion dropped significantly (30-50%) during the very early phase of acute brain ischemia using a cat brain ischemia model. From then, dMRI has been applied for the diagnosis of acute stroke within 3-6 hours of onset using the ADC map that displays an hyposignal in the infarcted areas.

In addition to stroke, dMRI is now widely used for the detection and management of cancers and metastases (breast, prostate, liver) [START_REF] Anwar R Padhani | Diffusionweighted magnetic resonance imaging as a cancer biomarker: consensus and recommendations[END_REF]. The ADC map provides information that can help for the diagnosis (water diffusion slows down when tumor cellularity increases, and a large Chapter 3. diffusion MRI: a powerful tool to probe the brain architecture 50 ADC decrease is usually associated with a high degree of malignancy [START_REF] Turkbey | Is apparent diffusion coefficient associated with clinical risk scores for prostate cancers that are visible on 3-t mr images[END_REF]), and also for the prediction of early response to chemotherapy [START_REF] Cui | Apparent diffusion coefficient: potential imaging biomarker for prediction and early detection of response to chemotherapy in hepatic metastases[END_REF].

Inference of structural connectivity using tractography

Originated in the late 1990s [START_REF] Peter | Fiber-tractography via diffusion tensor MRI (DT-MRI)[END_REF][START_REF] Mori | Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging[END_REF], fiber tracking, or "tractography", is a method for the reconstruction of neuronal pathways based on measurements of the anisotropic diffusion of water molecules in the white matter. Following the direction(s) with the highest probability(ies) provides the principal pathways of water molecules, corresponding to the paths where their motion is less restricted. These directions are, in white matter, the directions parallel to the fibers.

Fiber tracking algorithms can be classified into two types: local and global. Both techniques are detailed in the following two sections.

Local techniques

The first group of methods is based on local line propagation techniques (or streamline techniques) [START_REF] Mori | Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging[END_REF][START_REF] Poupon | Détection des faisceaux de fibres de la substance blanche pour l'étude de la connectivité anatomique cérébrale[END_REF]. Local techniques build, step-by-step, a fiber pathway from a seed point along the principal diffusion directions, which correspond to the principal eigenvectors of the diffusion tensors. There are two main classes of algorithm using a local approach: deterministic and probabilistic tracking.

• Streamline deterministic algorithms. Introduced by [START_REF] Peter | In vivo fiber tractography using DT-MRI data[END_REF], the deterministic tractography was designed to compute the tractogram from DTI data. Reconstructed streamlines are 3D curves presenting a tangent parallel to the main fiber direction in each voxel. At each step of the algorithm, a line is propagated, following the orientation having the highest probability according to the given local orientation field. In each voxel, several lines are drawn from different "seeds", typically 8 to 27 per voxel. Taking into account the low curvature of fibers, the algorithms generally consider an aperture cone (typically 30°), forwards or backwards, restricting the propagation domain within this cone. Streamline deterministic tractography is very fast. However, even if the method is not limited to the tensor model, it cannot resolve fiber crossings or kissings. In addition, deterministic algorithms are prone to local errors in the estimate of the fiber directions (caused by noise and partial voluming) and may deviate from the true neural pathway, thus creating plethora of false positives [START_REF] Maier-Hein | The challenge of mapping the human connectome based on diffusion tractography[END_REF].

• Probabilistic algorithms [START_REF] Behrens | Characterization and propagation of uncertainty in diffusion-weighted mr imaging[END_REF][START_REF] Parker | A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements[END_REF], Perrin et al., 2005a]. These methods incorporate the uncertainty of diffusion MR measurements to propagate according to a probability distribution function. Thus, the highest probability is not systematically followed: an orientation is randomly chosen within the angular cone, centered on the highest probability given by the local model. Probabilistic streamline algorithms can better handle fiber crossings and are more robust to noise as they can overcome propagation of errors. The other side of FIGURE 3.12: Result of a deterministic tractography performed on a subject from the Archi database [START_REF] Assaf | The connect project: combining macro-and micro-structure[END_REF] with one seed per voxel. a. b. and c. respectively show a sagittal, coronal and axial slice with a width of 1mm for a better visualization of the fibers.

the coin is that these algorithms are much slower than the deterministic methods. Moreover, if these techniques show a higher sensitivity compared to their deterministic counterparts, i.e., a higher rate of true positives, they also show a lower specificity, i.e., a higher rate of false positives.

Local techniques build each fiber independently of the others. The major advantage of local methods is that they are rather fast, but they also have several problems. The most apparent is probably that minor imperfections in the determination of local steps can accumulate and significantly affect the final result. Such an error can arise from the uncertainty in the determination of the ODF. Global tractography was developed as an alternative to deterministic and probabilistic algorithms, with the intention of further improving the robustness of fiber tracking using diffusion imaging [START_REF] Mangin | Toward global tractography[END_REF]. [START_REF] Poupon | Détection des faisceaux de fibres de la substance blanche pour l'étude de la connectivité anatomique cérébrale[END_REF][START_REF] Mangin | Toward global tractography[END_REF][START_REF] Bw Kreher | Gibbs tracking: a novel approach for the reconstruction of neuronal pathways[END_REF][START_REF] Fillard | A novel global tractography algorithm based on an adaptive spin glass model[END_REF][START_REF] Reisert | Global fiber reconstruction becomes practical[END_REF][START_REF] Jbabdi | Tractography: where do we go from here?[END_REF] try to reconstruct the fibers simultaneously by finding the configuration that describes best the measured data.

Global techniques Global tractography techniques

In 2002, [START_REF] Cointepas | A spin glass based framework to untangle fiber crossing in mr diffusion based tracking[END_REF] introduced the use of "spin-glass" approaches to infer white matter tracts. These spin-glasses are considered as pieces of tracts, and the idea is to optimize their configuration minimizing a global energy, attracting the spins to be oriented along the main fiber directions and to form long chains with low curvature. If the number of spins is not high enough to solve the local configuration, such as crossings, the algorithm allows them to be created on the fly. These global techniques are efficient since they are less blind than others but take longer computation time requiring strong optimization of the code and the use of high performance computing hardware.

In this section, we gave an overview of different techniques that are currently used to infer white matter connectivity from diffusion-weighted images. No matter which tractography technique is used, however, it is important to keep in mind that reconstructed fibers are "virtual" fibers. It is therefore important to treat tractography results with care and to try to corroborate them whenever possible with existing anatomical knowledge.

Inference of the human connectome [START_REF] Hagmann | From diffusion MRI to brain connectomics[END_REF][START_REF] Sporns | The human connectome: a structural description of the human brain[END_REF][START_REF] Hagmann | Mr connectomics: principles and challenges[END_REF][START_REF] Sporns | The human connectome: a complex network[END_REF]. The human "connectome" and its related science named "connectomics" refers to the mapping of brain connections. This field has recently acquired significant interest because of its fundamental role in understanding brain, aiming to connect its structure to function and behavior.

Connectivity maps have for instance been used to study the relationships between structural brain networks and aging [START_REF] Gong | Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography[END_REF], intelligence [START_REF] Li | Brain anatomical network and intelligence[END_REF], or the relationships between structural and functional connectivity [START_REF] Cj Honey | Predicting human resting-state functional connectivity from structural connectivity[END_REF]. More recently, the Human Connectome Project (HCP) was launched with the goal of mapping human brain connections and their variability in healthy adults. Since 2010, this project has gathered functional and diffusion MRI data from more than 1200 healthy subjects [Glasser et al., 2016a]. In connectomics, the brain is considered as a network made of neural connections and neural units. Depending on the scale, connections are axonal fiber bundles or individual axons, and neural units are cortical functional units, cortical columns, or individual neurons. This results in a structural connectivity matrix that can be obtained using a variety of seeding strategies (seeding from region of interest (ROI) and recording the number of streamlines that reach other ROIs, or seeding all the volume and counting the number of streamlines linking each pair of ROIs), each of these two methods having their own strengths and limitations [START_REF] Li | The effects of connection reconstruction method on the interregional connectivity of brain networks via diffusion tractography[END_REF].

The obtained matrix is symmetric, because efferent and afferent projections cannot be distinguished with diffusion MRI, and the exclusion of self-connections implies a zero diagonal line. In addition to the choice of the seeding method, other challenges have to be faced when transforming data into a network. For instance, the choice of nodes can be based on their topographical position or on fMRIbased functional localization protocol. The definition of connectivity between region can be chosen either as the connection density by counting the fibers between two regions of interest (ROI), or using diffusion-derived parameters (FA, MD) to better account for connective efficacy. At this point, all these methodological questions remain open.

Inference of the microstructure

As already shown in section 3.2.7.2, the third application of diffusion MRI is the inference of brain microstructure. Microstructural features (axon diameter or density) can be extracted from diffusionweighted multiple-shell data, using models such as CHARMED, ActiveAx, or NODDI [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF][START_REF] Assaf | Composite hindered and restricted model of diffusion (charmed) mr imaging of the human brain[END_REF], Alexander et al., 2010]. This research field, referred as diffusion MR microscopy, has become of significant interest for studying normal brain development, maturation and aging, as well as for characterizing a broad range of brain disorders. One of the first application involving living humans was performed by [START_REF] Tavor | Micro-structural assessment of short term plasticity dynamics[END_REF], who applied the CHARMED model to study structural plasticity induced by long-term learning. An increase of the neurite density was then observed in the hippocampus and the parahippocampal gyrus. [START_REF] Gavin P Winston | Advanced diffusion imaging sequences could aid assessing patients with focal cortical dysplasia and epilepsy[END_REF] applied Chapter 3. diffusion MRI: a powerful tool to probe the brain architecture 53 the NODDI model on a cohort presenting a focal cortical dysplasia, and reported a reduction of the neurite density index in focal lesions. In both study, the changes in neurite density were more conspicuous than the corresponding changes in MD or FA. Since then, NODDI has been applied to investigate normal brain development [START_REF] Eaton-Rosen | Longitudinal measurement of the developing grey matter in preterm subjects using multi-modal MRI[END_REF], neurodegeneration [START_REF] Colgan | Application of neurite orientation dispersion and density imaging (noddi) to a tau pathology model of alzheimer's disease[END_REF], neurodevelopmental [START_REF] Timmers | White matter microstructure pathology in classic galactosemia revealed by neurite orientation dispersion and density imaging[END_REF] or neurological disorders [START_REF] Lemkaddem | Connectivity and tissue microstructural alterations in right and left temporal lobe epilepsy revealed by diffusion spectrum imaging[END_REF]. Regarding the axon diameter estimation, in vivo investigations are more limited due to the inadequacy of clinical gradient strength. Taking advantage of the Connectome scanner with 300 mT/m, [START_REF] Huang | Characterization of axonal disease in patients with multiple sclerosis using high-gradient-diffusion mr imaging[END_REF] investigated the axon diameter of a multiple sclerosis (MS) cohort at the level of the mid-sagittal section of the corpus callosum, and demonstrated an increase of the axon diameter in the MS lesions, which was consistent with histological findings. Further details about the current microstructure models, their limitations and future directions can be found in section 3.2.7.2.

Conclusion

This chapter presents the main knowledge about MRI, and more specifically diffusion MRI, needed to develop the contributions of this thesis work. The first section covers MRI hardware, basics of NMR phenomenon, and the principle of signal generation, detection and localization. These aspects are important as this thesis involves a substantial number of acquisitions. The second section presents the theoretical aspects of diffusion MRI, from the acquisition scheme to the local modeling strategies, where signal and biophysical models make dMRI a potential tool to infer the brain connectivity and microstructure.

Chapter 4

Post mortem imaging

The typical voxel size for in vivo dMRI is in the range 1-3 mm. When studying an ex vivo sample, i.e. an excised post mortem tissue, dMRI can reach a few hundred micrometer. This high spatial resolution, being intermediate to that obtained using light microscopy, gives access to the mesoscale connectivity of the human brain and constitutes one of the first motivation to perform post mortem imaging.

The purpose of this chapter is to discuss the specifics of ex vivo imaging, and to go into more details regarding MRI acquisition techniques required to understand the choices made for the design of acquisition protocols developed in the frame of this thesis. The first section presents the main reasons motivating post mortem imaging. Then, the second section highlights the specific properties of fixed tissues, the challenges arising from it, and details some "good-practice" for ex vivo acquisitions. The third section details some criteria required for the evaluation of image quality as well as acquisition time, and presents the common artifacts met with post mortem ultra-high field (UHF) MRI. Finally, the last part of this chapter explains useful MR acquisition techniques which were successfully used during this thesis work.

Why studying an ex vivo human brain with a preclinical MRI?

This section summarizes the main reasons that motivate the use of post mortem MRI and why there has been renewed interest for it in recent years [START_REF] Roebroeck | Ex vivo diffusion MRI of the human brain: Technical challenges and recent advances[END_REF].

Ex vivo versus in vivo imaging

Diffusion MRI performed on in vivo subjects is limited in terms of spatial resolution and diffusion contrast, their improvements reducing the signal to noise ratio (SNR) [START_REF] Jones | Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI[END_REF] (see the definition of SNR in § 4.3.1). One possibility to partially overcome this SNR challenge involves performing longer acquisitions with an increased number of repetitions. This cannot be achieved with living subjects, as the acquisition time cannot exceed one to two hours. In contrast, ex vivo samples allow for prolonged scanning sessions, overnight or up to weeks, and dMRI with spatial resolution as high as 500 µm isotropic has been demonstrated in whole post mortem brains [START_REF] Tim B Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusionweighted imaging datasets[END_REF][START_REF] Foxley | Improving diffusion-weighted imaging of post-mortem human brains: Ssfp at 7 t[END_REF]. Another advantage of long acquisition times is the possibility to use slower sequences such as conventional diffusion-weighted spin-echo (DW-SE) sequences with single-line read-out, thereby ensuring minimal image distortions compared to faster sequences such as Echo Planar Imaging (EPI), where phase errors accumulated during the long echo train length can induce susceptibility artifacts ( § 4.4.2.3).

On another level, subject motion may occur during the acquisition, leading to corrupted image depicting various kind of artifacts according to the motion nature, such as stripes (

Preclinical versus clinical MRI systems

Clinical MRI systems have inherent limitations that prevent one from reaching ultra-high spatial and angular resolutions, mainly due to the characteristics of their gradient coils. The recent development of "Connectome" gradients, able to provide 300 mT/m, could offer an alternative, but they still limit the spatial resolution to the millimeter scale. This is due, first, to the static field being kept moderate (3T) in order to prevent the strong mechanical constraints that would occur at ultra-high field [START_REF] Jones | Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI[END_REF], McNab et al. [2013a], [START_REF] Setsompop | Pushing the limits of in vivo diffusion MRI for the human connectome project[END_REF]). Then, despite the high capacities of the system, the slew rate has to be kept lower than 200 mT/m/s when scanning in vivo subjects in order to avoid the stimulation of peripheral nerves (PNS).

Ex vivo MR imaging can be performed using ultra-high field preclinical scanners, provided a sample that fits into the small bore of the system (typically 10-20cm). In addition to their ultra-high static field (typically between 7 and 17.2T), that enables to reach high SNRs, these systems can be equipped with very strong gradients up to 1000 mT/m, enabling high spatial resolution.

Strong gradients are a key component for diffusion MRI [START_REF] Jones | Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI[END_REF]. In chapter 3, we emphasized that the angular resolution of the reconstructed ODFs increased with the b-value. According to equation 3.5, strong gradients give access to higher b-values by providing higher q-value and a shorter echo time (TE). The latter leads to a higher SNR per unit b-value, as the T2 decay is significantly reduced (equation 4.1). The b-values can thus exceed 10000 s/mm 2 , giving access to more degrees of freedom to refine the sensitization of images to processes occurring at the mesoscopic scale. The use of strong q-magnitudes enhance the angular resolution of ODFs or EAPs, and therefore improve the quality of fiber tracking. Moreover, it also gives access to a broader coverage of the diffusion time range which leads to a better inference of microstructural features such as the axon diameter. Indeed, as shown by [START_REF] Nilsson | Investigating tissue microstructure using diffusion MRI: how does the resolution limit of the axon diameter relate to the maximal gradient strength[END_REF], the resolution limit for the diameter estimation is proportional to G -1/2 max , SNR -1/4 , and δ -1/4 . Therefore, using preclinical MRI systems with strong gradients improves the resolution limit with the use of high G max and a higher SNR obtained thanks to a shorter TE, a higher B 0 , and a higher number of repetition (equation 4.1). Finally, preclinical systems have ultra high slew rate (e.g. 9500 mT/m/ms for the 11.7T Bruker MRI system used during this thesis, compared to 200 mT/m/ms for a clinical system), which enables to have ultra-short diffusion gradient pulses δ . Whereas it is not possible to exploit the slew rate to the full hardware limits in vivo due to physiology-related constraints (in particular to avoid peripheral nerve stimulation (PNS)), ex vivo experiments do not suffer from such a limitation and the obtained diffusion gradients can be closer to Dirac pulses, thus allowing EAPs to approach true PDFs.

Diffusion MRI validation

Another motivation for scanning post mortem brains is the ability to directly compare dMRI data to histological staining in the same tissue. Indeed, dMRI provides a method for probing white matter microstructure and connectivity in vivo. However, all these features still require anatomical validation to bridge the gap between human neuroanatomy and previous validation methods such as animal models [START_REF] Trygve B Leergaard | Quantitative histological validation of diffusion MRI fiber orientation distributions in the rat brain[END_REF][START_REF] Dauguet | Comparison of fiber tracts derived from in-vivo dti tractography with 3d histological neural tract tracer reconstruction on a macaque brain[END_REF][START_REF] Tim B Dyrby | Validation of in vitro probabilistic tractography[END_REF], computer simulations [START_REF] Tournier | Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution[END_REF][START_REF] Zhan | How accurately can the diffusion profiles indicate multiple fiber orientations? a study on general fiber crossings in diffusion MRI[END_REF][START_REF] Christopher P Hess | Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis[END_REF], and phantoms [START_REF] Tournier | Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data[END_REF], Perrin et al., 2005b[START_REF] Fieremans | The design of anisotropic diffusion phantoms for the validation of diffusion weighted magnetic resonance imaging[END_REF][START_REF] Pullens | Ground truth hardware phantoms for validation of diffusion-weighted MRI applications[END_REF], although the two latter remains far from being realistic enough to mimic real tissue. Performing both dMRI and histological studies on the same tissue enables to map the relationships between the underlying fiber architecture and the diffusion signal, and to reliably compare diffusion modeling approaches with a robust ground truth measurement. Therefore, this kind of studies can potentially yield important insights into deciphering the microstructural basis of diffusion contrasts in the human brain structures.

Exotic species exploration

A last motivation to study post mortem brains, even though this is quite out of the scope of this thesis, is the opportunity to study "exotic" species that could hardly be scanned within their lifetime. To date, a few databases have been established, such as the Mammalian MRI (MaMI) database (http://neuroimaging.tau.ac.il/ya) that contains MRI scans of 87 different species across the mammalian class (e.g. Free-Tailed Bat, European Hedgehog or Hyaena), the Brain Biodiversity Bank from the Michigan State University (http://www.msu.edu/brains/), the Brain Catalogue from the Institut Pasteur (https://braincatalogue.org/) or the digital fish library [START_REF] Rachel M Berquist | The digital fish library: using MRI to digitize, database, and document the morphological diversity of fish[END_REF]. These databases provide information not only about the gross anatomy of the brains but also, depending on the database, about their connectivity, which is increasingly of interest in comparative anatomy [START_REF] Rogier B Mars | Primate comparative neuroscience using magnetic resonance imaging: promises and challenges[END_REF]. This section gave an overview of the motivations justifying the recent interest for post mortem imaging. Ex-vivo samples not only prevent from artifacts that are inherent to in vivo measurements, but they also make possible the investigation of the human brain anatomy through the use of preclinical systems, thus removing a number of barriers imposed by clinical scanners. However, in order to infer in vivo anatomical properties of the human brain based on ex vivo experiments, it is important to understand the brain tissue modifications caused by natural tissue decomposition and chemical fixation, as well as their consequences on the tissue MR properties.

Ex vivo tissue characteristics

This section identifies the main tissue modifications occurring during the tissue decomposition and the fixation process. Afterwards, based on the resulting MR properties, the section discusses to what extent quantitative measures obtained from an ex vivo sample can be used to infer in vivo structural characteristics. Finally, the last part of this section lists the recommended good practices to perform successful post mortem imaging in light of the ex vivo tissue characteristics previously described.

Tissue fixation: why and how

Ideal post mortem MRI investigations would be in a condition where cells and tissue components are preserved in a "life-like" state. However, autolysis, corresponding to the cells destruction by their own enzymes, starts as soon as tissue is deprived of its blood supply. Fixation is a method to largely protect against this phenomenon. In routine, phosphate buffered formalin is the most frequently used for fixation [START_REF] Cecil H Fox | Formaldehyde fixation[END_REF]. As depicted in figure 4.1, formaldehyde (CH 2 O) first reacts with water (H 2 O) to form methylene glycol (OH(CH 2 OH) n ). Hydrated formalin is a coagulative protein (long chains of amino acid monomers linked by peptide bonds) fixative. The most common crosslink occurs between the nitrogen at the end of the side-chain of lysine (one of the 22 amino-acid involved in the creation of proteins) and the nitrogen of a peptide linkage. When two binding sites are sufficiently close, a methylene bridge (-CH 2 -) is built and the corresponding proteins are linked together, which results in large protein complexes. This chemical reaction is quite slow, and the penetration rate of paraformaldehyde is roughly 10 -3 mm/min [START_REF] Dempster | Rates of penetration of fixing fluids[END_REF][START_REF] Rd Start | Reassessment of the rate of fixative diffusion[END_REF], which means, considering the thickness of a human brain being around 8 cm, that the fixative would need around 33 days only to penetrate into the deepest structures.

An important difference between human and animal ex vivo studies is the way brain tissue is preserved and fixed. In most animal studies, the post mortem interval (PMI: the time between death and tissue fixation) can be very short, by following sacrifice of the animal immediately with fixation procedures. Pre mortem intracardial injection of fixative can also be performed, resulting in a PMI of zero. In contrast, the PMI in human ex vivo studies is always longer and perfusion fixation can only be performed post mortem by mechanical pumping. Perfusion fixation is usually followed by immersion in fixative. In the large human brain, immersion fixation is less effective than in smaller animal brains, because of the long times necessary for passive diffusion of fixative over large distances as described above. Therefore, although mechanical perfusion poses risk of microscopic damage induced by the pressure of pumping, this is a valuable technique when targeting the study of a whole human brain as immersion fixation alone would result in degraded tissus in the deepest areas. The effects of longer PMI and less effective fixation generally cause the quality of fixed human tissues to be lower than that of animal tissue. This suggests that comparisons between in vivo clinical MRI and MRI data from human autopsy tissues should be interpreted with caution [Shepherd et al., 2009a],

and PMI should be reduced as much as possible.

Physical properties of post mortem fixed tissues

Physical properties of fixed post mortem tissue such as magnetic properties (T1, T2) or diffusion properties (diffusion coefficient,...) are the result of both tissue decomposition and fixation. The observed values depend on many factors including the sample preparation protocol (time between death and fixation, formalin concentration, fixation duration, rehydration...) and the acquisition protocol (static field, temperature,...). Therefore, parameters evolution will only be given as ranges obtained from values of several studies.

Magnetic properties

Due to tissue decomposition and chemical fixation, tissue properties drastically change in post mortem tissue, with reduced proton density, T1 and T2 [Shepherd et al., 2009b[START_REF] Pfefferbaum | Effects of formalin fixation and temperature on mr relaxation times in the human brain[END_REF]. The exact mechanisms responsible for these changes are still a matter of debate, and the community only makes general assumptions. For instance, T1 being highly dependent on the size of molecules in the tissue environment, its reduction could be caused by the fixation step inducing large protein complexes formation [START_REF] Pfefferbaum | Effects of formalin fixation and temperature on mr relaxation times in the human brain[END_REF] ( § 4.2.1). Table 4.1 presents relaxation times obtained in various experimental conditions (in vivo and ex vivo experiments, and B 0 from 1.5 to 11.7T). In practice, T2 is reduced to 50-73% of in vivo values. The loss of T2 increases with field strength, but rehydration of the sample before scanning can partially rebound its T2 values.

T1 values are 23-56% of in vivo, and increase with B 0 . [START_REF] Mcnab | High resolution diffusion-weighted imaging in fixed human brain using diffusionweighted steady state free precession[END_REF][START_REF] Miller | Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner[END_REF].

Contributions of results from ex vivo experiments All the reported effects are heavily dependent on tissue preparation [Shepherd et al., 2009a] and compounded by the long PMI [Shepherd et al., 2009a[START_REF] Helen | An approach to high resolution diffusion tensor imaging in fixed primate brain[END_REF]. Nonetheless, fixation maintains the orientation of anisotropy and seems to preserve the broad microstructural environment of brain tissue, although aspects of the microenvironment relevant to dMRI can be changed such as membrane permeability and extracellular volume [Shepherd et al., 2009a,b]. The process of fixation, in particular with the 4% formaldehyde, is indeed known to reduce the membrane permeability of glial cells due to an interaction with aquaporin channels [START_REF] Peter E Thelwall | Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model[END_REF].

Therefore, post mortem tissue studies are relevant to infer brain connectivity, as fiber orientation remains the same. Regarding the inference of the microstructure, models might require corrections in order to take into account the reported changes such as the modifications of the membrane permeability.

Finally, while a long PMI results in poor ex vivo tissue quality with highly reduced diffusivity, the effect of scan interval (SI: time from death to scan) on diffusivity is much more limited, which means that well-fixed samples can be used for ex vivo dMRI studies for a considerable time, up to several years [START_REF] Tim B Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusionweighted imaging datasets[END_REF].

Good practices for imaging post mortem fixed tissues

MR properties changes reported in the previous paragraph represent challenges to overcome when designing an acquisition protocol for ex vivo tissue, especially for producing high quality and high resolution diffusion-weighted MRI data [START_REF] Tim B Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusionweighted imaging datasets[END_REF].

Sample preparation

First of all, the sample should be cooled to 4-5°C for long-term storage, in order to prevent the development of microorganisms and the deterioration of the tissue.

Dehydration being a well-known consequence of fixation, the sample should be transferred to a phosphate-buffered saline solution weeks before any MRI acquisition. This step washes out the fixative and rehydrates the tissue, which partly restores both D and T2 [Shepherd et al., 2009a,b].

Previous works suggest the possibility of soaking the sample in a gadolinium-doped buffer solution prior to imaging [START_REF] Helen | An approach to high resolution diffusion tensor imaging in fixed primate brain[END_REF][START_REF] Jean C Augustinack | Direct visualization of the perforant pathway in the human brain with ex vivo diffusion tensor imaging[END_REF][START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF]. The adjunction of gadolinium reduces the tissue T1, thereby reducing the T1 saturation effects at short TR, and has very little impact on T2 [START_REF] Helen | An approach to high resolution diffusion tensor imaging in fixed primate brain[END_REF]. Moreover, this procedure is reported to have no adverse effect for the histological analysis [START_REF] Helen | An approach to high resolution diffusion tensor imaging in fixed primate brain[END_REF], Augustinack et al. [2010] even observed an enhancement of the affinity of Nissl dye to neurons. Nonetheless, this doping is not adopted very often, the reasons given being an inability of the buffer to penetrate to the interior of the brain in the allotted time and a leaching of the gadolinium onto the brain [START_REF] Pfefferbaum | Effects of formalin fixation and temperature on mr relaxation times in the human brain[END_REF][START_REF] Miller | Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner[END_REF].

Since acquisitions usually take place at room temperature (approximately 20°C), the specimen should be transferred to the magnet room at least 4-5 h prior to scanning in order to stabilize its temperature to 20°C. This process is required to avoid effects related to temperature variations that would induce modifications of the local T2 relaxation time and the local apparent diffusion coefficient (ADC) up to a factor of 1.5-2 between 4 and 20°C [START_REF] Peter E Thelwall | Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model[END_REF].

Furthermore, in order to avoid drying of the tissue during the experiment and to reduce imaging artifacts, the sample is immersed in a perfluoropolyether (PFPE), such as Fomblin (Ausimont, Thorofare, NJ) or Fluorinert (FC-40, 3M Company, USA). PFPE are nearly ideal fluids as they do not provide any NMR signal, are non-toxic, non-inflammable, and have a similar susceptibility coefficient to the one of brain tissue. The last characteristic avoids the induction of static magnetic field variations close to the interfaces between air and tissue that would induce local geometrical and intensity distortions ( § 4.3.3.3). Lastly, it has been demonstrated that immersion of formalin-fixed tissue into PFPE for extended periods of time had no discernible effects on histological appearances (cellular detail and immunohistochamical staining) and did not alter MRI relaxation and diffusion properties [START_REF] Hyare | Perfluoropolyethers in magnetic resonance microscopy effect on quantitative magnetic resonance imaging measures and histological properties of formalin-fixed brain tissue[END_REF].

During the sample preparation, special attention should also be given to the removal of air bubbles, inducing susceptibility artifacts. This mainly relies on a manual task consisting of inducing light pressure on the sample to push air bubbles out of it. Another solution could be the use of a vacuum pump, but this solution is usually not adopted due to the risk of tissue degradation under high pressure.

Another important point is the stabilization of the sample in the container. The aim is to prevent motion during the scan, leading to motion artifacts, but also to prevent motion between acquisition sessions. Indeed, when numerous acquisitions are planned, it can be interesting to hold the sample in position between sessions, in order to facilitate the registration of all the acquired images. To that end, one solution is the use of a gelling agent to embed the sample. The choice of the gelling agent is usually based on MRI phantom design studies aiming at preparing tissue-equivalent phantoms, with T1 and T2 similar to those of gray matter, white matter, or CSF. The most commonly used are agar and agarose [START_REF] Hellerbach | MRI phantoms-are there alternatives to agar?[END_REF]. However, the latter need high thermal treatment (80-100°C) during the preparation process, and require the use of toxic additives such as sodium azide to retard mold formation [START_REF] Friedman | Report on a multicenter fMRI quality assurance protocol[END_REF]. The handling of phantoms prepared with toxic additives being problematic (shipping, disposal, risk of contamination,...), agar gels are not recommended for long-term storage. [START_REF] Hellerbach | MRI phantoms-are there alternatives to agar?[END_REF] studied the properties of various gelling agents that could be used as alternatives to agar. Alginate and xanthan gum had a texture too liquid, so they could be easily influenced by vibrational effects, and xanthan presented mold growth after only two weeks, meaning that this agent would also require toxic additives. Gels based on synthetic polymers of acrylic acid, especially Carbopol-974P and Carbomer-980 (Euro OTC Pharma GmbH, Germany), showed promise as potential alternatives to agar gels. They have a pH-dependent viscosity (easily tuned by the investigator), a simple preparation which does not require any thermal treatment, are stable for long periods of time (at least three months) and are inexpensive. Nonetheless, when embedding samples for an ex vivo scan, the required properties of the gel are not exactly the same as for MR phantoms, in particular regarding its MR properties. While a susceptibility coefficient nearly equal to that of the human brain is an asset, as it prevents from susceptibility artifacts, similar T1 and T2 are not desired, because it will lead to an unwanted signal. This is why gelling agents recommended in MR phantoms studies usually cannot be used directly as embedding gels for ex vivo samples ( § 7.1.1).

Acquisition protocols

The main challenge for ex vivo dMRI is the strong reduction of T2 and diffusivity.

Heating the sample during the scanning could limit the decrease of the diffusivity coefficient [START_REF] Helen | An approach to high resolution diffusion tensor imaging in fixed primate brain[END_REF][START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF][START_REF] Bastiani | Automatic segmentation of human cortical layer-complexes and architectural areas using ex vivo diffusion MRI and its validation[END_REF]. However, the sensitivity of diffusivity to temperature requires tight monitoring and control of a steady temperature, as temperature fluctuations could induce considerable uncontrolled signal fluctuations. Moreover, warming up a fixed sample, especially for long acquisitions, could lead to an irreversible degradation of the tissue, which is why this solution was not applied during this thesis work.

The diffusion contrast being proportional to e -bD , the reduction in D dictates a higher b-value (about three times higher than for in vivo experiments) in order to achieve a comparable contrast to in vivo experiment. Due to the limited gradient strength available on clinical scanners, high b-values can only be reached using long gradient pulses, which leads to longer TE and, consequently, extremely low signal levels because of the reduced T2. The new "Connectome" gradients could have been an alternative but their use remains limited by many technical constraints (slew rate limited to 200mT/m/s and even 150mT/m/s for gradients higher that 80mT/m, severe duty cycle constraints,...) [START_REF] Jones | Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI[END_REF].

These limitations imply either to develop a specific acquisition sequence on a clinical scanner, such as the diffusion-weighted steady-state free precession (dwSSFP) sequence [START_REF] Mcnab | High resolution diffusion-weighted imaging in fixed human brain using diffusionweighted steady state free precession[END_REF][START_REF] Miller | Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner[END_REF], or to use a preclinical scanner and take advantage of the very strong gradients that provide a high b-value while preserving a short TE.

Chapter 4. Post mortem imaging

64

In a nutshell, this section provided a summary of ex vivo samples characteristics, as natural tissue decomposition and chemical fixation cause the post mortem tissue's MRI properties to be different from those found in vivo. These changes require to adapt the acquisition protocol so as to reach contrasts comparable to in vivo. The following sections discuss more specifically image quality and scan time criteria, as well as acquisition techniques that were used in the frame of this thesis to obtain high resolution and high quality ex vivo images.

Scan time and image quality

The compromise between scan time and image quality drives the choices of the investigator when designing the protocol. Before going any further into the description of relevant acquisition techniques in the frame of this thesis work, it appears important to define the factors influencing the image quality and scan duration.

An evaluation criterion of the image quality: the signal to noise ratio (SNR)

The signal to noise ratio (SNR) is a common indicator used to evaluate image quality. It is obtained by dividing the mean signal value of the sample by the standard deviation of the noise. The following relation can be established in the case of a diffusion acquisition, depending on whether the acquisition is 2D or 3D ( § 4.4.1.1):

(2D) SNR ∝ e -T E T 2 e -bD (∆ x ∆ y ∆ z ) √ N y √ N rep B 0 √ RBW (3D) SNR ∝ e -T E T 2 e -bD (∆ x ∆ y ∆ z ) √ N y N z √ N rep B 0 √ RBW (4.1)
with ∆ x ∆ y ∆ z the spatial resolution, N y the number of phase encoding steps in the y-axis, N z the number of phase encoding steps in the z-axis, N rep the number of repetition (or averages), B 0 the static field and RBW the readout bandwidth. This formula provides insight into the reasons why MR systems manufacturers are racing for higher and higher field strengths, as well as for stronger and faster gradient coils.

Scan time

Depending on whether the acquisition is 2D or 3D, the acquisition time (T ac ) is given by:

(2D) T ac = T R.N y .N rep (3D) T ac = T R.N y .N rep .N z (4.2)
with TR the repetition time, N y the number of phase encoding steps in the y-axis, N rep the number of repetitions (or averages) and N z the number of slice (or phase encoding steps in the z-axis). In view of its influence on the acquisition time, the field of view (FOV) in the phase-encoding direction is usually chosen as short as possible, which can lead to artifacts such as truncation or aliasing if the FOV is chosen smaller than the sample size. Common MR artifacts are detailed hereafter.

Common artifacts

Motion artifacts

When scanning living subjects, movements are the most common cause of artifacts. Motion artifacts mainly propagate in the phase-encoding direction ( § 4.4.2.3). This is due to movement of the spins between two excitations or between phase-encoding and signal reading. During ex vivo scanning, samples need to be firmly stabilized in order to avoid bulk motion, that can occur when the rapid commutation of gradients induce mechanical vibrations. One solution consists in setting the brain in a gel (e.g. agar gel [START_REF] Pfefferbaum | Effects of formalin fixation and temperature on mr relaxation times in the human brain[END_REF]) or to wrap it with gauze pads.

Aliasing

Aliasing occurs when the object is bigger than the field of view (FOV) and corresponds to overlapping on the opposite side of the image of signals outside of the FOV (Figure 4.4.c.). This artifact is critical in the phase direction (and slice direction when using a 3D acquisition), and can be easily prevented by setting a FOV that encompasses all the imaged object in this(these) direction(s).

Susceptibility artifacts

When two tissues with different magnetic susceptibilities are juxtaposed, it causes local distortions in the magnetic field (T 2 * ). The most common interface producing this artifact is between air and tissue (Figure 4.4.d.), but it can also be created by the presence of any metal particle (Figure 4.4.e.). The observed artifact can be a loss of signal or a geometrical distortion of the image. Several solutions exist to reduce or eliminate these artifacts, especially for ex vivo imaging. First, care should be taken when preparing the sample in order to prevent the formation of air bubbles, and the presence of metal should be avoided, even outside the container. Finally, all the acquisition sequences don't have the same sensitivity to susceptibility artifacts: spin echo sequences are less prone to susceptibility artifacts than gradient echo sequences as the refocusing pulse corrects the susceptibility-induced dephasing of spins induced by T2* effects.

Eddy currents

When strong gradients are switched during the acquisition, Eddy currents are created in the conductive structures of the scanner. These currents will oppose the gradient fields and cause a decay in their profile. In dMRI, a large set of data is acquired with different diffusion sensitizations thus giv- This section presented some image quality criteria as well as common MR artifacts, with the exception of artifacts specific to rapid imaging techniques that are detailed in the following section. In fact, MRI artifacts are much more numerous and it may be difficult to investigate their cause, which is why establishing a new acquisition protocol can be time-consuming. The next section presents acquisition techniques (RARE and EPI) that are needed to understand the technical choices made during this thesis work.

Useful acquisition techniques

In chapter 3, we detailed the basics of MRI acquisition sequences with spin echo (SE), gradient echo (GRE), and pulsed gradient spin echo (PGSE) sequences. The latter can be tuned by varying parameters such as TE, TR, or the flip angle of the excitatory pulse. However, these parameters are not the only options that can be selected by the investigator. This section describes the imaging techniques that were used during this thesis work to scan post mortem human brain samples with an 11.7T preclinical MRI system.

Relevant techniques to increase image quality 4.4.1.1 3D versus 2D imaging

In 3D acquisitions, the complete volume is excited at each repetition, rather than a single 2D slice.

To this end, a partition encoding gradient is added along the slice direction (z-axis). This results in a SNR increased by a factor of √ N z and an acquisition time multiplied by N z (equation 4.1), with N z the number of slices (equation 4.2). Therefore, performing 3D acquisitions is very efficient to improve the SNR, but also drastically increases the acquisition time, which requires the use of rapid sequences.

Inversion recovery (IR) techniques

Inversion recovery (IR) is a preparation module composed of a 180°-pulse preceding the excitation pulse, that can be used in combination with any conventional sequence scheme (spin echo, gradient echo, ...) The time between the 180°inverting pulse and the 90°-pulse is called the inversion time (TI). The function of the inverting pulse is to flip the initial longitudinal magnetization of all tissues in the imaged slice or volume to point opposite to the direction of the main magnetic field. Due to longitudinal relaxation, longitudinal magnetization of each tissue increases to return to its initial value, passing through null value. When the 90°-pulse is applied, the initial longitudinal magnetizations of different tissues are separated based on their different intrinsic T1 relaxation times. IR thus produces an excellent image contrast, especially for T1-weighted imaging, as illustrated in figure 4.5, and can be combined with fast spin echo sequences ( § 4.4.2.2) that save considerable time, as inversion-recovery requires relatively long TR to allow magnetization the time to regrow.

Inversion-recovery has two major applications. The first one is the removal of a specific tissue on the final image. Indeed, if TI is set such that the longitudinal magnetization of the chosen tissue is null, the latter cannot emit any signal (absence of transverse magnetization due to the absence of longitudinal magnetization). This is the method used in the conventional STIR (Short-TI Inversion Recovery) that suppresses fat, and FLAIR (Fluid attenuation inversion recovery) that removes the CSF. The second one is T1 relaxometry, which corresponds to the measurement of the characteristic The multi-echo spin echo sequence is a sequence commonly used to estimate the T2 of a sample. After a single 90°-pulse, a series of n 180°-refocusing pulses generates a train of echoes. The amplitude of each echo is progressively smaller due to T2 decay, as depicted in Figure 4.6. The obtained image is 4D, with the 4th dimension corresponding to the n echoes acquired at t=T E i . The data can then be used to fit a mono-exponential model corresponding to the T2 decay, S(t) = S 0 e -t/T 2 , where S 0 and T2 are the two parameters to be determined.

Techniques to increase acquisition speed 4.4.2.1 Multi-slice techniques

Usually, and especially in the case of T2-weighted images, the delay between TE and TR is quite long (since TR T1). By setting the TR to long values, the T1 effect on tissue contrast is indeed well reduced. Moreover, increasing TR is one of the easiest way to reduce the duty cycle of a Introduced by [START_REF] Hennig | Rare imaging: a fast imaging method for clinical mr[END_REF], the RARE sequence is a fast spin echo technique that speeds up image acquisition by acquiring more than one k-space line per repetition. After a single 90°-pulse, a series of 180°-refocusing pulses generates a train of echoes. Contrary to a conventional multi-echo sequence that collects all echoes in a train with the same phase encoding, the phase-encoding gradient is changed for each echo, resulting in the acquisition of multiple lines of k-space within a given TR.

The number of echoes acquired in a given TR is tuned by the RARE factor (for Bruker systems), and evolves in inverse proportion to the acquisition time.

The major advantages of this sequence are its speed and its robustness with regard to magnetic field inhomogeneities, as the echo train is modulated by pure T2 as opposed to T 2 * . However, this modulation causes a k-space filtering as the lines of k-space are weighted unevenly by the T2 decay. This results in a blurring of the reconstructed image along the phase direction, which can be minimized by decreasing the echo spacing and increasing the number of echoes. A second artifact commonly encountered occurs when there are gradient and sequence timing imperfections, causing phase errors into the echo train, which translates into a ghosting on the image.

Echo planar imaging for diffusion acquisitions

Introduced by [START_REF] Mansfield | Multi-planar image formation using nmr spin echoes[END_REF], this technique is the fastest acquisition method in MRI. As originally defined, echo planar imaging (EPI) referred to a sequence in which data from all of k-space for an entire 2D plane was collected following a single RF-excitation pulse. More recently the term has been expanded to include any rapid acquisition sequence in which k-space is traversed in one or a small number of excitations, respectively referred to as single shot EPI and multi-shot EPI. Figure 4.9 depicts the "zig-zag" filling of the k-space, with subsequent positive and negative frequency-encoding lobes sweeping k-space from left-to-right and right-to-left respectively. Meanwhile, the blipped lowamplitude phase-encoding gradient pulses produce a step-wise increase along the k y axis. When Eddy currents occur ( § 4.3.3.4), the additional magnetic field induces a modification of gradients shape. This can lead to a phase offset between odd and even echoes when using EPI. This offset causes a misalignment of the acquired echoes in the k-space, resulting in the creation of a "ghost" image in the phase direction, shifted by N/2, N corresponding to the number of lines. This is called N/2 ghosting, and the more the sample is large, the more it is likely to happen. This section detailed useful acquisition techniques that can be used in order to investigate the brain relaxometry, connectivity, and microstructure. The RARE sequence can be used in 3D, and with the addition of an inversion recovery pulse with various TI, for T1 relaxometry. The multi-echo sequence can be combined with the multi slice technique, which is called with Bruker a multi-slice multi-echo (MSME) sequence, that is used for T2 relaxometry. Finally, diffusion EPI can also be used with the 3D option, to provide high resolution diffusion dataset in a reasonable time.

Conclusion

This chapter discussed the specificities of ex vivo tissue and the consequences regarding ex vivo imaging. While the first section detailed the motivations for performing post mortem MRI acquisitions, the second section highlighted the specific ex vivo tissue characteristics induced by the natural tissue decomposition, the fixation process, but also the room temperature or the static field of the MR system. As a general rule, fixed tissue display reduced proton density, T1 , T2 and diffusion coefficients.

All these characteristics constitute a challenge in terms of acquisition design, in particular for diffusion MRI that requires accurately tuned imaging protocols to provide an enhanced image quality.

The last section was dedicated to the presentation of specific imaging techniques and sequences that were applied during this thesis work.

The next chapters present the contributions of this thesis work regarding the investigation of the human brain connectivity and microstructure using post mortem approaches.

Part II In this chapter, we provide proofs of concept with regard to this thesis aim, which is the establishment of an ultra high resolution atlas of the human brain depicting its structural connectivity and microstructure. The idea is to define an acquisition protocol and an analysis pipeline that could be applied later to the entire brain. In order to do so, we focused our analysis on two brain structures known to play a key role in the neurodegenerative diseases above-mentioned: the hippocampus and the brainstem. The first section presents the contributions regarding the human hippocampus. After a brief review of the existing knowledge on the anatomical structure and functions of the hippocampus, the section describes the acquisition protocol set up, the manual segmentation method, the inference of the structural connectivity and finally the investigation of the axonal density. The second section investigates the human brainstem, following the same approach. The last section discusses the prospects and limitations of the work presented in this chapter.

Proofs of concept

The hippocampus

The human hippocampus plays a key role in memory management and is one of the first structures affected by Alzheimer's disease. The first part of this section describes the historical establishment of the relationship between hippocampus and memory and the current knowledge on the hippocampal anatomy necessary to proceed with the manual segmentation of its substructures. Then, the second part presents the exploration of the connectivity and microstructure of an ex vivo human hippocampus that was conducted in this thesis work using dMRI and diffusion MR microscopy at 11.7 T.

5.1.1

The human hippocampus: anatomy and function

Historical establishment of the relationship between hippocampus and memory

The importance of the hippocampus in the encoding and retrieval of memory processes has been recognized following the work of Scoville and [START_REF] Beecher | Loss of recent memory after bilateral hippocampal lesions[END_REF]. They described the case of a 29 year old man, called patient "H.M", who underwent a bilateral medial temporal lobectomy with the rejection of two thirds of both hippocampi in order to gain control of his epilepsy. After the surgery, the patient suffered from retrograde amnesia limited to a a decade prior to his surgery and could no longer create any new long-term memories. Despite this, he presented no disturbance of intelligence or personality. For the first time, an obvious link between memory and brain structure was revealed.

In another study conducted by [START_REF] Milner | Les troubles de la memoire accompagnant des lesions hippocampiques bilaterales[END_REF], "H.M." acquired the new skill of drawing a figure by looking at its reflection in a mirror. This study provided the first hint that there was more than one kind of memory in the brain and suggested that some kinds of memory (motor skills) must lie outside the province of the medial temporal lobe.

More recently, a study investigating the role of the hippocampus in spatial navigation showed that the posterior hippocampus of London's taxi drivers was larger than in a control group, with a positive correlation between the time spent as a driver and the increase of the volume of this part [START_REF] Maguire | Navigation-related structural change in the hippocampi of taxi drivers[END_REF]. This study thus provided evidence of the role of the hippocampus in spatial navigation as well as its plasticity.

In conclusion, the hippocampus plays a key role in memory encoding and retrieval, as well as in spatial navigation.

General features of hippocampal anatomy

This section aims at providing a fine understanding of the human hippocampal anatomy, required to analyze and interpret our results.

Localization and gross anatomy

The human hippocampus is a bilateral structure located in the medial temporal lobe, at the level of the fifth convolution (T5) as shown in Figure 5.1. This is a small elongated structure with a rostrocaudal extent of approximately 5 cm [START_REF] Insausti | Hippocampal formation[END_REF],

arched around the mesencephalon. The arch can be divided into three segments (Figure 5.2):

• the head, or anterior segment, that is transversely oriented and curves dorso-caudally to form the uncus. This is the largest part of the structure,

• the body, or middle segment, that is C-shaped and sagittally oriented,

• the tail, or posterior segment, that has an organization similar to that of the body, but with a transverse orientation. This segment rapidly narrows and finally joins the white matter bundle known as the fornix. The hippocampal formation refers to the hippocampus and its related structures that act like a single functional unit [START_REF] Larry R Squire | Mechanisms of memory[END_REF]. Three parts can be distinguished, all depicted in Figure 5.3.a:

• the input parahippocampal structures, namely the entorhinal cortex (EC) and the prosubiculum, subiculum proper, presubiculum, and parasubiculum, all grouped under the name "subicular complex" (SUB),

• the hippocampus, made of two intertwined laminae separated by a sulcus: the hippocampus proper, also called Ammon's horn or cornu Ammonis (CA), and the dentate gyrus (DG). The Ammon's horn is typically split into four subfields: CA1, CA2, CA3 and CA4 as suggested by Lorente de [START_REF] Nó | Studies on the structure of the cerebral cortex. ii. continuation of the study of the ammonic system[END_REF],

• the alveus and the fimbria, white matter bundles sheating the hippocampus and made of fibers coming from the pyramidal cells of the hippocampus and the subicular complex. The hippocampus is made of allocortex, known to depict only three layers (see § 2.3.1.1). The six layers described above are thus usually grouped into three: the stratum oriens, the stratum pyramidale, and a layer combining the strata radiatum, lacunosum, and moleculare, called the molecular zone [Lorente de [START_REF] Nó | Studies on the structure of the cerebral cortex. ii. continuation of the study of the ammonic system[END_REF].

The repartition of these layers varies along the cornu Ammonis which has led neuroanatomists to define subfields. Various nomenclatures have been proposed. In the following, we will use the one introduced by Lorente de [START_REF] Nó | Studies on the structure of the cerebral cortex. ii. continuation of the study of the ammonic system[END_REF], who described four fields, labeled CA1-CA4. CA1 is the largest subfield. It continues from the subicular complex and contains small scattered pyramidal cells, with triangular somas. CA2 consists of densely packed pyramidal cells with ovoid somas.

CA3 corresponds to the curve of the cornu Ammonis and contains cells similar to CA2 but less densely packed. This subfield depicts a supplementary layer between the strata pyramidale and radiatum, the stratum lucidum, made of non-myelinated fibers (mossy fibers) arising from the DG.

CA4 is located within the concavity of the DG and contains large ovoid somata. The boundaries between hippocampal subfields have been extensively studied in the neuroanatomy literature, using cytoarchitectonic features [START_REF] Henri | The human hippocampus: functional anatomy, vascularization and serial sections with MRI[END_REF][START_REF] Insausti | Hippocampal formation, paxinos g., the human nervous system[END_REF][START_REF] Gloor | The temporal lobe and limbic system[END_REF], but there are still discrepancies concerning whether it makes sense to separate some regions or not.

The dentate gyrus has a simpler structure than the cornu Ammonis, and the three layers of the allocortex are much more distinguishable (see Figure 5.3.b). From the sulcus to CA4:

1. the thick stratum moleculare, whose external two thirds near the hippocampal sulcus receive fibers from the perforant pathway (see Figure 5.4), whereas the inner third, in contact with the stratum granulosum, is occupied by commissural and septal fibers, 2. the stratum granulosum, containing somata of granular neurons, which are small and round but densely packed, making the layer easy to distinguish. Efferent axons from the granule cells are mossy fibers that synapse only with cells of CA2 and CA3, 3. the polymorphic layer, uniting the granular layer to CA4. This layer is crossed by axons of granular neurons.

Internal connectivity There are two major intrahippocampal pathways: the polysynaptic pathway (sometimes referred to as the trisynaptic pathway) and the direct pathway.

The polysynaptic pathway links all the territories of the hippocampus by a long neuronal chain. The first step is the perforant path, originating from the layer II of the entorhinal cortex and projecting to the dentate gyrus. Then, mossy fibers emerge from the DG to stimulate the dendrites of CA4 and especially those of CA3. The axons of CA3 and CA4 enter the alveus and then the fimbria after the emission of the Schaffer collaterals, which reach the apical dendrites of CA1 in the strata radiatum and lacunosum. Axons arising from CA1 produce collaterals which reach the subicular complex and then enter the alveus and the fimbria. Finally, the subicular complex emits the definitive response, by fibers constituting the major part of the alveus and then the fimbria.

In the direct pathway, fibers originate from the layer III of the EC and reach the pyramidal neurons of CA1. Then CA1 neurons project onto the subiculum, the axons of which return to the deep layers of the entorhinal area.

Relationships between structure and function

Each of the two pathways described above is assumed to be associated with specific functions: the polysynaptic pathway with episodic and spatial memory, and the direct pathway with semantic memory [START_REF] Henri | The human hippocampus: functional anatomy, vascularization and serial sections with MRI[END_REF]. Hippocampal regions also appear to be specialized for preferential functions.

For instance, the DG and CA3 have been shown to be respectively involved in pattern separation and completion, as well as CA2 in social memory [Leutgeb et al., 2007, Hitti and[START_REF] Frederick | The hippocampal ca2 region is essential for social memory[END_REF].

Furthermore, anterior-posterior functional differences within the hippocampal formation have been reported in humans and experimental animals [Fanselow andDong, 2010, Poppenk et al., 2013], but detailed anatomical studies are still not available in humans.

In addition, the structure and connectivity of hippocampal regions and layers are known to be selectively affected by multiple neurological disorders such as Alzheimer's disease or temporal lobe epilepsy, as well as by the normal process of aging [START_REF] Zhou | Abnormal connectivity in the posterior cingulate and hippocampus in early alzheimer's disease and mild cognitive impairment[END_REF], Wang et al., 2006[START_REF] Dinkelacker | Hippocampal-thalamic wiring in medial temporal lobe epilepsy: Enhanced connectivity per hippocampal voxel[END_REF][START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF][START_REF] Matthew W Prull | Age-related changes in memory: A cognitive neuroscience perspective[END_REF][START_REF] Wilson | Neurocognitive aging: prior memories hinder new hippocampal encoding[END_REF]. The hippocampus is one of the first structure affected by AD, and its loss of volume has become an early marker of the disease. Its complexity makes it one of the most mysterious regions of the central nervous system and also one of the most extensively studied. However, to our knowledge, no study on the internal connectivity and microstructure of the whole human hippocampus has been performed. This investigation, presented hereinafter, constituted the first project of this thesis work.

Post mortem inference of the human hippocampus connectivity and microstructure

In this study, we demonstrate for the first time on a human medial temporal lobe sample that ex vivo UHF MRI (11.7 T) with strong gradients (780 mT/m) gives the opportunity to map not only the complex anatomy of the hippocampus, but also its inner connectivity and its organization at the mesoscopic scale. Following the design of a relevant acquisition protocol, the first step is to investigate the combined use of anatomical and diffusion MRI to segment the inner structures of the hippocampus as well as the adjacent entorhinal cortex. Second, we demonstrate that HARDI allows the accurate reconstruction of elements of the polysynaptic pathway. Third, we show that diffusion MR microscopy is a powerful technique, that gives access to insights about cell populations of the hippocampal tissues, revealing the laminar structure of the cornu Ammonis (CA).

5.1.2.1

The use of MRI to investigate the human hippocampal anatomy and structural connectivity: state of the art Few in vivo imaging techniques are available to investigate the human hippocampus. MRI, and more precisely anatomical MRI (aMRI) and diffusion MRI (dMRI), remain the key modalities used nowadays. Studies using aMRI were first employed to segment the hippocampus and enable volumetric analysis to define early markers of Alzheimer's disease or depression [START_REF] Clifford R Jack | Mr-based hippocampal volumetry in the diagnosis of alzheimer's disease[END_REF][START_REF] Videbech | Hippocampal volume and depression: a meta-analysis of MRI studies[END_REF][START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF]. Several studies have also been conducted using diffusion tensor imaging (DTI) on clinical MRI systems to investigate the connectivity of the human hippocampus in order to better understand the anatomo-functional mapping of the limbic system [START_REF] Dinkelacker | Hippocampal-thalamic wiring in medial temporal lobe epilepsy: Enhanced connectivity per hippocampal voxel[END_REF][START_REF] Adnan | Distinct hippocampal functional networks revealed by tractography-based parcellation[END_REF][START_REF] Michael M Zeineh | Ultrahigh resolution diffusion tensor imaging of the microscopic pathways of the medial temporal lobe[END_REF]. However, clinical MRI systems have inherent limitations that prevent one from reaching ultra-high spatial and angular resolutions, mainly due to the characteristics of the available gradient coils ( § 4.1.2).

Alternatively, ex vivo MR imaging can be performed using ultra-high field preclinical scanners ( § 4.1). Specifically, ex vivo studies have been carried out on medial temporal lobe (MTL) samples containing the hippocampus [START_REF] Jean C Augustinack | Direct visualization of the perforant pathway in the human brain with ex vivo diffusion tensor imaging[END_REF][START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF][START_REF] Shepherd | Diffusion tensor microscopy indicates the cytoarchitectural basis for diffusion anisotropy in the human hippocampus[END_REF][START_REF] Luis M Colon-Perez | High-field magnetic resonance imaging of the human temporal lobe[END_REF][START_REF] Modo | Detection of aberrant hippocampal mossy fiber connections: Ex vivo mesoscale diffusion MRI and microtractography with histological validation in a patient with uncontrolled temporal lobe epilepsy[END_REF]. Most of the authors performed DTI-based tractography to map some of the larger connections of the hippocampus, such as the perforant pathway [START_REF] Jean C Augustinack | Direct visualization of the perforant pathway in the human brain with ex vivo diffusion tensor imaging[END_REF][START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF]. Although they remain landmark studies, these studies rely on a the DTI model known to present strong limitations ( § 3.2.6).

Since the hippocampus has a very complex fiber architecture with crossings, kissings and splittings, the use of HARDI models ( § 3.2.7) becomes mandatory to robustly infer its structural connectivity using tractography. To our knowledge, HARDI models have only been used once on a human hippocampus, by [START_REF] Luis M Colon-Perez | High-field magnetic resonance imaging of the human temporal lobe[END_REF], but the acquisition protocol was limited to 46 directions with a b-value of around 2000 s/mm 2 , which is not enough to obtain an accurate estimation of local fibers orientation [START_REF] Tim B Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusionweighted imaging datasets[END_REF].

In our study, a multi-shell diffusion-weighted acquisition protocol was developed to reach an ultrahigh spatio-angular resolution with a good SNR. The MRI data set was analyzed using analytical Q-Ball Imaging (aQBI), Diffusion Tensor Imaging (DTI), and Neurite Orientation Dispersion and Density Imaging (NODDI) models, in order to investigate the hippocampus anatomy and connectivity.

Tissue sample, container, and MRI hardware

The study was carried out on a post mortem right temporal lobe from an 87-year-old male with no abnormal neuropathology findings obtained from the donor program of the Institute of Anatomy, Rostock, Germany. The specimen measured approximately 38×50×55 mm 3 , and contained the Chapter 5. Investigation of the human hippocampus and brainstem 85 whole hippocampal formation and some of its surrounding structures. It was fixed with 4% formalin buffer 36 hours after death and stored 38 months until further processing.

Prior to MRI acquisition, the sample was transferred for one week to a 0,1M phosphate-buffered saline solution at 4°C to be rehydrated. Since acquisitions take place at room temperature (approximately 20°C), the specimen was placed into the imaging container 4-5 hours prior to scanning and transferred to the magnet room in order to stabilize its temperature to 20°C. Furthermore, to avoid drying of the tissue during the experiment and to reduce imaging artifacts, the sample was immersed in a proton-free fluid, Fluorinert (FC-40, 3M Company, USA). A dedicated container was manufactured to exactly fit the inner diameter of the MR coil antenna with a specific design aimed to prevent the formation of air bubbles that would be responsible for severe susceptibility-induced imaging artifacts. The suspension of the sample within its container is guaranteed by a plastic funnel that does not induce any MR signal and avoids motion artifacts during the commutation of the strong diffusion gradients. All these steps were inspired from ex vivo acquisitions good practices listed in § 4.2.3.

All the acquisitions were performed on a preclinical 11. sequence, b = (Gγδ ) 2 (∆δ /3) = q 2 τ with the approximation of rectangular gradients, with G the applied diffusion gradient vector, γ the nuclear gyromagnetic ratio for water protons, δ the duration time of gradient pulses, ∆ the time between two pulses, and τ the diffusion time ( § 3.2.5).

To reach high b-values, one can increase the gradient strength G, the gradient width δ , or the separation time between the two gradient pulses ∆. However, to keep the gradient pulses close enough to Dirac pulses, thus preserving the Fourier relationship existing between the diffusion propagator and the diffusion NMR signal with respect to the q wavevector, δ has to be kept at its minimum possible value, 4.3 ms in our case. Consequently, either ∆ or G have to be raised to increase the diffusion sensitization. The side effect of increasing ∆ is a net increase of the echo time T E . However, the PGSE sequence yields a NRM signal that integrates not only an exponential diffusion decay e -bD , but also a further exponential decay e -T E /T 2 linked to the T2 transverse relaxation inherited from the spin echo scheme present in a PGSE sequence.

An estimation of D and T2 was carried out to determine the range of usable echo time T E and diffusion sensitization b, in order to avoid excessive signal loss.

Histogram of the transverse relaxation time T2 Fixed tissues generally suffer from a significant reduction of their transverse relaxation time drastically reducing the time window available to acquire the signal with a good signal to noise ratio (SNR) ( § 4.2). To map the transverse relaxation time at each voxel of our sample, a standard multi-spin-multi-echo (MSME) pulse sequence ( § 4.4) was used.

In total, 12 echoes were collected corresponding to 12 echo times linearly spaced between 6. The mode corresponding to the lower value is identified as the white matter (T 2w ≈ 36.3 ms), and that corresponding to the higher value is identified as gray matter T2 (T 2g ≈ 46.4 ms): transverse relaxation time is lower where fibers are more concentrated, i.e. within the white matter. As the hippocampus is mainly composed of gray matter, we assumed its T2 value closer to 46ms. In practice, T E max was set to 59.1ms, which enabled an achievable b max of 10000 s/mm 2 .

Histogram of the mean diffusivity

Imaging protocol

The imaging protocol included anatomical and diffusion-weighted scans. The anatomical scan was tuned to reach a very high spatial resolution in order to perform accurate manual segmentation of the hippocampal subfields and of the entorhinal cortex. directions each. The acquisition of each block lasted 12h57min, giving a total duration of acquisition of 3 days and 7 hours. The parameters were tuned as listed in Table 5.1. It is important at this step to note that the three shells were acquired with linearly increasing separation times ∆ of 14.4 ms, 30.0 ms and 45.0 ms while keeping the gradient pulse width to δ = 4.3 ms, in order to vary the diffusion time. This choice was motivated by the willingness to be able to use alternative models to NODDI in the future, such as ActiveAx, which also requires sampling of the diffusion time. A further specificity of the HYDI protocol was to use the minimum echo time for each shell and not to impose the largest of the 3 minimum echo times. As a consequence, the data stemming from each shell has to be preprocessed to remove the T2-decay dependency, which is possible by means of the quantitative T2 calibration performed previously to characterize the magnetic and diffusion properties of the hippocampus sample.

Anatomical scan

Preprocessing

As mentioned earlier, the diffusion-weighted imaging protocol included the acquisition of a multipleshell HYDI dataset at 3 different b-values (4500, 7500, 10000 s/mm 2 ) with minimum echo times set Chapter 5. Investigation of the human hippocampus and brainstem

89

for each individual shell. This choice was motivated by the optimization of the SNR per shell, but it requires to correct for the T2-weighting equal to e

-T E T 2 that differs from one shell to another. To this aim, a correction was applied to the two larger shells at 7500 s/mm 2 and 10000 s/mm 2 that consisted of multiplying voxelwise all the diffusion-weighted images by the compensating factors e ∆T E T 2(v) for each voxel v. This resulted in an intensity comparable to the one obtained with an acquisition done with the TE used at b = 4500 s/mm 2 for all shells.

The conventional PGSE sequence is not sensitive to field inhomogeneities in comparison with its corresponding echoplanar version, such that the collected DW data are free from distortions induced by eddy currents or susceptibility effects. Consequently, there is no need to apply any correction. In addition, the measured SNR established to 9.9, 7.6, 4.2 for the 3 shells, respectively corresponding to an increasing b-value, are large enough to approximate the Rician noise distribution by a Gaussian distribution, thus allowing the use of conventional mean-square estimators without loss of information. Last, all the acquisitions were performed during 13 consecutive days avoiding the need to remove the sample from its container, and thus avoiding the presence of any motion between two diffusion-sensitized volumes. Consequently, the remaining transformation exiting between the two anatomical and diffusion datasets turns to be the simple rigid transformation between their two fields of view. This transformation was inferred using the registration tool of the Connectomist toolbox [START_REF] Assaf | The connect project: combining macro-and micro-structure[END_REF][START_REF] Duclap | Connectomist-2.0: a novel diffusion analysis toolbox for brainvisa[END_REF] based on a mutual information matching criterion optimized using a standard Nelder-Mead simplex algorithm. After registration, the two datasets perfectly matched, allowing to navigate between the structures inferred from the anatomical scans and the connectivity or microstructural quantitative maps inferred from diffusion MRI scans.

Delineation of the inner and surrounding structures of the hippocampus

An in-house developed software, PtkVoi, was used to trace the hippocampal subfields and surrounding structures. It was performed manually from the T2-weighted anatomical scan, using anatomical landmarks and following the different strategies prescribed and detailed in the literature [START_REF] Henri | The human hippocampus: functional anatomy, vascularization and serial sections with MRI[END_REF][START_REF] Insausti | Hippocampal formation[END_REF][START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF][START_REF] Insausti | Mr volumetric analysis of the human entorhinal, perirhinal, and temporopolar cortices[END_REF][START_REF] Lem Wisse | Subfields of the hippocampal formation at 7T MRI: In vivo volumetric assessment[END_REF].

Segmentations were traced in the coronal plane and the three-dimensional consistency was ensured by checking the axial and sagittal planes, as well as the 3D shapes of the delineated structures with respect to their known morphology. Considering the main intra-hippocampal circuits, and in particular the polysynaptic pathway, we endeavored to identify: the entorhinal cortex, the dentate gyrus with CA4, CA2/CA3, CA1, the alveus, the fimbria, and the subicular complex.

Inner structures of the hippocampus The number of inner segmented structures of the hippocampus resulted from a tradeoff between the feasibility to identify their boundaries on the high resolution anatomical MRI data (thus depending on their contrast to noise ratio), and the target regions involved in the circuits of interest. The segmentation process used a coarse to fine strategy involving a first step Chapter 5. Investigation of the human hippocampus and brainstem 90 in which the hippocampal head, body and tail were identified, followed by a second step to delineate regions and/or layers.

Coarse scale: segmentation of head, body and tail The segregation of the hippocampus in three parts was based on the protocol presented in [START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF]. The very anterior limit was not present in our sample because the head was partly cut. The most anterior part of the body corresponds to the first coronal slice where the median part of the uncus is no longer visible. The most posterior coronal slice of the body was identified at the level of the enlargement of the fimbria and the loss of the specific C-shape of the body.

Fine scale: segmentation of subfields In a second step, the following structures were segmented (Figure 5.9):

• Alveus and fimbria -These two structures belong to the white matter and are visible in the anatomical T2-weighted MRI data by the hypointense contrast at the level of the outer boundary of the hippocampus. This specific contrast was exploited to guide their delineation. In addition, the change in orientation of the underlying fibers between the alveus (oriented mainly parallel to the coronal plane) and the fimbria (oriented mainly parallel to the sagittal plane) can be easily identified in diffusion ODF fields, thus allowing identification of the boundary between the alveus and the fimbria. The lateral boundary of the fimbria was set at the end of the fiber orientation shift zone, where the fibers are entirely contained in the sagittal plane (white line in Figure 5.7). The inferior lateral boundary of the alveus was set at the junction with the collateral eminence of the lateral ventricle. The separation between the alveus and the fimbria was only possible in the body and the tail of the hippocampus. At the level of the hippocampal head, the white matter was associated to the alveus,

• The lacunosum-molecular layer of the CA1-CA3 regions -This zone can easily be identified in the anatomical T2-weighted MRI scan as a dark line in the CA region of the hippocampus, corresponding to an area of very low concentration of neural bodies (which are mainly located in the pyramidal layer),

• The pyramidal and radiatum layers of the CA1 region -This region is the thickest Ammon's field, while CA2 is the thinnest, thus easily enabling definition of the boundary between both portions of the hippocampus. The border with the subicular complex could often be identified based on differences in gray values, since the CA1 region appeared brighter when compared to the adjacent subicular component. In the tail region of the hippocampus, where differences in gray values were only very subtle, we applied the method suggested by [START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF], which consists of tracing the largest diameter of the hilum and a perpendicular line passing by the medium of the diameter that corresponds to the target boundary, • The pyramidal layer and radiatum of the CA2 and CA3 regions -These two regions were merged into a single ROI (CA2/CA3), because the boundary between them is almost impossible to identify in MR images. Furthermore, not only CA3 neurons project to the CA1 region, but also CA2 pyramids make strong excitatory synaptic contacts with CA1 neurons [Chevaleyre and Siegelbaum, 2010]. The limit with the dentate gyrus was defined by the end of the ribbon-like aspect of the Ammon's horn [START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF],

• The dentate gyrus -Its boundaries were defined by the other structures already segmented and the cisterna ambiens enlarging the cerebro-spinal fluid-filled space lateral to the cerebral crus,

• The subicular complex -The lateral limit of this region was identified based on differences in cortical thickness, as described by [START_REF] Lem Wisse | Subfields of the hippocampal formation at 7T MRI: In vivo volumetric assessment[END_REF]. Thus, the border was defined by drawing a line between the most medial part of the gray matter and the most medial part of the white matter of the temporal stem,

• The entorhinal cortex -Its lateral limit is slightly upstream of the collateral sulcus, itself located under the collateral eminence. In Wisse et al. [2012], the posterior border of the entorhinal cortex was set 0.7mm beyond the hippocampal head which corresponds to 4 slices for our spatial resolution.

The anatomical T2-weighted MRI dataset (200 µm, Fig. 2.a and 2.b.) presented a very good contrast and SNR (33.7), thus enabling accurate delineation of the entorhinal cortex and of several components of the hippocampal complex: dentate gyrus, pyramidal and radiatum layers of the CA1 and CA2/CA3 regions, lacunosum-molecular layer, alveus, fimbria, and subicular complex. Figure 3 shows series of coronal sections with all the delineated areas. The three-dimensional rendering of the Chapter 5. Investigation of the human hippocampus and brainstem 92 manual segmentation of the hippocampal regions and layers as well as of the entorhinal cortex is presented in Figure 5.10. The accuracy of the segmentations is a key factor to successfully discriminate the fiber tracts connecting them. The current trend is to use spherical deconvolution approaches to obtain sharp fiber orientation distributions resulting from the deconvolution of ODFs using an auto-estimated convolution kernel. While this approach is suitable to reconstruct the connectivity of the entire brain, it cannot be considered for this study of the inner hippocampal connectivity where the complex configuration of fibers does not enable the definition of an adequate convolution kernel: there is no equivalent of the corpus callosum within the hippocampal complex. Taking this into consideration, the analytical Q-ball (aQBI) model [START_REF] Descoteaux | Regularized, fast, and robust analytical q-ball imaging[END_REF][START_REF] Descoteaux | High angular resolution diffusion MRI: from local estimation to segmentation and tractography[END_REF]] was adopted in our study. This model relies on the decomposition of the DW signal onto a modified spherical harmonics basis, linked to the decomposition of the ODF onto the same basis by the Funk-Hecke matrix. Its use is relevant in our case because preclinical diffusion MRI allows the use of high diffusion sensitizations (≥4500 s/mm 2 ) with short echo, yielding sharp ODFs. The DTI model was also computed to compare with the aQBI model.

DTI and Q-ball imaging

The diffusion analyses were performed using the Connectomist toolbox.

The HARDI dataset was used to compute fields of ODFs stemming from the aQBI model and from the DTI model, as well as conventional quantitative maps stemming from the tensor model, including the FA map, the MD maps, and the color-encoded direction (CED) map. The aQBI model reconstruction was applied using a spherical harmonics order 8 and a regularization factor λ = 0.006, as defined in [START_REF] Descoteaux | Regularized, fast, and robust analytical q-ball imaging[END_REF]. The high anisotropy in the fimbria, oriented in the sagittal plane (orange arrowheads in Fig. 5.11 and Fig. 5.7), can be related to efferent axons from CA3, CA1 and the subicular complex, along with afferent axons from structures in the diencephalon and basal forebrain. These fibers run parallel to the septal-temporal axis of the hippocampus. This main orientation is also visible in Figure 5.11.a, where the fimbria appears in blue near the head, then pink, and almost red when it goes towards the fornix.

Regarding the alveus, oriented in the coronal plane (yellow arrowheads in Fig. 5.11 and Fig. 5.7), it contains the axons from the CA1 region and the subicular complex, reaching the fimbria through the alveus in an oblique septal direction. The wraping of the fibers around the surface of the hippocampus is also visible in Figure 5.11.c, where the alveus appears green and then pink when it gets close to the fimbria.

The fiber orientation observed in the pyramidal layer (Figs.5.11 and 5.12) can be attributed to the projection of the large apical dendrites of CA1 and CA3 through the lucidum (only in CA3) and radiatum layers towards their termination in the lacunosum-molecular layer. It is also affected by the perforant pathway. Orthogonally to the projection of CA1, CA2 and CA3 dendrites towards the lacunosummolecular layer, the Schaffer collaterals runs from CA3 to CA1 (probably corresponding to the red part in the pyramidal layer from CA3 to CA1 in Figure 5.11.c). Voxels between CA3 and CA1 contain multiple fiber crossings, which can-not be resolved by the DTI model. This demonstrates the relevance of using the HARDI/Q-ball model. Figure 5.12.b shows ODFs recovering multiple fiber crossings in the pyramidal layer with a shape revealing two main peaks (one for each principal direction). Fig. 5.12.c clearly depicts ODFs with two main peaks that can also be attributed to the Schaffer collateral crossing the projection of CA1, CA2 and CA3 dendrites towards the lacunosum-molecular layer.

In the lacunosum-molecular layer, and to a lesser extent in the radiatum layer, the apical dendrites of CA-pyramids diverge orthogonally into the terminal arborizations that tend to run parallel to the hippocampal sulcus. This corresponds to the area in the radiatum and lacunosum-molecular layers with ODF orthogonal to the coronal plane (pink arrowheads in Figure 5.12.b and Figure 5.11.c).

Hence, although color-encoded maps obtained with the DTI model show the main directions in each voxel and lead to a partial understanding of the fibers pathways, HARDI/QBall model is mandatory to resolve fiber crossings involved in the Schaffer collaterals and the perforant pathway. Inference of the structural connectivity A streamline regularized deterministic (SRD) and a streamline regularized probabilistic (SRP) tractography algorithms [Perrin et al., 2005a] were applied to the whole sample using the maps of aQBI and DTI ODFs previously computed, with the following parameters: 8 seeds per voxel yielding dense tractograms containing 11.6 millions of fibers, forward step 70µm, maximum solid angle 30°, minimum/maximum fiber length 0.5/100 mm to avoid loops and discard spurious fibers. This results in four tractograms (DTI/SRD, QBI/SRD, DTI/SRP and QBI/SRP) that will be used to analyze the differences in the inference of the structural connectivity with respect to the model and to the fiber tracking algorithm. and afferent projections cannot be distinguished with diffusion MRI, and the exclusion of self connections implies a zero diagonal line. These connectivity matrices give a concise overview of the main hubs of connections present in the hippocampus. In practice, whole brain studies performed on clinical systems rely on data suffering from low SNRs at high b-value, causing overweighting of short reconstructed fibers with respect to long ones. A simple way to counterbalance such effects is to normalize each point of the matrix by the logarithm of the average length of fibers connecting to the concerned subregions. In our case, the hippocampus remains a small structure internally connected with relatively short fibers (average length 34.15mm, standard deviation of length 21.85mm) Chapter 5. Investigation of the human hippocampus and brainstem 97 and tractography was relying on a high SNR diffusion MRI dataset, thus less prone to fiber tracking degeneration. Consequently, there is no need to apply any normalization of the connectivity matrix.

Finally, elements of the trisynaptic pathway, one of the most extensively studied pathways of the brain, were reconstructed from the four tractograms. The trisynaptic pathway, as presented in Duvernoy [2005], is composed of three elements:

• The perforant path -Axons from neurons in the entorhinal cortex that make synaptic contacts with dendrites of the granule cells in the dentate gyrus, located in the molecular layer of the dentate gyrus,

• The mossy fibers -The granule cells of the dentate gyrus project to the pyramids of the CA3 (and partly also CA2) region. Synaptic contacts are located in the lucidum layer, which is between the pyramidal and radiatum layers of CA3,

• The Schaffer collaterals -Pyramids of the CA3 region send their axons via the alveus-fimbriafornix to the mammillary bodies. Additionally, collaterals of these axons terminate on the dendrites of CA1 pyramids. These synaptic contacts are located in the lacunosum-molecular layer of CA1.

The four tractograms (QBI/SRP, QBI/SRD, DTI/SRP and DTI/SRD) were used to extract mossy fibers and the perforant pathway with the aim of performing a comparison of the accuracy of aQBI versus DTI as well as SRD versus SRP tractography algorithms in reconstructing known pathways.

In order to extract trisynaptic elements from the four tractograms, analysis pipelines were developed to intersect the connectograms with the starting and ending regions of interest corresponding to the termination of each element, plus a set of intermediate regions crossed by fibers to avoid the selection of false positives. The four tractograms were analyzed using a single filtering pipeline for each pathway.

Figures 5.13 and 5.14 show the connectivity matrices of the hippocampal substructures, obtained with the streamline regularized deterministic (Fig. 5.13) and the streamline regularized probabilistic algorithms (Fig. 5.14) applied with Q-ball model. As a general trend, the two matrices reveal a higher level of connectivity in the head compared to the body and the tail. The high connectivity of the lacunosum-molecular layer with CA1 can be explained by the location of the apical dendrites of pyramidal neurons of CA1 in this layer. As regards the connectivity between CA1 and the alveus in the head, this is likely due to pyramids of the CA1 region that send their axons via the alveus-fimbriafornix to the mammillary bodies and representing one source of output from the hippocampus. The same observation remains true for the connectivity between CA2/CA3 and the alveus. The high connectivity between CA1 and the alveus can be due not only to the presence in this structure of efferent axons from CA1 pyramids, but also to the basal dendrites of the pyramidal neurons bending into the alveus, as described in both polysynaptic and direct pathways [START_REF] Henri | The human hippocampus: functional anatomy, vascularization and serial sections with MRI[END_REF]. The connectivity Chapter 5. Investigation of the human hippocampus and brainstem 98 matrices also reveal connections that extend through the length of the hippocampus. Connections within each structure are also found. The subicular complex of the body is connected with the subicular complex of the head and the subicular complex of the tail. This is also the case for the dentate gyrus or CA2/CA3. This is in agreement with a primate study [START_REF] Kondo | Intrinsic connections of the macaque monkey hippocampal formation: I. dentate gyrus[END_REF] showing that the projections of the dentate gyrus extend bidirectionally along much of the length of the hippocampus.

Finally, longitudinal connectivity also occurs between related regions like the entorhinal cortex in the hippocampal head and subicular complex in its body. Thus, while the subfields are usually studied in the coronal plane, it appears that connections between subfields extend both in cross-section and longitudinally. All these results are in agreement with a recent literature review [START_REF] Bryan A Strange | Functional organization of the hippocampal longitudinal axis[END_REF] showing a gradient of connectivity that varies along the length of the hippocampus. Finally, the two matrices also depict different connectivity levels. For instance, the level of connectivity between the dentate gyrus and CA2/CA3 appears lower with probabilistic tractography than with deterministic tractography. Conversely, the level of connectivity between CA1 and the alveus is lower with the deterministic approach. These observations would benefit from further analysis and comparison with a gold standard, which is beyond the scope of this study. .15 shows how elements of the polysynaptic pathway could be extracted using high field-/strong gradients diffusion MR-based tractography with the QBI/SRP tractogram, and also illustrates the differences in the inference of the structural connectivity with respect to the model and to the fiber tracking algorithm. Mossy fibers could be extracted using the four approaches. However, probabilistic approaches display fibers with a more realistic distribution of their origins along the granular layer of the dentate gyrus. By contrast, when it comes to the extraction of the perforant pathway, probabilistic approaches were the only one to give satisfying results, thus playing in favor of the use of a probabilistic fiber tracking technique. The QBI/SRD method leads to a bundle with very few fibers and the DTI/SRD tractogram does not allow the extraction of any fiber of the perforant pathway. This can be attributed to the fact that probabilistic tractography with multiple fiber orientations shows more robustness to noise and more sensitivity than standard deterministic tractography as it explores all possible options, allowing to temporarily select suboptimal directions during the streamlining process [START_REF] Behrens | Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?[END_REF]. The comparison of the QBI/SRP and the DTI/SRP results shows the benefit arising from the use of Q-ball model, since the resulting bundle displays more fibers and with a more regular distribution. (a-d) mossy fibers in the body, from the granular layer of the dentate gyrus to the lucidum layer of CA3. 3D-rendering only shows the body segmentation; (e-f) perforant pathway from the entorhinal cortex to the molecular layer of the dentate gyrus in the body of the hippocampus. 3D-rendering shows the entire segmentation (head, body and tail) with the same color code as the one presented in Fig. 5.9 and a transparency of 0.2, except for the entorhinal cortex (opaque gray) and the dentate gyrus in the body (opaque dark blue)

Microstructure mapping

Inference of tissue microstructure using the NODDI model Because of its practical implementation, the NODDI model has become very popular to map the tissue microstructure in vivo in the frame of clinical applications [START_REF] Kunz | Assessing white matter microstructure of the newborn with multishell diffusion MRI and biophysical compartment models[END_REF][START_REF] Shin | White matter changes of neurite density and fiber orientation dispersion during human brain maturation[END_REF][START_REF] Jelescu | One diffusion acquisition and different white matter models: how does microstructure change in human early development based on wmti and noddi?[END_REF][START_REF] Kodiweera | Age effects and sex differences in human brain white matter of young to middle-aged adults: a dti, noddi, and q-space study[END_REF]. This model was specifically designed to map the biodistribution of dendrites and axons in the brain ( § 3.2.7.2). It has been mostly applied in vivo in human using low field conventional MRI scanners, limited to a millimeter spatial resolution. Some ex vivo preclinical studies have also been performed using NODDI in animal models (mice in [START_REF] Sepehrband | Brain tissue compartment density estimated using diffusion-weighted MRI yields tissue parameters consistent with histology[END_REF] and monkeys in Alexander et al. [2010]). However, to our knowledge, this is the first time that this model is used to explore the human hippocampus ex vivo. The NODDI model consists of four diffusive compartments [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF], Alexander et al., 2010] with no exchange between them. Each compartment contributes to the global diffusion attenuation A resulting from a linear combination of the individual signal attenuations associated to each compartment (cf. 3.2.7.2). To reduce the number of variables to fit, Equation 3.14) can be written as:

A = (1 -f iso )[ f ic .A ic + f ec .A ec + f stat ] + f iso .A iso = (1 -f iso )[(1 -f stat )( f * ic .A ic + f * ec .A ec ) + f stat ] + f iso .A iso (5.3) with f ic + f ec + f stat = 1 and f * ic + f * ec = 1, hence: A = (1 -f iso )[(1 -f stat )( f * ic .A ic + (1 -f * ic )A ec ) + f stat ] + f iso .A iso (5.4) with f stat = (1-f iso ) f stat and f ic = (1-f iso )(1-f stat ) f * ic .
In order to speed-up the fitting procedure, some parameters were fixed as suggested by Zhang et al.

[2012]. Watson's distribution was preferred to Bingham's distribution. For in vivo studies, intrinsic and isotropic diffusivities are usually set to 1.7 × 10 -3 and 3.0 × 10 -3 mm 2 /s respectively [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF]. Here, they were respectively set to 0.16 × 10 -3 mm 2 /s, corresponding to the mean diffusivity found in our sample, and to the diffusion coefficient of water at 20°C, i.e. 2.0 10 -3 mm 2 /s.

Investigation of the hippocampal neurite density

As already mentioned, the restricted intracellular volume fraction inferred from the NODDI model corresponds to an estimate of the neurite density. Within the hippocampus, Figs.5.16 and 5.17 clearly depict a positive gradient of this neurite density in the gray matter from the posterior to the anterior part of the hippocampus, and conversely, a negative gradient in the white matter.

Statistics of the intracellular volume fraction f ic were analyzed for each segmented structure of the hippocampus from the histogram of its values within the structure, in order to study their variation according to the structure of interest. Mean intracellular volume fractions of each segmented structure are reported in Table 5.2. Table 5.2 also assesses the positive gradient of intracellular fraction in the anterior part of the hippocampus, with a higher neurite density in gray matter regions, especially in the subicular complex and CA1. This result is consistent with the results obtained with the tractography, which also revealed a higher connectivity in the head than in the body or tail portions of the hippocampus (Fig. 5.13 and Fig. 5 along the rostrocaudal axis of the hippocampus. It has already been described to be higher in the body than in the head part in monkeys [START_REF] Willard | Cell number and neuropil alterations in subregions of the anterior hippocampus in a female monkey model of depression[END_REF]. Partial volume effects occurring with the segmentation can also have an impact, e.g. voxels labeled as CA2/CA3, but actually containing white matter.

Table 5.2 also shows the increased intracellular fraction in the tail, with a higher neurite density in white matter, i.e. the alveus and fimbria. This result can be interpreted on the basis of the polysynaptic pathway, since the principal outputs to the cortex merge along the different rostro-caudal levels of the hippocampus in the fimbria, which could explain the gradual increase in axonal density in the fimbria along the anterior-posterior direction.

Investigation of the laminar structure of the Ammon's horn The main hippocampal layers, referred to as layer I, II, and III in Fig. 5.18.c taken from Duvernoy [2005], can be segmented from T2-weighted images, but their contrast does not provide an indisputable boundary for each layer. As between layers and facilitates their segregation. This is particularly true when considering the delineation of the boundary separating layers II and III. Furthermore, the underlying physical principle driving this novel contrast mechanism is coherent with the anatomical knowledge. Layer I, with a high neurite density, corresponds to the alveus and to the oriens layers. Layer II, in contrast, shows a very poor neurite density, and corresponds to the pyramidal layer, mostly composed of the somas of neurons. Layer III, adjoining the vestigial hippocampal sulcus, appears with a higher neurite density than the pyramidal layer, which is consistent with the fact that it contains arborizations of the apical dendrites of pyramidal neurons, and corresponding to the molecular zone of the CA region, i.e., to the radiatum and lacunosum molecular layers.

The intracellular volume fraction map thus shows new contrasts, consistent with histology compartments, that could be applied in the future to other cortical brain in order to improve the quality of the segmentation at the level of cortical layers.

Discussion

The main contributions of this work are:

1. the presentation of a novel ultra-high field T2-weighted and diffusion MRI protocol providing high spatial and angular resolution data. It appears to be useful to propose a novel segmentation approach of the human hippocampus subfields that combines the available sources of contrast to enhance their segregation, 2. a proof of concept that ultra-high field high angular resolution diffusion imaging (UHF-HARDI) can robustly map the inner connectivity of the hippocampus and give evidence of a higher level of connectivity in the uncal region than in the body or tail portions. This result holds regardless of the tractography approach. The inference of known pathways was provided to illustrate the potential of UHF-HARDI. The comparison between the results obtained from the four tractograms highlights the need for using a probabilistic tractography algorithm and, when it comes to the reconstruction of more complex pathways like the perforant pathway, the benefit arising from the use of Q-ball model, 3. a proof of concept that ultra-high field diffusion MR microscopy could play an increasing role in the future to decipher the cytoarchitecture of the hippocampus. In our case, it provides evidence of a rostro-caudal heterogeneity that could be associated with differences in gene expression patterns and could support the long-axis functional specialization of the human hippocampus, [START_REF] Bryan A Strange | Functional organization of the hippocampal longitudinal axis[END_REF]. Indeed, the anterior portion of the hippocampus, but not its posterior one, is activated by tasks probing emotional and motivational aspects of cognitive processes [Kim andFanselow, 1992, Viard et al., 2011]. Furthermore, whereas the caudal portion of the hippocampus is involved in the encoding of memories or in the local component of spatial representation, its rostral part plays a crucial role in retrieval processes and in the global component of spatial representation [START_REF] Poppenk | Long-axis specialization of the human hippocampus[END_REF][START_REF] Zeidman | Investigating the functions of subregions within anterior hippocampus[END_REF][START_REF] Zeidman | Anterior hippocampus: the anatomy of perception, imagination and episodic memory[END_REF].

Chapter 5. Investigation of the human hippocampus and brainstem

106

Comparison with existing studies Several studies have been published to design a robust segmentation pipeline of the hippocampal substructures. Most of those relying on MRI were designed to exploit a single contrast, either T2 or T2* weighting [START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF][START_REF] Lem Wisse | Subfields of the hippocampal formation at 7T MRI: In vivo volumetric assessment[END_REF][START_REF] Daniel H Adler | Histology-derived volumetric annotation of the human hippocampal subfields in postmortem MRI[END_REF][START_REF] Paul A Yushkevich | A high-resolution computational atlas of the human hippocampus from postmortem magnetic resonance imaging at 9.4[END_REF]. The segmentation pipeline proposed in this study combines several contrasts stemming from T2-weighted anatomical MRI and diffusion-weighted MRI to take benefit from all the available information. Not only the scalar information of diffusion MRI data were exploited, but also the angular profiles of ODFs. Their singularities could be used to better identify the boundaries between substructures of the hippocampal formation when the T2 contrast did not provide enough valuable information, e.g. the transition from alveus to fimbria.

Most existing studies aiming at investigating hippocampal microstructure rely on a diffusion imaging protocol acquired using a single-shell sampling of the q-space, therefore not compatible with the use of the novel models emerging from the field of diffusion MR microscopy, requiring multiple-shell HYDI acquisition schemes. Most of them used the diffusion tensor model (DTI) and investigated the variations of FA, ADC, or just the contrast of the T2-weighted image between subregions and/or the layers of the hippocampus [START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF][START_REF] Shepherd | Diffusion tensor microscopy indicates the cytoarchitectural basis for diffusion anisotropy in the human hippocampus[END_REF]. Unfortunately, those invariant DTI-based scalar features are not specific to a particular cellular organization. A decrease in FA may correspond either to the degeneration of axons, or to their spreading. A decrease of the ADC may correspond either to a reduction of the axon diameter or to disorders in the extra-cellular space. For instance, [START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF] showed the seven hippocampal layers (i.e., alveus, sr pyramidale, sr radiatum, sr lacunosum, sr moleculare as well as the sr moleculare and granule cell layer of the DG) identified with the contrast of an T2-weighted image for a healthy sample. Sclerotic hippocampal samples depicted only four layers, and the non specificity of the method prevented from establishing the causes of this alteration. The HYDI acquisition scheme implemented in our study allowed us to use more advanced models of diffusion MRI giving more specific features to characterize the microstructure, like the neurite density inferred from the NODDI model. Such quantitative features lead to a better understanding of the variations occurring in the rostro-caudal direction at the cellular level and make correlations with the long-axis functional specialization of the human hippocampus.

Established pathways have already been reconstructed or identified in other studies. Zeineh et al. Last, it is the first time that connectivity matrices were used to assess the gradient of connectivity existing along the rostro-caudal axis of the hippocampus. Such observations were hypothesized from functional studies, but to our knowledge, have never been investigated from a structural point of view using diffusion MRI and tools coming from the field of connectomics.

Limitations In this study, we have established methods to delineate subfields and substructures of the hippocampal formation to infer their structural connectivity and microstructure. We have given evidence that using diffusion-based microstructural maps enables the segmentation of smaller hippocampal structures, like its lamination. Investigating this potential should be generalized in the future to develop a novel MRI-based post mortem atlas of the hippocampal complex. We have also demonstrated that UHF diffusion MRI using a preclinical system allows the reconstruction of hippocampal known pathways, like the perforant path and the mossy fibers. To go a step further, clustering techniques applied to the connectogram would provide clusters of co-localized fibers sharing similar geometries and belonging to the same white matter tract. Combined with the integration of more samples in order to better capture the intersubjet variability, fiber clustering should accelerate the construction of a probabilistic atlas of the hippocampal inner connectivity.

The choice of the diffusion sensitization that has been made in this study could impact the diffusion contrast and the quality of our results. Given the reduction factor of the mean diffusivity from D = 0.7×10 -3 mm 2 /s (standard value reported in vivo) to D = 0.16×10 -3 mm 2 /s, the diffusion attenuation at b = 4500 s/mm 2 should be equivalent to that of an in vivo scan performed at b = 1000 s/mm 2 . A higher diffusion sensitization is generally recommended to obtain sharp ODFs [START_REF] Christopher P Hess | Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis[END_REF].

The use of a single-shell at 4500 s/mm 2 was motivated by the literature, that typically mention the use of b-values of at least 4000 s/mm 2 to scan post mortem pieces. In particular, Dyrby et al. [2011] demonstrated that any HARDI acquisition with a b-value between 2000 and 8000 s/mm 2 allows for the inference of multiple fiber populations from ex vivo fixed specimens scanned at room temperature, with an optimal value around 4000 s/mm 2 . Furthermore, the application of a probabilistic fiber tracking method contributed to more robustly manage fiber crossings than deterministic approaches. Nowadays, there is no atlas of the human hippocampus connectivity and its microstructure at the mesoscopic scale. However, it would be of greatest value to clinical and cognitive neurosciences.

Clinical Prospects

Several tools are available to segment the hippocampus from MRI data, (the object-based ROI module of the Anatomist software (http://www.brainvisa.info/index.html in [START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF],

FIRST (FSL) or Freesurfer in Morey et al. [2009]), and numerical atlases of the human hippocampus Chapter 5. Investigation of the human hippocampus and brainstem 108 subfields have been established [START_REF] Chupin | Fully automatic hippocampus segmentation and classification in alzheimer's disease and mild cognitive impairment applied on data from adni[END_REF][START_REF] Paul A Yushkevich | Nearly automatic segmentation of hippocampal subfields in in vivo focal T2-weighted MRI[END_REF], Iglesias et al., 2015a].

But, to our knowledge, no numerical atlas of their connectivity or their microstructure has been established. However, in most pathologies affecting the hippocampus, there is a need to better understand which subfields are affected, at what rate, and if the modifications induced by the pathology affect the neuronal cell bodies and/or their connections. For instance, [START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF] showed, in the case of hippocampal sclerosis (HS), that type 1 and 2 depicted different rate of cell loss with a more pronounced cell loss in CA3 and CA4 in type 1. Both kinds of HS samples depicted a contrast that did not allow the discrimination of the seven hippocampal layers contrary to normal samples, likely because of pathological shrinkage and fiber alteration.

Regarding strengthen the auto-associative network of the CA3, amplifying the completion pattern (retrieval of previously stored information from a partial cue). The subject studied in this paper was an 87-yearold male. Regarding our results, that would mean that the outputs of the entorhinal cortex may be less significant than in a young hippocampus. As self-connections are excluded, there is no impact of the strengthening of the auto-associative network of CA3. Comparing these results to others obtained with a young hippocampus could highlight the reduction of the perforant path induced by the process of normal aging.

From a fundamental point of view, having access to a fine description of the hippocampal anatomy, including its subfields, its connectivity and its microstructure, and being able to perform functional imaging using various memory tasks, opens the way to an improved functional neuroanatomy of the sensory, short-term, working, and long-term memories. Better understanding the neural networks driving these various cognitive processes might be useful to design, for instance, novel educational tools to improve the efficacy of young children to learn.

Conclusion

This study forms a proof of concept of how ultra-high field MRI with strong gradients can be applied to analyze hippocampal connectivity and microstructure ex vivo. It introduces a unique acquisition and segmentation protocol and demonstrates that diffusion-weighted MRI offers a new opportunity to map the inner structural connectivity and microstructure of the human hippocampus, in good agreement with histology and current functional studies. The tractography and microstructure models highlight a higher connectivity and neurite density in the anterior hippocampus, whereas the intracellular volume fraction map reveals the laminar structure of the Ammon's horn and could be used Chapter 5. Investigation of the human hippocampus and brainstem 109 to improve segmentation protocols. In the future, these results could be of potential benefit to better correlate hippocampal atrophy, observed at low field in Alzheimer's patients, with modifications of its inner connectivity and neurite density.

The brainstem

The brainstem is a crossroad of the major motor and sensitive pathways, and is one of the first structure affected by Parkinson's disease. The first part of this section describes the current knowledge on the brainstem anatomy that is necessary to interpret the imaging results that were obtained in this work. The second part presents the study performed during this thesis work to explore an ex vivo brainstem using dMRI and diffusion MR microscopy at 11.7 T.

5.2.1

The human brainstem: anatomy and function

Localization and gross anatomy

The human brainstem is located at the juncture of the cerebrum and the spinal column, anterior to the cerebellum (Figures 2.1.a and 5.19) and is about 7 cm long. • The medulla, or medulla oblongata -This part is anterior and partially inferior to the cerebellum and measures around 3 cm in length with a diameter of 14 mm [START_REF] Raininko | The normal brain stem from infancy to old age[END_REF].

The transition of the medulla into the spinal cord is marked by the decussation of the pyramidal tracts, interrupting the anterior median fissure (Figure 5.20.a),

• The pons -This part, measuring about 2.5 cm in length with a diameter of 30 mm [START_REF] Raininko | The normal brain stem from infancy to old age[END_REF], is a bulge forming the origin of the middle cerebellar peduncles. At the dorsal surface of the brainstem, the frontier with the medulla is located at the level of the greatest width of the fourth ventricle (fastigium) (Figure 5.20.c),

• The mesencephalon, or midbrain -This part is the smallest (approximately 1.5 cm in length with a diameter of 18 mm [START_REF] Raininko | The normal brain stem from infancy to old age[END_REF]) and the most superior part of the brainstem.

The border between the pons and the mesencephalon is dorsally marked by the decussation of the trochlear nerve. The limit between the mesencephalon and the diencephalon is located at the posterior commissure dorsally, and caudal to the mammillary bodies ventrally (Figure 5.20.c). The brainstem contains multiple gray (cranial nerves, proper and reticular nuclei) and white matter structures (association and projection tracts). Major tracts crossing the brainstem are detailed in § 2.4.1 and § 5.2.1.3. Gray matter structures are presented in the following section.

Brainstem nuclei

The brainstem hosts three types of nuclei: cranial nerve, proper and reticular nuclei. Ten of the twelve cranial nerves (CN) originate in the brainstem and their associated nuclei are disseminated through all its segments (cf. § 2.3.3). Figure 5.21 depicts their circuit inside the brainstem as well as their associated nuclei. They form a complex network. Whereas some nerves have a single function (e.g. motor) and a single nucleus (e.g. CN IV), other cranial nerves can mix both sensory and motor functions and have multiple associated nuclei (e.g. CN V).

In addition, the brainstem encloses proper nuclei such as the red nuclei, the substantia nigra, the superior and inferior colliculi in the midbrain (Figure 5. Finally, reticular nuclei form the reticular formation throughout the brainstem and contains the raphe, gigantocellular, and parvocellular reticular nuclei. The locus coeruleus is a well-known nucleus of this formation involved in Parkinson's disease, more specifically related to the rapid eye movement (REM) syndrome.

Brainstem connectivity

The brainstem is primarily a crossroad between the brain and the body, and its nuclei are relay of many projection (ascending or descending) tracts (e.g. the cuneate and gracile nuclei in the medial lemniscus, cf. § 2.4.1 and Figure 2.9). Then, the brainstem hosts numerous nuclei playing a role in neuromodulation. This means that these nuclei are involved in dedicated biochemical processes to regulate diverse populations of neurons. For instance, the locus coeruleus, located in the pons, is the principal site for brain synthesis of noradrenaline. Its projections innervate the spinal cord, the brainstem, the cerebellum, the hypothalamus, the thalamic relay nuclei, the amygdala, the basal telencephalon, and the cortex. In addition, three cerebellar peduncles (green boxes in

Brainstem functions

The human brainstem plays a central role in connecting the cerebrum, the cerebellum and the spinal cord to one another. It hosts relay nuclei for afferent and efferent signaling, and provides source nuclei for CN III-XII, as well as for several neuromodulatory systems. This is one of the phylogenetically oldest structure of the brain [START_REF] Mai | Atlas of the human brain[END_REF], and is therefore a key region for almost all primitive survival-oriented functional and neuromodulatory systems (cholinergic, dopaminergic, noradrenergic, and serotonergic nuclei).

More specifically, the midbrain serves as a relay center for visual (superior colliculus), auditory (inferior colliculus), and motor system information (red nucleus), as well as pain (PAG) and temperature information. The pons regulates the breathing rate with a specific structure, called the pneumotaxic center, and is also involved in the auditory system through its cochlear nucleus, superior olivary complex and trapezoid body, in sensations like taste, balance, as well as the regulation of deep sleep through the locus coeruleus. The medulla oblongata plays a key role in heart rate and blood pressure, and is responsible for many reflexes in the body, or involuntary controls.

In a nutshell, the brainstem plays a key role in controlling body's vital functions. However, its in vivo exploration using clinical MRI scanners is challenging, which explains why, despite its major role in systems and circuitries that are otherwise extensively studied in neuroscience, it has received little attention from the neuroimaging community relative to studies of the cortex or even subcortical structures (e.g. striatum, thalamus). Ultra-high field ex-vivo diffusion MRI using strong gradients was proven to be useful to explore the brainstem connectivity [START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF]. In the second project of this thesis, that is presented hereinafter, we go further and demonstrate that using 11.7 T MRI with strong gradients (780 mT/m) enable to characterize its smaller structures while inferring their fine anatomical connectivity, as well as their microstructure using diffusion MR microscopy.

Post mortem inference of the human brainstem connectivity and microstructure

In this study, we demonstrate that UHF MRI gives the opportunity to map the complex anatomy of the brainstem, as well as its fine connectivity and microstructure. The acquisition protocol presented in the previous section was optimized to obtain 185 and 100 µm isotropic anatomical images and the number of acquired shell was increased to facilitate the computation of microstructural models.

The combination of anatomical and diffusion-weighted images was used by Dr F. Lechanoine (Bretonneau University Hospital, Tours) to manually segment, for the first time, 51 of the 73 brainstem nuclei, as well as ROIs intersecting well known fiber tracts. Based on these segmentations, the fine connectivity of the brainstem was investigated. Major tracts were successfully reconstructed and the projections of the locus coeruleus were investigated. Neurite density maps were established using the NODDI model. Their potential to highlight specific structures was analyzed, as well as the opportunity to better understand the evolution of the neurite density along tracts.

The use of MRI to investigate the human brainstem anatomy and structural connectivity: state of the art

Regarding the hippocampus, a considerable number of studies propose manual [START_REF] Boutet | Detection of volume loss in hippocampal layers in alzheimer's disease using 7 T MRI: A feasibility study[END_REF][START_REF] Lem Wisse | Subfields of the hippocampal formation at 7T MRI: In vivo volumetric assessment[END_REF][START_REF] Daniel H Adler | Histology-derived volumetric annotation of the human hippocampal subfields in postmortem MRI[END_REF][START_REF] Julie L Winterburn | A novel in vivo atlas of human hippocampal subfields using high-resolution 3 T magnetic resonance imaging[END_REF], Yushkevich et al., 2015a] or automated [Iglesias et al., 2015a[START_REF] Van Leemput | Automated segmentation of hippocampal subfields from ultra-high resolution in vivo MRI[END_REF][START_REF] Pipitone | Multi-atlas segmentation of the whole hippocampus and subfields using multiple automatically generated templates[END_REF], Yushkevich et al., 2015b] segmentation methods. An international collaboration group, named the "Hippocampal Subfields

Group", was even formed with the aim of harmonizing segmentation rules for hippocampal and parahippocampal subregions [START_REF] Laura | A harmonized segmentation protocol for hippocampal and parahippocampal subregions: Why do we need one and what are the key goals?[END_REF].

Nothing of the sort exists for the human brainstem.

In vivo studies generally focus on the delineation of one or two nuclei or subregions, such as the substantia nigra and/or the red nucleus [START_REF] Menke | Connectivitybased segmentation of the substantia nigra in human and its implications in parkinson's disease[END_REF][START_REF] Kwon | Seven-tesla magnetic resonance images of the substantia nigra in parkinson disease[END_REF][START_REF] Chowdhury | Parcellation of the human substantia nigra based on anatomical connectivity to the striatum[END_REF][START_REF] Max C Keuken | Quantifying inter-individual anatomical variability in the subcortex using 7T structural MRI[END_REF], Lehéricy et al., 2014[START_REF] Blazejewska | Increase in the iron content of the substantia nigra and red nucleus in multiple sclerosis and clinically isolated syndrome: a 7 Tesla MRI study[END_REF], Visser et al., 2016[START_REF] Langley | Reproducibility of locus coeruleus and substantia nigra imaging with neuromelanin sensitive MRI[END_REF][START_REF] Pyatigorskaya | Comparative study of MRI biomarkers in the substantia nigra to discriminate idiopathic parkinson disease[END_REF], the locus coeruleus [START_REF] Langley | Reproducibility of locus coeruleus and substantia nigra imaging with neuromelanin sensitive MRI[END_REF][START_REF] Noam I Keren | In vivo mapping of the human locus coeruleus[END_REF][START_REF] García-Lorenzo | The coeruleus/subcoeruleus complex in rapid eye movement sleep behaviour disorders in parkinson's disease[END_REF][START_REF] Peter R Murphy | Pupil diameter covaries with bold activity in human locus coeruleus[END_REF][START_REF] Matthew | In vivo MRI assessment of the human locus coeruleus along its rostrocaudal extent in young and older adults[END_REF][START_REF] Priovoulos | High-resolution in vivo imaging of human locus coeruleus by magnetization transfer MRI at 3T and 7T[END_REF] or the PAG [Satpute et al., 2013[START_REF] Olivia K Faull | Functional subdivision of the human periaqueductal grey in respiratory control using 7Tesla fMRI[END_REF][START_REF] Coulombe | Intrinsic functional connectivity of periaqueductal gray subregions in humans[END_REF].

Automated segmentation methods in MRI data are in their early stages. [START_REF] Lambert | Multiparametric brainstem segmentation using a modified multivariate mixture of gaussians[END_REF] used multimodal MRI data to produce probability maps for four tissue classes (gray matter, reticulated

Chapter 5. Investigation of the human hippocampus and brainstem 115 gray matter, PAG, white matter) using an unsupervised segmentation algorithm. [START_REF] Nigro | Fully automated segmentation of the pons and midbrain using human t1 mr brain images[END_REF] proposed a method to automatically segment the pons and the midbrain using thresholds and geometric criteria defined upon heuristic rules, Iglesias et al. [2015b] suggested a Bayesian method to segment four brainstem structures (midbrain, pons, medulla, SCP) relying on a probabilistic atlas built upon 49 manually labeled scans, and [START_REF] Bianciardi | A probabilistic template of human mesopontine tegmental nuclei from in vivo 7 T MRI[END_REF] established a probabilistic template of five mesopontine tegmental nuclei.

Despite its highly organized structure, the brainstem appears relatively homogeneous in conventional anatomical scans with clinical MRI systems, which requires the use of complementary techniques such as magnetization transfer [START_REF] Langley | Reproducibility of locus coeruleus and substantia nigra imaging with neuromelanin sensitive MRI[END_REF][START_REF] Priovoulos | High-resolution in vivo imaging of human locus coeruleus by magnetization transfer MRI at 3T and 7T[END_REF], quantitative susceptibility mapping (QSM) [START_REF] Max C Keuken | Quantifying inter-individual anatomical variability in the subcortex using 7T structural MRI[END_REF], Visser et al., 2016], functional [START_REF] Peter R Murphy | Pupil diameter covaries with bold activity in human locus coeruleus[END_REF][START_REF] Olivia K Faull | Functional subdivision of the human periaqueductal grey in respiratory control using 7Tesla fMRI[END_REF][START_REF] Coulombe | Intrinsic functional connectivity of periaqueductal gray subregions in humans[END_REF] or diffusion MRI [START_REF] Menke | Connectivitybased segmentation of the substantia nigra in human and its implications in parkinson's disease[END_REF][START_REF] Chowdhury | Parcellation of the human substantia nigra based on anatomical connectivity to the striatum[END_REF][START_REF] Lidia M Nagae-Poetscher | High-resolution diffusion tensor imaging of the brain stem at 3 t[END_REF][START_REF] Bianciardi | Toward an in vivo neuroimaging template of human brainstem nuclei of the ascending arousal, autonomic, and motor systems[END_REF].

Several studies using DTI have been conducted on clinical MRI systems. DTI metrics (FA, ADC)

or reconstructed tracts were used to help for nuclei delineation [START_REF] Menke | Connectivitybased segmentation of the substantia nigra in human and its implications in parkinson's disease[END_REF][START_REF] Chowdhury | Parcellation of the human substantia nigra based on anatomical connectivity to the striatum[END_REF][START_REF] Bianciardi | Toward an in vivo neuroimaging template of human brainstem nuclei of the ascending arousal, autonomic, and motor systems[END_REF] or to evaluate brainstem pathologies in clinical studies [START_REF] Lui | Brainstem corticospinal tract diffusion tensor imaging in patients with primary posterior fossa neoplasms stratified by tumor type: a study of association with motor weakness and outcome[END_REF][START_REF] Chen | Diffusion tensor imaging and white matter tractography in patients with brainstem lesions[END_REF][START_REF] Helton | Diffusion tensor imaging of brainstem tumors: axonal degeneration of motor and sensory tracts[END_REF][START_REF] Kovanlikaya | Assessment of the corticospinal tract alterations before and after resection of brainstem lesions using diffusion tensor imaging (dti) and tractography at 3 t[END_REF]. However, although the achievable resolution range with in vivo DTI (from 1.5 to 2.0 mm) enables the reconstruction of major brainstem tracts, it is too coarse to be used for the delineation of most of the brainstem nuclei and finer connections (e.g. the locus coeruleus measures approximately 16 mm in length but is only 1-2 mm 2 thick, [Paxinos andHuang, 2013, Sclocco et al., 2018], and the ambiguus and solitary nuclei are less than 1 mm 2 thick [START_REF] Thomas P Naidich | Duvernoy's atlas of the human brain stem and cerebellum: high-field MRI, surface anatomy, internal structure, vascularization and 3 D sectional anatomy[END_REF][START_REF] Sclocco | Challenges and opportunities for brainstem neuroimaging with ultrahigh field MRI[END_REF]). Finally, a few microstructure studies targeting the human brainstem using recent models such as NODDI [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF] or

ActiveAx [START_REF] Zhang | Axon diameter mapping in the presence of orientation dispersion with diffusion MRI[END_REF] were recently published, in the frame of neurological or developmental studies [START_REF] Shin | White matter changes of neurite density and fiber orientation dispersion during human brain maturation[END_REF][START_REF] Kamagata | Neurite orientation dispersion and density imaging in the substantia nigra in idiopathic parkinson disease[END_REF][START_REF] Surova | Alterations of diffusion kurtosis and neurite density measures in deep grey matter and white matter in parkinson's disease[END_REF][START_REF] Slattery | Longitudinal neurite orientation dispersion and density imaging in young-onset alzheimer's disease[END_REF][START_REF] Mah | Detailing neuroanatomical development in late childhood and early adolescence using noddi[END_REF][START_REF] Dc Dean | Mapping white matter microstructure in the one month human brain[END_REF].

The limited spatial resolution and contrast are not the only elements that hamper the investigation of the brainstem in vivo [START_REF] Sclocco | Challenges and opportunities for brainstem neuroimaging with ultrahigh field MRI[END_REF]. The close vicinity of the brainstem to large arteries and ventricles makes it sensitive to physiological noise (CSF and arterial pulsatility, chest motion) that can cause artifacts such as blurring or ghosting. In addition, the presence of large air-tissue interfaces at the level of the posterior part of the oral cavity is responsible for severe magnetic-susceptibilityinduced artifacts corrupting anatomical and diffusion MRI scans of the brainstem [START_REF] Elke R Gizewski | High-resolution anatomy of the human brain stem using 7-T MRI: improved detection of inner structures and nerves?[END_REF].

Alternatively, ex vivo anatomical and diffusion MRI do not suffer from the same limitations and can therefore reveal fiber architecture and nuclei that are not resolvable in vivo. Previous studies have reported post mortem DTI of the brainstem [START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF][START_REF] Soria | Improved assessment of ex vivo brainstem neuroanatomy with high-resolution MRI and dti at 7 Tesla[END_REF][START_REF] Prats-Galino | Functional anatomy of subcortical circuits issuing from or integrating at the human brainstem[END_REF]. However, regarding the complexity of the brainstem fiber architecture, the use of a DTI model does not appear suitable to infer the brainstem connectivity. A few studies have been Chapter 5. Investigation of the human hippocampus and brainstem 116 performed using more sophisticated diffusion sampling schemes and models like HARDI models. [START_REF] Calabrese | Postmortem diffusion MRI of the human brainstem and thalamus for deep brain stimulator electrode localization[END_REF] reconstructed the essential tremor circuit to improve deep brain stimulation, and Plantinga et al. [2016] studied the connectivity of the substantia nigra, but none of them inferred the brainstem anatomy and connectivity in its entirety.

In this work, a human brainstem sample was imaged with an 11.7 T Bruker MRI system. The MRI dataset, including a multiple-shell diffusion-weighted dataset at 300 µm, and two anatomical scans at 185/100 µm, was manually segmented by Dr. F. Lechanoine and analyzed in order to investigate the anatomy, structural connectivity and microstructure of the brainstem sample.

Tissue preparation, container and MRI hardware

One encaphalon with no neurological or vascular history was obtained from the body donation program of the Institute of Anatomy (Université Franc ¸ois-Rabelais, Tours, France). The brain was extracted less than 24 hours after death and fixed in a 10% formalin solution during six months. It was hanged within the solution by the basilar artery to limit deformations that could be induced by contact with the container. After fixation, cuts were performed at the level of the optic chiasm and

Determination of the magnetic and diffusion properties of the sample

As in § 5.1.2.3, an estimation of the mean T2 and diffusivity of the brainstem sample was carried out.

The transverse relaxation time was mapped using a standard MSME pulse sequence (cf. § 4.4) with the same acquisition parameters as for the hippocampus and a total scan duration of 8h54min. The histogram of the T2 relaxation time depicts a unique mode at 30.7 ms as shown in Figure 5.24.

The mean diffusivity was obtained from a single-shell diffusion-weighted acquisition with the same acquisition parameters as for the hippocampus. The resulting mean diffusivity value corresponding to the white matter mode was 0.22 × 10 -3 mm 2 /s.

Imaging protocol

The imaging protocol included anatomical, quantitative and diffusion-weighted scans.

Anatomical scans

The anatomical images were obtained using T2-weighted spin echo sequences.

A 2D-SE dataset was acquired with an isotropic resolution of 185 µm, TE/TR = 26.5/13000 ms, matrix size: 267×267, 406 slices, flip angle: 90°, receiver bandwidth: 66 kHz, 13 averages, and a total acquisition time of 10h09min. A 3D-SE dataset was acquired using the multi-slice option, an isotropic resolution of 100 µm, TE/TR = 20/500 ms, matrix size: 500*512, 800 slices, flip angle: 90°, receiver bandwidth: 50 kHz, 1 average, and a total scan time of 35h33min. In addition to the HARDI dataset, a further multiple-shell HYDI dataset was acquired with nine different diffusion sensitizations. Aside from the b-values used with the hippocampus (4500, 7500 and 10000 s/mm 2 ), lower b-values were added in order to improve the fit quality for the microstructural models, and all the shells were acquired with the same static gain. The parameters were tuned as listed in Table 5.3, using the shorter possible echo time to improve the SNR for each shell, and the shorter possible TR, to reduce the acquisition time. The use of various echo times implied a correction during the preprocessing step as presented in § 5.1.2.5.

This protocol lasted 9 days and 14h, including pauses. The different shells were acquired with increasing separation times ∆, gradient pulse widths of δ = 4.3 ms or δ = 8.5 ms, in order to vary the diffusion time. This choice was motivated by the willingness to be able to use alternative models to NODDI in the future, such as ActiveAx, which requires sampling the diffusion time as well.

Figure 5.25 shows the resulting images obtained at b = 1500, 4500 and 7500 s/mm 2 .

Relaxometry scans Two T2 relaxometry mapping were performed during the first and the tenth day of the acquisition session in order to assess the stability of the sample over time. The acquisition parameters for the MSME sequence were the same than those presented in § 5.2.2.3.

Preprocessing

As for the hippocampus (cf. § 5.1.2.5), the difference in T2-weighting of each shell was corrected taking b = 4500 s/mm 2 (TE = 24.6 ms) as the reference. All the acquisition were performed during 16 consecutive days. The transformation between anatomical and diffusion datasets is thus a simple rigid transformation between the field of views.

Local diffusion signal modeling and global connectivity mapping

Diffusion analysis was performed using the Connectomist toolbox. The HARDI dataset (at b = 4500 s/mm 2 ) was used to compute a field of diffusion tensors, with the DTI model, and a field of ODFs (order 8, λ = 0.006), with the aQBI model, as depicted in Figure 5.28. Diffusion tensors were not used for the tractography, but only to generate tensor-derived rotationally invariant scalar maps including FA, MD, but also color-encoded (CED) maps (see Figure 5.27). The structural connectivity was then Chapter 5. Investigation of the human hippocampus and brainstem 120 inferred from the ODFs field using a streamline regularized deterministic and a streamline regularized probabilistic tractography algorithms with the following parameters : 8 seeds per voxel yielding dense tractograms containing 13 millions of fibers, forward step of 70 µm corresponding to less than a quarter of the voxel resolution, angular threshold of 30°. (minimum/maximum fiber length 1.8/126 mm to avoid loops and discard spurious fibers). In order to determine the fiber length constraint that should be applied for the final tractography, preliminary tractograms were computed with both deterministic and probabilistic algorithms, with minimum/maximum fiber length of 0.6/300 mm. Figure Moreover, in order to study both cerebellum-brainstem and diencephalon-brainstem connections, cerebellar and diencephalic structures included in the specimen (e.g. the geniculate body or the dentate nucleus) were added to the nomenclature.

Manual segmentation

The segmentation was performed on the 100 µm anatomical image, using the PtkVoi software developed in Neurospin. This segmentation was based on the contrast of the 100 µm anatomical image (major tracts were visible as hyposignal, whereas nuclei appeared in hypersignal, with various shades of gray), with the help of further contrasts from the 185 µm anatomical scan as well as diffusion MRI (FA, MD, and CED maps) that provided an enhanced contrast for some Chapter 5. Investigation of the human hippocampus and brainstem 122 structures. The color-encoded map enabled to segregate various white matter pathways, which was of great help for the segmentation of the nuclei, the localization of the latter being inferred from their relationships with these white matter tracts.

To address the lack of existing protocol to manually segment the brainstem nuclei based on MR contrasts, a detailed description has been established for each of the segmented structure. The proposed protocol details, for each structure, the best MR contrast enabling its delineation (T2-weighted scan, FA, CED map), the landmarks that were used, as well as the putative pitfalls if any.

Major white matter tracts were also identified, based on their contrast on the FA map, their anatomical location, and their orientation visible on the CED map. For each bundle, an intersecting region of interest was drawn.

Results

In fine, 51 brainstem nuclei were segmented: 17 proper nuclei, 13 nuclei of cranial nerves,

Inference of the brainstem connectivity

Preprocessing of the image of labels The nomenclature associated to the manual segmentation described above did not include any distinction between right and left structures, which is necessary for the analysis of the connectivity. In order to fulfill this requirement, the nomenclature was adapted: even labels were associated to the structures belonging to the left part of the sample and odd labels to the structures of the right part. The first step was to modify the labels so that the image only contains even labels. Then, a mask with the value 1 for all the right part was generated, based on the inference of a plane separating the sample in its center. As the sample was not perfectly straight, this plane was replaced by a set of 14 planes (defined over 11 to 87 slices, depending on the variation of the sample shape), each of them constructed as the mean plane of N points, positioned manually at the Chapter 5. Investigation of the human hippocampus and brainstem 124 middle of the specimen (Figure 5.31.a,5.31.b,and 5.31.d). Following the addition of the generated mask to the image of labels, a few structures had to be corrected due to their position, close to the center. This was the case for the hypoglossal and gracile nuclei, as well as some raphe nuclei (the median, magnus, pallidus and obscurus). For these structures, a few voxels corresponding to outliers approaches. The choice of reconstructing the right LC connections instead of the left one was made because of the larger part of the remaining cerebellum at the level of the dentate nucleus on the right side of the sample. After a random-selection at 10%, the first step was to select fibers going through the LC. Then, a filter was applied so that only bundles containing less than 10 fibers are discarded.

Chapter 5. Investigation of the human hippocampus and brainstem 125

The last step was to manually discard spurious fibers displaying obvious aberrant connections. The final results highlight connections with the cerebellum (via the cerebellar nuclei, and in particular the dentate nucleus), the thalamus and the spinal cord, which is consistent with the connections of the neuropinephrine system presented in [START_REF] Rc Malenka | Chapter 6: widely projecting systems: monoamines, acetylcholine, and orexin[END_REF].

The same procedure was applied to reconstruct some of the main white matter tracts of the brainstem, as depicted in Figure 5.33 which shows the corticospinal tract (dark blue), the transverse pontine fibers (red), the superior cerebellar peduncles (yellow) and the inferior cerebellar peduncles (light blue). In conclusion, the acquired dataset gave the opportunity to investigate the brainstem connectivity, with the reconstruction of the major white matter bundles as well as the projections of the locus coeruleus. The next section is dedicated to the study of its microstructure.

Inference of the brainstem microstructure

Tuning of the Q-space sampling and data quality assessment The NODDI model was used to investigate human brainstem microstructure. The number of acquired shells was increased in this post mortem study in comparison to what is conventionally performed in vivo in standard protocols [START_REF] Zhang | Axon diameter mapping in the presence of orientation dispersion with diffusion MRI[END_REF]. However, not all of them were used, to keep a reasonable computation time. The choice of the shells kept for the computation is described bellow. A common way to visualize the data in the frame of qualitative assessment of microstructure models is to plot, for a specific voxel, the normalized signal S/S 0 against the cosine of the angle between the principal fiber orientation in the voxel and the applied diffusion direction. As the diffusion is highly restricted in the direction perpendicular to the fiber orientation (where the cosine is null), S/S 0 is less weighted by the diffusion process than in the case of a diffusion direction parallel to the fiber (where the cosine is 1), giving the highest attenuation.

This representation is performed for each acquired shell. However, in practice, the effective b-value is not constant as it depends on the diffusion gradients orientation and also on the other gradients of the sequence (e.g. the gradient slice selection). Figure 5.34 shows the repartition of the effective b-value for each single shell. The values were directly taken from the method file provided by the Bruker system. The median of effective b-values is, on average, 273 s/mm 2 higher than the input value, and represents a net increase of 3% (for b = 10000 s/mm 2 ) to 33% (for b = 500 s/mm 2 ) compared to the prescribed b-value. The variation of b between its minimum and maximum effective value is, on average, equal to 740 s/mm 2 .

The gap between the prescribed and the effective b-values is not detrimental to the algorithm fitting the NODDI model, which reads the real b-value corresponding to each direction. However, this induces a bias for the data visualization, as the variation of the attenuation is not only related to the gradient orientation but also to the variation of the b-value. Thus, this variation has been corrected specifically for the visualization process. Figure 5.35 presents the signal attenuation for a voxel located in a highly anisotropic region, with light blue dots corresponding to the data before the bvalue correction and the red dots corresponding to the data after the correction.

Considering the contamination of diffusion-weighted datasets by Rician noise, especially for the bvalues of 7500 and 10000 s/mm 2 , a denoising step has been added using a non-local means filter algorithm implemented by Dr F. Poupon [START_REF] Buades | Non-local means denoising[END_REF][START_REF] Condat | A simple trick to speed up and improve the non-local means[END_REF]. The algorithm was applied for a measured noise standard deviation of 0.3. Up to b = 4500 s/mm 2 , the noise model was chosen Gaussian and the degree of filtering of 0.3. Then, the degree of filtering was set at 0.5, and the noise model was chosen to be Rician, since the acquisition was performed using a single channel coil antenna. The combination of the shells used for the computation has been decided so as to limit the overlapping of the data between two shells. The final multiple-shell HYDI dataset was constructed using the datasets acquired at: b = 1000, 2500, 4500, 7500, 10000 s/mm 2 (see Figure 5.37). parameters being fixed to their initial value. Then, a non-linear programming (NLP) constrained optimizer was applied to all the parameters, with a maximum iteration number of 1000 and a step size of 0.001. Finally, a Rician Monte Carlo Markov Chain (MCMC) optimizer was applied to refine the parameter estimation using a burn-in count of 500, a sample count of 500, an interval count of 50, and a maximum iteration count of 100000.

Great care had to be taken for the choice of initial values and boundaries of NODDI parameters. The complete set of parameters for the NODDI model is:

• the isotropic fraction f iso -corresponding in vivo to the fraction of CSF, and expected to be close to 0 in our case (no PBS surrounding the sample). This parameter was thus set to 0,

• the intracellular fraction f intra -ranging from 0 to 1, • the parallel diffusivity d -this parameter is usually fixed for the computation, but contrary to the hippocampus, mainly made of gray matter, the brainstem is composed of both white and grey matter, making the choice of the fixed intrinsic diffusivity less straightforward. Few studies have reported the intrinsic diffusivity value used for ex vivo samples. Alexander et al.

[2010] studied a post mortem monkey brain and fixed the intrinsic diffusivity and the isotropic diffusivity to 6.0 × 10 -10 m 2 /s and 2.0 × 10 -9 m 2 /s. Kleinnijenhuis et al. [2013a] also applied the NODDI model on an ex vivo human cortex sample, but no mention was made of the intrinsic diffusivity coefficient that was used. In his thesis, [START_REF] Grussu | Microstructural imaging of the human spinal cord with advanced diffusion MRI[END_REF] computed the bayesian information criterion (BIC) obtained for various intrinsic diffusivities from 0.1 to 3.2 × 10 -9

in post mortem spinal cord samples and showed an optimal value of 1.5 × 10 -9 m 2 /s. The following work evaluates the impact of d modifications on the obtained results,

• the isotropic diffusivity d iso -fixed, and corresponding to the water diffusivity at 20°C, which is 2 × 10 -9 m 2 /s according to [START_REF] Peter E Thelwall | Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model[END_REF]. This is also the value used by Alexander et al.

[2010],

• the stationary fraction f stat -this offset corresponds to the plateau observed for the parallel diffusion-weighted signal component in Figure 5.37. Its value is expected to range between 0.0 and 0.3 [Alexander et al., 2010], but no constraint was imposed and its boundaries were set to 0 and 1.

Two tests have been performed on the half slice containing the voxel studied in Figure 5. 35 and 5.36.

The aim was to find the best initial setting in order to optimize the final fit and the accuracy of the results. Two cases were considered, evaluating the influence of d . d was fixed, or set free with a variation allowed between 0.1 and 1.7 × 10 -9 m 2 /s (in order to include the value found by [START_REF] Grussu | Microstructural imaging of the human spinal cord with advanced diffusion MRI[END_REF] in the spinal cord and to stay under the value fixed in vivo). The first configuration supposes to choose the optimal value for d . To this aim, the distribution of the Bayesian information criterion (BIC) median was studied as a function of the parameter d , all the other parameters kept constant [START_REF] Grussu | Microstructural imaging of the human spinal cord with advanced diffusion MRI[END_REF], the optimal d corresponding to the lowest BIC value. The optimal d was found to be 1.15×10 -9 m 2 /s (see Figure 5.37.a).

The tests results are summarized in Figure 5.37. Case 1 is the case where d is fixed. On the left, the distribution of the Bayesian information criterion (BIC) median was studied as a function of parameter d , all the other parameters remaining the same. This distribution highlights an optimal value of 1.15 × 10 -9 m 2 /s. On the right are shown the results obtained with d = 1.15 × 10 -9 m 2 /s: the orientation dispersion map, the intracellular volume fraction map, and the BIC map, with a median value of -678. Case 2 refers to the case where d is free. This case gave a better fit and a lower BIC value of -694. However, the obtained orientation distribution map seemed less consistent.

The two BIC values being close, case 1 was chosen for more consistency of the orientation dispersion map.

Use of a Bayesian information criterion (BIC) to select the fitting parameters The bayesian information criterion (BIC) [START_REF] Schwarz | Estimating the dimension of a model[END_REF] is a common statistical tool for model selection.

Lower BIC values imply better fits, while accounting for the number of free model parameters. The lowest BIC value indicates the best trade-off between a high likelihood and the number of free parameters. Voxel-wise BIC maps were calculated as follows: the number of non-fixed parameters, 3 for case 1: κ, f intra , f stat , and 4 for case 2: κ, f intra , f stat , d ) and M the total number of measurements (i.e. the number of acquired directions, M = 242).

BIC = -2log(L) + Plog(M) (5.5)
This criterion was computed to choose and fix d . However, the median BIC values obtained in case 1 and 2 (see Figure 5.37) being close (-694 against -678), the selected initialization was set such as to obtain a consistent orientation dispersion map, which did not correspond to the lowest BIC value, i.e. case 1.

Use of NODDI quantitative maps to improve the delineation of specific structures Figure 5.38 depicts the microstructural feature maps obtained from NODDI, in axial (top), sagittal (middle) and

Chapter 5. Investigation of the human hippocampus and brainstem 132 coronal (bottom) views. These maps particularly emphase structures such as: the inferior colliculus, the periaqueductal gray matter, the corticospinal tract, the inferior olivary, and the dentate nucleus.

The inferior colliculus (red circles) presents a high orientation dispersion (OD) and is well delineated from the intracellular volume fraction and the stationary fraction maps, which is consistent with the fact that this is a highly connected nucleus, in particular as part of the auditory pathway. The periaqueductal gray matter, or PAG (dotted red arrows), appears with a hypointense contrast in the intracellular volume fraction map, and a hypersignal in the OD map. This is in accordance with the fact that it is made of gray matter, and thus appears with the same contrast than the cerebellar cortex:

high orientation dispersion as well as low intracellular volume fraction and stationary fraction. The inferior olivary (light blue arrows) appears with a hyperintense contrast in the OD map, which is consistent with the fact that it is a nucleus. However, while this structure is well defined in the stationary volume fraction map, it is not visible in the intracellular volume fraction map. In fact, stationary fraction seems to embed part or all of the intracellular fraction at the level of the medulla. This is also the case for the corticospinal tract, or CST (deep blue arrow), depicting abnormally low intracellular volume fraction values (in the order of 10 -8 ), while its associated stationary volume fraction is high (0.7-0.8). Nevertheless, the CST depicts very low OD values, which is consistent with its underlying anatomy consisting of well organized fiber bundle (see Figure 5.27.b showing high fractional anisotropy values). The cerebellar dentate nucleus is clearly visible in the stationary fraction map, but not in the intracellular volume fraction map that also depicts abnormally low values in this area.

To conclude, microstructural features maps show new contrasts, consistent with the brainstem anatomy.

The stationary compartment seems to embed part or all of the intracellular compartment at the level of the medulla. This could be explained by the fact that d was fixed and maybe not adapted for this region, or the signal quality may be of lesser quality in this area. These results also call for prudence with regard to the stationary fraction that can take values much higher than 0.3 and probably embed other compartments. Nevertheless, NODDI maps unquestionably bring new contrasts that could be applied in the future in combination with the anatomical scan and tensor derived scalar images such as FA, MD or CED maps to further improve the brainstem segmentation. Moreover, the ability to analyze the axonal density profile along extracted tracts could be of potential benefit for the study of neurological diseases such as multiple sclerosis. For instance, comparing the axonal density profiles between control and MS patients on a set of extracted tracts could bring new insights about the disease specificities.

Discussion

The main contributions of this work are: 2. the establishment of a protocol to manually segment 51 of the 73 brainstem nuclei. This is the first step towards the establishment of a high resolution anatomical probabilistic atlas of the human brainstem structural delineation of most human brainstem nuclei, similar to existing probabilistic atlases for the cortex or the hippocampus.

3. the investigation of the human brainstem connectivity and microstructure, revealing not only the major tracts of the brainstem, but also projections of finer structures.

Comparison with existing studies In vivo segmentation of the brainstem is limited by the poor contrast and spatial resolution achievable with clinical MRI, as well as its anatomical position that Chapter 5. Investigation of the human hippocampus and brainstem 134 yields to many imaging artifacts in MRI. This is why in vivo studies generally focus on the delineation of one or two nuclei or subregions, such as the substantia nigra, the red nuclei, the PAG, or the locus coeruleus [START_REF] Lehéricy | 7 tesla magnetic resonance imaging: a closer look at substantia nigra anatomy in parkinson's disease[END_REF], Visser et al., 2016[START_REF] Langley | Reproducibility of locus coeruleus and substantia nigra imaging with neuromelanin sensitive MRI[END_REF][START_REF] Pyatigorskaya | Comparative study of MRI biomarkers in the substantia nigra to discriminate idiopathic parkinson disease[END_REF][START_REF] García-Lorenzo | The coeruleus/subcoeruleus complex in rapid eye movement sleep behaviour disorders in parkinson's disease[END_REF][START_REF] Priovoulos | High-resolution in vivo imaging of human locus coeruleus by magnetization transfer MRI at 3T and 7T[END_REF][START_REF] Olivia K Faull | Functional subdivision of the human periaqueductal grey in respiratory control using 7Tesla fMRI[END_REF][START_REF] Coulombe | Intrinsic functional connectivity of periaqueductal gray subregions in humans[END_REF]. The latest published probabilistic atlas of the brainstem is a template including five mesopontine nuclei [START_REF] Bianciardi | A probabilistic template of human mesopontine tegmental nuclei from in vivo 7 T MRI[END_REF]. Regarding ex vivo studies performed on preclinical MRI systems, [START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF] acquired an entire human brainstem at 11.7 T, using diffusion and anatomical scan with an isotropic resolution of 255 µm, and segmented cranial nerve, inferior olivary and pontine nuclei.

The MRI data were nonlinearly mapped to the Montreal Neurological Institute (MNI) stereotaxic coordinate space, in order to provide a prove the feasibility of creating an ex vivo MR-based atlas of the human brainstem. Thus, to our knowledge, the segmentation protocol proposed in this work is the most complete established using MRI data.

A few studies investigate the brainstem microstructure, and among them, rare are those including the brainstem in its entirety. The evolution of the orientation dispersion index (ODI) and the neurite density index (NDI) has been studied through the lifespan [START_REF] Shin | White matter changes of neurite density and fiber orientation dispersion during human brain maturation[END_REF], and in the late childhood [START_REF] Mah | Detailing neuroanatomical development in late childhood and early adolescence using noddi[END_REF]. The first study only included a ROI in brainstem projection tracts, and the second study included the brainstem to perform k-means clustering of ODI and NDI features.

Other studies quantified the changes induced by PD in the substantia nigra [START_REF] Kamagata | Neurite orientation dispersion and density imaging in the substantia nigra in idiopathic parkinson disease[END_REF],

and globally in the pons and the midbrain [START_REF] Surova | Alterations of diffusion kurtosis and neurite density measures in deep grey matter and white matter in parkinson's disease[END_REF]. Regarding ex vivo exploration of the human brainstem microstructure, only one study has been performed on a human brainstem at 11.7 T, but the results are not yet published. [START_REF] Sebille | Detection de cibles pour la neuromodulation dans les maladies neurodegeneratives: nouveaux apports de l'IRM de diffusion[END_REF] scanned a brainstem sample using a 3D segmented EPI sequence with three shells (b = 500/4000/10000 s/mm 2 ), 4/20/64 directions, and an isotropic resolution of 200 µm. The NODDI model was performed, providing ODI and intracellular volume fraction maps. Unfortunately, the thesis manuscript do not report any further analysis using these maps. This study provides diffusion data with a higher spatial resolution, but with less diffusion measurements. Therefore, our study is the first one providing an ultra-high spatial and angular resolution dataset. Moreover, NODDI maps were analyzed in order to extract, for the first time, profiles of NODDI characteristics along tracts.

Known large bundles have partly already been reconstructed or identified in other studies, in particular in ex vivo studies. [START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF] reconstructed fibers of the corticospinal tract, transverse pontine fibers, the medial lemniscus, and the middle cerebellar peduncle. Additionally, using ultrahigh resolution DTI images (125 µm isotropic but acquired with less than 20 diffusion directions) on the medulla, the medial longitudinal fascicle, the olivarycerebellar fibers, and the solitary tract were reconstructed. This is, to date, the most complete fibers extraction of the human brainstem, based on DTI model. A few studies have been performed using more sophisticated diffusion sampling schemes or signal models. [START_REF] Ford | Imaging white matter in human brainstem[END_REF] imaged a post mortem human brainstem at 11.1 T with an isotropic resolution of 333 µm along 64 directions. The water displacement probability was estimated using a mixture of Wishart distributions to account for crossings, and corticopontine/corticospinal tracts, the superior and middle cerebellar peduncle, as well as the medial lemniscus were extracted. [START_REF] Calabrese | Postmortem diffusion MRI of the human brainstem and thalamus for deep brain stimulator electrode localization[END_REF] used a HARDI dataset acquired with an isotropic spatial resolution of 200 µm along 120 diffusion directions, and a b-value of 4000 s/mm 2 . However, their reconstruction of the tremor circuit, aiming at improving deep brain stimulation, was based on the DT model. [START_REF] Birgit R Plantinga | Ultra-high field MRI post mortem structural connectivity of the human subthalamic nucleus, substantia nigra, and globus pallidus[END_REF] used constrained spherical deconvolution-based probabilistic tractography to infer the connectivity of the substantia nigra. Finally, [START_REF] Henssen | Ex-vivo visualization of the human trigeminal pathways using 11.7T diffusion MRI and unique microscopy data[END_REF] reconstructed the trigeminal pathways, scanning a post mortem brainstem at 11.7 T, along 256 diffusion directions and at an isotropic resolution of 500 µm. The BedpostX algorithm was used to account for fiber crossings within voxels [START_REF] Behrens | Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?[END_REF]. Our study is thus the first one to combine the use of an ultra-high resolution dataset (400 directions, 300 µm) isotropic, b = 4500 s/mm 2 ) and a reconstruction model resolving fiber crossings within a voxel (ODF field computed with aQBI model). The use of an analytical Q-ball model enabled a more precise deciphering of the complex connectivity of the brainstem and, for the first time, a fine reconstruction of the locus coeruleus projections.

Limitations The aim of this chapter was to provide proofs of concept for two specific anatomical regions (the hippocampus and the brainstem) that UHF MRI (11.7T) with strong gradients may offer unprecedented spatial and angular resolutions. The aim was to assess the feasibility of a larger project aiming at scanning an entire human brain.

To go a step further, clustering techniques could also been applied to the connectogram to provide clusters of co-localized fibers sharing similar geometries and belonging to the same white matter tract. This technique should accelerate the construction of a probabilistic atlas of the brainstem inner connectivity. Moreover, the brainstem connectivity being maddeningly complex, adding a fiber clustering step before or instead of the extraction of known pathways would reduce the dimensionality of the problem and facilitate the process.

Clinical prospects Nowadays, there is no MR-based atlas of the human brainstem anatomy, connectivity, or microstructure. However, it would be of greatest value for clinical applications.

This could contribute to precisely determine the nervous centers and pathways affected by brainstem lesions, but also to locate therapeutic targets in the brainstem. For instance, the combination of highresolution MRI, MR-based atlases of the brainstem anatomy and connectivity, and neuronavigation systems, might help for the localization of the PPN, whose electrical stimulation is an emergent therapy for parkinsonian patients suffering from intractable akinesia [START_REF] Mazzone | Implantation of human pedunculopontine nucleus: a safe and clinically relevant target in parkinson's disease[END_REF].

The brainstem is also well-known for being one of the first structure affected by Parkinson's disease.

According to Braak staging [START_REF] Braak | Staging of brain pathology related to sporadic parkinson's disease[END_REF], the disease first affects the dorsal IX/X nuclei and the intermediate reticular zone in the medulla and the olfactory bulb (stage 1), then gain setting nuclei of the lower brainstem (gigantocellular reticular nucleus, caudal raphe nuclei, locus coeruleus, stage 2), followed by the substantia nigra (stages 3 and 4), before reaching the thalamus and specific

Chapter 5. Investigation of the human hippocampus and brainstem 136 cortical areas (stages 5 and 6). Detecting anatomical modifications of these structures, especially those affected during the first stages, could thus provide an early marker for PD. Its diagnosis being currently based on neurological examination, it can lead to misdiagnosis. Moreover, in early PD, the full triad of clinical symptoms and signs (rest tremor, bradykinesia, and rigidity) are not visible.

Thus, there is a need for better diagnostic tools, and anatomical and diffusion MR-based atlases could be of great help.

Therefore, a PhD position has been opened in the University of Tours to continue and complement the work initiated here. Eight samples will be scanned at Neurospin, and manually segmented following the protocol presented in this chapter. The ultimate goal is to build a multimodal atlas of the human brainstem in order to automatically segment in vivo images obtained at lower resolution.

Conclusion

This study constitutes a second proof of concept for the use of ultra-high field MRI with strong gradients to decipher brain structures connectivity and microstructure. We demonstrated that UHF-MRI and diffusion MR microscopy are powerful to map not only the inner structures of the brainstem, but also its fine connectivity revealed by HARDI-based tractography, as demonstrated by the mapping of the structural connectivity of the locus coeruleus. The enhanced contrast brought by NODDI was also assessed, thus allowing to go a step forward in the undertstanding of the anatomo-functional organization of the brainstem. These first results encourage to further investigate this unique high resolution DW dataset to develop a novel atlas of the brainstem connectivity and its microstructure.

Moreover, an original ex vivo segmentation protocol of the human brainstem was established, including 17 proper nuclei, 13 nuclei of cranial nerves, 21 reticular nuclei, three structures of the diencephalon and four of the cerebellum. This segmentation, developed by Dr F. Lechanoine (Bretonneau University Hostpital, Tours), was performed from the 100 µm anatomical image and took advantage of various diffusion-based contrasts (FA or CED maps). This work paves the way for the establishment of a multimodal probabilistic atlas of the human brainstem.

In the future, these results could be of potential benefit to provide an early marker for Parkinson's disease by detecting anatomical modifications of brainstem structures affected during the first stages. only to the targeted cell populations. OCT [START_REF] Magnain | Optical coherence tomography visualizes neurons in human entorhinal cortex[END_REF] is a high resolution (up to 1 µm in plane) optical technique analogous to ultrasound imaging as it measures the backscattered light of the sample, and is sensitive to differences in the refraction index in tissue. 3D-PLI [START_REF] Axer | A novel approach to the human connectome: ultra-high resolution mapping of fiber tracts in the brain[END_REF] gives the opportunity to observe the 3D orientation of the myelinated fibers without any staining procedure, using the birefringence of the myelin sheath with an in-plane resolution of 1.3 µm and slices of 70 µm. In contrast with other optical methods, whole human brain imaging is feasible, even if axons with a diameter at the range of the spatial resolution can-not be distinguished. This optical technique has already been applied to ex vivo human hippocampi by Zeineh et al. [2016],

Global discussion

but the results have only been compared with in vivo DTI-based color-encoded maps. Despite their remarkable spatial resolution, optical methods also present inherent limitations compared with MRI.

First, the sample has to be cut into slices for PLI and STP, and at least into blocks with a flat surface for OCT [START_REF] Magnain | Blockface histology with optical coherence tomography: a comparison with nissl staining[END_REF]. Furthermore, contrary to dMRI, no real 3D acquisition is possible.

Given the extremely large image size, supercomputing facilities are then required to precisely align the serial sections and produce three-dimensional reconstructions. Contrary to diffusion MRI that gives access to quantitative microstructural characteristics, such as axonal density and diameter, the novel optical methods described above do not offer such a possibility.

In addition to optical methods, other techniques exist to study the human white matter. Histology is probably the most commonly used method to validate anatomical, connectivity, or microstructure results. However, this technique do not provide specific coloring of the fibers according to their orientation and cutting slices induce a loss of 3D coherence. An old but efficient approach to dissect white matter fibers was introduced by Klingler, relying on a freezing of the sample at -80°to separate individual fibers. It gave rise to a renew of interest with the recent combination of this technique with a laser scanner, allowing to digitize the layers of fibers during the dissection and thus providing a numerical mask of the dissected white matter bundle [START_REF] Zemmoura | How klingler's dissection permits exploration of brain structural connectivity? an electron microscopy study of human white matter[END_REF]. However, this method, requiring time and expertise, remains limited to the mesoscopic scale. In addition, it practically becomes really complex in regions of crossing fibers.

Among all these techniques, 3D-PLI was chosen to validate the hippocampus connectivity. Indeed, this method can probably be considered as mature enough for the validation of diffusion MRI [Zeineh et al., 2016, Mollink et al., 2017]. The human hippocampus sample scanned in the frame of this thesis was scanned using the 3D-PLI setup of our research partner in Jülich and is currently being analyzed.

Tractography can also be performed from the 3D-PLI data and compared to the results of this work.

The brainstem sample has not been analyzed by an alternative modality yet, but could be explored with 3D PLI in the same ways.

Chapter 5. Investigation of the human hippocampus and brainstem 138

Limitations

Some limitations are common to both studies.

First, the samples are fixed by immersion, and there is a risk for the fixation to be inhomogeneous, as the fixative has to diffuse from the surface to the deepest structures. The time it takes for fixative to permeate through the brain can lead to higher fixation time for the deepest structures, inducing higher degradation of the tissue, for instance from autolysis. This inhomogeneity could be a confound when reporting gradients in microstructure maps. In order to minimize this risk, the samples were immersed several months, which is enough to entirely fix the tissue. Moreover, in case of high inhomogeneities resulting from the fixation, clear non-anatomical borders would appear in the structural MRI images. Since no kind of severe contrasts (independent from anatomical structures) were observed neither with the hippocampus nor with the brainstem, the homogeneity of the fixation can be assumed. In addition, because these two structures are located in the periphery of the brain, there is a reduced risk of fixation inhomogeneities. However, it is impossible to completely eliminate this confound with one specimen, and further studies would benefit from having more samples.

For both studies, it would also be of great value to investigate alternative reconstructions using the acquired HYDI dataset, in order to go beyond HARDI models. Advanced models could be considered, like the mean average propagator (MAP-MRI) reconstruction [ Özarslan et al., 2013a] or the fiber orientation distribution (FOD) reconstruction [START_REF] Jeurissen | Multitissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data[END_REF], relying both on a multiple shell sampling of the q-space. On the one hand, MAP-MRI would provide the estimation of further information like the return-to-origin probability, sensitive to compartment sizes, or non-Gaussianity, providing insights about the tissue complexity. On the other hand, FODs inferred from multipleshell acquisitions are based on a multi-tissue constrained spherical deconvolution that would provide more precise fiber orientation estimates at the interface between tissues, thus yielding improved tractograms. Such HYDI-based models may improve the quality of the obtained tractograms.

Diffusion MR microscopy has become a growing topic of interest in the diffusion MRI community, and models are constantly improving. Nowadays, the NODDI model has become very popular due to its easy implementation from the acquisition protocol to the analysis pipeline. Alternative models should be investigated in the future, in particular those probing further features like the mean axon diameter or the myelin water fraction. Because we took a special care to establish an acquisition protocol densely sampling the q and diffusion time spaces, the ActiveAx model could be investigated in the future using our HYDI diffusion dataset. The latest improvements of the model now integrate a time dependence for the extra-axonal space that should allow to finely probe maps of the mean axon diameter within the human brain with fewer bias.

Finally, there is one point which has not yet been raised: the variation of the diffusion time. The hippocampus and brainstem datasets were designed to be used with multiple biophysical and signal models. Indeed, the variation of ∆ induces variable diffusion times, allowing to probe compartment sizes, e.g. axon diameters. However, this time dependence is not taken into account in the NODDI model, that has been developed considering a fixed diffusion time (and TE). Correcting terms exist Chapter 5. Investigation of the human hippocampus and brainstem 139 to compensate the diffusion time dependency in the extra-axonal space [START_REF] De Santis | Including diffusion time dependence in the extra-axonal space improves in vivo estimates of axonal diameter and density in human white matter[END_REF]. Contrary to NODDI or ActiveAx, in which the perpendicular diffusivity is set with a simple tortuosity model (d ⊥ =d (1-f intra )), a correcting term (A ln(∆/δ )+3/2 ∆-δ /3 ) is added to the perpendicular diffusivity term, taking into account the fact that the diffusion orthogonal to the bundle is dependent on ∆. The question is therefore whether this correction can be applied to our data. A has been shown to be proportional to the square of the axonal radius [START_REF] Burcaw | Mesoscopic structure of neuronal tracts from time-dependent diffusion[END_REF]. As the NODDI model considers that the axonal radius is null (stick model), applying this correction would not make any sense. Another point is that the variation of diffusion time (and TE) is not considered in signal models based on HYDI data such as MAP-MRI [ Özarslan et al., 2013a]. Therefore, for the rest of this thesis work, the acquisition protocol has been designed using a unique TE and diffusion time, in order to use NODDI and MAP-MRI without any additional contrast that would not be originally included in the models.

All these limitations were taken into account in the following work.

Conclusion

This chapter provided proofs of concept for the establishment of a post mortem ultra-high resolution atlas of the entire human brain. Acquisition protocols have been designed, improved, and tested with recent signal and biophysical models. High quality data of the human hippocampus and brainstem were obtained. In both cases, the anatomical scan was manually segmented, providing anatomical input for the connectivity or microstructural analysis. Streamline regularized deterministic and probabilistic tractograms, as well as quantitative microstructural maps were computed, giving access to fine connectivity and microstructure of the two samples. Known pathways were successfully reconstructed, and the intracellular volume fraction maps obtained from NODDI were shown to provide new contrasts facilitating the segmentation.

The following work took advantage of these preliminary results to obtain the final acquisition protocol used to scan the entire human brain sample at 11.7 T.

Chapter 6

Laminar structure of the cortex inferred from MR-based myelo-and cytoarchitectural features

The human cerebral cortex has a laminar structure, each layer presenting distinct cellular organization and myelination. Back in 1909, Brodmann characterized the cytoarchitecture of the cortical ribbon and divided a post mortem human brain cortex into 43 areas based on the shape and density of neuron bodies within the cortical layers. The boundary of a given area corresponded to a transition in the shape or density of neurons observed across the different layers, perpendicular to the pial surface. Characterizing the myelination of white matter fibers entering the cortex and connecting cortical areas brings a complementary information that can also be exploited to analyze the cortex. Indeed, it appeared that the degree of myelination of fibers varies from a layer to another, thus providing another way to probe the cortical lamination. This is called the myeloarchitecture. Probing the cytoarchitecture and myeloarchitecture of the cortical mantel in vivo remains a challenging task [START_REF] Zilles | Centenary of brodmann's map-conception and fate[END_REF]. To date, most studies have been performed ex vivo, for instance using immuno-histo-stainings specific to neuronal cells, myelin, or neurotransmitter receptors [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF][START_REF] Nieuwenhuys | A map of the human neocortex showing the estimated overall myelin content of the individual architectonic areas based on the studies of adolf hopf[END_REF], Amunts and Zilles, 2015].

More recently, in vivo MR based methods gave access to parcellations using tractography or a multimodal approach combining myeloarchitectony and function MRI [START_REF] Lefranc | Groupwise connectivity-based parcellation of the whole human cortical surface using watershed-driven dimension reduction[END_REF], Glasser et al., 2016b]. Going even further, in 2013, de Martino et al. showed that it was now possible to investigate laminar functional responses with the use of UHF MRI [START_REF] De | Cortical depth dependent functional responses in humans at 7T: improved specificity with 3D GRASE[END_REF].

It has therefore become of major interest to be able to segment the cortical layers in vivo. [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF] suggested the use of a Gaussian mixture model applied on a T1 quantitative map to automatically segregate cortical layers. However, T1 contrast is not the only contrast revealing the cortical lamination, the NODDI model having recently been shown to accurately highlight the lamination of Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 142 the human neocortex and hippocampus [Kleinnijenhuis et al., 2013a[START_REF] Beaujoin | Post-mortem inference of the human hippocampal connectivity and microstructure using ultra-high field diffusion MRI at 11.7[END_REF].

This chapter proposes to extend Lifshits' approach to the study of an ex vivo visual cortex by using not only T1 relaxation but also microstructural-based layers clustering. The first section reviews the existing techniques to identify the cortical layers based on MR contrasts. The second section presents the acquisition protocol and data analysis methods used to generate quantitative T1 and NODDI maps. In a third section, the unsupervised clustering algorithm applied to the T1 and the intracellular volume fraction map arising from NODDI is explained. Cluster maps obtained from T1 and neurite density maps are discussed and compared, which led to the combination of both quantitative maps to provide a multivariate clustering. The last section, dedicated to the discussion, compares this chapter work with other existing studies, discusses its limitations and possible improvements, and finally presents potential clinical prospects.

Investigating the cortical lamination using MRI: state of the art

With the technological improvement enabling the visualization of laminar functional responses, there is a growing need for the anatomical detection of the cortical layers, as evidenced by the number of publications on this issue as well as the two recent reviews summarizing the latest advances in MRI imaging of the cortical layers: [START_REF] Trampel | In-vivo magnetic resonance imaging (MRI) of laminae in the human cortex[END_REF] and [START_REF] Assaf | Imaging laminar structures in the gray matter with diffusion MRI[END_REF].

The challenge of recovering cortical layers

The cortical cyto-and myelo-architecture was primarily investigated through invasive histology.

While magnetic resonance imaging is the noninvasive, in vivo imaging modality providing the best spatial resolution, mapping cortical layers remains incredibly challenging. Cortical thickness varies according to the location, typically 4.2-5.7 mm in the primary motor cortex, 2.5-2.9 mm in the primary visual cortex, 2.0-3.4 mm in the secondary visual cortex, and only 2.4-2.7 mm in the primary somatosensory cortex, as reported by [START_REF] Zilles | Anatomical basis for functional specialization[END_REF]. High resolution is thus required to distinguish cortical layers, requiring the use of ultra-high magnetic fields to overcome low signal-tonoise levels. In addition, the variation of MR signal observed in the direction perpendicular to the cortex is very subtle when using conventional sequences and resolutions [START_REF] Braitenberg | A note on myeloarchitectonics[END_REF], which imposes the use of MR sequences able to provide high contrast levels ( § 6.1.3).

Study of the primary visual cortex

Despite these limitations, MRI remains a promising approach for visualizing intracortical anatomy, as it is highly sensitive to the presence of myelin (and iron) in the cortex [START_REF] Stueber | Myelin and iron concentration in the human brain: a quantitative study of MRI contrast[END_REF]. A significant part of existing MRI studies aiming at probing the cortical lamination concentrate their effort on the study of the primary visual cortex (V1) or Brodmann area (BA) 17. There are several Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 143 reasons for this. First, this region is characterized by a prominent inner granular layer, the layer IV, containing highly myelinated tangential fiber pathways that form the outer band of Baillarger or stria of Gennari [Gennari, 1782[START_REF] Girish M Fatterpekar | Cytoarchitecture of the human cerebral cortex: Mr microscopy of excised specimens at 9.4 tesla[END_REF] (see Figure 6.1). This cortex is thus often referred to as "striate cortex". The line of Gennari is a special case of the outer band of the lines of Baillarger (cf. Figure 2.12). The lines of Baillarger consist of two bundles of myelinated fibers, located in the internal granular layer of layer IV and internal pyramidal layer of layer V. Few MRI studies have reported the visualization of this particular dual-band structure in vivo and ex vivo [START_REF] Nathan B Walters | In vivo identification of human cortical areas using high-resolution MRI: an approach to cerebral structure-function correlation[END_REF][START_REF] Md Waehnert | Anatomically motivated modeling of cortical laminae[END_REF][START_REF] Aggarwal | Probing region-specific microstructure of human cortical areas using high angular and spatial resolution diffusion MRI[END_REF][START_REF] Fracasso | Lines of baillarger in vivo and ex vivo: Myelin contrast across lamina at 7 T MRI and histology[END_REF], probably due to the lower contrast and smaller thickness that characterize these lines, as compared to the stria of Gennari.

Despite its 300 µm thickness [START_REF] Von | The cytoarchitectonics of the human cerebral cortex[END_REF], the line of Gennari is visible to the naked eye and has been successfully visualized in studies performed at 1.5 T [START_REF] Vincent P Clark | In vivo myeloarchitectonic analysis of human striate and extrastriate cortex using magnetic resonance imaging[END_REF][START_REF] Nathan B Walters | Observer-independent analysis of high-resolution mr images of the human cerebral cortex: In vivo delineation of cortical areas[END_REF]] and 3 T [Barbier et al., 2002[START_REF] Bridge | High-resolution MRI: in vivo histology?[END_REF], Clare and Bridge, 2005[START_REF] Turner | Optimised in vivo visualisation of cortical structures in the human brain at 3 T using ir-tse[END_REF]. Another reason playing in favor of the study of the occipital cortex is that its anatomical structure has received extensive histological study [Palomero-Gallagher andZilles, 2017, Rockland and[START_REF] Kathleen | Terminal arbors of individual "feedback" axons projecting from area v2 to v1 in the macaque monkey: A study using immunohistochemistry of anterogradely transported phaseolus vulgaris-leucoagglutinin[END_REF] and is not as debated as other cortical areas1 . V1 was among the first areas for which a structure-function relationship was successfully established [START_REF] Shaw | The exact histological localisation of the visual area of the human cerebral cortex[END_REF], inspiring studies to investigate the correlation between cortical lamination and executed function [START_REF] Clare | Methodological issues relating to in vivo cortical myelography using MRI[END_REF], Bridge et al., 2005[START_REF] Hinds | Locating the functional and anatomical boundaries of human primary visual cortex[END_REF][START_REF] Peter J Koopmans | Layer-specific bold activation in human v1[END_REF][START_REF] Rosa M Sánchez-Panchuelo | Correspondence of human visual areas identified using functional and anatomical MRI in vivo at 7 T[END_REF] or another investigating the Gennari stripe in congenitally blind people, which was found to form and persist independently of visual sensation [START_REF] Trampel | Do the congenitally blind have a stria of gennari? first intracortical insights in vivo[END_REF].

MR contrasts revealing cortical features

For many decades, research aimed at finding which MR contrast was the most suitable to delineate the cortical lamination. PD, T1, T2 * contrasts, and, to a lesser extend T2 contrast, were suggested for discrimination between the layers. In 1992, Clark et al. showed that high-resolution ( 400 µm in plane resolution) PD-weighted MRI could be used to delineate the border between the striate (BA17)

and the extrastriate (BA18 and BA19) cortex. The ability to discriminate between these regions was attributed to the heavily myelinated layer IV of V1 (stria of Gennari). Other studies added a preparation (inversion-recovery) pulse ( § 4.4.1.2) to increase the T1-weighted contrast [START_REF] Sh Koenig | Relaxometry of brain: why white matter appears bright in MRI[END_REF][START_REF] Eickhoff | High-resolution MRI reflects myeloarchitecture and cytoarchitecture of human cerebral cortex[END_REF], and, for a further enhancement of the line of Gennari, a magnetization transfer contrast has been added to the T1-weighting with the use of a Turbo Spin Echo (TSE) after the inversion pulse [START_REF] Turner | Optimised in vivo visualisation of cortical structures in the human brain at 3 T using ir-tse[END_REF]. A discrimination of the stria of Gennari was obtained with post mortem samples from T2-weighted and intermediate-weighted images as well [START_REF] Girish M Fatterpekar | Cytoarchitecture of the human cerebral cortex: Mr microscopy of excised specimens at 9.4 tesla[END_REF][START_REF] Nathan B Walters | In vivo identification of human cortical areas using high-resolution MRI: an approach to cerebral structure-function correlation[END_REF][START_REF] Eickhoff | High-resolution MRI reflects myeloarchitecture and cytoarchitecture of human cerebral cortex[END_REF]. However, over the years, T1 contrast was preferred over T2 as the T1-weighted contrast, obtained from an inversion recovery (IR) sequence, remains . This is due to the fact that sections in (b) were obtained from deep-frozen, unfixed tissue, and no differentiation of the staining was performed much higher. Moreover, T1 has been shown to be closely related to myelin content, in particular to the cholesterol that is bound to myelin. This observation was made both in vivo [START_REF] Sh Koenig | Relaxometry of brain: why white matter appears bright in MRI[END_REF][START_REF] Seymour | Cholesterol of myelin is the determinant of gray-white contrast in MRI of brain[END_REF], and ex vivo [START_REF] Jp Mottershead | High field MRI correlates of myelin content and axonal density in multiple sclerosis[END_REF][START_REF] Schmierer | Magnetization transfer ratio and myelin in postmortem multiple sclerosis brain[END_REF]. Therefore, T1 contrast appears to be a good candidate to probe the cortical myeloarchitecture.

T2 * contrast has also been shown to successfully highlight the stria of Gennari, both its myelination and iron content contributing to its susceptibility difference compared to the surrounding gray matter [START_REF] Rosa M Sánchez-Panchuelo | Correspondence of human visual areas identified using functional and anatomical MRI in vivo at 7 T[END_REF][START_REF] Jeff H Duyn | High-field MRI of brain cortical substructure based on signal phase[END_REF][START_REF] Deistung | Toward in vivo histology: a comparison of quantitative susceptibility mapping (qsm) with magnitude-, phase-, and r2 * -imaging at ultra-high magnetic field strength[END_REF].

Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 145

In contrast to conventional weighted sequences, quantitative maps of T1, T2, PD and MT saturation can also be used to map cortical layers. These maps present the advantage of improving the comparability between subjects as the value does not depend on the shim adjustment or the static gain of the acquisition (except for PD). Recently, high-resolution T1 (or R1= 1/T1) quantitative images were leveraged to map the myeloarchitecture of the entire cortical ribbon [START_REF] Lutti | Using high-resolution quantitative mapping of r1 as an index of cortical myelination[END_REF], Sereno et al., 2012], as well as to obtain intracortical profiles of the auditory cortex [START_REF] Dick | In vivo functional and myeloarchitectonic mapping of human primary auditory areas[END_REF]. Adopting another approach, [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF] et al., 2011[START_REF] Aggarwal | Probing region-specific microstructure of human cortical areas using high angular and spatial resolution diffusion MRI[END_REF][START_REF] Stéphane V Sizonenko | Developmental changes and injury induced disruption of the radial organization of the cortex in the immature rat brain revealed by in vivo diffusion tensor MRI[END_REF][START_REF] Matthew | Quantification of anisotropy and fiber orientation in human brain histological sections[END_REF], Kleinnijenhuis et al., 2013b] and in vivo [START_REF] Matthew D Budde | The contribution of gliosis to diffusion tensor anisotropy and tractography following traumatic brain injury: validation in the rat using fourier analysis of stained tissue sections[END_REF], McNab et al., 2013b[START_REF] Truong | Cortical depth dependence of the diffusion anisotropy in the human cortical gray matter in vivo[END_REF]. Fiber orientation density function (fODF) is another feature of dMRI proven to give insights about the cortical lamination, for instance revealing structures of aligned fibers either perpendicular or parallel to the pial surface (e.g. lines of Baillarger) [START_REF] Tim B Dyrby | An ex vivo imaging pipeline for producing high-quality and high-resolution diffusionweighted imaging datasets[END_REF][START_REF] Aggarwal | Probing region-specific microstructure of human cortical areas using high angular and spatial resolution diffusion MRI[END_REF][START_REF] Stéphane V Sizonenko | Developmental changes and injury induced disruption of the radial organization of the cortex in the immature rat brain revealed by in vivo diffusion tensor MRI[END_REF][START_REF] Matthew | Quantification of anisotropy and fiber orientation in human brain histological sections[END_REF], Kleinnijenhuis et al., 2013b, McNab et al., 2013b[START_REF] Jaermann | Preliminary experience with visualization of intracortical fibers by focused highresolution diffusion tensor imaging[END_REF][START_REF] Robin M Heidemann | Diffusion imaging in humans at 7T using readoutsegmented EPI and GRAPPA[END_REF], Leuze et al., 2014[START_REF] Dudink | Recent advancements in diffusion MRI for investigating cortical development after preterm birth-potential and pitfalls[END_REF]. Finally, microstructural multicompartmental models such as NODDI or CHARMED are suitable for use in heterogeneous neural environment. NODDI has been used to observe the cortical lamination in both the primary visual cortex [Kleinnijenhuis et al., 2013a] and the hippocampus [START_REF] Beaujoin | Post-mortem inference of the human hippocampal connectivity and microstructure using ultra-high field diffusion MRI at 11.7[END_REF]. Kleinnijenhuis et al. [2013a] showed that the κ concentration map revealed several layers with different order of fiber orientation dispersion. In addition, the intracellular volume fraction was found to be the NODDI feature providing the largest contrast between cortical layers. As the tissue geometry, density, and general morphometry affect the signal, dMRI appears to be a good candidate for reflecting the underlying tissue cytoarchitecture ( § 3.2.7.2), which is the foundation of the original definition of cortical layers.

Another way to parcellate the cortex is to use the connectivity profile of a region and segregate this region into subregions with clustering methods. Several studies have succeeded in segregating cortical areas based on this method that only requires the individual connectograms obtained using fiber tracking methods [START_REF] Gong | Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography[END_REF][START_REF] Lefranc | Groupwise connectivity-based parcellation of the whole human cortical surface using watershed-driven dimension reduction[END_REF][START_REF] Anwander | Connectivity-based parcellation of broca's area[END_REF][START_REF] Johannes C Klein | Connectivity-based parcellation of human cortex using diffusion MRI: establishing reproducibility, validity and observer independence in ba 44/45 and sma/pre-sma[END_REF][START_REF] Stephan Gorbach | Hierarchical information-based clustering for connectivity-based cortex parcellation[END_REF][START_REF] Louise Cloutman | Connectivity-based structural and functional parcellation of the human cortex using diffusion imaging and tractography[END_REF][START_REF] Moreno-Dominguez | A hierarchical method for whole-brain connectivity-based parcellation[END_REF], Fan et al., 2016, Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 146 [START_REF] Gao | Tests of cortical parcellation based on white matter connectivity using diffusion tensor imaging[END_REF]. Other studies took advantage of T1/T2-weighted images or DT-based quantitative maps to provide a consistent parcellation as well [Glasser et al., 2016b, Glasser and[START_REF] Matthew | Mapping human cortical areas in vivo based on myelin content as revealed by T1-and T2-weighted MRI[END_REF]].

Towards an automatic segmentation of cortical layers

The previous mentioned studies have shown that at high spatial resolutions, the cortical lamination can be manually delineated based on the average organization of local neurite orientation as well as using T1/T2 * contrasts. However, few studies have explored the possibility to automatically segment the cortical layers. Beyond manual delineation of cortical layer and area boundaries, dMRI and

T1 relaxometry yet seem to lend themselves to automatic clustering of architectural properties and localization of boundaries of cortical layers [START_REF] Bastiani | Automatic segmentation of human cortical layer-complexes and architectural areas using ex vivo diffusion MRI and its validation[END_REF][START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF]. [START_REF] Bastiani | Automatic segmentation of human cortical layer-complexes and architectural areas using ex vivo diffusion MRI and its validation[END_REF] investigated the possibility to automatically segment human cortical layercomplexes and area boundaries by unsupervised clustering of their diffusion tensor-based scalar features. The study focused on a human primary motor and premotor cortex. [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF] applied a Gaussian mixture model (GMM) to a T1 quantitative map. The fit of the whole brain T1

histogram revealed classes assumed to correspond to cortical layers. The adequate number of components (classes) was determined using a Bayesian information criterion (BIC). Depending on the image resolution, they fitted from one T1-weighted component per voxel for high resolution data (rat brain acquired at 110 µm isotropic) to seven T1-weighted components for low resolution data (human brain acquired at 3 mm isotropic) in order to account for the partial volume effect.

In this chapter work, both approaches are compared and then combined to automatically cluster the cortical lamination, based on dMRI data (and more specifically microstructural quantitative maps from NODDI) and T1 relaxometry data assumed to be relevant to decipher the underlying cyto-and myelo-architectures.

6.2 Material and methods

Tissue sample and container

The study was carried out on a post mortem brain from a 92-year-old male with a history of macular degeneration and early stages of cognitive disorders. The sample was obtained from the donor program of the Institute of Anatomy, Tours, France, and contained the primary and secondary visual cortices. It was fixed with 4% formalin buffer 8 hours after death and stored five months until further processing. The specimen was maintained in the container with a sealing gel (BizGel, BizLine, Paris, France, see Chapter 7 for its characterization).

The sample was immersed in a proton-free fluid, Fluorinert (FC-40, 3M Company, USA), to prevent drying of the tissue during the experiment and reduce susceptibility artifacts at tissue margins. Since Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 147

acquisitions took place at room temperature (approximately 20°C), the specimen was transferred to the magnet room 4-5 hours prior to scanning in order to stabilize its temperature to 20°C.

Imaging protocol and preprocessing

The imaging protocol included anatomical and diffusion-weighted scans.

Anatomical scans The anatomical images were obtained using T2-weighted spin echo sequences. Diffusion scans Diffusion data were acquired using a conventional 2D PGSE sequence with a resolution of 300 µm isotropic. A multiple-shell HYDI dataset was obtained for 3 different shells corresponding to 3 diffusion sensitizations at b = 2000, 4000, 6000 s/mm 2 . The b-values were chosen lower than those of Chapter 5 (4500, 7500, 10000 s/mm 2 ) in order to keep a reasonable SNR. Causes of reduced SNR were two-fold. First, the sealing gel presenting a resonance frequency similar to that of fat, the addition of a fat saturation preparation was required to avoid chemical shift artifacts, the drawback being a loss of signal of about 20%. Then, the three shells were acquired with the same TE, ∆ and δ while varying the gradient strength (237, 327, 401 mT/m). This protocol is thus suitable to apply the NODDI model, without any preprocessing step to compensate the TE variation between the shells. However, using the same TE for each shell is not optimal for the SNR. Acquisition parameters and the resulting SNR are presented in S(T I i ) = S 0 (1 -2e -T I i /T 1 ) (6.1) with S(T I i ) being the signal corresponding to the i-th inversion recovery volume and S 0 being the signal at TI = 0 ms, related to the proton density. The factor 2 is induced by the use of an inversionrecovery pulse (180°) which doubles the distance for the regrowth compared to a 90°pulse.

The choice was made to fit a unique T1 per voxel, i.e. to consider that there is no more than one layer per voxel. In their paper, [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF] suggest a resolution limit of 200-300 µm to consider a unique T1 per voxel. Our dataset being acquired at 300 µm, the number of T1 to fit could thus be considered as one, even if partial volume effect can still occur. Fitting a unique T1 is partially compensated by the use of a soft clustering, enabling each voxel to be partially associated to several classes and thereby reflecting the partial volume effect. The results are presented in Figure 6.4.

Microstructure mapping using diffusion MRI

Microstructural features were inferred using the NODDI model, applied to the HYDI dataset. The isotropic diffusivity was set to 2.0×10 -9 m 2 /s since the post mortem sample is acquired at room temperature. Compared to the in vivo case where an isotropic-diffusion compartment is generally added to account for partial volume with cerebrospinal fluid (CSF) [START_REF] Barazany | In vivo measurement of axon diameter distribution in the corpus callosum of rat brain[END_REF], no CSF compartment was considered for an ex vivo sample and the isotropic fraction was set to zero. Taking into account the fact that stationary fraction could embed a part of the intracellular fraction (see Chapter 5), this compartment was also discarded and its volume fraction set to 0. The parallel diffusivity was not fixed, ranging from 0 to 2.0×10 -9 m 2 /s, the concentration κ was free, ranging from 0 to 3. Resulting maps of quantitative microstructural features are presented in Figure 6.5, as well as the fit obtained for a voxel belonging to the cortical ribbon in order to illustrate its quality. Figure 6.5 depicts maps of the intracellular volume fraction, orientation dispersion (OD), and the concentration factor κ. All these quantitative maps have been filtered using a non-local means filter algorithm [START_REF] Buades | Non-local means denoising[END_REF][START_REF] Condat | A simple trick to speed up and improve the non-local means[END_REF].

Automatic segmentation based on a Gaussian mixture model

The aim of automatic segmentation is to identify voxels containing tissue with similar myelo-and cyto-architectural features and to group them into clusters. The number of clusters found gives the number of identifiable tissue classes in the volume and, ultimately, the resulting cluster volume should depict expected cortical layers within the cortical ribbon.

The task to be fulfilled corresponds to an unsupervised cluster analysis. This technique differs from a supervised classification. In classification, the set of groups is given, and the task is to discriminate between groups. Today, current knowledge about the relaxation and diffusion MR-based characteristics of cortical layers are not sufficient to apply a supervised classification technique. The meaning and even the number of clusters is unknown and the objective is to discover them. SCAN, [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF]). Gaussian mixture models are well-established approaches currently used in data clustering [START_REF] Hasselblad | Estimation of parameters for a mixture of normal distributions[END_REF][START_REF] Nasser | Pattern recognition and machine learning[END_REF] and have been extensively used in tissue segmentation [START_REF] Lambert | Multiparametric brainstem segmentation using a modified multivariate mixture of gaussians[END_REF][START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF][START_REF] Ashburner | Unified segmentation[END_REF][START_REF] Hayit Greenspan | Constrained gaussian mixture model framework for automatic segmentation of mr brain images[END_REF]. These methods belong to the class of distribution-based techniques, and offer the advantage of not being exclusive, contrary to the k-means clustering method, in which one voxel is associated to one and only one cluster. The Gaussian mixture model provides, for each voxel, a probability of belonging to each cluster, which partly accounts for partial volume effect causing the presence of possibly two to three classes (layers) inside a voxel at a spatial resolution of 300 µm.

Distribution mixture: a classical unsupervised clustering method

Layers clustering was performed using a finite mixture model. The approach can be defined as follows. The sample mask contains N voxels. The dataset is D = {x 1 ,...,x N } where x i is a d-dimensional vector measurement. d = 1 when only one input map is considered (T1 map or intracellular volume fraction map), and d = 2 when two input maps are taken (T1 and intracellular volume fraction maps).

D is assumed to be generated from an underlying density p(x) defined as a finite mixture model of K components:

Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 152

p(x|Θ) = K ∑ k=1 α k p k (x|θ k ) (6.2)
with:

• p k (x|θ k ) the mixture components, 1 ≤ k ≤ K, with parameters θ k .

• α k are the mixing weights, representing the probability that a randomly selected x was generated by component k, where

∑ K k=1 α k = 1.
The complete set of parameters for a mixture model with K components is Θ={α 1 ,...,α N , θ 1 ,...,θ N }.

It is then possible to compute membership weights w ik of data point x i for each cluster k. Corresponding to the probability that data point x i belongs to cluster k, membership weights are computed according to the Bayes rule:

w ik = α k p k (x i |θ k ) ∑ K m=1 α m p m (x i |θ m ) (6.3)

Gaussian mixture model

As a first approach, the distribution model was chosen Gaussian, as in [START_REF] Lambert | Multiparametric brainstem segmentation using a modified multivariate mixture of gaussians[END_REF], Lifshits

p k (x|θ k ) = 1 (2π) d/2 |Σ k | 1/2 e -1 2 (x-µ) t Σ -1 k (x-µ)
(6.4)

The Expectation-Maximization algorithm for Gaussian Mixture Models

The Expectation-Maximization (EM) algorithm is defined as follows when applied to Gaussian mixture. The algorithm is iterative and starts from some initial estimate of Θ, and then proceeds to iterative updates of Θ until convergence is detected. Each iteration consists of an E-step and an M-step.

E-step

The membership weight w ik is computed using equation 6.3 for all voxels x i , 1 ≤ i ≤ N, and all mixture components 1 ≤ k ≤ K. Note that for each voxel x i , the membership weights are defined such that ∑ K k=1 w ik = 1. This yields an N × K matrix of membership weights, where each of the rows sums to 1. Specifically, the M-step computes, in the following order:

N k = ∑ N i=1 w ik α new k = N k N , 1 ≤ k ≤ K µ new k = 1 N k ∑ N i=1 w ik x i , 1 ≤ k ≤ K Σ new k = 1 N k ∑ N i=1 w ik (x i -µ new k )(x i -µ new k ) t , 1 ≤ k ≤ K (6.

Initialization and convergence

The EM algorithm can be started either at the E-step or at the Mstep. The initialization can be chosen randomly, or by using first a k-means algorithm to cluster the data and define membership weights based on k-means memberships.

Convergence is generally detected by computing the value of the log-likelihood after each iteration and stopped when its variation falls below a predefined threshold. The log-likelihood logL is defined as follows: where logL is the log-likelihood computed from Equation 6.6, P is the number of free parameters (for a d-dimensional Gaussian mixture model with arbitrary covariance matrices, P = 1 + d + d(d + 1)/2, [Huang et al., 2013]), and M is the number of measurements (i.e. the number of voxels N in our case).

logL = N ∑ i=1 log K ∑ k=1 α k p k (x i |µ k , Σ k ) ( 6

Clustering procedure and image regularization

The developed algorithm works as follows. First, the histogram of the quantitative feature is computed within a mask corresponding to the region of interest (eg. brain tissue). The number of bins of the histogram is typically set to 200 and the histogram is smoothed using a Parzen's window. Then, for a given number of components, the fitting procedure described above is applied, with initial means uniformly spread over a given range. The precision, i.e. the threshold value for the variation of the log-likelihood between two consecutive iterations, controls the stopping criterion. Finally, the number of clusters providing the lowest BIC value is kept for the further analysis. Clusters are ordered with respect to ascending means and the fitted histogram is overlaid on the original histogram to assess the quality of the fit. Finally, the probability for each voxel to belong to a given cluster is computed according to Equation 6.3, providing probabilistic maps for each cluster (soft clustering), and an additional label map allocating a cluster to each voxel is generated (exclusive clustering). The chosen cluster is the one corresponding to the highest probability w ik .

In a second phase, cluster maps were regularized to correct for irregularities and isolated points.

Clusters map volume is first oversampled, the oversampling factor being adjusted depending on the image complexity (typically 2 to 4). Then, an alternative solution to the FISTA algorithm [START_REF] Beck | A fast iterative shrinkage-thresholding algorithm for linear inverse problems[END_REF] used in [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF] was chosen. This approach was based on a Potts model [START_REF] Storath | Joint image reconstruction and segmentation using the potts model[END_REF] aiming at minimizing the following objective function providing the corrected label volume:

u * = arg max u∈R m×n γ S ∑ s=1 ω s ∇ p s u + u -f 2 2 (6.8)
with γ being a regularizing factor that controls the balance between data fidelity and jump penalty, (typically set to 0.3), ∇ p s u being the number of neighboring voxels with a label different from the considered voxel, ω s being non-negative weights, taken here as the sum of the inverse distance between a voxel and its neighbors having a different label. The term Auf 2 2 couples the minimizing candidate u to the data f.

Myeloarchitecture-based clustering from T1 relaxation time

The first step was to find the adapted level of precision, i.e. the difference of log-likelihood between to iteration halting the algorithm, providing an accurate number of clusters. The algorithm was run Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 155 for a number of Gaussian distributions, with a precision tuned from 10 -5 to 10 -8 . The minimal BIC value was obtained for six clusters given a precision of 10 -5 and was obtained for five clusters for a precision threshold set to 10 -6 , 10 -7 , 10 -8 . Figure 6.6 presents the evolution of the BIC according to the number of clusters, computed for a precision threshold set to 10 -7 giving the lowest Bayesian information criterion, which corresponds the precision chosen for the rest of this work. Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 156 Figure 6.7 highlights the fact that the closer the cluster is to the pial surface, the higher its associated T1 relaxation time is. This is consistent with the observation made in [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF]. Despite no anatomical or topological prior was considered to compute T1-based clusters, the approach shows consistent results, with a coherent laminar structure within the cortical ribbon. However, one can notice small irregularities and isolated points. The idea was then to regularize the results using the Potts model described in § 6.3.5. The resampling factor was set to 2, and the regularization factor γ to 0.3. Figure 6.8 presents the regularized cluster map. Irregularities included in the red circles on the left (before regularization) were removed after the application of the Potts regularization method (red circles on the right). FIGURE 6.8: Potts regularization applied on the T1 cluster map. On the left, the T1 cluster map before the regularization, with irregularities and isolated points (red circles), on the right, T1 cluster map before the regularization, with no irregularities in the red circles

After this successful replication of the work presented in [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF], a similar approach was attempted, using the intracellular volume fraction map obtained from NODDI as an input for the clustering, and therefore more related to the cyto-architecture. Each of the ten components was associated with a colored label. High f intra values were identified as white matter (Fig. 6.10.b). In this case, white matter could be associated to five components In a nutshell, it appears that myelo-(T1) and cyto-(f intra ) architectural features embed complementary information that need to be coupled to accurately segment the cortical layers.

Cytoarchitectural-based clustering from NODDI intracellular volume fraction

Discussion

Main contributions

The main contributions of this work are: Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 161

2. An automatic segmentation of the cortical ribbon from quantitative maps, using an unsupervised clustering algorithm with no anatomical prior. T1-based clusters were consistent with the clusters obtained by [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF], with higher associated T1 values as the classes were close to the pial surface. This method was also applied, for the first time, to a NODDI-based quantitative map: the intracellular volume fraction map, reported to be the NODDI contrast being the most sensitive to the cortical layers [Kleinnijenhuis et al., 2013a]. Intracellular volume fraction-based clusters, depicting one (sometimes two) clusters for outer layers one four for the inner layers, were consistent with the observations of [Kleinnijenhuis et al., 2013a]. Kleinnijenhuis et al. indeed showed that the f intra map provided distinct values depending on the depth, with neurite-dense deep layers (more than one layers were visually found) and a superficial layer sparser in neurites (only one layer could be observed).

3. A multi-contrast segmentation benefiting from complementary information arising from the myelo-and cyto-architecture and giving access, at the same time, to more inner and outer cortical layers.

4. An image regularization based on a Potts model to correct for isolated points and to smooth out irregularities.

Comparison with existing studies

This chapter work was originally inspired by [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF]. In this study, Lifshits et al. automatically segmented the cortical layers by using a Gaussian mixture model coupled with a Bayesian information criterion to find the best number of clusters. This method was applied to T1 quantitative maps obtained from a post mortem rat brain and in vivo human brains (33 healthy subjects), at low and high resolutions. The low resolutions corresponded to 3 mm isotropic in humans and 510 µm isotropic for the rat brain, while the high resolutions corresponded to 0.43×0.43×1.5 mm 3 for humans and 110 µm isotropic for the rat brain. To date, no post mortem validation on a human brain sample was done. In their paper, they suggested that, the cortical thickness in humans being about twice that of the rat, a comparable high resolution in the human brain (compared to the 110 µm isotropic for the rat brain, where only one T1 per voxel was estimated) would be in the order of 200- Considering the high spatial resolution of the dataset used in the thesis work, the choice was made to fit a single T1 per voxel, as Lifshits et al. did for the high resolution rat brain. However, the TI sampling (122 inversion times) was designed in such a way that it is possible to fit multiple (reasonably two, considering the potential partial volume effect) T1 per voxel. This could be investigated in the future to see whether the use of more components per voxel would depict more T1-based clusters.

Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 162

Regarding the clustering of the intracellular volume fraction map, the results obtained in this chapter are in line with the results presented in Kleinnijenhuis et al. [2013a]. Kleinnijenhuis et al. acquired diffusion weighted images on a small sample (1×1×1 cm) of the primary visual cortex V1 containing the line of Gennari. The NODDI model was applied on multi-shell diffusion-weighted images acquired a 9.4 T with a spatial resolution of 200 µm isotropic. Four gray levels were found along the cortical ribbon in the intracellular volume fraction map (neurite density map). A unique contrast was observed for superficial layers, with a very low neurite density, a high neurite density delineated the line of Gennari, and two layers were found in deep layers. This is in agreement with the fact that NODDI model, or at least the intracellular volume fraction map, better depicts inner layers than outer layers.

Automatic segmentation methods have also been applied to the signature of diffusion MRI signals by [START_REF] Bastiani | Automatic segmentation of human cortical layer-complexes and architectural areas using ex vivo diffusion MRI and its validation[END_REF], who mostly used the ADC profile and directional information. In this study, Bastiani et al. acquired diffusion-weighted images on a post mortem human primary and premotor cortex, with a spatial resolution of 340 µm isotropic. They sampled the cortical ribbon by nine equidistant meshes between the gray / white matter boundary and the pial surface, and the local coordinate system was obtained with the Laplace equation. At the end, each vertex included 31 features: the average, radial and tangential ADC, as well as spherical harmonics of the ADC profile (28 features as the harmonics order was 6). An unsupervised k-means algorithm was used to classify cortical locations into cortical layers, and the number of clusters was determined using a silhouette index. The alternative method used in this paper could be applied to our dataset in order to compare the clustering results.

Limitations and further improvements

Processing of the diffusion-weighted images As suggested in Chapter 5, filtering the diffusionweighted images before the application of the NODDI model could be of great benefit for the fitting procedure. In addition, similarly to the work presented in Chapter 5, more tests could be performed to improve the initialization of the algorithm in order to ensure that the selected initialization is the best possible. These tests could consist in finding the best value of d to fix by testing the dependence of the Bayesian information criterion to the value of d (the best d being the one giving the lowest BIC).

The precision of the NLP optimizer as well as the number of MCMC samples could also be optimized in order to find the best compromise between the fit quality and the computational efficiency.

Choice of the underlying distribution and clustering method As a first approach, a Gaussian mixture has been selected to model the underlying distribution. However, other models could be more adapted. The shape of the evolution of the Bayesian information criterion as a function of the number of components support this hypothesis because normally, it should increase in a more pronounced manner after reaching its minimum value. Other distribution models could thus be investigated in Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 163 further works, in particular the t-distribution [START_REF] Peel | Robust mixture modelling using the t distribution[END_REF]. To go a step further, it would also be possible to avoid the choice of a distribution model and to apply non-parametric clustering algorithms, such as Dirichlet process mixtures [START_REF] David M Blei | Variational inference for dirichlet process mixtures[END_REF]. Supervised methods would not be an option to cluster cortical layers, except for the line of Gennari, that is clearly visible on the images. Regarding the determination of the number of clusters, other metric than the Bayesian information criterion could be considered, such as the silhouette index used in [START_REF] Bastiani | Automatic segmentation of human cortical layer-complexes and architectural areas using ex vivo diffusion MRI and its validation[END_REF]. Linking MR contrasts to the underlying anatomy On initial examination, T1 is presented to reflect the myeloarchitecture, T2* the iron content, and diffusion features, such as NODDI features, the cytoarchitecture. However, this is not that simple [START_REF] Stueber | Myelin and iron concentration in the human brain: a quantitative study of MRI contrast[END_REF]. MRI contrast still cannot be directly linked to neuronal cell density or morphology, which is the foundation on which cortical layers were originally defined [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF].

There have been only a few quantitative attempts to find a relationship between myelin content and T1, as reviewed by [START_REF] Laule | Myelin water imaging of multiple sclerosis at 7 t: correlations with histopathology[END_REF]. Additionally it is unclear how much iron content contributes to T1 tissue contrast [START_REF] Gelman | Interregional variation of longitudinal relaxation rates in human brain at 3.0 t: relation to estimated iron and water contents[END_REF], since iron and myelin often colocalize within the cortex [START_REF] Fukunaga | Layer-specific variation of iron content in cerebral cortex as a source of MRI contrast[END_REF].

Diffusion MRI is often presented as a microstructural probe of the tissue. Indeed, its geometry, density, and general morphometry affect the signal, making dMRI a potential marker for layer composition, reflecting their cytoarchitecture (cf. § 3.2.7.2). However, no single cellular component correlates with fODF: the dendrites, axons, astrocyte processes, and the extracellular space probably all contribute to the obtained fODF to various degrees.

Therefore, as advocated by Assaf in his recent review [START_REF] Assaf | Imaging laminar structures in the gray matter with diffusion MRI[END_REF], the obtained layering of the cortical ribbon should not be regarded as the automatic identification of the traditional layers (I-VI), but as "diffusion MRI layers" or "T1 layers". Nonetheless, these layers arising from quantitative features could be used to delineate and classify architecturally distinct cortical areas.

Reproducibility of the results

Similarly to the previous chapter, a limitation of this proof-ofconcept methodological study is that it uses only one post mortem tissue sample. More samples could be integrated in the study in order to evaluate the reproducibility of the results and ensure that the observed contrasts are not due to imaging artifacts or an inhomogeneous fixation process. The Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 164 methodology could also be applied on more cortical areas and even on an entire human brain, which could evaluate the capacity of the clustering algorithm to provide relevant information to delineate cortical areas consistent with the underlying anatomy. Increasing the spatial resolution to 100-200 µm isotropic would increase the number of voxels containing only one layer and thus reduce the partial volume effect. Providing a dataset to investigate the cortical lamination with an enhanced spatial resolution on an entire post mortem human brain is one of the goals of this PhD thesis. Chapter 7 presents the acquisition protocol and the results on half of the left hemisphere of an ex vivo human brain, with anatomical images down to 100 µm isotropic and multi-shell diffusion-weighted images acquired at a spatial resolution of 200 µm isotropic, with 175 diffusion directions and b-values up to 8000 s/mm 2 .

Finally, a histological validation will be required in order to identify the anatomical substrate of the segmented layers, based on cytoarchitecture and myeloarchitecture. The myelin could be stained using the Gallyas method [START_REF] Gallyas | Silver staining of myelin by means of physical development[END_REF] and the cytoarchitecture could be investigated with cresyl violet as in [START_REF] Bastiani | Automatic segmentation of human cortical layer-complexes and architectural areas using ex vivo diffusion MRI and its validation[END_REF]. Histological analyses will be carried out after the completion of the Chenonceau project acquisition campaign (see Chapter 7), and will bring further information about the myelo-and cyto-architecture, as well as axonal microstructure (with Electron Microscopy) or connectivity (using Klingler's dissection).

Clinical prospects

Functional MRI can now investigates functional responses at the level of cortical layers with the use of ultra-high fields [START_REF] De | Cortical depth dependent functional responses in humans at 7T: improved specificity with 3D GRASE[END_REF], and there is therefore a growing need to segment the cortical layers in vivo. This chapter work only presents a proof-of-concept about the complementarity of quantitative T1 and diffusion features to decipher the lamination of the cortical ribbon. However, clinical applications could be considered. In vivo spatial resolution cannot reasonably fall below 1 mm for isotropic diffusion-weighted or T1 relaxometry images. This is therefore necessary to overcome the unquestionable partial volume effect, by fitting, for instance, multiple T1 per voxel as in [START_REF] Lifshits | Resolution considerations in imaging of the cortical layers[END_REF]. Regarding the NODDI model, multiple fitting could also be consider, but this would result in a very large number of features to evaluate, unless this multiple fitting only rely on κ and the intracellular volume fraction. Emerging approaches relying on brain tissue simulations and Monte Carlo simulations of the diffusion process might help going beyond the limitations of actual analytical models.

The automatic delineation of cortical layers could help to better understand the anatomical substrate of functional networks in the human brain, but could also be used as a potential imaging marker in many brain diseases (neurodegenerative or psychiatric). For instance, cortical thickness has been shown to be associated with neurodegenerative diseases such as Parkinson's or Alzheimer's [START_REF] Anders M Fjell | What is normal in normal aging? effects of aging, amyloid and alzheimer's disease on the cerebral cortex and the hippocampus[END_REF][START_REF] Jubault | Patterns of cortical thickness and surface area in early parkinson's disease[END_REF]. However, pattern of cortical damage at the laminar level remains unclear for these pathologies. Château de Chenonceau, French castle spanning the Cher. This castle is located 30 km from Tours, where the studied brain comes from. Its name was given to our project (image taken from https: // www. chenonceau. com )

Conclusion

Chapter 7

Towards a mesoscopic post mortem human brain MRI atlas

The human brain has been, and is still, extensively studied. Numerous anatomical atlases have been published, whether neuroanatomical books [START_REF] Henri | The human hippocampus: functional anatomy, vascularization and serial sections with MRI[END_REF][START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF][START_REF] Thomas P Naidich | Duvernoy's atlas of the human brain stem and cerebellum: high-field MRI, surface anatomy, internal structure, vascularization and 3 D sectional anatomy[END_REF][START_REF] Von | The cytoarchitectonics of the human cerebral cortex[END_REF][START_REF] Vogt | Allgemeinere ergebnisse unserer hirnforschung[END_REF][START_REF] Campbell | Histological studies on the localisation of cerebral function[END_REF][START_REF] Sa Sarkisov | Cytoarchitecture of the human cortex cerebri[END_REF][START_REF] Bailey | The isocortex of man[END_REF][START_REF] Talairach | Co-planar stereotaxic atlas of the human brain: 3-dimensional proportional system: an approach to cerebral imaging[END_REF][START_REF] Joseph | Atlas of neuroanatomy: With systems organization and case correlations[END_REF][START_REF] Voogd | The Human Central Nervous System[END_REF] The purpose of the work described in this chapter is to create a unique mesoscopic MRI atlas of the human brain, including anatomical and diffusion-weighted images. The idea is to provide a high spatio-angular resolution dataset suitable to apply recent advanced signal and biophysical models of the diffusion process such as NODDI [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF] or the 3D MAP-MRI model [ Özarslan et al., 2013a[ Özarslan et al., , Fick et al., 2015]]. The first section presents the studied specimen as well as the chosen methodology for its cutting and its storage. Then, the set up of the designed protocol is detailed, before presenting the current state of the atlas construction. Finally, prospective studies performed with this unique dataset are discussed. Embedding the specimen in a gel followed a twofold strategy. First, this gel should avoid the loss of pieces of the brain sample and minimize the deformation during the cutting step. Second, it should maintain all the blocks in a stable position within their container in order to facilitate their matching that will occur in a consecutive step. The acquisition campaign was planned to last more than a year (including the adjustment of the acquisition protocol), which imposed the use of a gel that does not degrade over time. Moreover, a second condition was to use a gel that reticulates at room temperature. As shown in § 4.2.3.1, the agar gel is not recommended for long-term storage despite its common use in MRI studies because of its limited conservation period even with the addition of sodium azide. The choice was made to use a gel originally designed for electrical sealing, such as junction boxes outdoors (Biz'gel sealing gel, 1L, BizLine, France). This gel provides the advantage of a fast reticulation at room temperature and a proper conservation over time, with an operating temperature after polymerization ranging from -40°C to +200°C.

Magnetic properties of the gel

MR characteristics of the gel (T1 and T2 relaxation times) were estimated in order to adequately tune the acquisition protocol. To this aim, a container (cf. Figure 6.2) was filled with the gel and scanned using an 11.7 T Bruker MRI system. The transverse relaxation time was mapped using a standard MSME pulse sequence. In total, 200 echoes were collected corresponding to 200 echo times linearly spaced between 5 and 1000 ms. Imaging parameters of this sequence were: isotropic spatial resolution of 600 µm, flip angle: 90°, TR = 61000 ms, readout bandwidth: 50 kHz, and a total scan time of 1h01min. Collected MSME data were then used to fit the log-linear model corresponding to the T2 decay, first with a least-square algorithm, and then with a Levenberg-Marquardt algorithm carefully initialized from the first fit in order to get robust estimates. The study was carried out on a post mortem brain from a 92-year-old male with a history of macular degeneration and early stages of cognitive disorders. The specimen was obtained from the donor program of the Institute of Anatomy, Tours, France (headed by Pr C. Destrieux). It was fixed with a 4% formalin buffer 8 hours after death and stored five months until further processing.

Containers and MR bed

Dedicated containers and their corresponding MRI bed were designed to fit into the MR coil offering a 60 mm inner diameter. Contrary to the previous experiments, the use of an automatic positioning system was required to ensure a precise and reproducible positioning of the samples within the MR coil antenna in order to facilitate the registration step afterwards. The bed was thus designed to be fixed on the automatic positioning system of the 11.7 T MRI. The materials of the bed and containers were chosen to avoid any interaction with MR field: all the elements were manufactured using plastic materials (POM, PVC KO, PMMA, nylon) except for the screws to fix the lip that were made of brass (non-magnetic) (see Figure 7.2.i.).

Cutting procedure

Cutting steps are presented in Figure 7. Before cutting, the entire specimen was imaged on a 3 T MRI system (Prisma, Siemens, Erlangen, Germany). A T2-weighted anatomical scan was acquired using a T2 SPACE sequence with an isotropic resolution of 500 µm, TE/TR = 105/700 ms, matrix size: 512×512, 320 slices, acceleration factor: 2, and a total acquisition time of 20 min. The volume was then realigned in the Talairach space [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain: 3-dimensional proportional system: an approach to cerebral imaging[END_REF] by identifying relevant landmarks: the midpoint of the anterior commissure (AC), the midpoint of the posterior commissure (PC), and an interhemispheric point.

Results are presented in Figures 7.3 The original idea consisted in applying the acquisition protocol developed for the hippocampus and improved for the brainstem, but this protocol turned out to be not applicable in the case of Chenonceau, due to the sealing gel. When using the PGSE sequence detailed in § 5.2.2.4, the gel produced a signal that partly overlapped with the tissue (Fig. 7.7.a). Figure 7.6 depicts the spectrum obtained with F1, showing that the sealing gel presents a resonance frequency similar to that of the fat. The first solution was thus to apply a fat saturation pulse. However, this resulted in a general signal loss between 20% and 40%. Moreover, a remaining signal still existed for the gel, especially for long repetition times.

Frequency (Hz)

Final acquisition protocol

The definitive acquisition protocol, including anatomical and diffusion-weighted sequences, is detailed hereafter.

Anatomical scans

The anatomical images were obtained using T2-weighted spin echo sequences.

A 2D-SE was acquired with an isotropic resolution of 150 µm isotropic, and using the following parameters: TE/TR = 16/6600 ms, 9 averages, matrix size: 274×256, 374 slices, flip angle: 90°, receiver bandwidth: 66 kHz, and a total acquisition time of 3h26min. A 3D-SE dataset was acquired using the multi-slice option, an isotropic resolution of 100 µm, TE/TR = 20/500 ms, matrix size: 400×400, 560 slices, flip angle: 90°, receiver bandwidth: 50 kHz, 1 average, leading to a total scan time of 22h13min.

Figure 7.8 shows the resulting images depicting a very good SNR (33 for the 100 µm image and 17 for the 150 µm image). Each sequence has particular benefits and disadvantages. On the one hand, as shown in 7.8.a, 7.8.b, 7.8.c (image at 150 µm), the contrast between white and grey matter is higher than in 7.8.d, 7.8.e, 7.8.f, and the signal is more homogeneous. The sequence is also less sensitive to the susceptibility artifacts caused by the presence of air bubbles and is much faster (3h30 against 22h at 100 µm). On the other hand, the second acquisition sequence, in addition to having a better spatial resolution, gives a higher contrast at the level of internal structures such as the substantia nigra of the red nuclei of the midbrain. This is why both sequences were retained for the final acquisition protocol. This preliminary processing must be considered as a first attempt to visualize the entire left hemisphere. Many improvements will be needed to deal with overlapping and transitions between neighboring blocks, and will be addressed in the future. These preliminary results, depicted in Figures 7. 15, 7.16, 7.17 and 7.18, are still quite encouraging.

Discussion

Summary of contributions

The main contributions of this work are:

1. The design of a protocol to prepare, store and acquire an entire human brain at 11.7 T. The acquisition protocol took into account the specific MR properties of the sealing gel that presented a resonance frequency close to the resonance frequency of fat.

Comparison to existing studies

This thesis work responds to the need of the creation of a high resolution (mesoscale) MRI atlas of an entire post mortem human brain. Preclinical MRI systems, initially dedicated to small animal imaging, are widely used to explore ex vivo human brain tissue samples and investigate fundamental questions of neuroanatomy at the mesoscale [START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF][START_REF] Modo | Detection of aberrant hippocampal mossy fiber connections: Ex vivo mesoscale diffusion MRI and microtractography with histological validation in a patient with uncontrolled temporal lobe epilepsy[END_REF][START_REF] Calabrese | Postmortem diffusion MRI of the human brainstem and thalamus for deep brain stimulator electrode localization[END_REF], while the investigation of whole post mortem human brains, too large to fit in the small bore of preclinical MRI systems, still had to be conducted on large bore clinical systems.

This work bridges the gap between these two approaches, taking advantage of preclinical systems hardware characteristics (11.7 T, 780 mT/m) to build an entire post mortem human brain atlas at high resolution (anatomical images at 100 and 150 µm, diffusion scans at 200 µm, b = 1500, 4500, 8000 s/mm 2 , and 175 directions in total), relying on the development of a heavy preparation, acquisition and analysis pipeline. The idea of scanning multiple fields of view using a preclinical MRI in order to finally reconstruct an entire post mortem human structure of the nervous system has already been applied by [START_REF] Calabrese | Postmortem diffusion MRI of the entire human spinal cord at microscopic resolution[END_REF]. In their work, Calabrese et al. scanned an entire post mortem human spinal cord on a 7 T preclinical system with several fields of view of 8 cm, covering a length of 100 cm. Anatomical images were acquired with a spatial resolution of 50 µm, and diffusion-weighted images were acquired at an isotropic resolution of 100 µm, b = 4000 s/mm 2 , and along 31 directions. The spatial resolution they reached on the spinal cord was thus higher than the one obtained in this chapter work.

However, there are numerous differences between these two projects. First, contrary to the scanning of an entire human brain which obviously requires the cutting of the sample, in the case of the spinal cord, there was no need to cut the specimen as it fits in a 100 cm long tube, that just needed to be translated along the Z axis. This configuration led to a much easier registration process than the one that will be required in the Chenonceau project, with linear transformations and weighted averaging at the level of overlapping segments. The small diameter of the sample (about 2 cm) enables the use of a smaller coil (31 versus 60 mm of inner diameter) providing a higher SNR. Last, the aim was only to apply the DTI model, requiring a single-shell acquisition with a few directions. In this thesis chapter, the higher b-value was twice the one used in [START_REF] Calabrese | Postmortem diffusion MRI of the entire human spinal cord at microscopic resolution[END_REF], and the obtained dataset was suitable to apply numerous analysis models. This is due to that fact that the spinal cord white Other studies aimed at scanning an entire post mortem human brain or large anatomical structures (in particular the occipital lobe) at a mesoscopic scale, using clinical systems with improved coils and acquisition sequences [START_REF] Miller | Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner[END_REF][START_REF] Lagos | Whole human brain diffusion MRI at 450 µm post mortem with dwSSFP and a specialized 9.4T RF-coil[END_REF][START_REF] Harms | Robust and fast nonlinear optimization of diffusion MRI microstructure models[END_REF][START_REF] Assaf | Imaging laminar structures in the gray matter with diffusion MRI[END_REF], Sengupta et al., 2018]. The use of dedicated RF-coil, B1+ optimized pulse sequence (kT-dSTEAM), and ultra-high field (9.4 T) allowed Fritz et al. [2018] to study the entire occipital lobe at a spatial resolution of 200 µm for anatomical images, and 400 µm for diffusion-weighted images, with b-values up to 7000 s/mm 2 . However, these high resolutions cannot be achieved on a whole human brain yet, and the obtained SNR are still far from what can be obtained on a preclinical scanner, where the gradient coils are more than ten times stronger than available gradient coils for UHF-MRI (780 mT/m versus 80 mT/m).

Finally, comparing the images obtained in the frame of the Chenonceau MRI atlas with other studies performed on preclinical systems, the image quality and resolution obtained in this work are close to the best resolutions achieved for samples of a comparable size. For instance, [START_REF] Calabrese | Postmortem diffusion MRI of the human brainstem and thalamus for deep brain stimulator electrode localization[END_REF] imaged the entire brainstem/thalamus complex on a preclinical 7 T and achieved a spatial resolution of 50 µm for anatomical images and 200 µm for diffusion-weighted images acquired at b = 4000 s/mm 2 along 120 directions. Still with regard to brainstem imaging, [START_REF] Aggarwal | Feasibility of creating a high-resolution 3d diffusion tensor imaging based atlas of the human brainstem: a case study at 11.7 t[END_REF] imaged a whole specimen with a spatial resolution of 255 µm isotropic for diffusion-weighting imaging, higher spatial resolution of 125 µm isotropic being achievable only for smaller samples (part of the medulla) that could fit into smaller (20 mm) diameter volume coils. Similarly, [START_REF] Modo | Detection of aberrant hippocampal mossy fiber connections: Ex vivo mesoscale diffusion MRI and microtractography with histological validation in a patient with uncontrolled temporal lobe epilepsy[END_REF] achieved an isotropic spatial resolution of 100 µm for the diffusion-weighted imaging of a hippocampus post mortem sample, with a sample small enough to fit in a 20 mm diameter volume coil.

Limitations and further improvements

The work presented in this thesis chapter is only the beginning of the scanning and then the reconstruction of an entire human brain. The scanning of the left hemisphere should be finished in January 2019 and will be followed by the scanning of the right hemisphere with the same protocol.

The acquisition protocol has been designed to investigate the fine connectivity of the human brain as well as to probe the microstructure of tissues. However, the diffusion time remaining constant for all the shells, it is not possible to apply advanced models developed to evaluate the axonal diameter or permeability. Several studies suggest that oscillating gradient spin-echo (OGSE) offers benefit over PGSE for imaging pore sizes, such as a higher sensitivity to axonal diameter ( [START_REF] Drobnjak | OGSE, and sensitivity to axon diameter in diffusion MRI: insight from a simulation study[END_REF], 2010, Aggarwal et al., 2012], see § 3.2.7.2). Consequently, it would be of major interest to design a complementary acquisition protocol using OGSE sequences to go deeper into the investigation of the brain microstructure.

Regarding the registration step of all the fields of view to the blockface image acquired at 3 T, the work presented in this chapter only constitutes the initialization step and requires several dedicated developments. Diffeomorphic transformations are required to accurately match the fields of view acquired at 11.7 T on the whole specimen acquired at 3 T. This is due to many factors that induced non linear deformations, from the elastic placing of the brain blocks into their containers to the differences of gradient non linearities between the clinical and preclinical MRI systems.

Then, two types of interfaces will have to be managed: the boundary between two blocs, corresponding to cutting issues, probably a little distorted, and the overlapping regions between two consecutive fields of view within a block. On the one hand, the first interface could be solved by using an "image inpainting" deep learning-based method able to reconstruct a corrupted image. On the other hand, the overlapping regions could be solved by a simple weighted average between the two fields of view, by optimizing the mutual information shared by the two sources of information.

A further dedicated step to correct the signal inhomogeneity should also be added, especially for the anatomical images at 100 µm and T2 (b = 0 s/mm 2 ) maps (see Figs. 7.18 and 7.15). This method should correct the signal intensity over the entire field of view corresponding to the brain, but taking into account specificities at the interfaces between fields of view to relax the regularization and allow more important corrections at these boundaries.

Clinical and general prospects

Once the MRI atlas will be fully reconstructed, ensuing findings may help to push forward tractography algorithms by providing anatomical priors. One of the limitations in tractography is that when Long-term perspectives would be to extend the developed approach to the study of other samples.

Scanning several human brain specimens would certainly require the establishment a multicenterstudy in order to have access to a network of similar preclinical MRI systems so as to scan the specimens in a reasonable amount of time.

Three approaches could be adopted. First, scanning several entire brain specimens of the same samples (same age, with no neurological disorder) could validate the observed contrast trends and would give access to the construction of probabilistic atlases of the anatomy, structural connectivity and microstructure of the human brain at ultra-high resolution, while capturing the inter-subject variability of this anatomical macro-/meso-/micro-structures.

A second project could be to study the variability between healthy and pathological populations. To date, there is no post mortem database established for neurological, psychiatric, or neurodevelopmental disorders. Scanning one ex vivo brain for such pathologies would definitively give a valuable insight about the these disorders from the macroscopic to the mesoscopic scale. Chapter 8

Conclusion and prospects

Conclusion and main contributions

The overall objective of this thesis was to provide a mesoscopic MRI atlas of the human brain, combining high resolution anatomical and diffusion-weighted data. The mesoscopic scale, corresponding to a resolution of a few hundreds millimeters, is currently only accessible through the use of preclinical MRI systems. The brain specimen had therefore to be cut into several blocks fitting in the small bore of the 11.7 T Bruker MRI system. The final dataset was intended to be compatible with the application of advanced signal (aQBI [START_REF] Descoteaux | Regularized, fast, and robust analytical q-ball imaging[END_REF], MAP-MRI [ Özarslan et al., 2013a[ Özarslan et al., , Fick et al., 2015]]) and biophysical (NODDI [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF]) models, in order to recover the fine structural connectivity and microstructure of brain tissues. The acquisition pipeline also had to be designed in a way that facilitates the final registration step aiming at reconstructing the entire human brain sample.

The completion of this tremendous project, named Chenonceau in honour of the beautiful French region from which the studied specimen was obtained, required preliminary studies to design the acquisition protocol as well as data analysis methods. These studies have been performed on three key structures of the human brain: the hippocampus, the brainstem, and the visual cortex, and have themselves led to several significant contributions. The following section summarizes the main contributions of this thesis work.

Subfields, internal connectivity and microstructure of the human hippocampus

The study of the human hippocampus has led to the design of an acquisition protocol performed at 11.7 T. This protocol included T2-weighted anatomical scans (200 µm isotropic) and diffusionweighted data acquired at 300 µm isotropic combining a HARDI dataset (b = 4500 s/mm 2 , 500 diffusion-directions) to perform the connectivity analysis, and a HYDI dataset (b = 4500, 7500, 10000 s/mm 2 , 60 diffusion-directions each) to apply microstructure models. The resulting dataset appeared to be useful to propose a novel segmentation approach of the human hippocampus subfields that combined the available sources of contrast, namely T2-weighted and diffusion-weighted contrasts. This work provided a proof of concept that ultra-high fields (UHF) combined with strong gradients (SG) high angular resolution diffusion imaging (UHF-SG-HARDI) could robustly map the inner connectivity of the hippocampus and gave evidence of a higher level of connectivity in the uncal region compared to the most posterior portions. This result holded regardless of the tractography approach. Bundles from the polysynaptic pathway were also reconstructed. A comparison has been made between four tractograms mixing the use of a deterministic and a probabilistic tractography algorithm, as well as DTI versus aQBI model. The results highlighted the enhanced accuracy of probabilistic tractography algorithms and, when it came to the reconstruction of more complex pathways like the perforant pathway, the benefit arising from the use of high angular resolution diffusion models has been emphasized. This work also provided a proof of concept that UHF diffusion MR microscopy could play an increasing role in the future to decipher the cytoarchitecture of the hippocampus. In our case, evidence was given for a rostro-caudal heterogeneity supporting the longaxis functional specialization of the human hippocampus. This first study was completed with the publication of an article in the journal Brain Structure and Function (see appendix A). The Human Brain Project (HBP) is creating a research infrastructure to push forward neuroscience, and to establish a first multiscale (from micro to macro) atlas of the human brain. Three overarching objectives can be distinguished. The first one is to address fundamental questions regarding the singularity of the human brain with respect to other species. The second one is to contribute to better understand brain diseases and to develop new therapeutic approaches. Finally, this project should lead to the development of the next generation of neuromorphic computers.

The project, started in 2013, is a large ten-year scientific research project, employing about 500 scientists from more than 100 universities, teaching hospitals and research centers across Europe.

As part of the European Commission Future and Emerging Technologies Flagship program, HBP is mostly funded by the European Union. In particular, the project undertakes targeted research and theoretical studies, and explores brain structure and function in humans, rodents and other species.

HBP's work plan is organized in the form of thirteen subprojects, each dedicated to a specific area of activity.

This thesis work is part of the subproject 2 (SP2), named "Human Brain Organization", and whose goal is to develop neuroscientific concepts, tools, knowledge and datasets to contribute to a better understanding of the human brain structure and functions. SP2 is led by Pr K. Amunts (Forschungszentrum Jülich, Germany), with deputy leaders Jean-Franc ¸ois Mangin (CEA Neurospin, UNATI, France)

and Francesco Pavone (University of Florence, Lens, Italy). The overall aim of SP2 is to create a multi-scale (micro to macro) mapping of the human brain, through the HBP Human Brain Atlas.

The work performed during this thesis, and more specifically the Chenonceau project that focused on obtaining ex vivo mesoscopic data of the human brain by studying the fine connectivity and microstructure of the white matter, falls within this context by providing mesoscale data for the entire human brain.

FibrAtlasII-III project initiation

The FibrAtlasII-III project, directed by Pr Destrieux's team (Bretonneau University Hospital, Tours),

proposes to address the validation of tractography methods trough the scanning of elder healthy subjects that gave their body to science. The subjects were scanned both in vivo and ex vivo, using MRI and Klingler's dissection.

Several validation techniques were proposed in the literature, but none of them was fully convincing in human. The objective of this project is thus to validate anatomical connectivity inference methods on a large database for which comparisons will be done between long white matter fiber bundles inferred from various tractography methods and Klingler's dissections.

This thesis project was carried out as part of the FibrAtlasII-III project. The acquisition protocol set up in for the study of Chenonceau will be used to precisely investigate the structural connectivity of the post mortem brains obtained from the subjects involved in the FibrAtlasII-III project.

Short and long-term prospects

Multiple prospects can be considered at the end of this thesis work. They are presented in the following section, from short to long term prospects.

Short-term prospects

Further use of the high resolution datasets acquired during this thesis work The datasets acquired during this thesis are quite unique and could be used to further investigate the hippocampus, the brainstem, or the entire human brain anatomy.

The hippocampus and brainstem datasets were scanned using ActiveAx protocol [Alexander et al., 2010], aiming at providing the average axon (or neurite) diameter in each voxel. This model could thus provide new insights about the microstructure of these two structures.

Moreover, regarding the connectivity results, a way to go a step further could be to apply clustering techniques to the connectograms in order to obtain clusters of co-localized fibers sharing similar geometries and belonging to the same white matter tract. This technique should accelerate the construction of a probabilistic connectivity atlases. Another improvement could be obtain one step before by applying a global tractography algorithm with anatomical constraints [START_REF] Teillac | Tractographie globale sous contraintes anatomiques[END_REF] in order to better capture the underlying structural connectivity. Contrary to the tractography algorithms used in this work, this global fiber tracking algorithm is able to take benefit from anatomical priors to optimize simultaneously the entire set of connections and to monitor the endings of fibers when connecting to the cortex. staining methods can be used to reveal both myelo and cytoarchitecture-based layers. Myeloarchitecture of cortical areas is typically mapped using techniques such as silver impregnation and Weigert staining [START_REF] Nieuwenhuys | A map of the human neocortex showing the estimated overall myelin content of the individual architectonic areas based on the studies of adolf hopf[END_REF][START_REF] Aggarwal | Probing region-specific microstructure of human cortical areas using high angular and spatial resolution diffusion MRI[END_REF][START_REF] Vogt | Allgemeinere ergebnisse unserer hirnforschung[END_REF], while the cytoarchitecture can be obtained using Nissl staining [START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF].

Long-term prospects

From the study of one sample to the construction of probabilistic atlases All the results presented in this manuscript rely on the study of a unique sample. However, it would be possible to extend the developed approach to the study of other samples, as acquisition protocol and analysis pipeline are stable. Scanning several human brain specimens would not be compatible with the duration of a PhD thesis, and would certainly require the establishment a multicenter-study in order to have access to a network of similar preclinical MRI systems so as to scan the specimens in a reasonable amount of time.

Three approaches could be adopted. First, scanning several entire brain specimens of the same population (same age, with no neurological disorder) could validate the observed contrast trends and would give access to the construction of probabilistic atlases of the anatomy, structural connectivity and microstructure of the human brain at ultra-high resolution, while capturing the inter-subject variability of this anatomical macro-/meso-/micro-structures.

A second project could be to study the variability between healthy and pathological populations. To date, there is no post mortem database established for neurological, psychiatric, or neurodevelopmental disorders. Scanning one ex vivo brain for such pathologies would definitively give a valuable insight about the these disorders from the macroscopic to the mesoscopic scale. Title: Post mortem inference of the human brain microstructure using ultra-high field magnetic resonance imaging with strong gradients Keywords: ultra-high field MRI; cortical cytoarchitecture; structural connectivity; white matter microstructure Abstract: The aim of ultra-high field strength (≥ 7T) and ultra-strong gradient systems (≥ 300mT/m) is to go beyond the millimeter resolution imposed at lower field and to reach the mesoscopic scale in neuroimaging. This scale is essential to understand the link between brain structure and function. However, despite recent technological improvements of clinical UHF-MRI, gradient systems remain too limited to reach this resolution. This thesis aims at answering the need for mapping the human brain at a mesoscopic scale by the study of post mortem samples. An alternative approach has been developed, based on the use of preclinical systems equipped with ultra-high fields (7T/11.7T) and strong gradients (780mT).

After its extraction and fixation at Bretonneau University Hospital (Tours), an entire human brain specimen was scanned on a 3T clinical system, before separating its two hemispheres and cutting each hemisphere into seven blocks that could fit into the small bore of an 11.7T preclinical system. An MRI acquisition protocol targeting a mesoscopic resolution was then set up at 11.7T. This protocol, including anatomical, quantitative, and diffusion-weighted sequences, was validated through the study of two key structures: the hippocampus and the brainstem. From the high resolution anatomical and diffusion dataset of the human hippocampus, it was possible to segment the hippocampal subfields, to extract the polysynaptic pathway, and to observe a positive gradient of connectivity and neuritic density in the posterior-anterior direction of the hippocampal formation. The use of advanced microstructural models (NODDI) also highlighted the potential of these techniques to reveal the laminar structure of the Ammon's horn. A high resolution anatomical and diffusion MRI dataset was obtained from the human brainstem with an enhanced resolution of a hundred micrometers. The segmentation of 53 of its 71 nuclei was performed at the Bretonneau University Hospital, making it the most complete MR-based segmentation of the human brainstem to date. Major white matter bundles were reconstructed, as well as projections of the locus coeruleus, a structure known to be impaired in Parkinson's disease. Buoyed by these results, a dedicated acquisition campaign targeting the entire left hemisphere was launched for total scan duration of 10 months. The acquisition protocol was performed at 11.7T and included high resolution anatomical sequences (100/150μm) as well as 3D diffusion-weighted sequences (b=1500/4500/8000 s/mm 2 , 25/60/90 directions, 200μm). In addition, T1-weighted inversion recovery turbo spin echo scans were performed at 7T to further investigate the myeloarchitecture of the cortical ribbon at 300µm, revealing its laminar structure. A new method to automatically segment the cortical layers was developed relying on a Gaussian mixture model integrating both T1-based myeloarchitectural information and diffusion-based cytoarchitectural information. The results gave evidence that the combination of these two contrasts highlighted the layers of the visual cortex, the myeloarchitectural information favoring the extraction of the outer layers and the neuritic density favoring the extraction of the deeper layers. Finally, the analysis of the MRI dataset acquired at 11.7T on the seven blocks required the development of a preprocessing pipeline to correct artifacts and to reconstruct the entire hemisphere using advanced registration methods. The aim was to obtain an ultra-high spatio-angular resolution MRI dataset of the left hemisphere, in order to establish a new mesoscopic post mortem MRI atlas of the human brain, including key information about its structure, connectivity and microstructure.

Université Paris-Saclay Espace Technologique / Immeuble Discovery Route de l'Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France

  8.1.2 Inner structures, internal connectivity and microstructure of the human brainstem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Laminar structure of the cortex inferred from MR-based myelo-and cytoarchitectural features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.4 Multi-contrast MR imaging of the human left hemisphere at a mesoscopic scale197 8.1.5 Contributions of this thesis regarding to the HBP and the FibrAtlasII-III projects198 8.1.5.1 One piece of the puzzle for the European Human Brain Project (HBP)198 8.1.5.2 FibrAtlasII-III project initiation . . . . . . . . . . . . . . . . . . . 8.2 Short and long-term prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Short-term prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Medium-term prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Long-term prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12 2 . 4 38 ix

 2438 Functional areas of the human brain . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 Brodmann's areas of the cerebral cortex . . . . . . . . . . . . . . . . . . . . . . . . 14 2.6 Basal ganglia in the cerebrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.7 Nuclei in the diencephalon and the midbrain coupled with an external view of cranial nerves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.8 Drawing of an axial view of the cerebellum . . . . . . . . . . . . . . . . . . . . . . 16 2.9 Schematic representation of projection fibers: descending and ascending tracts . . . . 19 2.10 Schematic representation of association fibers and a midsagittal view of a human brain highlighting the three main commissures . . . . . . . . . . . . . . . . . . . . . 20 2.11 Schematic representation of neurons and glial cells in the brain tissue . . . . . . . . 22 2.12 Drawing from a cross section of neocortex stained by three different methods . . . . 24 3.1 Schematic representation of a magnetic resonance system . . . . . . . . . . . . . . . 28 3.2 Diagram showing the process of the excitation-relaxation phenomenon . . . . . . . . 31 3.3 Schematic representation of the slice selection mechanism . . . . . . . . . . . . . . 32 3.4 K-space: the Fourier transform of an MR image . . . . . . . . . . . . . . . . . . . . 32 3.5 Line by line k-space filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.6 Spin echo and gradient echo sequences . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.7 Ellipsoid visualization of the DT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.8 Basic PGSE sequence diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.9 Schematic diagram explaining the relationship between water motion and observed signal attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of changing the direction of the diffusion-sensitizing gradients on the DW intensity and DTI maps reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Major microstructural models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 Deterministic tractography rendering . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Protein coagulation in a formaldehyde solution . . . . . . . . . . . . . . . . . . . . 4.2 Evolution of MR tissue properties as a function of the time spent in the fixative solution as well as the rehydration time . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Illustration of two methods to reduce effects of Eddy currents . . . . . . . . . . . . . 4.4 Illustration of common MR artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Increase of T1 contrast with the use of inversion-recovery . . . . . . . . . . . . . . . 4.6 Simplified diagram of a multi echo spin echo sequence . . . . . . . . . . . . . . . . 4.7 Simplified diagram explaining the multi-slice option . . . . . . . . . . . . . . . . . 4.8 Simplified diagram of the RARE sequence . . . . . . . . . . . . . . . . . . . . . . . 4.9 Diagram of a 2D spin-echo EPI sequence and resulting filling of the k-space . . . . . 4.10 Eddy currents leading to N/2 ghosting artifact . . . . . . . . . . . . . . . . . . . . . 5.1 Localization of the human hippocampus . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Aspect of the human hippocampus . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Schematic coronal section of the hippocampal formation and the surrounding structures, with a zoom in the hippocampus highlighting the subfields of the cornu Ammonis 5.4 Two major intrahippocampal pathways: the polysynaptic and the direct circuits . . . 5.5 Hippocampus specimen and its container . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Histograms showing the repartition of the T2 and mean diffusivity values of the hippocampus sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Close view of the shift in fiber orientation between alveus and fimbria . . . . . . . . 5.8 Anatomical and diffusion images of the human hippocampus at 200/300 µm . . . . . 5.9 Segmentation of the hippocampus subfields . . . . . . . . . . . . . . . . . . . . . . 5.10 Three-dimensional rendering of the manual segmentation of the inner and surrounding structures of the hippocampus from T2-weighted MRI at 200 µm . . . . . . . . . 5.11 Color-encoded diffusion directions of the human hippocampus at 300µm and 500 directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12 ODF field and the resulting tractogram obtained from a streamline regularized probabilistic tractography superimposed in a T2(b = 0) coronal slice of the hippocampus . 5.13 Connectivity matrix of the hippocampal substructures obtained with the streamline regularized deterministic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 Connectivity matrix of the hippocampal substructures obtained with the probabilistic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.15 3D-rendering of the perforant pathway and mossy fibers in the body of the hippocampus extracted from four tractograms (DTI/SRD, QBI/SRD, DTI/SRP, QBI/SRP) . . . 5.16 Neurite density gradient in hippocampal gray matter . . . . . . . . . . . . . . . . . . 5.17 Neurite density gradient in hippocampal white matter . . . . . . . . . . . . . . . . . 5.18 The laminar structure of the Ammon's horn revealed by the neurite density map from NODDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.19 Localization of the human brainstem . . . . . . . . . . . . . . . . . . . . . . . . . . 5.20 Schematic representation of a ventral, dorsal and medial view of the brainstem and part of the diencephalon, the spinal cord and the cerebellum . . . . . . . . . . . . . . 5.21 Cranial nerves originating from the brainstem . . . . . . . . . . . . . . . . . . . . . List of Figures xi 5.22 Axial sections of the brainstem acquired at 9.4 T highlighting the numerous nuclei contained in the structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.23 Brainstem specimen and its container . . . . . . . . . . . . . . . . . . . . . . . . . 5.24 Histograms showing the repartition of the T2 and mean diffusivity values of the brainstem sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.25 Anatomical and diffusion images of the human brainstem at 100/185/300 µm . . . . 5.26 Normalized cumulative histograms of the fiber length repartition obtained with a probabilistic and a deterministic algorithm . . . . . . . . . . . . . . . . . . . . . . . 5.27 Sagittal views of the brainstem DT maps (CED, FA, MD) . . . . . . . . . . . . . . . 5.28 Coronal view of the cortico-spinal tract and transverse pontine fibers crossing highlighting the benefit of using ODFs instead of tensors . . . . . . . . . . . . . . . . . . 5.29 Segmentation of the brainstem and its surrounding structures . . . . . . . . . . . . . 5.30 Three-dimensional rendering of the brainstem manual segmentation from T2-weighted MRI at 100 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.31 Preprocessing of the image of labels . . . . . . . . . . . . . . . . . . . . . . . . . . 5.32 Reconstruction of major brainstem white matter tracts . . . . . . . . . . . . . . . . . 5.33 Projections of the right locus coeruleus . . . . . . . . . . . . . . . . . . . . . . . . . 5.34 Box plot of the effective b-values for each shell . . . . . . . . . . . . . . . . . . . . 5.35 Representation of the signal attenuation for one voxel of the transverse pontine fibers 5.36 Representation of the signal attenuation for one voxel of the transverse pontine fibers after the non-local means filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.37 Representation of the fit quality and the resulting intracellular volume fraction map with four parameters settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.38 Brainstem microstructural features obtained from NODDI . . . . . . . . . . . . . . 6.1 Laminar patterns in cyto-and myelo-architecture of M1, S1, V1 and V2 . . . . . . . 6.2 Human brain specimen including part of the occipital lobe and its container . . . . . 6.3 Anatomical, diffusion and inversion-recovery images of the human occipital lobe at 100/185/300 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 T1 and proton density mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Microstructure maps inferred from the NODDI model . . . . . . . . . . . . . . . . . 6.6 Determination of the number of T1 clusters . . . . . . . . . . . . . . . . . . . . . . 6.7 T1 clustering results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 Potts regularization applied on the T1 cluster map . . . . . . . . . . . . . . . . . . . 6.9 Determination of the number of clusters in the intracellular volume fraction map . . . 6.10 Clustering of the intracellular volume fraction map . . . . . . . . . . . . . . . . . . 6.11 Potts regularization applied to the f intra cluster map . . . . . . . . . . . . . . . . . . 6.12 Comparison between T1-based and f intra -based clusters . . . . . . . . . . . . . . . . 6.13 Multivariate clustering combining myelo-and cyto-architecture information . . . . . 7.1 Fit quality for the estimation of the gel MR characteristics . . . . . . . . . . . . . . 7.2 Brain sample cutting steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Anatomical images acquired on a 3 T clinical system to facilitate the final registration 7.4 Identification of the field of views on the seven blocks obtained from the left hemisphere176 7.5 Example of an acquired field of view . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Spectrum of a block at 11.7 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Artifacts encountered during the acquisition protocol design . . . . . . . . . . . . . List of Figures xii 7.8 Anatomical images obtained on the field of view C2, depicting the human hippocampus and part of the midbrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 Time line of the Chenonceau acquisition campaign . . . . . . . . . . . . . . . . . . 7.10 Anatomical and diffusion weighted images of F3 . . . . . . . . . . . . . . . . . . . 7.11 Imaging of block B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.12 Imaging of block F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.13 Imaging of block G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.14 Registration of the seven blocks on the blockface image . . . . . . . . . . . . . . . . 7.15 Partial reconstruction of the left hemisphere at 200 µm . . . . . . . . . . . . . . . . . 7.16 Partial reconstruction of the left hemisphere at 200 µm with color-encoded direction maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.17 Partial reconstruction of the left hemisphere at 150 µm . . . . . . . . . . . . . . . . 7.18 Partial reconstruction of the left hemisphere at 100 µm . . . . . . . . . . . . . . . . List of Tables 4.1 Relaxation studies performed at various static fields and experimental conditions . . 5.1 Acquisition parameters for the HYDI dataset of the hippocampus sample . . . . . . . 5.2 Mean intracellular fraction of each segmented structure of the hippocampus . . . . . 5.3 HYDI parameters for the brainstem acquisition . . . . . . . . . . . . . . . . . . . . 6.1 HYDI parameters for the cortex acquisition with classical 2D PGSE . . . .

FIGURE 1 :FIGURE 2 :

 12 FIGURE 1: Rendu tridimensionnel de la segmentation manuelle des structures internes et avoisinantes de l'hippocampe, réalisée sur l'image anatomiqe acquise à une résolution spatiale de 200 µm

FIGURE 3 :

 3 FIGURE 3: Comparaison du contraste entre les trois couches principales de la corne d'Ammon, en observant (a) una image anatomique standard, obtenue par une spin-echo pondérée en T2, et (b) la carte de fraction volumique intracellulaire obtenue par le modèle NODDI et qui correspond à la densité en neurite en chaque voxel. L'échelle de couleur représente la fraction intracellulaire. Les couches théoriques de la corne d'Ammon sont dessinées dans la partie (c) adaptée de Duvernoy [2005]. En observant l'image (a), ces frontières, peu visibles, seraient positionnées au niveau des lignes en pointillé vertes. L'image (b) présente des frontières beaucoup plus marquées dont le positionnement est indiqué par des pointillés blanc, reportés en pointillé oranges sur l'image (a)

FIGURE 4 :

 4 FIGURE 4: Rendu tridimensionnel des segmentations du tronc cérébral réalisées sur l'image anatomique à 100 µm. Vues ventrale (a), latérale (b et d), et dorsale (c) des 51 noyaux segmentés; (e) région d'intérêt pour l'extraction des faisceaux de matière blanche; (f) noyaux du diencéphale et du cervelet, ainsi que la PAG du tronc cérébral; (g) rendu tridimensionnal de l'ensemble des structures segmentées. Pour les images allant de (d) à (g), les segmentations sont fusionnées avec le rendu tridimensionnel du contour du spécimen étudié

FIGURE 5 :

 5 FIGURE 5: Projections du locus coeruleus droit. (a) Localisation du locus coeruleus (LC) sur l'image anatomique à 100 µm et rendu volumique de sa segmentation (b). (c) et (d) présentent les différentes étapes nécessaires à la reconstruction de la connectivité du LC à partir d'un tractogramme obtenu par un algorithme déterministe (SRD) et probabiliste (SRP). La première étape est la sélection des fibres intersectant la zone identifiée comme étant le LC. Puis un filtre est apliqué pour ne sélectionner que les faisceaux contenant plus de dix fibres. Enfin, une étape de correction manuelle est nécessaire pour éliminer les fibres s'avérant être des faux positifs

FIGURE 6 :

 6 FIGURE 6: Segmentation multi-contrastes combinant des informations sur la myelo-et la cytoarchitecture. En haut, histogramme 2D représenté par 15 Gaussiennes, permettant d'obtenir une carte de labels (milieu gauche) régularisée à l'aide d'un modèle de Potts (milieu droite). Un zoom sur une zone du cortex permet d'observer la délimitation de deux à trois couches dans la partie la plus externe du cortex et de trois à quatre couches dans la partie interne

FIGURE 7 :

 7 FIGURE 7: Identification des blocs, avec une lettre de A à G, chaque bloc étant divisé en quatre champs de vue numéroté de 1 à 4 dans la direction postéro-antérieure. Abbreviations: A = Antérieur; P = Postérieur; I = Inferieur; S = Superieur

FIGURE 8 :

 8 FIGURE 8: Recalage des sept blocs sur l'image de référence. (a) blocs acquis à 3 T avant d'être retourné et recalé; les blocs ont été recalés avec une transformation affine sur l'image de référence. La fusion des blocs recalés et de l'image de cerveau entier est présentée en vue coronale (b) et sagittale (c, d)

Chapter 1. Introduction 5 Chapter 6 :

 56 Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features This chapter proposes to study the cortical lamination of an ex vivo sample containing part of the visual cortex, by using not only myeloarchitecture information stemming from T1 relaxation but also microstructural-based layer clustering. The first section reviews the existing techniques to identify cortical layers using MRI techniques and proposes a new approach combining myelo-and cytoarchitectural features. The second section presents the protocol designed to generate accurate data for the developed algorithm. Finally, the obtained results are discussed with regard to the actual knowledge on cortical layers. Part III -Chenonceau project Chapter 7: Towards a mesoscopic post mortem human brain MRI atlas

FIGURE 2 . 1 :

 21 FIGURE 2.1: Main regions of the human brain and intracranial cerebrospinal fluid distribution. (a)The encephalon can be divided into four structures. The cerebrum, consisting of the cerebral hemispheres, forms the largest part of the brain. The diencephalon is located deep within the brain, between the cerebrum and the brainstem. The brainstem connects the cerebrum via the diencephalon, the cerebellum and the spinal cord. It includes the midbrain, the pons, and the medulla oblongata (image adapted from[Marieb, 2009]). (b) Intracranial cerebrospinal fluid distribution highlighting the brain's ventricular system (image adapted from[START_REF] Blausen | Medical gallery of blausen medical[END_REF]).

Figure 2 .

 2 3.b.)and the limbic lobe(Figure 2.3.c.). Each of them is implicated in specific functional tasks as depicted in Figure2.4. The following overview is far from being exhaustive and only aims at giving examples of tasks associated to each lobe.

FIGURE 2 . 2 :

 22 FIGURE 2.2: Morphology of a neuron and differences between white and gray matter. a. Schematic representation of the structure of a typical neuron. The soma is the body of the cell and constitutes the gray matter, outside of the cerebrum. The axon (also called a nerve fiber) is a special cellular extension that arises from the cell body (image adapted from https: // www. matierevolution. fr ). b. Coronal cross section of human brain, showing the white and gray matters (image adapted from http: // www. anatomie-amsterdam. nl ).

FIGURE 2 . 3 :

 23 FIGURE 2.3: Lobes of the human brain. a. Lateral view of the external lobes: frontal, parietal, temporal and occipital, as well as two main sulci identified with the red dotted line: the lateral and central sulcus (image adapted from http: // www. anatomie-amsterdam. nl ); b. Lateral aspect of the insular lobe in blue exposed by removal of the frontal, parietal and temporal operculum. c. Medial view of the human brain depicting the frontal, parietal, occipital, temporal and also the limbic lobe that can only be visualized in a medial view. (images are taken from http: // www. healcentral. org ). Abbreviations: A: Anterior; P: Posterior

FIGURE 2 . 4 :

 24 FIGURE 2.4: Schematic visualization of major functional areas of the human left hemisphere. Dashed areas are commonly left hemisphere dominant. Four colors identify the four external lobes: occipital (green), temporal (beige), parietal (blue), and frontal (pink) (image taken from Blausen [2014])

FIGURE 2 . 5 :

 25 FIGURE 2.5: Brodmann's areas of the cerebral cortex. Each area presents a distinct cytoarchitecture and is labelled with a specific number (image taken from http: // philschatz. com/ anatomy-book , based on original work by Korbinian Brodmann)

FIGURE 2 . 6 :

 26 FIGURE 2.6: Basal ganglia in the cerebrum, with the internal capsule that separates the putamen and caudate nucleus. Strands of gray matter (pontes grisei) connect the caudate nucleus with the putamen. The putamen and the globus pallidus, collectively, are known as the lentiform nucleus (image adapted from http: // www. anatomie-amsterdam. nl )

  pairs of cranial nerves (I-XII), numbered in the order they emerge from the brain, front to back. With the exception of the olfactory (I) and optic nerves (II), the cranial nerves (III-XII) originate in the brainstem. Their nuclei are located in different regions of the brainstem: III and IV in the midbrain, V, VI, VII and VIII in the pons and IX, X, XI and XII in the medulla (see Figure2.7.b.). In addition to the cranial nerves nuclei, the brainstem encloses many other important clusters of neurons that will be reviewed in more details in chapter 5. Examples of such deep structures are: the substantia nigra, that is part of the basal ganglia control system, and whose dysfunction is implicated in Parkinson's disease, or the red nuclei that send a descending tract to motor neurons called the rubrospinal tract (see Figure2.7.a.).

FIGURE 2 . 7 :

 27 FIGURE 2.7: Nuclei in the diencephalon and the midbrain coupled with an external view of cranial nerves. a. Coronal section highlighting the thalamus, part of the diencephalon, and two major nuclei of the brainstem: the red nucleus and the substantia nigra (image adapted from http: // www. anatomie-amsterdam. nl ). b. Basal aspect of cerebellum and brainstem, showing cranial nerve attachments and some internal features of the medulla oblongata such as the olivary nucleus (image adapted from Williams et al. [1999])

FIGURE 2 . 8 :

 28 FIGURE 2.8: Drawing of an axial view of the cerebellum highlighting the position of the four cerebellar nuclei (in bold). In practice, on MR images, only the dentate nucleus is clearly visible. The cerebellum is covered by gray matter forming the cerebellar cortex (image adapted from https: // neupsykey. com )

Figure 2 .

 2 Figure 2.10.a. gives an illustration of some short and long association fibers.

FIGURE 2 . 9 :

 29 FIGURE 2.9: Schematic representation of projection fibers: descending and ascending tracts. a. Major descending motor tracts: pyramidal tracts are responsible for voluntary movements of the body via the corticospinal tract (1) and the face and the neck via the corticobulbar tract[START_REF]N b=0 N dir TR (ms) TE (ms) ∆ (ms) δ (ms) di Duration[END_REF]. Corticospinal tracts conduct impulses from the brain to the spinal cord whereas the corticobulbar tract conducts impulses from the brain to the medulla (part of the brainstem) in particular to the cranial nerves and also to the sensory nuclei including gracile nucleus, cuneate nucleus, solitary nucleus, and all trigeminal nuclei. 80% of the CST decussate in the most inferior part of the medulla. b. The medial lemniscus is a large ascending (sensory) bundle of heavily myelinated axons that decussate in the brainstem, specifically in the medulla oblongata. The first neurons synapse with neurons in the gracile nuclei (medulla) if they are lower body axons, or with the cuneate nuclei (medulla) if they are upper body axons. The second axons travel up the rest of the brainstem, and synapse at the thalamus that is a relay for sensory information. Then, third axons synapse in the primary somatosensory cortex (image adapted from[START_REF] Gray | Anatomy of the human body[END_REF])

FIGURE 2 . 10 :

 210 FIGURE 2.10: Schematic representation of association fibers and a midsagittal view of a human brain highlighting the three main commissures. a. This drawing represents various types of association fibers such as the U-fibers as well as some long association fibers: the superior longitudinal fasciculus, the cingulum, the perpendicular fasciculus, the inferior longitudinal fasciculus and the uncinate fasciculus (image adapted from[START_REF] Gray | Anatomy of the human body[END_REF]). b. Midsagittal view of a human brain highlighting the three main commissures: the corpus callosum and the anterior and posterior commissures (image adapted from http: // www. anatomie-amsterdam. nl )

Figure 2 .

 2 11. The myelin sheath is divided into segments along the axon with regular gaps called nodes of Ranvier. Myelin insulates the axon, which boosts the conduction speed along axons by a factor of about 5.5 and prevents the electric current from leaving the axon [Waxman and Bennett, 1972]. The g-ratio, obtained by dividing inner by outer diameter, is suggested to have a value that optimizes conduction speed. This value is about 0.7 in normal CNS [Smith and Koles, 1970].

FIGURE 2 .

 2 FIGURE 2.11: Schematic representation of neurons and glial cells in the brain tissue. a. Glial cells support neuronal function. Oligodendrocytes create the myelin sheath in the CNS, and thus have a function equivalent to the one performed by Schwann cells in the PNS. Nodes of Ranvier are the gaps between myelin sheaths segments. b. The thickness of the myelin around axons in normal conditions has a roughly constant ratio, called g-ratio, with the axon diameter. The space encapsulated by the axolemma, the cell membrane surrounding the axon, is the intra-axonal space. (image adapted from Nilsson et al. [2013a])

FIGURE 2 .

 2 FIGURE 2.12: Drawing from a cross section of neocortex stained by three different methods; the six cortical layers are indicated. The Golgi stain reveals the shapes of the arborizations of cortical neurons by completely staining a small percentage of them. The Nissl method stains the cell bodies of all neurons, showing their shapes and packing densities. The Weigert method stains myelin, revealing the horizontally oriented bands of Baillarger, Kaes and Cajal-Retzius stripes, as well as the vertically oriented collections of cortical afferents and efferents. (image adapted from[START_REF] Brodmann | Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues[END_REF])

  FIGURE 3.1: Schematic representation of a magnetic resonance system with a superconducting electromagnet. B 0 is the main static field. B 1 , the rotating magnetic field that tilts the spins to the XY plane, is orthogonal to B 0 (image adapted from[START_REF] Kastler | Comprendre l'IRM: manuel d'auto-apprentissage[END_REF])

FIGURE 3 . 2 :

 32 FIGURE 3.2:Diagram showing the process of the excitation-relaxation phenomenon after a 90°RF pulse is applied at equilibrium. a. The net magnetization M 0 (red arrow) is at equilibrium, aligned with the static magnetic field B 0 ; b. when a 90°RF pulse is applied with B 1 , the longitudinal magnetization M z becomes null and M 0 lies entirely in the XY plane; c., d. The net transverse magnetization decays as the spins (shown by the small black arrows) move out of phase with one another. The overall term for the observed loss of phase coherence (dephasing) is T 2 * relaxation, which combines the effect of T2 relaxation and additional dephasing caused by local inhomogeneities in the magnetic field; e., f. The additional decay caused by field inhomogeneities can be reversed by the application of a 180°refocusing pulse. Both T2 and T 2 * are exponential processes with times constants T2 and T 2 * respectively. The resultant decaying signal is known as the Free Induction Decay (FID); g., h. The longitudinal magnetization recovers gradually back to its equilibrium value. The recovery of M z is an exponential process with a time constant T1.

FIGURE 3 . 3 :

 33 FIGURE 3.3: Slice selective excitation of a human torso using a RF pulse applied concomitantly with a Slice Selection Gradient (GSS) along the Z direction. The frequency increases from ω 1 to ω 10 in each plan P perpendicular to the Z-axis. If ω r = ω 6 , only the protons in P6 will flip and contribute to the MR signal (image adapted from Kastler and Vetter [2011])

FIGURE 3

 3 FIGURE 3.4: K-space: the Fourier transform of the MR image. a. Raw data in the k-space. b. Image obtained from a Fourier transform (image adapted from Kastler and Vetter [2011])

FIGURE 3 . 5 :

 35 FIGURE 3.5: Filling of the k-space. The acquisition occurs line by line with the reading at t = TE for each line. The passage to the next line at t = TR is obtained by incrementing the phase gradient G φ . This example is based on a gradient echo sequence, but the principle remains the same for a spin echo (image adapted from Kastler and Vetter [2011])

FIGURE 3 . 6 :

 36 FIGURE 3.6: Sequence diagrams of a spin echo and a gradient echo sequence. a. Spin echo sequence, with a 90°RF pulse that flips net magnetization in the transverse plane, a 180°RF pulse applied at t=TE/2 to rephase the spins, and the signal reading at t=TE. b. Gradient echo sequence with a partial flip angle α usually lower than 90°. The low-flip angle excitation provides a faster recovery of the longitudinal magnetization that allows shorter TR/TE and decreases scan time. G s is for the slice selection, G φ for the line selection and G r for the line readout

FIGURE 3 . 7 :

 37 FIGURE 3.7: Ellipsoid visualization of the DT. The eigenvalues are λ 1 , λ 2 , λ 3 , where λ 1 ≥ λ 2 ≥ λ 3 , and the corresponding eigenvectors are e 1 , e 2 , e 3 . The principal diffusion direction is given by e 1 .

FIGURE 3 . 8 :

 38 FIGURE 3.8: Simplified diagram of the PGSE sequence developed by Stejskal and Tanner [1965]. A single pair of diffusion-encoding gradients is applied along a single axis with a given amplitude G, a duration δ and a separation time ∆.

FIGURE 3 . 10 :

 310 FIGURE 3.10: The figure shows the same brainstem slice (work presented in chapter 6). a., b., and c. correspond to three different gradient directions and show the effect of changing the direction of the diffusion sensitizing gradients on the DW intensity. The orange arrow highlights the signal intensity change of the pyramidal tract depending on the gradient direction. The amount of diffusion weighting (b=4500s/mm 2 ) is the same in all three cases. d., e. and f. are three maps reconstructed with the DTI model. d. is a RGB map that encodes the x-y-z coordinates of the principal eigenvector e 1 . The color-encoding cross at the upper left corner of the image depicts the direction of largest displacement probability orientation. e. is a fractional anisotropy (FA) map and f. a mean diffusivity (MD) map. Abbreviations: A = Anterior; P = Posterior; S = Superior; I = Inferior

  In 2005, Assaf et al. introduced a more realistic depiction of the intraaxonal space. Unlike Ball & Stick, CHARMED represents the intra-axonal space as a distribution of cylinders. Axons are represented as packed parallel and impermeable cylinders, with an individual diameter. This model combines a hindered diffusion process corresponding to the extra-cellular compartment in the white matter voxel and a restricted compartment defined by the diffusion process in axons. The model is able to recover the fiber orientation, the intracellular diffusivity parallel to the fibers, the extracellular diffusivities and the corresponding volume fractions (Figure 3.11.B.1.).

In 2011 ,

 2011 [START_REF] Zhang | Axon diameter mapping in the presence of orientation dispersion with diffusion MRI[END_REF] extended the ActiveAx model and introduced the possibility of characterizing the fiber dispersion by the use of an axonal orientation distribution, modeled as a Watson's distribution (see Figure 3.11.C.). This technique is suitable for estimating axon diameter and orientation dispersion from in vivo human data acquired with four different b-values and multiple gradient directions (four HARDI shells). In later work, Zhang et al. [2012] developed neurite orientation dispersion and density imaging (NODDI), a simplified version of the model above designed for clinical routine imaging, and which requires only two to three shells. NODDI models the signal contribution from three compartments: an intra-neurite compartment represented by sticks (instead of cylinders) following a Watson distribution, an extra-neurite compartment modeled by a cylindrically symmetric tensor and a CSF compartment which exhibits free isotropic diffusion. A stationary fraction is also added when considering ex vivo tissues (see Figure 3.11.D.

FIGURE 3 . 11 :

 311 FIGURE 3.11: This table presents the major microstructural models presented in section 3.2.7.2 with the corresponding compartments. the intra-axonal space can be modeled by sticks or impermeable cylinders. The extra-cellular space is modeled using a Gaussian anisotropic distribution, and the CSF with a free Gaussian distribution, except for the Ball & Stick model, in which extra-cellular and isotropic space are both modeled by a sphere. The stationary compartment corresponds to the water trapped in glial cells after tissue fixation and is consequently used only for ex vivo studies.

  Figure 4.4.b.) or massive loss of signal (Figure 4.4.a.).

FIGURE 4 . 1 :

 41 FIGURE 4.1: Protein coagulation in a formaldehyde solution. (1) Formation of methylene glycol by the addition of water to formaldehyde. (2) Formaldehyde reacts with various parts of proteins molecules forming adducts. This reaction is followed by the formation of methylene bridges (-CH 2 -) between closed proteins resulting in large protein complexes (image adapted from[START_REF] Lyng | Biomedical Applications of Synchrotron Infrared Microspectroscopy: A Practical Approach[END_REF])

FIGURE 4 . 2 :

 42 FIGURE 4.2: Evolution of MR tissue properties of a fixed tissue as a function of the time spent in the fixative solution as well as the rehydration time.Acquisitions have been performed on sheep brains acquired on a 7T clinical system. T1 decreases during the first eight weeks of fixation and is not impacted by rehydration. T2 and T 2 * behave the same way, with a decrease the first week of fixation, followed by a regrowth to a plateau after six weeks as reported by[START_REF] Robert J Dawe | Postmortem MRI of human brain hemispheres: T2 relaxation times during formaldehyde fixation[END_REF]. Rehydration induces an increase of T2 about 12% in the GW and 5% in the WM, which is much less than other reported results[START_REF] Helen | An approach to high resolution diffusion tensor imaging in fixed primate brain[END_REF] (image adapted from[START_REF] Leprince | Imagerie des couches corticales par résonance magnétique à 7 teslas[END_REF])

  Figure 4.3.3 shows two types of motion artifacts: the first one resulting in dark images (4.3.3.a.) and the second one in a distorted image (4.3.3.b.).

  ing birth to different Eddy currents and consequently different geometrical distortions. It is therefore important to correct them adequately previous to any advanced analysis. There are several methods to reduce the effects of these induced currents. First, all manufacturers use active gradient coil shielding, which reduces the generation of Eddy currents, and a purposeful distortion of the electric current profile sent to the gradient coils that compensates Eddy currents (see figure 4.3.a.). Regarding the remaining Eddy currents, two kind of strategies can be considered. The first one is the use of an acquisition sequence limiting Eddy currents effects, such as the twice-refocused SE (TRSE) introduced by Reese et al. [2003] that adds a second refocusing pulse and uses two bipolar gradients (see figure 4.3.b.). Another option is the image post-processing to correct for spatial nonlinearities due to Eddy currents. For instance, with the assumption of a short principle Eddy current decay time, global affine transformations can be used in the phase-encoding direction to align images from a diffusion-weighted set to a baseline image with no diffusion weighting[START_REF] Mangin | Eddy-current distortion correction and robust tensor estimation for mr diffusion imaging[END_REF].

FIGURE 4 . 3 :

 43 FIGURE 4.3: Illustration of two methods to reduce effects of Eddy currents. a. distortion of the electric current profile sent to the gradient coils to compensate the effects. On the left, the resulting gradients without the pulse distortions. On the right, more accurate resulting gradients obtained with distortions applied on the delivered pulse (images adapted from www. imaios. com ) b. Simplified diagram of the TRSE sequence proposed by Reese et al. [2003], with two refocusing pulses and the use of bipolar gradients (images adapted from Reese et al. [2003])

FIGURE 4 . 4 :

 44 FIGURE 4.4: Illustration of common MR artifacts. a. and b. Two types of motion occurring during diffusion-weighted imaging and resulting in two types of artifacts: 1. motion occurring along the slice direction between the excitation and the echotrain resulting in dark images (red boxes in a.) and 2. motion in the slice direction during the acquisition of the echotrain (b.) (images taken from Neurospin database) c. Aliasing in the phase-encoding direction due to a restricted FOV (image adapted from[START_REF] Kastler | Comprendre l'IRM: manuel d'auto-apprentissage[END_REF]). d. Susceptibility artifact induced by air bubbles trapped outside the cortex of a sheep brain. e. Susceptibility artifact induced by the presence of metal outside the sample container. f. Chemical shift caused by the lipid of the skin. This artifact can be avoided by the application of a fat saturation pulse (g.) and, more efficiently, a spectral-spatial pulse[START_REF] Pauly | Parameter relations for the shinnar-le roux selective excitation pulse design algorithm (nmr imaging)[END_REF] (images taken from https: // radiologykey. com )

Chapter 4 .

 4 Post mortem imaging 69 T1 of each voxel.This is achieved by running IR-SE sequences with various inversion times (t=TI) to sample the regrowth curve of the longitudinal magnetization. Then, the obtained data can be used to fit a mono-exponential model corresponding to the T1 regrowth, S(t) = S 0 1-2e -t/T 1 , where S 0 and T1 are the two parameters to be determined.

FIGURE 4 . 5 :

 45 FIGURE 4.5: Increase of T1 contrast with the use of inversion-recovery. a. Longitudinal magnetization regrowth following a 90°excitation pulse. This graph highlights the T1 recovery in a classical SE sequence. b. Longitudinal magnetization regrowth following a 180°excitation pulse. The time for T1 recovery becomes TI, instead of TR in the classical SE

  FIGURE 4.6: Simplified diagram of a multi echo spin echo sequence with five generated echoes. Additional 180°-refocusing pulses generate additional echoes, with a decreasing amplitude due to T2 decay. The obtained data can then be used to fit a mono-exponential model corresponding to the T2 decay in order to obtain the characteristic T2 of each voxel

FIGURE 4 . 7 :

 47 FIGURE 4.7: Simplified diagram explaining the multi-slice option based on a spin echo sequence with a T2 contrast (long TE and TR), with typical values of TE and TR used for a post mortem acquisition on a preclinical system. a. Simplified diagram of a spin echo sequence without the multi slice option. Signal echo and the second excitation are separated by a long idle time. b. Simplified diagram of a spin echo sequence with the multi slice option. Between the acquisition of the first and the second line of the slice 1, separated by the time TR, the first line of other slices (from 2 to n) is acquired

FIGURE 4 . 8 :

 48 FIGURE 4.8: Principle of the RARE sequence. a. Simplified diagram of the RARE sequence. The effective TE (T E e f f ) is the delay between the excitation pulse and the central phase-encoding step. This parameter determines the T2 contrast. b. Filling of the k-space: multiple lines are acquired with one excitation

FIGURE 4 . 9 :

 49 FIGURE 4.9: Diagram of a spin-echo EPI sequence and resulting filling of the k-space. a. Diagram of a spin-echo EPI sequence.The first downward-going frequency and phase encoding lobes imparted initial negative phase shifts to all spins, moving the signal from the middle of k-space to the far left bottom corner to a point we have previously identified as (-k xmax ,-k ymax ). Subsequent positive and negative frequency-encoding lobes swept k-space from left-to-right and right-to-left respectively. Meanwhile, the blipped low-amplitude phase-encoding gradient pulses produced a step-wise increase along the k y axis. b. k-space filling with a "zig-zag" shape. In this case, the sequence is single-shot

FIGURE 4 . 10 :

 410 FIGURE 4.10: Eddy currents leading to N/2 ghosting artifact. a. Eddy currents modify the actual shape of the gradient pulses. As a result, echo signals are not well refocused, and therefore misaligned in the k-space. b. After reconstruction, this misalignment induces a ghost image, shifted by half of the FOV in the phase encoding direction (N/2 ghost) (image adapted from [Le Bihan et al., 2006])

  internal connectivity and microstructure of two major structures of the human brain: the hippocampus and the brainstem According to a United Nations report published in 2015 on world population aging [DESA, 2015], the number of people aged 60 and older worldwide is projected to more than double in the next 35 years, reaching almost 2.1 billion people. As the population ages, the prevalence of neurodegenerative diseases will increase. The two most widespread neurodegenerative diseases are dementia 1 , Alzheimer's disease (AD) accounting for one half to three quarters of all cases, and Parkinson's disease (PD) 2 .

FIGURE 5 . 1 :

 51 FIGURE 5.1: Localization of the human hippocampus on a T1-weighted image of a subject from the Archi database [Assaf et al., 2013], acquired at 3T with a resolution of 1 mm isotropic. The hippocampus is the gray matter structure found inside the red boxes in a coronal (a), axial (b), and sagittal (c) view

FIGURE 5 . 2 :

 52 FIGURE 5.2: Aspect of the human hippocampus. (a) Dorsolateral view of the human hippocampus after removal of the overlying structures: 1. head 2. body 3. fimbria-fornix 4. hippocampal commissure, 5. temporal horn of the lateral ventricle, 6. amygdala, 9. corpus callosum (image taken from Insausti and Amaral [2012]) (b) Intraventricular aspect of the hippocampus. H: head, B: body, T: tail, f: fimbria, s: subiculum. White arrowheads highlight the limits of the hippocampus (image taken from Gérardin [2012] adapted from Duvernoy [2005])

FIGURE 5 . 3 :

 53 FIGURE 5.3: Schematic coronal section of the hippocampal formation and the surrounding structures, with a zoom in the hippocampus highlighting the subfields of the cornu Ammonis. (a) The hippocampal formation: 1. cornu Ammonis, 2. gyrus dentatus, 3. hippocampal sulcus, 4. alveus, 5. fimbria, 6. prosubiculum, 7. subiculum, 8. presubiculum, 9. parasubculum, 10. entorhinal area, 11. parahippocampal gyrus, 12. collateral sulcus, 13. collateral eminence, 14. temporal horn of the lateral ventricle, 15. tail of the caudate nucleus, 16. plexus choroid, 17. pons of the brainstem. The red box shows the part of the hippocampal formation represented on the right. (b) Cytoarchitecture of the cornu Ammonis and the dentate gyrus, highlighting the layers as well as the subfields CA1-CA4: 1. alveus, 2. stratum oriens, 3. stratum pyramidale, 4. stratum radiatum, 5. stratum lacunosum, 6. stratum moleculare, 7. hippocampal sulcus, 8. stratum moleculare, 9. stratum granulosum, 10. polymorphic layer, 11. fimbria, 12. subicular complex (images adapted from Duvernoy [2005])

FIGURE 5 . 4 :

 54 FIGURE 5.4: Two major intrahippocampal pathways: the polysynaptic and the direct circuits. (a) Schematic coronal view of the polysynaptic pathway. A-E are parts of the neural chain forming the polysynaptic intrahippocampal pathway. In the cornu Ammonis: 1. alveus, 2. stratum pyramidale, 3. Schaffer collaterals, 4. axons of pyramidal neurons, 5. strata lacunosum and radiatum, 6. stratum moleculare, 7. hippocampal sulcus. In the gyrus dentatus (GD): 8. stratum moleculare, 9. stratum granulosum. (b) Schematic coronal view of the direct pathway: 1. inputs through the perirhinal cortex, 2. neurons of the layer III of the entorhinal area (ENT) project onto CA1 pyramidal cells, 3. CA1 pyramidal neurons innervate the subiculum (SUB), 4. subicular axons project back to the deep layers of the EC, 5. neurons of these layers send axons to the association cortex (image adapted from Duvernoy [2005])

  7 T Bruker MRI system (BioSpec 117/16 USR Bruker MRI, Ettlingen, Germany) equipped with strong gradients (maximum gradient magnitude = 780 mT/m, slew rate = 9660 T/m/s) using a 60 mm transmit/receive volume coil. Although surface coils are known to provide better SNRs than volume coils, the 60 mm volume coil was preferred because it corresponded to the best tradeoff between the FOV coverage and the dimensions of the sample. Furthermore, the volume coil enabled the preservation of a relative homogeneity of the signal through the entire FOV.

FIGURE 5 . 5 :

 55 FIGURE 5.5: Hippocampus specimen and its container. (a) posterior view of the original hippocampus specimen. The sample has been cut to fir into its dedicated container (b)

  4 ms and 76.8 ms. Imaging parameters for this sequence were: isotropic spatial resolution of 300µm, 12 averages, matrix size: 192 192, 176 slices, flip angle: 90°, receiver bandwidth: 300 kHz, TR= 16000 ms, and a total scan duration of 10h14min. Collected MSME data were then used to fit the log-linear model corresponding to the T2-decay with a Levenberg-Marquardt algorithm carefully initialized to get robust estimates. The histogram of the T2 map depicts two main modes of T2 (Figure 5.6.a).

  D A histogram of the mean diffusivity D was inferred using the DTI model from a diffusion-weighted dataset acquired with a single-shell sampling of the qspace at b = 4500 s/mm 2 along 60 uniformly distributed diffusion directions, TR/TE = 9000/24.2 ms, ∆/δ = 14.4/4.3 ms, matrix size: 192×192, 176 slices, and an isotropic resolution of 300 µm. The distribution indicates a mean diffusivity of 0.16 × 10 -3 mm 2 /s for the first mode (Figure 5.6.b).

FIGURE 5 . 6 :

 56 FIGURE 5.6: Histograms showing the repartition of the T2 and mean diffusivity values of the hippocampus sample. (a) T 2w is assumed to be the characteristic T2 of the white matter and T 2g the characteristic T2 of the gray matter. (b) D w is the mean diffusivity of the white matter and D g is assumed to be the one characteristic of the gray matter

  The anatomical image was acquired using a standard T2-weighted spin-echo sequence with isotropic spatial resolution of 200 µm, matrix size: 268 × 268, 256 slices, flip angle: 90°, TR/TE = 12000/26.5 ms, 15 averages, and a total scan time of 10h46min.Diffusion scan Diffusion data were acquired using a conventional PGSE sequence. The protocol included a first single-shell HARDI dataset used to infer the structural connectivity of the human hippocampal formation, to which a multiple-shell HYDI dataset was added to infer quantitative microstructural features using diffusion MR microscopy.

  The structural connectivity was established from the HARDI dataset collected at b = 4500 s/mm 2 along 500 directions uniformly distributed over a sphere. It was split into 15 blocks of 32 directions and one of 16 because of the memory limitation of the MRI IT system. For each block, 6 b = 0 images were acquired. Scanning parameters were: isotropic spatial resolution of 300 µm, TR/TE = 9000/24.2 ms, ∆/δ = 14.4/4.3 ms, matrix size: 192 × 192, 176 slices, flip angle: 90°, receiver bandwidth: 66 kHz, and a total scan time of 8 days and 18 hours. The b-value was calibrated taking into account the reduction of the average diffusivity from D = 0.7 × 10 -3 mm 2 /s in vivo to D = 0.16 × 10 -3 mm 2 /s in our case. As mentioned earlier, the dataset was used first to perform tractography, but also to map microstructural features when merged with the next HYDI dataset.In addition to the HARDI dataset, a further multiple-shell HYDI dataset was acquired for 3 different shells corresponding to 3 diffusion sensitizations at b = 4500 s/mm 2 , b = 7500 s/mm 2 and b = 10000 s/mm 2 . The choice of the b-values was carried out based on the usual sensitizations taken for NODDI or ActiveAx models with a scaling factor of around 3 applied to account for the attenuation of the diffusivities observed ex vivo. For each shell, 60 diffusion-weighted volumes were acquired along 60 uniformly distributed diffusion directions. The acquisition was divided into two blocks of 30

FIGURE 5 . 7 :

 57 FIGURE 5.7: Close view of the shift in fiber orientation between alveus and fimbria. Yellow arrowheads highlight typical inferior-superior orientation of ODFs in the alveus (fibers in the coronal plane, as shown on upper left). Orange arrowheads highlight typical anterior-posterior orientation of ODFs in the fimbria (fibers in the sagittal plane, as shown on upper left). White line shows the boundary between alveus and fimbria, defined within the transition zone corresponding to the shift in the fiber orientation

FIGURE 5 . 8 :

 58 FIGURE 5.8: Raw images obtained with the anatomical acquisition at 200 µm (a,b), and with the diffusion acquisition at 300 µm, b = 4500 s/mm 2 (c)

FIGURE 5 . 9 :

 59 FIGURE 5.9: Segmentation of the hippocampus subfields. The upper figure shows a sagittal view with references to all the coronal images. Coronal images of the hippocampal formation are shown in an anterior-to-posterior direction from a to h. The head is displayed in Figs. a-d, the body in Figs. e-f and the tail in Figs. g-h. The segmentation is shown in a'-h'

FIGURE 5 .

 5 FIGURE 5.11: Color-encoded diffusion directions at 300µm and 500 directions. The white dotted lines indicate the correspondence between axial (a), sagittal (b) and coronal (c) slices. Orange arrowheads point at the fimbria, yellow arrowheads at the alveus and pink arrowhead at the lacunosum-molecular layer. The color-encoding cross at the bottom left of the image depicts the direction of largest displacement probability orientation. Abbreviations: A = Anterior; P = Posterior; M = Medial; L = Lateral; S = Superior; I = Inferior

FIGURE 5 .

 5 FIGURE 5.12: ODF field and the resulting tractogram obtained from a streamline regularized probabilistic tractography superimposed in a T2(b = 0) coronal slice of the hippocampus. On the left, fusion of the T2(b = 0) image and the color-encoded diffusion directions map obtained with the DTI model (a). The color-encoding cross at the bottom left depicts the direction of largest displacement probability orientation. On the right, the orientation diffusion functions field computed with the Q-ball model (b) with a zoom of ODFs showing a crossing at the level of the Schaffer collateral (c), and the SRP tractogram calculated with this field (d), superimposed on (a). Pink arrowhead point at the radiatum and lacunosum-molecular layers with ODF orthogonal to the coronal plane

FIGURE 5 . 13 :

 513 FIGURE 5.13: Connectivity matrix of the hippocampal substructures obtained with the streamline regularized deterministic model. Each matrix element represents the number of fibers connecting the ROIs indicated by the column and by the row. Self connections are excluded, which implies a zero diagonal line in the matrix. The map is symmetric because efferent and afferent projections can-not be distinguished with diffusion MRI. The heat scale represents the number of fibers connecting the ROIs

FIGURE 5 . 14 :

 514 FIGURE 5.14: Connectivity matrix of the hippocampal substructures obtained with the probabilistic model. Each matrix element represents the number of fibers connecting the ROIs indicated by the column and by the row. Self connections are excluded, which implies a zero diagonal line in the matrix. The map is symmetric because efferent and afferent projections can-not be distinguished with diffusion MRI. The heat scale represents the number of fibers connecting the ROIs

FIGURE 5 .

 5 FIGURE 5.15: 3D-rendering of the perforant pathway and mossy fibers in the body of the hippocampus extracted from four tractograms (DTI/SRD, QBI/SRD, DTI/SRP, QBI/SRP) (a-d) mossy fibers in the body, from the granular layer of the dentate gyrus to the lucidum layer of CA3. 3D-rendering only shows the body segmentation; (e-f) perforant pathway from the entorhinal cortex to the molecular layer of the dentate gyrus in the body of the hippocampus. 3D-rendering shows the entire segmentation (head, body and tail) with the same color code as the one presented in Fig.5.9 and a transparency of 0.2, except for the entorhinal cortex (opaque gray) and the dentate gyrus in the body (opaque dark blue)

FIGURE 5 . 16 :

 516 FIGURE 5.16: Neurite density gradient in hippocampal gray matter. The intracellular volume fraction obtained with NODDI model was set with a limit at 0.2 to highlight gradients in gray matter regions. White circle indicates a region of higher intracellular volume fraction in gray matter. The heat scale represents the intracellular volume fraction. Abbreviations: A = Anterior; P = Posterior; M = Medial; L = Lateral

  depicted in Figure 5.18.a, the boundary remains partially defined. Green dotted lines are the boundaries inferred only with the T2-weighted contrast and, in orange, limits obtained with the combination of the T2-weighted image and the neurite density map (Fig.5.18.b). Fig.5.18.b clearly demonstrates that the intracellular volume fraction of the neurite population significantly enhances the contrast Chapter 5. Investigation of the human hippocampus and brainstem 104

FIGURE 5 . 18 :

 518 FIGURE 5.18: Comparison of the contrast between the three hippocampal layers using (a) a standard anatomical T2-weighted spin-echo sequence and (b) the intracellular volume fraction map obtained with NODDI model. The heat scale represents the intracellular volume fraction. The theoretical layers in cornu Ammonis are drawn in (c), adapted from Duvernoy [2005]. Their boundaries have been recognized, based on the T2-weighted image, with the green dotted lines in (a) and also, with the help of the intracellular volume fraction map as shown with the orange dotted lines in (a) and the white dotted lines in (b)

[

  2012] reconstructed, from in vivo data, the best known pathways of the medial temporal lobe including the perforant pathway and the Schaffer collaterals.[START_REF] Coras | 7T MRI features in control human hippocampus and hippocampal sclerosis: an ex vivo study with histologic correlations[END_REF] also identified the perforant pathway on a DTI-based tractogram and Augustinack et al.[2010] reconstructed it from ex vivo DTIbased data. However, our study was one of the first to go beyond diffusion tensor imaging to probe the circuits and the inner connectivity of the human hippocampus. Assuming a Gaussian distribution of water molecule displacements, DTI can support only one fiber population per voxel, thus being unable to render complex fiber configurations like crossings, kissings or splittings. HARDI models, to which the analytical Q-ball model belongs, were designed to go beyond this limitation, and are particularly suitable for the hippocampus where such configurations are likely to happen.

  This work has been done at an intermediate mesoscopic scale, between the micrometer obtained with optical methods and the millimeter obtained with in vivo MRI. It prefigures what could be achieved with ultra high-field clinical MRI. This is just the beginning of a new era of brain exploration. Advances in knowledge by means of ex vivo studies, as well as microstructural models and hardware improvement, will allow, in fine, to consider a translational approach to reach the in vivo clinical routine.

FIGURE 5 . 19 :

 519 FIGURE 5.19: Localization of the human brainstem on a T1-weighted image of a subject from the Archi database [Assaf et al., 2013], acquired at 3T with a resolution of 1 mm isotropic. The brainstem is the structure found inside the red boxes in the coronal (a), axial (b), and sagittal (c) view, located at the juncture of the cerebrum and the spinal column, anterior to the cerebellum

FIGURE 5 . 20 :

 520 FIGURE 5.20: Schematic representation of a ventral, dorsal and medial view of the brainstem and part of the diencephalon, the spinal cord and the cerebellum. The major part of the diencephalon has been removed from (a) and (b) as well as the cerebellum from (c). Red lines indicate estimated limits of the brainstem, and blue lines show estimated limits of its three segments. For further clarity, the legend has been simplified and only part of the numbers is listed in the caption. For the missing legend, see Nieuwenhuys et al. [2007] (p.84, 82, 80) (a) Ventral view of the brainstem. The red dotted line indicates the limit between the brainstem and the spinal cord, given by the pyramidal decussation. 7. optic chiasm 8. optic nerve 9. optic tract 10. lateral geniculate body 11. oculomotor nerve 12. trochlear nerve 13-14. trigeminal nerve 15. abducens nerve 16-17. facial nerve 18. vestibulocochlear nerve 19. glossopharyngeal nerve 20. vagal nerve 21. accessory nerve 22. hypoglossal nerve 23. ventral spinal roots 26. infundibulum 27. mammillary bodies 28. cerebral peduncle 33. middle cerebellar peduncle 35. inferior olive 36. pyramid 37. pyramidal decussation 38. lateral funiculus; (b) Dorsal view of the brainstem. The red dotted line indicates the limit between the brainstem and the spinal cord, inferred from (a) 4. brachium of the superior colliculus 5. superior colliculus 6. brachium of the inferior colliculus 7. inferior colliculus 8. cerebral peduncle 17. cuneate tubercle 18. gracile tubercle 19. lateral funiculus 21. cuneate fascicle 23. gracile fascicle 32. medial geniculate body 33. lateral geniculate body 34. trochlear nerve 36. trigeminal nerve 37. superior cerebellar peduncle 38. middle cerebellar peduncle 39. inferior cerebellar peduncle 44. accessory nerve 47. dorsal root; (c) Medial view of the bisected brainstem, diencephalon, and part of the cerebellum. The red dotted line highlights the superior limit of the brainstem as defined by Nieuwenhuys et al. [2007], and the blue dotted line highlights the greatest width of the fourth ventricle, giving the dorsal border between the pons and the medulla 6. pineal body 8. posterior commissure 15. mammillary body 18. optic chiasm 20. infundibulum 21. superior colliculus 22. inferior colliculus 42. fastigium (images adapted from Nieuwenhuys et al. [2007])

  22.a), the pontine nuclei, the superior olivary nucleus, the trapezoid body nucleus in the pons (Figure 5.22.b), and the gracilis, cuneatus, and inferior olivary nuclei in the medulla (Figure 5.22.c).

  Figure 5.20.b) connect the cerebellum with the brainstem. The middle cerebellar peduncle (MCP) connects the pons with the cerebellum. The inferior cerebellar peduncle (ICP) carries connections from the spinal cord and the medulla oblongata to the cerebellum, whereas the superior cerebellar peduncle (SCP) represents the main efferent pathway stemming from the cerebellum.

FIGURE 5 . 21 :

 521 FIGURE 5.21: Cranial nerves originating from the brainstem. (a) Dorsal view of some of the cranial nerves associated with their nuclei. On the left: sensory nerves and nuclei; on the right: motor nerves and nuclei; roman numerals indicate the cranial nerves. 1. mesencephalic tract of the trigeminal nerve 2. nucleus of the mesencephalic tract of the trigeminal nerve 3. principal sensory nucleus of the trigeminal nerve 4. spinal tract of the trigeminal nerve 5. nucleus of the spinal tract of the trigeminal nerve 6. vestibular nuclei 7. cochlear nuclei 8. nucleus of the solitary tract 9. accessory nucleus of the oculomotor nerve 10. nucleus of the oculomotor nerve 11. nucleus of the trochlear nerve 12. motor nucleus of the trigeminal nerve 13. genu of the facial nerve 14. nucleus of the abducens nerve 15. nucleus of the facial nerve 16. salivatory nuclei 17. nucleus ambiguus 18. dorsal nucleus of the vagal nerve 19. nucleus of the hypoglossal nerve 20. nucleus of the spinal root of the accessory nerve. IV. trochlear nerve V. trigeminal nerve VI. abducens nerve VII. facial nerve VIII. vestibulocochlear nerve IX. glossopharyngeal nerve X. vagus nerve XI. hypoglossal nerve. Nerves I, II, III, and XII are not represented (image adapted from Nieuwenhuys et al. [2007]) (b) Ventral view of most of the cranial nerves with their associated nuclei (nerve I not represented) (image adapted from http: // what-when-how. com )

FIGURE 5 . 22 :

 522 FIGURE 5.22: Axial sections of the brainstem acquired at 9.4 T highlighting different types of nuclei contained in the midbrain, the pons or the medulla. On the left, a three-dimensional rendering of the brainstem studied in this thesis work, with dark planes showing estimated position of the axial images on the right, taken from Naidich et al. [2009]. For further clarity, only the legend corresponding to surrounded gray matter structures is listed in the caption. For more details, see Naidich et al. [2009] (p.355,295,259). (a) Axial section through the superior colliculus. 9'. Periaqueductal gray matter 64c. pars compacta of substantia nigra 64r. pars reticulata of substantia nigra 69. superior colliculus 95. red nucleus within its capsule (white arrowheads), Paired black arrows: Oculomotor nuclei (CN III) of both sides; (b) Axial section of the pons. 8. reticular formation 20. pontine nuclei 20'. lateral tegmental extension of pontine nuclei, L. site of the locus coeruleus, Open arrowhead: ventral nucleus of the lateral lemniscus; (c) Axial section in the low medulla. 1. nucleus gracilis 2. nucleus cuneatus 2". accessory cuneate nucleus 4. spinal trigeminal nucleus 8. extensive reticular formation (light gray) 19. arcuate nuclei, H. hypoglossal nucleus M. medial accessory olivary nucleus O. inferior olivary nucleus S. solitary nucleus (black S) surrounding the solitary tract (white S) V. dorsal nucleus of the Vagus

  middle cerebellar peduncles to isolate the brainstem from the brain and cerebellum, keeping intact the anterior portion of the cerebellum, and part of its deep nuclei. The final specimen measured approximately 70×41×44 mm 3 (see Figure 5.23.a, b, c). The brainstem was then preserved in a 5% formalin solution until being scanned. The container and the rehydration protocol were the same than those used for the hippocampus specimen (cf. § 5.1.2). During MRI acquisition, the specimen was immersed in a proton-free fluid (Fluorinert, FC-40, 3M Company, USA). All the acquisitions were performed on a preclinical 11.7 T Bruker MRI system (BioSpec 117/16 USR Bruker MRI, Ettlingen, Germany) equipped with strong gradients (maximum gradient magnitude = 780 mT/m, slew rate = 9660 T/m/s) using a 60 mm volume coil.

FIGURE 5 . 23 :

 523 FIGURE 5.23: Brainstem specimen and its container. Ventral (a) and lateral (b and c) views of the post mortem specimen as well as its dedicated container that fit the quadrature coil (d)

FIGURE 5 . 24 :

 524 FIGURE 5.24: Histograms showing the repartition of the T2 and mean diffusivity values of the brainstem sample. (a) T2 histogram depicting a unique mode at 30.7 ms (b) Mean diffusivity histogram with a value at 2.2 × 10 -10 m 2 /s

  Figure 5.25 (a, b) shows the resulting images with a SNR of 58.6 for the 100 µm image (a), and 57.3 for the 185 µm image (b). Diffusion scans Diffusion data were acquired using conventional 2D PGSE sequences. The structural connectivity was established from a HARDI dataset collected at b = 4500 s/mm 2 along 400 directions uniformly distributed over a sphere. It was split into 12 blocks of 31 directions each and one of 28, with a 15-minutes pause between each. For each block, 2 b = 0 images were acquired. time of 5 days 17h (pauses included).

FIGURE 5 . 25 :

 525 FIGURE 5.25: Raw images obtained with the anatomical acquisition at 100 µm (a), 185 µm (b), and 300 µm (i.e. b = 0 image of the acquisition diffusion) (c). The diffusion-weighted images at 300 µm are shown at b = 1500/4500/7500 s/mm 2 (resp. (d), (e), (f))

  5.26 depicts the cumulative histograms of the fiber length repartition obtained for each tractogram, plotted with a bin count of 1000. Red horizontal lines are plotted at 1 % and 99 % of the maximum fiber count value. The minimum and maximum limits correspond to 1.9-115 mm for the probabilistic and 1.8-125 mm for the deterministic tractogram. Based on these results, minimum/maximum fiber lengths were set to 1.8 and 126 mm.

FIGURE 5 . 26 :

 526 FIGURE 5.26: Normalized cumulative histograms of the fiber length repartition obtained with a probabilistic and a deterministic algorithm, with a bin count of 1000. Fiber length constraints for the final tractography were obtained from the fiber lengths corresponding to 1 % and 99 % of the maximum fiber count value (horizontal red lines): 1.9-115 mm for the probabilistic (a) and 1.8-125 mm for the deterministic (b) tractogram

FIGURE 5 . 27 :

 527 FIGURE 5.27: Sagittal views of the brainstem DT maps at 300 µm: color-encoded map (a), fractional anisotropy map (b) and mean diffusivity map (c) were obtained with the DTI model. The color-encoding cross at the upper left of (a) depicts the direction of largest displacement probability orientation. Abbreviations: S = Superior; I = Inferior; A = Anterior; P = Posterior

  and 21 reticular nuclei, in addition to three structures of the diencephalon and four of the cerebellum (see Figure 5.29). Therefore, this work provides an original method of segmentation of 51 anatomical classes of brainstem nuclei, based on high resolution post mortem MRI. The three-dimensional rendering of the manual segmentation of the brainstem nuclei, surrounding nuclei, and white matter ROIs, is presented in Figure 5.30.

FIGURE 5 . 29 :

 529 FIGURE 5.29: Segmentation of the brainstem and its surrounding structures. On the left, a sagittal view of the 100 µm anatomical scan with references to all the axial images on the right. Axial images of the sample are shown in an superior-to-inferior direction from a to h. The segmentation is shown in a'-h'

  were erased. At the end of the process, a new image of labels included the distinction between left and right structures (even and odd labels) was obtained (Figure5.31.c). A mask containing a distinct label for the left and the right part of the sample was also generated to facilitate the fiber clustering step to be performed afterwards (Figure5.31.e).

FIGURE 5 . 31 :

 531 FIGURE 5.31: Preprocessing of the image of labels. (a) Manually positioned points (red voxels) from which are generated a right/left plane (b). A collection of 14 planes creates the final separation between the right and the left part of the sample (d). From this separation, distinct labels are associated to the structures depending on their position (c), and a mask is generated for the fiber clustering algorithm (e)

Figure 5 .

 5 Figure 5.32 shows the reconstruction of the right locus coeruleus (LC) projections, obtained from the streamline regularized deterministic (SRD) and the streamline regularized probabilistic (SRP)

FIGURE 5 . 32 :

 532 FIGURE 5.32: Reconstruction of major brainstem white matter tracts. (a) Sagittal , (b) coronal, and(c,d) axial views of the transverse pontine fibers (red), the superior (yellow) and inferior (light blue) cerebellar peduncles as well as the corticospinal tract (dark blue). These fibers are superimposed with the three-dimensional rendering of the brainstem sample, the 100 µm anatomical scan, and a few segmented structures (the red nucleus, the inferior olive, and the cerebellar nuclei)

FIGURE 5 . 33 :

 533 FIGURE 5.33: Projections of the right locus coeruleus. (a) Localization of the locus coeruleus (LC) on the 100 µm anatomical scan and three-dimensional rendering of its segmentation (b). (c) and (d) present the different steps of the locus coeruleus connectivity reconstruction, from two distinct tractograms: the first one obtained with the streamline regularized deterministic algorithm (SRD) and the second one with the streamline regularized probabilistic algorithm (SRP). The first step was to select fibers going through the LC. Then, a filter was applied so that only bundles containing at least 10 fibers are kept. The last step was to manually discard spurious fibers displaying aberrant connections. The last reconstruction on the right includes the three-dimensional rendering of the cerebellar nuclei

  Figure 5.36 presents the data after the filtering step, on the same voxel than the one chosen for Figure 5.35. The positive effects of the denoising are particularly noticeable for the highest b-values 4500, 7500 and 10000 s/mm 2 , where the data dispersion with respect to the theoretical attenuation profile is significantly reduced.

FIGURE 5 . 34 :

 534 FIGURE 5.34: Box plot of the effective b-values for each shell. The median of effective b-values is, on average, 273 s/mm 2 higher than the input value, and represents an increase between 3% (for b = 10000 s/mm 2 ) and 33% (for b = 500 s/mm 2 ). The variation between the minimum and the maximum values is on average 740 s/mm 2

FIGURE 5 . 35 :

 535 FIGURE 5.35: Representation of the signal attenuation against the cosine of the angle between the diffusion gradient and the main direction of fibers in one voxel of the transverse pontine fibers (in blue in the FA and T2 images). The attenuation is plotted with (green dots) and without (light red dots) the compensation for the b-value variation. The TE correction (see § 5.2.2.5) is already included. S/S 0 denotes the normalized signal attenuation, G, the gradient direction, and n•G the dot product of the gradient direction and the mean fiber orientation

FIGURE 5 . 36 :

 536 FIGURE 5.36: Representation of the signal attenuation against the cosine of the angle between the diffusion gradient and the main direction of fibers in one voxel of the transverse pontine fibers (in blue in the CED and T2 images). This signal is shown after the non-local means filtering step, the TE and the b-value compensation. S/S 0 denotes the normalized signal attenuation, G, the gradient direction, and n•G the dot product of the gradient direction and the mean fiber orientation

FIGURE 5 . 37 :

 537 FIGURE 5.37: Rendering of the fit quality and the resulting NODDI quantitative maps. S/S 0 denotes the normalized signal attenuation, G, the gradient direction, and n•G the dot product of the gradient direction and the mean fiber orientation. The b-values are the average of the effective b-values for each shell. Case 1 corresponds to the case where d is fixed. On the left, the distribution of the Bayesian information criterion (BIC) median was studied as a function of parameter d , all the other parameters kept constant. This distribution highlights an optimal value of 1.15 × 10 -9 m 2 /s. On the right are shown the resulting orientation dispersion map, the intracellular volume fraction map, the stationary fraction map, and the BIC map, with a median value of -678. Case 2 refers to the case where d was let to evolve freely. The fits are obtained from the voxel drawn in blue belonging to the transverse pontine fibers

FIGURE 5 . 38 :

 538 FIGURE 5.38: Brainstem microstructural features obtained from NODDI model, in an axial (top), sagittal (middle) and coronal (bottom) view. Red circles highlight the inferior colliculus, dotted red arrows point at the periaqueductal gray matter (PAG), deep blue arrows point at the corticospinal tract, light blue arrows point at the inferior olivary, and red arrows point at the dentate nucleus

5. 3

 3 .1 Validation, comparison with alternative modalities Ultra-high field MRI is a powerful tool to acquire brain images at an intermediate scale, so called mesoscale, between the millimeter scale of in vivo MRI and the micrometer scale of ex vivo optical microscopy. Optical methods include, in particular, optical coherence tomography (OCT), serial two-photon (STP) tomography, and 3D-polarized light imaging (3D-PLI). STP tomography [Ragan Chapter 5. Investigation of the human hippocampus and brainstem 137 et al., 2012] combines fluorescence imaging with two-photon microscopy, but requires the use of histochemical dyes to label the cells with type-specific fluorescent proteins, therefore being sensitive

FIGURE 6 . 1 :

 61 FIGURE 6.1: Laminar patterns in cyto-and myelo-architecture of M1, S1, V1 and V2. (a) cyto-(upper row) and myelo-architecture (lower row) patterns of (from left to right): the primary motor cortex (M1), the primary somatosensory cortex (S1), the primary visual cortex (V1), the secondary visual cortex (V2) (images taken from Vogt [1919]); (b) Cyto-(left) and myelo-architecture (right) of M1, S1, V1 and V2 (images taken from Palomero-Gallagher and Zilles [2017]) The myelin stained sections of (b) show less details and fewer fibers than shown in (a). This is due to the fact that sections in (b) were obtained from deep-frozen, unfixed tissue, and no differentiation of the staining was performed

FIGURE 6 . 2 :

 62 FIGURE 6.2: Human brain specimen containing part of the occipital lobe and its container. The scanned field of view is surrounded by a dark square. The red gel is a sealing gel (BizGel, BizLine, Paris, France) whose MR characteristics are described in Chapter 7

A

  2D-SE dataset was acquired with an isotropic resolution of 150 µm, TE/TR = 12/6000 ms, matrix size: 260×260, 240 slices, flip angle: 90°, receiver bandwidth: 66 kHz, 16 averages, and a total acquisition time of 5h12min. A 3D-SE dataset was acquired using the multi-slice option, an isotropic resolution of 100 µm, TE/TR = 20/500 ms, matrix size: 400×350, 350 slices, flip angle: 90°, receiver bandwidth: 50 kHz, 1 average, and a total scan time of 19h26min. Figure 6.3 (a and b) shows the resulting images with a very good SNR (33.6 for the 150 µm image (a), and 48.3 for the 100 µm image (b)).

6. 2 . 3

 23 Reconstruction of myelo-and cyto-architectural features 6.2.3.1 Maps of quantitative T1 relaxation time Analysis of the quantitative TA relaxation time was done on a voxel-by-voxel basis by fitting the entire IR dataset to the exponential decay given in Equation6.1 using Powell's NEWUOA algorithm developed by[START_REF] Michael | The newuoa software for unconstrained optimization without derivatives[END_REF] and implemented for the team by K. Ginsburger. The objective function is:

FIGURE 6 . 3 :

 63 FIGURE 6.3: Raw images of the anatomical scan acquired at 100 µm (a), 150 µm (b), and 300 µm (i.e. b = 0 image of the diffusion acquisition) (c). Diffusion-weighted images acquired at 300 µm isotropic at b = 2000, 4000, 6000 s/mm 2 (resp. (d), (e), (f)); 3D-RARE images acquired with an inversion time of 280, 420, 2900 ms (resp. (g), (h), (i))

Chapter 6 .

 6 FIGURE 6.4: T1 and proton density mapping. (a) and (b) are the results of the fit, with (a) the proton density map and (b) the T1 quantitative map. The quality of the fit for the voxel in blue, in the red square in (c) is presented in the bottom right

Chapter 6 .

 6 FIGURE 6.5: Microstructure maps inferred from the NODDI model. On the left, the intracellular volume fraction map in an axial (top) and a coronal (bottom) view. The red square indicates the voxel used to visualize the fit quality. S/S 0 denotes the normalized signal attenuation, G, the gradient direction, and n•G the dot product of the gradient direction and the mean fiber orientation. On the right, the orientation dispersion map in an axial and coronal view. In the middle, the κ map. All these quantitative maps have been filtered using a non-local means filter

  et al. [2018]. In this case, θ k ={µ k , Σ k } with µ k the d-dimensional vector of means of the k-th component and Σ k the d × d covariance matrix of component k. Each component is a multivariate Gaussian density, such as:

Chapter 6 .

 6 Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 153 M-step This step computes the new parameter values using the new membership weights and the data. Let N k = ∑ N i=1 w ik , i.e. the sum of the membership weights for the k-th component. N k represents the effective number of data points assigned to component k.

  mixing weights, µ new k being the new d-dimensional vector of means, and Σ new k being the new covariance matrix of size d × d.

  .6)6.3.4 Determining the number of clusters in a data setThe knowledge of the number of clusters K is a prerequisite to compute the EM solution. Finding the number of clusters is a distinct issue from the process of solving the clustering problem. Several categories of methods exist to make this decision. Bayesian methods, such as Akaike information criterion (AIC) or Bayesian information criterion (BIC), are widely used for selecting the number of components in mixture models, and the Bayesian information criterion was found to outperform other methods in the case of Gaussian mixtures[START_REF] Russell | Performance of bayesian model selection criteria for gaussian mixture models[END_REF]. This criterion was computed for each candidate number of clusters, and the number of clusters presenting the lowest BIC was retained. This criterion can be computed as follows:BIC = -2logL + Plog(M) (6.7)Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 154

FIGURE 6 . 6 :

 66 FIGURE 6.6: Determination of the number of T1 clusters. (a) Bayesian information criterion (BIC) as a function of the number of clusters computed for a precision of 10 -7 and giving a minimum of 5 clusters; (b) Histogram of the T1 map fitted with the 5 Gaussian distributions

Figure 6 . 9 .

 69 Figure 6.9.a presents the BIC evolution depending on the number of clusters, computed for a precision of 10 -7 as for T1-based clustering. The minimal value for the Bayesian information criterion was found for 10 components.Figure 6.9.b shows the histogram of the intracellular volume fraction map fitted with these ten components, thus illustrating the good quality of the fit.

FIGURE 6 . 9 :FIGURE 6 . 10 :

 69610 FIGURE 6.9: Determination of the number of clusters in the intracellular volume fraction map. (a) Bayesian information criterion (BIC) as a function of the number of clusters computed with a precision of 10 -7 and giving a minimum of 10; (b) Histogram of the intracellular volume fraction map fitted with ten Gaussian distributions

Chapter 6 .

 6 FIGURE 6.13: Multivariate clustering combining myelo-and cyto-architecture information. On the top, 2D histogram fitted with 15 Gaussians, resulting in a cluster map (middle left) regularized with a Potts model (middle right). When zooming in the cortex, outer layers appear to be divided into two to three labels, while inner layers are divided into three to four labels

  300 µm isotropic, which is the spatial resolution reached in the present work. This spatial resolution being unachievable in vivo, Lifshits et al. decided to model the existing partial volume effects by fitting multiple T1-weighted components per voxel. The work presented in this chapter thus provides a port mortem validation of the automatic clustering method of the cortical lamination in humans.

Finally, anatomical priors

  could be added to the model. Other studies have segmented cortical layers based on the segmentation of the gray-white matter boundary and pial surface [Waehnert et al., 2014, Leprince et al., 2015]. In their paper, Waehnert et al. [2014] compared the layering defined based on the Laplace equation, the equidistant and the equi-volume model. The cortical curvature was shown to affect the estimated laminar thicknesses differently for the different models, and the equi-volume model to better predict the location of the hypointense band of Baillarger compared to the Laplace and equidistant models.

  This chapter investigated the potential of quantitative maps obtained from T1 relaxometry and diffusion MRI microscopy to give access to the delineation of cortical layers. Using an unsupervised clustering algorithm based on a Gaussian mixture model, T1 and neurite density maps were segmented without further anatomical priors. While more T1 clusters were found in outer layers, intracellular volume fraction-based cluster map better delineated inner layers but also the line of Gennari and the gray matter / white matter border. Therefore, these two contrasts seem to provide complementary information about tissue that need to be coupled to better segment the cortical ribbon. The combination of contrasts arising from the myelo-(T1) and cyto-(NODDI) architecture gave access to the delineation of two to three clusters in the outer layers and in the inner layers. Ultimately, being able to segment cortical layers might bring valuable insights about anatomical substrate of functional networks as well as patterns of cortical damage induced by neurodegenerative diseases. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 169

  Figure 7.1.a presents the fit quality obtained with the Levenberg-Marquardt algorithm. The T2 relaxation time of the gel was estimated to be 525 ms.T1 longitudinal relaxation time was mapped using a series of 3D inversion recovery (IR) rapid acquisition with relaxation enhancement (RARE) sequences ( § 4.4.2.2), with 57 inversion times ranging between 100 ms and 4700 ms (every 50 ms between 100 ms and 2000 ms, every 100 ms between 2000 ms and 3500 ms, and every 300 ms between 3500 ms and 4700 ms). Acquisition parameters were: isotropic resolution of 600 µm, flip angle of 90°, readout bandwidth of 50 kHz, TE/TR = 5.5/5000 ms, and a scan time of 15 min for each inversion time resulting in a total scan duration of 14h15min. As for the T2 estimation, T1 analysis was done on a voxel-by-voxel basis by fitting the entire IR dataset to an exponential decay using a least-square and then a Levenberg-Marquardt algorithm. The result is presented in Figure7.1.b. T1 relaxation time was estimated to be 1300 ms.

FIGURE 7 . 1 :

 71 FIGURE 7.1: Fit quality for the estimation of the gel MR characteristics. (a) T2-decay fitted with a monoexponential model giving a T2 of 525 ms; (b) T1-regrowth fitted with a monoexponential model giving a T1 of 1300 ms

2 .FIGURE 7 . 2 :

 272 FIGURE 7.2: Brain sample cutting steps. (a) Entire fixed specimen before cutting; (b) after the separation of the sample into two hemispheres and the removal of the brainstem and the cerebellum, the ventricle of the left hemisphere are filled with the gel; (c) the left hemisphere is surrounded by the sealing gel before its separation between the lateral (d) and the medial (e) part. (f) Cutting of the medial part of the left hemisphere into blocks, resulting to (g) seven blocks. The containers were filled with the gel (h) and closed with a screw-on lid (i)

  FIGURE 7.3: Anatomical images acquired on a 3 T clinical system to facilitate the final registration. (a) axial, (b) coronal, and (c) sagittal view of the entire specimen before cutting the left hemisphere. (d, e) sagittal views of the seven blocks forming the left hemisphere. Part of the gel has been removed in each container in order to keep a majority of tissue and thus prevent the MRI system for taking the basic frequency of the gel instead of water

FIGURE 7 . 4 :

 74 FIGURE 7.4: Identification of the field of views on the seven blocks obtained from the left hemisphere. The seven containers are identified by a letter from A to G, and the field of views from 1 to 4 in the posterior-anterior direction. Abbreviations: A = Anterior; P = Posterior; I = Inferior; S = Superior

FIGURE 7 . 6 :

 76 FIGURE 7.6: Spectrum of a block at 11.7 T. The red circle highlights the resonance frequency of the sealing gel, close to the principal resonance peak (screenshot taken from Paravision 6.0.1 (Bruker, Germany))

  FIGURE 7.8: Anatomical images obtained on the field of view C2, depicting the human hippocampus and part of the midbrain. Sagittal (a), coronal (b) and axial (c) views of the anatomical scan acquired at 150 µm isotropic are compared to sagittal (d), coronal (e) and axial (f) views of the anatomical scan acquired at 100 µm isotropic. The red arrows highlight a light overlapping of the remaining signal from the gel and part of the hippocampus. Abbreviations: S: Superior; I: Inferior; M: Medial; L: Lateral; A: Anterior; P: Posterior

FIGURE 7 . 9 :

 79 FIGURE 7.9: Time line of the Chenonceau acquisition campaign. This results in a total of 9 months to obtain and prepare the sample, 6 months to design the acquisition protocol, 9 months of intensive scanning, and 12 months of technical failure (quench)

Figure 7 .

 7 Figure 7.10 depicts, for the field of view F3, the two anatomical scans, the diffusion-weighted images before and after the application of a non-local means filter, as well as FA, ADC and CED maps derived from the DT model.

FIGURE 7 . 10 :FIGURE 7 . 13 :

 710713 FIGURE 7.10: Anatomical, diffusion weighted images, and DT quantitative maps of F3. Anatomical scans acquired at 100 µm (a) and 150 µm (b). (c) b = 0 image at 200 µm, with the related diffusion weighted images acquired at b = 1500, 4500, 8000 s/mm 2 , before (d, e, f) and after (g, h, i) the nonlocal means filtering. Images derived from the DT model are: FA (j), ADC (k) and CED (l) maps. On (a), white arrowheads point at two dark lines visible in the cortex, and the blue line shows the limit of the area where these lines are visible

Chapter 7 . 14 :

 714 FIGURE 7.14: Registration of the seven blocks on the blockface image. (a) blocks acquired at 3 T before flipping and registration; blocks registered with an affine transformation overimposed on the blockface image, in coronal (b) and sagittal (c, d) views

FIGURE 7 . 15 :

 715 FIGURE 7.15: Partial reconstruction of the left hemisphere at 200 µm, in sagittal (a, b), coronal (c) and axial (d) views. Images on the bottom right give the localization of the fields of view with respect to the blockface image

FIGURE 7 . 16 :

 716 FIGURE 7.16: Partial reconstruction of the left hemisphere at 200 µm with color-encoded direction maps, in axial (a, b) and sagittal (c) views. Images on the bottom right give the localization of the fields of view with respect to the blockface image

FIGURE 7 . 17 :

 717 FIGURE 7.17: Partial reconstruction of the left hemisphere at 150 µm, in coronal (a), axial (b) and sagittal (c) views. Images on the bottom right give the localization of the fields of view with respect to the blockface image

FIGURE 7 .

 7 FIGURE 7.18: Partial reconstruction of the left hemisphere at 100 µm, in axial view. On the left, a zoom on a cortical area depicts two highly myelinated lines in the cortex. On the right, a zoom on deep grey matter structures

Chapter 7 .

 7 Toward a post mortem human brain MRI atlas 192 a technique shows high sensitivity, i.e. a high rate of true positives, it will most likely show low specificity, i.e. a high rate of false positives[START_REF] Moreno-Dominguez | A hierarchical method for whole-brain connectivity-based parcellation[END_REF]. Therefore, adding constraints arising from anatomical priors, like fine connectivity or microstructural priors, is intended to drastically reduce the creation of false positives[START_REF] Teillac | Tractographie globale sous contraintes anatomiques[END_REF]. The Chenonceau project will be undertaken by R. Yebga Hot and A. Popov, who are both starting a PhD thesis and already participated to the acquisition campaign at the end of this PhD. A. Popov will design a new generation of global spinglass tractography algorithm using a simulation and deep-learning based inference of the local tissue microstructure and able to run on a high performance computing facility. The algorithm will exploit the simulation-based approach to replace the analytical local models currently used in the literature by virtual tissues. In the end, this algorithm could be applied to the acquired images to further improve the connectivity results. R. Yebga Hot will investigate the architecture of the human cortex and improve the work initiated in Chapter 6 on the automatic segmentation of the cortical layers based on multi contrast data. The outcome of this PhD thesis will consist of a new acquisition and processing pipeline allowing to extract at the individual scale the cortical layers and to parcellate the pial surface into cytoarchitectural areas. It will also consist of the construction of a probabilistic atlas of the cytoarchitecture of the cortical ribbon at the scale of a new scanned population that will undergo a massive sampling of the relaxation / diffusion spaces known to be sensitive to the myeloand cyto-architectures.

Finally, a third

  project could be to study the evolution of brain structures and microstructure occurring during development and aging, by scanning brains obtained from individuals of different age ranges. Chapter 7. Toward a post mortem human brain MRI atlas 193 7.5 Conclusion This chapter presented the fundamental work and overall objective of this PhD thesis. Obtaining a mesoscopic dataset including anatomical and diffusion-weighted images of a whole post mortem human brain specimen involved several steps, from the specimen preparation and cutting to the design of an acquisition protocol taking into account the signal of the sealing gel. The registration work was initiated with linear transformations, and will be further improved during the next months. Therefore, the work carried out during this thesis laid the foundation for the acquisition of an entire post mortem human brain. The acquisition campaign has only been partially completed, due to technical failures that occurred during these three years. However, the acquisition of the left hemisphere should be achieved for the end of this thesis (blocks B, F, G already acquired), and the second hemisphere should be imaged during the next 10 months by A. Popov and R. Yebga Hot, new PhD students of the Microstructure team.

8. 1 . 2

 12 Inner structures, internal connectivity and microstructure of the human brainstem The acquisitions performed at 11.7 T on a human brainstem sample leaded to the creation of a unique dataset of the human brainstem at ultra-high spatial and angular resolutions: 100 and 185 µm isotropic for the T2-weighted anatomical scans, and 300 µm isotropic for the diffusion-weighted dataset acquired with ten b-values up to 10000 s/mm 2 , and along 400 directions at b = 4500 s/mm 2 . A protocol to manually segment 51 of the 73 brainstem nuclei was established by Dr F. Lechanoine from the Bretonneau University Hospital (Tours), making it the most complete MR-based segmentation of the human brainstem to date. Major white matter bundles were reconstructed, including the corticospinal tract and cerebellar peduncles, as well as projections of the locus coeruleus, a structure known to be affected in Parkinson's disease. The use of the NODDI model also revealed new contrasts that could improve current segmentation methods. This work is currently under preparation for publication. 8.1.3 Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features This work presents a new method to automatically segment the cortical layers relying on a Gaussian mixture model and integrating both T1-based myeloarchitectural information and diffusion-based cytoarchitectural information. A human brain sample containing part of the primary and secondary visual cortex was scanned at 11.7 T and 7 T, resulting in high resolution anatomical scans (100/150 µm during the next 10 months by A. Popov and R. Yebga Hot, new PhD students of the Microstructure team.8.1.5 Contributions of this thesis regarding to the HBP and the FibrAtlasII-III projects 8.1.5.1 One piece of the puzzle for the European Human Brain Project (HBP)

Finally, applying the

  automatic clustering algorithm developed in Chapter 6 to the hippocampal and brainstem dataset would reveal probabilistic maps that could bring further information for their seg-three years Part of the projects initiated during this thesis work will be further investigated during the next years through new thesis works.Regarding the hippocampus study, a PhD student of the Forschungszentrum Jülich, D. Schmitz, is in charge of comparing PLI data obtained from the same sample with the diffusion MRI results summarized in § 8.1.1. The brainstem study, performed in collaboration with the Bretonneau University Hospital (Tours), has led to the opening of a new PhD position in Tours. The purpose of this thesis is to continue and complement the work initiated in Chapter 5. Eight brainstem samples will be scanned at 11.7 T at Neurospin, and will be manually segmented following the segmentation protocol established by Dr F. Lechanoine. The ultimate goal is to build a multimodal atlas of the human brainstem and to develop new automatic brainstem segmentation tools for MRI data scanned at lower fields in clinical MRI systems.Finally, with regard to the Chenonceau Project, the succession is undertaken by R. Yebga Hot and A.Popov, who are both starting a PhD thesis and already helped performing acquisitions at the end of this PhD. A. Popov will design a new generation of global spin-glass tractography algorithm using a simulation and deep-learning based inference of the local tissue microstructure and able to run on a high performance computing facility. The algorithm will exploit the simulation-based approach to replace the analytical local models currently used in the literature by virtual tissues. In the end, this algorithm could be applied to the acquired images to further improve the connectivity results. R. Yebga Hot will investigate the architecture of the human cortex and improve the work initiated in Chapter 6 on the automatic segmentation of the cortical layers based on multi contrast data. The outcome of this PhD thesis will consist of a new acquisition and processing pipeline allowing to extract at the individual scale the cortical layers and to parcellate the pial surface into cytoarchitectural areas.It will also consist in the construction of a probabilistic atlas of the cytoarchitecture of the cortical ribbon at the scale of the scanned population.Validation through the use of alternative modalities As discussed in Chapter 5, UHF MRI is a powerful tool to acquire brain images at an intermediate scale, between the millimeter scale of in vivo MRI and the micrometer scale of ex vivo optical microscopy, or histological methods. Optical methods, including optical coherence tomography (OCT), serial two-photon (STP) tomography, and 3D-polarized light imaging (3D-PLI), as well as histological techniques, could be considered to validate obtained results on the studied ex vivo samples. Among all these techniques, 3D-PLI was chosen to validate the hippocampus connectivity and scanned by our research partner in Jülich. Regarding the other samples (the brainstem and the entire human brain sample), other techniques could be considered to validate our results. The brainstem neurite density could be recovered using electron microscopy. It would be therefore possible to compare the evolution of the density of the corticospinal tract between the midbrain, the pons, and the Chapter 8. Conclusion, discussion and perspectives 201 medulla. This work would be comparable to the one typically performed on the corpus callosum and reported in numerous studies. Regarding the validation of the visual cortex lamination, histological

Finally, a third

  project could be to study the evolution of brain structures and microstructure occurring during development and ageing, by scanning brains obtained from individuals of different ages.F Fritz, R Harms, S Sengupta, S Hildebrand, and A Roebroeck. High resolution diffusion MRI and tractography of post mortem human brains using kT-dSTEAM at 9.4 T. In Proceedings ofOHBM, Vancouver, 2017. 190 F Fritz, R Harms, S Sengupta, S Hildebrand, and A Roebroeck. 400 µm dMRI and tractography of early human visual system projections ex vivo using kT-dSTEAM at 9.4T. In Proceedings ofOHBM, Singapour, 2018. 190 S Sengupta, FJ Fritz, RL Harms, S Hildebrand, DHY Tse, Benedikt A Poser, Rainer Goebel, and Alard Roebroeck. High resolution anatomical and quantitative MRI of the entire human occipital lobe ex vivo at 9.4 T. Neuroimage, 168:162-171, 2018. 190 Manisha Aggarwal, Melina V Jones, Peter A Calabresi, Susumu Mori, and Jiangyang Zhang. Probing mouse brain microstructure using oscillating gradient diffusion MRI. Magnetic resonance in medicine, 67(1):98-109, 2012. 191 Cibu Thomas, Q Ye Frank, M Okan Irfanoglu, Pooja Modi, Kadharbatcha S Saleem, David A Leopold, and Carlo Pierpaoli. Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited. Proceedings of the National Academy of Sciences, 111 (46):16574-16579, 2014. 192Titre : Etude de la microstructure du cerveau humain par imagerie post mortem à très haut champ magnétique et forts gradients Mots clés : IRM à très haut champ, cytoarchitecture du cortex, connectivité structurelle, microstructure de la substance blanche Résumé : L'ambition des très hauts champs magnétiques (≥ 7T) à forts gradients (≥ 300mT/m) est de dépasser la résolution millimétrique imposée à plus bas champ pour atteindre l'échelle mésoscopique en neuroimagerie. Etudier le cerveau à cette échelle est essentiel pour comprendre le lien entre fonction et substrat anatomique. Malgré les progrès réalisés sur les aimants cliniques à 7T, il n'en est pas de même des gradients. Cette thèse vise à cartographier le cerveau humain à l'échelle mésoscopique via l'étude de pièces anatomiques post mortem. Une approche alternative a été choisie, reposant sur l'utilisation d'imageurs précliniques à très hauts champs (7T et 11.7T) et forts gradients (780mT/m). Après une première étape de préparation (extraction et fixation) opérée au CHU de Tours, une pièce anatomique complète a été scannée à 3T, avant découpe de l'hémisphère gauche en sept blocs. Un protocole d'acquisition IRM ciblant une résolution mésoscopique a ensuite été mis en place à 11.7T. Ce protocole, incluant des séquences anatomiques, relaxométriques, et de diffusion, a été validé à l'aide de deux structures clé: un hippocampe et un tronc cérébral. Les données anatomiques et de diffusion acquises à une résolution mésoscopique sur l'hippocampe ont permis de segmenter ses sous-champs, d'extraire le circuit polysynaptique et d'observer l'existence d'un gradient de connectivité et de densité neuritique positif dans la direction postéroantérieure de l'hippocampe. L'utilisation de modèles avancés d'étude de la microstructure a également révélé l'apport de ces techniques pour la segmentation de l'hippocampe, les cartes de densité neuritique révélant les trois couches des champs ammoniens. Un tronc cérébral a ensuite été scanné, avec une résolution atteignant la centaine de micromètres. Une segmentation de 53 de ses 71 noyaux a été réalisée au sein du CHU de Tours, permettant d'établir la cartographie IRM du tronc cérébral humain la plus complète à ce jour.Les principaux faisceaux de la substance blanche ont été reconstruits, ainsi que les projections du locus coeruleus, structure connue pour être atteinte dans le maladie de Parkinson. Forts de ces résultats, la campagne d'acquisition de l'hémisphère gauche, d'une durée de 10 mois, a été initiée. Le protocole d'acquisition à 11.7T intègre des séquences anatomiques (100/150µm) ainsi que des séquences d'imagerie 3D pondérées en diffusion (b=1500/4500/8000 s/mm 2 , 25/60/90 directions) à 200µm. Des acquisitions complémentaires réalisées à 7T comprenant des séquence d'écho de spin rapide avec inversion-récupération ont par ailleurs permis d'étudier la myéloarchitecture du cortex cérébral et d'identifier automatiquement sa structure laminaire. Un nouveau modèle de mélange de Gaussiennes a été développé, intégrant les informations myéloarchitecturales issues de la cartographie T1 et les informations cytoarchitecturales issues de l'imagerie de diffusion. Il a ainsi pu être démontré que l'utilisation conjointe de ces deux informations permettait de mettre en évidence des couches du cortex visuel, l'information myéloarchitecturale favorisant l'extraction des couches externes et la densité neuritique celle des couches plus profondes. Enfin, l'exploitation des données IRM acquises à 11.7T sur les différents blocs a nécessité la mise en place d'une chaîne de prétraitements pour corriger les artéfacts d'imagerie et reconstruire l'hémisphère entier à l'aide de stratégies de recalage difféomorphe avancées. L'objectif de ce projet est l'obtention d'un jeu de données IRM de très haute résolution spatio-angulaire de l'hémisphère gauche. Ce jeu de données anatomique et de diffusion unique permettra à terme de constituer un nouvel atlas IRM mésoscopique de la structure, de la connectivité et de la cytoarchitecture du cerveau humain.

  Rendu tridimensionnel de la segmentation manuelle des structures internes et avoisinantes de l'hippocampe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix 2 Rendu tridimensionnel de la connectivité de l'hippocampe humain . . . . . . . . . . xx 3 Comparaison du contraste entre les trois couches principales de la corne d'Ammon . xxi 4 Rendu tridimensionnel des segmentations du tronc cérébral . . . . . . . . . . . . . . xxii 5 Projections du locus coeruleus droit . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii 6 Segmentation multi-contrastes combinant des informations sur la myelo-et la cyto-

	Table of contents	viii
	A Related publications	203
	1

architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv 7 Identification des blocs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv 8 Recalage des sept blocs sur l'image de référence . . . . . . . . . . . . . . . . . . . . xxvi 9 Identification des blocs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii 2.1 Main regions of the human brain and intracranial cerebrospinal fluid distribution . . . 10 2.2 Morphology of a neuron and differences between white and gray matter . . . . . . . 11 2.3 Lobes of the human brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  . . . . . Le cerveau est un système incroyablement complexe et sa compréhension représente un des enjeux majeurs du XXIème siècle. Le cerveau est ce qui nous définit en tant qu'individu et rend possible notre rapport au monde. Au tournant du XXème siècle, Ramon y Cajal, pionnier des neurosciences modernes, affirmait que le cerveau était constitué de neurones, cellules individuelles organisées selon une structure bien spécifique

	Glossary		xvi
	PNS	Peripheral Nervous System
	RARE	Rapid Acquisition with Refocused Echoes
	ROI	Region Of Interest
	SE	Spin Echo
	Glossary SNR Signal to Noise Ratio UHF Ultra High Field Résumé de la thèse
	WM	White Matter
		AD	Alzheimer's Disease
		aQBI	analytical Q-Ball Imaging
		BIC	Bayesian Information Criterion
		CSF	Cerebro Spinal Fluid
		CMR	Carcinogenic Mutagenic Reprotoxic
		CN	Cranial Nerve
		CNS	Central Nervous System
		EAP	Ensemble Average Propagator
		EPI	Echo Planar Imaging
		FA	Fractional Anisotropy
		FOV	Field Of View
		GM	Gray Matter
		HARDI High Angular Resolution Diffusion Imaging
		HYDI	HYbrid Diffusion Imaging
		IR	Inversion Recovery
		MD	Mean Diffusivity
		MRI	Magnetic Resonance Imaging
		dMRI	diffusion Magnetic Resonance Imaging
		MS	Multiple Sclerosis
		MT	Magnetization Transfer
		MSME Multi-Slice Multi-Echo
		ODF	Orientation Distribution Function
		PD	Parkinson's Disease
		PDF	Probability Density Function
		PGSE	Pulsed Gradient Spin Echo
			xiii xv

  Relaxation studies performed at various static fields and experimental conditions. The listed values are average values. Differences between the relaxation times obtained with the same static field from one study to another can relate to several factors, such as the usage of different formalin concentrations, fixation duration, sample preparation, PMI, as well as differences in the acquisition Diffusion properties The diffusion coefficient is reduced to 20-50% of in vivo values, with an additional loss due to the temperature at which the experiment is performed[START_REF] Peter E Thelwall | Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model[END_REF].Diffusion MRI quantitative maps of post mortem samples (MD, FA) depict decreased values compared to in vivo maps, with reductions in FA of 50-60% in fixed tissue reported in both WM and GM

	Study	B 0 (T)	T1(ms) GM WM GM WM T2(ms)	EV IV sample preparation
	McNab et al. [2009]	3.0	300	340	60	45	X	fixed
	Birkl et al. [2016]	3.0	962 233	696 132 231 65	91 58	X X	unfixed fixed and washed
	Whittall et al. [1997]	1.5	1200 756	80	77	X
	Wansapura et al. [1999]	3.0	1300 830 100	80	X
		4.0	1286 1097 65	58	X
	de Graaf et al. [2006]	9.4	1948 1752 42	36	X
		11.7 2073 1861 36	31	X
	TABLE 4.1:

temperature. All the cited papers study human brains, except de

[START_REF] De Graaf | High magnetic field water and metabolite proton t1 and t2 relaxation in rat brain in vivo[END_REF]

that reports rat brains relaxometry values. Abbreviations: GM: gray matter, WM: white matter, EV: ex vivo, IV: in vivo

  Acquisition parameters for the HYDI dataset of the hippocampus sample

	b (s/mm 2 ) N dir TR (ms) TE (ms) ∆ (ms) G (mT/m)
	4500	30	9000	24,2	14,4	684
	4500	30	9000	24,2	14,4	684
	7500	30	9000	39,8	30,0	595
	7500	30	9000	39,8	30,0	595
	10000	30	10315	54,8	45,0	556
	10000	30	10315	54,8	45,0	556
	TABLE 5.1:

  Investigation of the human hippocampus and brainstem

			103
	Region	Label	mean f ic
		Entorhinal cortex	0.135
		Subicular complex	0.202
		CA1	0.071
	Head	CA2/CA3	0.082
		Dentate gyrus	0.068
		Alveus	0.196
		Lacunosum-molecular layer	0.112
		Entorhinal cortex	0.131
		Subicular complex	0.098
		CA1	0.030
	Body	CA2/CA3 Dentate gyrus	0.084 0.037
		Alveus	0.443
		Fimbria	0.269
		Lacunosum-molecular layer	0.110
		Subicular complex	0.056
		CA1	0.021
		CA2/CA3	0.099
	Tail	Dentate gyrus Alveus	0.036 0.479
		Fimbria	0.604
		Lacunosum-molecular layer	0.074

.14)

. Only CA2/CA3 doesn't follow the gradient described for the gray matter regions. That might be due to the fact that cell packing density within CA2/CA3 varies Chapter 5. TABLE 5.2: Mean intracellular fraction of each segmented structure of the hippocampus

  structural modifications occurring with the normal process of aging, it is known that the hippocampus undergoes a particular volume decrease with age. MRI studies have suggested that, in typical aging, volume loss is more specific to CA1 and DG/CA3 subregions[START_REF] Susanne | Selective effect of age, apo e4, and alzheimer's disease on hippocampal subfields[END_REF]. This volume loss is probably not due to neuronal cell loss[START_REF] David R Riddle | Brain aging: models, methods, and mechanisms[END_REF], but rather to synapse loss [Burke and[START_REF] Sara | Neural plasticity in the ageing brain[END_REF], and occurs especially in the cortical inputs into the hippocampus such as the perforant pathway[START_REF] Michael A Yassa | Age-related memory deficits linked to circuit-specific disruptions in the hippocampus[END_REF].In 2006, Wilson et al. also suggested that changes

  fitted multiple T1-values per voxel in order to reveal subvoxel layer components, thus resolving the partial volume effect issue that occurs when imaging the cortical layers in vivo. Diffusion MRI techniques constitute another alternative to decipher the cortical structure. Four types of information can be explored: quantitative features stemming from ODF or PDF local models such as DTI-based features (FA, MD or CED maps), principal fiber orientation maps (depicting only one direction when obtained from DTI and possibly more than one with HARDI models), connectivity profiles to other regions of the brain, and microstructural quantitative maps obtained from advanced models such as CHARMED, AxCaliber, ActiveAx, or NODDI. Diffusion tensor imaging (DTI) is the simplest model of diffusion process ( § 3.2.4). However, DT-based quantitative scalar features (FA, MD) and color-encoded direction maps have been shown to provide meaningful information on the cortical organization, both ex vivo [Dyrby

Table 6

 6

	.1.

  Histological methods do not give access to the lamination of large Chapter 6. Laminar structure of the cortex inferred from MR-based myelo-and cyto-architectural features 165 fields of view and do not provide real 3D imaging. Therefore, being able to segment cortical layers in vivo or ex vivo with MRI methods would open up new fields of study and provide new insights about Alzheimer's or Parkinson's diseases, the two most widespread neurodegenerative diseases (see the introduction of Chapter 5 for figures about their prevalence).

In

2015, over 46 million people lived with dementia worldwide, and experts plan that this number will almost double every 20 years[Prince et al.] 2 PD affects 1-2 per 1000 of the population with 1% of the population above 60 years that is diagnosed[START_REF] Tysnes | Epidemiology of parkinson's disease[END_REF]. Nonetheless, these numbers may be underestimated as studies showed that clinicians diagnose the disease incorrectly in about 25% of the cases[Organization, 2006[START_REF] Tolosa | The diagnosis of parkinson's disease[END_REF]

Scanning parameters were: isotropic resolution of 300 µm, TE/TR = 24.6/9000 ms, ∆/δ = 14.4/4.3 ms, matrix size: 167×163, 250 slices, flip angle: 90°, receiver bandwidth: 66 kHz, and a total scan

For instance, the primary motor cortex, called for a long time 'agranular' because Brodmann did not observe any granular layer: the existence of layer IV (granular) in M1 has only recently been demonstrated [García-Cabezas andBarbas,

2014,[START_REF] Barbas | Motor cortex layer 4: less is more[END_REF]

The purpose of these two anatomical images was to facilitate the final registration step aiming at reconstructing the entire left hemisphere and, in fine, the entire specimen.

Acknowledgements

Diffusion-weighted scans Diffusion data were acquired using 3D segmented EPI sequences with an isotropic resolution of 200 µm. Acquisition parameters were as follows: TE/TR = 24.3/250 ms, δ /∆ = 5/12.3 ms, 1 average, matrix size: 212×204, 280 slices, flip angle: 90°, receiver bandwidth: 300 kHz, 30 segments, 16 b = 0 s/mm 2 images, b = 1500, 4500, 8000 s/mm 2 , 25, 60, 90 directions, and gradients strength: 289, 500, 666 mT/m. Diffusion-weighted sequences were divided into two sequences with one b = 0 s/mm 2 and respectively 12 and 13 directions at b = 1500 s/mm 2 , six sequences with one b = 0 s/mm 2 and 10 directions at b = 4500 s/mm 2 , and nine sequences with one b = 0 s/mm 2 and 10 directions each at b = 8000 s/mm 2 . The purpose of this splitting was to prevent from a drift of the basic frequency, the consequence of which being a slight translation of the sample observed on the final image between the first and the last diffusion direction. An automatic adjustment of the basic frequency was therefore applied every ten diffusion directions. Finally, the seventeen diffusion-weighted sequences lasted a total of 82h.

In a nutshell, the complete acquisition of one field of view (5.6 cm long) lasted 107h, which is equivalent to four days, the night before and the night after (typically from Wednesday evening to Monday morning).

Chenonceau project time line

Figure 7.9 summarizes the main stages of the Chenonceau project. Nine months were necessary to obtain a post mortem specimen and to adequately prepare it. The acquisition protocol design was interrupted by several quenches of the 11.7 T system, making the system unavailable for a total duration of twelve months. The design of the acquisition protocol represented a total of six months and the last nine months of this thesis were dedicated to the intensive scanning of the blocks at 11.7 T.

7.3 Image analyses: towards the reconstruction of the entire left hemisphere

Preprocessing pipeline

The multiple b-values were obtained by varying the gradient magnitudes (289, 500, 666 mT/m), with all other parameters (δ , ∆, TE) kept constant. This protocol is thus suitable to apply NODDI as well as MAP-MRI models (see § 3.2.7.1).

Initial SNR of the diffusion-weighted images were 13.9, 9.8, 7.4 respectively at b = 1500, 4500, 8000 s/mm 2 . These images were filtered using a non-local means filter algorithm [START_REF] Buades | Non-local means denoising[END_REF][START_REF] Condat | A simple trick to speed up and improve the non-local means[END_REF], resulting in a final SNR of 125, 81, 69 respectively for b = 1500, 4500, 8000 s/mm 2 . Anatomical scans presenting a high SNR of 33 at 100 µm and 17 at 150 µm were not filtered. isotropic), diffusion-weighted images with a spatial resolution of 300 µm isotropic acquired at bvalues of 2000, 4000, 6000 s/mm 2 along 60, 125, 125 directions, and T1-relaxometry images acquired at 7 T with an isotropic spatial resolution of 300 µm. The NODDI model applied on the diffusion dataset provided intracellular volume fraction maps representing the neurite density in each voxel, and the T1 relaxometry gave access to T1 quantitative maps. The unsupervised clustering integrating both T1 quantitative map and neurite density map gave evidence that the combination of these two contrasts could highlight layers of the visual cortex, the myeloarchitectural information obtained from the T1 map favoring the extraction of the outer layers and the neuritic density information obtained from NODDI favoring the extraction of the deeper layers. This work is currently under preparation for publication.

Multi-contrast MR imaging of the human left hemisphere at a mesoscopic scale

Obtaining a mesoscopic dataset including anatomical and diffusion-weighted images of a whole post mortem human brain specimen involved several steps. First, the extraction and fixation of an ex vivo human brain was performed at Tours University Hospital by Pr C. Destrieux. Following rehydration, the specimen was scanned on a 3 T clinical system, before cutting the hemispheres into seven blocks that could fit into the small bore of the 11.7 T preclinical system. Then, the seven blocks of the left hemisphere were scanned on the 3 T clinical system, which provided in the end two blockface images to facilitate the final registration step. The acquisition protocol performed at 11.7 T included anatomical sequences (100 and 150 µm isotropic) as well as 3D segmented EPI sequences (b = 1500, 4500, 8000 s/mm 2 , 25, 60, 90 directions) at 200 µm isotropic. This protocol was designed to scan each individual block in four times, each block (20 cm long) being divided into four overlapping fields of view (5.6 cm long).

A pipeline was developed as part of the internship of A. Popov to automatically preprocess the acquired fields of view, from the image reconstruction to the application of a non-local means filter.

Then, the registration work consisted in the registration of the anatomical scan acquired at 11.7 T with its reference acquired at 3 T (second blockface image), and, in a second step, the registration of each block acquired at 3 T with the post mortem acquisition of the entire brain performed at 3 T before the cutting, corresponding to the anatomical reference image. This work has been initiated with basic affine transformations, and will be improved in the next months with the use of a diffeomorphic registration based on the use of the MAP-R algorithm developed within the Microstructure team by K. Ginsburger. This method aligns the propagator fields inferred from the MAP-MRI model. Therefore, the work carried out during this thesis laid the foundation for the acquisition of an entire post mortem human brain. The acquisition campaign has only been partially completed, due to technical failures that occurred during these three years (quench of the 11.7 T MRI system that took a year to be replaced). However, the acquisition of the left hemisphere should be achieved for the end of this thesis (half of the blocks already acquired), and the second hemisphere should be imaged Appendix A

Related publications

Journal publications

• Beaujoin, J., Palomero-Gallagher, N., Boumezbeur, F., Markus, A., Bernard, J., Poupon, F., Schmitz, D., Mangin, J.F., Poupon, C. (2018) Post-mortem inference of the human hippocampal connectivity and microstructure using ultra-high field diffusion MRI at 11.7T. Brain Structure and Function, pp.1-23.

• Ginsburger, K., Poupon, F., Beaujoin, J., Estournet, D., Matuschke, F., Mangin, J.F., Axer, M., Poupon, C. (2018) Improving the Realism of White Matter Numerical Phantoms: A Step toward a Better Understanding of the Influence of Structural Disorders in Diffusion MRI. Frontiers in Physics, 6, P.12.

• Teillac, A., Beaujoin, J., Poupon, F., Mangin, J.F., Poupon, C. (2017, September)