Keywords: MRI pulse sequences, diffusion-weighted MRI, open-source programming . . . . . . . . . NDI neurite density index. NIFTI neuroinformatics technology initiative. NMR

Magnetic Resonance Imaging (MRI)

In summary, after presenting its scientific context and challenges, this thesis details the development of a toolbox allowing for the open-source and modular development of MRI pulse sequences. It demonstrates the robustness of its basis by providing images acquired with standard sequences and its capacity to efficiently produce pulses sequences that can be used in a research environment with the given examples of diffusion MRI and echo-volumar imaging.

General conclusion

Communications

References v vi List of Figures 1 Représentation schématique de l'intérieur d'un système d'acquisition IRM (entouré par un aimant générant un fort champ magnétique). . . . . . . . . . . . . . . . . . . . . . . . . . 2 Chronogramme d'une séquence d'acquisition IRM en écho de gradient avec lecture simple. 3

La programmation de séquences d'Imagerie Par Résonance Magnétique (IRM) repose sur l'utilisation d'environnements de développements fournis par les constructeurs. Ces derniers permettent l'élaboration de nouvelles méthodes d'acquisition mais sont limités par des questions de propriété intellectuelle.

Des solutions ont été proposées par la communauté scientifique permettant le prototypage de séquences indépendamment du constructeur. Cependant, ils utilisent une interface haut-niveau ne facilitant pas l'accès à toute les fonctionnalités des machines, ce qui restreint le développement de nouvelles séquences en ne permettant pas l'utilisation optimale de l'interface utilisateur, ni le déploiement de séquences optimisées pour le temps réel.

L'ouverture de ces possibilités présente un potentiel considérable pour la recherche en IRM et n'est pour le moment possible que dans les conditions imposées par le constructeur. Afin de proposer une solution à ce problème, cette thèse présente le développement de GinkgoSequence, un nouvel environnement libre de droits pour la programmation modulaire de séquences dans l'environnement Siemens.

La première partie présente les principes de la résonance magnétique nucléaire et de l'IRM, détaillant les notions d'encodage spatial et de séquence. Elle décrit les méthodes d'acquisition rapides, incluant l'imagerie écho-planaire et les techniques d'accélération reposant sur l'acquisition partielle des données, ainsi que les outils pour la programmation de séquences et la reconstruction des images, avec une description du kit IDEA de Siemens ainsi que des solutions libres de droits existantes. Elle introduit ensuite l'application de l'IRM à l'imagerie du cerveau humain, présentant l'anatomie de ce dernier avant de détailler les méthodes d'IRM anatomique, fonctionnelle, et pondérée en diffusion.

La deuxième partie se focalise sur le développement de GinkgoSequence, ses enjeux et modalités, avant de prouver sa robustesse et son efficacité à l'aide d'acquisitions sur fantôme et sur volontaire sain.

Dans un premier temps, elle décrit son contenu orienté-objet basé sur la notion de modules représentant les parties élémentaires d'une séquence IRM et pouvant être agencés à l'aide d'ancres temporelles. Ces modules sont générés en utilisant une factory et peuvent être agrégés dans des modules composites avant d'être organisés dans le temps pour former une séquence compilable avec IDEA. La toolbox inclut des exemples de séquences dont les images peuvent être reconstruites à l'aide de l'environnement open-source Gadgetron. Dans un second temps, elle présente des séquences de routine, montrant et analysant des images acquises sur un fantôme avant de les comparer avec l'existant. Ces essais prouvent la robustesse des modules de base et leur capacité à obtenir des résultats équivalents à ceux de séquences de référence.

Dans un troisième temps, elle introduit l'utilisation de la toolbox pour l'implémentation de séquences IRM pondérés en diffusion et leur utilisation sur quelques volontaires sains pour évaluer les résultats des cartes de connectivité structurelle et de description quantitative de la microstructure obtenues avec succès.

Enfin, elle aborde le développement d'une séquence écho-volumaire qui pourra être exploitée ans le cadre de séquences IRM fonctionnelles ou de diffusion. Elle montre l'utilisation de cette séquence pour scanner un hémisphère de cerveau human ex vivo et évaluer la qualité des images reconstruites.

En conclusion, après avoir présenté son contexte scientifique et ses enjeux, cette thèse présente GinkgoSequence, un outil pour le développement libre de droits et modulaire de séquences IRM. Elle démontre sa robustesse en présentant des images acquises avec des séquences des routine clinique et sa capacité à produire de nouvelles séquences avec les exemples donnés de l'IRM de diffusion et des séquences échovolumaires. pulse sequence programming relies on development kits provided by manufacturers and allows for the design of new acquisition methods. However, due to intellectual property issues, the sharing of these sequences for research purposes is restrained, thus hindering their development.

To overcome these difficulties, researchers proposed vendor-independent solutions for the prototyping of MRI pulse sequences. However, as these environments rely on high-level interfaces, their use for accessing and operating the user interface optimally or for performing real-time protocols is not straightforward. Allowing for the open-source development of MRI pulse sequences capable of using all the complex features proposed by the manufacturer would thus support the development of new pulse sequences for research purposes. Proposing a solution to this issue, this thesis presents the development of GinkgoSequence, a novel modular and open-source MRI pulse sequence programming framework for Siemens systems.

The first part of this work details the principles of nuclear magnetic resonance and MRI, specifying the notions of spatial encoding and pulse sequence. It presents several methods for rapid acquisition, including echo-planar imaging and accelerated methods relying on partial data acquisition; before introducing tools for MRI pulse sequence development and image reconstruction, with a description of Siemens's IDEA development kit as well as a panel of existing open-source solutions for pulse sequence programming. It also introduces the applications of MRI for human brain imaging, starting with a brief anatomical description before presenting the anatomic, functional, and diffusionweighted MRI modalities.

The second part of this thesis focuses on the development of the GinkgoSequence toolbox, defining its challenges and technical requirements and proving its robustness and efficiency by providing example acquisitions on phantoms and human volunteers.

First, it proposes a detailed description of its object-oriented source code based on sequence modules standing for fundamental parts of any MRI pulse sequence that can be ordered using anchor times. These modules are embedded into a factory and can be aggregated into composite modules before being organized in time to form a pulse sequences source code that can be compiled using the IDEA environment. The toolbox includes examples of sequences compatible with the opensource Gadgetron framework for reconstruction.

Second, it details the development of standard sequences, showing and analyzing images acquired on a phantom and comparing them with reference sequences. These trials prove the robustness of the basic modules provided in the GinkgoSequence toolbox and their ability to obtain results conforming with the images acquired using reference sequences.

Third, it describes the further development of the toolbox to implement a series of diffusionweighted MRI pulse sequences and evaluates their results on a few healthy volunteers for whom a reconstruction of the structural connectivity and quantitative microstructure was successfully achieved.

Last, it introduces the implementation of an echo-volumar sequence, allowing an ultra-fast acquisition that can be exploited both for diffusion and functional MRI, and its use to scan an ex-vivo human hemisphere, assessing the quality of the reconstructed data. 6.3 Images obtained using the GinkgoGradientEcho2d sequence on a KH 2 P O 4 /NaCl phantom. 6.4 Images obtained using the GinkgoGradientEcho3d sequence on a KH 2 P O 4 /NaCl phantom. 6.5 Images obtained using the GinkgoSpinEcho2d sequence on a KH 2 P O 4 /NaCl phantom. . . 6.6 Images obtained using the GinkgoSpinEcho3d sequence on a KH 2 P O 4 /NaCl phantom. . . 6.7 Images obtained using the GinkgoSteam2d sequence on a KH 2 P O 4 /NaCl phantom. . . . 6.8 Images obtained using the GinkgoSpinEcho2dEPI sequence accelerated using GRAPPA and PF 6/8 with decreasing resolutions (indicated here by the acquisition matrix size) on a KH 2 P O 4 /NaCl phantom showing less distortions for lower resolutions. . . . . . . . . . . 6.9 Images obtained using the GinkgoSpinEcho2dEPI sequence on a KH 2 P O 4 /NaCl phantom. ix 6.10 Images obtained using the GinkgoSpinEcho3dEPI sequence on a KH 2 P O 4 /NaCl phantom. 6.11 Images obtained using the GinkgoSteam2dEPI sequence on a KH 2 P O 4 /NaCl phantom. . 6.12 Comparison between GinkgoGradientEcho2d and Siemens' 2D gre sequence. . . . . . . . . 6.13 Comparison between GinkgoGradientEcho3d and Siemens' 3D gre sequence. . . . . . . . . 6.14 Comparison between GinkgoSpinEcho2d and Siemens' 2D se sequence. . . . . . . . . . . . 6.15 Comparison between GinkgoSpinEcho2dEPI and an ep2d_se sequence. . . . . . . . . . . . 8.1 obtained in their user interfaces. . . . . . . . .

xiii xiv

Synthèse

Introduction L'imagerie par résonance magnétique (IRM) est une technique permettant d'obtenir des images de l'intérieur du corps humain de manière non-invasive. Introduite par P. Lauterburg et P. Mansfield dans les années 70, elle repose sur le phénomène de résonance magnétique nucléaire qui peut être induit au niveau du spin des atomes d'hydorgène en les plongeant dans un fort champ magnétique et en les exposant à une impulsion radio-fréquence. Ce système de base est complété par un ensemble de gradients permettant un encodage spatial du signal pour l'obtention d'images tridimentionnel. Le signal mesuré en IRM se trouve dans l'espace de Fourier, plus communément appelé espace k, et doit passer par un processus de reconstruction à base de transformée de Fourier inverse pour être interprété dans l'espace image. Le signal IRM peut être obtenu avec différents contrastes, permettant d'observer différentes parties du corps et de détailler leur anatomie interne.

État de l'art

Pour obtenir des images en IRM, il est nécessaire de donner des instructions très précises et en temps réél aux différentes parties du système d'acuisition. Ces événements sont en général représentés sur différents axes représentant les éléments composant la machine à la manière s'une partition de musique dans ce que l'on appelle un chronogramme. La répétition de ces événements pour l'acquisition d'un volume de données s'appelle une séquence IRM. Il existe une grande variété de séquences pour l'acquisition d'images IRM, permettant d'obtenir différents contrastes et différents précisions d'acuiqistions. Elles sont basées sur différents types d'excitation (impulsions radio-fréquence), incluant la génération d'échos de gradient, d'échos de spin et d'échos stimulés.

Les séquences les plus simples lisent une ligne de l'espace k à la fois et sont très lentes. Pour contourner ce problème, différentes méthodes d'accéléréation ont été proposées:

• l'imagerie écho-planaire (EPI): reposant sur l'acquisition d'un train de lecture permettant d'obtenir les données pour de multiples lignes en une seule fois,

• l'utilisation du plan de Fourier partiel (PF): reposant sur la propriété de symmétrie Hermitienne de l'espace k et permettant de n'acquérir que la moitié de ce dernier pour récupérer toute l'information désirée,

• l'acquisition en spirale: tirant parti de la concentration de l'information au centre de l'espace k pour n'acquérir que ce dernier tout en conservant la qualité de l'image,

• l'imagerie parallèle: profitant des avancées techniques au niveau des antennes d'émission et de réception qui se composent de plusieurs bobines permettant l'acquisition d'un signal partiel et sa reconstruction à l'aide des cartes de sensibilité des différents bobines,

• l'acquisition parsimonieuse: ciblant l'acquisition de l'espace k seulement sur ses parties utiles grâce à sa répartition des données sporadique. système d'acquisition, des séquences exemples, un simulateur permettant d'observer le chrononogramme de la séquence et de vérifier sa cohérence, une interface graphique reproduisant celle de la console et des tests permettant de s'assurer du bon fonctionnement de la séquence. Il est généralement utilisé pour développer de nouvelles séquences en se basant sur des séquences déjà fournies par Siemens.

Les séquences obtenues en modifiant des séquences pré-existantes permettent de mettre en pratique de nouvelles modalités d'acquisition mais sont soumises à des clauses de propriété intellectuelle ne permettant pas leur libre partage. Ce dernier point est particulièrement limitant pour le développement et le partage de nouvelles séquences dans le monde la recherche. Afin de contourner ce problème, des environnements de développement de séquences pouvant se connecter aux systèmes de multiples vendeurs ont été propoposés. Leurs principaux représentants sont:

• ODIN: une librairie C++ permettant la programmation orientée objet de séquences et son déploiement via une interface générique sur des imageurs Siemens et Bruker,

• SequenceTree: un environnement de développement permettant le prototypage de séquences à l'aide d'une interface graphique pour les personnes souhaitant s'affranchir des difficultés de programmation,

• PulSeq: un cadre de développement en Matlab (ou Python) générant un fichier de séquence décrivant tous les événements à jouer au niveau du système d'acquisition en ordre chronologique et pouvant être interprété sur les machines General Electrics, Siemens et Bruker.

Ces solutions permettent, chacune à leur manière, de développer efficacement des séquences et de les exporter sur les machines de différents vendeurs. Ce sont de très bons outils de prototypage qui trouvent cependant leurs limites quand les séquences développées nécessitent d'avoir un accès complet à des fonctionnalités spécifiques d'un constructeur ou à des structures de séquences impliquant un très large nombre d'itérations.

Une seconde approche pour permettre le développement efficace et libre de droits de séquences est de développer des outils facilitant l'utilisation de l'environnement de développement fourni par le vendeur à ces fins. Un bon exemple de cette philosophie est donné par la librairie KSFoudation qui permet de faire de la programmation orientée object dans l'environnement de General Electrics. Le travail de cette thèse s'inscrit aussi dans ce type de démarche en fournissant un environnement de développement libre de droits et modulaire dans le cadre des outils de Siemens.

Si cette thèse repose principalement sur de développement informatique, les séquences permettant d'acquérir les images ont été testées dans un cadre applicatif permettant d'évaluer leur qualité: l'IRM cérébrale. Permettant de faire des images in vivo du cerveau de manière non-invasive, l'IRM a permi d'approfondir de nombreux sujets de recherche en neuroanatomie et en sciences cognitives, menant à diverses applications dans le domaine médical et à une meilleur connaissance de cet organe très complexe. La structure du cerveau peut être vue à l'échelle macroscopique, suivant le point de vue du radiologue, afin d'en observer les grandes structures et de décrire leurs caractéristiques. Elle peut aussi être considérée à l'échelle microscopique, selon le point de vue du biologiste, pour décrire ses oligodendrocytes, astrocytes et neurones. Plus précisément, les neurones sont principalement composés d'un corps duquel part un long appendice appelé axone. Les corps des neurones contenus dans le cerveau sont concentrés dans ses parties les plus superficielles et les plus profondes, appelées matière grise, et leurs axones composents sous forme de faisceaux de fibres la partie comprise entre ces deux couches et appelée matière blanche. Pour observer le cerveau humain avec l'IRM, il est possible d'utiliser différentes modalités d'imagerie, parmi lesquelles:

• l'IRM anatomique: utilisant différentes contrastes (T1, T2, T2*, FLAIR,...), elle permet d'observer l'anatomie de cerveau et d'en détecter les pathologies, les acquisitions sont faite à l'aide de séquence d'acquisition comme la MP-RAGE;

• l'IRM pondérée en diffusion (IRMd): sensible à la diffusion des molécules d'eau dans les tissus cérébraux, elle permet de reconstruire les faisceaux de matière blanche et d'étudier la cytoarchitecture du cerveau, les acquisitions en IRMd peuvent être faites en utilisant des séquences de type PGSE;

• l'IRM fonctionnelle (IRMf): basée sur l'acquisition du signal BOLD utilisant le processus de réponse hémodynamique, elle permet d'observer les activations du cerveau lorsqu'il est sollicité par un stimulus ou au repos, les signaux sont acquis rapidement dans le temps à l'aide d'une séquence écho-planaire accélérée (2D/3D GRE EPI).

Bien d'autres modalités d'imagerie du cerveau existent pour compléter celles présentées dans ce manuscrit, permettant entre autres d'observer le système vasculaire cérébral ou de mettre en valeur certaines structures à l'aide d'agents de contraste.

Développement de l'environnement GinkgoSequence

Les séquences d'acquisition sont indispensables pour obtenir des images IRM, quelle que soit la méthode d'acquisition envisagée. Leur développement est rendu possible par les environnements de programmation fournis par les différents constructeurs d'IRM, mais les séquences ainsi obtenues peuvent s'avérer difficile à partager par souci de propriété intellectuelle. Des solutions libres de droits existent, mais elles sont faites pour être indépendentes des constructeurs et fournir des prototypes de séquences qui peuvent être jouées sur différentes machines. Elles ne permettent donc pas d'accéder facilement à toutes les fonctionnalités proposées par les différents constructeurs.

Dans ce contexte, nous avons développé GinkgoSequence, un environnement de programmation orientéobjet, modulaire et open-soure, permettant de développer et de partager efficacement de nouvelles séquences. Ce dernier se base sur la décomposition des séquences IRM en suivant une analyse hiérarchique: chaque séquence peut être vue comme une succession de blocs traitant des tâches élémentatires et pouvant se retrouver dans de multiples séquences. Son développement a été fait de manière à respecter deux axes de développement: l'aspect libre de droits et l'architecture orientée objet. Pour le premier point, le code a été développé sans utiliser les codes de séquences fournis par Siemens, mais en respectant l'implémentation des méthodes obligatoires et bas niveau fournies dans les librairies d'IDEA afin que le code puisse compiler correctement. La programmation orientée-objet a été réalisée de manière a garantir une bonne lisibilité du code ainsi que sa flexibilité en utilisant des structures telle que les fabriques (factorys).

Le code source de GinkgoSequence est basé sur la classe SequenceModule représentant un élément de base pouvant être utilisé dans plusieurs séquences différentes. Cette classe structure un module contenant différents éléments en temps réel, agencés selon une chrononologie permettant de définir la durée du module ainsi qu'une ancre temporelle permettant de l'inscrire dans l'organisation temporelle de la séquence. Les instances de la classe SequenceModule sont générées à l'aide d'une fabrique en passant par la classe SequenceModuleFactory. Cette dernière permet de créer une instance de n'importe quel SequenceModule de manière générique en lui donnant un nom et en l'incluant dans une liste. Les modules ainsi créés peuvent être combinés en utilisant la classe CompositeSequenceModule qui hérite de SequenceModule et permet d'assembler des modules complexes à partir de modules plus simples, en définissant une durée et une ancre temporelle pour cet assemblage de modules. Pour finir, les instance de SequenceModule et de CompositeSequenceModule sont combinées par ordre chrnonologique pour former une séquence d'acqusition IRM en utilisant la classe GinkgoSequence. Dans cette classe, les méthodes obligatoires de l'architecture Siemens ainsi que les méthodes nécessaires à l'utilisation de l'interface utilisateur sont reprises, permettant la compilation de la séquence dans l'environnement IDEA.

De nombreux modules ont été impléméntés dans GinkgoSequence, ils couvrent toutes les fonctions de Les modules développés dans GinkgoSequence ont permi le développement de nombreux exemples de séquences, couvrant tous les cas simples (écho de gradient, écho de spin, écho stimulé, lecture simple et écho-planaire), ainsi que des séquences d'écho de spin avec lecture écho-planaire pondérées en diffusion. De plus, une séquence d'acquisition écho-volumaire est encore en développement. Toutes ces séquences ont été rendues compatible avec Gadgetron, un outil de reconstruction d'images IRM libre de droits pouvant être connecté directement au système d'acquisition afin de reconstruire les images en temps réel (online) ou après la fin de l'acquisition (offline).

Application au développement de séquences IRM

Les séquences de base, incluant des accélérations en Fourier partiel et en imagerie parallèle (GRAPPA) ont été testées sur un fantôme contenant une solution de phosphate de monopotassium et de chlorure de sodium et présentant des structures complexes permettant d'évaluer la qualité des images. Les images ont été acquises avec et sans accélérations et donnent toutes une représentation fidèle du fantôme en lecture simple et une représentation normalement déformée de ce dernier en lecture écho-planaire. Comparées à des séquences produit équivalentes de Siemens, les images présentent une qualité équivalente. Après leur évaluation visuelle, les images ont aussi été comparées en utilisant leur rapport signal sur bruit pour lequel des valeurs plus élevées ont été trouvées au niveau des séquences 3D par rapport aux séquences 2D, ainsi que des valeurs diminuées de moitié pour les séquences en échos stimulés, ce qui était attendu. La première comparaison a donné des images pondérées en diffusion très similaires pour la séquence d'écho de spin de GinkgoSequence et la séquence CMRR, montrant une augmentation du bruit avec la pondération en diffusion, ainsi que de premiers indices de la présence des faisceaux de fibres de matière blanche. Les cartes quantitatives obtenues avec les différents modèles ont aussi montré une grande similarité entre les les deux séquences, tout en fournissant des analyses précises et cohérentes de la microstructure cérébrale. Les tractogrammes obtenus avec les deux séquences sont quasiment identiques, montant de la même manière les faisceaux de matière blanche dans le cerveau. La correspondance avec l'atlas Ginkgo-Chauvel a permi, dans les deux cas, l'identification de tous les longs faisceux de matière blanche. De la même manière, la séquence d'écho stimulés a montré des résultats et des analyses très similaires à ceux obtenus avec la séquence d'écho de spin.

Ce travail de thèse s'est poursuivi avec l'implémentation d'un module de lecture écho-volumaire permettant l'acquisition de plusieurs coupes (alors appelées partitions) en une seule excitation menant à des temps d'acquisition très réduits. Ce dernier a permi l'implémentation rapide d'une séquence d'écho de spin 3D avec lecture écho-volumaire, acclélérée par du Fourier partiel (dans deux directions) et du GRAPPA. Elle a été comparée à une séquence d'écho de spin 3D écho-planaire aussi développée avec GinkgoSequence. Des résultats préliminaires ont été obtenus sur un hémisphère de cerveau humain ex vivo et montrent la capacité de l'acquisition écho-volumaire à obtenir des images représentant correctement la forme du cerveau mais ne présentant pas un rendu satisfaisant de ses détails. Ce souci est dû aux déformations générées par le trop long train de lecture et peut être atténué en implémentant l'accélération GRAPPA dans une deuxième direction et en acquiérant de plus petit champs de vue, rendus possibles par l'ajout de bandes de saturation.

Conclusion

Cette thèse a contribué à la facilitation du développement de séquences libres de droits pour les systèmes Siemens, en proposant GinkgoSequence, un environnement open-source, orienté-objet et modulaire pour le développement de séquences IRM. Cet outil inclut de nombreux modules pouvant être assemblés pour créer efficacement de nouvelles séquences. Ils ont été utilisés pour l'iplémentation de séquences de base, pondérées en diffusion et écho-volumaires, qui ont été testées in vivo et ex-vivo. Lorsque c'était possible, elles ont aussi été comparées à des séquences existantes afin d'évaluer leur qualité. Les images obtenues ont montré des résultats reproduisant correctement les objets observés et permettant une étude en IRMd sur des volontaires sains.

À partir de cette base, il est maintenant possible de développer de nouvelles séquences, notamment pour l'IRMd et l'IRMf, mais aussi pour le très haut champ magnétique (11.7T). L'acquisition écho-volumaire pourra être améliorée avant de l'utiliser pour des acquisitions avec une haute résolution temporelle pour l'IRMf. Elle pourra aussi servir à implémenter des protocoles d'IRMd novateurs pour améliorer la détection des accidents vasculaires cérébraux et pratiquer la biopsie virtuelle.

Introduction

Context and motivations

Since its first description by Paul Lauterburg and Peter Mansfield in the 1970s, Magnetic Resonance Imaging (MRI) has been widely used for medical diagnosis and clinical research. Its vast application field includes notably brain imaging, enabling its ex vivo and in vivo anatomical, functional, and metabolic exploration. If older imaging methods already provided a good understanding of brain anatomy and limited knowledge of some brain functions, MRI brought brain imaging to the next level by allowing its in-vivo anatomical and functional exploration, accessing its deeper and finer structures, including white matter fiber tracts, which could not be traced with other methods. Nowadays, it is used in medical routine, helping the diagnosis of several brain pathologies, as well as for research purposes, aiming to understand its specificities, ranging from anatomical and metabolic features exploration to neurodevelopmental and behavioral studies.

At the heart of this research, NeuroSpin (CEA, Paris-Saclay, France), in the frame of which this thesis has been done, is a research institute whose neuroimaging environment includes outstanding clinical MRI systems with ultra-high fields up to 7T and 11.7T, which is a world first. This environment gathers neuroscientists and MRI physicists, who are working together to explore the human brain in its various aspects and functionalities. Their studies range from instrumentation and methodology to neurodevelopmental and cognitive studies, from infant to elderly, with the support of calculation environments for machine learning and statistics as well as pre-clinical and clinical MRI devices.

The access to ultra-high field imaging devices paves the way to innovative studies allowing to explore the anatomy, function, and microstructure of the brain with innovative methods at unprecedented resolution. Expressing their potential involves accessing a large variety of acquisition schemes with a wide panel of application fields. As these share many common parts, it would be interesting to mutualize them for efficient future methodological development, thus empowering new research in the neuroimaging field.

MRI images are acquired using a complex system, including a strong magnet associated with coils as well as a radio-frequency transmission and reception electronic chain. An MRI system is controlled in real-time using a chronological description of events gathered into a pulse sequence, which implementation relies on programs developed using a programming environment generally provided by the MRI manufacturer. However, due to intellectual property considerations and development choices, the improvement or modification of such sequences is not straightforward and their diffusion in the research environment is hampered.

In this context, the MRI physics community has proposed open-source solutions providing support for manufacturer-independent MRI pulse sequence programming. Such tools enable pulse sequence prototyping using higher-level tools such as Matlab, Python, or graphical interfaces. Although they allow for the quick development and open-source sharing of new pulse sequences, these solutions reach their limits when implementing advanced pulse sequences, such as diffusion-weighted MRI (dMRI) acquisitions, or when using very specific vendor features, like real-time feedback or dedicated user interfaces. Such features require complete access to the vendor's source code, which is seldom possible.

Therefore, this work focuses on the development of an open-source and modular environment for MRI pulse sequence programming called GinkgoSequence. This environment allows for the efficient objectoriented development of new open-source pulse sequences that can be compiled in the Siemens toolkit and played on its MRI systems. This thesis describes the development and testing of all elementary features and of standard sequences as well as advanced diffusion and functional MRI pulse sequences.

Thesis organization

This document is organized in two parts: the first part reviews the literature on MRI acquisition techniques and pulse sequence programming, and the second part presents contributions of this thesis work focused on the development and testing of the GinkgoSequence framework.

The first part includes four chapters presenting the background of this thesis:

• Chapter 1 provides a description of nuclear magnetic resonance (NMR) and its application to MRI, including the notion of spatial encoding leading to the introduction of pulse sequences for image acquisition before explaining the notion of k-space and its reconstruction in the image space;

• Chapter 2 presents the accelerated MRI schemes in chronological order of development, from echoplanar readouts to compressed sensing methods through partial Fourier and parallel imaging;

• Chapter 3 focuses on pulse sequence programming and reconstruction tools, describing the frameworks provided by the various vendors with a focus on Siemens' environment, it also presents the open-source solutions available today;

• Chapter 4 encompasses the applications of MRI for human brain imaging, including a summary of human brain anatomy and a description of anatomical, functional, and diffusion-weighted MRI modalities.

The second part also covers four chapters and presents the contributions of this work:

• Chapter 5 describes the challenges and technical aspects at the heart of the development of the GinkgoSequence toolbox, highlighting its open-source and object-oriented philosophy with specific examples;

• Chapter 6 shows an application of GinkgoSequence to the development of basic MRI pulse sequences and studies its robustness with phantom acquisitions and signal-to-noise ratio (SNR) analysis;

• Chapter 7 demonstrates the usability of GinkgoSequnce to create a series of diffusion-weighted sequences by applying them to scan healthy volunteers and providing a demonstration of the robustness of the collected dMRI data to study the structural connectivity and microstructure of their white matter;

• Chapter 8 further explores the capacities of the toolbox through the implementation of a novel echo-volumar acquisition scheme, describing its technical aspects and perspectives based on ex vivo acquisitions.

This thesis ends with a general conclusion presenting the perspectives offered by the GinkgoSequence toolbox and its future works.

Part I State of the art

Chapter 1 Principles of magnetic resonance imaging

Nuclear magnetic resonance

Since its invention by Paul Lauterburg and Peter Mansfield in the 1970s, Magnetic Resonance Imaging (MRI) has been a flourishing technique for non-invasive imaging of the inside of the human body. It is based on the Nuclear Magnetic Resonance (NMR) phenomenon first described by Felix Bloch and Edward Purcell in 1946 and involves an intrinsic property of atoms called spin. This section presents the physical principles of magnetic resonance, from its quantum mechanics basis to its use in generating magnetic resonance (MR) images.

Nuclear magnetization

To understand what spin is, although it is inaccurate, it is common to imagine a particle spinning around an axis, as shown in Figure 1.1. In reality, the particle is not spinning, it is animated by one of its fundamental quantum properties known as spin angular momentum. Spin can be described using its magnitude I, its number of nuclear states N ns , and its magnetic moment µ expressed in J.T -1 . For protons, neutrons, and electrons, but also for the single-proton hydrogen nucleus, which is of special interest regarding body NMR, I = 1 2 ; for other particles, it can be equal up to 8, by steps of 1 2 . Using this magnitude, it is possible to calculate the number of nuclear spin states using equation (1.1) and the magnetic moment using equation (1.2):

N ns = 2I + 1, (1.1) µ = γL, (1.2)
where L is the angular momentum and γ expressed in rad -1 .T -1 is a constant specific to the considered nucleus and called the gyromagnetic ratio. γ can either be positive or negative and is aligned with the spin accordingly in the same or opposite direction. For instance, if equation (1.1) is applied to a hydrogen nucleus of spin I = 1 2 , N ns = 2 is obtained, meaning that hydrogen spins have two possible nuclear states, called spin-up for the state + 1 2 and spin-down for the state -1 2 . They correspond to two different levels of energy, E 1 for spin up and E 2 for spin down, described in equation (1.3):

   E 1 = -γℏB 0 2 , E 2 = + γℏB 0 2 ,
(1.3) with ℏ = h 2π , h = 6.62610 -34 J.s the Planck constant, and B 0 the magnetic field in which the spins are immersed expressed in T . Linked with these states of energy, the magnetic moment can be obtained using equation (1.2) and the gyromagnetic ratio of hydrogen γ = 2.657 × 10 8 rad -1 .T -1 , sometimes also expressed in its frequential form as γ = γ 2π = 42.57 MHz.T -1 . Since it is positive, its vector µ is colinear to the spin.

Magnetic resonance

In a biological sample, it is not practical, regarding quantum physics, to consider each spin orientation and magnetic moment. Thus, nuclear magnetic resonance is usually explained using the net magnetization M of a group of nuclei, corresponding to the integration of their spin over a volume of interest as described in equation (1.4):

M = i∈sample µ i .
(1.4) As explained in Figure 1.2-a, in the absence of a magnetic field, nuclei are spread out randomly between energy states and dephased, resulting in a null net magnetization. However, exposing them to a magnetic field B 0 aligns their spins in its direction with a non-equal spreading between the spin up and spin down states, as shown in Figure 1.2-b, leading to a non-null net magnetization. More precisely, in this equilibrium state, M is oriented parallel to B 0 and starts spinning around it at a specific frequency called the Larmor angular frequency ω 0 and expressed in rad.s -1 as defined in equation (1.5) and depicted in Figure 1.3-a. This reaction, called precession, is the first condition to generate the nuclear magnetic resonance phenomenon. The concomitant application of a second dynamic electromagnetic field B 1 rotating at the Larmor frequency is the second mandatory condition to induce the resonance phenomenon. This dynamic electromagnetic field B 1 corresponds to a radio frequency (RF) pulse whose frequency spectrum necessarily embeds the Larmor frequency. As depicted in Figure 1.3-b, this stimulation causes the spins to align and precess around both B 0 and B 1 in resonance, changing their levels of energy and re-phasing them so that M is tilted at an angle θ from its equilibrium state. This angle is obtained by varying the duration and the magnitude of the RF pulse. For instance, it can be set to 90°to move M from parallel to B 0 to perpendicular to it. If the axis of B 0 is aligned with the z-axis, an orthonormal coordinate system can be created around it using x and y for the other two axes, as displayed in Figure 1.3. To simplify the problem, this referential is considered rotating at the Larmor frequency around the z-axis. Then, the net magnetization M can be decomposed along the axes of the system as described in equations (1.6) and (1.7), and in Figure 1. 3-c.

M = M L + M T (1.6) M L = M z z M T = M x x + M y y , (1.7)
with M L the longitudinal magnetization and M T the transverse magnetization. Following this nomenclature, at the equilibrium, the only non-zero component of M is M L , and after the 90°RF pulse, this value is transferred to the M T component.

Relaxation

After the application of the RF pulse, the spins tend to come back to their previous equilibrium state along B 0 . This is driven by a regrowth of the longitudinal magnetization M L , characterized by the longitudinal relaxation T 1 corresponding to the time needed for M L to recover 63% of its signal value, and a decrease of the transverse magnetization M T , characterized by the transverse relaxation time T 2 corresponding to the time needed for M T to decrease of 37% of its initial signal value. It is described by the Bloch equation [Bloch, 1946]:

dM(t) dt = γM(t)B(t) + 1 T 1 (M 0 -M L (t))z - 1 T 2 M T (t),
(1.8)

with t the time and M 0 the net magnetization at the equilibrium in the B 0 magnetic field. During longitudinal relaxation, the excited spins, which changed their energy levels, return to their previous states, freeing their energy to their surroundings in a spin-lattice relationship. This phenomenon, as depicted in Figure 1.4-a, happens following the first solution of the Bloch equation:

M L (t) = M 0 (1 -e -t
T 1 ).

(1.9) At the same time, the transverse relaxation happens due to the spins going from the in-phase state to the dephased state. This induces a decrease in the transverse magnetization called the spin-spin relationship and follows the other solution of the Bloch equation (1.10), which effect on magnetization is shown in Figure 1.4-b.

M T (t) = M 0 e -t T 2
(1.10) However, due to magnetic field inhomogeneities, the NMR signal tends to follow another time constant, decreased compared to T 2 , that is called T * 2 , as shown in Figure 1. 4-c,d and equations (1.11), (1.12):

M T (t) = M 0 e -t T * 2 (1.11) 1 T * 2 = 1 T 2 + 1 T ′ 2 ,
(1.12)

with T ′ 2 modelizing the delay induced by the local magnetic field inhomogeneities. The transverse relaxation signal, oscillating at the Larmor angular frequency ω 0 with a T * 2 exponential decay, is called the Free Induction Decay (FID) and is the signal measured by the reception coils during an MR exam.

Spatial encoding

The dynamic electromagnetic field B 1 used to generate nuclear magnetic resonance can be induced in different ways, depending on the design of the RF excitation pulse. It is also possible to obtain more complex resonance effects by using more than one pulse to induce an NMR response. Furthermore, combining these pulses with small magnetic field gradients added in the B 0 field allows for the spatial encoding of the signal, paving the way to magnetic resonance imaging.

The design of the RF pulse is fundamental to induce any NMR signal. Depending on its waveform envelope, duration, and magnitude, it is possible to select a bandwidth of frequencies in which the spins are excited and an angle at which they are tilted from their equilibrium state. An appropriate design of RF pulses makes it possible to manipulate the tilting, the frequency, and the phase of the spins, allowing for the induction of nuclear magnetic resonance of spins in a limited layer of the 3D space bounded by two parallel planes.

Two-dimensional and three-dimensional excitations

There are two different possible excitation modes: 2D and 3D. The first one, as explained in Figure 1.5-a, consists in acquiring the signal generated by a slice selective excitation. This has to be repeated on different slices across the volume to acquire the whole image. It has the advantage of being time-efficient as slices can be excited in an interleaved scheme to optimize the signal decay duration, but it generates a lower signal-to-noise ratio (SNR) than the 3D method.

The 3D acquisition consists in exciting the whole volume and providing an extra encoding for partitions, as depicted in Figure 1.5-b. This way, the whole volume contributes to the signal instead of a single slice, thus yielding an appreciable gain in SNR.

The design of radio-frequency pulses

RF pulses are generated using a waveform envelope, as the ones shown in Figure 1.6, which modulates a sinusoidal RF signal oscillating at the Larmor frequency, and a phase profile. Their magnitude and duration can be tuned to control the flip angle they generate for the spins of the protons. The cardinal sine waveform is used for many classic excitation pulses but reaches its limits due to the non-linearities of the Bloch equations. (c) The Shinnar-Leroux waveform [START_REF] Shinnar | The synthesis of pulse sequences yielding arbitrary magnetization vectors[END_REF]][Pauly et al., 1991] allows for overcoming this limitation and optimizing the RF pulse for its applications.

Among the spectrum of possible RF pulse envelopes, the most simplistic one is known as the hard pulse, which is depicted in Figure 1.6-a. It is a non-spatially selective pulse with a rectangular envelope. Although it can be convenient for particular cases, such as 3D acquisition or composite pulses made of several short rectangular pulses with different phases and amplitudes [Hore, 1983], the hardware's difficulty in playing it correctly makes it rarely used.

Since the hard pulses are not readily applicable, the most commonly used pulses are the soft pulses like the ones modulated by a cardinal sine (SINC) or a Shinnar-Le Roux (SLR) envelope, as depicted in Figure 1.6-b,c. These pulses are easier to play using the standard RF amplifiers and have interesting MR properties.

As the Fourier transform of a SINC waveform is a rectangular pulse, the pulses modulated by this kind of envelope are good for providing selective excitation and refocusing or for saturating a given frequency range. They are remarkably efficient, especially with low flip angles. However, since it is actually impossible to play an entire SINC waveform as it is infinite, their truncation and the non-linearity of the Bloch equation make them not completely accurate regarding the minimum characteristic timings of the acquisition and more unstable regarding the frequency of excitation.

To overcome the difficulties encountered with the SINC pulses, Shinnar and Le Roux independently proposed in the late 1980s an algorithm [START_REF] Shinnar | The synthesis of pulse sequences yielding arbitrary magnetization vectors[END_REF]][Pauly et al., 1991] to mathematically optimize the waveform envelope of MRI RF pulses. Based on the mathematical representation of rotation in space and the hard pulse approximation, it provides waveforms close to those of hard pulses and retaining properties from the SINC pulses, as shown in Figure 1.6-c. These envelopes, which take into account the non-linearities In a spin echo generation scheme, a 90°excitation pulse sets the spins in phase and is followed by an FID signal characterized by a fanning out of the spins. A 180°refocusing pulse inverts this movement, thus retrieving the FID signal as an echo. (c) A stimulated echo is generated using 3 or more RF pulses. This diagram shows the behavior of the spin's phase ϕ when three 90°RF pulses are applied. The red line corresponds to the first and secondary spin echos, the dashed lines correspond to the second and third spin echoes retrieved from the residual signal of the first and the second RF pulses, and the dashed/dotted line corresponds to the stimulated echo generated by the 3 RF pulses using the mixing time T M between the second and third pulses.

of the Bloch equations, can be optimized regarding the application, considering parameters such as duration, bandwidth, or flip angle.

An important drawback in using RF pulses to induce NMR signals is that they deposit energy that can yield heating in the patient's body. This effect affects the entire part of the body covered by the RF coil and can be measured in terms of a Specific Absorption Rate (SAR). This measurement is specific to the MR system but can be scaled using equation (1.13) for classic clinical fields (eg 0.2T to 3T).

SAR ∝ B 2 0 θ 2 ∆f, (1.13)
with θ the flip angle and ∆f the bandwidth of the considered RF pulse in a B 0 magnetic field.

1.2.3 NMR signals: from free induction decay to stimulated echoes As the FID signal is very short and difficult to measure, excitation pulses are used to generate echoes from NMR at different times. The most commonly encountered echoes are the gradient and spin echoes (GRE and SE), to which it is possible to add the stimulated echoes (StE).

To generate gradient echoes, only one RF pulse is necessary, with a flip angle θ, usually set to 90°. The echo is generated based on the gradients, as depicted in Figure 1.7-a, causing a dephasing and a re-phasing of the spins and allowing the obtention of an echo.

To obtain spin echoes, as shown in Figure 1.7-b, a second RF pulse is necessary. Usually, the first one provides a flip angle of 90°and the second one of 180°. The first pulse sets the spins in phase, after which they begin to dephase by fanning out. Then, the second RF pulse mirrors the spins that start to dephase, inducing a rephasing of spins that triggers a spin echo at the echo time (TE).

To produce stimulated echoes, it is necessary to use at least 3 RF pulses. In the context of the STimulated Echo Acquisition Mode (STEAM) [START_REF] Haase | Mr imaging using stimulated echoes (steam)[END_REF]] method, they are all put to 90°to memorize the signal in the longitudinal axis between the two last pulses (z-memory) before retrieving the spin echo, as described in Figure 1.7-c. This figure summarizes all the echoes that can be created using 2 or 3 RF pulses. The phase diagram is made to clarify all possible phase routes and understand where all echoes come from.

Spatial encoding using gradients

Each time an RF pulse is performed, a volume of spins is excited and generates a relaxation signal. This signal can be retrieved for the complete excited volume, but this does not allow the discrimination of the signal. To overcome this, spatial encoding is performed using three encoding gradients, played by coils presented in Figure 1.8, which perform small modifications over B 0 . They correspond to the slice selection gradient G Slice , phase encoding gradient G P hase , and frequency (or readout) encoding gradient G Read . Activating them makes it possible to induce a linear dephasing of spins along the phase axis and a linear variation of frequencies along the frequency axis, thus providing an encoding system of the spin position along the two axes. The gradients only affect the transverse magnetization M T and cannot affect the longitudinal magnetization M L , which is modified by the RF pulses.

Two-dimensional encoding

With a 2D excitation, the spatial encoding is done slice by slice, allowing to change their acquisition order if necessary. Starting with all spins aligned in the B 0 magnetic field, G Slice is used to induce a gradient in the magnetic field along the z-axis, yielding the selection of a slice by exciting it with an RF pulse which bandwidth is set around the Larmor frequency, as explained in Figure 1.9-a. Then G P hase is activated to induce a phase shift along the y-axis inducing a linear dephasing of spins, as explained in Figure 1.9-b. And finally, G Read modifies the frequency of precession of the spins by applying a gradient on the x-axis, as depicted in Figure 1.9-c. The obtained signal is, for each voxel, a volume containing the spatially encoded information in the Fourier domain, named k-space. A 2D inverse Fourier transform can then transfer this information to the image space.

1.2.4.2 Three-dimensional encoding

With a 3D excitation, it is necessary to add another dimension to the process with a partition encoding gradient G P artition played on the slice selection axis. First, with all spins aligned with B 0 , the volume is selected using G Slice , which is also used for partition encoding by inducing a dephasing gradient G P artition in the z-axis. The 3D volume selection gradient is made larger than its 2D counterpart by using a wider RF bandwidth. After this, the encoding is the same as in 2D: a dephasing is induced in the phase axis, and a frequency encoding is done using the readout axis. Just like in 2D, the spatially encoded information is obtained in the k-space, and the image can be reconstructed with a 3D inverse Fourier transform.

Contrast mechanisms

To be able to identify and differentiate the tissues in the body and brain, it is possible to discriminate NMR signals stemming from the tissues. Indeed, tissues are characterized by their intrinsic T 1 and T 2 relaxation times. A contrast can be achieved using key parameters tuning the timeline of acquisitions: the echo time (TE), at which the echo is induced by the RF pulses, and the repetition time (TR), at which the next excitation occurs. contrast is generated with short TE and TR, which causes the interruption of the longitudinal regrowth, thus contrasting the signal based on their longitudinal relaxation time T 1 . The case when TE is long with a short TR induces a mixed contrast, which is not straightforward to interpret and is therefore not commonly used.

Since the MR signal S depends on TE and TR, as described in equation 1.14 and Figure 1.10, tuning them makes it possible to sensitize the MRI signal to T 1 , T 2 , T * 2 relaxation times or proton density:

S ∝ ρe -TE T 2 (1 -e -TR
T 1 ).

(1.14)

All these sensitizations rely on the fact that the tilted transverse magnetization depends on the previous level of regrowth of the longitudinal magnetization. On the other hand, if the repetition time is set to a large value (typically 3 to 4 times larger) with respect to the T 1 relaxation times of tissues, the regrowth of the longitudinal magnetization is therefore almost complete and only depends on the difference of proton density between the various tissues. There are no more dependencies on the T 1 relaxation time. Therefore, inducing a spin echo at a very short TE will sensitize the signal to proton density exclusively, whereas the choice of a large TE may sensitize the signal to the tissue's T 2 relaxation time.

If the repetition time is set to a short value smaller than the tissue's T 1 relaxation time, the level of regrowth will strongly depend on the differences in T 1 relaxation times in addition to the differences in proton densities. Then, if a short TE (eg much shorter than the T 2 relaxation times characterizing the tissues) is selected, the transverse magnetization (stemming from the tilted longitudinal magnetization) will only depend on the T 1 relaxation times and on the proton densities. The choice of a larger TE would induce a signal depending both on T 1 and T 2 , which is seldom used because of the difficulties of interpreting contrast mechanisms in this case.

To improve the contrast or to cancel the contribution of a given tissue to the signal, it is possible to use the inversion-recovery (IR) technique [START_REF] Bydder | Mr imaging: clinical use of the inversion recovery sequence[END_REF], which is described in Figure 1.11-a. It consists in adding a 180°RF pulse before the excitation to flip the magnetization longitudinally and to flip it again at the inversion time T I, corresponding to the time when the difference in signal between the different tissues is maximized for contrast improvement or to the cancellation time. The first option causes these different signals to be more separated than in a classic spin echo technique, as it is shown in Figures 1.11-b,c, and the second one uses T I = T 1 ln(2) for the cancellation of the signal generated by the tissue corresponding to the considered T 1 and is generally used to nullify the signal from the cerebrospinal fluid in brain MRI.

In a similar mindset, it is possible to prevent a selected tissue to participate in the signal by saturating it. This is done using a spectrally selective 90°RF pulse to tilt the spins of a selected frequency bandwidth in the transverse plane before proceeding to the general excitation. This technique is commonly used to remove the signal originating from fat and is known as fat saturation.

In addition to these RF-based techniques, it is possible to enhance the signal of a particular structure by injecting it with a contrast agent. The most frequently used one is Gadolinium, which is made from rare-earth elements and possesses a strong paramagnetism, making it easy to detect in MRI. For instance, it is used clinically to delineate tumors by enhancing the signal of their surrounding hypervascular structures. The drawbacks of this technique are that Gadolinium needs to be injected into the patient's veins (making the method invasive), that it does not remain in the body for a long time, and that it can settle in the kidneys sometimes generating health issues.

Pulse sequences

To form images using NMR, it is necessary to finely manage the different events happening in time: RF pulses, encoding gradients, repetition, and echo timings. This is usually done through an MRI pulse sequence, which is usually explained using a chronogram with four axes: RF for radio-frequency events, G Slice for slice selection gradient events, G P hase for phase encoding gradient events, and G Read for frequency encoding gradient (also known as readout gradients) events. This diagram can optionally be completed by adding a few axes, like one for analog-to-digital converter (ADC) events, depending on the MRI device. They can be seen as a lyric sheet for playing on the MRI system by telling which element should be activated, with which intensity and waveform envelope, and at what time. (time between two consecutive excitations). It is composed of an excitation pulse coupled with a slice selection and refocusing gradients, a phase encoding gradient, setting the line to be acquired, a readout gradient with its pre-encoding gradient, reading all the columns of the considered lines by performing frequency encoding, and spoiler gradients killing the residual signal.

Gradient echo and spin echo sequences

Figure 1.12 provides the chronogram for the gradient echo (GRE) sequence, which is composed of an RF pulse with a given flip angle θ, a slice selection gradient with its refocusing gradient, a reading gradient with its pre-encoding gradient, a phase encoding gradient, and optional spoiler gradients. This diagram shows only one kernel (i.e. one TR) of the full sequence chronogram. To obtain an MR image, this pattern is repeated as many times as necessary to sample the full volume. This is done by adjusting the slice selection and phase encoding gradients so that they will be encoding for the targeted slice and line. In the same way, Figure 1.13 shows a SE sequence with the same elements and a few additions necessary to obtain the spin echo signal: a refocusing RF pulse, with its slice selection and crusher gradients, is inserted between the excitation and readout events.

These two examples show many simple but necessary parts of a sequence. Because they use sliceselective RF pulses (like the SINC ones), every RF pulse comes with an associated slice selection gradient with the same timing and duration. For excitation pulses, this slice selection gradient is followed by a slice selection refocusing gradient, that eliminates the encoding after excitation. In both reading parts, the (time between two consecutive excitations). It is composed of an excitation pulse coupled with a slice selection and refocusing gradients, a refocusing pulse with its slice selection and crusher gradients, a phase encoding gradient, setting the line to be acquired, a readout gradient with its pre-encoding gradient, reading all the columns of the considered lines by performing frequency encoding, and spoiler gradients killing the residual signal.

readout gradient is preceded by a readout pre-encoding gradient which is half the reading gradient and is made to center the readout. The spoiling gradients, played on every axis at the end of both sequences, are optional. However, they help to attenuate the residual spatial encoding at the end of the sequence kernel shown in these chronograms so that another slice can be cleanly selected and encoded. In the same way, in the refocusing part of the SE sequence, crusher gradients are used to remove the residual FID signal that could result in artifacts in the image.

The spoiler and crusher gradients can be designed in the same manner. They aim to rotate the phase of the spins from a certain number of laps to ensure it is completely dephased. In the case of crusher gradients played before and after the 180°refocusing pulse, only the second one is necessary to eliminate the unwanted FID signal generated by the refocusing pulse. However, using it alone would also attenuate the spin echo signal, which may be counter-productive. This is why crusher gradients come in pairs: the first one is identical to the second one and pre-encodes the signal necessary for the generation of the spin echo so that the second gradient rephases it while attenuating the unwanted FID signal. The crusher and spoiler gradients can be generated using equation (1.15):

A = ∆Φ γ∆r , (1.15)
where A is the area under the crusher or spoiler gradient, ∆Φ is the phase dephasing expressed in mT.s.m -1 , γ is the gyromagnetic ratio, and r is the spatial resolution for the considered axis. It should be noted that more complex crusher gradients, providing rephasing instead of dephasing, or presenting an asymmetric scheme (the first gradient is different from the second one) can also be obtained following the same principle and depending on the sequence. It is possible to use methods such as fast gradient echo (FGRE) and fast spin echo (FSE) to be more efficient regarding the acquisition time. The FGRE sequence uses lower flip angles and acquires signals at very short TE. Its flip angle can be optimized depending on the time constants of the imaged tissue using the Ernst formula [START_REF] Ernst | Application of fourier transform spectroscopy to magnetic resonance[END_REF] described in equation ( 1 .16).

Fast gradient echo and spin echo sequences

θ E = arccos (e -TR T 1 ), (1.16)
with θ E the Ernst angle, TR the repetition time of the sequence, and T 1 the longitudinal relaxation time of the given tissue. To obtain a clean signal in FGRE, it is also necessary to use spoilers at the end of each kernel, and it can be even better to use them to balance the signal by eliminating the residual phase effect of the previous gradients.

Also known as Rapid Acquisition with Relaxation Enhancement (RARE) [START_REF] Henning | friedbury h. RARE imaging: A fast imaging-method for clinical[END_REF], the FSE sequence consists in repeating the refocusing pulse to acquire several lines of the k-space with one excitation (eg in one TR), as shown in Figure 1.14. This allows for the fast acquisition of many lines with one phase encoding per refocusing pulse, characterized in terms of echo train length (ETL), corresponding to the number of 180°RF pulses.

2D and 3D sequences

The previously introduced Figure 1.5 highlights the differences between 2D and 3D excitation modes: for a 2D acquisition, each RF pulse excites a different slice, and the phase and readout gradients encode the signal to read the lines and columns. For a 3D acquisition, the whole volume is excited as a single thick slice, and the encoding is done on the three axes, with the slice selection axis discriminating the different partitions in the same way as the phase encoding axis. This can also be shown in terms of gradients in the excitation part of the chronogram: the 2D excitation shown in Figure 1.15-a comes with a slice selection gradient different for each selected slice, and the 3D excitation described in Figure 1.15-b provides a 3D volume selection gradient which is identical for each kernel of the sequence.

From k-space to image

MRI relies on a twofold process that consists first in acquiring the signal in the Fourier space and second in reconstructing that data into the image space. The acquisition Fourier space is conventionally called a k-space, with k corresponding to a spatial frequency. Depending on the 2D and 3D acquisition scheme used to collect data, reconstructing data in the image domain typically consists in applying a 2D or 3D Inverse Fourier Transform (IFT) as described in equations (1.17) and (1.18):

f (x, y) = 1 2π 2 π -π π -π F (ω, ν)e iωx+iνy dωdν,
(1.17)

f (x, y, z) = 1 2π 3 π -π π -π π -π F (ω, ν, ξ)e iωx+iνy+iξz dωdνdξ, (1.18)
with f (x, y) the 2D inverse Fourier transform, F (ω, ν) the 2D Fourier transform, f (x, y, z) the 3D inverse Fourier transform, and F (ω, ν, ξ) the 3D Fourier transform.

It is usual to separate the obtained complex image into its corresponding phase and magnitude images, as shown in Figure 1.16. The magnitude image is usually exploited by radiologists, physicians, and researchers to observe brain anatomy and possible anomalies, while the phase image is only essentially used to correct artifacts.

Although the IFT is at the heart of the reconstruction procedure, other steps can be implemented depending on the sequence used to acquire the data. While the most simple acquisition methods, like single-line reading spin-echo or gradient-echo, only need a single IFT step, accelerated sequences may need additional correction steps to remove the artifacts generated by the acquisition method.

Artifacts

Fast acquisition sequences like the ones that will be described in chapter 2 can accumulate phase errors in the k-space trajectory that may lead to artifacts in the reconstructed image. Indeed, MR images can also suffer from various artifacts due to the imaging method, the hardware, or even the subject. As these can impact the quality of the image and its medical interpretation, they have to be corrected to recover unbiased images.

Artifacts linked to the acquisition method

The most common imaging artifact corresponds to a violation of the Shannon criterion along the phase axis when defining a Field Of View (FOV) shorter than the imaged object, yielding an aliasing of the image [Poupon, 1999]; others adapted from Allen D. Elster, MRIquestions.com.

as shown in Figure 1.17-a. To avoid this artifact, it is necessary to include the whole imaged object in the phase direction of the FOV or to suppress the signal coming from outside of FOV using saturation bands.

Another typical artifact is Gibbs' ringing, resulting from the digital sampling of the analog signal. It is related to the small number of harmonics used in the inverse Fourier transform which induce some ringing artifacts at the interfaces as shown in Figure 1.17-b. This artifact cannot be completely removed but can be attenuated with image processing methods after acquisition [START_REF] Veraart | Gibbs ringing in diffusion mri[END_REF]] [Lee et al., 2021] [Muckley et al., 2021].

Specific sequences such as echo-planar imaging can also produce artifacts like the Nyquist N 2 ghosting (detailed in chapter 2). As shown in Figure 1.17-c, it takes the form of a pale reminiscence of the image with part of the signal shifted of half the FOV. It is related to a misalignment of the centers of the even and odd readout gradients and can be corrected mathematically by estimating this misalignment using a few navigator echoes.

Another artifact of interest comes from unwanted radio-frequencies present in the magnet room resulting in a striped pattern in the reconstructed image, as depicted in Figure 1.17-d, due to spike noise generated by the acquisition, and can be attenuated by thresholding the k-space signal [Spraggins, 1987][Foo et al., 1994], or using Fourier transform-based methods [START_REF] Kao | Correction of mr k-space data corrupted by spike noise[END_REF].

Artifacts linked to the hardware

Although MRI hardware is developed with great precision to avoid hardware-related artifacts, not all of them can be suppressed. For instance, a fine calibration of the receiver gain is necessary to avoid generating a data clipping artifact, as shown in Figure 1.17-e. This artifact is due to the RF signal being too high compared to the limit voltage of the amplifier.

It is also sometimes possible to observe a stripped line on the image, as shown in Figure 1.17-f. This zipper artifact can be due to the RF transceiver producing an unwanted signal that is detected by the receiver or by an imperfection in the shielding of the room like a door not properly closed.

If it is easy to prevent the two previous artifacts from appearing with thorough attention to the hardware calibration and usage, some cannot be avoided, like those related to the use of surface coils whose reception profiles are good close to the antenna loops and degraded when moving away from the loops, as shown in Figure 1.17-g. It typically results in signal heterogeneity over the field of view. This artifact can, however, be reduced using post-processing methods [START_REF] Tustison | N4itk: improved n3 bias correction[END_REF].

Also linked to the hardware are the magnetic artifacts caused by Eddy currents. These arise from the rapid commutation of the gradient coils and result in generic distortions of the image (shearing, compression, shifting), as shown in Figure 1.17-h,i,j. Eddy currents' effects can be corrected using affine registration algorithms with an anatomical reference image.

Artifacts linked to the subject

The subject's motion is one of the main sources of artifacts encountered in MRI. The corresponding artifacts usually take the form of ghost images reproducing patterns in the image, as shown in Figure 1.17-k, because of the modulation of the signal induced by motion that is generating an extra signal in the Fourier domain. Motion can also cause shifts in the position of the subject between different slices or acquisitions, which can compromise its post-processing and result in the misinterpretation of the data, for instance in functional and diffusion-weighted MRI. To limit motion as much as possible, the sequences are usually kept short and the participants are often reminded to stay still during the acquisition.

Another commonly encountered subject-linked artifact in MRI is the susceptibility artifact, as shown in Figure 1.17-l. The presence of ferromagnetic or paramagnetic substances such as calcium salts, air, or small implants (compatible with MRI) causes a magnetic field distortion, which induces a deformation of the image. The acquisition of calibration maps like field maps [START_REF] Jezzard | Correction for geometric distortion in echo planar images from b0 field variations[END_REF] or top-up maps [START_REF] Andersson | How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging[END_REF]] makes it possible to correct susceptibility effects using non-linear registration techniques informed by the aforementioned calibration maps.

Conclusion

This chapter detailed the physical principles contributing to magnetic resonance imaging before clarifying the different methods used to generate images. It described the processes used for spatial encoding, including RF pulses and magnetic field gradients, and detailed the two-dimensional and three-dimensional ways of exciting a sample and acquiring its signal. To complete these acquisition methods, the notion of k-space and Fourier transform needed to convert the raw images to the image space was introduced. Furthermore, a collection of artifacts that can be observed in MRI datasets were showcased in the last section.

The classic way to acquire MR images is to use a line-by-line Cartesian trajectory to read the k-space, as shown in Figure 2.1-a. This is done using the single-line reading gradients previously introduced in Figures 1.12, 1.13, and 1.15 and usually requires a long acquisition time. As such, it hampers the patient's comfort, and it is quite often not acceptable in clinical practice when a diagnosis has to be established in a few minutes. Many different methods have been proposed to accelerate image acquisition, including accelerated trajectories, partial Fourier acquisition, and parallel imaging methods, which can often be combined to achieve greater acceleration rates with preserved image quality.

Ultra fast imaging

Echo-Planar Imaging (EPI)

The Echo-Planar Imaging (EPI) technique, proposed by Peter Mansfield in 1977 [Mansfield, 1977], acquires one slice per excitation instead of one line for the single-line readout, hereby dividing the acquisition time by the number of phase-encoding lines. The EPI trajectory, described in Figure 2.1-b, reads a line in one direction, skips over to the next line, reads it in the opposite direction, and so on. This readout method is embodied by an alternate gradient train along the readout axis, coupled with a blipped gradient train along the phase axis, as described in Figure 2.2.

An EPI readout combined with a gradient or spin echo excitation results in an ultra-fast sequence. However, the collected MRI signal acquired with an EPI trajectory needs to be post-processed to revert k-space lines acquired with a negative frequency-encoding gradient pulse and corrected for several artifacts accumulated during the echo-train readout. Indeed, due to the imperfections of the RF pulse and the hardware, phase errors occur, producing artifacts in the final image. An example of a directly reconstructed EPI image is shown in Figure 2.3-a. of a 90°excitation pulse, with its slice-selection and refocusing gradients, a pre-encoding part with its navigator gradients allowing for the acquisition of reference lines for phase correction, a 180°refocusing pulse with its slice-selection and crusher gradients, an EPI echo-train readout with its phase and readout pre-encoding gradients, followed by alternating readout gradients and phase blips covering the echo-planar trajectory for one slice, and spoiler gradients, attenuating the residual signal.

It describes the main artifacts encountered in EPI:

• a duplication of the image due to the odd and even lines being read in opposite directions,

• a Nyquist N 2 ghost generated by a misalignment of the center of the odd and even spectra acquired along the read axis resulting from imperfection in the gradient and reception hardware forming eddy currents induced in the field of view,

• a distortion linked to the low acquired bandwidth in the phase direction.

If the duplication is corrected by reversing the odd lines, as shown in Figure 2.3-b, the two other artifacts need more complex methods to be attenuated.

To remove the Nyquist N 2 ghost, the EPI signal is modeled using equation ( 2.1):

S(p, q) = l m I(l, m)e -2iπlp nx e -2iπmq ny e -iφ , (2.1)
with S the k-space signal, p and q the k-space indices along the readout and phase encoding axes, I the ideal image intensity, l and m the indices corresponding to p and q in the image domain, φ the phase error, n x the number of frequency encoding steps, and n y the number of phase encoding steps. The reconstructed image obtained from S is then given by equation (2.2):

I R (l, m) = I(l, m)cos(φ) + iI(l, m - N y 2 )sin(φ), (2.2)
with I R the real image obtained after applying an inverse Fourier transform to S, and N y the size of the matrix along y in the image domain. The Nyquist N 2 ghost occurs due to a shift of s encoding steps along the reading axis and g encoding steps along the phase encoding axis in the k-space domain, s and g being positive for odd lines and negative for even lines. These shifts correspond to phase errors in the image domain, which can be formalized in equation (2.2) by replacing φ with the corresponding errors.

These linear phase errors can be approximated using linear regression, as proposed by Ahn and Cho [START_REF] Ahn | A new phase correction method in nmr imaging based on autocorrelation and histogram analysis[END_REF], from a set of reference lines acquired in the frame of a calibration step using the same EPI readout encoding but without phase encoding. These calibration data are then transformed to the image domain, allowing for the measurement of the phase error, which is then removed from the original and2.3-c all show the same distortion artifact, which is due to the nature of the EPI acquisition train. It uses a very low bandwidth in the phase direction to acquire many lines in a reduced time, creating stronger distortions in regions with substantial magnetic susceptibility variations, like air/tissue interfaces, and magnetic field variations due to imperfections in the hardware or concomitant fields. Since the phantom used for this figure has many air-water interfaces, with a large bubble of water at its bottom, the distortion is particularly severe. It is possible to reduce it by decreasing the echo spacing or the echo train length, which is usually done using other acceleration methods like partial Fourier or GRAPPA, as shown in Figure 2.4, which will be discussed later in this chapter, or by increasing the readout bandwidth, at the price of a lower signal to noise ratio.

The EPI reading train can be combined with either 2D or 3D excitation schemes. Therefore, a 3D-EPI acquisition can be designed by encoding for the partition before reading the 2D EPI echo train. However, to get better acceleration, it is possible to generalize its principle in 3D with the Echo-Volumar Imaging (EVI) method [START_REF] Mansfield | Echo-volumar imaging (evi) of the brain at 3.0 t: first normal volunteer and functional imaging results[END_REF].

Echo-Volumar Imaging (EVI)

The EVI trajectory is single-shot for the whole volume; it reproduces the pattern of the EPI trajectory, then changes partition, goes down to the next start of the EPI trajectory, and so on, filling all the lines of the 3D k-space in one repetition time, as depicted in Figure 2.5. Variations of this 3D trajectory are possible, for instance, by ignoring the fly-back gradient pulse allowing for going back to the same initial k-space position as for the former partition and starting the readout directly after changing the partition.

To produce an EVI pulse sequence, it is necessary to use a few more encoding gradients compared to the EPI sequence. 3D excitation is implemented, along with partition encoding gradients, as first presented in Figure 1.15-b (chapter 1-section 1.1.3). The EVI echo-train readout, which is presented in Figure 2.6, contains EPI echo-train readouts combined with:

• a partition pre-encoding gradient, setting the starting point of the trajectory along with the phase and readout pre-encoding gradients,

• partition encoding blips, changing partitions at the end of each EPI trajectory,

• phase encoding fly-back gradients resetting the starting point of each partition after the partition encoding blip.

EVI images present similar but worse artifacts to the ones encountered in EPI, with the phase error artifact being repeated along the partition encoding axis. These artifacts can also be corrected using linear regression to approximate the phase errors based on a preparation scan with no phase or partition encoding.

Partial Fourier (PF)

K-space is a complex space presenting a Hermitian symmetry, implying that information is redundant. Each point has a twin point containing the same information located diagonally from the origin point. Precisely, these two points are complex conjugates, meaning that they have the same values but an opposite phase, as shown in equation (2.3). with A a point in the k-space and A ′ its complex conjugate. Partial Fourier (PF) uses this property to acquire half of the k-space and mathematically recover the missing points. However, since there are noise and imperfections in the MR signal, it is better to acquire a little more, to ensure the coherence of the center of the k-space, which contains the core of the information (see section 2.3 for details). In practice, this method can be applied very smoothly by acquiring 4 8 to 7 8 of the k-space lines with any cartesian reading method, as presented in Figure 2.7.

A = a + ib A ′ = a -ib , (2.3)
From the point of view of the sequence, the only change necessary to implement PF is to reduce the number of acquired lines. For instance, with an original k-space slice of 128 lines, using a PF factor of 6/8, the number of actually acquired lines is 6 8 × 128 = 96. With a single-line reading, this means that only 96 kernels are played, with the corresponding phase encodings to match the trajectory in Figure 2.7-b, and with an EPI sequence, this means that the echo train is reduced to acquire 96 lines instead of 128. Images acquired using the PF method cannot be directly reconstructed. Their complex partial signal needs to be completed using a processing method adapted to the usage of the final data. The most straightforward way to do so is to fill in the missing k-space part with zeroes (zero-filling). This has the advantage of preserving phase for the lower frequencies but generates a Gibbs ringing artifact on the final image. It is also possible to replace these zeroes with the complex conjugates of the acquired data, which is known as the Conjugate Synthesis method [START_REF] Feinberg | Halving mr imaging time by conjugation: demonstration at 3.5 kg[END_REF], but this does not preserve phase consistency.

To improve the PF reconstruction, more complex methods like Homodyne processing [START_REF] Noll | Homodyne detection in magnetic resonance imaging[END_REF] have been proposed. This technique is based on the unwrapping of the Fourier transform for low and high frequencies, the latter being completed with their complex conjugates as described in equations (2.4).

I(x) = kmax -kmax S(k)e i2πkx dk ⇔ I(x) = -k 0 -kmax S * (-k)e i2πkx dk + kmax -k 0 S(k)e i2πkx dk ⇔ I(x) = kmax k 0 S(k ′ )e i2πk ′ x dk ′ * + kmax -k 0 S(k)e i2πkx dk ⇔ I(x) = k 0 -k 0 S(k)e i2πkx dk + 2 Re kmax k 0 S(k)e i2πkx dk ⇔ I(x) = Re k 0 -k 0 S(k)e i2πkx dk + 2 kmax k 0 S(k)e i2πkx dk , (2.4)
with S(k) a 1D k-space signal, S * (k) its complex conjugate, I(x) the corresponding signal in the image space of S(k), -k max and k max the boundaries of the k-space signal, and -k 0 and k 0 those of the completely sampled signal.

By introducing the Homodyne high-pass filter H(k) described in equation ( 2.5):,

H(k) =    0 k < -k 0 1 -k 0 ≤ k < k 0 2 k ≥ k 0 , (2.5)
the signal in the image space I(x) can be obtained thanks to equation (2.6):

   I(x) = Re[I H (x)] I H (x) = kmax -kmax H(k)S(k)e i2πkx dk .
(2.6)

This Homodyne processing method allows for a more accurate reconstruction of the real data.

The imaginary component can also be corrected using a phase correction based on the completely acquired low frequencies as clarified in equation (2.7), but the result is not accurate enough due to rapidly varying phases for precise phase map use.

I(x) ≈ Re[I H (x)e -iϕ L (x) ],
(2.7) with ϕ L (x) being the phase approximated using only the low-frequency phases from the fully acquired k-space data (between -k 0 and k 0 ).

To obtain an even better reconstruction, iterative algorithms like Cuppen [Cuppen, 1989] and Projection Onto Convex Sets (POCS) [START_REF] Haacke | A fast, iterative, partial-fourier technique capable of local phase recovery[END_REF] methods have been proposed. Their principle is to perform the correction once, reconstruct the completed image, transform it back to the frequency domain, and loop between reconstruction and correction in an iterative process. The POCS algorithm goes even further by correcting the phase more accurately using the observation that the corrected image should be among all the images containing measured data and those using the same phase as the estimated one. This way, more accurate images can be obtained using the PF method, as the example shown in Figure 2.8-b, which is not so much altered compared to its full k-space equivalent shown in Figure 2.8-a. Acquisition trajectories can be split into two categories: single-shot and multi-shot trajectories. A single-shot trajectory covers an entire k-space within a single shot (eg repetition time), whereas a multi-shot trajectory needs several shots to cover the full k-space. The EPI trajectory presented in Figure 2.1-b is a good example of a single-shot trajectory. On the other hand, a multi-shot single-line reading trajectory is presented in Figure 2.1-a. There are many variations of possible trajectories, and it is possible to create multi-shot trajectories from single-shot trajectories by repeating them over the k-space like the multi-shot EPI scheme presented in Figure 2.9. The interest of these trajectories is to reduce the echo-train length, thus minimizing the distortions obtained by the original single-shot method while maintaining a satisfying level of acceleration, though it cannot be as quick as with the single-shot version.

Multi-shot acquisitions

Spiral

As presented in Figure 2.10, the k-space data can be separated into two parts: the center containing low spatial frequencies corresponding to the main contrast of the image (Figure 2.10-b), and the edges containing high spatial frequencies corresponding to the details of the image (Figure 2.10-c). Therefore, most of the meaningful signal is contained in a disc as presented in Figure 2.10-d.

Unlike the Cartesian trajectories, the spiral trajectory proposed by Schmitt and his colleagues in 1998 [START_REF] Schmitt | Spiral echo-planar imaging[END_REF]] and shown in Figure 2.11-a exploits this property by acquiring only a disc centered over the k-space for each slice. It can also be declined in multi-shot versions like the example shown in Figure 2.11-b. This trajectory can be combined with excitation schemes such as gradient echo or spin echo and is generated using the frequency and phase encoding gradients. Both of them play together the same gradient waveforms, presented in Figure 2.12, which is obtained by combining two criteria: a linear velocity and a sampling rate following the Nyquist requirement. The linear velocity of the spiral requires the gradients to verify equation (2.8) at all times, which is not possible considering the hardware constraints. Therefore, the trajectory is played using a maximum slew rate until it reaches its maximum amplitude, bounded by the Nyquist requirements as explained in equation (2.9). G 0 = 2∆ν γF OV ,

G = G Read (t) 2 + G P hase (t) 2 ,
(2.9)

with ∆ν the receiver bandwidth, F OV the field of view, and γ the gyromagnetic ratio in its frequential expression. Spiral acquisition is very time-efficient but generates aliasing and blurring artifacts that must be accounted for. Aliasing is not easy to avoid and is generally eluded by defining the acquisition FOV meticulously. Blurring can be reduced by applying a phase correction calculated using two pre-scan images acquired at different echo times. Therefore, field maps describing frequency offsets as a function of their spatial location are computed and compared to the error in the spiral data that is formalized in equation (2.10). This frequency offset leads to a phase accumulation of ∆ϕ = 2π∆f t, which can be developed into equation (2.11).

∆f = f 0 + f x x + f y y, (2.10) ∆ϕ = 2πf 0 t + 2π∆k x (t)x + 2π∆k y (t)y, (2.11)
with ∆k x (t) = f x t and ∆k y (t) = f y t the time-dependent k-space shifts induced by their respective frequency offsets along the x and y axes. The k-space data acquired with the spiral trajectory is then expressed in equation (2.12), showing a modulation of e 2iπf 0 t that can be removed before performing the reconstruction: S(t) = e 2iπf 0 t M (x, y)e 2iπ((kx+∆kx)x+(ky+∆ky)y) dxdy.

(2.12)

The obtention of the final image from the spiral data is not straightforward, as the k-space data is not collected in a Cartesian grid. In such cases, Gridding [Matej andBajla, 1990] [Rosenfeld, 1998] [ Van de Walle et al., 2000] [Sarty et al., 2001] is the most popular reconstruction method: it projects the non-cartesian data onto a Cartesian grid so that classic inverse Fourier transform reconstruction can be performed on it. PROPELLER [Pipe, 1999] is an acquisition strategy based on the use of blade trajectories rotating in the k-space as depicted in Figure 2.13-a. The phase and frequency encoding are set to the classic single-line readout scheme, taking into account the rotation for each blade. In the same way, the spiral method does, PROPELLER samples a disk in k-space, which is more time efficient than the methods sampling the whole k-space. Furthermore, as it samples the center many times, it is more resilient to motion and depicts a higher SNR.

The PROPELLER trajectory is usually associated with RARE [START_REF] Henning | friedbury h. RARE imaging: A fast imaging-method for clinical[END_REF] or Gradient And Spin Echo (GRASE) [START_REF] Feinberg | Grase (gradient-and spin-echo) mr imaging: a new fast clinical imaging technique[END_REF] pulse sequences, providing k-space images that need to be corrected before reconstruction. Using the center as a reference with multiple points closely related to each other, it is possible to correct the phase errors and to determine weightings for each blade depending on its cross-correlation degree with the other blades of the image. PROPELLER is used in acquisitions that are subject to considerable motion artifacts in which it can provide good quality images with a high SNR, but at the cost of longer acquisition times compared to other methods like EPI.

To combine the motion-robustness of PROPELLER and the time-efficiency of EPI, it is possible to associate them in a PROPELLER EPI trajectory [START_REF] Wang | Propeller epi: an mri technique suitable for diffusion tensor imaging at high field strength with reduced geometric distortions[END_REF], as shown in Figure 2.13-b, which has the advantage of accelerating the acquisition further but necessitates more post-processing to correct the image before reconstruction since the artifacts from both EPI and PROPELLER methods cumulate. MRI systems now broadly include multiple coil sets in an array acquiring the NMR signal simultaneously, each coil acquiring its own sensitivity profile, thus allowing to accelerate the acquisition. This is usually done with all coils acquiring every other line, the ratio of the acquired lines with respect to the total number of lines being defined as the acceleration factor R. A simple example with R = 2 is shown in Figure 2.14-a,b. The acquisition of every other line generates a phantom image that can be corrected using an algorithm based on the sensitivity maps of the different coils. These low-frequency maps can be computed using reference lines at the center of the k-space, which can be embedded in the acquisition as depicted in Figure 2.14-c, or by performing a full low-resolution acquisition before the accelerated one. A first method to process parallel imaging acquisitions in k-space was proposed by D. Sodickson in 1995: SiMultaneous Acquisitions of Spatial Harmonics (SMASH) [START_REF] Sodickson | Simultaneous acquisition of spatial harmonics (smash): fast imaging with radiofrequency coil arrays[END_REF]. It has been improved to become selfcalibrating (AUTO-SMASH) [START_REF] Jakob | Autosmash: a self-calibrating technique for smash imaging[END_REF]] and finalized in the GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) [START_REF] Griswold | Generalized autocalibrating partially parallel acquisitions (grappa)[END_REF] method. A technique to process parallel imaging acquisition directly in the image space is the SENSitivity Encoding (SENSE) method, proposed by K.P. [START_REF] Pruessmann | [END_REF]al. in 1999 [Pruessmann et al., 1999].

SENSitivity Encoding (SENSE)

SENSE is a method for parallel imaging acquisition based on the post-processing of MR data in the image domain, compatible with any Cartesian reading. A B 1 map is computed using a low-resolution reference scan to process the coil sensitivity maps, highlighting the reception profile of each receiver loop of the coil. Once the complex coil sensitivity maps have been computed, the reduced FOV images for each coil can be reconstructed and processed. In these images, one point corresponds to two in the final image and can be separated by weighting them using the coil sensitivity maps.

The folded image corresponds to a linear composition of the unfolded target image, with weights involving the complex sensitivity maps of the antenna reception loops combined with pure Fourier harmonics. The SENSE reconstruction technique consists in finding the solution to this multilinear equation.

GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA)

GRAPPA [START_REF] Griswold | Generalized autocalibrating partially parallel acquisitions (grappa)[END_REF] is directly correcting the k-space. The partial Fourier data (one line over R is acquired) is completed using a reconstruction frame inferred from interpolating the full acquisition of the central lines, as presented in Figure 2. 14-c.

GRAPPA uses the extra acquired lines in the center of the k-space, also known as Auto Calibration Signal (ACS) lines, to produce weights and infer the missing lines of the k-space. This is done by exploiting the different signals from each array coil without computing coil sensitivity maps. [START_REF] Griswold | Generalized autocalibrating partially parallel acquisitions (grappa)[END_REF] The partial spatial frequency data from each coil is completed using a block-wise method which calculates the weights using equation (2.13).

S j (k y -m∆k y ) = L l=1 N b -1 lb=0 n(j, b, l, m)S l (k y -bR∆k y ),
(2.13) with S j (k y -m∆k y ) the signal from coil j for the line (k y -m∆k y ), L the number of coils, N b the number of blocks, n(j, b, l, m) the weight for coil j (using block b, coil l, and line shift m), and R the parallel imaging acceleration factor.

This calculation relies on the definition of a block that is shown in Figure 2.15: one acquired line and its neighboring missing line. In GRAPPA, multiple blocks are used to compute multiple versions of the one missing line in each coil. For instance, using 3 blocks results in 3 versions of the same missing line for the same coil-associated image. These multiple lines are combined using a weighted average to form a single line in the final coil image. Once all missing lines for all coils are completed, they are transformed using IFT 51 to form an image I l for each coil, and the final image I is formed using a sum of squares as presented in equation ( 2.14):

I(y) = L l=1 |I l (y)| 2 ,
(2.14)

with I(y) the image signal along the y-axis.

A visual example of a GRAPPA reconstruction is shown in Figure 2.16. It shows a reference image with no acceleration factor (Figure 2.16-a), an image acquired with parallel imaging but with no correction for the missing lines (Figure 2.16-b), and the same image using central ACS lines and corrected using GRAPPA (Figure 2.16-c). With only a small loss in SNR, it is difficult to differentiate Figure 2.16-a and Figure 2.16-c, the latter being acquired in almost half the time necessary for the other.

Compressed sensing

As it is possible to compress any image into a lighter format like JPEG (Joint Photographic Experts Group), MR images can be compressed as described in Figure 2.17-a. The idea of compressed sensing [START_REF] Candès | Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[END_REF]][Donoho, 2006][Lustig et al., 2007] is to acquire only the meaningful k-space data that would be obtained after compression, generating good-quality images with a shorter acquisition time. As presented in Figure 2.17-b, this is done using an undersampling of the k-space to generate a reading trajectory. A compressed sensing acquisition is optimal if it verifies these two conditions:

• the sampling is done using a variable density distribution,

• the k-space should be covered in a locally uniform way. This method creates a randomly spread-out noise that can be removed by performing mathematical filtering using a wavelet transform. The ideal number of sampling points for this transform can be obtained through an optimization problem materializing the data as a vector x of length n and minimizing its L 1 norm ||x|| 1 as described in equation (2.15):

(a) Image compression (b) Compressed sensing

||x|| 1 = n i=1 |x i |.
(2.15)

The spatial encoding for compressed sensing acquisitions can vary between methods and sets the encoding gradients to acquire each undersampled point of the k-space. This acquisition method often needs many iterations as it is not easy to optimize the sampling method and the noise-removing method.

Multiband excitation

The MultiBand (MB) or Simultaneous Multi-Slice (SMS) [START_REF] Setsompop | Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor penalty[END_REF]] method described in Figure 2.18 uses excitation pulses that are designed to excite multiple slices at the same time. By default, it yields a reconstructed image corresponding to the superposition of several 2D images located in different slice positions. Since each slice is measured by the antenna receiver loops with a different complex sensitivity, the resulting image can be expressed as the linear combination of the various slices weighted by their different sensitivity maps. Again, a linear combination can be composed, which inversion leads to adequate slice reconstructions. These can be obtained by combining RF pulses with different phase offsets φ and optimized to respect the limits of energy deposition (SAR) using methods like Variable-Rate Selective Excitation (VERSE) [START_REF] Hargreaves | Variable-rate selective excitation for rapid mri sequences[END_REF], or Power-Independent of Number of Slices (PINS) [START_REF] Norris | Power independent of number of slices (pins) radiofrequency pulses for low-power simultaneous multislice excitation[END_REF]. With this complex excitation, a classic 2D encoding is used for phase and frequency, along with an intricate pattern for slice selection. This pattern is generated using a combination of RF phase encoding, gradient phase encoding, and coil encoding:

• the RF phase encoding method applies a phase gradient with cycling patterns for each frequency band on the RF pulse,

• the gradient phase encoding involves applying phase encoding like in a 3D excitation, selecting each slice with a gradient similar to the one used for partitions,

• the coil encoding applies the same principles as parallel imaging to separate the data from each slice, allowing for their simultaneous acquisition.

If coil encoding is theoretically more efficient than the other methods, it is limited by the number of available coils in the slice direction, which is rarely enough to obtain a satisfying result. However, using it jointly with one of the two other methods solves the problem and enables a very efficient accelerated sequence capable of simultaneously acquiring multiple slices. [START_REF] Lazarus | Sparkling: variable-density k-space filling curves for accelerated t2*-weighted mri[END_REF] In the logic of compressed sensing, it is possible to optimize image acquisition using mathematical methods, including machine learning and deep learning. A good example of this is the Spreading Projection Algorithm for Rapid K-space SampLING (SPARKLING) [START_REF] Lazarus | Sparkling: variable-density k-space filling curves for accelerated t2*-weighted mri[END_REF], which enables the fast ac-quisition of images with a very high resolution. It optimizes a trajectory composed of points in the k-space by respecting the two conditions of compressed sensing, eg (1) variable density distribution sampling and ( 2) locally uniform k-space, along with a third one: for each shot, at a given sampling rate, the distance between two consecutive samples is smaller than ∆k = 1 F OV . The SPARKLING algorithm starts from an input trajectory, such as a multi-shot spiral, and optimizes it regarding the above-mentioned criteria, along with the hardware and acquisition constraints, such as gradient slew rate or the correspondence between echo time and k-space center. This optimization is done using a projected gradient descent and accelerated by a step-size choice strategy [START_REF] Barzilai | Two-point step size gradient methods[END_REF] and a repartition of the generation for each segment with a multi-scale algorithm. Depending on the input parameters, the SPARKLING trajectories deviate from the input ones by covering more efficiently the k-space with a variable density and local circumvolutions, as described in Figure 2.19.

The spatial encoding for these trajectories, mainly multishot, is done by optimizing the phase and frequency encoding gradients regarding their slew rate. The SPARKLING method can be used either for 2D or 3D [El Gueddari, 2019] trajectories allowing for great flexibility. If this technique allows for greater acceleration (up to 7 times faster) than parallel or spiral imaging, it comes at a cost because the very quickly acquired data should be post-processed for a long time before reconstruction to account for the non-linearity in the acquisition and the compression of the data.

Conclusion

This chapter presented, in chronological order of development, the various techniques available to accelerate an MRI acquisition. Starting with the echo-planar reading trajectories and the partial Fourier acquisition mode, it detailed multi-shot, multi-band, parallel imaging, and compressed sensing. All the methods have been explained from a theoretical point of view, giving elements to encompass their challenges and provide an intelligible reconstruction of their images. An MRI system comprises many hardware elements, including the magnet, the gradient coils, and the RF emission and reception electronics. Different manufacturers, like Siemens Healthineers (Erlangen, Germany), Bruker Biospin (Ettlingen, Germany), Philips Healthcare (Amsterdam, Netherlands), or General Electrics (GE) Healthcare (Milwaukee, USA), compete over hardware challenges, such as ultra-high field magnets, powerful gradients sets, or multiple array coils for RF emission or reception. To accommodate such complex systems, they developed softwares that provide an environment to operate them, thus enabling the programming of pulse sequences, which are used to tune the acquisition parameters in a user interface and acquire images by playing the sequence on the scanner. The acquired raw data are saved and sent to a reconstruction server, which can perform either online or offline reconstruction, and generates an output image readable in the user interface.

Chapter 3 Sequence programming and reconstruction tools

Pulse sequence programming tools

The first step of image acquisition in MRI is to prepare a pulse sequence, which is done by providing a sequence program to be run on a real-time operating system, playing its instructions.

Real-time events scheduler

On any MRI system, a scheduler running a real-time operating system (such as Linux or VxWorks) paces the timings of all the events of a sequence driving the hardware and the software from the measured data to the reconstructed images. For instance, it can send orders to the phase gradient coil to play a trapezoidal gradient for a given duration and amplitude, using the gradient slew rate, which is the smallest time step possible to use the spatial encoding gradients. All the events are put in a queue and chronologically played while verifying that security checks, like SAR calculation or stimulation levels, are not growing over predefined limits.

The programming of the scheduler is usually done through the definition of real-time events embedding the temporal characteristics (such as the start time and duration) and hardware-specific characteristics (such as the gradient magnitude and ramp time or the readout bandwidth) of the pulse to be played through a target hardware part. The collection of all events driving the various hardware parts of an MRI system constitutes an MRI pulse sequence that is typically represented by a set of chronograms summarizing the chronologically ordered events on their corresponding axes: RF, slice encoding, phase encoding, frequency encoding, ADC, and other specific parts depending on the hardware. For instance, on Siemens systems, there is an additional line to the chronogram corresponding to a Numeric Cristal Oscillator (NCO), which manages the phase and frequency shifts needed to acquire off-center images.

Aiming to simplify programming, the system can also automate the management of the multi-coil RF arrays by converting the orders to the right format for them. This way, it is possible to use only the number of coils adapted to the sample and not always every coil of the system. Other tasks, like active shimming or temperature checking, are also performed by this system.

Programming environments

On a little higher level, the sequence program should be organized as a code or a diagram to define which real-time events should be played and which parameters should be accessible to the user at the console. Manufacturers have their own programming environment, like ParaVision for Bruker, MR-Paradise for Philips, WTools for GE, or IDEA (standing for Integrated Development Environment for Applications) for Siemens. All manufacturers provide a development kit dedicated to pulse sequence programming on their MRI systems. It can be composed of C/C++ libraries, like the ones proposed by Philips and Siemens, higher-level programming languages, like the PPD scripts proposed by Bruker, or custom programming languages, like the EPIC language from GE, corresponding to the C-language with a series of programming directives used to specify the real-time scheduling part and the host interface part which are prepared before compilation.

Depending on the development kit, the codes can be more or less complex to read and program, but they all allow for programming any new pulse sequence from scratch, consisting in defining all its parameters (either user-tuned or resulting from computations) and events on all the hardware axes. To check if the code can be run on the actual scanner, the developing environments provide simulation tools showing the chronograms as well as various inherited parameters characterizing the sequence, such as the estimated stimulation level or SAR deposit.

Programming paradigms

MRI pulse sequences are implemented through a complex programming structure in the chosen language for the vendor's development kit. When a C/C++ or similar environment is used, it is possible to take advantage of two different programming paradigms, which are detailed in Figure 3.1: procedural and objectoriented. This technique, born in the 60s with languages like C, Fortran, or Pascal, consists in writing a series of instructions in chronological order while using functions for modularity. This forms a procedure that can be self-contained or re-used by the program. Procedural programming separates a task into data structures, subroutines, and variables. It is performant in the implementation of algorithms and in prototyping. Still, it can reveal itself limited when it comes to implementing different code versions or gaining flexibility in development and usage.

Object-oriented programming

Developed concomitantly in the 60s, object-oriented programming focuses on the program's structure, with the idea to introduce modularity and general reusability of elementary parts of code. Although other patterns exist, this paradigm is usually based on classes, which can be instantiated into objects, meaning that a single piece of code can virtually generate any number of likewise objects sharing the same characteristics. These objects can have attribute variables that can be modified by internal functions called methods. The object-oriented code also relies on organizing these classes and objects in an inheritance tree, allowing efficient code use.

A choice linked to the programming language

Historically, the development of MRI pulse sequences has been done by MRI physicists and thus uses a procedural programming paradigm that is well known to them. However, depending on the programming environment, this choice may not be the most appropriate. Therefore, each MRI manufacturer has considered its constraints and chosen between procedural and object-oriented programming: Siemens' and Philips' environments are using C/C++ and can implement object-oriented structures such as the Sequence Building Blocks (SBBs) for Siemens, while Bruker and GE are rather exploiting the procedural programming paradigm to develop their sequences.

Reconstruction tools

To obtain the best quality images from any sequence, it is important to carefully design and implement the image reconstruction algorithm. This step is performed either online, giving a reconstruction of each acquired slice almost instantaneously on the MRI console, or offline, computing the final image after the whole acquisition is done whether on the MRI console or on a separate computer. The reconstruction server is directly provided by the manufacturer and performs optimized reconstructions for all their proprietary sequences. If it is possible to use such a server to develop a new reconstruction algorithm, it is not as flexible as other tools, and many researchers prefer to use open-source external reconstructors.

Raw data management

A reconstruction algorithm is run on the raw k-space data obtained directly from the system. The format of this data is very important for it to be correctly read and understood by the reconstruction tools. It has to present the raw data signal in an array corresponding to its 2D, 3D, or 4D (3D with a time component) format and provide metadata about the acquisition, like the matrix size and field of view. It can be done in a single file or in separate raw data and header files, the latter containing the metadata.

Since the different manufacturers have their own proprietary hardware, they all propose a format adapted to their specificities, like Measurement Data (MD) and Measurement Data Header (MDH) formats for Siemens systems, private data elements for GE systems, or pdata directories for Bruker systems. These formats are adapted to their reconstruction framework and contain all the acquired data and metadata necessary for reconstruction. However, their use outside of the manufacturer's environment is not straightforward, which led researchers in the frame of the ISMRM conference (International Society for Magnetic Resonance in Medicine) to propose in 2017 a new harmonized ISMRM Raw Data (ISMRMRD) standard format [START_REF] Inati | Ismrm raw data format: A proposed standard for mri raw datasets[END_REF], which can be used to accommodate MR data from Bruker, Philips, Siemens, and GE devices.

As shown in Figure 3.2, the ISMRMRD format comprises two parts: the data and the header. In the data part, k-space data from MR measurements are stored, along with their reconstruction flags. In the header part, general information is found about the data acquisition, such as FOV specifications, TE and TR timings, or the number of coils used for the acquisition. Such data are stored in a Hierarchical Data Format (HDF5) structure, allowing for the formatting and structuration of heavy files using multidimensional arrays known as datasets and groups containing additional data. These files can either be read by the ismrmrdviewer toolkit or exported in Matlab, C/C++, and Python languages. The XML header includes all information necessary for the reconstruction of the k-space data, like encoding space limits, and reconstruction space size. The raw data part contains all the measurements from the MR system, coupled with data headers that specify the type of the acquired data (reference line, reversed line, normal line, ...). Adapted from [START_REF] Inati | Ismrm raw data format: A proposed standard for mri raw datasets[END_REF].

The ISMRMRD format can also be used to store reconstructed images, which can also be visualized using the ismrmrdviewer program. However, for reconstructed data, formats like DICOM (Digital Imaging and COmmunications in Medicine) or NIFTI (NeuroInformatics Technology Initiative) formats can be used to store the original data or inherited data stemming from its post-processing. As they are widely used, the manufacturers provide embedded converters to directly export reconstructed data to such formats. Similarly, they provide interfaces to export raw data and convert it to other formats, like the aforementioned ISMRMRD format.

Key features for image reconstruction

The aim of a reconstruction pipeline is to transform MR k-space raw data into MR images readable by a radiologist. It comprises a pipeline of reconstruction blocks, accounting for each step of a reconstruction algorithm, which depends on the type of acquisition performed and the post-processing needed. This pipeline is generally executed after the acquisition, but some advanced systems propose to perform it during the acquisition process.

The different manufacturers provide their own reconstruction environments, directly included in their software, like the ParaVision image reconstruction in the Bruker environment or the Image Calculation Environment from Siemens. They can be directly embedded in the acquisition machine and thus process the data efficiently and in real-time. In order to do this, their steps are performed as events and integrated into the sequence timing. However, as it is not possible or necessary to implement such a complex feature for every sequence, they are also capable of performing classic reconstruction after the sequence has been run.

Although it is possible to get access to these environments and to develop new reconstruction algorithms from manufacturers' reconstruction toolboxes, researchers do not often choose to use them for their developments. They prefer to resort to more accessible and sharable tools for prototyping and generally use an external reconstruction system, which can be a Matlab, Python, or C++ program running on a dedicated server. The use of such external reconstruction frameworks often leads to reconstructions performed after acquisition.

To tackle the issues of experimental reconstruction programming, the community developed different tools like the Berkeley Advanced Reconstruction Toolbox (BART) [START_REF] Uecker | Berkeley advanced reconstruction toolbox[END_REF] or the Gadgetron framework [START_REF] Hansen | Gadgetron: an open source framework for medical image reconstruction[END_REF]. These environments rely on key features for efficient reconstruction, like a robust data structure with various mathematical operators, a fast Fourier transform (FFT) library accommodating 2D and 3D FFTs and inverse FFTs, and an architecture allowing for the use of multithreading and Graphics Processing Units (GPUs). Their goal is also to propose a stable version of the main reconstruction algorithms, like the EPI or parallel imaging, and to be able to combine them in a modular manner to provide flexibility in the reconstruction pipeline. Crystallizing all these features, a good external reconstruction server would also require to connect with the scanner and provide online acquisition tools, automatically retrieving the raw data and allowing for the visualization of reconstructed images in real-time during the acquisition.

The Siemens environment

The work presented in this thesis has been done at NeuroSpin (CEA) using its MRI acquisition platform, which is composed of six MRI systems: a 7T, an 11.7T , and a 17.2T Bruker MRI devices available for preclinical imaging, and a 3T, a 7T, and an 11.7T (Iseult) Siemens MRI devices available for clinical imaging on human and non-human primates. The goal of this thesis was to develop sequences with clinical applications, therefore requiring the use of the Siemens IDEA development kit.

Along with the MRI systems, Siemens provides a two-fold software, with a first part operating under a Linux system and managing real-time events by communicating directly with the hardware and a second part operating under a Windows system and providing a graphical user interface (GUI) with many tools to program medical exams and manage MR data. The real-time event scheduler is known as the Measurement And Reconstruction System (MARS). It has two main roles:

• to play the sequences on the system; the MARS receives a binary file corresponding to a pulse sequence, which contains system specifications and events, monitoring in real-time the different parts of the hardware, including RF emitter and receptor, gradient coils, analog-to-digital converter, and numeric crystal oscillator;

• to perform reconstructions; it hosts the Image Calculation Environment (ICE), which is responsible for converting raw k-space data to readable MR images through a pipeline of functors.

Completing the MARS environment, the Windows host system operates the SyngoMR software, which GUI provides a series of tools for the visualization and storage of acquired images. These two systems communicate closely with each other and perform security tests during acquisition to ensure the safety of the patient.

MRI pulse sequence development environment (IDEA)

This IDEA toolkit (standing for Integrated Development Environment for Applications) is the C/C++ software toolbox provided by Siemens Healthineers to develop MRI pulse sequences, including advanced libraries of methods allowing to schedule and program the MRI hardware. It also embeds a series of testing tools to ensure that a sequence is properly programmed as well as simulation tools to visualize the sequence chronogram. IDEA compiles the C++ code of a sequence into two binary files, one for the host system, managing the user interface, and one for the MARS, managing the real-time events and reconstruction.

The C++ code used to program a pulse sequence has directives for both Linux and Windows machines that are separated when necessary with #ifdef directives. It relies on four data structures:

• SeqLim, which manages default parameters and hard limits,

• MrProt, which manages the parameters given by the user,

• SeqExpo, which manages the dynamic information on the sequence in the Measurement Data Header (MDH),

• YAPS, standing for Yet Another Parameter Set, which manages specific reconstruction information.

Using these structures, a pulse sequence source code must include four mandatory methods:

• initialize: by filling in the SeqLim dataset, this method specifies what is used in the default protocol and what can be accessed in the GUI;

• prepare: this method is used to perform all preliminary calculations necessary for real-time events, it selects the reconstruction mode and ensures that security tests are passed;

• run: by defining a kernel of events and looping over it, this method is the core of the sequence scheduling the timing of the events which compose the sequence while running coherence tests;

• check: finally, this method is used to perform further testing and prevent gradient overflow and other events that could result in aborting the sequence.

These methods are filled using various other methods and classes from the libraries provided in IDEA, which prepare trapezoidal or arbitrarily-shaped gradients, import waveforms, use parametric curves to design RF pulses, manage off-center acquisitions using a numeric crystal oscillator, etc.

The sequences provided with IDEA have been developed as product sequences and are good examples of what can be achieved using the development kit. However, due to the tight development timings in a competitive environment among manufacturers, these codes are mainly independent of each other, only centered on the sequence they implement. This results in non-optimal use of the object-oriented aspects of C++, producing a very long and redundant code containing thousands of specific lines for most of their sequences.

3.3.2 Reconstruction and post-processing system ICE (standing for Image Calculation Environment) is a reconstruction server located mainly on the MARS system (Linux), but communicating with and sometimes also using the host system, which allows for offline and online reconstructions. It is optimized to retrieve the data in time from the machine, performing reconstruction along the acquisitions. The operations are materialized with functors that can be combined together to form a whole reconstruction pipeline, which can be split into multiple threads for parallel processing. Additional offline post-processing steps can be added on the host if necessary. The implementation of a reconstruction pipeline is done by pointing to a reconstruction algorithm directly from the sequence code, which provides the required information in the sequence header.

It is sometimes possible to adapt the programming of a custom sequence to fit an existing ICE reconstruction program using a constrained reconstruction pipeline, which is not always optimal for the new sequence. It is also possible to implement a new ICE reconstruction workflow by modifying an existing one, but the ICE programming environment is very complex, with lots of patented codes and therefore inaccessible to perform reverse engineering, often yielding long software development times. Furthermore, a reconstruction implemented using ICE is bound to Siemens MRI systems and cannot be distributed to other researchers without Siemens Healthineers' approval.

Limitations imposed by the manufacturer

As the manufacturer providing the MRI hardware, Siemens proposes agreements for researchers to use their IDEA development kit in their work. This agreement allows for accessing the development tools and a set of example sequences, which can be used as a basis to implement new ones. However, the other part of this agreement claims that sequences developed using Siemens' source code as a basis are also Siemens' property and are not freely sharable. To use them, it is necessary to negotiate a contract and get access to their binaries or their source codes for a limited time. As the manufacturer runs a business based on patents, these open-source hard constraints cannot be avoided and significantly hinder the development and sharing of new acquisition methods.

Open-source pulse sequence development kits

Since the sequences programmed in a given manufacturer's environment are difficult to share and export to other manufacturers' machines, the MR Physics community has developed alternatives to tackle these issues. Some of them, like KSFoundation [START_REF] Skare | An abstraction layer for simpler epic pulse programming on ge mr systems in a clinical environment[END_REF], facilitate the programming work for one targeted manufacturer, while others, like PulSeq [START_REF] Layton | Pulseq: a rapid and hardware-independent pulse sequence prototyping framework[END_REF], provide a cross-manufacturer developing environment. In the following section, a selection of open-source pulse sequence development frameworks is presented. Adapted from [Jochimsen and Von Mengershausen, 2004] The Object-oriented Development Interface for NMR (ODIN) [Jochimsen and Von Mengershausen, 2004], which flowchart is presented in Figure 3.3, includes a high-level interface in C++ that allows for crossplatform pulse sequence programming on Bruker and Siemens systems and a graphical interface to visualize and simulate the obtained sequence. Its object-oriented design relies on encapsulating low-level features to monitor the hardware that are aggregated into complex objects used to develop sequences. To support the architecture of the sequence, the framework divides objects into two categories: vector objects which can be repeated with different parameters, and loop objects which repeat the appropriate part of the sequence and update the vector objects when necessary. This results in a clear and simple code that is independent of any manufacturer.

The ODIN framework

In addition to the sequence programming high-level interface, ODIN provides visualization and simulation tools. Its graphical interface allows to unfold the sequence as a tree, display a chronogram, tune the frequently modified parameters, and even simulates the sequence on a virtual phantom. To acquire real data, the ODIN sequences can be interfaced through a hardware driver, which generates the appropriate events by reading the sequence tree in real time. Although ODIN is a very performant sequence development environment, its interface does not allow easy access to vendor-specific features nor the implementation of already developed pulse sequence codes from the manufacturer's development kit. [START_REF] Magland | Pulse sequence programming in a dynamic visual environment: Sequencetree[END_REF]

The SequenceTree environment

SequenceTree [START_REF] Magland | Pulse sequence programming in a dynamic visual environment: Sequencetree[END_REF] focuses on enabling non-programmers to develop pulse sequences with the use of a graphic environment. This framework includes a graphic user interface that allows for intuitively programming MRI pulse sequences using a tree architecture composed of a hierarchy of nodes. The root node is used to program the general parameters of the sequence, the loop nodes manage the iterations, the block nodes define the course of events for one loop, and the segments provide detailed information on low-level events. The higher-level nodes can be customized using manual parameters whereas the segments are updated by inheritance. The graphic interface also provides easy access to the parameters and the code, which can be directly tuned, generating a simulation of the sequence chronogram after every update of parameters. A screenshot of the SequenceTree graphic interface showing all these features is provided in Figure 3.4.

The sequences can be customized with RF pulses defined either with an analytical formula or with a text file including sampled points. SequenceTree also provides automatically calculated trapezoidal spatial encoding gradients, which frees the developer from the gradient design step of pulse sequence programming. If the tool is independent of any vendor, its sequences must however be exported using a vendor-specific interface to be compiled for a specific scanner. For now, this is done only for Siemens systems with a VD13 release. A simulation tool is also available to generate simulated NMR data showing the artifacts generated by the sequence, along with simulated noise and field inhomogeneity profiles. These simulations are useful to optimize the sequence beforehand and save on-system debugging time.

SequenceTree has been tested in various studies which required customization and achieved good results with only a few added lines of code and modified parameters. It can communicate parameters to the console graphic interface, but it is not easy and remains very limited. However, it does not allow for online reconstruction on the scanner and cannot perform other gradient waveforms than trapezoidal ones. It achieved its goal of being a user-friendly yet performant pulse sequence programming and simulating tool for research and education but is still not usable for development outside of the prototyping and testing domain.

The PulSeq cross-platform interface

Aiming to provide a vendor-independent and quick prototyping tool for research and education, Pulseq [START_REF] Layton | Pulseq: a rapid and hardware-independent pulse sequence prototyping framework[END_REF] relies on a high-level interface to build a low-level sequence file, which can be interpreted by vendor-specific modules to run on GE, Siemens, or Bruker devices. The pulse sequence development can be done directly in Matlab or with a PyPulseq Python interface [START_REF] Ravi | Pypulseq: A python package for mri pulse sequence design[END_REF], or with employing the Jülich Extensible MRI Simulator (JEMRIS) [START_REF] Stöcker | Highperformance computing mri simulations[END_REF] graphical interface. All the information concerning RF, gradients, ADC, timing events, and core hardware specifications must be defined at this step. Using this high-level programming, a low-level Pulseq text file is generated containing all the sequence specifications in terms of timed events that can easily be read by the interpreter. This file doesn't include loops, meaning that each sequence block is detailed as many times as it should be played. Depending on the available MR device, this text file sometimes needs to be further converted by the means of an interpreter module, before being imported into the device without further compilation. The Pulseq architecture is summarized in Figure 3.5.

Although Pulseq has achieved its goal of providing a quick cross-platform prototyping tool, it lacks userinterface flexibility when acquiring images and reaches its limits when the sequence includes many loops. Adapted from [START_REF] Layton | Pulseq: a rapid and hardware-independent pulse sequence prototyping framework[END_REF] Therefore, it is actually impossible to implement features like physiological triggering or real-time feedback and a fortiori to prototype very long sequences such as the ones used for diffusion-weighted MRI. Pulseq is available on GitHub and has been used in an end-to-end acquisition framework using the ISMRMRD raw data format and the BART environment for reconstruction.

The KSFoundation library

To facilitate pulse sequence programming on GE systems using the EPIC C-based language, a C-library has been proposed by [START_REF] Skare | An abstraction layer for simpler epic pulse programming on ge mr systems in a clinical environment[END_REF]. It includes features to hide the low-level EPIC functions, thus providing an abstraction layer that encapsulates important information and clarifies the code. It is based on emulating C++ classes in C using typedef structures with an associated set of functions. In this environment, the creation of sequences relies on instances of these typedef structures that are considered like C++ objects.

Open-source reconstruction frameworks

On the reconstruction side, it is also difficult to handle the manufacturers' constraints, and researchers developed a panel of libraries to improve the prototyping of reconstruction algorithms. Many of them provide an offline environment for reconstruction after the acquisition, as it is easier to develop and does not need to be interfaced directly with the MR system. However, these offline reconstruction libraries, although they allow for very performant and flexible algorithm design, are not compatible with the development of new real-time techniques, which need to reconstruct images while acquiring 4D data or adjust specific parameters in real-time. To our knowledge, the only open-source project capable of this is the Gadgetron framework. Therefore, to illustrate these concepts, we present an example of an external reconstruction library before introducing the Gadgetron environment.

The Berkeley advanced reconstruction toolbox (BART)

BART [START_REF] Uecker | Berkeley advanced reconstruction toolbox[END_REF] provides a library of C/C++ codes that can be run using a command-line interface to provide a rapid and efficient prototyping tool for MRI reconstruction. It has been developed in a Linux environment but is also available for MacOS and Windows. It is compatible with higher-level interfaces like Matlab or Python. It can also use the computational power of GPUs to accelerate processing. BART has been tested on various applications, from very simple educational examples to complex parallel imaging and compressed sensing algorithms. Its limitation relies on its inability to be connected to the imaging device, preventing it to be used directly in a clinical context. [START_REF] Hansen | Gadgetron: an open source framework for medical image reconstruction[END_REF] Gadgetron [START_REF] Hansen | Gadgetron: an open source framework for medical image reconstruction[END_REF]] is an open-source environment for online and offline reconstruction. It has been developed to provide a free, efficient, and flexible open-source MRI reconstruction environment. As shown in Figure 3.6, its workflow is based on a timeline architecture built upon a stream of "Gadgets", readers, and writers.

The Gadgetron framework

The raw data from any scanner can be converted to the ISMRMRD format and go through a reader, which deserializes it before sending it to the next steps. Each Gadget has a specific task corresponding to a reconstruction step and uses open-source libraries as well as internal toolboxes to perform its computations. These toolboxes and the Gadgetron streams are designed to handle high-performance computing tasks, like multithreading on CPUs or on GPUs using a CUDA (NVIDIA) implementation. In addition to the already available Gadgets, it is possible to implement specific reconstruction steps as new gadgets thanks to a Python integration module.

Gadgetron provides pre-implemented and optimized reconstruction pipelines, including corrections for Nyquist ghosting in EPI images, POCS algorithms for partial Fourier images, parallel imaging reconstruction algorithms, and corrections for non-cartesian acquisition trajectories like the spiral one. These are organized using different XML files as pipeline supports that can run with any properly formatted data. To ensure that the raw data is correctly set, the ISMRMRD format is obtained using parameter maps, which associate raw data header fields to the corresponding fields in the converted image.

Conclusion

This chapter presented the mechanisms and challenges for the acquisition and reconstruction of MR images in a research environment. It highlighted the advantages and difficulties of working with a vendor to develop new MRI pulse sequences and provided an overview of the open-source solutions that have been proposed by the community to make pulse sequences easier to develop and share. Many of these solutions focus on providing a manufacturer-independent high-level design and are intrinsically limited by this structure, which makes the integration of complex features (depending strongly on the MR system architecture) very difficult.

In this context, the next chapter introduces specific pulse sequences that are used to probe the brain's microstructure and function through the use of different MRI modalities: anatomical, functional, and diffusion MRI.

The human brain is a complex structure that centralizes metabolic, sensorial, motor, and cognitive functions. It has been studied in terms of macroscopic and microscopic anatomy, physiology, and functionality and is still the object of numerous studies, which aim at understanding its natural development from youth to old age, as well as the different pathologies that may affect it throughout life. MRI is a key tool to observe the brain in a non-invasive way, with the possibility of observing in vivo its functional activity or probing its in or ex vivo microstructure.

In this context, specific brain imaging methods and associated sequences have been developed by combining several common and specific features, such as excitation or readout schemes. Pulse sequence programming is the key tool to implement such diversity, which needs a thorough understanding of each method to be implemented.

Therefore, with the aim to support the understanding of brain MRI pulse sequence development, this chapter introduces fundamental notions in brain anatomy from the macroscopic to the microscopic point of view before focusing on different MRI modalities for brain imaging and their corresponding pulse sequences.

Anatomy of the human brain

The human nervous system is a complex structure that includes nerves, plexuses, and ganglia forming the peripheral nervous system (PNS) as well as the brain and spinal cord composing the central nervous system (CNS). Since this work focuses on the latter, this section describes macroscopic, mesoscopic, and microscopic anatomies of the human brain to provide the knowledge that allows for understanding the MRI applications that are detailed in the next section (4.2).

Macroscopic anatomy

The human brain is protected by the skull, along with three membranes called meninges. The dura mater is the thicker one and the closest to the skull, it is adjoined by the arachnoid mater, separated from it by the Cerebro Spinal Fluid (CSF), and the pia mater that directly covers the CNS and supplies it with blood. The CSF, which has the role of mechanically and physiologically protecting the brain, is continuously secreted around it by choroid plexuses composed of ependymal cells and is absorbed in the arachnoid layer. Inside this protective system and as shown in Figure 4.1-a, four parts of the brain can be distinguished: the cerebrum, i.e. the largest part that is separated into two hemispheres, the cerebellum, which is smaller and also separated into two hemispheres, the brainstem, representing the central axis of the brain, and the diencephalon connecting the cerebrum and the brainstem.

The outer surface of the cerebrum presents a highly folded pattern composed of sulci and gyri. As shown in Figure 4.1-b, the cerebrum can be separated into lobes, each associated with different functions and characteristics:

• the insular lobe: located in the innermost region of the cerebrum, it is responsible for the processing of sensory and decisional information, along with reflexes and motor control;

• the temporal lobe: occupying the middle-low position on each hemisphere, it is responsible for speech comprehension, visual object representation, auditory processing, memory, and semantic knowledge of objects; • the parietal lobe: just above the temporal lobe, it is responsible for practical aspects of language, abstraction, and mathematical cognition;

• the frontal lobe: at the front of the cerebrum, it products language and speech and is implicated in motor, behavioral, and cognitive tasks;

• the occipital lobe: in the rear of the cerebrum, it is mainly dedicated to visual processing.

The cerebrum presents two hemispheres of similar size, separated by meninges and connected by internal structures called commissures. The most important commissure is the corpus callosum, which links the different lobes together, transferring information and coordinating processes across the two hemispheres. Inside the intricate structure formed by the cerebral lobes, cavities known as ventricles renew the CSF through choroid plexuses.

The cerebellum is located under the cerebrum and behind the brainstem. Separated into two hemispheres, it is a major actor of automatic movements, including gait and balance. It represents around 10% of the total brain volume and contains more than half of its neurons.

The brainstem occupies the central axis of the brain, starting from the cerebrum and connecting to the cerebellum and the spinal cord. Representing a hub for ten out of twelve nervous origins and terminations, it is composed of three distinct parts: the midbrain, the pons, and the medulla oblongata. They all work together to relay information from the rest of the nervous system to the cerebrum or the cerebellum while coordinating movements and vital flows like heartbeat or breathing.

The brainstem is connected to the cerebrum by the diencephalon, which is composed of important deep brain structures: the thalamus, the hypothalamus, and the pituitary gland. Located in the innermost part of the brain, the thalamus relays sensory and motor signals and is implicated in consciousness and sleep processes. Below it, the hypothalamus is composed of small nuclei playing a role in metabolic regulation and complex functions such as hunger, circadian rhythm, and body temperature. Connected to the hypothalamus, the pituitary gland is a small structure responsible for secreting hormones that control blood pressure, saline concentration, and temperature, as well as pain relief, reproduction, and growth.

The brain is supplied with blood by a three-fold vascular system, including the carotid and basilar arteries providing blood influx, an anastomosis system connecting these arteries, and cerebral arteries fanning out to the deep brain structures and maintaining blood pressure in case of emergency.

Microstructure

: Schematic view of a neuron. A neuron is a brain cell composed of a cell body including a nucleus, which is surrounded by dendrites serving as receptors, and prolongated by an axon protected by a myelin sheath and conveying information to its terminal parts, including synapses that relay this information to the next neuron's dendrites. Adapted from www.britannica.com

The fundamental cells of the CNS are neurons, which process the information in the brain by conveying electrical signals through their axons. Their size can vary from 4 to 130 µm and they communicate with each other through chemical signals and neurotransmitters. As shown in Figure 4.2, they present a structure composed of a cell body, surrounded by dendrites, and giving birth to an axon, itself surrounded by a myelin sheath and terminated by synapses.

The cell body -or soma -comprises a nucleus and is the metabolic center of the neuron. The axon is a conductive part whose length can range from a few millimeters to a meter and is capable of transmitting an electrical signal. This feature allows for the conveying of information among neurons but also to other parts of the nervous system, such as muscles and glands. It is surrounded by a myelin sheath responsible for insulating it and improving its conductivity. This sheath is regularly interrupted by uncovered parts called Ranvier nodes, which also play their role in the neurotransmission being responsible for the saltatory conduction. At the end of the axon, synapses ensure the connexion between the cells of the nervous system by releasing neurotransmitters, which are received by the dendrites of the next neuron cell.

Besides neurons, the brain is composed of other cells responsible for providing the neurons with metabolic and structural support: the glial cells, illustrated in Figure 4.3. They are present in greater proportions than neurons and can be subdivided into two families: the macroglia and the microglia. The astrocytes, the oligodendrocytes, and the ependymal cells are the most important cells and belong to the macroglia. Astrocytes are responsible for maintaining the blood-brain barrier and providing metabolic and structural support to neurons, while the oligodendrocytes are in charge of producing and maintaining the myelin sheath around axons. Ependymal cells form an interface between the brain and the CSF, which they produce and circulate. Complementing their roles, the microglia is composed of macrophage immune cells, which are responsible for the protection of the other brain cells, as well as for neurogenesis in the adult brain. Furthermore, they are the first barrier between the brain and pathogens, and provide support in repairing damaged tissues. As shown in Figure 4.4-a, the gray matter represents a great part of the diencephalon. It composes the outermost parts of the cerebrum, called the cerebral cortex, and of the cerebellum, and is present in deep structures of the cerebrum called basal ganglia and illustrated in Figure 4.4-b. The cerebral cortex presents a laminar structure composed of three to six layers presenting differences in their cytoarchitecture. This structure is mainly composed of neuronal bodies and has been described, in terms of cellular characteristics, into 52 cytoarchitectural areas by Brodmann [Brodmann, 1909].

White matter, which is also presented in Figure 4.4-a, represents around 40% of the brain tissue and is located in the innermost parts of the cerebrum and the cerebellum, as well as in the brainstem. It is mainly composed of axons, which interconnect neuronal bodies and allow for neuronal communication. Taking the form of tracts composed of densely packed parallel axons, white matter forms a complex network relaying information within and between the hemispheres. These tracts are composed of fibers, which can be divided into three different kinds, as presented in Figure 4.4-a: commissural fibers, which connect the two hemispheres of the cerebrum, projection fibers, which provide pathways from the outer part of the cerebrum to its deeper structures, and association fibers, which link the different gyri of the cortex within a hemisphere.

Magnetic resonance imaging of the human brain

Since its first development in the 70s, MRI has been used for a large panel of applications. It has been found to be versatile and to open the way to many great discoveries and medical applications in the field of neuroimaging where there are no other means to do non-invasive in vivo imaging. Brain MRI is nowadays used in many hospitals to diagnose brain diseases such as edemas, tumors, or strokes, as well as in research for two main purposes:

• to explore the physiopathology of neurodegenerative, neurovascular, neurodevelopmental, and psychiatric diseases for public health purposes;

• to investigate the structure of the brain and the way it works from the young child to the aging subject.

These studies led to the development of advanced techniques such as functional MRI (fMRI), showing activations in the brain, or diffusion-weighted MRI (dMRI), enabling the early detection of strokes and the study of brain microstructure. The most common application of MRI is to provide a non-invasive way to observe the human brain. This is done to diagnose brain diseases such as edemas, neurodegenerative, and neurodevelopmental diseases. Radiologists are used to look at axial, coronal, or sagittal views described in Figure 4.5 to observe the brain and detect its putative disorders.

Mapping the brain anatomy

These anatomical images are acquired with SE or GRE sequences (possibly with preparation such as FLuid-Attenuated Inversion Recovery (FLAIR) sequences [START_REF] Hajnal | Use of fluid attenuated inversion recovery (flair) pulse sequences in mri of the brain[END_REF]) and using accelerated versions for time efficiency. Depending on the goal of the observation, they can either be T 1 -weighted or T 2 -weighted, as presented in Figure 4.6. Contrary to T 1 -weighted sequences which present an anatomical contrast in which gray matter is darker than white matter, T 2 -weighted images feature a brighter gray matter compared to white matter. To observe the anatomical structure of the brain, T 1 -weighted images are obtained using inversion-recovery techniques combined with gradient echo excitations. The most frequently used sequence is the Magnetization-Prepared Rapid Gradient Echo (MP-RAGE) [Mugler III and Brookeman, 1991], which is a 3D fast gradient echo sequence with inversion-recovery. As presented in Figure 4.7, it is composed of a first non-selective inversion pulse and a train of fast gradient echo excitations with associated readouts. An extension of the MP-RAGE sequence, called Magnetization Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE) [START_REF] Marques | Mp2rage, a self bias-field corrected sequence for improved segmentation and t1-mapping at high field[END_REF], is also widely used for anatomic T 1 -weighted imaging. As explained in Figure 4.8-b, it consists in using two inversion times (T I), one short and one long, to acquire two images that can be post-processed to produce a quantitative T 1 (qT 1 ) mapping in addition to T 1weighted images. Importantly, qT 1 maps depict a better contrast and do not depend on proton density.

T 2 -weighted MRI sequences

While the T 1 -weighted contrast gives a greater signal for fat and a lower signal for water, the T 2 -weighted contrast highlights the signal for water. This difference is interesting to specifically observe structures involving more water. It is possible to find tumors and degradation of white matter by using fast spin echo sequences, which are described in chapter 1 (1.3.2), or their extension in 3D: Sampling Perfection with Application optimized Contrasts using different flip angle Evolution (SPACE) [Mugler III, 2014]. Edemas can be observed using FLAIR [START_REF] Hajnal | Use of fluid attenuated inversion recovery (flair) pulse sequences in mri of the brain[END_REF] sequences and bleedings using T * 2 -weighted sequences.

4.2.2 Mapping brain functions using MRI Functional MRI (fMRI) has been developed in the 90s by Ogawa [START_REF] Ogawa | Brain magnetic resonance imaging with contrast dependent on blood oxygenation[END_REF] and Belliveau [START_REF] Belliveau | Functional mapping of the human visual cortex by magnetic resonance imaging[END_REF] and relies on an indirect observation of NMR signal modification occurring in activated areas due to the level of oxygen present in the blood locally irrigating brain tissues. M1. This function is characterized by its peak amplitude, its peak latency, and its full width at half maximum (FWHM). It is observed when measuring the BOLD signal in an fMRI experiment. Adapted from [START_REF] Do | Hemodynamic modeling of aspirin effects on bold responses at 7t. medRxiv[END_REF].

Principles of functional imaging

Performing a key role in the function and bioenergetics of the brain, the production of Adenosine Tri-Phosphate (ATP) goes through the Krebs cycle involving a glycolysis reaction, thus causing oxygen consumption. Because the efficiency of the brain for energy storage is not optimal, its vascular system supplies activated areas with a greater quantity of oxygenated blood than necessary to ensure a sufficient oxygen supply to produce ATP. This phenomenon induces a significant increase in the concentration of oxyhemoglobin in the activated area, followed by a decrease at the end of the activation when oxyhemoglobin is replaced by deoxyhemoglobin. This behavior is known as the Hemodynamic Response Function (HRF) and is described in Figure 4.9. As the paramagnetic properties of deoxyhemoglobin globally disturb the NMR signal in the brain, its reduced presence in oxygenated blood can be detected as susceptibility effects using MRI. Thus, the activated areas present a less disturbed signal than the resting ones. This phenomenon is measured through the Blood Oxygen Level Dependent (BOLD) signal, which allows for the computation of activation maps through time as the signal from oxygenated blood varies locally with activations, as shown in Figure 4.10. The areas presenting a greater fluctuation in blood oxygenation are highlighted and correspond to activated areas that were required to perform the task.

fMRI studies use different paradigms to induce already known reactions and study behavior. An easy example is a visual stimulus, which can be an image, a sentence, or a video. With an image, for instance, it is very likely to obtain the activations shown in Figure 4.10. As the image stimulates the vision, the occipital area known to be linked to visual processing is active, along with the frontal cognitive area, which corresponds to working memory, certainly linked to the image's content.

Acquisition of fMRI data

Since it performs many acquisitions of the same image through time to recover the time-dependent signal, fMRI is commonly performed using a 2D or 3D GRE EPI sequence with accelerations. This sequence is repeated to acquire the same volume many times during the execution of one task, which allows for the computation of the BOLD signal from the susceptibility variations through this series of images. In this process, the repetition time between each sequence instance is very important and defines the resolution in the fourth dimension corresponding to time.

Mapping brain microstructure using diffusion-weighted MRI

Probing the microstructure of brain tissue requires an MRI modality sensitive to its organization at the cellular level. Diffusion MRI (dMRI) tackles this issue by measuring the diffusion of water molecules whose trajectories are restricted or hindered by cell membranes, thus embedding information about their geometry.

Diffusion of water molecules

Water molecules have an intrinsic movement describing a Brownian motion [Brown, 1828], which makes them move in random directions to fill up the space, as depicted in Figure 4.11-a,b. This movement, which is due to the interaction between the molecules, is described by Fick's laws introduced in equations (4.1) and (4.

∂C ∂t = D∇ 2 C, (4.2)
with J the flux of the diffusing element expressed in mol.m -2 .s -1 (eg water in our case), C its concentration in mol.m -3 , and D its diffusion coefficient (equal to 2.299 × 10 -9 m 2 .s -1 for self-diffusing water molecules at 25 • C). The first law (equation (4.1)) introduces the diffusion coefficient as the proportionality factor between the concentration gradient of the considered diffusing element and its flux in the fluid. The second law (equation (4.2)) specifies the evolution of the concentration of diffusing molecules through time.

In the case of diffusion-weighted MRI, where the self-diffusion of water molecules is studied, the diffusing particles as well as the fluid in which this diffusion occurs are water, which allows for the use of the propagator function for isotropic environments P (a, b, t) introduced in equation ( 4.3) to describe the probability of moving from a point a to a point b in a time t for a single water molecule:

P (a, b, t) = 1 √ 4πDt e -||b-a|| 4Dt , (4.3)
This way, the characterization of isotropic diffusion of water molecules is done using a combination of equations ( 4.3) and (4.2) as described in equation (4.4):

∂P (a, b, t) ∂t = D∇ 2 P (a, b, t). (4.4)
However, in the brain, the diffusion of water molecules is hindered by the complex microstructure of tissues and cannot be considered isotropic. As it is difficult to define generalized equations for anisotropic diffusion, the notion of mean squared displacement ⟨R 2 ⟩ [Einstein, 1905] presented in equation (4.5) is used as a basis to describe more intricate diffusion processes:

⟨R 2 ⟩ = 6τ D. (4.5)
It highlights the link between the diffusion time τ and the diffusion coefficient D, thus allowing for measurements of diffusion relying on time-dependent processes like diffusion-weighted MRI.

Sensitizing MRI to the diffusion process

The human brain is composed of intricate structures containing a large number of water molecules that are going through the diffusion process. The brain cells, with their semi-permeable membranes, constrain their movement in various ways, depending on their shapes. In gray matter, as the arrangement of neuronal bodies is dense, the mean diffusivity corresponds to an isotropic diffusion scheme, while in white matter it is anisotropically oriented by the fiber bundles. .12 : Diffusion weighting process. Two cases are presented: the first when no diffusion occurs, and the second when one spin is diffusing. In the first case, the application of two identical diffusion-weighting gradients around the refocusing pulse is transparent: the first gradient tilts all spins identically, and this movement is integrally compensated by the second gradient. However, in the second case, if a spin diffuses between the two gradients, the application of the second one does not result in its return to the exact previous state. This diffusing spin stays tilted and contributes less to the resulting NMR signal. Adapted from the lecture on MRI physics (Centrale-Supelec), courtesy of Cyril Poupon.

Relying on Fick's laws and on the definition of mean diffusivity, diffusion-weighted MRI encodes the NMR signal using gradients and timings related to the diffusion coefficient of water molecules in the brain. Its principle relies on the use of strong gradient pulses which encode the spins of water molecules with a specific phase depending on their position. As explained in Figure 4.12, they are turned on before and after the refocusing RF pulse, in between which diffusion can happen. If no diffusion occurred, the signal obtained corresponds to the NMR signal of a standard spin echo sequence. However, as diffusion happens, the obtained signal is weaker in the areas where it occurred. This is especially true when the diffusion process develops in an anisotropic manner, giving a clear signal loss in the considered area. Following this principle, a diffusion-weighted Pulsed Gradient Spin Echo (PGSE) sequence, presented in Figure 4.13, was proposed by Stejskal andTanner in 1965 [Stejskal andTanner, 1965]. The diffusion signal is encoded through pairs of gradients in a selected direction. The parameters of diffusion encoding are directly linked to their shape, amplitude, and timing. They are obtained using the notion of b-value b, a factor corresponding to the intensity of the diffusion-weighting, as defined in equation (4.6):

M T (t) = M 0 e -t
T 2 e -bD .

(4.6)

In the case of diffusion MRI, the Bloch equation introduced in Chapter 1 can be further developed into the Bloch-Torrey equation [Torrey, 1956]:

dM(t) dt = γM(t)B 0 (t) + 1 T 1 (M 0 -M L (t))z - 1 T 2 M T (t) + D∇ 2 M(t), (4.7)
with D the diffusion coefficient in m 2 .s -1 and γ the gyromagnetic ratio. The first term corresponds to the precession of spins in the magnetic field B 0 , the second to the longitudinal regrowth of the magnetization characterized by the T 1 relaxation time, the third to its transversal relaxation characterized by the T 2 relaxation time, and the fourth to the diffusion process characterized by the diffusion coefficient D. Using the definition of M T given in equation (4.6), it is possible to obtain the corresponding b-value b described in equation (4.8):

b = γ 2 T E 0 ( t 0 G(t ′ )dt ′ )dt, (4.8)
with G(t) the amplitude of the considered diffusion gradient in mT.m -1 . For instance, using this equation with a trapezoidal gradient like the ones presented in Figure 4.13, the b-value can be further computed as such:

b = γ 2 G 2 (δ 2 (∆ - δ 3 ) + ξ 3 30 -δ ξ 2 6
), (4.9)

with δ the plateau duration of the diffusion gradients, ∆ the separation time between the starts of the diffusion gradients, and ξ the ramp time of the gradients, as introduced in Figure 4.13. This weighting results in a drop of signal for the molecules having a diffusion movement in the direction for which it is encoded. Different diffusion directions can be explored by modulating the amplitude of the gradients using an orientation matrix.

A model-free approach to describe diffusion MRI goes through the definition of a wavevector q presented in equation ( 4.10): with τ = ∆ -δ 3 the diffusion time. These definitions are given under the assumption that the duration of the diffusion gradients' ramp time ξ is very small compared to their plateau duration δ. They allow for projecting the NMR signal in the diffusion space, consequently named q-space, and defining its attenuation E(q) detailed in equation ( 4.12): E(q) = S(q) S( 0) , (4.12)

q = γ 2π δG, ( 4
with S(q) the diffusion-weighted signal, and S(0) the signal without diffusion encoding.

Local models of diffusion

In brain tissues, the diffusion of water molecules is hindered by the cell walls as described in Figure 4.14 and can be considered either isotropic or anisotropic. In the first case, their hindered diffusion corresponds to a Gaussian model [Le Bihan et al., 1986] in which the attenuation can be expressed as a function of the apparent diffusion coefficient ADC as described in equation 4.13: (4.13) This Gaussian model description already shows the effects of the diffusion process on the NMR signal, allowing for the obtention of ADC maps, which can be used for stroke detection. However, it lacks information about the anisotropic characteristics of the tissues. To solve this issue, the Diffusion Tensor Imaging (DTI) model was proposed in [START_REF] Basser | Mr diffusion tensor spectroscopy and imaging[END_REF]. It modelizes the diffusion coefficient D as a 3x3 symmetric tensor matrix quantifying the diffusion of water molecules in 3D as shown in equation (4.14): The eigenvectors of this matrix form a 3D system in which it is possible to project the corresponding eigenvalues as the parameters of an ellipsoid, which is a good approximation of the complex diffusion direction and intensity information. From the eigenvalues (λ 1 , λ 2 , λ 3 ), it is also possible to compute four microstructural metrics defined in equations (4.15), (4.16), (4.17), and (4.18):

E(q) = e -bADC .
ADC = λ 1 + λ 2 + λ 3 3 , (4.15) FA = 3 2 (λ 1 -⟨λ⟩) 2 + (λ 2 -⟨λ⟩) 2 + (λ 3 -⟨λ⟩) 2 λ 2 1 + λ 2 2 + λ 2 3 , (4.16
)

λ P arallel = λ 1 , (4.17) λ T ransverse = λ 1 + λ 2 2 , (4.18)
with FA the fractional anisotropy characterizing the anisotropy of the diffusion process in a voxel (FA = 1 corresponds to highly anisotropic diffusion, while FA = 0 stands for isotropic diffusion), λ P arallel the parallel diffusivity measured along the principal diffusion direction (m 2 .s -1 ), and λ T ransverse the transverse diffusivity perpendicular to the principal diffusion direction. With this model, only six different dMRI acquisitions corresponding to 6 diffusion directions and a reference scan with no diffusion weighting are necessary to compute all these metrics. However, due to the presence of noise in the image, it is usually better to acquire 30 diffusion directions when computing the DTI model. Furthermore, as it is based on a Gaussian model, it lacks specificity and cannot account for complex structures like crossing white matter fibers. This issue was challenged over the past years by several acquisition protocols like the High Angular Resolution Diffusion Imaging (HARDI) [Tuch et al., 2002] model, which projects 20 to 250 measurements on single or multiple spheres called "shells", each shell corresponding to a specific b-value, thus improving the diffusion direction angular resolution, or the HYbrid Diffusion Imaging (HYDI) [START_REF] Wu | Hybrid diffusion imaging[END_REF] model, which follows the same principle with different diffusion directions for each shell. The images obtained with these methods can be post-processed using models such as:

• Diffusion Spectrum Imaging (DSI) [START_REF] Wedeen | Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging[END_REF], which uses a probability density function to describe crossing fibers with diffusion-weighted images sampled on a specific q-space sphere;

• Q-ball imaging (QBI) [Tuch, 2004], which computes diffusion Orientation Distribution Functions (ODF) capable of highlighting multiple diffusion peaks underlying multiple crossing fiber populations;

• Constrained Spherical Deconvolution (CSD) [START_REF] Tournier | Direct estimation of the fiber orientation density function from diffusion-weighted mri data using spherical deconvolution[END_REF], which computes fiber Orientation Distribution Functions (fODF) relying on the representation of the diffusion-weighted signal as the spherical deconvolution of a single fiber response function.

This figure illustrates diffusion-weighted imaging, which needs 3 orientations to compute mean diffusivity; diffusion tensor imaging (DTI) which relies on 6 orientations to compute a diffusion tensor; diffusion spectrum imaging (DSI) which uses a probability density function to describe crossing fibers; high angular resolution diffusion imaging (HARDI) which can be single-or multiple-shell with each shell corresponding to one b-value; and hybrid diffusion imaging (HYDI) which is multiple-shell, including different diffusion directions for each shell.

To complete these models focusing on fibers, analytical multicompartment models such as Neurite Orientation and Dispersion Density Imaging (NODDI) [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF] and Soma and Neurite Density Imaging (SANDI) [START_REF] Palombo | Sandi: a compartment-based model for non-invasive apparent soma and neurite imaging by diffusion mri[END_REF] have been developed. NODDI is based on the representation of axons and dendrites as impermeable sticks displaying a highly anisotropic diffusion pattern. It is used to compute metrics such as the orientation dispersion index (ODI) characterizing the angular dispersion of neurites using a Watson distribution, the κ concentration parameter of this Watson distribution, and the neurite density index (NDI), corresponding to axon density in the white matter and dendrite density in the gray matter. The SANDI extension of NODDI also enables the measurement of cell body -soma -density within the cortex, based on dMRI acquisitions with strong b-values. This reveals the other aspect of dMRI, which is to probe the microstructural composition corresponding to each acquired voxel and is an active research field.

Applications

dMRI is nowadays used in hospitals to detect strokes at early stages by showing an increase in the diffusion-weighted signal (corresponding to a drop in diffusivity) in the case of arterial occlusion and a drop (corresponding to an increase in diffusivity ) in the case of hemorrhagic lesions. Its sensitivity to microstructural structure is also used in research with several applications, enabled by fiber tracking using tractography methods such as connectomics, white matter atlases, and tract-based statistics. From diffusion-weighted images, it is possible to use deterministic, probabilistic, or global tractography algorithms to compute a map of the bundles of tracts present in the brain, as the one shown in Figure 4.16. Deterministic tractography methods [START_REF] Pierpaoli | Toward a quantitative assessment of diffusion anisotropy[END_REF]] [Poupon et al., 1998] [Mori et al., 1999[START_REF] Perrin | Validation of q-ball imaging with a diffusion fibre-crossing phantom on a clinical scanner[END_REF] compute tracts along the most likely path given by the ODF or fODF peaks. For better robustness to noise corruption, probabilistic tractography methods [START_REF] Behrens | Characterization and propagation of uncertainty in diffusion-weighted mr imaging[END_REF]] [Parker et al., 2003] allow the tracts to deviate moderately from the most likely path. Furthermore, to ensure the obtention of fibers with plausible anatomic connections, global tractography methods [Poupon, 1999] [Reisert et al., 2011[START_REF] Jbabdi | Tractography: where do we go from here?[END_REF]] compute all trajectories in a simultaneous way.

As it reconstructs the microstructure of white matter, tractography allows for the computation of white matter atlases like [START_REF] Guevara | Robust clustering of massive tractography datasets[END_REF] that rely on the automatic clustering of fibers into bundles at the individual and population levels. With the definition of metrics such as inter-subject variability, these atlases can be used to develop new imaging markers in relation to brain pathologies. Tractography can also be used to compute connectivity matrices [START_REF] Sporns | The human connectome: a structural description of the human brain[END_REF], which reflect the degree of anatomical connectivity of each brain region towards the others. This method establishes the connectome of the human brain and is used to provide new parcellations of the cortex [Van Essen and Glasser, 2016]. To go further, it is possible to compute tract-based statistics, thus enabling a precise analysis of the tractogram.

Alternative sequences to PGSE

Diffusion-weighted imaging can be used to perform either in vivo or ex vivo acquisitions. These two acquisition modes have different constraints and goals, which led to the development of multiple dMRI sequences. If the PGSE sequence shown in Figure 4.13 illustrates the principles of dMRI correctly, it is not sufficient to achieve optimal quality images in a reasonable time.

Since the computation of local models for diffusion requires lots of samples, dMRI sequences used in vivo are accelerated as much as possible while maintaining a resolution suitable for diffusion models. The most popular scheme is the single-shot 2D spin-echo EPI sequence with parallel imaging, multiband excitation, and partial Fourier acceleration. This sequence is composed of alternating RF pulses with α and -α flip angles, prepared in diffusion, followed by a single-line readout and spoilers. It is commonly used to acquire ex vivo diffusion-weighted brain images.

In the case of ex vivo acquisitions, the conditions are different: the duration is not anymore a constraint, and the diffusivity of fixed tissues (using paraformaldehyde, PFA) is scaled down by a factor of 3 to 4, thus requiring to significantly increase the b-value above 4000s.mm -2 to maintain the diffusion contrast, which in turn significantly increases the echo time while the T 2 relaxation time of fixed tissues is also decreasing. Single-shot 2D EPI sequences are no longer adapted and are replaced by alternative sequences depending on the gradient set capacities: [START_REF] Westin | Measurement tensors in diffusion mri: generalizing the concept of diffusion encoding[END_REF] in a spin-echo sequence. For comparability, all waveforms are adapted to yield b = 2000s.mm -2 at a minimal encoding time constrained to a maximal gradient amplitude of 80mT.m -1 and maximal slew rate of 100T.m -1 .s -1 . g(t) shows the gradient trajectory, and q(t) the q-space trajectory associated with the gradient waveform. Adapted from [START_REF] Szczepankiewicz | Gradient waveform design for tensor-valued encoding in diffusion mri[END_REF].

• multi-shot 2D or 3D EPI sequences, mainly used in a pre-clinical environment, allowing for the obtention of a higher SNR with fewer distortions than single-shot EPI;

• diffusion-weighted STEAM sequences, enabling the use of significantly longer separation times between diffusion gradients and of greater b-values while preserving a short echo time;

• diffusion-weighted steady-state free precession (SSFP) sequences like diffusion-weighted balanced SSFP (bSSFP) [START_REF] Mcnab | Steady-state diffusion-weighted imaging: theory, acquisition and analysis[END_REF] sequence, presented in Figure 4.17, which is composed of alternated GRE excitations with single-line readouts and balanced spoiler, allowing for flow compensation.

Furthermore, to improve the sensitivity of diffusion-weighted pulse sequences, alternative gradient waveforms to single-lobe trapezoids have been proposed. Oscillating gradients [START_REF] Does | Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain[END_REF] are made of alternating gradient lobes, which can be sine, cosine, trapezoidal-sine, or trapezoidal-cosine, and they provide the same diffusion-weighting as equivalent plain trapezoidal gradients but makes the signal more sensitive to micro-elements in the structure.

Furthermore, through the modelization of diffusion-weighting as a b-tensor [START_REF] Westin | Measurement tensors in diffusion mri: generalizing the concept of diffusion encoding[END_REF], it is possible to optimize the waveform of the gradients to fit a distribution in the q-space as shown in Figure 4.18, thus obtaining an improved weighting of different structures and performing a more accurate estimation of microstructural characteristics.

Conclusion

This chapter presented the anatomy of the human central nervous system, including the cerebrum, the brainstem, the cerebellum, and the diencephalon. At the mesoscopic scale, it described gray and white matter, outlining the cerebral cortex and the different types of white matter fibers that can be found in the brain. It reached the microscopic level by introducing the different brain cells, including neurons and neuroglia. This anatomic description served as an introduction to the applications of MRI for brain imaging. The anatomic, functional, and diffusion-weighted MRI modalities were described, including a presentation of the key pulse sequences for each technique.

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Part II Contributions

Introduction

Since the introduction of NMR in the 1940s, when acquisitions were made in a very artisanal way, considerable progress has been made in the programming of NMR pulse sequences. All manufacturers now provide dedicated software development kits with advanced programming languages and simulation environments to facilitate the development of MRI pulse sequences. Despite initially being created for the own manufacturer's needs, these environments are accessible to researchers and provided with a few sequence code examples as a chargeable option when purchasing a new MRI system. Most of the time, their access comes along with license agreements putting strong constraints on the conditions the developers need to respect concerning their ability to share and disseminate their codes. Indeed, because of the limitations induced by intellectual property and business models, vendors cannot allow these sequences to be widely shared independently from them, thus hindering research in this domain.

In order to go beyond such limitations, researchers have developed open-source tools to facilitate the prototyping of MRI pulse sequences independently from the manufacturer's toolkits. Focusing mainly on providing tools enabling a cross-manufacturer usage of the sequences, the community of pulse sequence programmers gave birth to innovative tools such as SequenceTree [START_REF] Magland | Pulse sequence programming in a dynamic visual environment: Sequencetree[END_REF] or PulSeq [START_REF] Layton | Pulseq: a rapid and hardware-independent pulse sequence prototyping framework[END_REF], which support the development of new acquisition methods while setting aside the difficulties encountered in the vendor's programming environment. Still, if these tools solve many issues concerning the prototyping and sharing of new pulse sequences, they are limited by their high-level interfaces, from which all the complex features proposed by the vendor's environment are unreachable, preventing the implementation of original graphical interfaces or real-time updating of the sequence. To enable the creation of such projects, all the features of the vendor's development kit should be reachable, with a trade-off to be made regarding ease of use and accessibility.

To make the development of sequences smoother in the manufacturer's environment, some projects have proposed libraries that provide programming support, like the KSFoundation library [START_REF] Skare | An abstraction layer for simpler epic pulse programming on ge mr systems in a clinical environment[END_REF], that has been proposed for GE systems. Unfortunately, such libraries do not exist for Siemens MRI systems, and no open-source solution has been developed, to our knowledge, to facilitate the development and sharing of MRI pulse sequences in this environment. Indeed, it is possible to develop new methods using their tools and base sequences, but these are under an agreement that makes them the property of Siemens if they are inheriting some of their source code, thus hampering their sharability to the community. Furthermore, the sequences provided in their development kit have been developed with the constraints of a competitive business environment and do not use the C++ object-oriented structure to its best, taking the form of thousands-of-line-long sequence codes. As a counterpart, the Siemens IDEA development kit provides dedicated concepts such as the Sequence Building Blocks (SBBs), which allow for the modular creation of common sequence parts. However, the various SBB-based source codes are not completely accessible to external sequence programmers and are often given only as binaries, thus preventing their modification.

In this context, the prototyping, development, and sharing of new MRI pulse sequences in the Siemens IDEA environment is laborious and necessitates coping with the intellectual property and business model issues, using external cross-manufacturer solutions with limited access to vendor-specific features or redeveloping compatible source code from scratch. If the last approach seems tedious and not worth investing in for a single sequence development project, we think that providing a sharable basis for Siemens pulse sequence programming source code, implemented in a truly object-oriented architecture, would allow for the open-source development of new sequences integrating all the features available in the development kit, and which could be used in clinical research. Building on this hypothesis, this chapter presents GinkgoSequence, a novel open-source, modular, and object-oriented pulse sequence development framework for Siemens systems.

Challenges and development basis of the GinkgoSequence toolbox

The interest of such a toolbox lies in its design and in the rules adopted for its development. As it needs to be open-source, it is mandatory for the code to be standalone and not based on Siemens' source code. Indeed, the libraries and basic methods provided in the development kit are used, but the programming philosophy is different, showing its own architecture and naming policy. A second important point is that the object-oriented programming angle should provide a modular and flexible structure and allow for the rapid and smooth development of new sequences with a very short learning time. This leads to the design of an architecture separating sequences into multiple base elements which can be easily recombined and adapted.

Open-source policy

The sequences provided along with the IDEA development kit all rely on a structure based on four methods previously detailed in chapter 3 (section 3.3.1): the initialize(), prepare(), run(), and check() methods, which are mandatory for any Siemens MRI pulse sequence. Thus, every sequence has to implement them, but as long as the content is not stemming from sequences provided by the vendor, they can be opensourced. In the same way, using the proprietary libraries provided in the development kit to write original programs does not hinder their free sharing as long as the code itself is original. This makes a significant difference in terms of sharability for sequences developed this way: indeed, it is mandatory to have a research agreement with Siemens to compile the aforementioned sequences using IDEA, although the developed codes themselves can be modified and shared independently of any contract. Adopting this point of view also means that any feature included in the Siemens library for which source code is not accessible, like SBBs, should be avoided.

This environment led to the definition of rules needed to develop an open-source pulse sequence programming framework using the IDEA toolkit:

• no Siemens source code is used, the code is written in its entirety with a new architecture and new names;

• the four mandatory methods are implemented, as well as the codes related to the graphical interface management;

• only low-level methods and functions from the Siemens libraries are used.

Following these guidelines ensures the possibility for the code to be shared, compiled, and run on any Siemens system using the same version of IDEA (VE11C).

Object-oriented architecture: basic concepts

Providing a source code allowing for the flexible and modular development of new sequences yields great importance when developing a pulse sequence programming toolkit. Such a framework should include intelligible features that can be understood by all MR scientists. A convenient approach seems to design any pulse sequence using a top-down hierarchical analysis providing terminal elements corresponding to basic concepts aggregated into high-level concepts, thus defining generic modules shared between pulse sequences. These sequence modules are then directly organized in a timeline, allowing for the smooth implementation of a sequence based on its chronogram.

Using this class as a basis, an inheritance tree can be built, including intermediary classes regrouping common features and giving birth to more specialized classes. To bind these classes together, it is then possible to call them from a main class or to use an intermediary class to create composite sequence modules from the generic ones. Therefore, the main class is able to call either the composite classes or the module classes to build a general timeline for the sequence, including the setting of its parameters and the management of the loops to go through lines, slices, partitions, or repetitions.

As such, the use of too many global variables is avoided with this object-oriented architecture which relies on its modularity to maximize the reusability of the code for new pulse sequences. Furthermore, the source code for an equivalent sequence is significantly shorter than the one proposed in the Siemens code structure.

Progamming rules

To ensure the coherence and the readability of the open-source and object-oriented GinkgoSequence toolbox, programming rules were established for the entire development and should be kept in future works:

• names: including all the information about the variable, class, or method they describe, with no abbreviation, and using the CamelCase writing convention, they allow for a comprehensive reading of the code with no pre-requisite;

• comments: neither too numerous nor too long, they provide key information about the following performed task in the code;

• code width: to facilitate code reading and portability, it is limited to 80 columns;

• tabulation: as they are not set identically in every code editor, double spaces are used instead;

• braces: to make them clear, they are set at the beginning of a line and another line is skipped to separate them from the code;

• private or protected attributes: start with a "_".

These rules ensure coherent programming of the source code, which facilitates its reading and reverseengineering for new users.

Object-oriented design stemming from a top-down hierarchical analysis

It is possible to analyze any MRI pulse sequence as a series of events anchored in time. Performing a top-down hierarchical analysis, they can be divided into general categories, such as excitation events, which can then be subdivided into more specialized types like 2D or 3D excitation pulses, which can again be subdivided into 2D and 3D single or multiple transmission excitation pulses, reaching a terminal branch of this analysis. This generic and object-oriented software architecture should allow to design any MRI pulse sequence in a modular way and to maximize the reusability of the code to build new pulse sequences. To design such an architecture, the concept of SequenceModule must be well defined: it corresponds to an elementary series of real-time events characterized by input parameters, total duration, anchor time, and before and after anchor time durations. This definition allows for every module to be included in a timeline only by using its anchor time and duration.

Within this top-down hierarchical analysis, intermediate levels are populated by high-level modules, corresponding to aggregates of terminal modules. With this aim, a CompositeSequenceModule concept inheriting from the SequenceModule concept has been created to aggregate a series of SequenceModule instances. The aggregated SequenceModule instances can also be inherited from the CompositeSequenceModule class, thus providing a generic way to design complex modules from simpler ones. As presented in Figure 5.1, these are then aggregated into the main GinkgoSequence class to form a complete pulse sequence. Associated with the GinkgoSequence class, a GinkgoSequence_UI class manages the user interface according to the information contained in the SequenceModule instances composing its structure.

The SequenceModule concept: creating terminal elements

Stemming from the terminal elements of the top-down hierarchical analysis, the SequenceModule instances are sorted chronologically using anchor times to form a sequence, enabling their instinctive positioning based on a sequence chronogram. To simplify this integration, the anchor time should be defined in coherence with the expected NMR physics and allow for a smooth calculation of the TE and TR of the sequence. For instance, since the TR can be calculated as the difference between the centers of two consecutive excitations, and since the TE can be calculated from the center of the excitation pulse to the center of the readout gradient, the natural anchor time for a single-channel transmission excitation module is the center of its RF pulse. A generic SequenceModule instance is presented in Figure 5.2, it includes four real-time events in a relative internal timeline and defines the anchor time, duration before anchor time, duration after anchor time, and total duration of the modules. The classes inheriting from the SequenceModule class follow an inheritance tree with intermediate levels composed of six main nodes standing for preparation, excitation, pre-encoding, refocusing, reading, and spoiling events, and extremities populated with specialized modules:

• preparation events can include diffusion-weighting gradients, fat saturation pulses, or FOV saturation pulses,

• excitation events can include single-channel and multiple-channel transmissions, along with 2D and 3D pulses,

• as the pre-encoding is specific to the reading and excitation, it can be declined in many versions, including trajectory start point encoding and reference line acquisitions,

• the refocusing RF pulse can be tuned with a panel of flip angles and waveforms to generate a variety of spin echoes,

• reading events can include single-line, echo-planar, or spiral trajectories,

• depending on the type of sequence, a standard or balanced spoiling can be used.

Many variations of the end leaves can be imagined to implement a large variety of pulse sequences.

The SequenceModule class is the parent class of multiple sequence modules. As detailed in Pseudo-code 1, it defines the anchor time and duration of events before and after the anchor as presented in Figure 5.2, along with the corresponding getters and setters. It also forces the implementation of mandatory methods such as initialize or prepare in the child classes. To simplify the creation of complex modules from simpler ones, the CompositeSequenceModule class, inherited from the SequenceModule class, allows for aggregating SequenceModule objects to generate a standalone module including all events in an intrinsic timeline and providing its own anchor time and duration. It is programmed, as presented in Pseudo-code 2, to manage a list of SequenceModule objects, to execute all their respective methods when its eponymous methods are called, and to manage its timeline.

The interest of this CompositeSequenceModule class lies in the possibility of assembling complex modules based on already existing ones which can be specific SequenceModule or CompositeSequenceModule instances. It provides a flexible frame to generate generic modules and assemble them independently from any pulse sequence scheme.

The SequenceModuleFactory concept: providing generic access to modules

As all SequenceModule instances are built using a common scheme, their creation can be automated through a SequenceModuleFactory. This C++ structure provides an abstraction layer allowing for the flexible creation of modules by mapping their creators with generic names that can directly be called in the main sequence. Furthermore, this architecture provides the tools for future implementation of a graphical interface allowing for the generic creation of sequences using the GinkgoSequence source code.

The SequenceModuleFactory class is presented in Pseudo-code 3. It allows for the generic instantiation of SequenceModule objects linked to their moduleName in a map of objects generated by the factory. This way, any module called in the main GinkgoSequence class using the SequenceModuleFactory, can be found, called, and modified simply by finding its associated name in the map and pointing to the right object. Define registeredSequenceModuleCreator ← factory object linking a SequenceModule object with its moduleName 5: 6:

Method registerSequenceModuleCreator ▷ defining an iterator to find a module in the factory map

7:

Define iterator to identify a module name in all the created names 8: 9:

Method create ▷ creating a module associated with a name 10:

Reset the space allocated for the module's name 11:

Return pointer to the created module 12: 13:

Method getSequenceModuleTypeNames ▷ returns a list of the modules present in the factory map 14: Define moduleNameList ← an empty list of moduleName objects 15: for all SequenceModule in listOfModules do 16:

Add moduleName to moduleNameList 17:

end for 18:

Return moduleNameList 19: 20: ClassEnd

The GinkgoSequence and GinkgoSequence_UI concepts: putting all together

Along with the GinkgoSequence_UI class, the GinkgoSequence class presented in Pseudo-code 4 is the heart of the sequence. It calls different SequenceModule objects in chronological order and arranges them through time by forming a sequence kernel and looping over it. It implements the mandatory methods to compile a sequence in the IDEA environment: initialize, prepare, check, and run. However, since the run method includes both kernel building and looping structures, an additional runKernel method was added to manage timings in one repetition time, thus using the class' constructor along with the five main methods of GinkgoSequence:

• constructor: calling the SequenceModuleFactory to create modules in chronological order,

• initialize: setting the default parameters and limits for the sequence,

• prepare: defining real-time events by calling the eponymous method for every module,

• check: enabling internal tests from the development kit when necessary,

• runKernel : orchestrating the timing of every module by setting its anchor time for one kernel (eg one repetition time), • run: sewing the sequence together by looping over the runKernel method for several slices, partitions, lines, repetitions, or diffusion orientations.

As this GinkgoSequence class is used to define the chronological organization of the sequence, it can also support accelerated acquisition schemes. This implementation goes through the definition of start-line and end-line indexes, allowing for the definition of appropriate loops for PF and GRAPPA. This mechanism is completed with the addition of a GRAPPA flag, triggering GRAPPA-specific behaviors in the different modules.

The implemented GinkgoSequence modules

Stemming from the top-down hierarchical analysis of pulse sequences, the sequence modules can be separated into six main categories, which have been implemented as children classes of the SequenceModule class. These intermediate classes give birth to specialized modules defined as their child classes. This section describes all the SequenceModule classes implemented in GinkgoSequence, detailing their real-time events and showing them concretely on chronograms. The ExcitationModule class supports 2D and 3D single transmission RF excitation pulses using cardinal sine (SINC) or externally defined waveform envelopes:

Excitation modules

• the SingleTxCardinalSinePulseExcitation2dModule class defines a single 90°SINC pulse with slice selection and refocusing gradients,

• the SingleTxExternalPulseExcitation2dModule class is identical to the previous module with the possibility to import an RF waveform from an external file,

• the SingleTxCardinalSinePulseExcitation3dModule class defines a single 90°SINC pulse with 3D volume selection and refocusing gradients,

• the SingleTxExternalPulseExcitation3dModule class is identical to the previous module with the possibility to import an RF waveform from an external file.

These modules, depicted in Figure 5.3, allow for the generation of classic as well as customized excitation pulses. External pulse waveforms can be generated as text files containing their envelope as points in function of time. To enable the formation of spin echoes, the RefocusingModule class works with the ExcitationModule class by providing SINC and externally defined refocusing RF pulses:

Refocusing modules

• the CardinalSinePulseRefocusingModule class includes a 180°refocusing cardinal sine RF pulse with crushers and slice selection gradients,

• the ExternalPulseRefocusingModule class similarly allows for using an external waveform for the refocusing RF pulse.

Additionally, the SteamModule class contains two 90°RF pulses with their corresponding slice selection, refocusing, and crusher gradients to enable the formation of stimulated echoes. These modules are presented as chronograms in Figure 5.4.

Pre-encoding modules

The PreEncodingModule class provides the necessary reference lines to correct Nyquist N 2 ghosting artifacts when using 2D and 3D EPI as well as EVI readouts, its child classes are: • the EPI2dPreEncodingModule class providing navigators with phase and readout pre-encoding gradients,

• the EPI3dPreEncodingModule class providing navigators with partition, phase, and readout preencoding gradients.

These modules described in Figure 5.5 should be placed just after excitation, ensuring that no phase or partition encoding has been done before their execution.

Reading modules

The ReadingModule class allows for designing sequences using various Cartesian readout schemes, its child classes are:

• the SingleLineReadingModule, which includes a single-line frequency-encoding gradient along with its ADC event,

• the MultiLineEPIReadingModule, which provides an echo-planar reading echo train with no ramp sampling and its associated ADC events, allowing for reading all lines of a slice using alternate up and down trapezoid readout and blipped phase encoding gradients,

• the MultiLineEVIReadingModule, which forms an echo-volumic reading echo train, including features from the MultiLineEPIReadingModule with partition encoding blips and phase fly-back gradients to acquire an entire volume in one excitation.

These reading modules presented in Figure 5.6 are centered around the echo time, allowing their easy implementation in the sequence.

Preparation modules

The PreparationModule class separates into two sub-modules: The single-line readout is done in the simplest way with a pre-encoding to reach the beginning of the line from its center and a readout gradient which should be centered at TE. The EPI and EVI reading modules present their respective echo trains for a small number of acquired lines. Their anchor time is set at the center of the train, i.e. the center of its central readout gradient. When using an even number of lines and slices or partitions, this center is located in the upper half of the indexes. • the SaturationModule class provides a saturation RF pulse centered around a frequency peak along with its gradients,

• the DiffusionModule class includes TrapezoidDiffusionGradientModule, with a pair of trapezoidal diffusion gradients, and ArbitraryDiffusionGradientModule, with free-waveform gradients for the design 109 of any pattern of diffusion gradients.

These very different modules, depicted as chronograms in Figure 5.7, can be used either separately or together. The spoiling gradients in the StandardSpoilingModule class are defined as the crushers of the RefocusingModule classes. In the BalancedSpoilingModule class, they are defined using the pre-encoding part of their corresponding sequence, in order to balance the gradients on each axis (the sum of the areas under all the gradients of one axis is set to 0).

Spoiling modules

The SpoilingModule class provides support for spoiling the signal at the end of a sequence kernel:

• the StandardSpoilingModule class places a crusher gradient on each axis (slice, readout, and phase),

• the BalancedSpoilingModule class introduces spoiler gradients on each axis, designed to provide a balanced sequence in every case proposed in the toolbox.

These optional modules, presented in Figure 5.8, can be placed at the end of any sequence kernel to attenuate or balance the signal before the next excitation.

End modules

Finally, the EndModule class closes one kernel of the sequence by defining the blank time between its last real-time event and the next excitation pulse, thus relying only on the repetition time. This module is mandatory for any sequence; its absence would result in a minimal repetition time for any instance of the sequence.

Summary UML diagram of the GinkgoSequence toolbox

The GinkgoSequence class diagram provided in Figure 5.9 describes seven parent classes standing for the principal categories of SequenceModule and divided into more detailed children modules, which have individually been described with chronograms in the previous subsections. This diagram highlights the top-down hierarchical analysis of pulse sequence programming by providing the inheritance tree of SequenceModule classes with two levels of granularity: the first one defining the general types of events, like excitation or readout, and the second one embodying a concrete expression of these events for specific applications, such as single transmission cardinal sine 2D excitation pulse, or echo-planar readout.

If this implementation of the GinkgoSequence toolbox already includes many features, these could be completed with many other options, such as multiband excitation or FOV saturation modules.

First proof-of-concept: a simple 2D gradient-echo sequence

As a first example, a simple 2D gradient-echo sequence was built in the frame of the top-down hierarchical analysis of pulse sequences implemented in GinkgoSequence. For this example, the sequence is composed of three parts: excitation, readout, and spoiling. The GinkgoGradientEcho2dSequence main class should then include instances of the SequenceModule class, stemming from the ExcitationModule, ReadingModule, and SpoilingModule classes, as well as one from the EndModule class. Descending to the end leaves, these instances originate from the specific SingleTxCardinalSinePulseExcitation2dModule, Sin-gleLineReading2dModule, and StandardSpoilingModule classes. The chronogram presented in Figure 5.10 shows the detailed contents of the obtained sequence, highlighting its four SequenceModule objects and their respective anchor times that correspond to:

• the center of the excitation pulse for the SingleTxCardinalSinePulseExcitation2dModule,

• the center of the readout gradient for the SingleLineReading2dModule,

• the end of the SingleLineReading2dModule for the StandardSpoilingModule,

• and the repetition time for the EndModule. These modules are called in the main GinkgoGradientEcho2d class constructor using the SequenceMod-uleFactory as presented in the source code of Figure 5.11. A name is given for each module, associated with a number corresponding to the chronological order of appearance in the sequence. Then, the create method is called, giving the name of the module of interest in the SequenceModuleFactory, followed by two parameter lists including a collection of double or string parameters.

This constructor is followed by a destructor presented in Figure 5.12, which is simply deleting the user interface.

After the constructor and destructor, the four mandatory methods (initialize, prepare, check, and run) are presented in Figures 5.13 to 5.20.

Figure 5.13 shows the source code of the initialize method, which uses the iterator of the Sequence-ModuleFactory to call the inner initialize method of each module of the sequence. Figures 5.14,5.15,and 5.16 present the three parts of the prepare method. The first part is very similar to the initialize method and calls the prepare method for all modules in the sequence. The second part sets the minimal value for the repetition and echo times, by getting the necessary durations from the modules. The third part sets hardware-specific parameters, defining the gain type and the energy deposit for SAR calculations, along with reconstruction instructions for ICE (which are mandatory but not used in this sequence).

Figure 5.17 presents the check method, and Figure 5.18 describes the run method. The former calls the runKernel method for the extremum lines and checks whether it will run correctly on a simulated MR system. The latter loops over repetitions, slices, and lines, calling the runKernel method that defines one kernel of the sequence, as well as some optional features, managing the real-time feedback and the measurement data header (MDH) information of the sequence.

The echo-volumar acquisition scheme is implemented similarly to the 3D EPI one, alternating the readout trains with partition blips and phase fly-back gradients. It is completed with the same pre-encoding module: EPI3dPreEncodingModule.

GinkgoSequence enables to perform GRAPPA acquisitions with an acceleration factor of 2. It is also spread out between the GinkgoSequence and the SequenceModule classes and includes the definition of multiple metrics. The separation between acquired and skipped lines is done for the even and odd line indices, and the phase encoding is incremented by 2 steps instead of one. For the single-line readout scheme, reference lines are acquired in the same acquisition and tagged in the MDH, while for the EPI readout scheme, they are done in a separate acquisition before the main one.

Stimulated-echoe sequences

Building over the SteamModule class, the GinkgoSequence toolbox includes examples of stimulatedecho-based sequences with single-line or echo-planar readouts:

• the GinkgoSteam2d class, including the following modules: SingleTxCardinalSinePulseExcitation2d-Module, GinkgoSteamModule, SingleLineReading2dModule, StandardSpoilingModule, EndModule;

• the GinkgoSteam2dEPI class, including the following modules: SingleTxExternalPulseExcitation2d-Module, EPIPreEncodingModule, GinkgoSteamModule, MultiLineEPIReadingModule, StandardSpoil-ingModule, EndModule.

Diffusion-weighted PGSE sequences

To prove the usefulness of GingkoSequence in the development of cutting-edge research applications, the focus was made on diffusion-weighted imaging sequences by providing diffusion gradient modules, which can be used for classic trapezoidal gradients or any other waveform, thus paving the way for oscillatinggradients-based sequences (OGSE) or even more complex gradient use, like the ones performed for the acquisition of b-tensors. Therefore, diffusion-weighted sequences that could be compared to the already existing ones were implemented following these rules:

• the implementation of diffusion gradients: any gradient waveform can be used in the framework by providing a diffusion module using arbitrary-shaped gradients. These can be generated using an external file listing the points of the gradient waveform;

• the ergonomy of the diffusion sequence: the smoothness of execution was ensured by implementing a loop on diffusion orientations and setting the diffusion parameters (orientations, b-value, and timings) in an external test file using the INIAccess library from IDEA;

• the compatibility of the obtained data with the in-house Ginkgo diffusion analysis toolbox (available at https://framagit.org/cpoupon/gkg): the data and header are saved so that the different diffusion directions are registered as repetitions in the raw data file, making them compatible with the Ginkgo post-processing pipelines.

For example, the GinkgoSequence toolbox reproduces PGSE schemes with various readout patterns:

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• the GinkgoSpinEcho2dPGSE class, including the following modules: SingleTxCardinalSinePulseEx-citation2dModule, TrapezoidDiffusionGradientModule, CardinalSinePulseRefocusingModule, Single-LineReading2dModule, StandardSpoilingModule, EndModule;

• the GinkgoSpinEcho2dDwEpi class, including the following modules: FatSaturationModule, Sin-gleTxExternalPulseExcitation2dModule, EPI2dPreEncodingModule, TrapezoidDiffusionGradientModule, ExternalPulseRefocusingModule, MultiLineEPIReadingModule, StandardSpoilingModule, End-Module;

• the GinkgoSpinEcho3dDwEpi class, including the following modules: FatSaturationModule, Sin-gleTxExternalPulseExcitation3dModule, EPI3dPreEncodingModule, TrapezoidDiffusionGradientModule, ExternalPulseRefocusingModule, MultiLineEPIReadingModule, StandardSpoilingModule, End-Module;

• the GinkgoSteam2dDwEpi class, including the following modules: FatSaturationModule, SingleTxEx-ternalPulseExcitation2dModule, EPIPreEncodingModule, TrapezoidDiffusionGradientModule, Ginkgo-SteamModule, MultiLineEPIReadingModule, StandardSpoilingModule, EndModule.

Image reconstruction for GinkgoSequence

As important as the pulse sequence itself, the reconstruction process allows for the data to be transformed from the k-space to the image space and to be corrected for artifacts. To complete the GinkgoSequence framework, reconstruction support is mandatory.

The ISMRM raw data format

Before performing reconstruction, the raw data acquired using the GinkgoSequence sequences is in the raw Siemens format and cannot be directly converted at the console into an easily readable format. Therefore, the data must be retrieved from the console and externally converted to the ISMRM Raw data format using the Siemens_to_Ismrmrd package available at https://github.com/ismrmrd/siemens_to_ismrmrd. The MDH was implemented to match the fields of the ISMRMRD header correctly and obtain easily readable k-space data.

Furthermore, to allow for the use of different file formats, we designed a C++ converter to transform the ISMRMRD data to the Nifti or in-house Gis formats. This way, all acquired images can be read using standard neuroimaging tools.

Challenges of open-source reconstruction

For single-line readouts without acceleration, the reconstruction is a simple inverse Fourier transform that can be performed by any mathematical library in many programming languages. However, for accelerated trajectories, the reconstruction comes with more complex algorithms to correct for artifacts, making it more difficult to develop a standalone application with cutting-edge reconstruction algorithms. Therefore, although in-house reconstruction codes in C++ were available, an external reconstruction server was considered to be a more robust option.

To fit the philosophy and requirements of the GinkgoSequence environment, this reconstruction server should implement the following features:

• it should be open-source,

• it should implement efficient reconstruction algorithms for EPI, PF and GRAPPA,

• it should support 2D and 3D reconstructions,

• it should be able to connect with the hardware and to perform online reconstruction. This last point being the most restrictive, as many reconstruction software do not provide an interface with the MRI system's console, the open-source Gadgetron framework presented in section 3.5.5 was used in this work.

The Gadgetron framework

GinkgoSequence can be used with any reconstruction pipeline handling the Siemens raw data format. It should then be possible to use the ICE reconstruction server from Siemens, as well as external solutions such as BART or Gadgetron. As the latter is used by many researchers and provides good support while allowing for online reconstruction, the GinkgoSequence framework has been set to be compatible with it.

By providing both offline and online reconstruction options and including a large panel of reconstruction algorithms for 2D and 3D sequences with both non-Cartesian and Cartesian acquisition schemes, the Gadgetron framework proposes a flexible environment to reconstruct k-space data from custom sequences. Furthermore, it interfaces with the ISMRMRD format that is already supported by the raw data obtained from the GingkoSequence acquisitions. Therefore, because it was practical to implement and because it corresponded to the abovementioned requirement regarding open-source philosophy and online reconstruction, the GinkgoSequence sequences were interfaced with the Gadgetron environment.

This implementation is performed through the tuning of the references used for corrections in EPI, EVI, and GRAPPA cases and the management of the header to match the required fields in the reconstruction pipelines from Gadgetron. To simplify its use, the GinkgoSequence sequences were made compatible with the default reconstruction pipelines as much as possible.

Conclusion

This chapter introduced the GinkgoSequence toolbox by replacing it in the general context of MRI pulse sequence programming and detailing its programming philosophy before presenting its contents. This framework contains all the elementary parts used to build any pulse sequence and proposes specialized modules to support fast and diffusion-weighted acquisition. It is supported by an object-oriented structure relying on an inheritance tree of module classes generated by a factory, on an intermediary class able to combine them into composite modules, and on a main class manipulating them to form a sequence in a way corresponding to the physics and easily understandable using chronograms. The whole GinkgoSequence source code available online (https://framagit.org/cpoupon/gkg/-/tree/master/pulse-sequence) has been developed without using the sequence codes from Siemens and is, therefore, completely open-source and ready to use for other researchers in the field.

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As seen before, the GinkgoSequence framework allows the flexible development of MRI pulse sequences. It is important to assess the quality of its core modules used to generate spin echoes, gradient echoes, and stimulated echoes, along with the modules for single-line and echo-planar readouts. In a preliminary study, prototype sequences were tested on an ex vivo Nyala (a kind of antelope) brain provided in the frame of the Neuro2Co project (coordinated by Dr. Elodie Chailloux, INRAE-Nouzilly). The sequences used for this first test were similar to the ones described in section 5.6.1 with the addition of a FatSaturationModule before excitation and without any acceleration. Using the parameters detailed in Table 6.1, satisfying images were obtained and are shown in Figure 6.1. These were reconstructed using ICE reconstruction as the sequences were not compatible with the Gadgetron framework at the time of their development. This preliminary study hinted that all basic GinkgoSequence modules were correctly working, still it was not sufficient to assess the quality of the images. Therefore, an evaluation was performed for all available features, including gradient, spin, and stimulated echoes generation, single-line, and echo-planar readouts, as well as partial Fourier and GRAPPA features. To cover these cases, the sequences presented previously in section 5.6.1 were used and those which had an equivalent Siemens sequence were compared to it.

Material and methods

The implemented sequences can be separated depending on their tested features:

• GinkgoGradientEcho2d and GinkgoGradientEcho3d for the gradient echo generation with single-line readout in 2D and in 3D,

• GinkgoSpinEcho2d and GinkgoSpinEcho3d for the spin echo generation with single-line readout in 2D and in 3D,

• GinkgoSpinEcho2dEPI and GinkgoSpinEcho3dEPI for the EPI readout in 2D and in 3D,

• GinkgoSteam2d and GinkgoSteam2dEPI for the stimulated echo generation with single-line and EPI readouts. All tests were performed on a 3T Siemens Prisma device, using a 20-channel Tim-Coil Head/Neck coil, on a KH 2 P O 4 /NaCl phantom with a complex structure including grids and gels as presented in Figure 6.2. All images were acquired with a 256 × 256mm 2 field of view (FOV) and an isotropic resolution of 1 × 1 × 1mm 3 . The other parameters presented in Table 6.2 were chosen to be as much comparable as possible with stable TE and TR for an excitation type, coherent readout bandwidth-per-pixel (RBW) for EPI sequences, and matching mixing times (TM) for STEAM sequences.

The Siemens 2D and 3D gradient-echo gre, 2D spin-echo se, and 2D EPI spin-echo ep2d_se product sequences were also timed with similar parameters presented in Table 6.3 for comparison. However, since some of their source codes are not freely available, it was not possible to assess the exact difference between their implementation and the one proposed in GinkgoSequence. This is especially the case with the spin echo 2D EPI sequence, which has a limited readout bandwidth-per-pixel compared to our sequence but reaches similar TE and TR. Indeed, while the readout bandwidth-per-pixel in the GinkgoSequence version was set to its maximum value of 1400Hz/P x, it was limited to 976Hz/P x for the Siemens sequence. This particularity might be due to a difference in implementation using ramp sampling, a higher amplitude of gradients, or hard limitations avoiding mechanical vibrations. For each GinkgoSequence sequence, a series of images were acquired, including a version with no acceleration, followed by five accelerated versions using Partial Fourier (PF) and GRAPPA with an acceleration factor of 2: PF 6/8, PF 5/8, GRAPPA, GRAPPA with PF 6/8, and GRAPPA with PF 5/8. The k-space data was retrieved from the interface of the scanner (TWIX) and transferred to a Gadgetron server for reconstruction, using the standard Generic_Cartesian_Grappa and Generic_Cartesian_Grappa_EPI Gadgetron pipelines already implemented and corresponding to the sequences, as presented in Table 6.4.

The same protocol was applied for Siemens sequences with a version with no acceleration, and an accelerated version using PF 6/8 and GRAPPA R = 2 when available. To ensure a coherent comparison, the reconstruction was performed using the exact same steps as for the GinkgoSequence images and ignoring the provided noise measurement, which were not set in GinkgSequence.

These pipelines are composed as follows:

• the "Generic_Cartesian_Grappa" pipeline including coil compression, GRAPPA algorithm, partial Fourier handling (using POCS), k-space filtering, and image scaling;

• the "Generic_Cartesian_Grappa_EPI" pipeline is identical to the previous one with the addition of an EPI correction feature, including phase correction [START_REF] Ahn | A new phase correction method in nmr imaging based on autocorrelation and histogram analysis[END_REF] and line flipping. [START_REF] Pruessmann | Sense: sensitivity encoding for fast mri[END_REF]:

SNR GRAPPA = SNR g √ R , (6.1)
with SNR GRAPPA the SNR value of an image obtained using GRAPPA, SNR the SNR value of an equivalent image obtained without GRAPPA, R the acceleration factor, and g the geometry factor which depends on the reception profile of the antenna and the acquisition settings. Table 6.5 presents the g factors obtained for our single-line reading sequences. For 2D sequences, a g-factor inferior to 1 was obtained, which is coherent with [START_REF] Robson | Comprehensive quantification of signal-to-noise ratio and g-factor for imagebased and k-space-based parallel imaging reconstructions[END_REF], and for 3D sequences, it still presents values around 1, which is satisfying.

Sequence

SNR analysis of echo-planar readout sequences

The images obtained with the GinkgoSpinEcho2dEPI, GinkgoSpinEcho3dEPI, and GinkgoSteam2dEPI sequences are detailed in Figures 6.9,6.10,and 6.11 respectively, along with their SNRs. For GinkgoSpinE-cho2dEPI, images with decreasing resolution and optimized readout bandwidth are presented in Figure 6.8. As expected from the echo-planar readout, all images present a strong distortion, which is attenuated when decreasing the echo-train length, either using GRAPPA acceleration, decreasing the spatial resolution, or using PF acceleration. In addition to the general distortion due to the echo-train length, more local distortions can be observed, especially at the air-liquid interface, and are due to susceptibility effects. As the ghosting correction is done with only three navigators, it is not perfect, and a residual ghost can be observed on every image.

In conclusion, GRAPPA-accelerated EPI sequences are able to adequately provide images of the phantom, allowing to perfectly render the finer details of its structure. Using EPI, such phantoms always present a worse-case situation than in vivo brains, thus indicating that the GinkgoSequence sequences should give good results on human brains.

Synthesis of SNR results

A summary of the SNR values obtained for each acquisition is presented in Table 6.6. It shows the clearly identifiable and expected gaps between 2D single-line (SNR∼40-70), 3D single-line (SNR∼100-200), 2D echo-planar (SNR∼40-70), and 3D echo-planar (SNR∼70-80) readouts, with a stronger decrease for STEAM sequences.

Comparison with Siemens sequences

To complete this analysis of the GinkgoSequence images, similar acquisitions were performed with comparable Siemens sequence products (gre, se, and ep2d_se) for 2D and 3D gradient-echo, 2D spin-echo, as well as 2D EPI spin-echo sequences with and without acceleration. The obtained images are presented in Figures 6.12,6.13,6.14,and 6.15 respectively. For all sequences, the images obtained using GinkgoSequence were very similar to the ones obtained using Siemens' sequence products., showing the same appearance for all images, and especially similar distortion and ghosting for EPI sequences. Furthermore, the images show an equivalent signal-to-noise ratio for GinkgoSequence images compared to their equivalent Siemens images, as summarized in Table 6.7, which is satisfying.

Conclusion

This chapter presented an SNR study of the basic sequences developed in the GinkgoSequence framework, using the gradient, spin, and stimulated echo 2D and 3D excitations, the single-line and echo-planar readouts, and the standard spoiling modules, along with the acceleration from partial Fourier and GRAPPA with an acceleration factor R = 2. The results showed coherent images with good signal-to-noise ratios, displaying the expected differences between 2D and 3D acquisitions and accelerated/unaccelerated schemes. Furthermore, comparisons to Siemens' sequence products were performed, showing that the GinkgoSequence acquisitions presented similar results with quite comparable artifacts and similar SNR trends. All these observations validated the basic modules for Cartesian acquisition with single-channel excitation and accelerations using the GinkgoSequence framework.

As described in chapter 4 (section 4.2.3), diffusion-weighted MRI (dMRI) has become a key tool for the detection of strokes and the exploration of brain microstructure through a plethora of various biophysical models allowing for the inference of quantitative maps. A popular example of such applications is the inference of structural connectivity relying on the anisotropy of the orientational profile of the displacement probability of water molecules. Fiber tracking methods, together with fiber clustering approaches, have led to the establishment of outstanding atlases of white matter bundles [START_REF] Guevara | Robust clustering of massive tractography datasets[END_REF].

Beyond fiber tracking, the dMRI community has proposed numerous innovations both on the acquisition and modeling sides to transform diffusion-weighted MRI into a fantastic tool to perform non-invasive virtual biopsies addressing clinical applications as well as fundamental research. Most brain diseases are associated with microstructural disorders encouraging the community to develop novel surrogate markers at the cellular level. From a fundamental point of view, mapping the cytoarchitectonics of brain functions might help to better understand their anatomical substrate beyond PGSE. To this aim, various diffusion-encoding schemes have emerged, including oscillating gradient spin echo (OGSE) [START_REF] Does | Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain[END_REF], double encoding, twice refocusing, free-form gradient shapes to implement Matrix formalism [Callaghan, 1997] [Drobnjak et al., 2010] and more recently b-tensors [START_REF] Westin | Measurement tensors in diffusion mri: generalizing the concept of diffusion encoding[END_REF]] [Topgaard, 2017]. The same stands for readout methods, including single-line reading, echo-planar (2D or 3D) reading, with single-shot or multi-shot echo-trains, or sparse sampling approaches like SPARKLING [START_REF] Lazarus | Sparkling: variable-density k-space filling curves for accelerated t2*-weighted mri[END_REF]. Last, alternative schemes to spin echo have been introduced, such as STEAM, balanced SSFP, or turbo spin echo sequences. In this context, it would be constructive to develop a tool designed for dMRI pulse sequence programming that allows for all the new acquisition schemes to be implemented, tested, and shared. Fulfilling this need, a panel of diffusion sequence modules has been implemented in GinkgoSequence, allowing for the generic development of dMRI pulse sequences in its open-source framework. A first proof of concept was made by developing a prototype GinkgoSpinEcho3dDwEpi sequence, including fat saturation, cardinal sine 3D excitation and refocusing, trapezoidal diffusion-weighted gradients, EPI readout, and standard spoiling. This sequence was used on the same ex vivo Nyala brain as presented in chapter 6, with no partial Fourier or GRAPPA acceleration to collect a dataset composed of a T 2 -weighted reference image and N O = 250 diffusion orientations at a b-value of 5000s.mm -2 . The obtained images presented in Figure 7.1 reproduce the anatomy of this brain correctly in the T 2 -weighted image, and the diffusion-weighted images allow for the obtention of a fractional anisotropy (FA) map showing the main tracts of the white matter. The distortion that appears in every image is the classic distortion expected for an EPI echo-train readout without acceleration and could be attenuated by implementing methods that shorten the echo-train length, such as GRAPPA or PF.

These encouraging preliminary results led to the development of further dMRI sequence modules in the GinkgoSequence framework, which are highlighted in the class diagram shown in Figure 7.2. They provide the possibility to add diffusion-weighting gradients with trapezoid or free waveforms and a main sequence class architecture allowing for looping over diffusion orientations described in an external file read on the fly.

To assess the efficiency of the GinkgoSequence toolkit in developing dMRI sequences, a first project targeted the development of a standard 2D pulsed gradient spin echo (PGSE) single-shot EPI diffusionweighted pulse sequence called GinkgoSpinEcho2dDwEpi. This sequence was benchmarked with the reference sequence stemming from the CMRR [Setsompop et al., 2012a] and called CMRR_diff. A second project aimed at the development of a diffusion-weighted STEAM sequence, called GinkgoSteam2dDwEpi, which was compared to the first one.

Material and methods

The GinkgoSpinEcho2dDwEpi and GinkgoSteam2dDwEpi pulse sequences were designed following a similar pattern, including the basic modules for a spin-echo and a STEAM 2D EPI sequences and coupling them with trapezoid diffusion-weighting gradients in a structure allowing to loop over diffusion orientations. This section describes the design of these two sequences and the protocol applied to assess their capacity to provide diffusion-weighted data reflecting the organization of white matter fiber tracts along with quantitative data describing neuritic density.

Design of diffusion-weighted pulse sequences

As described in chapter 5 (section 5.6.4), the GinkgoSpinEcho2dDwEpi sequence was created based on the GinkgoSpinEcho2dEPI sequence, including SingleTxExternalPulseExcitation2dModule, EPIPreEncoding-Module, ExternalPulseRefocusingModule, MultiLineEPIReadingModule, StandardSpoilingModule, and End-Module classes, with the addition of FatSaturationModule and TrapezoidDiffusionGradientModule classes to respectively implement fat saturation (with a saturation bandwidth of 450 Hz centered around -420 Hz from the water peak frequency) for in vivo acquisitions and diffusion weighting for dMRI acquisitions. The same was done for the GinkgoSteam2dDwEpi, which is based on the GinkgoSteam2dEPI sequence and substitutes the ExternalPulseRefocusingModule from the previous sequence with a GinkgoSteamModule. The GinkgoSpinEcho2dDwEpi sequence is described in Pseudo-code 5 and presented as a chronogram in Figure 7.3. The kernel shown in the chronogram is assembled in the main GinkgoSpinEcho2dDwEpi class, including the call of the SequenceModuleFactory to first create each module in chronological order, second enable the use of accelerations through partial Fourier and GRAPPA, and third loop over diffusion orientations using an external file, which is designed as shown in Figure 7.4. From this file, the Trapezoid-DiffusionGradientModule class defines diffusion-weighted gradients and places them in the sequence with respect to the other limits that are internally calculated.

#----------[General] #orientationsCount orientationsCount = 21 <-number of diffusion orientations + reference acquisitions (b=0s/mm²) #----------[Timings] #bigDelta smallDelta bigDelta = 63710 <-difference between the start times of the diffusion encoding and decoding gradients (µs) smallDelta = 3710 <-plateau duration of the trapezoid diffusion gradients (µs) rampTime = 800 <-ramp duration of the trapezoid diffusion gradients (µs) #----------[GradientAmplitudes] #Gx Gy Gz <-amplitudes of the three diffusion gradients based on a spatial representation of diffusion orientations (identical for encoding and decoding) in mT/m amplitudes[0]= 0.0 0.0 0.0 <-First case: b=0s/mm² amplitudes[1]= -25.9941 18.8754 62.1935 <-second case: 20 orientations with b=300s/mm² amplitudes [2] The other parameters of the GinkgoSpinEcho2dDwEpi sequence can be set at the console of the MRI system directly using the graphical interface. This structure contains several features, including parameters for acceleration. An example user interface generated in the IDEA environment is shown in Figure 7.5. It allows tuning classic parameters, such as TE and TR, with respect to hard limitations directly set in the mrProt part of the sequence, and soft parameters calculated to ensure the respect of the sequence timings and to make sure that no conflicting event occurs. These limits are materialized with green bars (see Figure 7.5-a) and are instantly updated when impacting parameters are changed. The accelerated acquisition can be activated in the Resolution tab and necessitate no other change. The readout bandwidth is accessible in the Sequence tab, as well as the parameters for the saturation module, including its flip angle, its center frequency offset (from the peak water frequency), and its number of iterations.

With the setting of sequence parameters in the user interface, the acquisition field of view is placed either at the isocenter or at an off-centered position, allowing for the acquisition of the diffusion-weighted images scheduled in the orientation file. These images are extracted as raw k-space data from the scanner (using the "TWIX" interface) and include a measurement data header (MDH) containing all key information for reconstruction: matrix sizes, number of lines and slices, enabled acceleration modes, and number of navigators. This MDH file is accompanied by the main measurement data (MD) containing the raw measurements as well as information concerning each of them, like their role as a phase correction or parallel imaging reference line and their labeling as reversed lines for echo-planar readout schemes. These data are converted to the ISMRMRD format, which translates the information from both MDH and MD, allowing for their reconstruction using the Generic_Cartesian_Grappa_EPI pipeline from the Gadgetron environment.

Design of the 2D STEAM DW EPI sequence

Using the same structure, the GinkgoSteam2dDwEpi sequence presents very similar features as clarified in Pseuldo-code 6. Its chronogram is detailed in Figure 7.6. It shows the SteamModule instance that is anchored around its center and defines a mixing time (TM) during which the net magnetization of the spins is tilted to the longitudinal plane and starts a T 1 regrowth, thus preserving the signal for the duration of TM. With the second RF pulse, the net magnetization is returned to its original transverse state, allowing for a measurement of a stimulated echo. However, these manipulations of the net magnetization are not perfect and result in the signal losing half of its intensity. This STEAM sequence presents an interesting application for dMRI as it can be used to preserve the signal during the diffusion time. Thus, the GinkgoSpinEcho2dDwEpi sequence implements TrapezoidDiffu-sionGradientModule instances before the first and after the second RF pulses of the SteamModule instance. This design allows for the use of narrower diffusion gradients with a longer diffusion time, which reduces the minimal possible TE. For flexibility and as presented in Figure 7.7, the mixing time can be set directly in the user interface of the GinkgoSteam2dEpi sequence, which is identical to the one of the GinkgoSpinE-cho2dDwEpi for other settings.

Similarly to the previous protocol comparing the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences, the images can be retrieved from the scanner using the TWIX interface and converted to the ISMRMRD format along with their MDH information. They are then reconstructed using the same Generic_ Carte-sian_Grappa_EPI pipeline in the Gadgetron environment.

Benchmarking the GinkgoSequence diffusion-weighted sequences

To assess the performances of the GinkgoSpinEcho2dDwEpi and GinkgoSteam2dDwEpi sequences, they were tested on two healthy volunteers on a Siemens 3T Prisma scanner with a 20-channel Head/Neck antenna using a 3-shell dMRI protocol.

General methodology

The volunteers were recruited in the frame of the 3T methodological protocol of the NeuroSpin research institute (CEA, Gif-sur-Yvette), which respects ethical values and personal information. The recruitment only criteria for this protocol were to be healthy and aged between 20 and 40 years old.

In order to be able to run advanced microstructure models, a 3-shell HYDI [START_REF] Wu | Hybrid diffusion imaging[END_REF]] protocol was designed using the parameters summarized in Table 7.1 and Figure 7.8. This protocol includes 20 orientations at b = 300s.mm -2 , 30 orientations at b = 1200s.mm -2 , and 60 orientations at b = 2500s.mm -2 . The diffusion orientations were generated using the general energy-minimization electrostatic model proposed in [START_REF] Dubois | Optimized diffusion gradient orientation schemes for corrupted clinical dti data sets[END_REF]. Each b-value (i.e. each shell) also implemented one b = 0s.mm -2 T 2 -weighted anatomical acquisition for reference. The images were retrieved as raw data from the acquisition system and reconstructed using the Generic_ Cartesian_Grappa_EPI pipeline from Gadgetron. They were then converted to the in-house Gis format to

Post-processing based on diffusion models

In order to assess the quality of the data acquired with GinkgoSequences and validate their usability for the establishment of whole-brain in vivo connectomics and quantitative microstructure, the in-house C++based Ginkgo software (https://framagit.org/cpoupon/gkg), interfaced with a Python wrapper was used. A pipeline including a pre-processing step before applying diffusion models was implemented as described in Figure 7.9. To prepare the images for the application of diffusion models, a pre-processing protocol was implemented. All data were flipped to fit the anatomical standards using a Flipping module, denoised using a non-local means algorithm with a NonLocalMeansFiltering module, masked to isolate the brain from the background noise using binary thresholding (Binarizer module), followed by morphological operations such as dilatation, erosion, and closing with a MorphologicalOperation module, and corrected from Eddy currents artifacts using an EddyCurrentCorrection module.

The prepared images were then processed with the three diffusion models. First, the diffusion tensor imaging (DTI) [START_REF] Basser | Mr diffusion tensor spectroscopy and imaging[END_REF] model was used to provide classic quantitative maps (fractional anisotropy (FA), mean diffusivity (ADC), parallel and transverse diffusion coefficients) using a LocalModel-ingDTI module. Second, the neurite orientation and dispersion density imaging (NODDI) [START_REF] Zhang | Noddi: practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF] model was used in a NoddiMicrostructureField module to evaluate the neurite (i.e. dendrites in gray matter and axons in white matter) density and orientation dispersion in the brain with their associated metrics: neurite density index (NDI), orientation dispersion index (ODI) and κ. Third, the analytical q-ball imaging (QBI) model [Tuch, 2004] [Descoteaux et al., 2007] was applied with a LocalModelingQBI module using a spherical harmonics order of 2 and a Laplace-Beltrami regularization factor of 0.006 to compute generalized FA (GFA), its color-encoded direction (CED), and ODF diffusion orientation distribution functions (ODFs) within each voxel, able to disentangle fiber crossings. The results were qualitatively and quantitatively compared with SNR and histogram measures.

To go further, the ODF maps were used to compute tractograms (composed of several million fibers) based on a streamline regularized deterministic (SRD) tractography algorithm [Perrin et al., 2005a] with 8 seeds per voxel, implemented in Ginkgo as a TractographySRD module. The obtained tractograms were then projected into the MNI space [START_REF] Fonov | Unbiased nonlinear average age-appropriate brain templates from birth to adulthood[END_REF]] [Fonov et al., 2011] (mean representation of the human brain obtained with 152 subjects and being used as a reference for comparisons among brain images) using an MNIRegistration module to identify their fiber bundles and label them using the fiber labeling approach from [START_REF] Guevara | Automatic fiber bundle segmentation in massive tractography datasets using a multi-subject bundle atlas[END_REF] (identifying similar fibers which are close to each other using a distance threshold) with 21 re-sampling points on the Ginkgo-Chauvel atlas [START_REF] Chauvel | Ginkgo Chauvel's deep white matter atlas of the human brain[END_REF] with a LongFiberLabellingSRD module. As a summary, the complete Ginkgo post-processing pipeline is illustrated in Figure 7.10.

Results and discussion

The GinkgoSpinEcho2dDwEpi and GinkgoSteam2dDwEpi sequences were imported on a Siemens Prisma 3T MRI system and acoustic noise measurements were carried out, ensuring that the sequence is safe for the subject, besides being automatically monitored for SAR and stimulation levels. The two comparisons were performed on two healthy volunteers. The first subject was imaged with the GinkgoSpinEcho2dEpi and the CMRR_diff sequences, while the second was acquired with the GinkgoSteam2dDwEpi and GinkgoSpinE-cho2dDwEpi sequences.

This section presents the raw results and their dMRI analysis using quantitative maps and tractograms for each GinkgoSequence and reference sequences and discusses their ability to provide accurate fiber tracking and neurite information for diffusion-weighted MR studies.

Benchmarking of the GinkgoSpinEcho2dDwEpi sequence

First, dMRI images were acquired with the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences using the protocol and parameters described in sections 7.2.2.1 and 7.2.2.2. Raw images were post-processed with the Ginkgo diffusion pipeline described in section 7.2.3.

Raw data

The raw images obtained with GinkgoSpinEcho2dDwEpi and the reference sequence are presented respectively in Figures 7.11 and 7.12, which show the anatomical T 2 -weighted reference along with diffusionweighted coronal slices corresponding to four orientations for each shell of the acquisition protocol.

The images obtained using GinkgoSequence look very similar to the ones acquired using the CMRR_diff sequence:

• the observed anatomical characteristics are identical,

• the distortions stemming from the EPI echo-train readout are similar,

• the level of noise for each shell is comparable.

The SNR values for each shell and each pulse sequence are presented in Table 7.6. They show that the images from the GinkgoSpinEcho2dDwEpi sequence and those from the reference sequence present the same order of magnitude for the SNR, which corroborates the similarities already observed in the images. The maps obtained for the two sequences with the DTI and QBI models are presented in Figure 7.13. All of them show very coherent results, highlighting the white matter tracts in the brain of the subject. More precisely:

• the ADC maps show similar contrasts, reflecting the mobility of the water molecules;

• the FA and GFA maps depict the same patterns with a very high anisotropy in the corpus callosum, a high anisotropy for the cortico-spinal tracts, and a low anisotropy in the cortex and basal ganglia, which correctly highlights the white matter structures' high anisotropy due to the tubular pattern of axons;

• the parallel and transverse diffusivities also emphasize this organization with a higher parallel diffusivity and lower transverse diffusivity in white matter, and a mean value for both of them in weak anisotropy or crossing regions;

• the GFA color-encoded direction (CED) map adequately renders the principal diffusion directions, with the cortico-spinal tracts depicted in blue (vertical-dorsal direction) going down from the cortex to the brainstem, red corpus callosum commissure linking the two hemispheres, and green anterior and posterior longitudinal fasciculus communicating between different cortex areas.

These results are very similar for the two sequences, showing correctly the same brain structures, with almost no noticeable difference. The only disparity is caused by the automatized masking of the brain, which included CSF in some areas of the image (around the brainstem, for instance) in the CMRR_diff images and did not include it in the GinkgoSpinEcho2dDwEpi images.

To confirm the visual results, corresponding histograms of ADC, FA, D P arallel , D T ransverse , and GFA are presented in Figure 7.14. All present similar profiles for the two sequences, with almost identical peak values. Minor amplitude differences can be observed, still staying in the same order of magnitude. These results confirm the very high similarities between the images obtained with the two sequences, thus validating their use for DTI and QBI quantitative mapping.

Similarly, the quantitative maps obtained with the NODDI model are displayed in Figure 7.15. They correctly depict the NDI, ODI, and κ distributions in the observed brain, showing a lower ODI in the main white matter tracts corresponding to a high NDI and being coherent with the intra-axonal diffusion happening in axons bundles. The images obtained with GinkgoSequence are again very similar to the ones acquired with the CMRR_diff sequence.

Corresponding histograms of the NDI, neurite ODI, and κ are shown in Figure 7.16 and depict similar distributions for the NDI and κ maps, as well as a similar but slightly shifted shape for the orientation dispersion. As these results remain comparable among sequences, they further validate the pertinence of the GinkgoSpinEcho2dDwEpi sequence for the analysis of neurites orientation with the NODDI model. The Q-ball ODF maps obtained with the GinkgoSpinEcho2dDwEpi sequence are presented in Figure 7.17, and those obtained with the CMRR_diff sequence are shown in Figure 7.18. Their lobes depict local orientations in agreement with the known underlying anatomy of white matter, especially showing the crossing of the corpus callosum (red) and the cortico-spinal tracts (blue). As expected from the previous observations, the results obtained with the two sequences are comparable.

Tractograms computed from ODF maps corresponding to the two sequences are displayed in Figure 7.29 (top). The axial view correctly depicts the corpus callosum (red) between the two hemispheres of the brain; the coronal view highlights the cortico-spinal tracts (blue) and the corpus callosum (red), and the sagittal view shows the midsagittal representation of the corpus callosum (red) as well as the corona radiata (blue). All these structures can be observed alike for the GinkgoSpinEcho2dDwEpi and the CMRR_diff sequences.

The labeled version of these tractograms is presented in Figure 7.29 (bottom). These images identify coherently 15 white matter fiber tracts (right and left versions) based on the Ginkgo-Chauvel atlas, with the exception of the anterior commissure, which is small enough to be difficult to detect with the used resolution. All deep white matter tracts depicting associative fiber bundles like the arcuate fasciculus, as well as projection fiber bundles such as the cortico-spinal fasciculus, are depicted. The quality of the tracts varies slightly among versions, with, for instance, the left arcuate fasciculus being thinner for the reference and thicker for the GinkgoSequence image. However, these small variations that are likely due to the acquisition and post-processing conditions (like subject movement, field inhomogeneities, and imperfections in the brain mask) between acquisitions do not hamper the similarity of the other tracts. fiber bundles were inferred using a streamlined deterministic tractography algorithm with 8 seeds per voxel. They are presented with a color encoding stemming from their directions: red corresponds to the left-right axis, blue to the top-bottom axis, and green to the antero-posterior axis. In the three views and for the two sequences, the corpus callosum can be correctly identified in red, which is representative of its cross-hemisphere right-left position. In both coronal views, the corticospinal tracts are correctly highlighted in blue for their top-down path from the cortex to the brainstem. In sagittal views, the corona radiata is visible for both sequences, with a bluish color corresponding to its mainly top-down pathways. [START_REF] Guevara | Automatic fiber bundle segmentation in massive tractography datasets using a multi-subject bundle atlas[END_REF] approach on the Ginkgo-Chauvel atlas of long white matter fibers, these images present the fiber fasciculus identified in the previously shown tractograms. With the exception of the anterior commissure, which is too small to be detected here, all the main fiber tracts of the human brain have been identified and colored similarly for the two sequences, thus showing the ability of the GinkgoSpinEcho2dDwEpi sequence to provide trustworthy data for the analysis of white matter fiber bundles.

7.3.2 Benchmarking of the GinkgoSteam2dDwEpi sequence Second, dMRI images were acquired with the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences using the protocol and parameters described in sections 7.2.2.1 and 7.2.2.3. The raw images were post-processed with the Ginkgo diffusion pipeline described in section 7.2.3.

Raw data

Similarly to the first test, the raw images acquired using the GinkgoSteam2dDwEpi and its equivalently set GinkgoSpinEcho2dDwEpi sequences are presented respectively in Figures 7.21 and 7.22. If the general rendering is close for the two sequences, the conserved contrast is not identical, which was expected with the different echo times used for the two acquisitions, leading to dissimilar contrasts, and is not due to the sequence. Nonetheless, the images are of very similar quality, which is confirmed by the SNR analysis presented in Table 7.7 and shows similar SNR for the two sequences. This result was expected from the protocol settings, aiming at erasing the 1/2 ratio between the signal obtained in STEAM and the signal obtained in SE. 7.27 and 7.28 show the ODF fields obtained using the QBI model with GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences respectively. The obtained orientation distributions are quite similar for the two sequences, and the corpus callosum (red), as well as the cortico-spinal tracts (blue), can be correctly identified in the axial, coronal, and sagittal views.

The tractograms computed using these ODF maps are presented in figure 7.29 for both sequences. Comparatively to the images obtained in the first test, the same commissural structure and fiber tracts can be identified in the different views. Furthermore, the views obtained from the STEAM and SE sequences look very similar.

The white matter bundles identified after fiber labeling with the Ginkgo-Chauvel deep white matter atlas are shown in Figure 7.30. Although the labeling algorithm failed to identify the left arcuate fascicle in the STEAM version, which is likely due to an error in masking leading to an accumulation of small holes interrupting the tracts and could be corrected with further optimization of the masking and labeling process, all the other fascicles were correctly reconstructed for both versions (with the exception of the anterior commissure, which is too small to be detected at the used resolution).

By demonstrating the capacity of the GinkgoSteam2dDwEpi sequence to generate coherent white matter fiber bundles and to identify them using an atlas, these results validate its use in deep white matter fiber studies. sequences. These fiber bundles were inferred using a streamlined deterministic tractography algorithm with 8 seeds per voxel. They are presented with a color encoding stemming from their directions: red corresponds to the left-right axis, blue to the top-bottom axis, and green to the antero-posterior axis. In the three views and for the two sequences, the corpus callosum can be correctly identified in red, which is representative of its cross-hemisphere right-left position. In both coronal views, the corticospinal tracts are correctly highlighted in blue for their top-down path from the cortex to the brainstem. In sagittal views, the corona radiata is visible for both sequences, with a bluish color corresponding to its mainly top-down pathways. the application of a fiber labeling algorithm following the [START_REF] Guevara | Automatic fiber bundle segmentation in massive tractography datasets using a multi-subject bundle atlas[END_REF] approach on the Ginkgo-Chauvel atlas of long white matter fibers, these images present the fiber fasciculus identified in the previously shown tractograms. With the exception of the anterior commissure, which is too small to be detected here, and the arcuate fasciculus, whose detection has been hampered by holes in the brain mask, all the main fiber tracts of the human brain have been identified, and colored similarly for the two sequences, thus showing the ability of the GinkgoSpinEcho2dDwEpi sequence to provide trustworthy data for the analysis of white matter fiber bundles.

Conclusion

All the images acquired in this protocol were of sufficient quality to perform dMRI analysis based on multiple diffusion models. In comparison with the reference sequences, the results were almost identical, thus validating the features of GinkgoSequence for diffusion-weighted imaging with 2D accelerated EPI acquisition, STEAM acquisition, and trapezoidal diffusion-weighting gradients.

Although further testing would be needed to assess the quality of the results obtained from equivalent 3D sequences or with free waveform diffusion-encoding gradients, these results show the potential of the GinkgoSequence toolkit in producing efficiently new diffusion-weighted MRI pulse sequences by replacing or upgrading the already existing modules and sequence structures. Indeed, it will allow to efficiently combine any kind of diffusion gradient and readout trajectory, paving the way for innovative dMRI sequences based on recent models like b-tensors and complex acquisition schemes such as SPARKLING.

Introduction

Echo-volumar imaging (EVI) is an MRI readout technique allowing for the acquisition of a whole 3D volume after one excitation. First presented by [START_REF] Mansfield | Echo-volumar imaging (evi) of the brain at 3.0 t: first normal volunteer and functional imaging results[END_REF], it is a 3D generalization of the echoplanar readout scheme, alternating echo-train readouts with partition blips. Although it has tremendous potential for ultra-fast imaging, EVI has not been a very popular method in the past years due to the important distortions it generates in both phase and partition directions. Indeed, without strong gradients and proper acceleration, even a very small field of view acquired at low resolution does not provide a satisfying image of the target object. To overcome this limitation, accelerations stemming from partial Fourier encoding [Heid, 1995] and parallel imaging techniques [START_REF] Witzel | Single-shot echo-volumar imaging using highly parallel detection[END_REF] in the two directions can be implemented. These methods allowed for the obtention of interpretable low-resolution images, thus opening the field for further applications using EVI.

As the EVI readout allows for the acquisition of one volume in 150 to 200ms, which corresponds to the acquisition time of one slice with EPI readout, it presents a great interest for research in fMRI and dMRI applications. As presented in previous studies such as [START_REF] Rabrait | High temporal resolution functional mri using parallel echo volumar imaging[END_REF]] [Posse et al., 2012], EVI pulse sequences allow to lower the time resolution by a factor of 10 in fMRI acquisitions, enabling a better sampling of the BOLD signal and thus an improved distinction of brain activations. Combined with a diffusion-weighting scheme, EVI would also open the way to innovative techniques by providing an improved diagnosis for strokes in clinical routine. Indeed, the current clinical protocols only acquire 3 diffusion orientations leading to the computation of a pseudo-ADC due to time constraints. With EVI, it would be possible in the same time to acquire 20 diffusion orientations which would enable the computation of more accurate models. Furthermore, this diffusion-weighted EVI sequence design could allow for the implementation of more advanced models for quantitative mapping of brain microstructure by increasing ten times the number of diffusion orientations or b-values acquired in a single protocol.

As it is not currently used in clinical routine, there is no available EVI product sequence from MRI manufacturers. The only existing versions are prototypes designed by researchers, which are not always freely accessible and modifiable. To enable its potential in both clinical and research applications, it would be convenient to provide the community with a flexible implementation of the EVI pulse sequence, enabling all the proper acceleration schemes and allowing for the implementation of diffusion-weighting gradients.

In this chapter, the development of such an EVI pulse sequence in the GinkgoSequence framework is described, highlighting the possibilities it offers for fMRI and dMRI. To assess the quality and potential of the developed sequence, preliminary results on an ex vivo anatomical sample are shown, highlighting the already working functionalities of the sequence while pinpointing the need for further developments.

Material and methods

The implementation of an EVI sequence has been done in the GinkgoSequence framework to enable its modular use with the other features proposed in its environment, including diffusion-weighting gradients. This section presents the development of the GinkgoSpinEcho3dEVI sequence using the SequenceModule classes and its application to the acquisition of ex vivo images. A GinkgoSpinEcho3dEVI pulse sequence was developed using the GinkgoSequence toolbox. As described on the chronogram presented in Figure 8.1, it includes SingleTxExternalPulseExcitation3dModule, EPI3dPreEncodingModule, ExternalPulseRefocusingModule, MultiLineEVIReadingModule, StandardSpoil-ingModule, and EndModule instances. The MultiLineEVIReadingModule was created to describe a one-shot 3D trajectory (presented in Chapter 2, section 2.1.2) made of echo-planar readouts linked with partition blips and phase flybacks to obtain the same data organization as for 3D EPI data. With this architecture clarified in Figure 8.2, the EPI3dPreEncodingModule class can be used to generate reference lines for phase correction, exactly the same way it is used for a 3D EPI sequence.

Implementation of a 3D spin-echo EVI pulse sequence

The main difference between EVI and 3D EPI schemes is the amount of data acquired in one excitation:

• the 3D EPI echo-train readout provides the k-space data for one partition in one excitation,

• the EVI echo-train readout provides the k-space data for several partitions in one excitation.

This property makes the EVI acquisition way faster than with the EPI readout, reducing the acquisition time from minutes to seconds. For instance, with a TR of 200ms for an EPI sequence, a volume including 10 partitions is acquired in 2s, whereas with an EVI readout, the same volume is acquired in 200ms. However, this spectacular acceleration comes with a cost, as the distortions already present in EPI accumulate in both phase and partition directions when using the EVI scheme.

A solution is to reduce the echo train by cumulating several methods:

• decreasing the spatial resolution to keep the number of phase and partition encoding steps small,

• applying partial Fourier in both phase and partition directions,

• reinforcing GRAPPA acceleration using acceleration factors greater than 2 and generalizing it in both phase and partition directions,

• adding FOV saturation bands allowing to keep a high spatial resolution on a smaller field of view without generating aliasing artifacts.

Aiming to propose the best quality of EVI imaging, the GinkgoSpinEcho3dEVI sequence should implement all these features and thus obtain readable and interpretable images in a very short time.

The first part of this development involved reproducing the GinkgoSpinEcho3dEPI sequence with an echo-volumar readout train. This implementation already included the phase partial Fourier and GRAPPA (R = 2) options. To complete this scheme and enable quicker acquisitions, the partial Fourier acceleration was also implemented in the partition direction, following the same protocol as for the phase partial Fourier:

• a slice partial Fourier factor was defined in the main GinkgoSpinEcho3dEVI class and in the Sequence-Module class,

• from this factor, a start partition index was computed and used to reduce the echo train directly in the sequence structure,

• to do so, the involved modules (mainly the readout module) were modified to implement conditions based on this start line index.

As for the phase partial Fourier acceleration, the partition partial Fourier settings were made available directly at the console in the same part of the user interface as depicted in Figure 8.3. Pseudo-code 7 summarizes this implementation by presenting the differences with the GinkgoSequence generic pseudocode introduced in chapter 5 (section 5.3.4). Due to the phase fly-back gradients, partitions are not alternatively reversed (like for the reversed lines in EPI). Thus, the same Generic_Cartesien_Grappa_EPI Gadgetron reconstruction pipeline as for GinkgoSpinEcho2dEPI and GinkgoSpinEcho3dEPI can be used for GinkgoSpinEcho3dEVI. Furthermore, since this pipeline includes both phase/partition partial Fourier and GRAPPA features, it can be used for all further developments on this EVI pulse sequence.

If the current version of the GinkgoSpinEcho3dEVI pulse sequence only implements GRAPPA in the phase direction with an acceleration factor of 2, its future releases will implement a generalized version with a more adaptable acceleration factor and an option to apply it in the partition direction. These versions will also support FOV saturation to bring more flexibility to the acquired reduced field of view.

The implementation of GRAPPA in the partition direction will be done following a similar approach to the one used for GRAPPA in the phase direction:

• definition of GRAPPA-specific start and end indexes,

• definition of a GRAPPA-usage boolean,

• creation of specific cases in the readout modules to implement correctly the acceleration based on the newly defined indexes and the boolean flag.

However, this would not be enough if the acceleration factor stays at 2. This implementation will be upgraded with the definition of a floating point acceleration factor and the adaptation of the conditional events in the readout modules to correctly adapt the gradient's number and amplitudes. Furthermore, based on the SaturationModule class, a FOV saturation module will be built, providing the ability to saturate bands of signal, thus isolating a smaller region of interest. The implementation of this module will result in the possibility of acquiring a significantly shorter echo train in a wisely chosen part of the imaged object, thus improving the performances of the EVI sequence for both temporal and spatial aspects.

Preliminary testing of the GinkgoSpinEcho3dEVI sequence

To assess the usability of the EVI echo-train readout in more complex applications, a simple GinkgoSpinE-cho3dEVI implementation was made following the method described in the last section (with a GRAPPA acceleration of 2 and a partition/phase partial Fourier factor of 5/8). This sequence was tested on a Siemens 3T Prisma device with a 20-channel head coil on an ex vivo human brain left hemisphere immersed in a phosphate-buffered saline (PBS) solution. For comparison, an equivalent image was acquired with the GinkgoSpinEcho3dEPI pulse sequence. As partial Fourier in the partition direction is not yet implemented in this 3D EPI sequence, the full k-space was sampled along the partition direction (with a partial Fourier factor of 8/8). The acquisition parameters for both sequences are presented in Table 8.1, and their respective minimal durations are presented in Table 8 8.1 obtained in their user interfaces. TE min stands for the minimal possible echo time, TR min for the minimal possible repetition time between two consecutive excitations, and TA min for the minimum possible acquisition time. For the EPI scheme, one TR corresponds to the acquisition of one partition, while for the EVI scheme, it corresponds to the acquisition of all partitions. Combined with the extra-acquisition time generated by the GRAPPA reference line acquisition, the actual TA corresponds to 2 TRs for EVI acquisitions and to twice the number of partitions times TR for EPI acquisitions. These timings show the difference between EVI and EPI acquisitions: the EPI scheme can achieve shorter TE and TR but acquire only one partition, which results in a longer TA, while the EVI scheme is subject to longer TE and TR, which includes the acquisition of multiple partitions, thus obtaining a much shorter TA.

The minimal durations describe the potential of the EVI acceleration technique over its EPI counterpart: the acquisition of multiple partitions in one repetition time induces a significantly shorter global acquisition time. While performing a protocol with multiple acquisitions, this duration reduction becomes tremendously important. For instance, if a dMRI protocol with 30 orientations was applied with the parameters described in these tables (with minimal timings) for an EPI sequence, it would take at least 3.2s to acquire one image and then 1min36s to acquire 30 orientations. With the EVI sequence, the exact same protocol will only take 6s to acquire.

Results and discussion

The images obtained with the current version of GinkgoSpinEcho3dEVI (including slice/phase PF and GRAPPA R = 2) and GinkgoSpinEcho3dEPI pulse sequences following the protocol described in the previous section are presented in Figure 8.4. They show that the GinkgoSpinEcho3dEVI sequence correctly reproduces the shape of the brain with no ghosting artifact similarly to the GinkgoSpinEcho3dEPI sequence. However, more artifacts, due to accumulated phase errors of the image in the partition direction, do not allow a correct visualization of the fine anatomical structures of the brain.

In addition, the brain hemisphere was immersed in PBS, resulting in the presence of higher flow artifacts, which also contribute to the accumulation of further phase errors during the EVI echo train. The EVI scheme used in this preliminary test is not accelerated enough to reach the best performances. This will be solved by implementing GRAPPA in the partition direction with a higher acceleration factor and by reducing the acquisition FOV using saturation bands.

Still, these images hint that a further accelerated sequence will deliver good-quality images and will be suitable to be used in more complex fMRI or dMRI studies. Indeed, such an accelerated acquisition could bring a new dimension to stroke detection with dMRI by allowing the acquisition of more diffusion directions in a few seconds, enabling more accurate quantitative inferences of the DTI model. Furthermore, it would enable the use of higher time resolutions for functional imaging, opening the way to more precise interpretation of real-time activations.

Conclusion

This chapter presented the development of the GinkgoSpinEcho3dEVI pulse sequence, including an echovolumar readout and accelerations with PF in both slice and phase direction as well as GRAPPA in phase direction only. It showed preliminary results that already depict the shape of the imaged object correctly and can be improved with the implementation of echo-train shortening solutions.

With its capacity to acquire one volume for one excitation, the GinkgoSpinEcho3dEVI sequence has great potential in improving acquisition-time-related protocols, such as the ones used for dMRI or fMRI. Further development of this sequence will include the implementation of generalized GRAPPA acquisitions and FOV saturation, opening the way to the development of a diffusion-weighted GinkgoSpinEcho3dDwEvi pulse sequence combining the EVI echo-train readout with diffusion-encoding gradients. This sequence should provide the basis for a new protocol enabling ultra-fast dMRI acquisitions for more accurate detection with a preserved acquisition time. realistic the development of interactive functional protocols embedding biofeedback to establish the next generation of innovative functional paradigms. These developments and studies have been presented through communications in international and national conferences. The first prototype was presented as a poster at the International Society for Magnetic Resonance in Medicine (ISMRM) annual conference and as a poster and an oral presentation at the Organization for Human Brain Mapping (OHBM) annual conference in 2022. The advanced version, including the development and testing of the diffusion-weighting tools, has been presented as a poster presentation at the ISMRM and OHBM annual conferences in 2023, and as a poster and short oral presentation at the french society for magnetic resonance in Biology and Medicine (SFRMBM) bi-annual conference in 2023, where it received the best poster presentation award.

Upcoming work

The development of an object-oriented and open-source environment for MRI pulse sequence development on Siemens systems enables the development and sharing of source codes independently from the vendor while allowing for using all the features available on their systems. This contribution opens the way for faster and generic development of innovative pulse sequences in this frame, thus facilitating their dissemination and sharing.

Since the toolbox has been optimized for diffusion-weighted imaging, it will be improved in the next years to fit state-of-the-art dMRI protocols, including multi-band excitations and arbitrary gradient waveformbased methods. Furthermore, the ultra-fast acquisitions using EVI will be used in diffusion-weighted as well as in fMRI protocols. These advances should enable improved real-time features for these two modalities by drastically improving their time resolution.

Another development axis will include the implementation of specialized readout gradients for compressed sensing methods like SPARKLING. Recent developments by the team of P. Ciuciu have shown that the combination of EVI Cartesian and SPARKLING sampling of the k-space might be optimal to accelerate the collection of k-space information. As the EVI sequence has already been developed, it should be straightforward to modify it to add further SPARKLING trajectories and to propose ultrafast sequences benefiting from both high temporal and spatial resolutions.

As the GinkgoSequence toolbox has been developed and tested on a 3T system, it will be imported on other machines, including ultra-high field machines at 7T and 11.5T (Iseult). This will lead to further developments, optimizing MRI and dMRI pulse sequences for ultra-high fields by integrating novel sequence modules, for instance, to implement efficient parallel transmission techniques. It should then prove its portability and its capacity to sustain new development in the Iseult environment.

Furthermore, since the toolbox is freely available online (https://framagit.org/cpoupon/gkg/-/tree/ master/pulse-sequence), it is strongly hoped that GinkgoSequence will be used by other research groups, thus building a community of open-source pulse sequence developers. Their participation would widen the fields of application of the framework and reveal its potential for more sharable and reproducible research works.

Titre:

  Développement d'un nouvel environnement open-source et modulaire pour la programmation de séquences IRM optimisé pour l'IRM de diffusion Mots clés: Séquences IRM, IRM de diffusion, programmation open-source Résumé:

5

  Diagramme de classes de l'environnement GinkgoSequence. . . . . . . . . . . . . . . . . . 6 Comparaison entre les séquence d'écho de gradient avec lecture simple de GinkgoSequence et de Siemens. (RSB: rapport signal sur bruit) . . . . . . . . . . . . . . . . . . . . . . . . 7 Procédure d'acquisition et d'analyse des données pondérées en diffusion. . . . . . . . . . . 1.1 A simplified view of a spinning particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 A sample of spins with and without magnetic field. . . . . . . . . . . . . . . . . . . . . . 1.3 Net magnetization M reacting to magnetic fields B 0 and B 1 . . . . . . . . . . . . . . . . 1.4 NMR relaxation times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 A schematic view of the difference between 2D and 3D acquisitions. . . . . . . . . . . . . 1.6 Examples of RF waveform envelopes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Generation of echoes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Gradient coil hardware. The RF excitation pulse is played by the RF emitter and receptor, which also receives the signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9 Spatial encoding in MRI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10 MR signal plots explaining the different contrasts. . . . . . . . . . . . . . . . . . . . . . . 1.11 The inversion-recovery (IR) technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.12 Chronogram of a gradient echo sequence, characterized by its echo time TE and repetition time TR (time between two consecutive excitations). . . . . . . . . . . . . . . . . . . . . 1.13 Chronogram of a spin echo (SE) sequence, characterized by its echo time TE and repetition time TR (time between two consecutive excitations). . . . . . . . . . . . . . . . . . . . . 1.14 Chronogram of a fast spin echo (FSE or RARE) sequence with an echo train length (ETL) of 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. 3

 3 Flowchart of an NMR experiment performed with the ODIN framework. . . . . . . . . . . 3.4 Screenshot of the SequenceTree user interface showing the tree window (left), parameter window (top right), and pulse diagram window (bottom right). . . . . . . . . . . . . . . . 3.5 Overview of the Pulseq environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Gadgetron architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Macroscopic anatomy of the human brain. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Schematic view of a neuron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Schematic view of neuroglia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Internal anatomy of the human brain presenting basal ganglia and white matter fibers. . . 4.5 Axial, coronal, and sagittal T 1 -weighted images of the brain. . . . . . . . . . . . . . . . . 4.6 MR contrasts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Chronogram of the MP-RAGE sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Schematic view of an MP-RAGE compared to an MP2RAGE sequence. . . . . . . . . . . . 4.9 Sample of a Hemodynamic Response Function (HRF) for one subject in the right primary motor cortex M1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Example of an fMRI image showing activated areas. . . . . . . . . . . . . . . . . . . . . . 4.11 Diffusion of water molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Diffusion weighting process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Chronogram of a Pulsed Gradient Spin Echo (PGSE) sequence. . . . . . . . . . . . . . . . 4.14 Hindered diffusion in white matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15 q-space sampling for different diffusion models, in chronological order. . . . . . . . . . . . 4.16 Example of a tractogram computed using a deterministic tractography algorithm on a healthy volunteer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17 Chronogram of a diffusion-weighted balanced steady-state free precession (DW-bSSFP) sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

viii 4 .

 4 18 A variety of gradient waveform designs using the b-tensor model[START_REF] Westin | Measurement tensors in diffusion mri: generalizing the concept of diffusion encoding[END_REF] in a spin-echo sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Generic UML diagram of a sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Generic SequenceModule composed of four real-time events. . . . . . . . . . . . . . . . . 5.3 Chronograms representing the details of the ExcitationModule's child classes implemented in the GinkgoSequence toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Chronograms representing the details of each RefocusingModule's child class, along with the SteamModule class of the GinkgoSequence toolbox. . . . . . . . . . . . . . . . . . . . . . 5.5 Chronograms representing the details of each PreEncodingModule class of the GinkgoSequence toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Chronograms representing the details of each ReadingModule class of the GinkgoSequence toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Chronograms representing the details of each PreparationModule class of the GinkgoSequence toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Chronograms representing the details of each SpoilingModule class of the GinkgoSequence toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Class diagram of the GinkgoSequence framework. . . . . . . . . . . . . . . . . . . . . . . 5.10 Chronogram of the GinkgoGradientEcho2d sequence. . . . . . . . . . . . . . . . . . . . . 5.11 Source code of the constructor method in the GinkgoGradientEcho2d class. . . . . . . . . 5.12 Source code of the destructor method in the GinkgoGradientEcho2d class. . . . . . . . . . 5.13 Source code of the initialize method in the GinkgoGradientEcho2d class. . . . . . . . . . . 5.14 Source code of the prepare (part 1) method in the GinkgoGradientEcho2d class. . . . . . . 5.15 Source code of the prepare method (part 2) in the GinkgoGradientEcho2d class. . . . . . . 5.16 Source code of the prepare method (part 3) in the GinkgoGradientEcho2d class. . . . . . . 5.17 Source code of the check method in the GinkgoGradientEcho2d class. . . . . . . . . . . . 5.18 Source code of the run method in the GinkgoGradientEcho2d class. . . . . . . . . . . . . . 5.19 Source code of the runKernel method (part 1) in the GinkgoGradientEcho2d class. . . . . 5.20 Source code of the runKernel method (part 2) in the GinkgoGradientEcho2d class. . . . . 5.21 Source code of the createUI and getUI methods in the GinkgoGradientEcho2d class. . . . 6.1 Preliminary images obtained with a first prototype of GinkgoSequence on an ex vivo Nyala brain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 KH 2 P O 4 /NaCl phantom used for sequence testing. . . . . . . . . . . . . . . . . . . . .

7. 1

 1 Preliminary results on an ex vivo Nyala brain with a diffusion protocol using 250 orientations at a b-value of 5000s.mm -2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Class diagram of the GinkgoSequence toolbox, highlighting in red its dMRI-oriented tools. . 7.3 Chronogram of the GinkgoSpinEcho2dDwEpi sequence, highlighting its modular architecture. 7.4 External text file defining the specific parameters for diffusion-weighting gradients in GinkgoSequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Screenshots of the graphical user interface for the GinkgoSpinEcho2dDwEpi pulse sequence. 7.6 Chronogram of the GinkgoSteam2dDwEpi sequence, highlighting its modular architecture. . 7.7 User interface of the GinkgoSteam2dEpi. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Graphic representation of the q-space sampling used for the 3-shell HYDI diffusion protocol. 7.9 Details of the diffusion post-processing pipeline implemented in the Gingko framework. . . 7.10 Summary of the post-processing pipeline used to assess the quality of the GinkgoSequence images for dMRI qualitative and quantitative analysis. . . . . . . . . . . . . . . . . . . . . 7.11 Raw data for a 3-shell diffusion-weighted acquisition using GinkgoSpinEcho2dDwEpi on a healthy volunteer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.12 Raw data for a 3-shell diffusion-weighted acquisition using the CMRR_diff sequence on a healthy human volunteer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.13 Maps obtained with GinkgoSpinEcho2dDwEpi and the comparative reference sequence showing in the axial, coronal, and sagittal views apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), and transverse diffusivity (D T ransverse ) based on the DTI model, along with generalized fractional anisotropy (GFA) and color-encoded diffusion direction (CED) based on the QBI model. The images correctly render the information about white matter fiber tracts and are similar for the two sequences. . . . . . . . . . . . 7.14 Histograms of the apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), transverse diffusivity (D T ransverse ), and generalized fractional anisotropy (GFA) values for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. . . . 7.15 Quantitative maps obtained with GinkgoSpinEcho2dDwEpi and the comparative CMRR_diff reference sequence showing in the axial, coronal, and sagittal views neurite density index (NDI), orientation dispersion index (ODI), and κ concentration based on the NODDI model. 7.16 Histograms of the neurite density index (NDI), orientation dispersion index (ODI), and kappa values for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. . . . . . . . . . . . . 7.17 ODF maps for the GinkgoSpinEcho2dDwEpi sequence. . . . . . . . . . . . . . . . . . . . 7.18 ODF maps for the CMRR_diff sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.19 Tractograms (T 2 in background) for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. 7.20 Labeled tractograms for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. . . . . .

x 7 .

 7 21 Raw data for a 3-shell diffusion-weighted acquisition using GinkgoSteam2dDwEpi on a healthy volunteer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.22 Raw data for a 3-shell diffusion-weighted acquisition using GinkgoSpinEcho2dDwEpi to compare with GinkgoSteam2dDwEpi on a healthy volunteer. . . . . . . . . . . . . . . . . . . . 7.23 Quantitative maps obtained with GinkgoSteam2dDwEpi and the comparative reference GinkgoSpinE-cho2dDwEpi sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.24 Histograms of the apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), transverse diffusivity (D T ransverse ), and generalized fractional anisotropy (GFA) values for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.25 Maps obtained with GinkgoSteam2dDwEpi and the comparative reference GinkgoSpinE-cho2dDwEpi sequence showing in the axial, coronal, and sagittal views neurite density index (NDI), orientation dispersion index (ODI), and κ concentration based on the NODDI model. 7.26 Histograms of the neurite density index (NDI), orientation dispersion index (ODI), and kappa values for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. . . . . . . . 7.27 ODF maps for the GinkgoSteam2dDwEpi sequence. . . . . . . . . . . . . . . . . . . . . . 7.28 ODF maps for the reference GinkgoSpinEcho2dDwEpi sequence. . . . . . . . . . . . . . . 7.29 Tractograms (T 2 in background) for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.30 Labeled tractograms for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. 8.1 Chronogram of the GinkgoSpinEcho3dEVI sequence for 3 partitions. . . . . . . . . . . . . 8.2 EVI trajectory for 3 partitions, highlighting the phase flyback process. . . . . . . . . . . . 8.3 User interface of the GinkgoSpinEcho2dEVI sequence. . . . . . . . . . . . . . . . . . . . . 8.4 Sagittal reconstructed images obtained for 3 partitions (3, 5, 7) with the GinkgoSpinE-cho3dEVI and the GinkgoSpinEcho3dEPI sequences of the same ex vivo human brain. . . . used for the preliminary study of single-line readout sequences. . . . . . . . . . 6.2 Parameters used for the evaluation of GinkgoSequence basic sequences. . . . . . . . . . . 6.3 Parameters used for the evaluation of Siemens basic sequences. . . . . . . . . . . . . . . . 6.4 Gadgetron reconstruction pipeline used for each example sequence of the GinkgoSequence framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 g-factors for all single-line reading GinkgoSequence acquisitions. . . . . . . . . . . . . . . 6.6 SNR measures obtained for single-lines, EPI, and STEAM GinkgoSequence images with different acceleration schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 SNR comparison between GinkgoSequence and Siemens sequences. . . . . . . . . . . . . . 7.1 3-shell HYDI dMRI protocol used to test the GinkgoSpinEcho2dDwEpi and GinkgoSteam2dDwEPI sequences on healthy volunteers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Acquisition parameters used for GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. . . . 7.3 Diffusion parameters for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. . . . . . 7.4 Acquisition parameters used for GinkgoSteam2dDwEpi and the GinkgoSpinEcho2dDwEpi sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Diffusion parameters for the GinkgoSteam2dDwEpi sequence. . . . . . . . . . . . . . . . . 7.6 SNR values for the raw data of the first test. . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 SNR values for the second test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Acquisition parameters for the GinkgoSpinEcho3dEVI and GingkoSpinEcho3dEPI sequences. 8.2 Minimal timing parameters for the GinkgoSpinEcho3dEVI and GingkoSpinEcho3dEPI sequences using the parameters of Table

Figure 1 :

 1 Figure 1 : Représentation schématique de l'intérieur d'un système d'acquisition IRM (entouré par un aimant générant un fort champ magnétique). Ce schéma présente les différents éléments nécessaires à l'encodage spatitaldu signal ainsi qu'à sa génération et sa réception. Image adaptée de[Coyne, 2012].

Figure 2 :

 2 Figure 2 : Chronogramme d'une séquence d'acquisition IRM en écho de gradient avec lecture simple.

Figure 4 :

 4 Figure 4 : Images IRM anatomiqes dans les vues axiale, coronale et sagittale. Ce sont les vues couramment utilisées par les radiologues dans les routines cliniques. Images adaptées du cours d'IRM (Centrale-Supelec) donné par Cyril Poupon.

Figure 5 :

 5 Figure 5 : Diagramme de classes de l'environnement GinkgoSequence. Les modules permettent l'assemblage en ordre chrnologique de nombreuses séquence d'acqusition IRM libres de droit utilisant l'environnement de développement de Siemens.

Figure 6 :

 6 Figure 6 : Comparaison entre les séquence d'écho de gradient avec lecture simple de GinkgoSequence et de Siemens. (RSB: rapport signal sur bruit)

Figure 7 :

 7 Figure 7 : Procédure d'acquisition et d'analyse des données pondérées en diffusion. (DTI: imagerie du tenseur de diffusion, NODDI: imagerie de l'orientation et de la dispersion des neurites, QBI: imagerie Q-ball).

Contents 1 . 1

 11 Nuclear magnetic resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Nuclear magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Magnetic resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Spatial encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Two-dimensional and three-dimensional excitations . . . . . . . . . . . . 1.2.2 The design of radio-frequency pulses . . . . . . . . . . . . . . . . . . . . 1.2.3 NMR signals: from free induction decay to stimulated echoes . . . . . . . 1.2.4 Spatial encoding using gradients . . . . . . . . . . . . . . . . . . . . . . 1.2.4.1 Two-dimensional encoding . . . . . . . . . . . . . . . . . . . . 1.2.4.2 Three-dimensional encoding . . . . . . . . . . . . . . . . . . . 1.2.5 Contrast mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Pulse sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Gradient echo and spin echo sequences . . . . . . . . . . . . . . . . . . . 1.3.2 Fast gradient echo and spin echo sequences . . . . . . . . . . . . . . . . 1.3.3 2D and 3D sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 From k-space to image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 Artifacts linked to the acquisition method . . . . . . . . . . . . . . . . . 1.5.2 Artifacts linked to the hardware . . . . . . . . . . . . . . . . . . . . . . . 1.5.3 Artifacts linked to the subject . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1

 1 Figure 1.1 : A simplified view of a spinning particle, giving birth to a spin angular momentum

Figure 1 . 2 :

 12 Figure 1.2 : A sample of spins with and without magnetic field. In absence of a magnetic field, spins are oriented in a random direction. When a magnetic field is applied along an axis, spins tend to align, either positively or negatively, along this axis. Adapted from the lecture on MRI physics (Centrale-Supelec), courtesy of Cyril Poupon.

Figure 1 . 3 :

 13 Figure 1.3 : Net magnetization M reacting to magnetic fields B 0 and B 1 . (a) In the presence of the static magnetic field B 0 applied along the z-axis, the net magnetization M is aligned with this same axis and precesses around it. This rotation allows for the definition of a rotating frame based on the z-axis and the corresponding x and y axes forming an orthonormal referential. (b) When a rotating B 1 magnetic field is applied concomitantly to B 0 , the net magnetization M is tilted from an angle θ and starts precessing around both axes, thus describing a spiraled trajectory. (c) In this situation, it is possible to decompose the net magnetization vector M along the three axes of the rotating frame, with its projections on x, y, and z: M x , M y , and M z .

  Figure 1.4 : NMR relaxation times. (a) Regrowth of the longitudinal magnetization M L , 63% of the maximal M 0 value is reached at the relaxation time T 1 . (b) Attenuation of the transverse magnetization M T , 37% of the maximal M 0 value is reached at the relaxation time T 2 . (c) Actual attenuation of the transverse magnetization M T , accelerated by magnetic field inhomogeneities and corresponding to the T * 2 relaxation time when 37% of the maximal M 0 value is reached. (d) During this T * 2 relaxation, the transverse relaxation signal measured by the reception coils is called the free induction decay (FID).

Figure 1 . 5 :

 15 Figure 1.5 : A schematic view of the difference between 2D and 3D acquisitions. (a) For a 2D acquisition, the slice-selective excitation covers the width of a slice, corresponding to an excitation bandwidth. Each excitation corresponds to a unique slice and the sum of all the slices forms the acquired volume. (b) For a 3D acquisition, the full volume is excited by the 3D excitation, corresponding to a larger bandwidth than for slices. This volume is then partitioned using a phase encoding in the z-axis.

Figure 1 . 6 :

 16 Figure 1.6 : Examples of RF waveform envelopes. (a) The rectangular waveform envelope is used to generate hard pulses, which are non-spatially selective. (b) The cardinal sine waveform is used for many classic excitation pulses but reaches its limits due to the non-linearities of the Bloch equations. (c) The Shinnar-Leroux waveform[START_REF] Shinnar | The synthesis of pulse sequences yielding arbitrary magnetization vectors[END_REF]][Pauly et al., 1991] allows for overcoming this limitation and optimizing the RF pulse for its applications.

Figure 1 . 7 :

 17 Figure 1.7 : Generation of echoes. (a) A gradient echo is generated using an excitation pulse with dephasing and rephasing gradients. The first gradient disperses the phases of the spins, and the second inverses this trend giving birth to an echo signal. (b) In a spin echo generation scheme, a 90°excitation pulse sets the spins in phase and is followed by an FID signal characterized by a fanning out of the spins. A 180°refocusing pulse inverts this movement, thus retrieving the FID signal as an echo. (c) A stimulated echo is generated using 3 or more RF pulses. This diagram shows the behavior of the spin's phase ϕ when three 90°RF pulses are applied. The red line corresponds to the first

Figure 1 . 8 :

 18 Figure 1.8 : Gradient coil hardware. The RF excitation pulse is played by the RF emitter and receptor, which also receives the signal. The spatial encoding is played by the three gradient coils G Slice , G Read , and G P hase . This structure is inserted at the center of the larger magnet generating the B 0 field. Adapted from[Coyne, 2012].

  Figure 1.10 : MR signal plots explaining the different contrasts. (a) A proton-density (ρ-density) weighting is generated when a short TE is coupled with a long TR. At this time, the longitudinal regrowth is complete and the transverse relaxation has not started, yielding a signal only contrasted by the differences in proton densities among tissues. A T 2 -weighting is obtained when a long TE is used together with a long TR, allowing for the transverse relaxation to happen, thus contrasting the signals depending on their transverse relaxation time T 2 . (b) A T 1 contrast is generated with short TE and TR, which causes the interruption of the longitudinal regrowth, thus contrasting the signal based on their longitudinal relaxation time T 1 . The case when TE is long with a short TR

  (a) Using a 180°RF pulse to tilt M L in its plane: the signal originates from M T , so it is not affected. (b) M L regrowth in SE, showing a difference between 3 tissues. (c) M L regrowth in SE with IR, showing a larger difference between the same tissues.

Figure 1 .

 1 Figure 1.11 : The inversion-recovery (IR) technique. (a) Applying a first 180°inversion pulse before the excitation tilts the longitudinal magnetization, leading to the obtention of a larger spin echo signal. (b) Without IR, the signal is bounded between 0 and M 0 , leading to the obtention of classic T 1 relaxation times for the different tissues. (c) With IR, this signal is contained between -M 0 and M 0 , yielding larger and more spaced T 1 relaxation times for the same tissues.

Figure 1 .

 1 Figure 1.12 : Chronogram of a gradient echo sequence, characterized by its echo time TE and repetition time TR

Figure 1 .

 1 Figure 1.13 : Chronogram of a spin echo (SE) sequence, characterized by its echo time TE and repetition time TR

Figure 1 .

 1 Figure 1.14 : Chronogram of a fast spin echo (FSE or RARE) sequence with an echo train length (ETL) of 4. This sequence is composed of a 90°excitation pulse with its slice selection and refocusing gradients, followed by four repetitions of spin-echo generation and single-line readouts with different phase encoding gradients allowing for the rapid acquisition of four different lines using four spin echoes as clarified in the signal diagram.

Figure 1

 1 Figure 1.15 : Chronogram of a GRE sequence using 2D or 3D excitation with a cartesian space encoding. (a) For the 2D excitation, a large slice selection gradient corresponding to a narrow excitation bandwidth is used. (b) For the 3D excitation, the excitation bandwidth is wider, leading to the use of a small volume-selection gradient, which is coupled with a partition encoding gradient on the same axis.

Figure 1

 1 Figure 1.16 : MR image reconstruction (a) The raw MR data obtained in the Fourier domain is called k-space. By performing an inverse Fourier transform (IFT) on it, a complex image is reconstructed, which can be separated into its magnitude (b) and phase (c) images. Adapted from Allen D. Elster, MRIquestions.com

Figure 1

 1 Figure 1.17 : Example of MRI artifacts. (a)(b)(c)(d) are linked to the acquisition method, (e)(f)(g)(h)(i)(j) are linked to the hardware, and (k)(l) are linked to the subject. Images: (h)(i)(j) adapted from C. Poupon[Poupon, 1999]; others adapted from Allen D. Elster, MRIquestions.com.

  Figure 2.1 : Single-line and single-shot echo-planar readouts. The red dotted lines correspond to the pre-encoding necessary to start the acquisition at the beginning of the line. (a) The single-line readout trajectory starts from the center of the k-space and covers it line by line. (b) The trajectory for the echo-planar imaging (EPI) readout starts from the center of the k-space and covers it with a single shot by reading a line, going over to the next line, reading it in a reversed way, and so on.

Figure 2 . 2 :

 22 Figure 2.2 : Chronogram of a spin echo sequence with EPI readout and pre-encoding. This sequence is composed

Figure 2 .

 2 Figure 2.3 : Post-processing and correction of imaging artifacts with EPI. (a) The raw k-space data obtained with an EPI sequence presents reversed lines due to the acquisition trajectory and a shifted center caused by hardware imperfections, which can be respectively observed as symmetric and horizontal ghostings in the image reconstructed using a simple IFT. (b) The first artifact can be suppressed by flipping the reversed lines, thus obtaining an image with only a Nyquist N 2 ghosting due to the shifted centers. (c) This ghosting can be attenuated by correcting this dephasing using navigator echoes.

Figure 2 . 4 :

 24 Figure 2.4 : Same phantom as in Figure 2.3a, acquired using the same spin echo 2d EPI sequence, with acceleration from GRAPPA (R = 2) and partial Fourier (6/8): the image is showing less distortions.

Figures 2 .

 2 3-c all show the same distortion artifact, which is due to the nature of the EPI acquisition train. It uses a very low bandwidth in the phase direction to acquire many lines in a reduced time, creating stronger distortions in regions with substantial magnetic susceptibility variations, like air/tissue interfaces, and magnetic field variations due to imperfections in the hardware or concomitant fields. Since the phantom used for this figure has many air-water interfaces, with a large bubble of water at its bottom, the distortion is particularly severe. It is possible to reduce it by decreasing the echo spacing or the echo train length, which is usually done using other acceleration methods like partial Fourier or GRAPPA, as shown in Figure2.4, which will be discussed later in this chapter, or by increasing the readout bandwidth, at the price of a lower signal to noise ratio.

Figure 2 . 5 :

 25 Figure 2.5 : Example of EVI trajectory with 5 partitions. The red dotted line from the center corresponds to the general pre-encoding to the start of the trajectory. The other red dotted lines correspond to the change of partition (blip), followed by the phase fly-back going to the start of the next EPI trajectory.

Figure 2 . 6 :

 26 Figure 2.6 : Chronogram of an echo-volumar imaging (EVI) sequence. It is composed of the same elements as the EPI sequence, with an EVI echo-train readout replacing the EPI echo-train readout. This part is composed of partitions, phase, and readout pre-encoding gradients, and is followed by alternated readout trains with phase blips, separated by partition blips and phase fly-back gradients, thus describing an EVI trajectory.

Figure 2 . 7 :

 27 Figure 2.7 : Comparison between a full and an accelerated acquisition using partial Fourier (PF). (a) Acquired with full sampling, the k-space is read line-by-line. (b) Using PF, only part of the k-spaced is acquired.

8 Figure 2 . 8 :

 828 Figure 2.8 : 2D spin-echo images of a phantom acquired without (a) and with 6/8 partial Fourier (b). The fully sampled image is very similar to the PF image, which has been reconstructed using the projection onto convex sets (POCS) algorithm.

Figure 2 .

 2 Figure 2.9 : Three-shot Cartesian EPI trajectory. The segmentation of the EPI trajectory allows for a rapid acquisition (although longer than the single-shot one) showing less distortion than its single-shot counterpart.

Figure 2 .

 2 Figure 2.10 : K-space contrast and details. (a) When the full k-space is sampled, an image with accurate contrasts and details can be reconstructed. (b) If only the center of the k-space is acquired, the corresponding image will only render the main contrast. (c) Inversely, acquiring only the edges of the k-space leads to the reconstruction of details only. (d) As there is less information at the extremities of the k-space, choosing an optimized disc in the k-space leads to an accurate reconstruction of the image. Images: courtesy of Philippe Ciuciu

Figure 2 .

 2 Figure 2.12 : Chronogram of a spiral spin echo sequence scheme. This sequence includes all the classic elements of a spin echo sequence, with a spiral readout scheme composed of lobes of readout and phase gradients alternating and growing in intensity to describe the spiral trajectory.

  Figure 2.13 : PROPELLER trajectories. (a) The single-line readout PROPELLER trajectory is based on the use of cartesian readout blades rotated around the center of the k-space. (b) It is possible to implement the PROPELLER method with EPI readouts instead of single-line readouts to form the acquisition blades.

Figure 2 .

 2 Figure 2.14 : Parallel imaging. Compared to the full k-space sampling (a), the parallel-imaging sampling (b) is based on the acquisition of one line over an acceleration factor R. However, this technique requires reference lines to compute the missing ones, leading to the design of (c) with fully sampled central lines in the parallel-imaging acquisition scheme.

Figure 2 .

 2 Figure 2.15 : The basic GRAPPA algorithm shown schematically using four blocks and an acceleration factor R of 2. The missing lines are approximated by computing weights out of acquired/unacquired line blocks. Adapted from[START_REF] Griswold | Generalized autocalibrating partially parallel acquisitions (grappa)[END_REF]

  Figure 2.16 : Comparison between reconstructed images obtained with and without parallel imaging. (a) The full k-space sampling shows the phantom correctly. (b) A parallel imaging acquisition without correction shows a ghosted image of the phantom. (c) A parallel imaging acquisition with central reference lines corrected using the GRAPPA algorithm satisfyingly restores the phantom's image.

Figure 2 .

 2 Figure 2.17 : Principles of compressed sensing. (a) An MR image can be compressed into a lighter format like JPEG by reducing it to meaningful information only. (b) Compressed-sensing takes this logic backward by acquiring only a sampling of meaningful information before reconstructing the image, thus drastically reducing the acquisition time.

Figure 2 .

 2 Figure 2.18 : A schematic view of multiband imaging using only coil encoding for slice discrimination. Multiple slices are excited using a composite multiband RF pulse and their complex signal is decoupled using coil encoding with classic phase and readout gradients.

Figure 2 .

 2 Figure 2.19 : Generation of SPARKLING trajectories for different initializations and target densities. These trajectories are represented along with their point spread functions (PSF). Stemming from classical trajectories likeCartesian (a), radial (b), or spiral (c), SPARKLING trajectories are computed using a target density and specific hardware constraints. Adapted from[START_REF] Lazarus | Sparkling: variable-density k-space filling curves for accelerated t2*-weighted mri[END_REF]

Contents

3. 1

 1 Pulse sequence programming tools . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Real-time events scheduler . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Programming environments . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Programming paradigms . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3.1 Procedural programming . . . . . . . . . . . . . . . . . . . . . 3.1.3.2 Object-oriented programming . . . . . . . . . . . . . . . . . . . 3.1.3.3 A choice linked to the programming language . . . . . . . . . . 3.2 Reconstruction tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Raw data management . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Key features for image reconstruction . . . . . . . . . . . . . . . . . . . 3.3 The Siemens environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 MRI pulse sequence development environment (IDEA) . . . . . . . . . . . 3.3.2 Reconstruction and post-processing system . . . . . . . . . . . . . . . . . 3.3.3 Limitations imposed by the manufacturer . . . . . . . . . . . . . . . . . . 3.4 Open-source pulse sequence development kits . . . . . . . . . . . . . . . . . . . 3.4.1 The ODIN framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 The SequenceTree environment . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 The PulSeq cross-platform interface . . . . . . . . . . . . . . . . . . . . 3.4.4 The KSFoundation library . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Open-source reconstruction frameworks . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 The Berkeley advanced reconstruction toolbox (BART) . . . . . . . . . . 3.5.2 The Gadgetron framework . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3 . 1 :

 31 Figure 3.1 : Operational diagram of procedural vs. object-oriented programming. Procedural programming is based on global variables that are modified and used by general functions in procedures. Object-oriented programming is based on the flexibility and instanciablilty of classes that serve as molds for objects and can be structured using inheritance. Adapted from https://openclassrooms.com/

Figure 3 . 2 :

 32 Figure 3.2 : A minimal dataset in the ISMRMRD file format. The XML header includes all information necessary for

Figure 3 . 3 :

 33 Figure 3.3 : Flowchart of an NMR experiment performed with the ODIN framework. The sequence source code is developed using the C++ sequence programming interface and is transferred to different MR platforms or simulation tools to generate raw k-space data, which is then reconstructed using the data processing interface.Adapted from[Jochimsen and Von Mengershausen, 2004]

Figure 3 . 4 :

 34 Figure 3.4 : Screenshot of the SequenceTree user interface showing the tree window (left), parameter window (top right), and pulse diagram window (bottom right).The tree presents a top-down hierarchical decomposition of the sequence as simple elements. The parameter window allows for the modification of parameters that is executed directly on the sequence code. The pulse diagram window shows a simulation of the sequence that is updated in real-time when changes are applied. Adapted from[START_REF] Magland | Pulse sequence programming in a dynamic visual environment: Sequencetree[END_REF]

Figure 3 . 5 :

 35 Figure 3.5 : Overview of the Pulseq environment. Stemming from a Matlab, Python, or JEMRIS source, a Pulseq sequence file is transferred to different interpreters allowing for its playing on the corresponding MR systems.Adapted from[START_REF] Layton | Pulseq: a rapid and hardware-independent pulse sequence prototyping framework[END_REF]

Figure 3 . 6 :

 36 Figure 3.6 : Gadgetron architecture.The raw ISMRMRD data is going through a Gadgetron pipeline in the shape of a message, that is modified by Gadgets performing elementary reconstruction events. Adapted from[START_REF] Hansen | Gadgetron: an open source framework for medical image reconstruction[END_REF]

  (a) Human brain anatomy. Adapted from www.informedhealth.org (b) Cerebrum lobes. Adapted from J. Sobotta (1909) and radiopaedia.org

Figure 4 . 1 :

 41 Figure 4.1 : Macroscopic anatomy of the human brain. (a) The human brain is composed of the cerebrum, the cerebellum, the diencephalon, and the brainstem. (b) The cerebrum can be separated into four lobes: frontal, temporal, occipital, and temporal, which are completed by an inner insular lobe.

Figure 4 . 2

 42 Figure 4.2 : Schematic view of a neuron. A neuron is a brain cell composed of a cell body including a nucleus,

Figure 4 . 3 :

 43 Figure 4.3 : Schematic view of neuroglia. Astrocytes are responsible for maintaining the blood-brain barrier and providing structural and metabolic support for neurons. Oligodendrocytes generate and maintain the myelin sheath around axons. Ependymal cells generate and regulate the cerebrospinal fluid (CSF). Microglial cells protect the other brain cells against pathogens and are responsible of neurogenesis in the adult brain. Adapted from human-memory.net

Figure 4 . 4 :

 44 Figure 4.4 : Internal anatomy of the human brain presenting basal ganglia and white matter fibers. (a) The brain is composed of gray matter, which is located mainly in the cortex and in the deep structures and is mostly made of neuronal bodies, and of white matter, which is included in the inner parts of the brain and mostly made of axons. These axonal structures form fiber fascicles in the white matter, which can be separated into association, commissural, and projection fibers. (b) The basal ganglia are inner structures of the brain and are part of the gray matter.

Figure 4 . 5 :

 45 Figure 4.5 : Axial, coronal, and sagittal T 1 -weighted images of the brain. These views are conventionally used by radiologists to observe the human brain in clinical protocols. Adapted from the lecture on MRI physics (Centrale-Supelec), courtesy of Cyril Poupon.

Figure 4 . 6 :

 46 Figure 4.6 : MR contrasts. These contrasts are obtained using the TE and TR settings to weight the image with a predominant contribution of the T 1 or T 2 relaxation times as well as proton density (ρ) of the imaged tissues in the final rendering. (a) The T 1 -weighted signal presents a contrast close to the anatomical images, with white matter appearing white, gray matter appearing gray, and CSF appearing black. (b) Inversely, the T 2 -weighted images present a lighter gray matter than white matter and a bright CSF. (c) The ρ-weighted images present a similar contrast than T 2 -weighted images with a darker CSF.Adapted from[Hot, 2021]

Figure 4 . 7 :

 47 Figure 4.7 : Chronogram of the MP-RAGE sequence. This sequence starts with a 180°inversion pulse, followed by a repeated structure including a 3D excitation RF pulse and a single-line readout. This structure allows for the fast acquisition of multiple lines by generating a new spin echo at each excitation.

Figure 4 . 8 :

 48 Figure 4.8 : Schematic view of an MP-RAGE compared to an MP2RAGE sequence. The MP2RAGE sequence acquires two different images with different inversion times to compute a quantitative map (qT 1 ) in addition to the T 1 -weighted image. Adapted from Allen D. Elster, MRIquestions.com

Figure 4 . 9 :

 49 Figure 4.9 : Sample of a Hemodynamic Response Function (HRF) for one subject in the right primary motor cortex

Figure 4 .

 4 Figure 4.10 : Example of an fMRI image showing activated areas. This image has been generated in an experiment showing a visual stimulus to the participant. The activated areas identified through the BOLD signal correspond to visual processing and working memory, which was expected with a visual stimulus. Courtesy of Bastien Herlin.

  Diffusion of colored ink particles in a glass of water (b) Brownian motion

Figure 4 .

 4 Figure 4.11 : Diffusion of water molecules. (a) When added to a glass of water, colored ink particles diffuse following the Brownian motion of water molecules. (b) This motion is governed by Fick's laws which describe the interaction between water molecules. Images adapted from the lecture on MRI physics (Centrale-Supelec), courtesy of Cyril Poupon.

Figure 4

 4 Figure 4.12 : Diffusion weighting process. Two cases are presented: the first when no diffusion occurs, and the

Figure 4 .

 4 Figure 4.13 : Chronogram of a Pulsed Gradient Spin Echo (PGSE) sequence. This classic diffusion-weighted sequence is a spin-echo sequence with diffusion-weighting gradients inserted before and after the refocusing part. These gradients are characterized by their ramp time ξ, their plateau duration δ, and the time separating their starts ∆. Their amplitude is different on each axis and is linked with the diffusion orientation.

  .10) with G = [G x , G y , G z ] the diffusion-encoding gradient vector. q is linked to the b-value by equation 4.11: b = |q| 2 τ,(4.11)

Figure 4 .D

 4 Figure 4.14 : Hindered diffusion in white matter. As the white matter is mainly composed of axons, it can be modeled as tubes, showing the hindered diffusion process inside and outside them. Adapted from the lecture on MRI physics (Centrale-Supelec), courtesy of Cyril Poupon.

Figure 4 .

 4 Figure 4.15 : q-space sampling for different diffusion models, in chronological order. From the pulsed gradient spin echo (PGSE) to the multiple-shell models. This figure illustrates diffusion-weighted imaging, which needs 3 orientations to compute mean diffusivity; diffusion tensor imaging (DTI) which relies on 6 orientations to compute a diffusion tensor; diffusion spectrum imaging (DSI) which uses a probability density function to describe crossing fibers; high angular resolution diffusion imaging (HARDI) which can be single-or multiple-shell with each shell corresponding to one b-value; and hybrid diffusion imaging (HYDI) which is multiple-shell, including different diffusion directions for each shell.

Figure 4 .

 4 Figure 4.16 : Example of a tractogram computed using a deterministic tractography algorithm on a healthy volunteer. This rendering shows the white matter pathways as fibers forming identifiable tracts. Courtesy of Cyril Poupon.

Figure 4 .

 4 Figure 4.17 : Chronogram of a diffusion-weighted balanced steady-state free precession (DW-bSSFP) sequence.

Figure 4 .

 4 Figure 4.18 : A variety of gradient waveform designs using the b-tensor model[START_REF] Westin | Measurement tensors in diffusion mri: generalizing the concept of diffusion encoding[END_REF] in a spin-echo

Figure 5 .

 5 Figure 5.1 : Generic UML diagram of a sequence: the main GinkgoSequence class aggregates either SequenceModule or CompositeSequenceModule instances, which are themselves aggregations of SequenceModule instances generated through the SequenceModuleFactory.

Figure 5 . 2 :

 52 Figure 5.2 : Generic SequenceModule composed of four real-time events. It shows the notions of anchor time (chosen reference time to insert the module in the sequence timeline), duration before anchor time, duration after anchor time, and total duration.

  Definition RegisterSequenceModuleCreator ▷ associating an instance of SequenceModule to a name in the factory map 4:

Figure 5 .

 5 Figure 5.3 : Chronograms representing the details of the ExcitationModule's child classes implemented in the GinkgoSequence toolbox. The Excitation2dModule class is generic for SingleTxCardinalSinePulseExcitation2dModule and SingleTxExternalPulseExcitation2dModule classes which difference lies only in the waveform of the RF excitation pulse. The Excitation3dModule class is representing the SingleTxCardinalSinePulseExcitation3dModule and SingleTxExternalPulseExcitation3dModule classes in the same way.

Figure 5 . 4 :

 54 Figure 5.4 : Chronograms representing the details of each RefocusingModule's child class, along with the SteamModule class of the GinkgoSequence toolbox. The RefocusingModule class is used with an excitation pulse to generate spin echoes, while the SteamModule class is used in the same way to generate stimulated echoes.

Figure 5 . 5 :

 55 Figure 5.5 : Chronograms representing the details of each PreEncodingModule class of the GinkgoSequence toolbox. These pre-encoding modules are specific to 2D and 3D EPI or EVI readout schemes. They acquire reference lines at the center of the k-space to correct Nyquist N 2 ghosting.

Figure 5 . 6 :

 56 Figure 5.6 : Chronograms representing the details of each ReadingModule class of the GinkgoSequence toolbox.

Figure 5 . 7 :

 57 Figure 5.7 : Chronograms representing the details of each PreparationModule class of the GinkgoSequence toolbox. The SaturationModule provides a saturation pulse for a given frequency and bandwidth. It is independent from the two other preparation pulses, which are diffusion gradient modules. These are designed to be used with spin-echo sequences in a symmetric way and thus provide the same triplet of gradients separated by a diffusion time for trapezoid as well as arbitrary waveforms.

Figure 5 . 8 :

 58 Figure 5.8 : Chronograms representing the details of each SpoilingModule class of the GinkgoSequence toolbox.

Figure 5 .

 5 Figure 5.9 : Class diagram of the GinkgoSequence framework. This diagram summarizes all the implemented modules of the GinkgoSequence toolbox and highlights its top-down architecture relying on an inheritance tree based on the SequenceModule class.

Figure 5 .

 5 Figure 5.10 : Chronogram of the GinkgoGradientEcho2d sequence. It shows in a dilated way (the modules should be starting right before their first pulse and ending right after their last pulse) the arrangement of SequenceModule instances along the sequence timeline (anchor times), highlighting the use of the EndModule.

:

  Parameters used for the preliminary study of single-line readout sequences. TE stands for echo time, and TR for repetition time.

Figure 6 . 1 :

 61 Figure 6.1 : Preliminary images obtained with a first prototype of GinkgoSequence on an ex vivo Nyala brain. Images obtained with a FOV of 128 × 128mm 2 , a matrix size of 256x256, and a readout bandwidth per pixel (RBW) of 725 Hz/px.

Figure 6 . 2 :

 62 Figure 6.2 : KH 2 P O 4 /NaCl phantom used for sequence testing. Its complex structure, including grids and gels, allow for an adequate estimation of the image's quality.

Figure 6 . 3 :(Figure 6 . 4 :Figure 6 . 5 : 2 (Figure 6 . 6 :Figure 6 . 7 :

 63646526667 Figure 6.3 : Images obtained using the GinkgoGradientEcho2d sequence on a KH 2 P O 4 /NaCl phantom.

Figure 6 . 8 :

 68 Figure 6.8 : Images obtained using the GinkgoSpinEcho2dEPI sequence accelerated using GRAPPA and PF 6/8 with decreasing resolutions (indicated here by the acquisition matrix size) on a KH 2 P O 4 /NaCl phantom showing less distortions for lower resolutions.

Figure 6

 6 Figure 6.9 : Images obtained using the GinkgoSpinEcho2dEPI sequence on a KH 2 P O 4 /NaCl phantom.

7 Figure 6 .Figure 6 .

 766 Figure 6.12 : Comparison between GinkgoGradientEcho2d and Siemens' 2D gre sequence.

Figure 6 .Figure 6 .

 66 Figure 6.14 : Comparison between GinkgoSpinEcho2d and Siemens' 2D se sequence.

Figure 7 . 1 :

 71 Figure 7.1 : Preliminary results on an ex vivo Nyala brain with a diffusion protocol using 250 orientations at a b-value of 5000s.mm -2 . These images show a first proof-of-concept for the diffusion-weighted GinkgoSequence sequences, with 3d excitation, EPI readout, and no acceleration from PF or GRAPPA. (a) The T 2 -weighted reference shows a coherent brain anatomy. (b) The diffusion-weighted images present a noisier image with sensitization to diffusion, as expected, and (c) the FA map highlights the main white matter fibers tracts of the observed brain.

Figure 7 . 2 :

 72 Figure 7.2 : Class diagram of the GinkgoSequence toolbox, highlighting in red its dMRI-oriented tools. These elements include DiffusionModule classes, allowing for the definition of PGSE-like trapezoid diffusion-weighting gradients with the TrapezoidDiffusionGradientModule class and arbitrary waveform (for OGSE, b-tensors, etc.) with the ArbitraryDiffusionGradientModule class. The SteamModule class allows for the implementation of stimulated-echo-based dMRI sequences, thus enabling the use of longer diffusion times. The structure of the main GinkgoSequence class is adapted to dMRI protocols by adding a loop on diffusion orientations, which manages the parameters of the diffusion gradients through an external file.

7. 2

 2 .1.1 Design of the 2D PGSE DW EPI sequence

Figure 7 . 3 :

 73 Figure 7.3 : Chronogram of the GinkgoSpinEcho2dDwEpi sequence, highlighting its modular architecture. The SingleTxExternalPulseExcitation2dModule coupled with the ExternalPulseRefocusingModule instance define a 2D spin-echo excitation scheme. They are completed with a MultiLineEPIReadingModule and an EPI2dPreEncodingModule class, which perform an echo-planar readout and acquire reference lines for Nyquist ghost correction. Within this classic 2D spin-echo EPI sequence scheme, a TrapezoidDiffusionGradientModule class adds trapezoid diffusion-weighting gradients around the refocusing pulse, thus sensitizing the acquisition to the diffusion process.

Figure 7 . 4 :

 74 Figure 7.4 : External text file defining the specific parameters for diffusion-weighting gradients in GinkgoSequence.It contains the number of volumes (i.e. number of diffusion directions + reference volumes with b = 0s.mm 2 ), the time parameters for the trapezoid diffusion-weighting gradients with their separation time (∆), plateau duration (δ), and ramp time (ξ), as well as the amplitudes (G x , G y , G z ) of these gradients for each orientation of the shell.

Figure 7 . 5 :

 75 Figure 7.5 : Screenshots of the graphical user interface for the GinkgoSpinEcho2dDwEpi pulse sequence. (a) The Routine tab includes a summary of the most commonly used parameters such as field of view (FOV), slice thickness, number of slices, TE, and TR. (b-c) The Resolution tab allows for tuning the resolution of the image as well as the acceleration modes, including partial Fourier (PF) with 5/8, 6/8, and 7/8 options (b) and GRAPPA with an acceleration factor of 2 and 20 reference lines (c). (d-e) The Sequence tab allows for the definition of the readout bandwidth (d) and of fat-saturation-related parameters (e).

Figure 7 . 6 :

 76 Figure 7.6 : Chronogram of the GinkgoSteam2dDwEpi sequence, highlighting its modular architecture. This sequence includes a SingleTxExternalPulseExcitation2dModule coupled with a SteamModule, which generates a stimulated echo with a mixing time TM separating its two RF pulses. It is completed with EPI readout and pre-encoding, with the addition of diffusion-weighting gradients around the STEAM pulses.

Figure 7 . 7 :

 77 Figure 7.7 : User interface of the GinkgoSteam2dEpi. It is identical to the one of the GinkgoSpinEcho2dDwEpi sequence, showing the same limits and flexibility for the parameters, with the addition of a mixing time field in the Sequence tab.

Figure 7 . 8 :

 78 Figure 7.8 : Graphic representation of the q-space sampling used for the 3-shell HYDI diffusion protocol. Each sphere represents one shell (with its associated b-value and number of diffusion orientations N O ), with the points on these spheres representing the acquired orientations obtained using a general energy-minimization electrostatic model.

Figure 7 . 9 :

 79 Figure 7.9 : Details of the diffusion post-processing pipeline implemented in the Gingko framework. The pre-processing steps prepare the raw data to be used with diffusion models by removing artifacts and noise, as well as computing a mask of the brain. The DTI, NODDI, and QBI models are then applied to compute quantitative maps and tractograms, including the labeling of the deep white matter fiber bundles.

Figure 7 .

 7 Figure 7.10 : Summary of the post-processing pipeline used to assess the quality of the GinkgoSequence images for dMRI qualitative and quantitative analysis. From the 3-shells dMRI acquisition, DTI, NODDI, and QBI models are used to generate quantitative maps including apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), and transverse diffusivity (D T ransverse ) for the DTI model; neurite density index (NDI), orientation dispersion index (ODI) and κ for the NODDI model; as well as generalized fractional anisotropy (GFA), GFA color-encoded direction (CED), and orientation distribution function (ODF) field for the QBI model. The ODF maps are also used to perform a deterministic tractography algorithm, which result is labeled using a deep white matter bundle atlas.

Figure 7 .

 7 Figure 7.11 : Raw data for a 3-shell diffusion-weighted acquisition using GinkgoSpinEcho2dDwEpi on a healthy volunteer. Along with the T 2 -weighted reference image, four identical coronal views of different diffusion orientations O are presented for each shell, characterized by the b-value and number of diffusion directions N O . The expected exponential decrease of the SAR with the b-value is correctly observed. The diffusion-weighted images already show hints of the white matter tracts.

Figure 7 .

 7 Figure 7.12 : Raw data for a 3-shell diffusion-weighted acquisition using the CMRR_diff sequence on a healthy human volunteer. Along with the T 2 -weighted reference image, four identical coronal views of different diffusion orientations O are presented for each shell, characterized by the b-value and number of diffusion directions N O . The expected exponential decrease of the SAR with the b-value is correctly observed. The diffusion-weighted images already show hints of the white matter tracts.

Figure 7 .

 7 Figure 7.13 : Maps obtained with GinkgoSpinEcho2dDwEpi and the comparative reference sequence showing in the axial, coronal, and sagittal views apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), and transverse diffusivity (D T ransverse ) based on the DTI model, along with generalized fractional anisotropy (GFA) and color-encoded diffusion direction (CED) based on the QBI model. The images correctly render the information about white matter fiber tracts and are similar for the two sequences.

Figure 7 .

 7 Figure 7.14 : Histograms of the apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), transverse diffusivity (D T ransverse ), and generalized fractional anisotropy (GFA) values for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. All maps present a corresponding histogram profile with a similar peak value for the two sequences.

Figure 7 .

 7 Figure 7.15 : Quantitative maps obtained with GinkgoSpinEcho2dDwEpi and the comparative CMRR_diff reference sequence showing in the axial, coronal, and sagittal views neurite density index (NDI), orientation dispersion index (ODI), and κ concentration based on the NODDI model. These results depict a lower ODI and higher NDI for the main deep white matter fiber tracts, which is coherent with their highly organized structure.

Figure 7 .

 7 Figure 7.16 : Histograms of the neurite density index (NDI), orientation dispersion index (ODI), and kappa values for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. Showing similar profiles and peak values for each map, these histograms further validate the GinkgoSpinEcho2dDwEpi sequence's performances for the NODDI model.

Figure 7 .

 7 Figure 7.17 : ODF maps for the GinkgoSpinEcho2dDwEpi sequence. These maps have been generated using the q-ball imaging analytic model with a spherical harmonics order of 2 and a Laplace-Beltrami regularization factor of 0.006. Each element represents an orientation distribution function (ODF) representative of the main directions of diffusion in the considered voxel. à The axial (a), coronal (b), and sagittal (c) views are represented, along with a zoom (d) on the white-framed region of the coronal view. Among many other white matter fiber structures, they correctly depict the intersection between the corpus callosum and the cortico-spinal tracts.

Figure 7 .

 7 Figure 7.18 : ODF maps for the CMRR_diff sequence. These maps have been generated using the q-ball imaging analytic model with a spherical harmonics order of 2 and a regularization factor of 0.006. Each element represents an orientation distribution function (ODF) representative of the main directions of diffusion in the considered voxel. The axial (a), coronal (b), and sagittal (c) views are represented, along with a zoom (d) on the white-framed region of the coronal view. Among many other white matter fiber structures, they correctly depict the intersection between the corpus callosum and the cortico-spinal tracts.

Figure 7 .

 7 Figure 7.19 : Tractograms (T 2 in background) for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. These

Figure 7 .

 7 Figure 7.20 : Labeled tractograms for the GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. With the application of a fiber labeling algorithm following the[START_REF] Guevara | Automatic fiber bundle segmentation in massive tractography datasets using a multi-subject bundle atlas[END_REF] approach on the Ginkgo-Chauvel atlas of long white matter fibers, these images present the fiber fasciculus identified in the previously shown tractograms. With the exception of the anterior commissure, which is too small to be detected here, all the main fiber tracts of the human brain have been identified and colored similarly for the two sequences, thus showing the ability of the GinkgoSpinEcho2dDwEpi sequence to provide trustworthy data for the analysis of white matter fiber bundles.

Figure 7 .

 7 Figure 7.21 : Raw data for a 3-shell diffusion-weighted acquisition using GinkgoSteam2dDwEpi on a healthy volunteer. Along with the T 2 -weighted reference image, four identical coronal views of different diffusion orientations O are presented for each shell, characterized by the b-value and number of diffusion directions N O . The expected exponential decrease of the SAR with the b-value is correctly observed. The diffusion-weighted images already show hints of the white matter tracts.

Figure 7 .

 7 Figure 7.22 : Raw data for a 3-shell diffusion-weighted acquisition using GinkgoSpinEcho2dDwEpi to compare with GinkgoSteam2dDwEpi on a healthy volunteer. Along with the T 2 -weighted reference image, four identical coronal views of different diffusion orientations O are presented for each shell, characterized by the b-value and number of diffusion directions N O . The expected exponential decrease of the SAR with the b-value is correctly observed. The diffusion-weighted images already show hints of the white matter tracts.

Figure 7 .

 7 Figure 7.23 : Quantitative maps obtained with GinkgoSteam2dDwEpi and the comparative reference GinkgoSpinEcho2dDwEpi sequence. They include, in the axial, coronal, and sagittal views, apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), and transverse diffusivity (D T ransverse ) maps based on the DTI model, along with generalized fractional anisotropy (GFA) and color-encoded diffusion direction (CED) maps based on the QBI model. The images correctly render the information about white matter fiber tracts and are similar for the two sequences.

Figure 7 .

 7 Figure 7.24 : Histograms of the apparent diffusion coefficient (ADC), fractional anisotropy (FA), parallel diffusivity (D P arallel ), transverse diffusivity (D T ransverse ), and generalized fractional anisotropy (GFA) values for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. These results show similar shapes for the two sequences, with comparable peak values, although they are more spread out for the GinkgoSpinEcho2dDwEpi sequence.

Figure 7 .

 7 Figure 7.25 : Maps obtained with GinkgoSteam2dDwEpi and the comparative reference GinkgoSpinEcho2dDwEpi sequence showing in the axial, coronal, and sagittal views neurite density index (NDI), orientation dispersion index (ODI), and κ concentration based on the NODDI model. These results depict a lower ODI and higher NDI for the main deep white matter fiber tracts, which is coherent with their highly organized structure.

Figure 7 .

 7 Figure 7.26 : Histograms of the neurite density index (NDI), orientation dispersion index (ODI), and kappa values for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. With similar shapes and peak values, although the NDI presents a lower amplitude, these results show the coherence among the NODDI maps obtained from the two sequences.

Figures

  Figures 7.27 and 7.28 show the ODF fields obtained using the QBI model with GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences respectively. The obtained orientation distributions are quite similar for the two sequences, and the corpus callosum (red), as well as the cortico-spinal tracts (blue), can be correctly identified in the axial, coronal, and sagittal views.The tractograms computed using these ODF maps are presented in figure7.29 for both sequences. Comparatively to the images obtained in the first test, the same commissural structure and fiber tracts can be identified in the different views. Furthermore, the views obtained from the STEAM and SE sequences look very similar.The white matter bundles identified after fiber labeling with the Ginkgo-Chauvel deep white matter atlas are shown in Figure7.30. Although the labeling algorithm failed to identify the left arcuate fascicle in the STEAM version, which is likely due to an error in masking leading to an accumulation of small holes interrupting the tracts and could be corrected with further optimization of the masking and labeling process, all the other fascicles were correctly reconstructed for both versions (with the exception of the anterior commissure, which is too small to be detected at the used resolution).By demonstrating the capacity of the GinkgoSteam2dDwEpi sequence to generate coherent white matter fiber bundles and to identify them using an atlas, these results validate its use in deep white matter fiber studies.

Figure 7 .

 7 Figure 7.27 : ODF maps for the GinkgoSteam2dDwEpi sequence. These maps have been generated using the q-ball imaging analytic model with a spherical harmonics order of 2 and a regularization factor of 0.006. Each element represents an orientation distribution function (ODF) representative of the main directions of diffusion in the considered voxel. The axial (a), coronal (b), and sagittal (c) views are represented, along with a zoom (d) on the white-framed region of the coronal view. Among many other white matter fiber structures, they correctly depict the intersection between the corpus callosum and the cortico-spinal tracts.

Figure 7 .

 7 Figure 7.28 : ODF maps for the reference GinkgoSpinEcho2dDwEpi sequence. These maps have been generated using the q-ball imaging analytic model with a spherical harmonics order of 2 and a regularization factor of 0.006. Each element represents an orientation distribution function (ODF) representative of the main directions of diffusion in the considered voxel. The axial (a), coronal (b), and sagittal (c) views are represented, along with a zoom (d) on the white-framed region of the coronal view. Among many other white matter fiber structures, they correctly depict the intersection between the corpus callosum and the cortico-spinal tracts.

Figure 7 .

 7 Figure 7.29 : Tractograms (T 2 in background) for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi

Figure 7 .

 7 Figure 7.30 : Labeled tractograms for the GinkgoSteam2dDwEpi and GinkgoSpinEcho2dDwEpi sequences. With

Figure 8 . 1 :

 81 Figure 8.1 : Chronogram of the GinkgoSpinEcho3dEVI sequence for 3 partitions. The sameEPI3dPreEncodingModule as for the GinkgoSpinEcho3dEPI sequence is used to provide reference lines for Nyquist ghost correction (which happens exactly in the same way as for EPI readouts). In the MultliLineEVIReadingModule, the alternating readout gradients are punctuated with partitions blips, which go to the next partition, and phase flyback gradients, which go back to the starting point of the partition, thus avoiding the artifacts that an alternated scheme in the partition direction would have created.

Figure 8 . 2 :

 82 Figure 8.2 : EVI trajectory for 3 partitions, highlighting the phase flyback process. The thick red lines materialize the combination of partition blips, going from one partition to the next, followed by a phase flyback gradient reaching the starting point of the new partition.

Figure 8 . 3 :

 83 Figure 8.3 : User interface of the GinkgoSpinEcho2dEVI sequence. This console interface presents the same features as the one used for the GinkgoSpinEcho2dEPI sequence, with (a) a main difference in the Routine tab presenting the parameter for 3D acquisitions (identical for the GinkgoSpinEcho3dEPI sequence) with slabs corresponding to acquired volumes and slices per slabs defining the number of partitions acquired in one slab, as well as (b) an additional field for the partition partial Fourier settings (called Slice partial Fourier) in the Resolution tab.

Figure 8 . 4 :

 84 Figure 8.4 : Sagittal reconstructed images obtained for 3 partitions(3, 5, 7) with the GinkgoSpinEcho3dEVI and the GinkgoSpinEcho3dEPI sequences of the same ex vivo human brain. The EPI images correctly reproduce the shape and the inner structure of the brain, while the EVI acquisitions provide a good rendering of the shape with strong distortions that hamper the reproduction of detailed structures. Both images are satisfyingly corrected for ghosting artifacts.

  1.15 Chronogram of a GRE sequence using 2D or 3D excitation with a cartesian space encoding. 1.16 MR image reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.17 Example of MRI artifacts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Single-line and single-shot echo-planar readouts. . . . . . . . . . . . . . . . . . . . . . . . 2.2 Chronogram of a spin echo sequence with EPI readout and pre-encoding. . . . . . . . . . . 2.3 Post-processing and correction of imaging artifacts with EPI. . . . . . . . . . . . . . . . . 2.4 Same phantom as in Figure 2.3a, acquired using the same spin echo 2d EPI sequence, with acceleration from GRAPPA (R = 2) and partial Fourier (6/8) . . . . . . . . . . . . . . . . 2.5 Example of EVI trajectory with 5 partitions. . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 2D spin-echo images of a phantom acquired without (a) and with 6/8 partial Fourier (b). . 2.9 Three-shot Cartesian EPI trajectory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 K-space contrast and details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Spiral trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Chronogram of a spiral spin echo sequence scheme. . . . . . . . . . . . . . . . . . . . . . 2.13 PROPELLER trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14 Parallel imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.15 The basic GRAPPA algorithm shown schematically using four blocks and an acceleration factor R of 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16 Comparison between reconstructed images obtained with and without parallel imaging. . . 2.17 Principles of compressed sensing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.18 A schematic view of multiband imaging using only coil encoding for slice discrimination. . . 2.19 Generation of SPARKLING trajectories for different initializations and target densities. . . .

2.6 Chronogram of an echo-volumar imaging (EVI) sequence. . . . . . . . . . . . . . . . . . . 2.7 Comparison between a full and an accelerated acquisition using partial Fourier (PF). . . . . vii 3.1 Operational diagram of procedural vs. object-oriented programming. . . . . . . . . . . . . 3.2 A minimal dataset in the ISMRMRD file format. . . . . . . . . . . . . . . . . . . . . . . .

Table 6 .

 6 2 : Parameters used for the evaluation of GinkgoSequence basic sequences. TE stands for echo time, TR for repetition time between two consecutive excitations, TM for mixing time, FOV for field of view, RBW for readout bandwidth-per-pixel, and N for the number of slices or partitions. All sequences use the same parameters for their unaccelerated, GRAPPA R = 2, PF 5/8 and 6/8, and combined (GRAPPA R = 2 + PF 5/8, GRAPPA R = 2 + PF 6/8)versions.

	Sequence	TE	TR	TM	FOV	Matrix size	RBW	N
		(ms)	(ms)	(ms)	(mm 2 )		(Hz/Px)
	GinkgoGradientEcho2d	10	200	-	256×256 256×256×192	980	1
	GinkgoGradientEcho3d	10	200	-	256×256 256×256×256	980	16
	GinkgoSpinEcho2d	60	2000	-	256×256 256×256×256	780	1
	GinkgoSpinEcho3d	60	2000	-	256×256 256×256×256	1400	16
	GinkgoSteam2d	60	2000	19	256×256 256×256×256	1420	1
	GinkgoSpinEcho2dEPI	310	500	-	256×256 256×256×256	1400	1
	GinkgoSpinEcho3dEPI	310	500	-	256×256 256×256×256	1400	64
	GinkgoSteam2dEPI	310	500	30	256×256 256×256×256	1390	1
	Sequence	TE	TR	FOV	Matrix size	RBW	N
		(ms)	(ms)	(mm 2 )			(Hz/Px)
	2D gre	10	200	256×256 256×256×192	980	1
	3D gre	10	200	256×256 256×256×256	980	16
	2D se	60	2000 256×256 256×256×256	781	1
	ep2d_se	310	500	256×256 256×256×256	976	1
	Table 6.3 : Parameters used for the evaluation of Siemens basic sequences. TE stands for echo time, TR for
	repetition time between two consecutive excitations, FOV for field of view, RBW for readout bandwidth-per-pixel, and
	N for the number of slices or partitions. All sequences use the same parameters for their unaccelerated and
	accelerated versions: PF 6/8 for 2D se (GRAPPA not available), and GRAPPPA R = 2 + PF 6/8 for the other sequences.

Table 6 . 5

 65

		GRAPPA GRAPPA	GRAPPA
			PF6/8	PF5/8
	GinkgoGradientEcho2d	0.94	0.89	0.86
	GinkgoGradientEcho3d	1.11	1.12	1.47
	GinkgoSpinEcho2d	0.61	0.61	0.59
	GinkgoSpinEcho3d	1.13	0.83	1.43
	GinkgoSteam2d	0.87	0.87	0.84

Table 6 . 6

 66

	Sequence	Simple	PF6/8	PF5/8	GRAPPA GRAPPA	GRAPPA
						PF6/8	PF5/8
	GinkgoGradientEcho2d	36.4	39.9	41.8	48.3	53.7	55.6
	GinkgoGradientEcho3d	100.0	116.3	121.1	133.9	160.6	92.12
	GinkgoSpinEcho2d	40.3	43.6	46.2	46.4	50.7	55.7
	GinkgoSpinEcho3d	125.9	141.2	143.2	135.1	168.9	95.0
	GinkgoSpinEcho2dEPI	67.4	70.2	58.6	44.9	40.7	40.6
	GinkgoSpinEcho3dEPI	74.3	78.7	82.3	28.3	27.1	28.5
	GinkgoSteam2d	20.7	23.1	23.8	16.9	18.7	20.0
	GinkgoSteam2dEPI	53.1	53.5	50.3	28.2	28.5	30.8
	: SNR measures obtained for single-lines, EPI, and STEAM GinkgoSequence images with different
		acceleration schemes.

Table 6 . 7

 67 : SNR comparison between GinkgoSequence and Siemens sequences.

	Sequence	Ginkgo	Siemens
	GRE 2D	36.4	37.5
	GRE 2D GRAPPA & PF6/8	53.7	51.7
	GRE 3D	100.0	101.9
	GRE 3D GRAPPA & PF6/8	160.6	129.3
	SE 2D	40.3	30.6
	SE 2D PF6/8	43.6	37.8
	SE 2D EPI	67.4	45.7
	SE 2D EPI GRAPPA & PF6/8	40.7	36.0

Table 7 . 6

 76 : SNR values for the raw data of the first test. They present the same order of magnitude, with a slightly better result for the GinkgoSpinEcho2dDwEpi sequence.

	Sequence	T 2 -	SNR	SNR	SNR
		weighted	(Shell 1)	(Shell 2)	(Shell 3)
	GinkgoSpinEcho2dDwEpi	88.4	41.0	25.1	16.9
	CMRR_diff	70.6	32.2	20.3	12.6

Table 7 .

 7

	Sequence	T 2 -	Shell 1	Shell 2	Shell 3
		weighted
	GinkgoSteam2dDwEpi	50.9	25.1	17.2	9.2
	GinkgoSpinEcho2dDwEpi	63.3	30.1	18.1	11.0

7

: SNR values for the second test. Equivalent values are obtained for the two sequences, with slightly higher results for the GingkoSpinEcho2dDwEpi sequence, which was expected from the experimental setup aiming to obtain similar signal values by adapting the TE of the SE sequence.

Table 8 .

 8 .2. 1 : Acquisition parameters for the GinkgoSpinEcho3dEVI and GingkoSpinEcho3dEPI sequences. TE stands for echo time, TR for repetition time between two consecutive excitations, RBW for readout bandwidth, FOV for field of view, N for number of partitions, TA for total acquisition time, and R for GRAPPA acceleration factor (in the phase direction).

	Sequence	TE	TR	RBW		FOV	Matrix	N	phase	partition	R TA
		(ms)	(ms)	(Hz/Px)	(mm 2 )	size			PF	PF	(s)
											factor	factor
	GinkgoSpinEcho3dEVI	70	1000	5580	256×256 64×64×64 16	5/8	5/8	2	2
	GinkgoSpinEcho3dEPI	70	1000	5580	256×256 64×64×64 16	5/8	8/8	2	32
	Sequence		TE min	TR min	Partitions	TA min
					(ms)	(ms)			in 1 TR	(s)
	GinkgoSpinEcho3dEVI	67		84			16	0.17
	GinkgoSpinEcho3dEPI	18		35			1	1.1

Table 8 . 2 :

 82 Minimal timing parameters for the GinkgoSpinEcho3dEVI and GingkoSpinEcho3dEPI sequences using the parameters of Table

ghosting correction, the approximated centers rephase; Bottom-reconstructed image.

Acknowledgements

Chapter 5 An open-source object-oriented toolkit to develop MRI pulse sequences gkg::GinkgoGradientEcho2d::GinkgoGradientEcho2d() : _userInterface( NULL ), _lineCountPerSecond( 0 ) { std::vector< double > singleTxExcitation2dDoubleParameters( 5U ); singleTxExcitation2dDoubleParameters[ 0 ] = 15.00; // default flip angle singleTxExcitation2dDoubleParameters[ 1 ] = 2560; // RF duration singleTxExcitation2dDoubleParameters [ 2 ] = 128; // RF sample count singleTxExcitation2dDoubleParameters[ 3 ] = 2.70; // RF bandwidth time product singleTxExcitation2dDoubleParameters [ 4 ] NLSStatus gkg::GinkgoGradientEcho2d::initialize( SeqLim& seqLim ) { static const char *ptModule = { "gkg::GinkgoGradientEcho2d::initialize" }; NLS_STATUS status = SEQU__NORMAL; seqLim.setSequenceOwner( "GINKGO TEAM" ); ////////////////////////////////////////////////////////////////////////////// // initializing sequence modules ////////////////////////////////////////////////////////////////////////////// std::map< std::string, gkg::RCPointer< gkg::SequenceModule > >::iterator sm = _sequenceModules.begin(), sme = _sequenceModules.end(); while ( sm != sme The runKernel method is described in Figures 5.19 and 5.20. It starts by looping over the modules, calling their modifyKernel methods, before managing the sequence timings. The fRTEBInit method, which initializes one kernel of real-time events, is called at the start of the kernel in which the anchor times of each module are set before calling their respective setKernelTiming methods, including their real-time events.

Finally, the createUI and getUI methods presented in Figure 5.21 are used to manage the user interface of the sequence, in correspondence with the GinkgoGradientEcho2d_UI class.

All the sequences included in the GinkgoSequence framework, although they may be more complex, follow the same scheme, implementing the same methods in an identical manner. The full GinkgoSpinEcho2d class code is 375-line long, which is significantly shorter than its Siemens counterpart (FLASH sequence), which is 1020-line long.

NLS_STATUS gkg::GinkgoGradientEcho2d::runKernel( MrProt& mrProt, SeqLim& seqLim, MrProtocolData::SeqExpo& seqExpo, long kernelMode, long sliceIndex, long partitionIndex, long lineIndex ) { static const char *ptModule = { "gkg::GinkgoGradientEcho2d::runKernel" }; NLS_STATUS status = SEQU__NORMAL; ////////////////////////////////////////////////////////////////////////////// // modifying kernels of all module(s) ////////////////////////////////////////////////////////////////////////////// std::map< std::string, gkg::

Application of the GinkgoSequence toolbox to the implementation of various sequences

The GinkgoSequence toolbox proposes a large panel of example sequences that can be used as they are or modified to fit other applications. These sequences have been built to assess the robustness of the toolbox and to test it in a research application in the field of diffusion MRI. They provide examples of use cases for every module provided in the toolbox and the information needed to assemble the modules to form a working sequence.

Basic sequences

Stemming from the most simple MRI pulse sequence schemes, GinkgoSequence includes classic example sequences using spin-echo and gradient-echo excitations with single-line readouts:

• the GinkgoGradientEcho2d class, including the following modules: SingleTxCardinalSinePulseExcita-tion2dModule, SingleLineReading2dModule, StandardSpoilingModule, EndModule;

• the GinkgoGradientEcho3d class, including the following modules: SingleTxCardinalSinePulseExcita-tion3dModule, SingleLineReading3dModule, StandardSpoilingModule, EndModule;

• the GinkgoSpinEcho2d class, including the following modules: SingleTxCardinalSinePulseExcitation2d-Module, CardinalSinePulseRefocusingModule, SingleLineReading2dModule, StandardSpoilingModule, EndModule;

• the GinkgoSpinEcho3d class, including the following modules: SingleTxCardinalSinePulseExcitation3d-Module, CardinalSinePulseRefocusingModule, SingleLineReading3dModule, StandardSpoilingModule, EndModule.

As expected from the structure of the GinkgoSequence toolbox, many modules are redundant among the sequences, making them easy to implement and maximizing the reuse of already tested source code. They all implement partial Fourier and GRAPPA with R = 2 and can be freely modified.

Fast imaging sequences

The framework also provides accelerated sequences using echo-planar and echo-volumar readouts along with partial Fourier and GRAPPA methods:

• the GinkgoSpinEcho2dEPI class, including the following modules: SingleTxExternalPulseExcitation2d-Module, EPI2dPreEncodingModule, ExternalPulseRefocusingModule, MultiLineEPIReadingModule, StandardSpoilingModule, EndModule;

• the GinkgoSpinEcho3dEPI class, including the following modules: SingleTxExternalPulseExcitation3d-Module, EPI3dPreEncodingModule, ExternalPulseRefocusingModule, MultiLineEPIReadingModule, StandardSpoilingModule, EndModule;

• the GinkgoSpinEcho3dEVI class, including the following modules: SingleTxExternalPulseExcitation3d-Module, EPI3dPreEncodingModule, ExternalPulseRefocusingModule, MultiLineEVIReadingModule, StandardSpoilingModule, EndModule;

The echo-planar acquisition scheme is directly implemented as a ReadingModule class in the form of a MultiLineEPIReadingModule. It uses odd and even lines and partitions to alternate between positive and negative readouts, separated by phase blips. To complete this readout scheme, a corresponding PreEncod-ingModule class provides navigators allowing for the correction of phase errors induced by the acquisition and pre-encoding gradients for partition, phase, and frequency encodings.

Sequence

Gadgetron pipeline

Generic_Cartesian_Grappa_EPI Table 6.4 : Gadgetron reconstruction pipeline used for each example sequence of the GinkgoSequence framework. The Generic_Cartesian_Grappa pipeline includes coil compression, GRAPPA algorithm, partial Fourier handling (using POCS), k-space filtering, and image scaling; and the Generic_Cartesian_Grappa_EPI pipeline is identical with the addition of an EPI correction feature, including phase correction and line flipping.

The images were acquired twice with the same settings for each sequence and each acceleration mode to compare their signal-to-noise ratios (SNR), calculated as a ratio between mean signal intensity measured on a binary mask of the phantom and standard deviation of the noise corresponding to the background of the image. From these values, the mean SNR between the two versions for each sequence was compared among all tested sequences. In addition, the spatial resolution of the EPI sequences was varied to check the effect of these changes on the level of distortion of the images.

It should be noted that, although it provides a good comparison basis by using a uniformized measurement, this SNR study could benefit from more specific methods such as [START_REF] Robson | Comprehensive quantification of signal-to-noise ratio and g-factor for imagebased and k-space-based parallel imaging reconstructions[END_REF] in the case of GRAPPA acceleration as well as similarity coefficient measures or point spread functions, which were not implemented in the frame of this work due to time constraints.

Presentation and analysis of GinkgoSequence images

The images resulting from the GinkgoSequence sequences are presented in this section, along with their signal-to-noise ratios. For single-line readout sequences using GRAPPA acceleration, these results are completed with the calculation of their corresponding g-factor.

SNR analysis of single-line readout sequences

The images obtained with the GinkgoGradientEcho2d, GinkgoGradientEcho3d, GinkgoSpinEcho2d, Ginkgo-SpinEcho3d, and GinkgoSteam2d sequences are displayed respectively in Figures 6.3,6.4,6.5,6.6,and 6.7 along with their mean SNR values. All sequences yielded adequate representations of the phantom. As expected, the images obtained from 3D sequences depicted less noise and showed a higher SNR than their 2D counterparts. The STEAM images presented a reduced SNR compared to the spin echo images, which is coherent with the loss of signal occurring during the tilting of the transverse magnetization to the longitudinal plane and its return.

As expected from [START_REF] Mcgibney | Quantitative evaluation of several partial fourier reconstruction algorithms used in mri[END_REF], the images acquired using partial Fourier presented a stronger Gibbs ringing artifact. Their SNRs are in the same range as the images with no PF, although they are slightly higher.

The images using GRAPPA do not present any visual difference but show a reduced SNR from the ones not using it. As for any parallel imaging method, this SNR loss can be quantified using equation ( 6 An SNR analysis was performed on the raw images. The SNR was computed using the mean value of the signal in the corpus callosum and the standard deviation of the noise in the background of the image. With these measures, it was expected to find a reduced SNR for diffusion-weighted images, decreasing with the increasing b-values, and an equivalent SNR for images acquired with an equivalent protocol using either GinkgoSequence or external sequences.

Application to the GinkgoSpinEcho2dDwEpi sequence

To assess the quality of the images obtained using the GinkgoSpinEcho2dDwEpi sequence, a reference CMRR_diff sequence [Setsompop et al., 2012a] was chosen among those currently used for dMRI studies. As the version of GinkgoSequence used for these tests does not implement multi-band excitations, this feature was deactivated in the reference sequence. Therefore, these two sequences were very similar, implementing fat saturation and trapezoid diffusion-encoding gradients on a 2D spin-echo EPI sequence.

They were used for acquisitions following the aforementioned 3-shell dMRI protocol and the parameters described in Tables 7.2 and7.3. To reduce the distortions generated by the echo-planar readout, partial Fourier (5/8) and GRAPPA (R = 2) were activated. The echo time and repetition time (separation time between two consecutive excitation pulses) were tuned to obtain a T 2 -weighted contrast and respect the limits imposed by the diffusion-encoding gradients.

The exact same reconstruction was used for both sequences, including retrieving raw data from the console (TWIX), converting them to the ISMRMRD format, and processing the images with the Generic_Cartesian_Grappa_ reconstruction pipeline from Gadgetron. To ensure coherence, as it has not yet been set in the GinkgoSpinE-cho2dDwEpi sequence, the noise measurement provided with the Siemens images was ignored. Table 7.2 : Acquisition parameters used for GinkgoSpinEcho2dDwEpi and CMRR_diff sequences. TR stands for the repetition time between two consecutive RF excitation pulses, FOV for the field of view, N for the number of acquired slices, RBW for readout bandwidth, and R for the acceleration factor used for GRAPPA acceleration.

Application to the GinkgoSteam2dDwEpi sequence

The GinkgoSteam2dDwEpi sequence was compared to an equivalent GinkgoSpinEcho2dDwEpi sequence following the same protocol. To compensate for the loss of half the signal during the process of z-memory in the stimulated echoes acquisition scheme, the echo time used for the two sequences was chosen according to equation 7.1:

with TE STEAM the echo time used for the STEAM sequence, TE SE the equivalent echo time for the obtention of the same signal intensity with the spin-echo sequence, and T 2 the relaxation time of the observed tissue (for brain white matter T 2 ≈ 80ms). Using this calculation, different contrasts but similar SNR values were expected with the two sequences. Furthermore, considering the constraints of the repetition time for an in vivo acquisition, the mixing time (TM) of the STEAM sequence was set to a value allowing for a reduction of approximately half the duration of the diffusion-encoding gradients to obtain the same b-value. The parameters for this test are summarized in Tables 7.4 and 7.5. The diffusion parameters used for the GinkgoSpinEcho2dDwEpi sequence are the same as in the previous section (Table 7.3). The maps obtained with the DTI and the QBI models for the two sequences are shown in Figure 7.23. Similarly to the first test, they correctly highlight the main paths for white matter tracts and present comparable results for the two sequences.

The histograms corresponding to the quantitative maps of Figure 7.23 for the two sequences are shown in Figure 7.24. As expected from the visual observations, they all present similar profiles and peak values. However, their amplitude and spreading are slightly different, with more widespread and lower amplitude values for the GinkgoSpinEcho2dDwEpi sequence, which might be due to the difference between SE and STEAM excitations. Still, as the information is correctly retrieved with high comparability for both sequences, these results validate the GinkgoSteam2dDwEpi sequence for the analysis of quantitative maps from the DTI and QBI models.

Obtained with the NODDI model, the maps presented in Figure 7.25 also show great similarity between the two sequences. They both correctly depict the expected lower orientation distribution and higher neurite density index for the main deep white matter tracts.

The histograms of the NDI, ODI, and κ values per voxel are displayed in Figure 7.26. Although the NDI profiles present a difference in intensity and spreading, they all have the same general shape and peak value, which confirms the high similarities of the corresponding images and validates the use of the GinkgoSteam2dDweEpi sequence with the NODDI analysis of neurites orientations.

General conclusion

Scientific contributions

A novel open-source and modular MRI pulse sequence development framework for Siemens systems was developed in the frame of this thesis. This work relied on a complete refactoring of a large series of elementary sequence modules designed using an object-oriented philosophy to enable the development of any new pulse sequence in a generic approach maximizing their sharability. Design patterns have been extensively used to propose a robust design allowing the hierarchical construction of composite modules using a coarse-to-fine strategy. Although it has been originally designed for Siemens MRI systems, the GinkgoSequence framework could evolve towards an even more generic environment to cover implementations for other manufacturers. It is also of importance to mention that this framework has been developed following an open science strategy, allowing for any MRI physicist to freely get access to the GinkgoSequence toolkit.

The basis of this source code was extensively tested using acquisitions on a phantom to perform SNR benchmarks. For each sequence developed in the frame of this thesis, including 2D and 3D spin-and gradientecho excitation with single-line or echo-planar readouts accelerated by partial Fourier and GRAPPA, images have been acquired and compared when possible with existing sequences from the vendor. These were able to deliver images of good quality comparable to those acquired using reference sequences. They proved the robustness of the basic sequence modules and architecture proposed in GinkgoSequence and their usability in the flexible creation of multiple classic MRI pulse sequences.

The GinkgoSequence toolbox was then used in an actual research application with the creation of dedicated modules and sequences for diffusion-weighted MRI, which were tested on healthy volunteers at 3T. These dMRI sequences allowed the use of advanced diffusion models and showed similar results when compared to a reference sequence from the CMRR. They proved the capacity of GinkgoSequence to serve as a basis for further dMRI pulse sequence development, notably allowing the use of free-waveform diffusionencoding gradients and further opening the way to real-time applications.

Last, the GinkgoSequence environment was applied in the development of an echo-volumar echo-train readout module, allowing for the ultra-fast acquisition of entire volumes (eg requiring a single excitation) and opening the way to cutting-edge applications in fMRI or dMRI. This innovative sequence was tested ex vivo on a human hemisphere, showing encouraging preliminary results, but still needs development to be completely accessible. Nonetheless, the images proved the potential of this technique by providing coherent images at 3T, which could be used with diffusion-sensitization to perform a more accurate stroke diagnosis than current EPI-based sequences in a shorter acquisition time, fulfilling the need to shorten scan duration in case of emergency.

In the future, being able to collect a whole dMRI volume within the second opens a wide range of applications: one could think of using incremental computation of diffusion models with real-time feedback to be able to refine diffusion quantitative maps in a more efficient way to stop the scan when a quality factor is reached. It would allow, for instance, to explore and reconstruct the structural connectivity in real-time at the operator console, to explore the tissue microstructure providing a totally non-invasive biopsy tool for medical applications, or to infer the cytoarchitectonics of brain functions of interest in real-time.

Echo-volumar imaging would also drastically increase the temporal resolution of fMRI and make more

Communications

Conference publications

Journal publications

• Artiges A., Granier E., Uszynski I., Mauconduit F., Ciuciu P., and Poupon C., GinkgoSequence: an open-source and modular MRI pulse sequence programming toolbox with dedicated tools for diffusionweighted imaging. -In writing.

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