Multimodal analysis of neurovascular coupling in the newborn

Neurovascular coupling (NVC) has become the key aspect for understanding brain function. A multimodal exploration would aim to identify the early NVC biomarkers and determine their predictive character. Paper (1): In this chapter, the photothermal interaction of NIR laser on human tissues were modelled in silico. The results demonstrated the safety of the noninvasive optical evaluation of the brain function and the maximum temperature increase was higher in the neonatal brain than in the adult brain.

Paper (2 & 3):

The main purpose of this thesis was to provide a multimodal view of the NVC and cerebrovascular regulation in the neonatal premature brain. Paper (2): Key findings included that rCBV and rCMRO2 have a predominant driving influence on rCBF at the resting-state in the preterm neonatal brain.

Paper (3):

The bursts of electroencephalographic activity in neonates in resting state were found to be coupled to a transient hemodynamic response involving different types of hemodynamic response including: (a) positive stereotyped hemodynamic responses (increases in HbO, decreases in HbR together with increases in CBF and CMRO2), (b) negative hemodynamic responses (increases in HbR, decreases in HbO together with decreases in CBF and CMRO2), (c) Increases and decreases in both HbO-HbR and CMRO2

together with no changes in CBF. The establishment of neurovascular coupling system was observed as a function of age. High coherence was observed between the cerebral hemodynamic (vascular) and electrical (neuronal) oscillations which was less in the non-encephalopathic newborns than in the two pathological groups.

Analyse multimodale de couplage neurovasculaire chez le nouveau-né

Une exploration multimodale permettrait d'identifier les biomarqueurs précoces du CNV permettrait de déterminer leur caractère prédictif. Chapitre (3): Dans ce chapitre, les résultats présentés montrent que l'augmentation maximale de la température était plus élevée dans le cerveau néonatal que dans le cerveau adulte. Chapitre (4 et 5): Le but principal de cette thèse était de fournir une approche multimodale du CNV et de la régulation neurovasculaire dans le cerveau du nouveau-né prématuré. Chapitre (4): Les résultats montrent que le volume sanguin cérébral régional (rCBV) et le rCMRO2 (Cerebral metabolic rate of oxygen) exercent une influence prédominante sur le débit sanguin cérébral régional (rCBF) à l'état de repos chez le prématuré. Chapitre (5): Les bouffées d'activité électroencéphalographique caractéristiques chez les nouveau-nés au repos se sont révélés couplées à une réponse hémodynamique transitoire complexes avec différents types de réponses incluant: (a) des réponses hémodynamiques stéréotypées positives (augmentations de HbO, CBF et CMRO2, diminution de HbR), (b) des réponses hémodynamiques négatives (augmentations de HbR, diminutions de HbO avec des diminutions de CBF et CMRO2), (c) des augmentations et des diminutions à la fois de HbO -HbR et de CMRO2 sans modification du CBF. Malgré des profils de réponse hémodynamique différents qui reflètent l'immaturité et la complexité des systèmes vasculaires et des réseaux neuronaux, l'établissement d'un couplage neurovasculaire a été caractérisé avec une évolution en fonction de l'âge.

grateful for all his constant support, excellent guidance, critical comments, creating an energetic atmosphere with his warmth and humor, and encouragement throughout my studies without which I would not have been able to produce this piece of work. I am especially appreciative of his patience in reviewing my thesis. I owe a huge debt of gratitude to Dr. Guy Kongolo for his support, patience, excellent guidance and advice. It has been my privilege to work closely with Dr. Fabrice Wallois and Dr. Guy Kongolo, I have enjoyed the opportunity to watch and learn from their knowledge and experience.

I would like to thank Dr. Mahdi Mahmoudzadeh, for his thoughtful supervision, for taking my hand and guiding me in this path and for all what he taught me.

I also wish to thank Dr. Sabrina Goudjil, for help during the recruitment and clinical data collection phases in NICU of the South hospital of Amiens, France.

This project was generously funded by the "Conseil Régional de Picardie", France. I am grateful for their financial support.

List of publications and presentations

Journal papers

• Nourhashemi M, Mahmoudzadeh M, Wallois F. "Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging. Neurophotonics". 2016 Jan;3(1):015001. doi: 10.1117/1. NPh.3.1.015001. Epub 2016 Jan 14.

• Mina Nourhashemi, Guy Kongolo, Mahdi Mahmoudzadeh, Sabrina Goudjil, Fabrice Wallois. "

Introduction & background Introduction

The localized increase in blood flow to regions of elevated neuronal activity is known as the neurovascular coupling (NVC). Even though many studies have been focused on this relationship in adult, the dynamic of the maturation and how much the maturation of the many compartments of this complex mechanism are unstable are still not completely understood especially in the preemies. NVC remains a key area of research due to its substantial consequences for medical diagnostics and fundamental neuroscience research. In the following sections of this chapter, at first, we will briefly describe the structure of the neuronal and vascular system and of the neurovascular unit, We will described the principle mechanisms underlying the neurovascular coupling, and some aspects of the immaturity of the neuronal, vascular and cardiovascular compartments. Finally, we will summarize the factors of immaturity of the neurovascular system that can influence the characteristics of the cerebral hemodynamic responses.

Structural aspects of the neuronal and vascular system

The brain consists of approximately 86 billion neurons. About 19% of the neurons constitute the cerebral cortex with the remaining 81% constitute the cerebellum [START_REF] Azevedo | Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain[END_REF], [START_REF] Herculano-Houzel | The human brain in numbers: a linearly scaled-up primate brain[END_REF]. Communication between neurons occurs via synaptic interaction mediated by neurotransmitter release and a combination of electrical and chemical signals in the form of action potentials that propagate along the neuron's axons [START_REF] Attwell | An energy budget for signaling in the grey matter of the brain[END_REF]. The neurons are functionally localized in a small area notably in the superficial grey matter (GM) [START_REF] Mountcastle | The columnar organization of the neocortex[END_REF] and largely interconnected via short and long distance interconnecting fibers that built up progressively in the course of development realizing a dense network for distributed neuronal functions. Almost 50% of the brain's energy cost can be attributed to the action potentials [START_REF] Attwell | An energy budget for signaling in the grey matter of the brain[END_REF]. All this energy is provided by oxygen and glucose supply related to cardiac output via an intricate network of blood vessels [START_REF] Duvernoy | Cortical blood vessels of the human brain[END_REF].

The anterior cerebral arteries arise from the Circle of Willis, to supply the primary motor and sensory areas of the cortex. Arteries have a thicker layer of smooth muscle along the vessel walls, which makes it possible for them to maintain vessel tone in the presence of blood pressure fluctuations and to provide active vasomotion. From the cortical surface, arteries and arterioles penetrate the neuronal layers perpendicularly to the surface and supply oxygen (95-100% oxygen saturation) to the neuronal tissues. Vascular density enhances in the cortical grey matter with increasing cortical depth in layers mainly involved with information processing [START_REF] Herkenham | Laminar organization of thalamic projections to the rat neocortex[END_REF][START_REF] Weber | The microvascular system of the striate and extrastriate visual cortex of the macaque[END_REF]. Capillaries lead back to small vessels known as venules (diameter 20 μm) that flow into the larger veins (diameter 120 μm) which are oriented perpendicular to the cortical surface and drain blood from capillaries compartments towards the largesurface cortical veins. Blood then finally exits the gray matter via the pial veins (diameter: 200 μm) and larger draining veins (diameter: 1-3 mm) with approximately 60% oxygen saturation. [START_REF] Duvernoy | Cortical blood vessels of the human brain[END_REF]. In contrast to arteries, veins undergo passive changes in vessel tone and diameter that result from changes in blood flow and pressure.

The different structural compartments of the neurovascular unit structure

The neurovascular unit is a dynamic structure consisting of neurons, astrocytes, pericytes, vascular endothelial cells and extracellular matrix components. It plays an essential role in the maintenance of a satisfactory levels of oxygen and nutrients in the brain (Fig. 1) [START_REF] Kratzer | Barrier mechanisms in neonatal stroke[END_REF][START_REF] Mcadams | The role of cytokines and inflammatory cells in perinatal brain injury[END_REF][START_REF] Moretti | Blood-brain barrier dysfunction in disorders of the developing brain[END_REF]. Astrocytes play a pivotal role in the regulation of the blood-brain barrier (BBB), as well as in neuronal synapses, to provide nutrients for neurons. The molecules are regulating astrocytic networks, and are coupling neuronal signals and metabolic activities to the cerebral vascular tones, thereby balancing oxygen and energy demands with the supply of cerebral blood flow [START_REF] Winkler | Central nervous system pericytes in health and disease[END_REF]. A unique feature of the brain vasculature is related to the endothelial vascular cells and the astrocyt endfeets, which define the blood-brain barrier (BBB). Inadequate blood supply leads to energy unbalance and reduction of ATP, followed almost by the deactivation of ion pumps, depolarization of neuronal membranes, accumulation of intracellular calcium, and cellular dysfunction [START_REF] Allen | Oxidative stress and its role in the pathogenesis of ischaemic stroke[END_REF]. Hence, the brain relies on a complex dynamic network of vessels and regulatory mechanisms to maintain proper perfusion and prevent from the injurious effects of low levels of inadequate blood supply. The neurovascular coupling following activation (adapted from Iadecola, 2004).

Astrocytes

Astrocytes used to be considered as passive elements and have a central position in the neurovascular coupling (Fig. 2A). The astrocytes, as primary glucose-consuming cells for energy-generating, play a central role to convey neuronal signals to the blood vessels playing a crucial role in facilitating stimulus-evoked changes in cerebral blood flow [START_REF] Attwell | Glial and neuronal control of brain blood flow[END_REF][START_REF] Petzold | Role of astrocytes in neurovascular coupling[END_REF].

Synaptic activities may propel the release of components (e.g., glutamate, ATP, K+, Ca++…) that are detected by neighboring astrocytes that induced an upstream arteriolar vasodilatation effect. Calcium is an indispensable factor in the link between neural activation, inter-astrocyt communication, increased astrocyt glucose utilization, and vasodilation. ATP and glutamate also interact with receptors on astrocytes that result in an increase in the calcium waves, across many astrocytes, which ultimately reache astrocyt endfeet in contact with cerebral arterioles and finally propel vasodilation. The calcium waves provide stimulus for a variety of vasodilating pathways, such as an increase in arachidonic acid (AA) [START_REF] Paulson | Cerebral blood flow response to functional activation[END_REF]. In addition the extracellular ATP can be rapidly converted to adenosine which also plays a key role in vasodilatation [START_REF] Paulson | Cerebral blood flow response to functional activation[END_REF]. Another factor linked to inter-astrocytic communication and vasodilation is the changes in K+ ion flux and local production of prostanoids [START_REF] Paulson | Cerebral blood flow response to functional activation[END_REF].

Beside their general vasodilatory facilitating effect astrocytes might also elicited vasoconstriction depending on the oxygen supply [START_REF] Gordon | Brain metabolism dictates the polarity of astrocyte control over arterioles[END_REF].

The immaturity of astrocytes is known (in size, number, branching and connectivity,) in the postnatal rat brain until postnatal day 21. In addition, the density of astrocytes does not reach the adult levels until postnatal day 50 [START_REF] Seregi | Are cerebral prostanoids of astroglial origin? Studies on the prostanoid forming system in developing rat brain and primary cultures of rat astrocytes[END_REF]. Finally, astrocytes gap junction coupling is established only at postnatal day 11 in the rat visual cortex [START_REF] Binmoller | Postnatal development of dye-coupling among astrocytes in rat visual cortex[END_REF].

Pericytes

Pericytes have also been identified as essential contributors to regulate blood flow in the brain. Pericytes are related to vascular smooth muscle cells and vascular mural cells that are found on the outer surface of microvessel endothelium (Fig. 2B) (capillaries, pre-capillary arterioles, and post-capillary venules) [START_REF] Armulik | Endothelial/pericyte interactions[END_REF]. As pericytes are found at discrete locations along capillary vessels, their capability to induce localized vasoconstriction was Chapter 1: Introduction & background demonstrated [START_REF] Peppiatt | Bidirectional control of CNS capillary diameter by pericytes[END_REF], but the functional role of pericytes in vivo may be limited [START_REF] Fernandez-Klett | Pericytes in capillaries are contractile in vivo, but arterioles mediate functional hyperemia in the mouse brain[END_REF]. Pericytes are deeply involved in the structural patterning and the stabilization of the vasculature of the brain during angiogenesis, but the origin and function of pericytes in the human cerebral cortex are controversial [START_REF] Fujimoto | Pericyte-endothelial gap junctions in developing rat cerebral capillaries: a fine structural study[END_REF]. The distribution of pericytes seem to decrease in adulthood, a situation that might be related to the maturation of the blood brain barrier. These developmental changes imply that pericytes might be not able to actively modulate capillary diameter during this dynamic period [START_REF] Diaz-Flores | Microvascular pericytes: a review of their morphological and functional characteristics[END_REF].

Fig. 2 A) Structural and molecular astrocytes connections within the neurovascular unit (Iadecola, 2004), B) The capillary network showed the structures around of pericytes [START_REF] La Torre | Morphological characteristics and distribution pattern of the arterial vessels in human cerebral cortex: a scanning electron microscope study[END_REF].

Endothelial cells

Whereas the longitudinal orientation of endothelial cells conducts signal along the length of vessels, the smooth muscle cells, are oriented perpendicularly to the endothelial cells, and are capable of actuating changes in vascular diameter by relaxing and contracting actions.

Endothelial cells react to a variety of pharmacological substances such as acetylcholine (ACh) and adenosine (Ado), which cause endothelial cells to release the vasodilator nitric oxide (NO) that leads to relaxation of smooth muscle cells. Endothelium-independent vasodilator act on the biochemical pathways in smooth muscle cells instead, triggering a chain of reactions that lead to either relaxation or contraction [START_REF] Ignarro | Nitric oxide as a signaling molecule in the vascular system: an overview[END_REF].

Interneurons

Interneurons, which primarily use inhibitory neurotransmitters GABA and glycine, have also been demonstrated to elicit microvessel diameter changes. The large number of interneurons exhibiting complex morphology and connectivity, makes it difficult to fully understand their entire role in vascular response [START_REF] Cauli | Cortical GABA interneurons in neurovascular coupling: relays for subcortical vasoactive pathways[END_REF]. They might be involved in the neurogenic neurovascular coupling.

Mechanisms of neurovascular coupling

Neurons primarily function with high levels of aerobic mitochondrial metabolism, in addition they function via anaerobic glycolysis and net lactate extrusion. Under normal conditions, glucose and its oxidation are the main energy source producing a metabolic pathway for the brain [START_REF] Siesjo | Brain energy metabolism and catecholaminergic activity in hypoxia, hypercapnia and ischemia[END_REF]. Since complete glucose oxidation has a stoichiometry of (C6H12O6 + 6O2 → 6CO2 + 6H2O), the cerebral metabolic rate of oxygen consumption (CMRO2) is equal to six times the cerebral metabolic rate of glucose consumption (CMRglc). Glucose breakdown in the vicinity of oxygen releases about 36 mol of ATP per mole of glucose (in aerobic mechanisms), whereas in the absence of oxygen (in anaerobic mechanisms) glycolysis and glycogenolysis releases 1-2 mol ATP per mole of glucose. The required oxygen for the brain was carried by hemoglobin while glucose can be stored in the glia. Neuronal and glial activities have a tight correlation with their energy consumption. Since the brain's energy stock is not sizeable, CBF dynamics is essential for normal brain function by providing nutrients and removing waste. CBF helps for oxygen delivery and clearance of the products of metabolism.

Cerebral tissues use about 20% of the body's oxygen via aerobic mechanisms. CBF controls the balance of metabolic demand to the oxygen supply, oxygen supply to the metabolic consumption and the metabolic consumption to product clearance.

Roy and Sherrington (1890) explained neurovascular coupling mechanism and the concept of a neurovascular unit, in this way; "the chemical products of cerebral metabolism contained in the walls of the arterioles can cause variations of the cerebral vessels: so its vascular supply can be varied locally in correspondence with local variations of functional activity." In the early 1960s, Lassen and Ingvar introduced a methodology to measure rCBF, and during the 1970s, it was more widely accepted that rCBF increases in response to cerebral activation [START_REF] Lassen | Brain function and blood flow[END_REF]. In general, the oxygen or glucose consumption or an increase in CO2

would act as a metabolic signal which then triggered vasodilatation [START_REF] Attwell | Glial and neuronal control of brain blood flow[END_REF]; Chapter 1: Introduction & background [START_REF] Attwell | An energy budget for signaling in the grey matter of the brain[END_REF]). However, the other studies provided evidence against this hypothesis, showing that the underlying mechanisms responsible for increases in CBF upon neuronal activation are more complex [START_REF] Mintun | Blood flow and oxygen delivery to human brain during functional activity: theoretical modeling and experimental data[END_REF][START_REF] Powers | Effect of stepped hypoglycemia on regional cerebral blood flow response to physiological brain activation[END_REF]. A mismatch in CBF-metabolism coupling was reported by Fox and Raichle [START_REF] Fox | Focal physiological uncoupling of cerebral blood flow and oxidative metabolism during somatosensory stimulation in human subjects[END_REF], who described that, during neuronal activation, regional CBF increased without substantial increases in oxygen demand. In fact, CBF can increase in the absence of any significant variations of the cerebral metabolic rate of oxygen (CMRO2) [START_REF] Fujita | Oxygen consumption of cerebral cortex fails to increase during continued vibrotactile stimulation[END_REF], and inversely, CMRO2 can increase with no significant increase of CBF [START_REF] Okazawa | Effect of vascular radioactivity on regional values of cerebral blood flow: evaluation of methods for H(2)(15)O PET to distinguish cerebral perfusion from blood volume[END_REF]. Whether or not a precise coupling exists between CBF and CMRO2 during neural stimulation has been the subject of numerous studies in both adults [START_REF] Raichle | Behind the scenes of functional brain imaging: a historical and physiological perspective[END_REF] and preemies (Mahmoudzadeh et al., 2013b;Mahmoudzadeh et al., 2017b;Nourhashemi et al., 2017b;Nourhashemi et al., 2016c). The essential point is that although it may not be a relationship between the CBF-CMRO2 changes, there is a relationship between the CMRO2 -CMRglc changes given glucose oxidation maintained over a wide range of activity [START_REF] Siesjo | Brain energy metabolism and catecholaminergic activity in hypoxia, hypercapnia and ischemia[END_REF]. With the limits of oxygen extraction, the cells switch to anaerobic metabolism. The recent evidence supports the functional attempt to accommodate the cerebral tissue's increased demand for glucose supply during neural activation with a crucial role of astrocytes in rCBF regulation [START_REF] Paulson | Cerebral blood flow response to functional activation[END_REF].

Local regulation of cerebral blood flow

A tight regulation of CBF is achieved through a complex interaction of functional brain mechanisms. In relation to Ohm's Law, pressure gradient and vascular resistance of the blood vessel are two inversely-related physiological factors affecting cerebral perfusion, (eq. 1). The pressure gradient is the difference between arterial blood pressure (ABP) and intracranial pressure (ICP) in which ICP is related to the pressure inside the skull and thus in the brain tissue and cerebrospinal fluid (CSF). Ohm's law analogy of cerebral blood flow regulation can be descriebed as follow: CBF = (arterial blood pressureintracranial pressure) / vascular resistance (1)

Flow is assumed to be constant in this linear relationship, although flow is pulsatile in the macrovasculature, this linear relationship explains the general circulatory system [START_REF] Rowell | Human Cardiovascular Control[END_REF]. The parameters in Equation ( 1 blood pressure (ABP) changes are more dominant than the fluctuation in ICP [START_REF] Hughson | Critical analysis of cerebrovascular autoregulation during repeated head-up tilt[END_REF]. Thus in the absence of cerebrovascular disease, ICP is assumed to be constant and equal to zero [START_REF] Aaslid | Cerebral autoregulation dynamics in humans[END_REF] and CBF changes is assumed to be more related to the changes in the vascular resistance. Poiseuille's law (Eq. 2) indicates that vascular resistance is a function of blood viscosity, vessel length, and vessel radius.

Vascular resistance = 8η•L/πr 4 (2)

Where η = viscosity, L = vessel length and r = vessel radius. The exponential influence of vessel radius indicates the complex local mechanisms that control vascular resistance and blood flow. The change in vascular diameters results from a combination of myogenic, neurogenic, and metabolic processes that regulate cerebrovascular resistance to maintain CBF [START_REF] Paulson | Cerebral autoregulation[END_REF].

Myogenic regulation

The myogenic regulation relates to the apparent reflexive response of the vascular muscle of arteries to changes in blood pressure via stress sensing mechanism. This regulation is primarily due to inherent properties of the vascular smooth muscle cells to contract when they are stretched and conversely, via changing the concentration of intracellular calcium through the opening or closing of voltage-gated calcium channels [START_REF] Harder | Pressure-induced myogenic tone and role of 20-HETE in mediating autoregulation of cerebral blood flow[END_REF]. The regulation of vascular smooth muscle tone is complex. The vasodilatory and vasoconstricting mediators exert their effects by the level of calcium concentration (such as angiotensin II and norepinephrine result in an increase calcium, which activates myosin kinase) and/or by direct activation of the enzymes (such as arterial natriuretic peptide and nitric oxide activate myosin phosphatase and, by dephosphorylating myosin, cause vasoralaxation). Astrocytes dilate arterioles by acting on smooth muscle cells through many intermediates such as nitric oxide (NO) and/or prostaglandin (PG), epoxyeicosatrienoic acids (EET) or potassium release [START_REF] Takano | Astrocyte-mediated control of cerebral blood flow[END_REF] and produce arachidonic acid (AA) that can act as a vasoconstrictor [START_REF] Metea | Glial cells dilate and constrict blood vessels: a mechanism of neurovascular coupling[END_REF]. KATP channels (adenosine triphosphate (ATP)-dependent potassium channel) are also involved in the regulation of the vascular tone [START_REF] Landry | The pathogenesis of vasodilatory shock[END_REF]. Recent study suggest that pericytes surrounding capillaries may also participate to vasodilation even faster than SMC in response to neural activity [START_REF] Hall | Capillary pericytes regulate cerebral blood flow in health and disease[END_REF].

Metabolic regulation

The metabolic regulatory mechanism refers to the relationship between local neural activity and cerebral perfusion [START_REF] Park | Nox2-derived reactive oxygen species mediate neurovascular dysregulation in the aging mouse brain[END_REF]. The hypothesis of metabolic regulation assumes the balance between cerebral metabolism and oxygen delivery by CBF.

Action potentials associated with increased extracellular potassium levels that lead to depolarization of the neuronal membrane potentials can directly or indirectly influence vascular tone through alteration of endothelial [START_REF] Filosa | Local potassium signaling couples neuronal activity to vasodilation in the brain[END_REF]. The metabolites from dynamic processes including lactate and adenosine can directly influence vascular smooth muscle tone that seeks to balance CBF to demand [START_REF] Liu | Relative contribution of cyclooxygenases, epoxyeicosatrienoic acids, and pH to the cerebral blood flow response to vibrissal stimulation[END_REF]. Metabolic regulation is a negative feedback control system that acts via a vasoactive substance.

Neurogenic regulation

The hypothesis of neurogenic regulation is about sympathetic innervation that controls the vessels resistance by the autonomic nervous system [START_REF] Rowell | Human Cardiovascular Control[END_REF]. In contrast to both myogenic and metabolic, neurogenic regulation on CBF is likely restricted to the more extensive cerebral arteries. Larger arteries on the brain's surface are innervated by the sympathetic and the parasympathetic nervous system. Sympathetic nerves directly innervate the vascular smooth muscle through the release of norepinephrine and neuropeptide Y [START_REF] Farkas | Cerebral microvascular pathology in aging and Alzheimer's disease[END_REF].

In addition neurogenic regulation is related to the effects of interneurons and neurons.

Interneurons such as γ-Aminobutyric acid (GABA) and glutamate-mediated NVC have vasodilator effects on the microvasculature in cortical and subcortical regions [START_REF] Cauli | Cortical GABA interneurons in neurovascular coupling: relays for subcortical vasoactive pathways[END_REF][START_REF] Kocharyan | Specific subtypes of cortical GABA interneurons contribute to the neurovascular coupling response to basal forebrain stimulation[END_REF], and the neurons mainly contribute to the large and rapid vasodilation during NVC [START_REF] Lacroix | COX-2-Derived Prostaglandin E2 Produced by Pyramidal Neurons Contributes to Neurovascular Coupling in the Rodent Cerebral Cortex[END_REF]. Thus neurovascular coupling is a complex interaction between many parameters and the coupling phenomenon is not merely described as a direct relation. Balloon model: The balloon model incorporates the conflicting effects of dynamic changes in both blood oxygenation and blood volume in the presence of tight coupling of cerebral blood flow and oxygen metabolism throughout the activation period. In this model, it was assumed that there is no capillary recruitment and by considering the oxygen limitation, the blood volume changes occur primarily in the venous compartment. The arteriolar expansion that produces a flow increase is assumed to be a negligible change in blood volume. The vascular bed is then modelled as a dilatational venous compartment like a balloon. The volume flow rate into the tissue, as a driver of system, is defined as a function of time. The volume flow out of the system, is assumed to be dependent on the pressure in the venous compartment. As the physical picture of this model, after the arteriolar resistance is decreased, producing an increase in flow into the venous balloon, then the venous balloon swells, and the pressure increases until the flow into the balloon matches the flow out of balloon. The relationship between flow (F) and volume (V) in a compliant compartment in balloon model was defined: 𝑑𝑉 𝑑𝑡 = 𝐹 𝑖𝑛 (𝑡) -𝐹 𝑜𝑢𝑡 (𝑣), [START_REF] Buxton | Dynamics of blood flow and oxygenation changes during brain activation: the balloon model[END_REF].

Windkessel model: A physiologic model was proposed for the observed temporal mismatch between rCBF and rCBV. rCBF is determined by vasomotor control of arterioles, which produce about 70% of cerebral vascular resistance, but 80% to 85% of CBV is contained in capillaries and veins. The capillary and venous compliance was modelled in windkessel model to passively respond to pressure modulated by arteriole dilation and contraction. The relationship between flow and volume in a compliant compartment in this model was defined:

= V τ + dV dt
, where 𝞃 is the transit time for a volume element and dV/dt is the rate of volume change. At steady state, where dV/dt= 0, the changes in flow is equal to V/𝞃 as the central volume principle. Alternatively, F and V/𝞃 may represent flow into and out of an arbitrary compartment, this equation is then conservation of mass as described by the balloon model 𝐹 𝑖𝑛 -𝐹 𝑜𝑢𝑡 = 𝑑𝑉 𝑑𝑡 [START_REF] Mandeville | Evidence of a cerebrovascular postarteriole windkessel with delayed compliance[END_REF].

Cerebral autoregulation

Cerebral autoregulation (CA) [START_REF] Lassen | Cerebral blood flow and oxygen consumption in man[END_REF], refers to the physiological mechanisms that maintain CBF at an appropriate level during changes in ABP. It is functional for perfusion pressures between 60 and 150 mmHg [START_REF] Paulson | Cerebral autoregulation[END_REF][START_REF] Van Beek | Cerebral autoregulation: an overview of current concepts and methodology with special focus on the elderly[END_REF].

Autoregulation is independent of endothelial function, but is endogenous to all vascular smooth muscle cells as an intrinsic myogenic reflex. These mechanisms provide the main protection to the brain when the pressure increases or decreases [START_REF] Lassen | Normal average value of cerebral blood flow in younger adults is 50 ml/100 g/min[END_REF]. Outside this range of pressures, a cerebral blood flow pressure-passivity occurs, results in changes in CBF that track changes in MAP. The myogenic mechanism is thought to contribute as a primary mechanism of the cerebral autoregulation process, in vitro [START_REF] Harder | Pressure-induced myogenic tone and role of 20-HETE in mediating autoregulation of cerebral blood flow[END_REF] and in vivo [START_REF] White | Effect of inhibition of nitric oxide synthase on dynamic cerebral autoregulation in humans[END_REF]. Other studies demonstrate the subsidiary role of surrounding tissues including the endothelium, neuronal glia and/or autonomic nervous system.

There is a linear relationship between the changes in CBF, CMRO2, and CBV under normal conditions. To assess cerebral autoregulation the correlation between cerebral perfusion pressure (CPP) and CBF should be examined, here CPP is the difference between the meanarterial pressure (MAP) and the intracranial pressure (ICP). When cerebral perfusion pressure (CPP) decreases below the limit of autoregulation, the CBF also falls, but CMRO2 remains the same temporarily. This condition is considered as "misery perfusion" where cerebral autoregulatory capacity is exhausted, and cerebral blood supply is insufficient to meet metabolic demand. This "misery perfusion" results in a focal increase in the oxygen extraction fraction (OEF) up to the maximum value and leads to sustain brain's oxygen despite decreased CBF. Extra drops in CPP lead to ischemia and impaired neuronal function [START_REF] Sette | Local brain haemodynamics and oxygen metabolism in cerebrovascular disease. Positron emission tomography[END_REF].

Ischemic damage can be potentially reversible, or irreversible depending on CBF and CMRO2 threshold values [START_REF] Baron | Inter relationships of local CBF, OEF and CMRO2 in ischemic areas with variable outcome: further PET studies in humans[END_REF]. In adult, gray matter generally progresses to infarction if CMRO2 reach values below 1.3-1.5 mll.l00 g/min during more than 2-6 hours after a stroke.

If CMRO2 is maintained above these values, tissue can be salvageable, consistent with the concept of potentially reversible ischemia. If oxygen supply is more than demand, a reduction of the OEF can be observed, which supposed that perfusion had been re-established [START_REF] Ackerman | PET studies in acute stroke: Findings and relevance to therapy[END_REF][START_REF] Powers | Cerebral blood flow and cerebral metabolic rate of oxygen requirements for cerebral function and viability in humans[END_REF].

When blood flow is failing, there are several lines of defensive mechanisms against oxygen insufficiency and thus tissue damage. First, when blood pressure drops, autoregulation of CBF Chapter 1: Introduction & background will decrease vascular resistance to maintain blood flow almost unchanged (in newborn, the conduit arteries are very reactive and have a more critical contribution to the vascular resistance). If the blood pressure falls toward the lower limit of autoregulation, or in impaired autoregulation due to the pathology or immaturity, CBF decrease. Then oxygen extraction increases up to 50-60% (typical oxygen extraction is about 30%). When the limits of this compensation of oxygen extraction have been reached (up to 50-60%), the cells switch to anaerobic metabolism -increase glucose consumption to produce lactate. Insufficient oxygen or decreased oxygen consumption lead to a loss of metabolic function and cellular death (Fig. 3). In newborn infants, "hypoxic hypometabolism" is a mechanism that can be partially protected against hypoxic-ischemic injury [START_REF] Greisen | Chapter 2 -Autoregulation of Vital and Nonvital Organ Blood Flow in the Preterm and Term Neonate A2 -Kleinman[END_REF].

In autoregulation mechanism arterial smooth muscle tone is affected by different factors such as hypoxia, PCO2, changes in pH, local production of adenosine, ATP and NO, and other local neural mechanisms.

Autoregulation and hypoxia

Hypoxia induces tissue lactic acidosis and affects the entire endothelial function and the local nitric oxide (NO) production. Hypoxia decreases smooth muscle membrane potential by affecting the calcium-activated and ATP-sensitive K+ channels in the cell membrane. In the immature brain, adenosine is another factor that affects the vascular response to hypoxia. Since the membrane potential response to hypoxia is independent of the pressure, at lower pressures and in a hypotensive neonate, a superimposed hypoxic event cannot compensated this low perfusion pressure, thus leading to hypoxia-ischemia [START_REF] Greisen | Chapter 2 -Autoregulation of Vital and Nonvital Organ Blood Flow in the Preterm and Term Neonate A2 -Kleinman[END_REF].

Autoregulation and PCO2

Arteries and arterioles constrict with hypocapnia and dilate with hypercapnia. This reaction is mediated through changes in pH, which affect outward K+ current (in arterial smooth muscle cells) and calcium channels [START_REF] Greisen | Chapter 2 -Autoregulation of Vital and Nonvital Organ Blood Flow in the Preterm and Term Neonate A2 -Kleinman[END_REF]. Chapter 1: Introduction & background Fig. 3 The lines of defense against oxygen insufficiency, modified from: [START_REF] Greisen | Chapter 2 -Autoregulation of Vital and Nonvital Organ Blood Flow in the Preterm and Term Neonate A2 -Kleinman[END_REF].

Autoregulation in the immature brain

Regulation of blood flow depends on many parameters in neonates. Recruitment of capillaries and extraction of oxygen plays a fundamental role in CBF regulation as well as other systemic factors like blood pressure, cardiac output, central venous pressure, systemic vascular resistance, partial pressure of oxygen and carbon dioxide in the arteries, postnatal and gestational age and patent ductus arteriosus (PDA).

There is less vasodilator reserve in the pressure-flow autoregulation in the immature cerebral vasculature, which restrains the efficacy of CBF autoregulation at earlier stages of development. Some studies of autoregulation in stable neonates without evidence of major brain injury suggest that autoregulation is intact [START_REF] Greisen | Cerebral blood flow, PaCO2 changes, and visual evoked potentials in mechanically ventilated, preterm infants[END_REF]. In contrast, evidence of absence autoregulation has been found under pathologic conditions such as birth asphyxia and in preterm infants with brain injury [START_REF] Milligan | Failure of autoregulation and intraventricular haemorrhage in preterm infants[END_REF]. It was shown that the lower threshold of blood pressure for CBF autoregulation might be about 30 mmHg or below in premature neonates. Moreover, autoregulation can be assumed to be operate in most newborn infants, even the most immature. In neonates a significant blood flow can be present until the blood pressure is less than 20 mmHg [START_REF] Greisen | Cerebral blood flow, PaCO2 changes, and visual evoked potentials in mechanically ventilated, preterm infants[END_REF].

Cellular hypoxic injury

↓ Oxygen consumption

Anaerobic metabolism

↑ Oxygen extration fraction

Vasodilataion (autoregulation) Arterial hypotension Chapter 1: Introduction & background

Neuronal network development

In this section, a summary of the essential characteristics of the cerebral electrical activity of the premature and full-term newborn according to conceptional age (CA) will be presented.

Spontaneous electrocerebral activity in premature newborn infants -especially during the last trimester-evolves more rapidly than at any other time during human life. The rapid enlargement of the brain takes place from 28 weeks to 40 weeks CA. Its appearance changes take place before 24 weeks when the surfaces of the cerebral hemispheres are smooth, to 28 weeks when the major sulci have appeared and continue to develop. Rapid maturational changes are also apparent in the neurochemical milieu; in interneuronal connectivity, in dendritic trees and synaptogenesis; and in the myelination of axons. Despite maturational changes in anatomy, progress in brain's function is rather extensive. The premature infant of 28 weeks CA is capable of motor activity, vigorous crying, and response to syllables stimulation (Mahmoudzadeh et al., 2013b). The appearance and disappearance of specific electroencephalographic features for a given age are related to the transient activation of underlying neural networks. Such the temporal theta activities of immaturity are present before 23 weeks CA and disappear around 30 weeks CA in quiet sleep [START_REF] Lamblin | Electroencephalography of the premature and term newborn. Maturational aspects and glossary[END_REF].

The cerebral activity of the premature newborn is composed of bursts containing specific patterns such as theta bursts, delta brushes, sharp frontal transients and rhythmic frontal delta activity. The characteristics of these activities are presented in the following figure (Fig. 4). The delta brushes consist of a slow wave (delta) associated with fast rhythms (the brushes) which suggests the synchronization or coalescence of two generators. These elements disappear simultaneously by decreasing amplitude gradually as the premature infant approaches term.

Neither the structure of these generators, nor the neural network, nor their distribution, nor the neurochemical mechanisms, nor their roles have been yet elucidated. The following figure summarizes the various EEG change as the premature infant matures to term.

Interhemispheric synchrony of cerebral bursts of activity during discontinuous portions of the EEG recording is another character of the premature neonatal brain. The degree of interhemispheric synchrony in the very young premature infant (younger than 29 weeks CA) is high around 90 to 100 percent, but it decreases to 60 to 80 percent from 30 to 35 weeks CA and gradually approaches 100 percent as the infant reaches term [START_REF] Hahn | Chapter 4 -Neonatal and Pediatric Electroencephalography A2 -Aminoff[END_REF]. The EEG patterns of the newborn are also dependent on the behavioral states during the recording that includes active (rapid eye movement or REM) and quiet (non-REM) sleep. EEG should be recorded in both sleep states since abnormalities may be found only in one sleep state [START_REF] Hahn | Chapter 4 -Neonatal and Pediatric Electroencephalography A2 -Aminoff[END_REF]. [START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF].

Fig.4 Synopsis of maturation of specific features in EEG of premature neonates

The development of the subplate and thalamocortical connections in neonatal brain

By 5-6 wGA, neuroblasts, or neuronal precursors, are proliferating rapidly within the ventricular zone (de [START_REF] De Graaf-Peters | Ontogeny of the human central nervous system: what is happening when?[END_REF]. The radial and tangential neuronal migrations continue to be completed. The disturbances of this migration could explain the disorders observed at the 25th wGA in the periventricular zone which will affect brain development. Cortical connectivity is set up corresponding to the growth of axons and dendrites and will be influenced by surrounding neuronal and synaptic activity (Le [START_REF] Bé | Spontaneous and evoked synaptic rewiring in the neonatal neocortex[END_REF]. Chapter 1: Introduction & background As early as 9-11 wGA, and before maturation of the brain connections, a transitional structure is set up called "subplate" (Fig. 5). This sub-plate is located under the cortical plate which is four times thicker than the cortical plate. It consists of well-differentiated postmigratory neurons, migrating neurons, glial cells and especially thalamocortical axons "waiting" before they penetrate to the cortical plate. It contains pre-synaptic elements, synapses, and postsynaptic elements. This contrasts with the cortical plate that does not contain synapses during this developmental period. At this time, the subplate is an essential site of synaptic interaction [START_REF] Tau | Normal development of brain circuits[END_REF]. In addition, it receives information conveyed by the thalamocortical fibers capable of activating the subplate in response to peripheral sensory stimulation. When the electrical activity of subplate neurons is recorded from cerebral fetal tissues (20-21 wGA), several types of activity have been identified [START_REF] Moore | Spontaneous electrical activity in the human fetal cortex in vitro[END_REF]. These activities are recorded in vitro from brain slices even at 20 wGA, while functional synaptic contacts at the cortical level are still scarce. This suggests that subplate neurons play a crucial role in the activities recorded in EEG. Thus, the generation of a discontinuous activity could be an intrinsic property of the subplate neurons.

Before 26 weeks GA, thalamocortical afferents accumulate in the subplate without penetrating to the cortical plate. They establish connections with the neurons of the subplate, which constitutes the emergence of the first neural networks with the appearance of a spontaneous endogenous activity. Between 28 and 30 weeks, the thalamocortical afferents invade the cortical plate where they establish the first synapses with the final cortical neurons.

The subplate that already processed the information from the thalamus would play an essential role in providing a thalamic, sensory influence in the development of neural circuits of the cortical plate [START_REF] Kanold | The subplate and early cortical circuits[END_REF].

Between 31 and 33 weeks of GA, the thalamocortical axons establish synapses with the neurons of the layer IV and have their activity which begins to be modulated by the sensory afferents. In parallel with this cortical synaptogenesis, the theta temporal activities on the EEG tend to disappear and to be replaced by slow waves surmounted by fast rhythms: the deltabrushes. It is interesting to note that these delta-brushes were recently considered as neurobiomarkers of sensory synaptogenesis in the somaesthetic and visual modalities without demonstrating that subplate is involved [START_REF] Colonnese | A conserved switch in sensory processing prepares developing neocortex for vision[END_REF]. This period is marked by a revival of inter-hemispheric asynchrony. During the period from 28 wGA up to 33-34 wGA maximum, pathological elements, specific to periventricular leukomalacia, called positive rolandic spikes may appear. These are slow, high amplitude waves that share specific shape features with theta temporal activities (Laura paper 2017). In addition to their morphological characteristics, these pathological elements provide additional arguments on the role of the subplate in the activities recorded in EEG. Indeed, the source localization of these activities is related to an activation of structures located under the cortical plate that could very well correspond to the subplate and the usual locations of white matter lesions of periventricular leukomalacia [START_REF] Sarnat | Cajal-Retzius and subplate neurons: their role in cortical development[END_REF].

Between 34 and 37 weeks of GA, the subplate disappears, the neurons of the subplate join the layer VI or die by apoptosis. This period is dominated by the growth of inter-hemispheric connections. At the same time, inter-hemispheric synchronization are taking place. The EEG inter-hemispheric asynchrony disappears, the amplitude of the delta-brushes decreases. The rolandic positive spikes of periventricular leukomalacia are no longer recorded by EEG.

Thus in the age group 28-32 wGA, we can observe the initiation of the functional and sensory connectivity of the cortical plate. Nevertheless, the subplate is the most active structure in preterms and could participate in the recorded brain activity on the surface of the scalp. The subplate could also participate in the development of the functional organization of neural networks of the cortical plate. It could participate in the guidance of neuronal axons of cortical layers V and VI, as well as in inter-hemispheric synchronization. We are thus in a situation of two networks operating in parallel: subplate and cortical plate, both of which receive sensory information and have synaptic substances capable of interacting with each other and producing signals recorded on the surface of the scalp. [START_REF] Kostovic | The development of the subplate and thalamocortical connections in the human foetal brain[END_REF].

Burst of activities

One of the essential characteristics of the newborn's cerebral activity (especially in the premature infants) is the discontinuity (Fig. 6). These specific EEG patterns serve as useful markers for determining the CA of the infant's nervous system. The mean duration of this discontinuity (interburst intervals) in the healthy premature infant decreases with increasing gestational age; the mean IBI at 27 to 29 wCA is approximately 6 seconds, and at 30 to 34 wCA is approximately 4 to 5 seconds. The maximum IBI should not exceed approximately 30 seconds at any age and ay any sleep stage beyond 27 wCA [START_REF] Hayakawa | Background electroencephalographic (EEG) activities of very preterm infants born at less than 27 weeks gestation: a study on the degree of continuity[END_REF][START_REF] Selton | Normal EEG in very premature infants: reference criteria[END_REF]. The excessive discontinuity can be considered as a neuorobiomarker of cerebral disorder, so the time dimension must be taken into account. This discontinuity suggests complex maturation processes that play an essential role in endogenous brain oscillators. The patterns of EEG burst of activities can be specified based on age in the preterm infant (Fig. 7, Fig. 8).

At 23 to 26 wCA, bursts can be longer and IBI shorter. [START_REF] Biagioni | Occipital sawtooth: a physiological EEG pattern in very premature infants[END_REF] found that the maximum IBI duration ranged between 20 -62 seconds and the minimum burst length was 1 -2 seconds, while, Hayakawa et al. found the maximum IBI duration about 87 seconds at 23-24 w CA and 44 seconds at 25-26 wCA [START_REF] Hayakawa | Background electroencephalographic (EEG) activities of very preterm infants born at less than 27 weeks gestation: a study on the degree of continuity[END_REF].

At 27 to 29 wCA, the maximum IBI are generally less than 30 seconds and there may be EEG differentiation of active sleep (REMs are observed with a burst of slow waves admixed 32 Chapter 1: Introduction & background with theta activity) and quiet sleep states (REMs are absent, and the background becomes more discontinuous) [START_REF] Selton | Normal EEG in very premature infants: reference criteria[END_REF].

At 30 to 32 wCA, discontinuous background composed of an admixture of the occipital delta, theta, and alpha range activity occurs in quiet sleep. More continuous background occurs in active sleep [START_REF] Hahn | Chapter 4 -Neonatal and Pediatric Electroencephalography A2 -Aminoff[END_REF]. At 38 to 42 wCA, sleep, and waking cycles are well established [START_REF] Hahn | Chapter 4 -Neonatal and Pediatric Electroencephalography A2 -Aminoff[END_REF]. Fig. 7 Longest continuous period of cerebral activity at various conceptional ages (CAs). Image source: (Hahn JS et al., 1989).

Chapter 1: Introduction & background

Fig. 8 The maximum interburst interval (IBI) versus conceptional age (CA). A, For type 1 IBIs (intervals of at least 2 seconds containing no cerebral activity greater than 15 mV in any channel). B, For type 2 IBIs (similar to type 1 IBIs, except for a transient lasting less than 2 sec in one or two electrodes or continuous cerebral activity greater than 15 mV in one electrode) (Hahn JS, et al. 1989).

Vascular network development

Parallel to the maturation of brain structures and neural networks, there is a maturation of the vascular system in newborns. At birth, there is an increase in vascular volume and approximately 30% decrease in the distance between any point of the brain tissue and the nearest vessel [START_REF] Risser | A 3D-investigation shows that angiogenesis in primate cerebral cortex mainly occurs at capillary level[END_REF]. Different studies suggest that vascular proliferation may be partly related to metabolic demand and structures requiring increased energy demand [START_REF] Weber | The microvascular system of the striate and extrastriate visual cortex of the macaque[END_REF]. Some studies in preterm infants demonstrated that functional small vessel density changes over the first postnatal month and directly correlates with hemoglobin concentration and environmental temperature. In the neonatal brain, vascular density growth is rapid between 26 and 35 wGA and continues beyond 36 weeks [START_REF] Miyawaki | Developmental characteristics of vessel density in the human fetal and infant brains[END_REF]. From the 28th to the 32nd wGA, the irrigation of the CBF decreases in the germinal zone in favor of the cortex. The arteries increase in size to irrigate the white substance, and small cortical arteries appear to irrigate the gray matter [START_REF] Saliba | Hémodynamique cérébrale postnatale (débits sanguins cérébraux et autorégulation cérébrale[END_REF]. Before 30th wGA, the vessels are still immature, and the immaturity prevents them from participating in the regulation of CBF and makes them vulnerable to sudden changes in intraluminal pressure. Also it was reported, the aminergic systems which release the transmitters as vasoconstrictors for the maintenance of resting vascular tone, expand postnatally [START_REF] Goldman-Rakic | Postnatal development of monoamine content and synthesis in the cerebral cortex of rhesus monkeys[END_REF].

In neonates, the highest glucose uptake was observed in the sensorimotor cortex, with low functional activity over of the other regions. Increased glucose uptake in the parietal, temporal and primary visual cortices were observed during the second and third months of neonatal life, coinciding with improvements in motor, auditory and visual skills [START_REF] Albers | Bayley Scales of Infant and Toddler Development-Third Edition[END_REF][START_REF] Ferry | Neurological assessment during the first year of life[END_REF] in addition to changes in the neonatal EEG [START_REF] Kellaway | Orderly approach to visual analysis: Elements of the normal eeg, and their characteristics in children and adults[END_REF]. Moreover, similar developmental dynamics have been observed in CBF [START_REF] Altman | Cerebral blood flow requirement for brain viability in newborn infants is lower than in adults[END_REF][START_REF] Tokumaru | The evolution of cerebral blood flow in the developing brain: evaluation with iodine-123 iodoamphetamine SPECT and correlation with MR imaging[END_REF]. Increasing in regional myelination is accompanied by increases in glucose uptake and CBF [START_REF] Peterson | Regional brain volumes and their later neurodevelopmental correlates in term and preterm infants[END_REF], accompanying with the augmentation of energy demand and cerebral activity in myelinated regions. CMRO2 was reported higher in term neonates compared to premature neonates [START_REF] Elwell | Measurement of CMRO2 in neonates undergoing intensive care using near infrared spectroscopy[END_REF][START_REF] Skov | Estimation of cerebral venous saturation in newborn infants by near infrared spectroscopy[END_REF][START_REF] Yoxall | Measurement of cerebral oxygen consumption in the human neonate using near infrared spectroscopy: cerebral oxygen consumption increases with advancing gestational age[END_REF]. The reaction of CBF to acute changes in CO2 would be strongly attenuated in the preterm infants supported by mechanical ventilation for about the first 24 hours of life, for reasons which are not explicitly established [START_REF] Pryds | Heterogeneity of cerebral vasoreactivity in preterm infants supported by mechanical ventilation[END_REF].

During the first six weeks of life whatever the GA, Labarbe et al. show (i) a constant decrease in SO2 due to the decrease in hemoglobin (HGB) while CBV remains stable, and (ii) a constant increase in CBF to maintain appropriate brain oxygenation despite the HGB decrease [START_REF] Roche-Labarbe | Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates' brains in the first six weeks of life[END_REF]. Lin et al. show that hemodynamic (CBV, CBFi, and SO2) and metabolic (CMRO2i) parameters were higher in the temporal and parietal regions than in the frontal region and that these differences increased with postmenstrual age (PMA). Also, all these parameters were significantly higher in the right hemisphere than in the left (Lin et al., 2013b). Labarbe et al. show that cerebral hemoglobin oxygenation (SO2) is not correlated with postmenstrual age (PMA) but varies with chronological age and HGB; suggesting that SO2 depends on systemic changes whereas CBF and rCMRO2 correlate better with PMA. CBF and rCMRO2 are more accurate biomarkers of the brain development than SO2 in the premature newborns [START_REF] Roche-Labarbe | Near-infrared spectroscopy assessment of cerebral oxygen metabolism in the developing premature brain[END_REF].

Since the density of neuronal and vascular networks and also the neurovascular coupling itself are not as mature in the preemies as in the adult, the responses to neuronal activation may have different hemodynamic characteristics depending on age [START_REF] Harris | The physiology of developmental changes in BOLD functional imaging signals[END_REF].

Cerebral hemodynamic response in developmental brain

It is commonly accepted the hypothesis that regional brain activation is accompanied by increases in CBF and CMRO2. As the increase in rCBF exceeds the increase in rCMRO2, this results in a decrease in the HbR in venous blood and increases in HbO (Fig . 9). Several studies [START_REF] Hoshi | Dynamic multichannel near-infrared optical imaging of human brain activity[END_REF][START_REF] Kato | Human visual cortical function during photic stimulation monitoring by means of near-infrared spectroscopy[END_REF][START_REF] Kleinschmidt | Simultaneous recording of cerebral blood oxygenation changes during human brain activation by magnetic resonance imaging and near-infrared spectroscopy[END_REF] have shown either an absence of HbT variation with an increase in HbO/decrease in HbR, or an increase/absence of HbR accompanying HbT and HbO increases. Besides, the initial dip may correspond to an increase in HbR due to a mismatch between CMRO2 and CBF [START_REF] Kim | Temporal dynamics and spatial specificity of arterial and venous blood volume changes during visual stimulation: implication for BOLD quantification[END_REF], or increases in CBV [START_REF] Buxton | Dynamics of blood flow and oxygenation changes during brain activation: the balloon model[END_REF]. Both negative and positive hemodynamic responses to stimulation have been observed in the developing human brain using NIRS as well as fMRI BOLD responses. An increase in HbT, HbR, and HbO suggest insufficient hyperemia to meet oxygen demands (Fig. 10B).

Further, a decrease in HbT and HbO with an HbR increase, suggest that the local vasoconstriction reinforce HbR increases (Fig. 10C). Kozberg, 2016).

fNIRS reflects Hb oxygenation in arterioles, capillaries, and venules because fNIRS is more sensitive to small vessels since light is almost entirely absorbed by large vessels [START_REF] Mancini | Validation of near-infrared spectroscopy in humans[END_REF]. Although there is no precise vascular specificity of fNIRS, one argument is that fNIRS signals particularly corresponds to capillary oxygenation [START_REF] Rasmussen | Capillary-oxygenationlevel-dependent near-infrared spectrometry in frontal lobe of humans[END_REF]. Chapter 1: Introduction & background Alternatively another argument is that fNIRS corresponds to venous, capillary, and arterial blood within the sampling volume (Murkin and Arango, 2009) (Fig.11). Different studies of the developing brain indicated differences in postnatal brain hemodynamic responses compared to the adult brain as it was shown in (Fig. 12) (M. Kozberg, 2016). The newborn brain was observed to have a lower baseline synaptic and vascular density, a lower CBF and CMRO2, which increases to adolescence rates by increasing age. These values then decline to adulthood values by the late teenage years. But capilary density increas after childhood (Fig. 12).

Neurovascular coupling in resting state

Much of what we currently know about brain function and neurovascular coupling have been derived from studies using external stimulus. In recent years, another rapidly growing approach called resting-state is being used to understand the neuronal and vascular function of the brain in the absence of an externally provoked task [START_REF] Fox | Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging[END_REF][START_REF] Power | Studying brain organization via spontaneous fMRI signal[END_REF]. The goal of a resting state study is to evaluate spontaneous brain activity without presenting any external task or stimuli, i.e., measuring brain activity at "rest". The initial studies of the spontaneous brain activity were met with doubt, as it was suspected that this signal was driven by noise and was not explicitly organized as it is in response to tasks. In 1995, Biswal and colleagues were the first group that showed spontaneous hemodynamic fluctuations in the absence of a task, occurring in the same brain regions that were active during finger tapping [START_REF] Biswal | Functional connectivity in the motor cortex of resting human brain using echo-planar MRI[END_REF]. Other groups have been worked on resting state in other brain regions as Chapter 1: Introduction & background well [START_REF] Cordes | Mapping functionally related regions of brain with functional connectivity MR imaging[END_REF][START_REF] Hampson | Detection of functional connectivity using temporal correlations in MR images[END_REF][START_REF] Lowe | Functional connectivity in single and multislice echoplanar imaging using resting-state fluctuations[END_REF][START_REF] Stein | Functional connectivity in the thalamus and hippocampus studied with functional MR imaging[END_REF][START_REF] Xiong | Interregional connectivity to primary motor cortex revealed using MRI resting state images[END_REF].

Using combined fNIRS-EEG, Hoshi et al. [START_REF] Hoshi | Relationship between fluctuations in the cerebral hemoglobin oxygenation state and neuronal activity under resting conditions in man[END_REF] demonstrated that the changes in HbO in the frontal and occipital regions during a 15-min resting period in healthy adult brains could correspond to brain activities.

Relatively recent findings in premises, at rest, performed in our laboratory, show that there is a correlation between EEG discontinuity of prematurity and cerebral metabolic activity in resting-state (Roche-Labarbe et al., 2007a). The results suggest that the interactions between the two neuronal and vascular networks are likely to participate in the modulation of the cerebrovascular activity.

Cardiovascular development

Fetal circulation is characterized by low systemic vascular resistance with high systemic blood flow and high pulmonary vascular resistance with low pulmonary blood flow. Given the low oxygen tension in the fetus, fetal circulation with the placenta helps to provide more oxygenated blood to the vital organs. The arterial canal (ductus arteriosus) is a vessel that connects the left pulmonary artery with the descending aorta in the fetus. The foramen ovale is a small hole located in the wall between the two upper chambers of the heart. The most of the right ventricular output is passed through the patent ductus arteriosus (PDA) to the systemic circulation. The pulmonary blood flow constitutes 11-25% of the combined cardiac output that supplies blood to the lungs with the peak around 30 wGA. The systemic blood flow depends on the connections between the systemic and pulmonary circuits via the foramen ovale and PDA during fetal life [START_REF] Mielke | Cardiac output and central distribution of blood flow in the human fetus[END_REF].

Transitional physiology

At birth, the systemic vascular resistance increases due to the removal of low resistance placental circulation and the increase in catecholamines and other hormones. The pulmonary vascular resistance and CBF decrease due to the act of breathing air and pressure of oxygen. A drop in CBF in the first few minutes after birth in normal term neonates was also reported (Noori et al., 2012b). This decrease in CBF was due to the increase in arterial blood oxygen, a possible role of PDA and the inability of the immature myocardium to pump against the suddenly increased systemic vascular resistance (Noori et al., 2012b). Chapter 1: Introduction & background After birth, in term infants, PDA will be closed and the circulation changes from parallel to series. However in very preterm infants, due to the inability of the ductus arteriosus to close, the left and right ventricular outputs could not become equal. Due to the persistence of the PDA, the hemodynamics significantly alters during the transition.

Microcirculatory physiology

Under resting physiologic conditions, CBF is regulated by a baseline vascular tone under the influence of the autonomic nervous system. On the other hand, microcirculation (the small arteries and arterioles and the venules and small veins) plays a significant role in regulating systemic and local hemodynamics. The inverse relationship between microvascular CBF and systemic vascular resistance (SVR) and mean BP immediately after delivery was no longer present by the fifth day of postnatal life [START_REF] Kroth | Functional vessel density in the first month of life in preterm neonates[END_REF].

Oxygen delivery is dependant on the oxygen content of the blood, on the cardiac output and on the blood pressure. It is determined by the interaction between SVR and cardiac output (systemic blood flow). In fact, if systemic vascular resistance is too low, blood pressure may decrease below a critical level where oxygen delivery becomes compromised despite normal or even high cardiac output. Some studies have described the possible lower limits of BP below which autoregulation of CBF are impaired in very low birth weight in preterm infants [START_REF] Munro | Hypotensive extremely low birth weight infants have reduced cerebral blood flow[END_REF][START_REF] Victor | Relationship between blood pressure, cerebral electrical activity, cerebral fractional oxygen extraction, and peripheral blood flow in very low birth weight newborn infants[END_REF]. When the supply of oxygen to the tissues does not meet oxygen demand, neuroendocrine compensatory mechanisms and increased oxygen extraction maintain perfusion pressure and blood flow, to compensate oxygen delivery. The uncompensated phase of oxygen delivery results in the loss of vital organ blood flow autoregulation and the development of lactic acidosis, and then cellular function become compromised.

The circulatory function is dependant on the neural, hormonal, and metabolic mechanisms at the central and local levels, and is regulated by peripheral baroreceptors and chemoreceptors in the aortic arch and carotid sinus as well as by the mechanoreceptors to balance between sympathetic and parasympathetic outflow. Even though many of these mechanisms have been identified, much work remains to better define this complexity and the developing aspects of the cardiovascular control in the immature infant. The effect of gestational and postnatal age, the patient's ability to compensate with increased cardiac output and regulation of CBF, and the underlying pathophysiology on the dependency of CBF on BP in premature infant remain to be determined (Noori et al., 2012a).

The pathophysiology of neonates

The hemodynamic disturbance in preterm neonates can be caused by the impact of immaturity and pathologic events on the physiology of the neonatal cardiovascular regulation, which lead to the end-organ damage caused by the decrease in oxygen delivery to the organs.

Patent ductus arteriosus (PDA) and intraventricular hemorrhage (IVH), are the main neurological pathological situations of preterms.

Patent ductus arteriosus in premature infants

PDA is a common problem in preterm infants with less than 30 weeks GA. During fetal life, increased pulmonary vascular resistance, decreased pulmonary blood flow, diversion of the blood from the pulmonary to the systemic circulation (right-to-left) through ductus arteriosus occurred. After birth, increased pressure and blood flow in the pulmonary vascular bed would occur (Fig. 13). In term infants, the PDA within the first 48 hours after birth will be closed. In contrast, preterm infants frequently fail to constrict their ductus. As it was explained in transitional physiology part, this will happened due to the effect of the separation of placental, the pressure of oxygen and hormonal secretions. The direction of flow in the PDA in preterm infants depends on the relative resistances in the systemic and pulmonary circulation. 52% of neonates less than 30 weeks GA have left-to-right ductal shunts, 43% of neonates during the transitional period left-to-right bidirectional shunts, and only 2% have right-to-left shunts by 5 hours of postnatal life [START_REF] Greisen | Chapter 2 -Autoregulation of Vital and Nonvital Organ Blood Flow in the Preterm and Term Neonate A2 -Kleinman[END_REF].

Signs of PDA:

The degree of PDA depends on the size and direction of the shunt and on the duration of the ductal patency that can be measured by Doppler. A PDA size ≥1.6 or ≥2 mm at 5 hours of postnatal life in preterm infants younger than 30 weeks GA is considered as a hemodynamically significant patent ductus arteriosus (hsPDA) [START_REF] Kluckow | Early echocardiographic prediction of symptomatic patent ductus arteriosus in preterm infants undergoing mechanical ventilation[END_REF].

More recently, diastolic flow velocity in the left pulmonary artery, transductal velocity ratio, the ratio of left ventricular output to superior vena cava flow, the presence of holodiastolic retrograde flow in the descending aorta, have been used to quantify the hsPDA [START_REF] Flynn | The use of a bedside assay for plasma B-type natriuretic peptide as a biomarker in the management of patent ductus arteriosus in premature neonates[END_REF].

Cardiovascular Adaptation to PDA:

The presence of a PDA with a left-to-right shunt, results in an increase blood flow to the lungs. Consequently, venous return from the pulmonary circulation to the left atrium is also increased and leads to an increase in the preload of the left ventricle. The increase in myocardial muscle fiber stretch from higher preload results in a higher cardiac output and augments stroke volume (since there is no change in heart rate). The increase in cardiac output may offset the hsPDA, at least initially. However, this compensatory mechanism may fail in some very low birth weight infants, and systemic perfusion may become inadequate. In infants with very low birth weights and hsPDAs, have significantly lower systolic, diastolic and mean blood pressures. When this occurs, signs of tissue hypoperfusion may occur in the form of decreased urine output [START_REF] Clyman | Chapter 13 -The Very Low Birth Weight Neonate with Hemodynamically Significant Ductus Arteriosus During the First Postnatal Week A2 -Kleinman[END_REF]. CBF and PDA: Some studies suggest that CBF is maintained in the presence of an hsPDA, but the most studies have demonstrated a decrease in CBF. In preterm infants with the presence of hsDPA, Perlman et al. showed a decrease in diastolic blood flow velocity in the anterior cerebral artery [START_REF] Perlman | The effect of patent ductus arteriosus on flow velocity in the anterior cerebral arteries: ductal steal in the premature newborn infant[END_REF]. Besides, Lemmers et al. demonstrated a decrease in cerebral oxygenation that resolved after treatment with indomethacin [START_REF] Lemmers | Impact of patent ductus arteriosus and subsequent therapy with indomethacin on cerebral oxygenation in preterm infants[END_REF]. Moreover, Shortland et al. found no difference in anterior CBF velocity between infants with or without a PDA [START_REF] Shortland | Patent ductus arteriosus and cerebral circulation in preterm infants[END_REF]. There is a study suggesting that CBF progressively decreases as left-to-right shunts across the PDA become larger [START_REF] Jim | Cerebral hemodynamic change and intraventricular hemorrhage in very low birth weight infants with patent ductus arteriosus[END_REF]. Further, in the presence of a PDA, CBF is maintained at a constant level as long as the left ventricular output is increased [START_REF] Shimada | Effects of patent ductus arteriosus on left ventricular output and organ blood flows in preterm infants with respiratory distress syndrome treated with surfactant[END_REF]. In contrast, Baylen et al. demonstrated a decrease in CBF when cardiac output was compromised in preterm lambs with a PDA [START_REF] Baylen | Left ventricular performance and regional blood flows before and after ductus arteriosus occlusion in premature lambs treated with surfactant[END_REF].

To sum up, it seems that the increase in cardiac output can compensate cerebral perfusion at least to a certain point in patients with a PDA. Chapter 1: Introduction & background PDA treatment: To treat PDA, surgical ligation produces definitive ductus arteriosus closure, but it is associated with its own set of illness. Indomethacin and ibuprofen have been used as the preferred therapy instead of surgery for closing a PDA. Indomethacin reduces CBF and cerebral oxygenation in experimental animals, adults, and preterm neonates [START_REF] Pryds | Indomethacin and cerebral blood flow in premature infants treated for patent ductus arteriosus[END_REF]. Although indomethacin decreases the severity of peri-intraventricular hemorrhage (PIVH), this may affect long-term neurodevelopmental outcomes [START_REF] Schmidt | Long-term effects of indomethacin prophylaxis in extremely-low-birth-weight infants[END_REF].

Contrary to indomethacin, ibuprofen does not have significant cerebrovascular effects [START_REF] Mosca | Comparative evaluation of the effects of indomethacin and ibuprofen on cerebral perfusion and oxygenation in preterm infants with patent ductus arteriosus[END_REF]. However, it is not known whether the use of ibuprofen for the treatment of patent ductus arteriosus (PDA) affects long-term neurodevelopmental outcomes. Dopamine increases blood pressure and effects on CBF, without a (dilatory) effect on brain vessels [START_REF] Zhang | Mechanisms of blood pressure increase induced by dopamine in hypotensive preterm neonates[END_REF]. In infants with a large PDA, dopamine at doses of 8 to10 mcg/kg/min may increase systemic blood pressure and pulmonary vascular resistance resulting in a reduction of left to right shunt [START_REF] Bouissou | Hypotension in preterm infants with significant patent ductus arteriosus: effects of dopamine[END_REF]. But autoregulation might also be impaired during high concentrations of dopamine [START_REF] Alderliesten | Cerebral oxygenation, extraction, and autoregulation in very preterm infants who develop peri-intraventricular hemorrhage[END_REF].

Intraventricular hemorrhage in premature infants

Intraventricular hemorrhage is the neurological pathology of prematurity in the neonatal period (Fig. 14). The occurrence of intraventricular hemorrhage is 50% in the first 8 hours of life. 75% of cases occur in the first 24 hours and 95% before the 4th day of life. The cerebral hemorrhages are more frequent in the premature with low weight and the gestational age lower than 32 wGA. The cerebral hemorrhages are classified into four stages according to Sarnat [START_REF] Johnson | Cerebral palsies: epidemiology and causal pathways[END_REF]: Mahmoudzadeh et al. tested how preterm neonates with IVH react to external stimulation (i.e., speech syllables). By combined EEG and fNIRS, a neural response to syllables was observed in IVH infants but did not induce a vascular response in contrast with healthy neonates. These results clearly demonstrate that the cerebral vascular network in IVH preterm neonates was unable to compensate for the increased metabolism resulting from neuronal activation in response to external stimulation (Fig. 15) [START_REF] Mahdi Mahmoudzadeh | Consequence of intraventricular hemorrhage on neurovascular coupling evoked by speech syllables in preterm neonates[END_REF].

Objective and Approach

Understanding the relationship between hemodynamic responses and neural activity in the resting-state immature brain, is so complex. The maturation of the many components related to the mechanism of neurovascular coupling in the neonatal brain is unstable and at varying pace, that has inspired a wide array of investigations ranging from the systems level to the molecular level. In this thesis, we have focused on the following questions:

It makes sense to assume that there is a coupling between hemodynamic and neuronal activity in the premature neonatal brain in resting state (Roche-Labarbe et al., 2007a), but whether the hemodynamic responses to the burst of activities have the same patterns or not has to be analyzed? Is it possible to predict the hemodynamic response of neural activity in resting state in the premature infant considering all the complexity of the immature brain? Is the neurovascular coupling age-dependent at resting state? Does neurovascular coupling occurs in pathological cases in immature infants? Under resting-state conditions, what are the causality and linear/nonlinear relationship between cerebral blood flow and cerebral blood volume and cerebral metabolic rate of oxygen? What is the impact of the different gestational ages and/or pathologic events on the cerebral hemodynamic changes/disturbance in the immature neonatal brain? In this thesis, we have focused on the following general points:

Multimodal hybrid EEG-NIRS-DCS: to answer these questions, we used multimodal hybrid EEG-NIRS-DCS and non-invasive beat-to-beat blood pressure monitoring techniques, since the multimodal imaging is a suitable approach for monitoring different aspects of hemodynamic and neural activities in the neonatal brain. Multimodal simultaneous recording suggests a complementary approach and makes it possible to minimize the inaccuracies related to each of the individual techniques.

Resting state: our analysis is based on the assumption of only minor alterations from the baseline condition (resting-state) rather than the hemodynamic response for task-evoked conditions. Chen et al. (e.g., Chen et al. Neuroimage 2015), suggest that HRF (Hemodynamic Response Function) models should be modified for resting-state conditions compared to traditional task-based models implying different hemodynamic behaviors in these two conditions. This is even more important considering immature neonates.

Complexity of the immature neonatal brain: our knowledge concerning cerebral autoregulation in preterm neonates remains limited and how cerebral oxygenation develops over time is unknown. Moreover, given the very limited knowledge concerning the spontaneous activity of the premature brain at present, the mechanisms underlying the present observations have not been elucidated, which would be a fascinating subject for future studies.

Thermal impact of near-infrared laser: Increasing temperature as a result of the propagation of laser light in human tissues is an essential issue in functional optical imaging.

The purpose of this part was to model the photothermal interaction of NIR laser on human tissues. The results presented in this part could be useful to optimize laser spot size and power for a variety of laser applications of functional imaging systems (e.g., DCS which need NIR light with relatively high laser power). A combination of simulation and adequate in vitro experiments could help to develop a more effective optical imaging to avoid any possible tissue damage.

Thesis overview

This thesis beginning with a general introduction in the first chapter and I provided an overview of the neuronal and vascular components likely to be involved in the neurovascular coupling and their roles in mediating blood flow changes. The mechanism Chapter 1: Introduction & background underlying the neurovascular coupling (aerobic and anaerobic mechanisms) are also described. Then I rapidly reviewed fetal, transitional, and post-transitional neuronal/vascular and cardiovascular physiology and described some pathophysiological aspects of neonates with IVH or PDA.

I briefly present the different chapters of the thesis in sequence, that aims to evaluate the neurovascular coupling in premature infants in resting state through a non-invasive multimodal approach that combines the evaluation of neuronal activity (EEG), local hemodynamic activity (fNIRS-DCS) and systemic hemodynamic activity (non-invasive beat-to-beat blood pressure monitoring).

Chapter 2: Material and Methods. In Chapter 2, I provided an overview of the multimodal imaging systems used in our study. Their underlying principles were also briefly described.

This chapter contains a general methodological introduction to near-infrared spectroscopy, diffusion correlation spectroscopy together with the mathematical and physical basis of photon propagation in biological tissue. Calculating the parameter of the cerebral metabolic rate of oxygen (CMRO2), measuring and estimating the blood pressure with the Finometer device (non-invasive beat-to-beat blood pressure monitoring) were also explained.

Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging. In Chapter 3, we modeled the photothermal interaction of NIR laser of advanced optical imaging, on neonatal and adult quasi-realistic head models. We modeled the thermal effect of different laser powers with various spot sizes and different head tissue characteristics by numerical simulation using finite-element analysis. The results of chapter 3 can be useful to optimize laser parameters for a variety of laser applications in the adult and neonatal brain.

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain. In Chapter 4, directionality and a causal relationship between relative cerebral blood flow and relative cerebral blood volume rCBF-rCBV (also between relative cerebral blood flow and relative cerebral metabolic rate of oxygen rCBF -rCMRO2) in preterms at resting state were identified by using transfer entropy. This help to elucidate the principles of cortical hemodynamics during development. The coupling between spontaneous physiological burst of activity with a transient stereotyped hemodynamic pattern in resting state premature infants, consisting of deoxygenation, oxygenation, cerebral blood flow, cerebral blood volume and cerebral metabolic rate of oxygen is identified, which help to elucidate the principles of neuronal and cortical hemodynamic during development. The multi-frequency aspect of neurovascular coupling was presented using wavelet coherence analysis, in comparing between two normal and pathological groups and represent as a function of age.

Chapter 6: Conclusion and Perspective. In the final chapter 6, I summarize the main conclusions and consider the perspectives for future research.

Introduction

The simultaneous acquisition of electroencephalography (EEG), near-infrared spectroscopy (NIRS) and diffuse correlation spectroscopy (DCS) is a potentially powerful multimodal imaging technique for measuring the functional activity of the human brain. Non-invasive beat-to-beat systemic blood pressure was simultaneously recorded by Finometer®. The Finometer® is a solution for accurate blood pressure monitoring. Given that EEG measures the electrical activity of neural populations while NIRS and DCS measure local cerebral hemodynamics via a blood oxygenation and blood flow signal related to neuronal activity. Simultaneous EEG/NIRS/DCS offer a unique modality to investigate the relationship between these three phenomena within the context of noninvasive neuroimaging. The rationale for combining EEG/NIRS/DCS and systemic blood pressure monitoring is the fact that the individual modalities measure obviously different physiological phenomena at the same time. That is, there is a need for a more comprehensive understanding of the specific mechanisms underlying neurovascular coupling in neonates.

Cortical electrical activity measurements in premature infants by EEG

The cortical neurons that are activated or inhibited by stimulation or in resting state appear to be involved in basal forebrain-mediated changes in electroencephalogram (EEG) activity [START_REF] Lee | Neuromodulation of brain states[END_REF]. The EEG is presumed to reflect the synchronized synaptic activity of large numbers of neurons [START_REF] Buzsaki | The origin of extracellular fields and currents--EEG, ECoG, LFP and spikes[END_REF]. The EEG oscillations have been subdivided into five frequency It has been suggested that ongoing activity in the EEG (background activity), plays a decisive role in functional communication in the brain [START_REF] Basar | Gamma, alpha, delta, and theta oscillations govern cognitive processes[END_REF]. EEG records all brain's spontaneous electrical activity over a period from multiple electrodes placed on the scalp.

Cortical hemodynamic measurements in premature infants by fNIRS and DCS

The basic idea from the propagation of light through tissues to probe tissues such as tumors has been around since about 1930s. In the late 1970s, Jobsis founded out that there exists a "window" (range 700 to 900 nm), in the near-infrared spectrum wherein photons, could deeply penetrate into tissue because of the reduced absorption of water (Fig. 1) [START_REF] Jobsis | Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters[END_REF]. The measurements of scattering and absorption of the photon were used in the late 1980s for different applications ranging from imaging of breast tumors to functional imaging of the brain (A. G. Yodh, 2003). By the diffuse optical technique, it is possible to measure oxyhemoglobin (HbO), deoxyhemoglobin (HbR), water, lipid, and scattering as well as some less common variants of hemoglobin and other tissue chromophores (A. Yodh, 1995). O2Hb,HHb,proteins,water,collagen,fat,and cytochrome oxidase (CtOx) in the region from 100 nm to 10,000 nm. The spectra are given with respect to the specific concentration in mM. [START_REF] Scholkmann | A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology[END_REF] 50 50 Chapter 2: Material and Methods This has been only possible for a few clinical applications in the preterm infants' neuroimaging such as hemorrhage detection (Gibson et al., 2006) or disturbed cerebral autoregulation detection in newborns. NIRS is portable and provides bedside monitoring. It is noninvasive and safe as it uses nonionizing radiation with less energy than a head ultrasound.

Methodology for oxy and deoxy-hemoglobin measurement (NIRS)

To probe tissue by the diffuse optical technique, three main paradigms can be used: Continuous wave (CW), Time domain (TD) and Frequency domain (FD) functional near-infrared spectroscopy (fNIRS).

Continuous wave NIRS

CW-NIRS makes use of a steady state light beam that is continuously injected into the tissue.

The reduction in transmitted light amplitude modulated at a low (a few kHz) frequency is measured.

CW methods are becoming increasingly popular also in clinical due to their simplicity, low cost, size and speed [START_REF] Siegel | Design and evaluation of a continuous-wave diffuse optical tomography system[END_REF].

In CW-NIRS, changes in tissue chromophore concentrations from the baseline value can be obtained from the modified Beer-Lambert law. The original Beer-Lambert law describes the absorption of light in a medium. The attenuation of light is related to the change in concentration of the compound and to the optical pathlength: A = E × C × P, where A is absorbance (no units), E is extinction coefficient or molar absorptivity (measured in L/ mol/cm), P is pathlength of the sample (measured in cm), and C is concentration of the compound (measured in mol/L) [START_REF] Victor | Chapter 7 -Near-Infrared Spectroscopy and Its Use for the Assessment of Tissue Perfusion in the Neonate A2 -Kleinman[END_REF].

The modified Beer-Lambert law, include an additive term, K, due to scattering losses, is expressed as A = P × L × E × C + K, where L is the differential pathlength factor. K is a constant value and is unknown because K is dependent on the measurement geometry and the scattering coefficient of the tissue investigated. This equation cannot provide the absolute value of the concentration of the chromophore, but if K is constant during the measurement period, it is possible to calculate a change in concentration (ΔC) of the chromophore, with following formula:

ΔA = P × L × E × ΔC or ΔC = ΔA/P × L × E (1)
In a medium containing several chromophores (C1, C2, and C3) the overall absorbance is:

A = (E1C1 + E2C2 + E3C3) P × L, (2)

ΔC1=Q1ΔA1+R1ΔA2+S1ΔA3+T1ΔA4,

(3) ΔC2=Q2ΔA1+R2ΔA2+S2ΔA3+T2ΔA4, (4) ΔC3=Q3ΔA1+R3ΔA2+S3ΔA3+T3ΔA4,

Where ΔA1, ΔA2, ΔA3, and ΔA4 represent changes in absorption at different wavelengths such as 774 nm, 825 nm, 843 nm, and 908 nm. ΔC1, ΔC2, and ΔC3 represent changes in the concentrations of C1, C2, and C3 (such as HbR, HbO, and Cytochrome aa3). Because the pathlength is wavelength dependent, the inverse matrix coefficients is presented in Table .1 [START_REF] Victor | Chapter 7 -Near-Infrared Spectroscopy and Its Use for the Assessment of Tissue Perfusion in the Neonate A2 -Kleinman[END_REF]. The CW method allows only relative measurements, to solve this problem (for a pathlength correction) multiple optodes operating are placed simultaneously around the head, but the tissue should assume to be homogeneous. This modification is called spatially resolved spectroscopy with the reasonable signal-to-noise ratio and with the depth from the surface between 1 and 3 cm. If the distance between the light source and the detector is large enough (> 3 cm), it can be assumed that scatter distribution becomes so homogeneous that the loss due to scattering is the same at all the detectors. Tissue oxygenation index (TOI) is calculated as follows:

 ()= 𝐾.𝐻𝑏𝑂2 𝐾.𝐻𝑏𝑂2+𝐾.𝐻𝑏𝑅 ()
Where K is the constant scattering contribution.

The NIRO-200NX (Hamamatsu Photonics, Hamamatsu City, Japan) was used to monitor cerebral tissue oxygenation. This instrument uses three light emitting diodes with wavelengths of 735, 810 and 850 nm, respectively, and two detecting photodiodes to measure light attenuation at different distances from the source. The emitter and receiver were fixed to the probe holder to ensure an inter-optode distance. This spectrometer uses both the modified Beer-Lambert law (MBL) -to measure changes in oxyhemoglobin and deoxyhemoglobin concentrations (HbO and HbR)-and 52 52 Chapter 2: Material and Methods spatially resolved spectroscopy (SRS) method -to measure an absolute ratio of oxyhemoglobin to total hemoglobin, known as the tissue oxygenation index (TOI) [START_REF] Wong | Impaired autoregulation in preterm infants identified by using spatially resolved spectroscopy[END_REF]. The SRS method uses a mathematical model based on the light diffusion equation to calculate TOI. SRS assumes a homogeneous pathlength and uniform light scattering for all emitted light frequencies.

Although it does not entirely eliminate the contribution from extracranial contents, the use of multiple detectors and the thinness of the neonatal skull minimizes this component from the overall measurement.

Time domain NIRS

Time domain (TD) methods use the pulsed laser and photo-detection techniques with picosecond resolution. This method uses a mathematical approximation based on diffusion theory to allow better estimation of light scattering properties by measurement of differential pathlength factors. Thus the method permits differentiation of one tissue from another. This system can provide the absolute quantification of hemodynamic variables. TD fNIR provides the highest information with a large amount of data, which means that data are collected and analyzed relatively slowly (in minutes), but it has the reputation of being cumbersome, bulky, and very expensive (F. E. W. [START_REF] Schmit | A 32-channel time-resolved instrument for medical optical tomography[END_REF].

Frequency domain NIRS

Frequency domain (FD) methods provide an amplitude modulated sinusoid at a single (generally 100-1000 MHz) frequency. Even though FD techniques provide less information than TD, it provides a direct measurement of absorption and scattering coefficients of the tissue by the reduction in amplitude and the phase shift of the transmitted light [START_REF] Yang | Low-cost frequency-domain photon migration instrument for tissue spectroscopy, oximetry, and imaging[END_REF]. This method allows for the different scattering effects of the fluid and tissue components of the brain.

Methodology for cerebral blood flow measurement (DCS)

Additional information can be obtained from the monitoring of the fluctuations of the scattered light in tissue which reflects the dynamics of the scatterers such as red blood cells. Measuring the electric field temporal autocorrelation function or its Fourier Transform reflects the motions of scatterers within the tissue; the most significant signal is from blood flow (Durduran et al., 2010b).

DCS is similar to NIRS, uses near-infrared light to penetrate through tissue (~1 cm) to noninvasively measure CBF in small vessels, in comparaison to the transcranial Doppler (TCD) that estimates blood flow only in the main arteries. By incorporating NIRS with DCS, the cerebral 53 53 Chapter 2: Material and Methods metabolic rate of oxygen (CMRO2) can be estimated. DCS was presented in the early 1990s and has been accredited in some animal and human studies for CBF measurement.

Historically, optically regional CBF in neonates using NIRS was measured by either changing the inspired oxygen in ventilated infants, or by injection of an indocyanine green bolus [START_REF] Patel | Measurement of cerebral blood flow in newborn infants using near infrared spectroscopy with indocyanine green[END_REF] have ethically limitation for the healthy infants. Although these methods give reliable estimates of CBF, they are not ethically applicable in all infants. Diffuse correlation spectroscopy (DCS) is a more succeeding technique, providing a measure of CBF based on the movement of scatters such as blood cells inside the tissue. DCS can directly measure CBF without injecting bolus or oxygen manipulations.

Photon diffusion in tissues

The physical basis of the optical properties can be explained by the "diffusion equation", where the measurable, near-infrared photon fluence rate, 𝜱(r, t) (photons/[cm 2 .s]) obeys the following diffusion equation (Durduran et al., 2010b):

∇. (𝐷(𝑟)∇𝛷(𝑟, 𝑡)) -𝑣µ 𝑎 (𝑟)𝛷(𝑟, 𝑡) - 𝜕𝛷(𝑟,𝑡) 𝜕𝑡 = -𝑣𝑆(𝑟, 𝑡) (7)
Here 𝜱(r, t) is proportional to the photon number density (U(r, t) (photons/cm 3 )), v is the speed of light in medium (cm/s), 𝜇 𝑎 (𝑐𝑚 -1 ) is the absorption coefficient, 𝜇 𝑠 ′ (𝑐𝑚 -1 ) is the reduced scattering coefficient and D= 𝑣 3𝜇 𝑠 ′ is the photon diffusion coefficient. S(r, t) is an isotropic source term which gives the number of photons emitted at position r and time t per unit volume per unit time. The equation 7 represents the rate of change of photons within a sample volume element, the number of photons scattered minus the number of photons absorbed per unit time, plus the number of photons emitted per unit time from any sources within the volume element. Since, the frequency domain methods were employed the amplitude and phase of the AC component of the transmitted diffuse light waves were measured. In this case, the source term is written as:

𝑆(𝑟, 𝑡) = (𝑆 𝐷𝐶 + 𝑆 0 𝑒 -𝑖𝑤𝑡 )𝛿(𝑟) (8)
The reduction in amplitude and the phase shifts of diffuse light density are detected with multiple source-detector separations (Fig. 2). Then by plotting the detected amplitude and fitting the slope, the optical properties are extracted (Durduran et al., 2010b).

54 54 Chapter 2: Material and Methods Fig. 2 The photons are injected at the source position and detected some distance away. The reduction in amplitude and the phase shifts of diffuse photon density waves are detected at multiple source-detector separations.

Diffuse correlation spectroscopy (DCS)

To find the index of blood flow and learn about the motions of red blood cells, the electric field temporal autocorrelation function is measured and analyzed by DCS device. E(r, t) represents the temporal variations of the light electric field at time t and position r, which propagate through tissue.

The decline of the autocorrelation function by a factor of 1/e occurred when the scatters particles such as the red blood cells have moved [START_REF] Durduran | Diffuse correlation spectroscopy for non-invasive, micro-vascular cerebral blood flow measurement[END_REF].

The temporal electric field autocorrelation function diffuses through tissue in a manner that is similar to light fluence rate, so diffusion equation are used for transport of autocorrelation function.

Thus, many tissue optical properties such as tissue absorption (μa) and scattering coefficient (μ′s), are the same. The difference between them is an additional absorption term that is dependent on the dynamics of the scatterers. Diffuse correlation spectroscopy is a measure of tissue perfusion that depends on both the movement of scatterers inside the blood vessels and the optical tissue properties. The diffusion equation of autocorrelation function:

[𝛻. 𝐷(𝑟)𝛻 -𝑣𝜇 𝑎 (𝑟) - 𝛼 3 𝑣𝜇 𝑠 ′ 𝑘 0 2 〈∆𝑟 2 (𝜏)〉] 𝐺 1 (𝑟, 𝜏) = -𝑣𝑆(𝑟) (9)
Here τ is the correlation time, α is the ratio of moving scatterers such as red blood cells to the total number of scatterers in the sample, ko is the wave-number of the light in the sample, and 𝐷(𝑟)

≡ 𝑣 3(𝜇 𝑠 ′ (𝑟)+𝜇 𝑎 (𝑟)) ≈ 𝑣 3(𝜇 𝑠 ′ (𝑟))
is the photon diffusion coefficient, 𝐺 1 (𝑟, 𝜏) = 〈𝐸 * (𝑟, 𝑡). 𝐸(𝑟, 𝑡 + 𝜏)〉 2 is the temporal field autocorrelation function, 〈∆𝑟 2 (𝜏)〉 is the mean-square displacement of these moving red blood cells in time τ. Here the angle brackets denote ensemble averages or averages over time.

The mean-square particle has been found as a Brownian motion, i.e., 〈∆𝑟 2 (𝜏)〉 = 6𝐷 𝐵 𝜏 where D 𝑩 is the effective diffusion coefficient of the moving scatterers. It is assumed that the measured relative changes of D 𝑩 are equal to the relative changes in blood speed, and that α is proportional In practice, the light intensity is more accessible to measure than the light electric field. The measured normalized intensity auto-correlation function 𝑔 2 (𝜏) ≡ 〈𝐼(𝑟, 𝑡)𝐼(𝑟, 𝑡 + 𝜏)⟩/⟨𝐼(𝑟, 𝑡)〉 2 is related to the normalized electric field correlation function 𝑔 1 (𝜏) = 〈𝐸 * (𝑟, 𝑡). 𝐸(𝑟, 𝑡 + 𝜏)⟩/ ⟨|𝐸(𝑡)| 2 〉 by the Siegert relation (g 2 (τ) = 1 + β|g 1 (τ)| 2 ). DCS intensity auto-correlation curves has a delay time range of 200 ns~1 s. The intensity, I(r, t)~|E(r, t)| 2 and β is a constant in an ideal experiment setup that depends on the source coherence, detection optics, ambient light and other external factors.

By fitting the measured intensity autocorrelation functions to solutions of Eq. (1), it can be possible to estimate blood flow from DCS data. The best-fit defines a tissue blood flow index (BFI) from the data. Relative changes in BFI (i.e., rBFI) at time t are defined as 𝑟𝐵𝐹𝐼(𝑡) = 𝐵𝐹𝐼(𝑡)/𝐵𝐹𝐼(𝑡 0 ), where t0 denotes a time during the baseline period. Percent changes in BFI (i.e.,∆𝐵𝐹𝐼) are sometimes defined with respect to zero, i.e ∆𝐵𝐹𝐼(%) = (𝑟𝐵𝐹𝐼 -1) × 100.

The theoretical solutions of equation ( 1) is (Boas et al., 1995b);

𝑔 2 (𝑟 𝑠 , 𝑟 𝑑 , 𝜏) = (1 + exp (-(3𝜇 𝑠 ′ 𝜇 𝑎 + (𝑃 𝑅𝐵𝐶 𝜇 𝑠 ′ ) 2 𝑘 0 2 〈∆𝑟 2 (𝜏)〉) 1 2| 𝑟 𝑠 -𝑟 𝑑 |)) (10)
Where the source is at position 𝑟 𝑆 , the detector is at position 𝑟 𝑑 , the correlation time is 𝜏, the reduced scattering coefficient is 𝜇 𝑠 ′ , the absorption coefficient is μa, the wave number for the laser light is 𝑘 0 , 〈∆𝑟 2 (𝜏)〉 is the mean square displacement of the scatters (such as the red blood cells), and 𝑃 𝑅𝐵𝐶 is the probability of scattering from a moving red blood cell. Brownian motion is the most common model for the mean square displacement of the moving particles:

〈∆𝑟 2 (𝜏)〉 = 6𝐷 𝐵 𝜏 (11)
Where 𝐷 𝐵 is the Brownian diffusion coefficient. Since 𝑃 𝑅𝐵𝐶 is generally unknown, these two parameters (𝐷 𝐵 𝑃 𝑅𝐵𝐶 ) to assign a blood flow index (𝐶𝐵𝐹 𝑖𝑥 ) [START_REF] Yu | Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy[END_REF]. Relative changes in 𝐷 𝐵 are correlated with relative changes in tissue blood flow.

The curves decay faster with increasing 𝐷 𝐵 , i.e. increased flow, and increased source-detector separation. The slope and/or the decay rate provides information about the optical properties and the motion of the scatterers (Fig. 3). The temporal autocorrelation functions of the intensity are then calculated using an autocorrelator [START_REF] Durduran | Diffuse correlation spectroscopy for non-invasive, micro-vascular cerebral blood flow measurement[END_REF].

Methodology for cerebral metabolic rate of oxygen (CMRO2) measurement

Measuring the parameter of the cerebral metabolic rate of oxygen (CMRO2), finding the relationship between CMRO2 and CBF, and the mechanisms of oxygen transport from the blood to the brain is an important issue to understand the underlying mechanisms of neurovascular coupling. Based on a theory of [START_REF] Crone | THE PERMEABILITY OF CAPILLARIES IN VARIOUS ORGANS AS DETERMINED BY USE OF THE 'INDICATOR DIFFUSION' METHOD[END_REF] [START_REF] Crone | THE PERMEABILITY OF CAPILLARIES IN VARIOUS ORGANS AS DETERMINED BY USE OF THE 'INDICATOR DIFFUSION' METHOD[END_REF], because the only source of oxygen is blood (i.e., hemoglobin), the oxygen extraction from blood to cerebral tissue could be related to the arteriovenous concentration difference (Ca -Cv) by detecting tracer amounts of an exogenous indicator's dilution (within the blood) or diffusion (into the tissue). According to Fick's principle CMRO2/CBF was defined [START_REF] Siesjo | Brain energy metabolism and catecholaminergic activity in hypoxia, hypercapnia and ischemia[END_REF]; CMRO2/CBF=(Ca -Cv) ( 12) [START_REF] Hill | The Combinations of Haemoglobin with Oxygen and with Carbon Monoxide[END_REF] found the relation between saturation of hemoglobin with oxygen and the changing of the color of erythrocytes: the fully oxygenated hemoglobin being bright red whereas the fully deoxygenated hemoglobin being nearly black [START_REF] Hill | The Combinations of Haemoglobin with Oxygen and with Carbon Monoxide[END_REF]. Penfield (1933) found that cerebral arterial vessels were almost always red whereas venous ends were purple, and veins became redder when neuronal activity increased [START_REF] Chorobski | Cerebral vasodilator nerves and their pathway from the medulla oblongata: With observations on the pial and intracerebral vascular plexus[END_REF]. These findings provided an essential contention about the equation of CMRO2 during neuronal activity.

In an activated region, the difference between Ca and Cv become smaller, because the blood is almost fully oxygenated at the arterial end, venous oxygenation is increased and accompanied with a drop in deoxyhemoglobin concentration at the venous end of the capillary. Thus the arteriovenous difference in capillaries decreased. It has been known for several decades that blood oxygenation raised with increased neuronal activity. In other words, in the activated region, there is a more substantial increase in CBF than CMRO2, which is commensurate with a decrease in OEF.

CMRO2 calculation

1) rCMRO2 calculation can be estimated from the difference in oxygen saturation between arterial and venous blood(relative oxygen extraction fraction, rOEF), and from the relative cerebral blood flow, which can be estimated from DCS data. The relative cerebral metabolic rate of oxygen was estimated as [START_REF] Culver | Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia[END_REF]: Where rOEF is defined as:

𝑟𝐶𝑀𝑅𝑂 2 = 𝑟𝐶𝐵𝐹 × 𝑟𝑂𝐸𝐹 (
𝑟𝑂𝐸𝐹 = 𝑆𝑎𝑂 2 (𝑡)-𝑆𝑣𝑂 2 (𝑡) 𝑆𝑎𝑂 2bl (𝑡 0 )-𝑆𝑣𝑂 2bl (𝑡 0 ) = 𝑆𝑎𝑂 2 (𝑡)-𝑆𝑂 2 (𝑡) 𝑆𝑎𝑂 2bl (𝑡 0 )-𝑆𝑂 2bl (𝑡 0 ) (14)
With venous oxygenation 𝑆𝑣𝑂 2 = (𝑆𝑂 2 -𝑎 × 𝑆𝑎𝑂 2 ) 𝑏 ⁄ , where a+b=1, a and b are the arterial and venous contributions that are constant over time [START_REF] Watzman | Arterial and venous contributions to near-infrared cerebral oximetry[END_REF]. SO2 is the microvascular tissue oxygen saturation [START_REF] Wray | Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation[END_REF] (𝑆𝑂 2 = 𝐻𝑏𝑂 2 /𝐻𝑏𝑇), (𝐻𝑏𝑇 = 𝐻𝑏𝑂 2 + 𝐻𝑏, where 𝐻𝑏 is the deoxy-hemoglobin concentration and 𝐻𝑏𝑂 2 is the tissue oxy-hemoglobin concentration that measure by NIRS). "bl" is used to indicate baseline values. Baseline 𝑆𝑂 2 (𝑆𝑂 2𝑏𝑙 ) is estimated from the literature values. 𝑆 𝑎 𝑂 2 is the arterial blood oxygen saturation which can be estimated by pulseoximetry or by blood gas sampling. Mechanical ventilation parameters and inspired oxygen concentrations can be maintained constant at sufficiently high levels to saturate arterial hemoglobin (SaO2 ≈ 100%). If SaO2 is not considered equal to 100%, the rCMRO2 was estimated as:

𝑟𝐶𝑀𝑅𝑂 2 = 𝑟𝑂𝐸𝐹 × 𝑟𝐶𝐵𝐹 = ( 𝑆 𝑎 𝑂 2 (𝑡)-𝑆𝑂 2 (𝑡) 𝑆 𝑎 𝑂 2𝑏𝑙 (𝑡 0 )-𝑆𝑂 2𝑏𝑙 (𝑡 0 ) ) ( 𝛾 𝑏𝑙 𝑆 𝑎 𝑂 2𝑏𝑙 𝛾𝑆 𝑎 𝑂 2 ) 𝑟𝐶𝐵𝐹 ≈ ( 𝑆 𝑎 𝑂 2 (𝑡)-𝑆𝑂 2 (𝑡) 𝑆 𝑎 𝑂 2𝑏𝑙 (𝑡 0 )-𝑆𝑂 2𝑏𝑙 (𝑡 0 ) ) ( 𝑆 𝑎 𝑂 2𝑏𝑙 𝑆 𝑎 𝑂 2 ) 𝑟𝐶𝐵𝐹 (15)
γ is an empirical parameter that is constant and can be estimated by optical methods such as spiroximety (denotes the percentage of blood in the venous compartment).

2) rCMRO2 can generally be calculated by combining relative changes in rCBF and oxygen extraction fraction, but monitoring rCBV independently of rCBF by the NIRS device allows rCMRO2 to be evaluated independently of rCBF (Roche-Labarbe et al., 2010) by using (𝑟𝐶𝐵𝑉) 𝛽 instead of rCBF in relation (1). By considering Grubb's relation between changes in rCBF and rCBV [START_REF] Davis | Calibrated functional MRI: mapping the dynamics of oxidative metabolism[END_REF], the relative cerebral metabolic rate of oxygen was estimated as:

𝑟𝐶𝐵𝐹 = 𝐶𝐵𝐹 𝑖 (𝑡) 𝐶𝐵𝐹 𝑖 (𝑡 0 ) = ( 𝐶𝐵𝑉(𝑡) 𝐶𝐵𝑉(𝑡 0 ) ) 𝛽 = (𝑟𝐶𝐵𝑉) 𝛽 (16) 𝑟𝐶𝑀𝑅𝑂 2 = (𝑟𝐶𝐵𝑉) 𝛽 × 𝑟𝑂𝐸𝐹 (17)
As 'beta' could be time-variant, time-invariant characteristic of beta should be validated statistically. In some studies (Roche-Labarbe et al., 2010) a constant power law relation between changes in CBF and CBV was assumed. [START_REF] Kida | Dynamics of changes in blood flow, volume, and oxygenation: implications for dynamic functional magnetic resonance imaging calibration[END_REF], reported the variation of β, ranging from 0.19 to 0.23 for the plateau CBF during stimulation, although it was not statistically significant. CBV (cerebral blood volume) was defined as:

(𝐻𝑏𝑇×𝑀𝑊 𝐻𝑏 ) 𝐻𝐺𝐵×𝐷 𝑏𝑡
, where CBV is expressed in ml/100 g, HbT in µmol, 𝑀𝑊 Hb (64,500 g/mol) is the molecular weight of hemoglobin, D bt (1.05 g/ml) is the brain tissue density and HGB (g/dl) is the blood hemoglobin concentration. The control state at time t0 was defined as the mean value of the signal and was considered to be the reference value.

The standard normal values for HGB were used, as HGB was not available in clinical charts (de [START_REF] De Alarcón | Neonatal Hematology[END_REF][START_REF] Wolff | Hematopoiesis in premature infants with special consideration of the effect of iron and of animal-protein factor[END_REF]. Some studies have been reported about uncertainties in the above physiologic parameters [START_REF] Franceschini | Assessment of infant brain development with frequency-domain near-infrared spectroscopy[END_REF]. rCBV was calculated using the following equation:

(18)
3) The index of the absolute value of CMRO2 was estimated as [START_REF] Dehaes | Cerebral oxygen metabolism in neonatal hypoxic ischemic encephalopathy during and after therapeutic hypothermia[END_REF]:

CMRO 2𝑖 = 𝐶𝐵𝐹 𝑖 . (𝐶𝑎𝑂 2 -𝐶𝑣𝑂 2 ) = 𝐶𝐵𝐹 𝑖 . 𝐻𝐺𝐵 𝑀𝑊 𝐻𝑏 . (𝑆𝑎𝑂 2 -𝑆𝑣𝑂 2 ) = 𝐶𝐵𝐹 𝑖 . 𝐻𝐺𝐵 𝑀𝑊 𝐻𝑏 . 1 𝑏 . (𝑆𝑎𝑂 2 - 𝑆𝑂 2 ) (19)
Where was estimated as:

𝑟𝐶𝑀𝑅𝑂 2 = (1 + 𝛾 𝑟 ∆𝐻𝑏𝑅 𝐻𝑏𝑅 ) × (1 + 𝛾 𝑡 ∆𝐻𝑏𝑇 𝐻𝑏𝑇 ) -1 × ( ∆𝐶𝐵𝐹+𝐶𝐵𝐹 𝐶𝐵𝐹 ) ( 20
)
𝛾 𝑟 = ∆𝐻𝑏𝑅 𝑣 /∆𝐻𝑏𝑅 𝐻𝑏𝑅 𝑣 /𝐻𝑏𝑅 𝑎𝑛𝑑 𝛾 𝑡 = ∆𝐻𝑏𝑇 𝑣 /∆𝐻𝑏𝑇 𝐻𝑏𝑇 𝑣 /𝐻𝑏𝑇 (21)
Γr and γt may range from 0.5 to 2, with 0.75 to 1.25, and under the assumption SaO2=100%, γr, and γt equal to 1 [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF].

5)

To assign the effect of the blood transit time from the arterial to venous compartment on the OEF, the rOEF and then rCMRO2 was estimated as [START_REF] Buxton | Dynamics of blood flow and oxygenation changes during brain activation: the balloon model[END_REF][START_REF] Hoge | Simultaneous recording of task-induced changes in blood oxygenation, volume, and flow using diffuse optical imaging and arterial spin-labeling MRI[END_REF];

𝑟𝑂𝐸𝐹 = 𝑟𝐻𝑏𝑅 𝑟𝐶𝐵𝑉 + 𝜏 𝑟𝐶𝐵𝐹 (∆𝑟𝐻𝑏𝑅 - 𝑟𝐻𝑏𝑅 𝑟𝐶𝐵𝑉 × ∆𝑟𝐶𝐵𝑉) (22) 𝑟𝐶𝑀𝑅𝑂 2 = 𝑟𝐶𝐵𝐹 × 𝑟𝑂𝐸𝐹 ( 23
)
Where τ is the mean transit time through the venous compartment. The value of τ in adults has been estimated to be 3-4 s.

Systemic pressure measurements in preterm infants by Finometer®

The Finometer® is a non-invasive instrument that can be used in clinics and laboratories.

Ambulatory Finometer enables measuring of the equivalent of brachial blood pressure (brachial BP) from the finger blood pressure (finger BP). Although the primary problem resides in the noninvasive aspect of the Finometer®, as noninvasive methods are usually associated with reduced accuracy, this innovative device has many potentials to measure the different parameters. It has the potential for providing estimates of stroke volume (SV) and cardiac output (Q) from the finger blood pressure. The Finometer® monitors hemodynamic by using three different main steps:

measuring finger BP, estimating brachial BP and then, estimating Q.

Monitoring finger blood pressure

Finger blood pressure is measured with a cuff wrapped around the finger. The blood pressure

is measured with the method of volume-clamp presented by Juan Peñáz [Peñáz, 1973] that is based on keeping fixed the finger arterial diameter (Fig. 4.A).

A 61 61 Chapter 2: Material and Methods Fig. 4 A) Wrist and finger Cuff, B) Finger photoplethysmography [START_REF] Fantini | Cerebral blood flow and autoregulation: current measurement techniques and prospects for noninvasive optical methods[END_REF].

The finger arterial diameter is kept constant at a preset point that is defined by an algorithm, in which search for the "unloaded" diameter when the pressure of the arterial wall is zero; meaning that the pressure inside is the same as the pressure outside the artery [START_REF] Wesseling | Physiocal, calibrating finger vascular physiology for finapres Homeostasis in health and disease : international journal devoted to integrative brain functions and homeostatic systems[END_REF]. So, the pressure applied by the servo controller to the cuff to hold constant the artery diameter will represent the finger blood pressure. The pressure in the finger cuff is tuned by an air control unit placed around the wrist of a subject (Fig. 4.A). Because the changes in hematocrit, stress and the tone of smooth muscle in the arterial wall will influence the unloaded diameter, the defined algorithm will recalibrate the unloaded diameter after each several heartbeats.

The information of changing in diameter is detected by an infrared photo-plethysmograph and sent to the servo-controller located in the finger cuff [Boehmer et al., 1987]. A photoplethysmography sensor consists of a light emitting diode (LED) and an optical detector (photodiode). The features of the detected optical signal related to the dynamic changes in arterial blood volume. When the finger cuff is not inflated (Fig. 4.B, left panel), the plethysmography sensor which built into the finger cuff, detects the oscillations of light intensity due to the arterial expansion and contraction at the cardiac rate. Then a pulsating pressure is applied to the finger cuff by means of a fast pneumatic servo system that lets for arterial unloading. When the finger cuff is inflated to achieve arterial unloading at zero transmural pressure and the optical signal flattens out (Fig. 4.B, right panel). In this state, there is no change in the arterial blood volume and the arterial pressure equals the cuff pressure. In this condition the temporal trend applied to the cuff pressure equals the temporal trend of ABP [START_REF] Fantini | Cerebral blood flow and autoregulation: current measurement techniques and prospects for noninvasive optical methods[END_REF]. In order to automatically determine the setpoint value at which to clamp the arteries under the cuff, a strategy was designed to determine this unloaded volume from the pressure-volume pulsations over a limited number of heartbeats when the counter pressure is gradually varied from zero to supra-systolic. This strategy was called "Physiocal", that calibrates the physiology of the finger arteries under the cuff (K.H. [START_REF] Wesseling | Physiocal, calibrating finger vascular physiology for finapres Homeostasis in health and disease : international journal devoted to integrative brain functions and homeostatic systems[END_REF]. The counter pressure generated in the cuff and the volume signal from the plethysmograph was shown in the (Fig. 5).

The optical signal detected is also sensitive to the systolic and diastolic phases of the heart cycle. In this step, the servo controller of Finometer can estimate the heart rate (HR) with a new waveform. [START_REF] Ehrenfeld | Monitoring Technologies in Acute Care Environments: A Comprehensive Guide to Patient Monitoring Technology[END_REF].

Estimation of brachial blood pressure

To estimate the brachial blood pressure from the finger blood pressure, an inverse modeling correction is used [Bos et al., 1996] because the pressure waveforms change in the path of going from brachial to finger arteries (Fig. 6). The inverse modeling correction is a frequency dependent transfer function used as a filter, which has been developed by Gizdulich et al. in 1997 (Fig.7).

Chapter 2: Material and Methods

There is a distortion due to resonating at a frequency ranging from 4.26Hz to 10.58Hz depending on the subject (with the mean value of 8Hz). A frequency-dependent filter with an antiresonance frequency of 8Hz was used in Finometer device to remove this distortion [Gizdulich et al., 1997]. [START_REF] Ehrenfeld | Monitoring Technologies in Acute Care Environments: A Comprehensive Guide to Patient Monitoring Technology[END_REF].

In the case of an average person, figure 7 shows the effect of the inverse model on the shape of the brachial blood pressure with different frequencies. As shown, the inverse model would have a little bit effect on the shape of the brachial blood pressure in the low frequencies. But it will have a more significant influence in the high frequencies, which means the significant influence of the systolic pressure [Bos et al., 1996] (Fig. 7B). Chapter 2: Material and Methods The hydrostatic pressure is caused by the force of gravity on blood and has effect in the pressure gradient. So a height corrector is necessary to equilibrate the pressure gradient driving the flow from the brachial artery to the finger artery (Fig. 7B). This correction was applied by using two sensors for the finger and the brachial level (in upper-arm cuff). The return to flow calibration is done by an upper arm cuff positioned on the same arm as the finger cuff. Such as the idea of a standard sphygmomanometer, the upper arm cuff will completely stop the flow through the brachial artery if its pressure is higher than the systolic blood pressure (SBP). The pressure is then reduced until it reaches the SBP and lets the first pulsation that will be sensed and recorded by the finger cuff.

Therefore the parameters such as: the systolic blood pressure (SBP), the diastolic blood pressure (DBP), the mean arterial pressure (MAP), and the pulse pressure (PP) can be estimated with the Finometer.

Estimation of stroke volume and cardiac output

Cardiac output and Stroke Volume are estimated from finger arterial blood pressure by using the Langwouters' equation and the Model flow method. The Model flow method is a non-linear method by using the three elements model of the systemic vascular resistance (RP), the aortic input impedance (Z0) and Windkessel arterial compliance (CW) [Wesseling et al., 1993].

The impedance element (Z0) displays the aortic opposition to the flow from the contracting left ventricle, the Windkessel arterial compliance element (CW) represents to the aortic elastic storing capacity and the resistance to an increase in blood volume, and the systemic vascular et al., 1993;Harms et al., 1999]. Both elements of (Z0) and (CW) are dependent to the pressure as the elastic behavior of the aorta changes nonlinearly with the changing pressure [Langwouters et al., 1985;Bogert et al., 2005]. The values of (Z0) and (CW) are then calculated with an algorithm to achieve the aortic diameter from the intra-arterial pressure [Langwouters et al., 1984].

𝐴(𝑝) = 𝐴 𝑚𝑎𝑥 [0.5 + 1 π 𝑎𝑟𝑐𝑡𝑎𝑛 ( p-𝑝 0 p 1 )] (24)
Where Amax, p0, and p1 are the parameters related to the age and the sex of the subject.

The aortic flow waveform will be estimated from the finger arterial blood pressure waveform in the modelflow (Fig. 8). Stroke volume (SV) will be calculated from the integral (area under the curve) of the aortic flow waveform and cardiac output (Q) can be calculated from the following equation: Thus, this device can regularly be used to investigate cerebral processes of normal and abnormal adult subjects as well as neonates.

Safety issues of optical imaging

The propagation of laser light energy through the tissues is an important issue in optical imaging. Thus, the impact of lasers is a critical factor that requires being considered to evaluate the effectiveness and laser safety of these systems, especially with high power consumption.

Due to the specificity of neonatal head tissues, it is therefore essential to test the safety of our new optical imaging set up (e.g., DCS lasers) in preemies as a very specific, sensitive population.

Increasing the body temperature leads to several effects such as hyperthermia, coagulation, and other irreversible tissue effects. The thermal impact on tissue changes drastically when the temperature rise exceeds 42 °C (Jeong et al., 2003a). No evident thermal impacts are detected from 37 to 41°C. By increasing the temperature, the first effect is hyperthermia (Table 1). The hyperthermia mechanism by which some molecular bonds are destroyed and the membrane is altered ranging from approximately 42-50°C. However, these effects in this temperature range are reversible. Beyond 50°C, a measurable reduction in enzyme activity is observed. From 60°C, denaturation of proteins and collagen occurs which leads to tissue coagulation and cell necrosis. From 100°C, water molecules start to vaporize. At temperatures exceeding 100°C, carbonization is observable. Finally, beyond 300°C, melting might occur. Table 1 depicts the summarized heat effects for different temperatures.

Table 1. Thermal effects of laser radiation. Adapted from Niemz (2003) [START_REF] Niemz | Laser-Tissue Interactions: Fundamentals and Applications[END_REF] Temperature for example at a rate of less than 0.5 °C per minute, then a person can be unaware of a 4-5 °C change in temperature [START_REF] Kenshalo | Temporal course of thermal adaptation[END_REF], providing that the temperature of the skin remains within the neutral thermal region of 30-36 °C. If the rate of energy deposition is faster than the rate of thermal diffusion (thermal confinement), then the temperature of the exposed tissue rises. If a critical temperature is reached (typically about 10°C above basal), then thermal damage occurs [START_REF] Glickman | Phototoxicity to the retina: mechanisms of damage[END_REF]. This critical temperature varies very slowly with time and is a function of the thermal reaction considered.

In this study, we investigated the thermal effect of different laser powers with various spot

Abstract

The propagation of laser light in human tissues is an important issue in functional optical imaging. We modeled the thermal effect of different laser powers with various spot sizes and

Introduction

Conventional optical imaging systems typically include certain basic components such as various types of lasers and flexible fiber optics [START_REF] Scholkmann | A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology[END_REF]. Over recent decades, optical methods have been used to monitor brain function [START_REF] Izzetoglu | Functional near-infrared neuroimaging[END_REF], neurovascular coupling that is correlated with brain activity, brain hemodynamics, cerebral blood volume and oxygenation [START_REF] Goldman | Dye laser principles: with applications[END_REF], [START_REF] Duarte | Tunable Laser Applications[END_REF]. Such modalities have a broad range of practical imaging applications, in both adults and neonates [START_REF] Ferrari | A brief review on the history of human functional near-infrared spectroscopy (fNIRS) development and fields of application[END_REF], [START_REF] Obrig | NIRS in clinical neurology -a 'promising' tool?[END_REF], particularly in premature neonates (Roche-Labarbe et al., 2007a), (Mahmoudzadeh et al., 2013b), ranging from changes in tissue oxygenation (by Near-Infrared Spectroscopy, NIRS) and cerebral blood flow measurement (by Diffuse Correlation Spectroscopy, DCS) (Durduran et al., 2010c), [START_REF] Duarte | Dye Laser Principles: With Applications[END_REF] to changes in membrane configuration such as neuron swelling and shrinking (Fast Optical Signal, FOS) (Manoochehri et al., submitted). The photothermal impact of lasers is a critical parameter that needs to be determined in order to evaluate the effectiveness and laser safety of these systems especially with high power consumption, (50mW) (Roche-Labarbe et al., 2010), (Boas et al., 1995a), [START_REF] Boas | Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation[END_REF], [START_REF] Pine | Diffusing wave spectroscopy[END_REF], (~60mW) (Lin et al., 2013a) and (300mW) [START_REF] Milej | Assessment of ICG inflow to the brain by time-resolved measurements of diffuse reflectance at 16 source-detector separations[END_REF]. Laser has photothermal interactions with tissues [START_REF] Dua | A novel modeling and simulation technique of photo--thermal interactions between lasers and living biological tissues undergoing multiple changes in phase[END_REF], caused by the temperature rise due to laser irradiation, which may cause damage to the tissues [START_REF] Welch | Optical-Response of Laser-Irradiated Tissue[END_REF], including protein denaturation, increased mitochondrial Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging membrane permeability and ultimately vaporization [START_REF] Ganguly | Analyzing Thermal and Mechanical Effects of Pulsed Laser Irradiation on Tissues[END_REF]. Temperature increases can also lead to changes in cellular metabolism, electrical membrane capacitance and, in the long term, can lead to necrosis [START_REF] Fujii | Effects of heating on electrical activities of guinea pig olfactory cortical slices[END_REF], [START_REF] Seese | Characterization of tissue morphology, angiogenesis, and temperature in the adaptive response of muscle tissue to chronic heating[END_REF], [START_REF] Thompson | Modeling of light absorption in tissue during infrared neural stimulation[END_REF], [START_REF] Lamanna | Stimulus-activated changes in brain tissue temperature in the anesthetized rat[END_REF], [START_REF] Dewey | Cellular responses to combinations of hyperthermia and radiation[END_REF], [START_REF] Ito | Assessment of heating effects in skin during continuous wave near infrared spectroscopy[END_REF]. However, the mechanisms responsible for tissue damage from heat exposure are complex and still poorly understood. Although no obvious thermal impacts are detected at skin temperatures of 37 to 41°C, a temperature increase above 41°C and up to 50°C likely results in reversible membrane alterations [START_REF] Dewey | Cellular responses to combinations of hyperthermia and radiation[END_REF], [START_REF] Kim | Radiofrequency hyperthermia for clinical cancer therapy[END_REF], [START_REF] Jeong | Temperature control in deep tumor treatment[END_REF]. The normal skin surface temperature, depending on environmental conditions, is usually around 31°C; a sustained temperature increase by more than 10°C can therefore lead to tissue damage [START_REF] Ito | Assessment of heating effects in skin during continuous wave near infrared spectroscopy[END_REF], [START_REF] Vander | Human Physiology: The Mechanisms of Body Function[END_REF]. Irreversible mechanisms then occur, resulting in cell death [START_REF] Jeong | Temperature control in deep tumor treatment[END_REF]. The temperature known to induce cell injury is 10°C when studied in vitro, resulting in vascular damage such as angiogenesis or necrosis (3°C) [START_REF] Seese | Characterization of tissue morphology, angiogenesis, and temperature in the adaptive response of muscle tissue to chronic heating[END_REF], aberrant neuronal activity in guinea pig olfactory cortical slices (2°C) [START_REF] Fujii | Effects of heating on electrical activities of guinea pig olfactory cortical slices[END_REF], cortical spreading depression (3.4°C) [START_REF] Ueda | Spreading depression elicited by thermal effects of ultrasonic irradiation of cerebral cortex in rats[END_REF] or axonal injury (1°C). Furthermore, temperature increases greater than 1°C can have long-term effects on brain tissue [START_REF] Lamanna | Stimulus-activated changes in brain tissue temperature in the anesthetized rat[END_REF], [START_REF] Denda | Topical application of TRPM8 agonists accelerates skin permeability barrier recovery and reduces epidermal proliferation induced by barrier insult: role of cold-sensitive TRP receptors in epidermal permeability barrier homoeostasis[END_REF].

The propagation of laser light energy through the tissues is therefore an important issue in optical imaging. Effective functional optical imaging can be achieved by tailoring the laser parameters to the optical characteristics of the target tissue (heat capacity, thermal conductivity, absorption coefficient, scattering coefficient). Laser parameters (e.g. radiant energy, frequency, spot size, pulse duration) should be carefully chosen to optimize imaging efficacy while minimizing undesirable tissue damage. The energy delivered to the tissues must be determined in order to ensure safety standards in optical imaging. The specific limits of laser power that determine the harmful effects of heat on neonatal tissue are poorly elucidated. Due to the specificity of neonatal head tissues, such as thin skin and skull, tissue absorption coefficients may be different from those observed in adults [START_REF] Cope | System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination[END_REF]. It is therefore essential to test the safety of optical imaging lasers in this specific, sensitive population.

The purpose of this study was to model the photothermal interaction of NIR laser on human tissues. We investigated the influence of heat and fluence rate of various laser radiant powers on two head models (adult vs neonate). The temperature distribution inside the tissue was modeled using FEM simulations and the bio-heat transfer equation to determine the transient Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging temperature function required to calculate the photothermal interaction. A range of different laser powers (1mW-100mW) with various spot sizes, different skin and brain absorption coefficients, temperature distribution profiles in adults vs neonates and the influence of blood perfusion were investigated using the simulated model. Laser irradiation was simulated using the diffusion theory and was validated by comparing with Monte-Carlo method.

Laser wavelength and power are the effective parameters in tissue-delivered energy. These properties, using wavelengths longer than 950 nm, have been extensively used for laser surgery [START_REF] Bozkurt | Safety assessment of near infrared light emitting diodes for diffuse optical measurements[END_REF]. In this paper, we investigate the effect of laser on neonatal and adult head tissues in the lower NIR spectrum [600nm-900nm] used in functional optical imaging. We also discuss our mathematical approach and its limitations.

The laser hazard class depends on the potential to cause biological damage (ANSI Z136.1-2014, IEC 825-1) [START_REF] Institute | American National Standard for Safe Use of Lasers ANSI Z136[END_REF]. Accessible Emission Limit (AEL) and Maximum

Permissible Exposure (MPE) for a given wavelength and exposure time were considered to evaluate the risk of injury (Table 1) (AEL= MPE × Area of Limiting Aperture). According to the above standards, the MPE (frequency and time-dependent) is the highest power (W/cm 2 ) of a light source that is considered to be safe and is usually about 10% of the dose associated with a 50% chance of causing damage [START_REF] Schröder | Handbook on Industrial Laser Safety[END_REF] under worst-case conditions.

According to ANSI3 , the 3.5 mm Limit Aperture Diameter (LAD) of irradiated laser was selected, as, for Near-IR exposures to the skin lasting longer than 10 seconds, involuntary movements of the body and heat conduction will result in an average irradiance profile over an area of about 10 mm 2 (even when the irradiated body part is intentionally kept still) (Protection).

Materials and Methods

To evaluate the thermal impact of NIR laser light in optical imaging in human head tissues, we used Finite Element Analysis (FEA), using the laser radiant power and exposure time. Two quasi-realistic six-layered models of neonatal and adult head tissues were simulated during irradiation by a focal infrared laser beam. To simulate the thermal interaction due to laser irradiation by different laser radiant powers and head model tissues (neonate vs adult), the bioheat diffusion model was calculated by finite-element solver COMSOL Multiphysics. The resulting thermal distribution under steady-state conditions and their time profiles were investigated. As blood flow is a factor with a major impact on heat, we further investigated the influence of blood perfusion on local heating induced by laser irradiation.

Numerical analysis and modeling of heat transfer in the tissues due to the laser source

Heat transfer from the laser source to the surrounding tissues was simulated by using the FEA method and bio-heat equation. This model includes heat conduction, convection through blood flow, metabolic heat generation in the tissue, and heat generation by the laser source. In this model, the tissues were assumed to be homogeneous and isotropic. The temperature distribution was obtained by solving the bio-heat transfer equation (BHTE) [START_REF] Pennes | Analysis of tissue and arterial blood temperatures in the resting human forearm[END_REF]:

𝐶𝜌 𝜕𝑇 𝜕𝑡 = ∇. (𝑘∇𝑇) + 𝐴 0 -𝐵 0 (𝑇 -𝑇 𝐵 ) + 𝑄 𝑒𝑥𝑡 [ 𝑤 𝑚 3 ] (1)
Where T is temperature (

•C), C is specific heat [J/ (kg •C)], ρ is tissue density (kg/m 3 ), k is thermal conductivity [J / (m s •C)], 𝐴 0 is the basic metabolic rate [J / (m 3 s)], B 0 (ρbcbωb) is the blood perfusion coefficient [J / (m 3 s •C)] that includes blood specific heat 𝐶 𝑏 ( 𝑗 𝑘𝑔.𝐾 ), blood perfusion rate 𝑤 𝑏 ( 1 𝑠
) and mass density of blood 𝜌 𝑏 ( 𝑘 𝑚 3 ), T B is the temperature of blood (•C), and Q ext is the external heat source (W/m 3 ). This equation computed the temperature distribution within the tissue at different times during laser irradiation.

To solve the bio-heat equation, the boundaries of the model, except for the surface of the skin layer exposed to air, were considered to be at body temperature. At the surface in contact Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging with air, it was assumed that heat transfer occurred as a result of free convection into air (heat transfer by radiation into the air would be negligible), which is described by: .( ) ( )

ext n k T h T T  = - (2)
Where n is the outward normal vector, h is a heat transfer coefficient to control convective cooling to the model (W/m 2 .K), defined as 5 W/m 2 .K for air, Text is the external temperature defined as 24°C for air, T is the internal temperature of model, and k is the thermal conductivity (W/m.K) (2006; [START_REF] Kim | Thermal impact of an active 3-D microelectrode array implanted in the brain[END_REF].

Modeling the Laser Source

To simulate the heat generated by the laser irradiation (the source term Qext), a spatially

Gaussian and temporally continuous laser beam was modeled perpendicular to the surface of the model to simulate an optical fiber positioned orthogonally to the surface.

Light propagation in biological tissue results from the diffusion approximation of the radiative transfer equation and is defined by [START_REF] Saouli | Modelling of the near infra-red radiation pulse propagation in biological tissues for medical imaging application[END_REF]:

( ) ( ) ( ) ( ) 1 () 3( ) 1 , , , , a as d r t r t r t r t c dt S     -  + += (3)
Where: c is the light speed in a vacuum, μa is the absorption coefficient, μs is the reduced scattering coefficient, 𝝓 is the photon intensity and S(r, t) is the local photon source (Qext=µa.𝝓). The photon-diffusion equation was used to calculate photon propagation in strongscattering media such as biological tissues. The diffusion approximation can correctly predict light transport in a region far from the laser source, where all photons are scattered at least several times [START_REF] Farrell | Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium[END_REF][START_REF] Gobin | Integrating the digitized backscattered image to measure absorption and reduced-scattering coefficients in vivo[END_REF]. In skin, these conditions are only satisfied in the deeper levels of the dermis and do not apply to the epidermis, where scattering of radiation remains highly anisotropic. A skin depth of 0.4mm was therefore used for further skin investigation. Different power levels were investigated and the results were compared between neonatal and adult head models. Dirichlet and Robin boundary conditions were applied by equations ( 4), (5). Where, n is the normal vector and (R= 0) is the reflection parameter.

Model

Two quasi-realistic six-layer head models in a 3-D Cartesian (x, y, z) coordinate, were simulated to solve light propagation equations in neonatal and adult head tissues, as shown in Figure 1. The thickness of the skin, fat, skull, dura, CSF and brain were defined as shown in Table 2, for the adult and neonatal models. The minimum thickness of neonatal skin was extracted from the distribution of skin thicknesses measured in vitro as a function of gestational maturity (Saidi, 1992b). For the sake of simplicity, the curvature of the 6 layers was not considered. To assume that the temperature at the boundary of the selected region was equal to body temperature (37 °C), a sufficiently large thickness (80mm) of brain tissue was selected.

The model size was defined as (radius=80mm, height=80mm), fourfold larger than the area affected by laser radiation, in order to conserve the semi-infinite nature of the model (X.

Ronghou, 2014). The optical source was simulated in which the laser source emits a Gaussian and temporally continuous laser beam. Different radii of laser spots (0.2, 0.4, 0.6, 1, 3, 5, 7, 11, 15mm) for different powers (from 10 to 200mW) were investigated. (Bamett et al., 2003; Kiguchi et al., 2007; Madsen, 2012) 1.4 (Khodabakhshi and Cheldavi, 2010; Rahmat-Samii and Kim, 1998) 7 (Bamett et al., 2003; Kiguchi et al., 2007; Madsen, 2012) 0.5 (Genina et al., 2005; Khodabakhshi and Cheldavi, 2010)

2 (Kiguchi et al., 2007; Rahmat-Samii and Kim, 1998) 80 Neonate 0.5 (Saidi, 1992b) 1.4 (Khodabakhshi and Cheldavi, 2010; Rahmat-Samii and [START_REF] Rahmat-Samii | Antennas and human in personal communications: applications of modern EM computational techniques[END_REF] 2 (Kiguchi et al., 2007) 0.5 (Genina et al., 2005; Khodabakhshi and Cheldavi, 2010) 0.5 (Kiguchi et al., 2007) 80

The adult and neonatal models consisted of 1,564,530 and 1,024,918 tetrahedral elements, respectively. The maximum element size of the refined mesh around the light source was 0.01 mm. The diffusion equation is valid in the case of large scattering compared to absorption and Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging when studying diffuse light propagation, i.e. at sufficient distances from any light sources.

These considerations were applied to the physics of the model.

Thermal and optical properties for various tissues

The tissue parameters of the model, such as thermal conductivity, density, heat capacity at constant pressure, metabolic rate, blood perfusion for the six different layers, are shown in Table 3, 4 (DeMarco et al., 2003). The brain perfusion rate used in this study was 0.00932 s -1 ≈ 0.56 min -1 , which is comparable to the value measured in vivo with ASL-fMRI [START_REF] Rowland | Clinical Pharmacokinetics: Concepts and Applications[END_REF][START_REF] Shargel | Applied Biopharmaceutics & Pharmacokinetics, Fifth Edition[END_REF]. Grey and white matter were considered to have the same thermal properties [START_REF] Kim | Thermal impact of an active 3-D microelectrode array implanted in the brain[END_REF]. The effect of cerebral metabolism on brain temperature was considered to be negligible [START_REF] Iwata | Dual role of cerebral blood flow in regional brain temperature control in the healthy newborn infant[END_REF][START_REF] Kauppinen | Assessment of human brain temperature by 1H MRS during visual stimulation and hypercapnia[END_REF], allowing the metabolic rate for adults and neonates to be considered to be identical. Brain function and metabolic activity are indicated by oxygen concentration and glucose intake in brain cells [START_REF] Gordon | A mathematical model of the human temperature regulatory system--transient cold exposure response[END_REF][START_REF] Scheinberg | Effects of vigorous physical exercise on cerebral circulation and metabolism[END_REF].

The NIR laser wavelength in the middle of biological optical windows (600nm-900nm)

was selected for further investigation (isosbestic point: 800 nm) (Vo-Dinh, 2014). The scattering coefficients were acquired by the following equation:

' .( / 500 ) b s a nm  - = (6)
Where a, b, λ are scattering amplitude (related to scatterer density (cm -1 )), scattering power (related to scatterer size distribution) and wavelength in nm, respectively. a and b coefficients Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging for different tissues were selected according to [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF]. Absorption and scattering coefficients of different adult and neonatal tissues are given in Table 5. For the 800 nm wavelength, similar optical properties for neonatal and adult skin were obtained from [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF] and (Vo-Dinh, 2014), respectively.

Discrepancies were observed concerning the precise value of absorption and scattering coefficients. This difference could be derived from the discrepancy between theoretical and experimental results. In general, in vivo μa and μs values for human skin were significantly smaller than those obtained in vitro (about 10 and 2 times, respectively [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF]). For μa, the discrepancy may be attributed to the low sensitivity of the doubleintegrating sphere, and goniometric techniques were applied for in vitro measurements at weak absorption combined with strong scattering (μa <<μs) and sample preparation methods.

The absorption coefficients in our study were adopted from the most recent complete reference concerning the optical properties of tissues (Vo-Dinh, 2014). Different percentages of melanin [Melanosomes per unit volume]%=0.87, 1.15, 1.65% corresponding to the skin absorption coefficient µa(skin)= 0.52cm -1 , 0.65cm -1 , 0.88cm -1 [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF] were applied in our model. A wide range of skin absorption coefficients (0.5 cm -1 also including 0.1 cm -1 , 0.2 cm -1 , 0.3 cm -1 , 0.4 cm -1 ) was investigated. In addition, different ranges (0.01 cm -1 , 0.05 cm -1 , 0.1 cm -1 , 0.5 cm -1 ) of adult brain absorption coefficients were considered [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF]. et al., 2003).

Table 5 Optical properties of the tissue components, corresponding to the six layers of the head (skin, fat, skull, dura, CSF and brain): absorption coefficient (Vo-Dinh, 2014), scattering coefficient [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF], (Saidi, 1992a), [START_REF] Van Der Zee | Optical properties of brain tissue[END_REF]. (Altman et al., 1988; Edwards et al., 1988; Kusaka et al., 2005) 1060 10000

Blood

Absorption coefficients (cm -1 ) Scattering coefficients (cm -1 ) Skin 0.52 (Jacques, 2013; Vo- Dinh, 2014) 23.58 (Jacques, 2013) Fat 0.11 (Vo-Dinh, 2014) 13.41 (Jacques, 2013) Skull 0.11 (Vo-Dinh, 2014) 16.35 (Jacques, 2013) Dura 0.70 (Vo-Dinh, 2014) 12.61 (Jacques, 2013) CSF 0.01 (Vo-Dinh, 2014) 3.2 (Okada and Delpy, 2003) Adult Brain 0.90 (Vo-Dinh, 2014) 11.34 (Jacques, 2013) 79 79 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

Results

The first section describes the light-induced heating due to exposure from various laser powers and the distribution profile due to photothermal interactions in various types of adult and neonatal head tissues. The following sections describe the effects of blood perfusion, various skin and brain absorption and scattering coefficients, laser spot size and different tissue thickness on the temperature distribution in head tissues. Moreover, Monte Carlo simulation was used to validate the diffusion theory. Neonate). The maximum temperature increase, using NIR for laser powers between 1 mW and 100 mW (laser irradiance, I, between 0.127 W/cm 2 and 12.73 W/cm 2 ), with 10 mW increments, ranged from 0.16 to 16.12°C (on the adult head) and 0.13 to 13.51°C (on the neonatal head) at a skin depth of 0.4mm. However, the maximum temperature increase on the brain for laser powers between 1 mW and 100 mW ranged from 0.0025 to 0.26°C and from 0.03 to 2.85°C at depths of 15.9 mm and 4.9 mm in the adult and neonatal brain, respectively. Fig. 2c demonstrate the temperature changes at the depth of 0.4mm with various powers: 10 mW to 100 mW in 10 mW increments over time.

Effect of various laser radiant powers on neonatal and adult head models

Neonatal Skin 0.52 (Saidi, 1992a) 23.58 (Saidi, 1992a) Neonatal Brain 0.08 (Tuchin and Engineers, 2007) 8.42 (Tuchin and Engineers, 2007) 81 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

Effect on neonatal vs adult tissue

The intensity and correlative temperature changes in adult and neonatal head tissues according to the depth from the surface under steady-state conditions were evaluated in order to compare temperature distribution profiles in the adult versus the neonatal model (Fig. 3).

For instance, Figures 3 and4 show the heat distributions for 3.81 W/cm 2 and the magnitude of laser penetration, respectively. As the skin and skull are much thinner in neonates, more light reaches the neonatal brain than the adult brain, which consequently results in a more marked temperature increase in the neonatal than in the adult brain. In the present study, using similar characteristics for neonatal and adult skin, the temperature increase was obviously the same in the two models. Due to the shorter distance of the other tissues from the surface in the neonatal head, the maximum temperature increase for 3.81 W/cm 2 was higher in the neonatal brain (T=0.85°C) than in the adult brain (T=0.07°C) (Fig. 3).

The light-distribution profiles on the brain surface for the respective models are presented in Figure 4, which shows the comparative distributions of the normalized intensity of photons (I/I0) from the laser source (30 mW) for six layers of adult (lower diagram) and neonatal head models (skin, fat, skull, dura, CSF and brain). The depths of the brain from the skin surface were 15.9 mm for the adult model and 4.9 mm for the neonatal model. The horizontal axis represents the distance along the surface of the brain from the source. Comparison of the adult and neonatal models showed deeper scattering of light in the neonatal brain.

Effect of blood perfusion

As blood flow has a major impact on tissue temperature regulation, we simulated two different conditions (presence and absence of blood perfusion) in the adult model to investigate the influence of blood perfusion on local heating induced by laser irradiation (Fig. 5a). The maximum temperature increase in the brain in the presence of blood perfusion (T=0.07°C) was lower than in the absence of blood perfusion (T=0.5°C), suggesting that, based on the numerical simulation, blood perfusion decreases the temperature rise by 0.43°C for 3.81 W/cm 2 . Figure 5b shows the effect of different blood perfusion and metabolic rates on induced heat distribution in neonatal brain. Doubling the blood perfusion rate decreased temperature changes in the brain by about 0.1°C (Fig. 5b), whereas the laser-induced heat changes in the brain when the normal adult metabolic rate (10000 W/m 3 ) is decreased by one half can be considered to be negligible.

Effect of different skin and brain absorption coefficients

As accurate in vivo measurements of optical properties are not available, a wide range of these values had to be modeled. Figure 6 presents the evolution of the temperature profile as function of radial distance for different skin (Fig. 6a) and brain (Fig. 6b) absorption coefficients for 3.81 W/cm 2 . The curves depict the temperature distribution in the skin and brain, in which a variation of the absorption coefficient (µa(skin): 0.1 cm -1 to 0.88 cm -1 ; µa(brain): 0.01 cm -1 to 0.5 cm -1 ) had a significant influence at a depth of 0.4mm in the skin (T = 1.8°C to 6.9°C) but not in brain tissue (T = 0.07100°C to 0.7148°C).

Effect of different Laser spot sizes

Laser spot size impacts the temperature profile. The effect of laser spot size on the temperature distribution in the skin and brain tissue of the adult and neonatal head models was investigated in the laser power range of 10 -200mW (in order to investigate the effect of higher powers on the temperature profile by changing spot size). Figure 7 shows a more marked temperature decrease as the laser spot size was increased from 0.2mm to 15mm.

Figure 8 shows the temperature changes vs. irradiance (Fig. 8a: skin, Fig. 8b: brain).

Temperature changes in the brain were 0.6059°C and 0.7182°C for the same irradiance of 0.113W/cm 2 with different powers and spot sizes (150mW, spot size=13mm) and (200mW, spot size=15mm), respectively. Higher powers and larger spot sizes (but with the same irradiance) therefore induced higher temperatures, implying that temperature changes depend not only on the magnitude of irradiance but also on the photon distribution (which depends on both power and spot size). Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging (3,4,5,6 mm),fat (0.4,1.4,2,3 mm),skull (5,6,7,8 mm),CSF (0.1,1,2,3 mm). In particular, the effect of thickness variations on deep tissues is negligible.

Validation of Diffusion Theory

The diffusion theory and the Monte Carlo approach have complementary attributes for modelling photon transport in a scattering medium. The Monte Carlo approach is precise but computationally inefficient, whereas the diffusion theory is inaccurate but computationally efficient. A trade-off must therefore be reached between the computational accuracy and efficiency of the two models. Using Monte Carlo improves the computational accuracy at the expense of computational efficiency. Although the diffusion theory is acceptable when the 90 90 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging isotropic point source is situated far from the surface of the scattering medium, it becomes less accurate as the source approaches the surface (Fig. 10). To demonstrate this point, we compared the results obtained with the Monte Carlo method (http://omlc.org/software/mc/) and the diffusion theory. In this section, we evaluate each step of the approximation described above using the accurate Monte Carlo method. The optical properties from table 5 were used. As shown in Figure 8, the fluence derived from the diffusion theory was only accurate when r was greater than 0.3cm. Deviations caused by each step of the approximation are illustrated in

Discussion

To the best of our knowledge, this is the first study to use two quasi-realistic models (sixlayered neonatal vs adult head models) to quantify the temperature distribution by bio-heat diffusion modelling. Furthermore, despite the use of animal models [START_REF] Kim | Thermal impact of an active 3-D microelectrode array implanted in the brain[END_REF], this is the first study to use an FEA approach to investigate the influence of heat and fluence rate of various laser radiant powers on human head models (adult and neonatal) with blood perfusion.

Effect of various laser radiant powers on neonatal and adult head models

By ignoring the optical discontinuity and anisotropic properties of the tissues, the temperature distribution showed a higher surface temperature for a highly scattering medium during laser irradiation. Current research into laser-induced tissue damage has focused on damage generated in superficial tissues in adults [START_REF] Ito | Assessment of heating effects in skin during continuous wave near infrared spectroscopy[END_REF]. [START_REF] Ito | Assessment of heating effects in skin during continuous wave near infrared spectroscopy[END_REF] investigated the heating effect of near-infrared irradiation at 789 nm. A 0.101°C/mW temperature elevation was detected at a depth of 0.5 mm in the human forearm in which µa(forearm)= 0.2cm -1 (Vo-Dinh,

2014).

In agreement with the results of this previous study [START_REF] Ito | Assessment of heating effects in skin during continuous wave near infrared spectroscopy[END_REF], our results show a 2.7°C temperature increase at a depth of 0.4 mm in the skin (using µa(skin)=0.2cm -1 , NIR-light at 800 nm and a power of 30mW, I = 3.81 W/cm 2 ) (Fig 6a). On the other hand, for a power of In adults, a 10°C temperature increase is considered to be the safety limit to avoid skin injury [START_REF] Widmaier | s Human Physiology: The Mechanisms of Body Function[END_REF]) (assuming a skin surface temperature of around 31°C).

Consequently, our results show a temperature increase of up to 10°C at a power of about 50 mW (I= 6.36 W/cm2) and 60 mW (I= 7.63 W/cm 2 ) under steady-state conditions on adult and neonatal skin, respectively.

Considering a 1mm spot size and assuming a brain blood perfusion rate equal to 0.00166 s -1 , the temperature increase in the adult brain for powers ranging from 1mW to 100mW (0.127 W/cm 2 < I < 12.73 W/cm 2 ) was much lower (T = 0.002°C to 0.26°C) than the temperature known to induce cell injury when studied in vitro (10°C). In contrast, in the neonatal brain, the temperature increase was lower (T = 0.03°C to 0.86°C) than the critical temperature (1°C) for powers ranging from 1 to 30mW (0.127 W/cm 2 < I < 3.81 W/cm 2 ) and a 1 mm spot size.

Effect on neonatal vs adult tissue

As expected, with an irradiance of 0.31Wcm -2 , the temperature increase in the neonatal brain was higher than that in the adult brain (when comparing the T of each neonatal head layer with the same layer in the adult model), notably because of the thinner skin and skull in neonates, facilitating penetration of photons into the brain. Despite similar optical properties of neonatal and adult skin at 800 nm (Saidi, 1992b), (Vo-Dinh, 2014), additional factors predisposing to a more marked temperature increase are the greater transparency and lower absorption coefficient of neonatal brain tissues [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF].

Nevertheless, the temperature increase at 3.81 W/cm 2 was about 4.5°C vs 4°C at a depth of 0.4 mm in skin (neonate vs adult) and 0.85°C vs 0.07°C on the brain (neonate vs adult), which is still much lower than the previously reported limit for the skin (10°C) and the brain (1°C) under steady-state conditions [START_REF] Lamanna | Stimulus-activated changes in brain tissue temperature in the anesthetized rat[END_REF] and also well below the safety limits adopted for laser-induced tissue injury. However, if the temperature changes very slowly (e.g. at a rate of less than 0.5 °C per minute), the subject may can be unaware of a 4-5 °C change in temperature [START_REF] Kenshalo | Temporal course of thermal adaptation[END_REF], provided the skin temperature remains within the neutral thermal range of 30-36 °C.

Effect of blood perfusion

Blood perfusion plays a significant role in thermal regulation of a living body. In the present study, blood perfusion removed heat away from the laser source and appeared to 94 94 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging constitute a cooling mechanism for the brain. Local heating of the model was considerably reduced when blood perfusion in the tissues was taken into account. Body fluids, transporting heat throughout the tissues, act as a convection mechanism. The present study did not consider the blood flow increase induced by vasodilatation resulting from the temperature rise [START_REF] Charkoudian | Mechanisms and modifiers of reflex induced cutaneous vasodilation and vasoconstriction in humans[END_REF], which would have further reduced laser-induced heating of the skin as a result of the normal physiological thermoregulation processes. In addition, the superficial brain is spontaneously cooled by the environment and is cooler than arterial blood. Under physiological conditions, an increase in CBF may lead to an increase in superficial brain temperature and a simultaneous decrease in deep brain temperature, emphasizing the complexity of the effects of blood perfusion rate.

Our results show that changes in cerebral metabolism had no significant impact on local brain temperature changes congruent with the experimental results [START_REF] Sukstanskii | Theoretical model of temperature regulation in the brain during changes in functional activity[END_REF]) (Fig 5b). However, changes in brain temperature were linked with cerebral blood perfusion and blood perfusion contributed to maintain a low brain temperature.

Effect of various skin and brain absorption and scattering coefficients

Discordant values have been reported for the exact absorption and scattering coefficients.

These discordant values could be due to the discrepancies between theoretical and experimental investigations. In general, in vivo μa and μs values for human skin are significantly lower than those obtained in vitro (about 10-fold and 2-fold lower, respectively [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF]). The discordant values for μa may be related to the low sensitivity of the doubleintegrating sphere, the goniometric techniques used for in vitro measurements at low absorption combined with strong scattering (μa <<μs) and sample preparation methods [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF]. Consequently, in the absence of accurate absorption coefficients, these values need to be chosen cautiously, and our temperature profiles were probably overestimated, as data were presented as the maximum temperature rise resulting from intentional selection of the maximum absorption coefficients available in the literature. As skin absorption is usually dominated by melanin absorption, various melanin levels in the skin have therefore been investigated to study the effect of darker skin. Figure 6 presents the temperature distributions with broad ranges of skin (Fig. 6a) and brain (Fig. 6b) absorption coefficients and shows that changes in brain or skin absorption coefficients had a greater impact on superficial layers, 95 95 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging closer to the source, and a lesser impact on deeper tissues. Nevertheless, as the brain is situated far from the source, this impact is limited to the brain surface (Fig. 6b inset).

Photons are less scattered and penetrate much more deeply for lower values of scattering coefficient, as they are able to travel over a longer distance with greater step size before they interact with the tissue at a new position. As the value of the scattering coefficient increases, scattering increases and photons undergo frequent scattering with smaller step sizes, resulting in a more circular profile of fluence rate. For lower scattering coefficients, photon penetrate much more deeply with intensity decreasing outwards according to the radial distance. While changes in scattering coefficients can impact on the photon density distribution, their effect on temperature is negligible, in view of the small range of scattering coefficients of these head layers is low (brain scattering coefficient:8.74_12.17cm -1 , skin:15.09_26.75cm -1 , fat:8.30_22.12cm -1 , skull: 8.89_19.24cm -1 , CSF: 0.1_3.2cm -1 [START_REF] Okada | Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer[END_REF]) [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF].

Effect of various Laser spot sizes

The mechanisms involved in the interaction between laser and biological tissue are also intimately related to the Laser characteristics (e.g. wavelength, energy density, and spot size).

By increasing the beam spot size, Laser light can be diffused over larger areas and, in these situations, laser power can be increased while maintaining safe levels of skin irradiation. Figure 7 shows that the temperature decreased as the laser spot size increased from 0.2mm to 15mm.

This figure shows that, for a specific Laser power, Laser spot size should be kept above a specific limit to avoid skin temperatures exceeding safety limits (e.g. in adults, assuming a skin safety threshold of 10°C, if Laser power = 100mW, the spot size should be  11 mm).

In the brain, a few orders of magnitude of difference in spot size does not induce any change of brain temperature, but smaller differences in laser power cause measurable differences in brain temperature, due to smaller spot size leading to higher irradiance but smaller penetration depth. Laser beam spot size determines the depth of penetration. A larger spot size decreases scattering of light and increases the depth of penetration. A larger spot size therefore results in deeper penetration, while smaller spot size induces more rapid scatter and more rapid decay of fluence with depth [START_REF] Keijzer | Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams[END_REF]. Since the e -1 depth of scattered light is unclear when scattering dominates absorption (μa << μs'), the exact depth of light penetration in tissue has not been determined [START_REF] Welch | Optical-Response of Laser-Irradiated Tissue[END_REF]. Therefore, by 96 96 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging maintaining the same power, using larger spot size (sp↑) decreases irradiance (I↓), but increases the depth of penetration of the light (depth↑), resulting in insignificant temperature changes in deeper tissues (e.g brain). By maintaining the same spot size, higher power (P↑) increases irradiance (I↑) and the depth of penetration of the light (depth↑), resulting in significant brain temperature changes. The temperature in the brain therefore depends on the laser power more than on the spot size.

Figure 7 (A,B) shows that spot size changes at constant power have a lesser intense heating effect on deeper tissue.

Figure 8 illustrates the temperature changes vs. irradiance and shows higher temperature due to higher power and higher spot size with the same irradiance. In skin tissue, for small spot sizes, cooling of surrounding non-irradiated tissue is much more effective than for large spot size. With larger spot sizes, heat transfer from the center of the spot size cannot occur radially (sideways). Consequently, for the same level of skin irradiance, larger spots produce higher temperatures than smaller spots. This effect of higher temperatures for larger spot sizes reduces the exposure limit, since the effect of cooling means that the damage threshold does not simply depend on the skin irradiance. Exposure limits decrease with increasing spot sizes, reflecting the fact that, for the same level of irradiance, larger spots are more hazardous than smaller spots. However, this dependence of the risk threshold on spot size diameter does not apply to very large spot sizes, since the temperature profile in the center of the spot has a more or less flat profile, and this value is not affected by any further increase in the actual spot size, as the edges that are cooled radially are situated too far away from the center. Consequently, for large sources, the risk threshold depends only on the irradiance and no longer on the spot diameter [START_REF] Schulmeister | Laser Safety[END_REF].).

During exposure of the skin to IR radiation for several seconds, involuntary body movements and heat conduction disperse the irradiance profile over an area of at least several square millimetres (~3.5mm), even when the irradiated body part is intentionally kept still, even the smaller spot sizes (0.2 to 1mm) has been considered in our model in order to study the effect of these range of spot size (i.e. which is below the 10°C limit skin temperature at 3mm but not below the 10°C limit at 1mm at the same power). For a wavelength of 800 nm used in our study, with the maximum anticipated exposure time (Table 1), with an ANSI standard MPE equal to 0.3Wcm -2 , larger power would be allowable with larger spot size.

Systematic model errors

Our simulated model remains a mathematical model, meaning that errors could be come from the simplifications. These errors are essentially due to the following causes:

The inaccuracy of the optical and thermal properties is main point in the model's set of equations, as these properties are essential for the accuracy of the simulated model's outcome.

Many approaches have been demonstrated to estimate these properties, but various authors have reported very discordant values, reflecting the difficulty of estimating these properties. In addition, the inaccuracy is further increased by the dependency of the properties on the various parameters (temperature) over time, resulting in a nonlinear difference.

The error of Pennes' bio-heat equation is that it does not account for directionality of blood perfusion, which is an important factor in the energy exchange between vessels and tissue. In addition, Pennes' equation does not consider the local vascular geometry. While Pennes' bioheat model is based on incorrect anatomical views about the temperature distribution of blood through the tissues, it is still universally employed and its relative accuracy in tissue situated away from large vessels which introduce local convection has been confirmed [START_REF] Arkin | Recent developments in modeling heat transfer in blood perfused tissues[END_REF].

Another error is related to computer performance limitations: accessible memory, the size of mesh nodes used to make the model. Our simulated model was established on the basis of the above conditions, with COMSOL standard refining processes at the crucial areas (around the heat source).

Absolute numeric tolerance: Whole numerical approaches have a permitted error (absolute numeric tolerance) that expresses the reference point of the convergence. Different solvers commonly use different absolute tolerances. In our model, we used the COMSOL default tolerance value of 0.01 which leads to a final error of 1%, considered to be a reasonable criterion for modelling.

Diffusion theory limit: Despite the fact that diffusion theory suggests a fast approach, it is not valid close to the light source or the boundary, where the photon intensity is strongly anisotropic. This is due to the fact that, at short distances, the radiance rate is not linearly anisotropic and the basic assumptions required for the diffusion approximation to Boltzman transport equation are not satisfied. On the other hand, strong absorption prevents photons from 98 98 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging engaging in an extended random walk and the approximation µt = µs' becomes insufficient. The diffusion approximation is therefore only valid in highly scattering media (i.e., µa << µs') and when the point of interest is situated far from sources or boundaries.

The simulated head model consists of six types of tissues. However, the sophisticated geometry of the tissue structure is ignored and tissue layers are parallel to each other. In a real head, the thickness of superficial tissue, such as the scalp and skull, is not uniform and brain surface is folded with sulci. The thickness of the skull is known to vary significantly around the head and between individuals. In addition, the thickness of the CSF can vary because the brain can move to a limited degree within the skull, this change is more prominent in the neonatal head. Moreover, there is a relationship between skin thickness and the neonate's gestational maturity (Saidi, 1992a).

Conclusion

A laser-tissue interaction model was developed to predict the spatial dynamic changes in temperature rise during laser exposure of human head tissues. We describe the bases necessary to calculate the effects of the temperature changes caused by the absorption of light energy in the tissues, using the bio-heat equation and including the cooling effects of blood perfusion in tissue in order to model the photothermal interaction of NIR laser on human tissues.

The temperature changes of the radiated zone calculated from our simulation and in vitro experiments presented a small deviation. Two of the main reasons for this deviation are the lack of accurate values of the tissue optical properties and diffusion approximation theory in superficial surfaces.

Further studies under different conditions are necessary to achieve full agreement with in vivo data, and, if necessary, define error correction factors to be added to the equation set.

However, this would not eliminate the need for precise values for the optical and thermal properties of the tissue. On the other hand, our model remains practical, as it introduces a step in using simulated head tissues as a basis for much more detailed NIR laser photothermal interaction experiments.

The results presented in this work should be useful to optimize Laser spot size and power for a variety of laser applications of functional imaging systems (e.g. Diffuse Correlation Spectroscopy (DCS) which need near-infrared (NIR) light with relatively high laser power). A

Supplementary

In the following we explained some parts of study in more details:

1) Model Geometry included:

The head (with 6 layers) was modeled in a 3-D Cartesian (x, y, z) coordinate, as shown in the following figure. The thickness of the skin, fat, bone, dura, CSF and brain were set according to the following table, for the adult and neonatal models. The minimum thickness of neonatal skin (in the different gestational maturity) was selected as measured in vitro [START_REF] Sajjadian | Transcutaneous bilirubin measurement in preterm neonates[END_REF], as shown in the following figure. For the sake of simplicity, the curvature of 6 layers was not considered. To assume the temperature at the boundary of the selected region is equal to body temperature (37 °C), the thickness of brain tissue was selected sufficiently large (80mm). Optical source was simulated in which the laser source sends out a Gaussian and temporally continuous laser beam and Qext in bioheat equation for each layer of tissue was defined as absorption coefficient × 𝜱 (photon intensity). Different radii of laser spot (0.2, 0.4, 0.6, 1, 3, 5, 7, 11, 15mm) were investigated (refer to chapter 3). Khodabakhshi, 2010;[START_REF] Kiguchi | Comparison of light intensity on the brain surface due to laser exposure during optical topography and solar irradiation[END_REF] The boundaries of the selected region (except the surface exposed to the air), was considered to be at the body temperature. This is reasonable since the volume to be analyzed chosen to be sufficiently large and the boundaries are not affected by the heating source. The third boundary condition corresponds to convection at a surface was considered to solve the bioheat equation, at the surface contacting with air, assumed .( ) ( )

Skin

ext n k T h T T  = - (7)
➢ Semi-infinite domain:

To have sufficient distances from light sources in case of large scattering, a semiinfinite domain was required. The layer sizes of the model were selected sufficiently large to be able to assume a semi-infinite domain. The model size was taken as (radius=80mm, height=80mm), which by being 4 times larger the area affected by the laser radiation, conserves the semi-infinite nature of the model. The same relative dimensions (4 times larger) for a semi-infinite domain have been used by Wilson et al., Bianco et al., and Ronghou et al. (Bianco, 2008;[START_REF] Ogoh | Stefan's Problem: Validation of a One-Dimensional Solid-Liquid Phase Change Heat Transfer Process[END_REF]Ronghou, 2014).

To demonstrate that the domain is large enough to assume a semi-infinite geometry, it should calculate solutions for different sizes of the domain and show that the lateral and depth profiles of temperature and light do not change as extend the domain. The following figure shows that the lateral and depth profiles of temperature and light do not change when the dimensions are changed to 70, 80, 90 mm.

Fig.13

The lateral and depth profiles of temperature and light for different sizes of the domain.

➢ The thermal equilibrium between the 'head' and the 'ambient':

For an ambient temperature that is lower than the skin surface temperature, heat loss from the skin to the environment takes place via convection. Heat transfer by radiation into the air would be negligible. The boundary condition in the above surface is:

.( ) ( )

ext n k T h T T  = - (8)
➢ The assumptions that lead to simplifying the diffusion approximation from the radiative transfer equation (RTE):

Two assumptions permit the diffusion approximation as a simplification of the radiative transfer equation: (1) Relative to scattering events, there should be very few absorption event, and the radiance will become nearly isotropic.

(2) In a primarily scattering medium, the time for substantial current density change is much longer than the time to traverse one transport mean free path. Thus, over one transport mean free path, the fractional change in current density is much less than unity. This property is sometimes called temporal broadening [START_REF] Wang | Biomedical Optics: Principles and Imaging[END_REF].

To reduce the complexity of the RTE, a standard method for approximating equation called the PN approximation was employ. When L(r,Ω,t) (source) is nearly isotropic, the so-called P1 approximation:

∇𝛷(𝑟, 𝑡) = - Here we defined the photon diffusion coefficient D(r)≡v/3(µ ′ 𝑠 (𝑟) + µ 𝑎 (𝑟)) (Durduran et al., 2010a). Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

The diffusion equation is valid according to the assumptions that (1) the scattering is large compared to the absorption and (2) studying diffuse light propagation at sufficient distances from any light sources which is the case in our study. However, the main aim of current study is to investigate the thermal effect of the laser source on brain tissue.

➢ The limitations of using the diffusion approximation:

According to Lorenzo and Schweiger [START_REF] Munro | Principles of Diffuse Light Propagation: Light Propagation in Tissues with Applications in Biology and Medicine, by Jorge Ripoll Lorenzo[END_REF][START_REF] Schweiger | Application of the finite element method in infrared image reconstruction of scattering media[END_REF], the applicability of the diffusion equation can be restricted by the limitation of the expansion of the transfer equation to the first two terms (P1 approximation), and the above assumptions.

In biological tissue (µ a ≪ µ ′ s ), the P1 approximation can be acceptable. The directionality of the laser beam diminishes across a tiny distance, afterward light propagation changes state to isotropic, because of high scattering in tissue. This permits the diffusion approximation to be applied. Inconsistency between the diffusion model and experimental measurements are expected in the region close to the laser source.

Based on the assumptions and approximations, the diffusion equation will go wrong very close to the surfaces or laser sources (this would, in theory, abolish the angular dependence and perhaps make the contribution of the term ∂J/∂t not negligible).

Commonly, these (flexible) restrictions are determined by comparing the outcomes of the diffusion approximation to the RTE, and not the whole solution to Maxwell equations and generally ignore the contribution from the reduced intensity. By comparing the outcomes of the diffusion approximation to the RTE, and not the whole solution to Maxwell equations and generally ignore the contribution from the reduced intensity, commonly these (flexible) restrictions can be determined.

In this manner, we are not doing an equitable comparison: the RTE suffers from many approximations of its own which are clearly not being accounted for. If a strict comparison of theories is to be performed, it should be with regards to the exact problem using Maxwell equations, since the diffusion equation is not something unique to the RTE, it is an equation which can also be extracted directly from Maxwell. Moreover, as occurred with the RTE, results predicted by the diffusion approximation are assumed to deviate significantly in cases where there might be a highly coherent contribution. What we can clearly determine is when the diffusion approximation is expected to hold (far away from source and detectors, at long time-scales, and in the absence of coherent effects). Determining where it does not hold is a different matter since there are no rigorously defined limits.

The diffusion approximation can predict light transport correctly far from the light source and far from the air-tissue boundary [START_REF] Farrell | Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium[END_REF][START_REF] Gobin | Integrating the digitized backscattered image to measure absorption and reduced-scattering coefficients in vivo[END_REF]. In the skin, this is only satisfied in the deeper level of the dermis and does not apply to the epidermis and the upper level of the dermis where the scattering of radiation is anisotropic. Therefore, the total fluence rate, especially in the superficial area of skin, is overestimated when the diffusion approximation is used [START_REF] Motamedi | Light and temperature distribution in laser irradiated tissue: the influence of anisotropic scattering and refractive index[END_REF].

Although the main aim of our study is to investigate the thermal effect on brain tissue (far away laser source), to verify our results of superficial tissue with the experimental study [START_REF] Ito | Assessment of heating effects in skin during continuous wave near infrared spectroscopy[END_REF] we consider temperature changes at 0.4 mm radial distance from the laser source (considering epidermis thickness is 0.06mm).

➢ To solve heat and light diffusion equations:

The finite element method was used to simultaneously solve the diffusion equations of light and heat [START_REF] Shafirstein | Laser tissue interaction modeling for treatment planning of port-wine stain[END_REF]. In this study, the diffusion and bio-heat equations were solved simultaneously, and results are shown at steady state. To obtain On the other hand, the diffusion approximation can predict light transport correctly in a region far from the light source and far from the air-tissue boundary where all photons are scattered at least several times [START_REF] Farrell | Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium[END_REF][START_REF] Gobin | Integrating the digitized backscattered image to measure absorption and reduced-scattering coefficients in vivo[END_REF]. In the case of skin, this is only satisfied in the deeper level of the dermis and does not apply to the epidermis and the upper level of the dermis where the scattering of radiation remains highly anisotropic. Therefore, the total fluence rate, especially in the superficial area of skin, is overestimated when the diffusion approximation is used [START_REF] Motamedi | Light and temperature distribution in laser irradiated tissue: the influence of anisotropic scattering and refractive index[END_REF]. Although the main aim of our study is to investigate the thermal effect on brain tissue (far away laser source), to verify our results of superficial tissue with the experimental study (Ito et al.) we consider temperature changes according to 0.4 mm radial distance from the laser source (considering epidermis thickness is 0.06mm).

➢ The distributions of the photon-fluence rate between experimental measurements (Ito et al.) and our simulation:

The measured spatial temperature distribution reported by Ito et al. is

➢ Comparing the chosen perfusion value of brain with values measured in vivo with ASL-fMRI:

The brain perfusion rate used in the current study is 0.00932 s -1 ≈ 0.56 min -1 which is comparable with the value measured in vivo with ASL-fMRI [START_REF] Rowland | Clinical Pharmacokinetics: Concepts and Applications[END_REF][START_REF] Shargel | Applied Biopharmaceutics and Pharmacokinetics[END_REF]. According to these studies [START_REF] Gordon | A mathematical model of the human temperature regulatory system--transient cold exposure response[END_REF][START_REF] Scheinberg | Effects of vigorous physical exercise on cerebral circulation and metabolism[END_REF], the brain function and metabolic activity are indicated by oxygen concentration and glucose intake to the brain cells.

The variation in cerebral metabolism had no significant effect on regional brain temperature [START_REF] Iwata | Dual role of cerebral blood flow in regional brain temperature control in the healthy newborn infant[END_REF] and the effect of cerebral metabolism on brain temperature is considered to be small [START_REF] Kauppinen | Assessment of human brain temperature by 1H MRS during visual stimulation and hypercapnia[END_REF].

About the effect of the complexity of blood perfusion rate, the superficial brain is spontaneously cooled by the environment and is cooler than the arterial blood. This suggests that, under physiological conditions, an increase in CBF may lead to an increase in superficial brain temperature and a simultaneous decrease in deep brain temperature. In addition, the neonatal perfusion rates have been used for infant model (by taking and not taking account the perfusion rate) [START_REF] Altman | Cerebral blood flow requirement for brain viability in newborn infants is lower than in adults[END_REF][START_REF] Edwards | Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy[END_REF][START_REF] Kusaka | Cerebral distribution of cardiac output in newborn infants[END_REF].

➢ The chosen absorption and scattering coefficients:

There is a discrepancy over the precise value of absorption and scattering coefficients.

The difference may derive from the discrepancy between the theoretical and experimental results. In general, in vivo μa and μs values for human skin proved to be significantly smaller than those obtained in vitro (about 10 and 2 times, respectively [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF]). For μa, the discrepancy may be attributed to the low sensitivity of the double-integrating sphere, and goniometric techniques have been applied for in vitro measurements at weak absorption combined with strong scattering (μa <<μs) and sample preparation methods. In our study, the absorption coefficients are adopted from the most recent complete reference about optical properties of tissue (Vo-Dinh, 2014).

The absorption coefficient of tissue is between 10 -2 and 10 -1 cm -1 due to the fact that they did not consider melanin absorption of the skin (In figure 16

BS B S W F M       = + - + + + (9)
Skin absorption coefficient would equal to µa (skin)= 0.52cm -1 , 0.65cm -1 , 0.88cm -1 . These skin absorption coefficients (including also 0.1, 0.2, 0.3, 0.4 cm -1 ) have been investigated in our study. On the other side, by considering volume fraction of melanosomes in the epidermis in another reference for optical properties of tissue 8 (Steven L. Jacques), the absorption coefficient of skin is higher (µa=17) than chosen one in our study. For example, a moderately pigmented adult with a 10% volume fraction of melanosomes will have absorption coefficients as listed below: In addition, different range (0.01, 0.05, 0.1, 0.5 cm -1 ) of adult brain absorption coefficients is considered [START_REF] Tuchin | Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis[END_REF].

➢ The maximum exposure times and the repetition frequency can use:

To avoid the temperature of the exposed tissue rises, the rate of energy deposition should be slower than the rate of thermal diffusion. Therefore, the maximum exposure duration should be shorter than time point of critical temperature. Hence, the interexposure interval should be at least twice than time duration reaches critical point.

However, in our study, thermal effect of laser on brain is the main objective thus for skin effect refer to ANSI standard.

➢ Effect of different scattering coefficient on temperature:

Photons are less scattered and penetrate much more deeply for lower values of scattering coefficient, as they are able to travel over a longer distance with greater step size before they interact with the tissue at a new position. As the value of the scattering coefficient increases, scattering increases and photons undergo frequent scattering with smaller step sizes, resulting in a more circular profile of fluence rate. For lower scattering coefficients, photons penetrate much more deeply with intensity decreasing outwards according to the radial distance. While changes in scattering coefficients can impact on the photon density distribution, their effect on temperature is negligible, in view of the small range of the scattering coefficients of these six head layers (brain scattering coefficient: 8.74_12.17 cm -1 , skin: 15.09_26.75cm -1 , fat: 8.30_22.12cm -1 , skull: 8.89_19.24cm -1 , CSF: 0.1_3.2_8cm -1 (8cm -1 scattering caused by the arachnoid trabeculae)) [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF].

Despite the insignificant effect of scattering coefficient on temperature, the following figure shows that higher value of scattering coefficient leads to a higher temperature; on the other hand, the other studies show that increasing temperature leads to a decrease of scattering coefficient in the tissue [START_REF] Kim | Effects of temperature-dependent optical properties on the fluence rate and temperature of biological tissue during low-level laser therapy[END_REF].

➢ Scalp thickness:

According to [START_REF] Kiguchi | Comparison of light intensity on the brain surface due to laser exposure during optical topography and solar irradiation[END_REF], scalp thickness is 5 to 7 mm, by considering the maximum value of 7mm for the scalp and 1.4mm (or less) for fat, skin thickness can be considered to be 5 mm. However, the error analysis for different skin thicknesses shows that temperature changes were not largely affected by variations the thickness of skin on the brain. In a real head, the thickness of superficial tissue, such as the scalp and skull, is not uniform.

➢ The brain scattering coefficient: Jacques et al. [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF] indicate that brain scattering ranges from 10 to 40 cm -1 for a wavelength of 500nm. By using this equation [ ' .( / 500 ) was equal to 9. 55, 9.31, 8.74, 9.3, 15.04, 9.99, 9.05, 12.17 cm -1 for Brain, Cortex (frontal lobe), Cortex (temporal lobe), Astrocytoma of optic nerve, Normal optic nerve, Cerebellar white matter, Medulloblastoma, and Brain, respectively. The value of 11.34 cm -1 was chosen according to Table 2 in (Jacques, 2013) (with the average parameters for reduced scattering coefficient of the brain). The skin scattering coefficient at 500nm is higher than brain scattering (Table 1, [START_REF] Jacques | Optical properties of biological tissues: a review[END_REF]).

➢ Irradiance, power and spot size:

The temperature in the skin and brain depends on the laser power more than on the irradiance. For example, the temperature changes were 0.6059°C and 0.7182°C for the same irradiance of 0.113W/cm2 with different powers and spot sizes (150mW, spot size=13mm) and (200mW, spot size=15mm), respectively. A higher temperature due to a higher power and higher spot size (but with the same irradiance), implying that temperature changes depend not only on the magnitude of irradiance but also on the distribution of photons (which depends on both power and spot size). The primary source of tissue irradiation is typically a laser beam, and the delivered light is characterized by its spot size and power. Smaller spot size leads to higher irradiance, but the smaller depth of penetration. The spot size of a laser beam determines its depth of penetration. A larger spot size reduces scattering of light and achieves deeper penetration. Hence, the larger the spot size, the deeper will be the penetration and the smaller the spot size, the more rapid the scatter and the more rapid the decay of fluence by depth (Figure 19) [START_REF] Keijzer | Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams[END_REF]). Since the e-1 depth of scattered light is unclear when scattering dominates absorption (μa << μs), the exact depth of light penetration in tissue cannot be determined ( [START_REF] Welch | Optical-Thermal Response of Laser-Irradiated Tissue[END_REF], page 53).

Therefore, by maintaining the same power, using larger spot size (sp↑) decreases irradiance (I↓) but increases the depth of penetration of light (depth↑), resulting in insignificant temperature changes in deeper tissues (e.g. brain). By maintaining the same spot size, higher power (P↑) increases irradiance (I↑) and depth of penetration of the light (depth↑), resulting in significant brain temperature changes, which is why a 4 orders of magnitude difference in irradiance in the brain does not change brain temperature, but smaller differences in laser power induce measurable differences in brain temperature. At constant power, changes in spot size have a lesser heating effect on deeper tissues ((Welch and van Gemert, 2011), page 865).

118 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging Fig. 19 The source of tissue irradiation of laser beam and the delivered light by its spot size and power.

A higher temperature is observed due to a higher power and higher spot size with the same irradiance in the skin. In skin tissue, for small spot sizes, cooling to neighboring non-irradiated tissue is a lot more effectual than for large spot sizes. For larger spot sizes, heat transfer from the center of the spot size cannot occur radially (sideways), as illustrated schematically in the following figure. Hence, for the same level of skin irradiance, larger spots produce a higher temperature than smaller spots. This impact of higher temperatures for larger spot sizes decreases the exposure limit since the effect of cooling means that the damage threshold does not depend simply on the skin irradiance. The exposure limit would decrease with increasing spot sizes, reflecting the fact that, for the same level of irradiance, larger spots are riskier (have a lower exposure limit) than smaller spots. However, this dependence of hazard threshold on spot size diameter does not apply to very large spot sizes, since the temperature profile in the center of the spot has a more or less flat profile, and this value is not influenced by any 119 119 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging further increase in the real spot size, as the borders that are cooled radially are located too far away from the center. Hence, for large sources, the hazard threshold depends only on the irradiance and no more on the spot size [START_REF] Henderson | Laser Safety[END_REF].

Abstract

The mechanisms responsible for coupling between relative cerebral blood flow (rCBF), cerebral blood volume (rCBV) and relative cerebral metabolic rate of oxygen (rCMRO2), an important function of the microcirculation in preterm infants, remain unclear. Identification of a causal relationship between rCBF-rCBV and rCBF-rCMRO2 in preterms may, therefore, help to elucidate the principles of cortical hemodynamics during development. We simultaneously recorded rCBF and rCBV and estimated rCMRO2 by two independent acquisition systems:

Diffuse Correlation Spectroscopy (DCS) and Near Infrared Spectroscopy (NIRS), respectively, in 10 preterms aged between 28 and 35 weeks of gestational age. Transfer entropy was calculated in order to determine the directionality between rCBF-rCBV and rCBF-rCMRO2.

The surrogate method was applied to determine statistical significance. The results show that High coupling between changes in CBF and CBV has been demonstrated in both resting state and stimulus-induced activity. The relationship between CBF and CBV has been shown to be adequately quantified by a simple power law equation in both steady state and dynamic state (Grubb's law which assumes a constant relationship between rCBF and rCBV: 𝑟𝐶𝐵𝑉 = (𝑟𝐶𝐵𝐹) 1/𝛽 ) (GRUBB et al., 1974a). Several groups have observed different values of 𝛽 when measured during functional challenges [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF]. Under steady-state conditions, CBF and CBV have been shown to have steady values in response to a physiological challenge such as hypercapnia or hypocapnia (GRUBB et al., 1974a;[START_REF] Ito | Changes in human cerebral blood flow and cerebral blood volume during hypercapnia and hypocapnia measured by positron emission tomography[END_REF]). Grubb's exponent has often been measured under dynamic conditions during neural stimulation experiments, in which both CBF and CBV changed following stimulation [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF]. Previous stimulation studies have reported that CBV increased progressively during the first few seconds of stimulation, while CBF did not change. After several seconds, CBF started to increase much more rapidly than CBV and returned to baseline before CBV returned to baseline (Roche-Labarbe et al., 2014) , [START_REF] Buxton | Dynamics of blood flow and oxygenation changes during brain activation: the balloon model[END_REF]. Under resting state conditions, the causality and nonlinear relationship between CBF and CBV changes can be used to determine whether CBV drives CBF or vice versa.

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain [START_REF] Roy | On the Regulation of the Blood-supply of the Brain[END_REF] proposed the hypothesis of stimulusinduced increases in CBF driven by local metabolic demand. Strong coupling between CBF and CMRO2 is observed during neural stimulation in adults [START_REF] Buxton | A model for the coupling between cerebral blood flow and oxygen metabolism during neural stimulation[END_REF], but a mismatch in CBF-metabolism coupling was reported by Fox et al., who described that, during neuronal activation, regional cerebral blood flow (CBF) increased by 50%, while CMRO2 increased by only 5% [START_REF] Fox | Focal physiological uncoupling of cerebral blood flow and oxidative metabolism during somatosensory stimulation in human subjects[END_REF]. In fact, CBF can increase in the absence of any significant variations of CMRO2 [START_REF] Fujita | Oxygen consumption of cerebral cortex fails to increase during continued vibrotactile stimulation[END_REF], and inversely, CMRO2 can increase with no significant increase of CBF [START_REF] Vafaee | CMRO2-CBF changes by finger motion: evidence of no flow-metabolism coupling[END_REF]. Whether or not a precise coupling exists between CBF and CMRO2 during neural stimulation has been the subject of numerous studies in both adults [START_REF] Raichle | Behind the scenes of functional brain imaging: a historical and physiological perspective[END_REF] and preterms (Mahmoudzadeh et al., 2013a;Mahmoudzadeh M).

While the linear relationship between CBF and CMRO2 changes at the resting state has been demonstrated in adults [START_REF] Roy | On the Regulation of the Blood-supply of the Brain[END_REF], it remains a subject of debate in preterms [START_REF] Wong | Dopamine therapy promotes cerebral flowmetabolism coupling in preterm infants[END_REF]. This study was designed to address whether rCBV drives rCBF in preterms or vice versa and to provide information about the directionality and causality between measured changes in rCBV and rCBF (also, between evaluated rCMRO2 and rCBF).

We used the transfer entropy (TE) method based on information theory [START_REF] Shannon | A Mathematical Theory of Communication[END_REF] to evaluate the nonlinear interactions between rCBV-rCBF and rCBF-rCMRO2 in resting preterm infants. Transfer entropy determines the intensity and direction of the relationship and the dominance between two discrete random variables [START_REF] Gourevitch | Evaluating information transfer between auditory cortical neurons[END_REF] (i.e.

rCBF and rCMRO2). Based on the concept of causality [START_REF] Wiener | The theory of prediction[END_REF], we investigated a possible causal interaction between rCBF and rCBV by predictive analysis of time-series of rCBF (or rCBV) measurements by incorporating data from another previous rCBV (or rCBF) time-series.

Near-infrared spectroscopy (NIRS) [START_REF] Wolf | Advances in near-infrared spectroscopy to study the brain of the preterm and term neonate[END_REF] and diffuse correlation spectroscopy (DCS) (Durduran et al., 2010d) are optical imaging techniques that noninvasively and repeatedly measure cerebral vascular parameters at the bedside in preterms (Nourhashemi et al., 2016a;[START_REF] Roche-Labarbe | Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates' brains in the first six weeks of life[END_REF]. NIRS device allows to monitor relative changes in To evaluate rCMRO2 independently from rCBF it required calculated rCMRO2 by rCBV and OEF. This can be achieved due to the independent measurement of rCBV by NIRS and rCBF by DCS. Although [START_REF] Leung | Estimating a modified Grubb's exponent in healthy human brains with near infrared spectroscopy and transcranial Doppler[END_REF] suggested that Grubb's relation cannot be inverted to estimate CBF from CBV. Using independent estimation of rCMRO2 by rCBV [START_REF] Franceschini | Assessment of infant brain development with frequency-domain near-infrared spectroscopy[END_REF], the causality investigation could be performed by analyzing the interactions between estimated rCMRO2 (NIRS) and directly measured rCBF (DCS). rCBF and rCMRO2 are linked in a complex way, notably, they are affected by autoregulation mechanisms [START_REF] Paulson | Cerebral autoregulation[END_REF]. These adaptive mechanisms act to preserve constant CBF over a range of blood pressures by adapting cerebrovascular resistances or vasodilation. The mechanisms of cerebral autoregulation in preterm infants remain unclear and may involve a combination of myogenic, neurogenic, and metabolic processes that regulate cerebrovascular resistance to maintain CBF [START_REF] Paulson | Cerebral autoregulation[END_REF]). In the present study, we evaluate the possible relationships and causalities between rCBF, rCBV, and rCMRO2 in resting state in preterms.

Materials and Methods

Ten preterm neonates (6 females; mean gestational age (GA) at birth: 28.5 weeks GA and 4 males; mean gestational age (GA) at birth: 27.5 weeks GA) were tested in the supine position (recording age: 31 wGA, Table 1). This study is part of the French public hospital Clinical

Research Project (PHRC National). The study was approved by the Amiens University

DCS and NIRS instrumentation

DCS and NIRS devices were synchronized and all events detected by DCS were also recorded by the NIRS devices (Fig. 1). The overall measurement duration was between 30 and 40 minutes for each subject. NIRS/DCS data were acquired simultaneously from the frontal area providing large volumes of data in order to converge transfer entropy and investigate the relationships between rCBF-rCBV and rCBF-rCMRO2 at the resting state.

Diffuse Correlation Spectroscopy (DCS)

DCS is an optical blood flow measurement modality that uses intensity fluctuations of The correlation diffusion equation is applied to fit the autocorrelation function in order to calculate a cerebral blood flow index (CBFi). Neuro-Monitor-FloMo (Hemophotonics SL, Spain) consists of a narrowband CW laser (785 nm, Crystalaser Inc., NV) with a long coherence length (> 50 meters), four fast photon-counting avalanche photodiodes (APD) (SPCM-AQR-14-FC, Pacer Components Inc., UK), and a four-channel autocorrelator board (Flex03OEM-4CH, Correlator Inc., NJ). The system uses continuous-wave (CW) lasers in the NIR range (~785 nm) with an acquisition rate of 0.3921 Hz (one sample every 2.55 s). The light was delivered to the brain surface via multi-mode fibers and light on the head surface was detected by 4 single-mode fibers dDCS=2 cm away from the source. The light was detected by singlephoton counting avalanche photo-diodes (SPADs) (SPCM-AQR(H) series, Excelitas, Canada).

Continuous wave tissue oximeter (NIRS)

Near-infrared spectroscopy probes NIRO-200NX (Hamamatsu Photonics Corp., Tokyo, Japan) were placed on the infant's forehead to measure cerebral oxygenation in the frontal cortex. The NIRO 200 NX uses spatially resolved spectroscopy at three wavelengths (λ=735 nm, 810 nm, and 850 nm). It is based on the solution of the diffusion approximation for a highly scattering semi-infinite homogeneous medium. The effective light attenuation coefficient can be estimated by measuring the decrease in reflected light as a function of distance. By assuming wavelength dependence of the reduced scattering coefficient, the spectral shape of the absorption coefficient can then be calculated and tissue oxygen saturation can be estimated (Matcher et al., 1995b). The average output power of the lasers was less than 2 mW and the CW acquisition rates were 5 Hz (200 ms).

The DCS and NIRS probe

To simultaneously measure rCBF and rCBV dynamics, we developed a specific probe that supports DCS and NIRS emitters and detectors. Recording sites on the subject's head and a diagram of the two combined probes are shown in Figure 1(a). The infants were placed in the supine position on a comfortable pad in a dark and quiet incubator. The incubator was further protected against ambient light by dark sheets. The probe was smoothly secured to the infant's head with straps and foam padding. A z-score-based algorithm was used to reject artifact signals (Mahmoudzadeh et al., 2013a). As individual features, such as skull thickness and hair color, influence signal strength, the signal was first homogenized in each participant by computing a z-score across all measurement periods for each channel. A z-score greater than 4 in any channel was considered to be an artifact, in which case, the entire artifact time-window was excised from the data for all channels (Mahmoudzadeh et al., 2013a). The mean value of rCBF signals recorded from 4 paired source-detectors was calculated. The remaining cleaned rCBV, rCBF signals were bandpass filtered [0.03-0.5 Hz] using a zero phase filter (Butterworth, order: 3) to eliminate physiologic noise (e.g. slow drifts, arterial pulse oscillations).

rCMRO2 calculated by NIRS data

CMRO2 can generally be calculated by combining relative changes in CBF and oxygen extraction fraction, but monitoring rCBV independently of rCBF by the NIRS device allows rCMRO2 to be evaluated independently of rCBF (Roche-Labarbe et al., 2010) by using (𝑟𝐶𝐵𝑉) 𝛽 instead of rCBF in relation (1) (Fig. 1c). The relative cerebral metabolic rate of oxygen was estimated as [START_REF] Culver | Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia[END_REF]: Where rOEF is defined as:

𝑟𝐶𝑀𝑅𝑂 2 = 𝑟𝐶𝐵𝐹 × 𝑟𝑂𝐸𝐹 (
𝑟𝑂𝐸𝐹 = 𝑆𝑎𝑂 2 (𝑡)-𝑆𝑣𝑂 2 (𝑡) 𝑆𝑎𝑂 2 (𝑡 0 )-𝑆𝑣𝑂 2 (𝑡 0 ) = 𝑆𝑎𝑂 2 (𝑡)-𝑆𝑂 2 (𝑡) 𝑆𝑎𝑂 2 (𝑡 0 )-𝑆𝑂 2 (𝑡 0 ) (2)
With venous oxygenation 𝑆𝑣𝑂 2 = (𝑆𝑂 2 -𝑎 × 𝑆𝑎𝑂 2 ) 𝑏 ⁄ , where a+b=1, a and b are the arterial and venous contributions that are constant over time [START_REF] Watzman | Arterial and venous contributions to near-infrared cerebral oximetry[END_REF], and arterial oxygenation SaO2=100%. Mechanical ventilation parameters and inspired oxygen concentrations were maintained constant at sufficiently high levels to saturate arterial hemoglobin (SaO2 ≈ 100%).

SO2 is the microvascular tissue oxygen saturation [START_REF] Wray | Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation[END_REF] (𝑆𝑂 2 = 𝐻𝑏𝑂 2 /𝐻𝑏𝑇).

By considering Grubb's relation between changes in rCBF and rCBV [START_REF] Davis | Calibrated functional MRI: mapping the dynamics of oxidative metabolism[END_REF] (β=0.9) (Roche-Labarbe et al., 2010) (time invariant characteristic of beta has been validated statistically),

𝑟𝐶𝐵𝐹 = 𝐶𝐵𝐹 𝑖 (𝑡) 𝐶𝐵𝐹 𝑖 (𝑡 0 ) = ( 𝐶𝐵𝑉(𝑡) 𝐶𝐵𝑉(𝑡 0 ) ) 𝛽 = (𝑟𝐶𝐵𝑉) 𝛽 (3)
𝑟𝐶𝑀𝑅𝑂 2 = (𝑟𝐶𝐵𝑉) 𝛽 × 𝑟𝑂𝐸𝐹 (4)
CBV (cerebral blood volume) was defined as:

= (𝐻𝑏𝑇×𝑀𝑊 𝐻𝑏 ) 𝐻𝐺𝐵×𝐷 𝑏𝑡
, where CBV is expressed in ml/100 g, HbT in µmol, MW Hb (64,500 g/mol) is the molecular weight of hemoglobin, Dbt

(1.05 g/ml) is the brain tissue density and HGB (g/dl) is the blood hemoglobin concentration.

The control state at time t0 was defined as the mean value of the signal and was considered to be the reference value.

Nonlinear Flow-Metabolism interaction by transfer entropy

Transfer entropy was used to define the strength of causality and the coupling between rCBV-rCBF and rCBF-rCMRO2. The concept of entropy is related to the degree of uncertainty associated with a signal random variable (i.e. rCBF). In other words, it provides a measure of the average uncertainty in a random variable. The determination of entropy of a random variable rCBF with a probability mass function P(rCBF) is defined by the following equation:

𝐻(rCBF) = ∑ -𝑃(𝑟𝐶𝐵𝐹 𝑖 ). 𝑙𝑜𝑔[𝑃(𝑟𝐶𝐵𝐹 𝑖 )] 𝑁 i=1 (5)
The first step consisted of the evaluation of the entropy (H) corresponding to the uncertainty associated with one of the 2 variables, rCBV, and rCBF. The analysis was based In order to produce time-series with identical probability variables of rCBF and rCBV, raw rCBF and rCBV data were quantized using 25th, 50th, 75th and 100th percentiles and rCBF and rCBV values between the (0, 25th), (25th, 50th), (50th, 75th) and (75th, 100th) percentiles, corresponding to 1, 2, 3, 4, respectively in Figure 2(b). The quantized rCBF and rCBV values presented the required flat distribution, (Fig. 2c).

The reduction of the uncertainty of one random variable obtained by the addition of a second variable (i.e. rCBV) (where rCBV is not completely independent of rCBF), is defined as mutual information (MI). Mutual information is a measure of the amount of information that one random variable provides about another random variable, defined by H(rCBF, rCBV) corresponding to the entropy of the two variables, rCBF, and rCBV.

𝑀𝐼(rCBF, 𝑟𝐶𝐵𝑉) = 𝐻(rCBF) + 𝐻(rCBV) -𝐻(rCBF, rCBV)

The second step consisted of the evaluation of the Mutual Information (MI) shared by the 2 variables. To evaluate the interdependency between the 2 variables, rCBV, and rCBF, the Mutual Information MI was compared to the Entropy (H) of each variable. When MI between these 2 variables is less than entropy (H), it can be concluded that the 2 variables are dependent.

As MI is symmetrical for the exchange of signals, it captures the information shared by two signals but is unable to distinguish the driving signal. The reduction in the uncertainty of rCBF due to the information provided by rCBV can also be obtained by introducing a third variable, resulting in conditional mutual information (CMI). The mutual information between rCBF and rCBV conditioned by a third variable corresponds to the part of the information derived from simultaneous analysis of rCBF and rCBV that is unrelated to the third variable (i.e. Z).

𝐶𝑀𝐼(𝑟𝐶𝐵𝐹, 𝑟𝐶𝐵𝑉|𝑍) = 𝐻(𝑟𝐶𝐵𝐹, 𝑍) + 𝐻(𝑟𝐶𝐵𝑉, 𝑍) -𝐻(𝑟𝐶𝐵𝐹, 𝑟𝐶𝐵𝑉, 𝑍) -H(Z) (7)

To obtain an asymmetrical measure, the bivariate version of CMI was used, wherein the third variable is a lagged version of variable rCBF or rCBV (delayed mutual information). It states that a signal rCBF is caused by signal rCBV when the future of signal rCBV is more accurately predicted by appending information from the past and present of signal rCBF than by using information from the present and past of signal rCBV alone [START_REF] Wiener | The theory of prediction[END_REF]. Delayed MI shows a causal dependence related to the information exchanged rather than the information shared (for instance, due to a common drive of both signals by a third, external source) [START_REF] Schreiber | Measuring Information Transfer[END_REF]. Transfer entropy from rCBF to rCBV is defined by the following formula, where t is a discrete time-index value:

𝑇𝐸(𝑟𝐶𝐵𝑉 → 𝑟𝐶𝐵𝐹) = 𝐶𝑀𝐼(𝑟𝐶𝐵𝐹 𝑡 , 𝑟𝐶𝐵𝑉 𝑡-1 |𝑟𝐶𝐵𝐹 𝑡-1 ) = 𝐻(𝑟𝐶𝐵𝐹 𝑡 , 𝑟𝐶𝐵𝐹 𝑡-1 ) + 𝐻( 𝑟𝐶𝐵𝑉 𝑡-1 , 𝑟𝐶𝐵𝐹 𝑡-1 ) -𝐻(𝑟𝐶𝐵𝐹 𝑡 , 𝑟𝐶𝐵𝑉 𝑡-1 , 𝑟𝐶𝐵𝐹 𝑡-1 ) -𝐻(𝑟𝐶𝐵𝐹 𝑡-1 ) (8)

𝑇𝐸(𝑟𝐶𝐵𝐹 → 𝑟𝐶𝐵𝑉) = 𝐶𝑀𝐼(𝑟𝐶𝐵𝑉 𝑡 , 𝑟𝐶𝐵𝐹 𝑡-1 |𝑟𝐶𝐵𝑉 𝑡-1 ) = 𝐻(𝑟𝐶𝐵𝑉 𝑡 , 𝑟𝐶𝐵𝑉 𝑡-1 ) + 𝐻( 𝑟𝐶𝐵𝐹 𝑡-1 , 𝑟𝐶𝐵𝑉 𝑡-1 ) -𝐻(𝑟𝐶𝐵𝑉 𝑡 , 𝑟𝐶𝐵𝐹 𝑡-1 , 𝑟𝐶𝐵𝑉 𝑡-1 ) -H(𝑟𝐶𝐵𝑉 𝑡-1 ) (9)
The information transfer between rCBV and rCBF was measured by the time-lagged Conditional Mutual Information (CMI). By applying time-lagged CMI to the two variables (rCBF and rCBV), if 𝑇𝐸(rCBF → rCBV) is less than 𝑇𝐸(rCBV → rCBF) , it can be concluded that rCBF is more dependent on rCBV.

Then, because transfer entropy is based on transition probabilities, it can be used to determine the dominant direction in the relationship between two variables. The directionality index (DI) between two variables rCBF and rCBV is calculated by:

DI(%) = 𝑇𝐸(𝑟𝐶𝐵𝑉→𝑟𝐶𝐵𝐹) -𝑇𝐸(𝑟𝐶𝐵𝐹→𝑟𝐶𝐵𝑉) 𝑇𝐸(𝑟𝐶𝐵𝑉→𝑟𝐶𝐵𝐹) +𝑇𝐸(𝑟𝐶𝐵𝐹→𝑟𝐶𝐵𝑉)
× 100 (10)

When DI> 0, it was concluded that the rCBV was predominant over rCBF. Contrariwise, when DI <0, rCBF controlled rCBV and, DI = 0 indicates balanced bilateral interactions between the two variables. The statistical significance of TE and MI measurements was evaluated by using a surrogate method by measuring the dependency of two time-series (rCBF and rCBV) with one of the signals randomly shuffled and reorganized and with each sample replaced in a random position in the series. The limit of statistical confidence corresponding to the 95th percentile was found by repeating a different permutation on one of the signals 300

times.

The third step consisted of the evaluation of the direction of the relationships between rCBF and rCBV, which can be determined by the directionality index (DI) on both measured and surrogate data. The confidence intervals can be used to calculate statistical power in order

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain to conclude that a surrogate explains at least a certain proportion of the correct direction. If the test statistic from the data is higher than the 95th percentile of the surrogate, it demonstrates the reliability of the estimation procedure (Fig. 2d). All steps were identical for investigation of the relationship between rCBF and rCMRO2.

Results

Linear interaction between rCBF-rCBV and rCBF-rCMRO2

Changes in rCBV were plotted as a function of rCBF for 10 subjects (Fig. 3a), resulting in a fluctuating correlation between rCBV and rCBF with a tendency towards a positive correlation in 6/10 preterms and a negative correlation in the remaining 4 preterms with an average slope of 0.02±0.12.

Computation of transfer entropy

The entropy (H) of rCBF and rCBV for each subject and each parameter was equal to 2.

For each subject, the mutual information MI of rCBF and rCBV was less than the entropy (H)

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain of rCBV and rCBF (MI (rCBF, rCBV) < H (rCBV) and MI(rCBF, rCBV) < H(rCBF)), (Fig. 3b). By considering rCMRO2 as a product of the measured HbT and HbO2, the same analysis was performed to test the relationship between rCBF and rCMRO2 (Fig. 4). Selected parts of rCMRO2 and rCBF for subjects #4 and #10, illustrating the evaluation of TE from rCMRO2 to rCBF as indicated by circles on signals in the dark gray box, suggest that the source signal (rCMRO2) drives the target signal (rCBF) (Fig. 4a). The entropy (H) of rCBF and rCMRO2 for each subject and each parameter was equal to 2. For each subject, MI of rCBF and rCMRO2

was less than the entropy (H) of rCMRO2 and rCBF. The average value of Mutual Information (MI=0.0343) was less than the entropy (H=2) (Fig. 4b). These results indicate that rCBF and rCBV (also, rCBF and rCMRO2) can be considered to be dependent variables at the resting state in the preterm brain.

Causal relationship between rCBF-rCBV and rCBF-rCMRO2

Transfer Entropy (TE) was used to identify a causal relationship between rCBF and rCBV, as it detects the relationship between the past of one signal (rCBV) and the present of another signal (rCBFt+). For each subject, 𝑇𝐸 (rCBF →rCBV) was less than 𝑇𝐸 (rCBV →rCBF) and the average value of 𝑇𝐸 (rCBF →rCBV) (0.0476) was less than the average value of 𝑇𝐸 (rCBV →rCBF) (0.2702) (Fig. 3b). These results demonstrate that rCBFt+ appears to be more dependent on rCBV than rCBVt+ on rCBF, suggesting that rCBV drives rCBF at the resting state in the preterm brain.

This relationship can be summarized by the Directionality Index (DI) between rCBF and rCBV (Fig. 3b). The negative values of the Directionality Index (DI<0) suggest that rCBV was predominant over rCBF. Statistical analysis with a limit of statistical confidence corresponding to the 95 th percentile of the 300 trials was performed according to the surrogate method. As the Directionality Index (DI) measured in each of the 10 subjects was higher than the 95 th percentile, statistical analysis robustly detected the correct direction of rCBV on rCBF. By applying the same analysis to the relationship between the rCBF and rCMRO2, the negative values of DI<0 suggest that estimated rCMRO2 would be predominant over measured rCBF (Fig. 4c,d).

Relationship between rCMRO2 and mean arterial blood pressure at the resting state in preterm neonatal brain

Figure 6 shows the relationships between rCMRO2 and mean arterial blood pressure.

The nonzero mutual information between rCMRO2 and mean arterial blood pressure demonstrates that the two variables are partially dependent on each other, suggesting that rCMRO2 might also partly be dependent on other systemic variables.

On the other hand, the grand averages of 10 subjects for the linear correlation between (rCMRO2 and mean arterial blood pressure (MABP)) and (rCMRO2 and heart rate (HR)) were not statistically significant (YrCMRO2=-0.0059 .XMABP+0.0005, P = 0.4 and YHR =-0.0056 .

XrCMRO2+0.00056, P = 0.6, respectively).

Impact of possible time lag variability

Analysis of directionality is often based on synchrony assumptions of the two signals,

suggesting that time lag variability would have an impact on the conclusions. It is therefore important to assess this time lag effect by means of sensitivity analyses. We considered different time lags between 0.8s to 2.4s (DCS sampling period (2.5s) is the maximum possible time lag). Figure 7 shows that time lag changes had a negligible impact on the directionality index. The consistency between the results of primary analysis and the results of maximum possible time lag analysis therefore support the conclusions and the credibility of the results.

The effect of different beta values on transfer entropy

We used a constant value for beta in (TE) between rCBF and rCMRO2 was investigated (Fig. 8). Regardless of the β value considered, the directionality of rCMRO2 was predominant over rCBF.

Discussion

This study demonstrates that, in very preterm newborns (<32 wGA), rCBV is predominant over rCBF and that neurovascular interactions appear to be sufficiently efficient for rCMRO2

to be already able to drive rCBF at rest.

While our previous data (Mahmoudzadeh et al., 2013a;Mahmoudzadeh M) supported the existence of neurovascular coupling in response to neuronal activations by auditory stimuli in very preterm infants, little is known about the interactions between rCBF and rCBV (and between rCBF and rCMRO2) in preterms at rest [START_REF] Wong | Dopamine therapy promotes cerebral flowmetabolism coupling in preterm infants[END_REF], in whom the cardiovascular and autonomic nervous systems remain largely immature. The linear relationship between rCBF and rCBV (rCBF and rCMRO2) has been extensively studied at rest in adult humans [START_REF] Ito | Changes in human cerebral blood flow and cerebral blood volume during hypercapnia and hypocapnia measured by positron emission tomography[END_REF] (during sleep [START_REF] Kozberg | Cerebral O2 metabolism and cerebral blood flow in humans during deep and rapid-eye-movement sleep[END_REF] and under general anesthesia [START_REF] Lam | Change in cerebral blood flow velocity with onset of EEG silence during inhalation anesthesia in humans: evidence of flow-metabolism coupling?[END_REF]) and in animals (GRUBB et al., 1974b;[START_REF] Sokoloff | The [14C]deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat[END_REF],

showing that CBF and CBV (as well as CBF and CMRO2) [START_REF] Cohen | Abnormalities of regional distribution of cerebral vasculature in schizophrenia detected by dynamic susceptibility contrast MRI[END_REF] are tightly coupled under normal conditions. In the present study, the linear correlation between rCBF and rCBV was fluctuating with a tendency to be either positive (n=6) or negative (n=4) (Fig. 3a), which is consistent with the results in preterm infants reporting rather stable rCBV whatever the changes in rCBF [START_REF] Roche-Labarbe | Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates' brains in the first six weeks of life[END_REF]. In comparison to the mature adult brain, presenting high coupling between CBF and CBV, a weaker correlation between these two variables was observed in the developing neonatal brain.

Most studies have explored the linear relationships between rCBF and rCBV (Roche-Labarbe et al., 2010) (rCBF and rCMRO2 [START_REF] Wong | Dopamine therapy promotes cerebral flowmetabolism coupling in preterm infants[END_REF]). To the best of our knowledge, this is the first study to evaluate the nonlinear relationships between rCBF and rCBV in preterm infants, demonstrating the intensity and asymmetry of the interactions between these two autonomic variables, ie, rCBF and rCBV, using transfer entropy (TE) analysis derived from information theory [START_REF] Shannon | A Mathematical Theory of Communication[END_REF]. To ensure the independency of the recorded parameters, rCBF and rCBV were simultaneously recorded by two separate devices using two different approaches, DCS and NIRS, respectively.

In preterms, the negative Directionality Index (DI<0) between rCBV and rCBF suggests that rCBV has a more predominant driving influence on rCBF (vs. rCBF to rCBV) at the resting state. We tested to what degree the maximum time lag between the two separate devices would affect the results, despite the fact that the acquisition devices were synchronized by an external event trigger. The maximum possible lag changes (Fig. 7) and the effect of different constant values of β (Fig. 8) had a negligible impact on the directionality index. Our results at resting state are in agreement with those reported by Roche-Labarbe et al., [START_REF] Roche-Labarbe | Somatosensory evoked changes in cerebral oxygen consumption measured non-invasively in premature neonates[END_REF], although their study was conducted under different conditions, with large in-flow modeled related to task-evoked conditions such as somatosensory stimulation [START_REF] Roche-Labarbe | Somatosensory evoked changes in cerebral oxygen consumption measured non-invasively in premature neonates[END_REF]. During the first few seconds of stimulation, rCBV increased progressively, while changes in rCBF started to increase abruptly after only a few seconds [START_REF] Roche-Labarbe | Somatosensory evoked changes in cerebral oxygen consumption measured non-invasively in premature neonates[END_REF], suggesting a lag between changes in rCBV and rCBF.

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

Notwithstanding the methodological limitations ((i) small differences in tissue volume sampled, (ii) optimization of the distances between emitters and detectors of the NIRS and DCS probes to minimize light interferences, (iii) higher integration time for DCS than for NIRS to achieve a balance between signal quality and temporal resolution) and the physiological complexity (arteriole resistance, arterial/venous/capillary compartment), the use of information entropy has the advantage of combining the probabilities for multiple outcomes to one meaningful measure, ie the directionality from rCBV to rCBF, and it does not assume a specific statistical distribution or an estimate of a mean.

Transfer entropy implies to quantify the causal relationship between the variables (i.e.

rCBV and rCBF). The causality does not necessarily imply that two variables have a time lag, they also could have taken place simultaneously. Increased volume followed by increased flow with a slight delay (i.e. time lag between the rCBV and rCBF), direct us to explore for a suitable physiological underlying mechanism. Although the reports of relative CBV and CBF dynamics have been controversial [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF]Malonek et al., 1997b;[START_REF] Sheth | Spatiotemporal evolution of functional hemodynamic changes and their relationship to neuronal activity[END_REF], our finding (rCBV followed by rCBF changes) support the assumption of a process of capillary filling (increase in rCBV) (Malonek et al., 1997b) followed by a delayed neurovascular regulation of rCBF in the capillary bed. Functional recruitment of capillaries is the changeover of low blood flow to high blood flow capillaries [START_REF] Kuschinsky | Capillary circulation in the brain[END_REF]). An initial phase of activation can be expected when local capillary blood volume increases, but at a time when arterioles have not yet dilated and the blood flow has not yet increased (Malonek et al., 1997b). This type of lagged relationship between blood volume and blood flow has been described to be valid if the outflow from the capillary compartment in the activated regions is briefly lower than the inflow to this capillary compartment (Malonek et al., 1997b). Following the neuronal activation, the capacitance of the capillaries was to raise and their resistance was to reduce (i.e. the capillary bed might play as a ''sink'' for red blood cells) (Malonek et al., 1997b). This in turn allows the outflow from the compartment to decrease, before the occurrence of upstream arteriolar dilatation that would provoke an increased inflow.

Thereafter, when the arteriolar part has dilated, the increased inflow causes a flow increase in the entire capillary compartment, oxyhemoglobin increases, and deoxyhemoglobin decreases (Malonek et al., 1997b).

Leung et al. [START_REF] Leung | Estimating a modified Grubb's exponent in healthy human brains with near infrared spectroscopy and transcranial Doppler[END_REF] suggested that Grubb's relation cannot be used to estimate CMRO2 because the variances in log(CBF/CBF0) and log(CBV/CBV0) measurements would

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain be different, but, in contrast, Boas and Payne noted that: "both of these calculations assume that the dependent variables are functionally dependent on the independent variable and that the variance in the linear regression is exclusively derived from the variance in the dependent variable". rCBF can therefore be estimated from rCBV, allowing rCMRO2 to be estimated when only rCBV measurements are available [START_REF] Boas | Comment on 'Estimating a modified Grubb's exponent in healthy human brains with near infrared spectroscopy and transcranial Doppler[END_REF].

By considering the neurovascular coupling cascade (multiple signaling pathways encompassing perivascular astrocytes, vasoactive chemical agents, and direct neuronal connections) [START_REF] Cauli | Revisiting the role of neurons in neurovascular coupling[END_REF][START_REF] Mccaslin | In vivo 3D morphology of astrocytevasculature interactions in the somatosensory cortex: implications for neurovascular coupling[END_REF] and estimation of rCMRO2 index by rCBV [START_REF] Boas | Comment on 'Estimating a modified Grubb's exponent in healthy human brains with near infrared spectroscopy and transcranial Doppler[END_REF], the linear correlation between rCBF and rCMRO2 was also fluctuating with a tendency to be either positive (n=6) or negative (n=4). This fluctuation in the linear correlation between rCBF and rCMRO2 has already been described in preterm infants, with no relationship observed in healthy preterms, while a strong relationship was observed after dopamine treatment [START_REF] Wong | Dopamine therapy promotes cerebral flowmetabolism coupling in preterm infants[END_REF], suggesting that the underlying mechanisms of the interactions between rCBF and rCMRO2 in preterms are fairly complex, immature and have yet to be determined [START_REF] Greisen | Cerebral blood flow in preterm infants during the first week of life[END_REF]. The direction of the nonlinear relationship between rCBF and rCMRO2 is an accepted hypothesis in adults [START_REF] Roy | On the Regulation of the Blood-supply of the Brain[END_REF] and supports the idea that rCBF could be controlled by oxygen demand [START_REF] Baumgartner | Handbook on Neurovascular Ultrasound[END_REF].

Nonlinear analysis can be used to detect a wider range of interactions between variables compared to conventional analysis, such as linear correlation. Analysis of the nonlinear relationship between rCBF and rCMRO2, and the negative values of DI suggest that rCMRO2 is significantly predominant over rCBF in the resting state in the preterm healthy brain. As rCMRO2 depends on the degree of brain activity at the resting state [START_REF] Kuschinsky | Coupling of function, metabolism, and blood flow in the brain[END_REF], rCBF variations may be partly driven by brain activity at rest. This hypothesis is now being tested in the laboratory by combining EEG, NIRS and DCS in preterms.

The relationship between rCMRO2 and mean arterial blood pressure were also assessed.

The nonzero mutual information between rCMRO2 and mean arterial blood pressure implies that, although rCMRO2 might be affected by changes in systemic variables, some of the variations of rCMRO2 depend on other variables such as rCBF. This study also demonstrates a possible relationship between rCBF and rCMRO2 with a directionality from estimated rCMRO2 to measured rCBF.

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

The already functional directionality between rCBF and rCBV or between rCBF and rCMRO2 suggests that the intimate cellular mechanisms observed in adults, such as the participation of astrocytes and the various signals arising from activated neuronal assemblies and transmitted to perivascular glial endfeet, might be already functional in preterms from 28 wGA, resulting in changes in arterial tone [START_REF] Paulson | Cerebral blood flow response to functional activation[END_REF].

This type of analysis could be applied in clinical practice to investigate whether this relationship between rCBF and rCBV (rCBF and rCMRO2) persists in patients at risk of neuronal or vascular brain injury (IntraVentricular Hemorrhage (IVH), hydrocephalus, etc.).

The results of this study demonstrate the lowest directionality value (rCMRO2 to rCBF) for neonate #9 with bilateral IVH-III and hydrocephalus. Although a greater number of subjects must be included in future studies, this result is in agreement with those we reported in [START_REF] Mahdi Mahmoudzadeh | Consequence of intraventricular hemorrhage on neurovascular References coupling evoked by speech syllables in preterm neonates[END_REF], showing the absence of hemodynamic responses induced by phoneme stimuli in IVH III-IV preterms. The results also demonstrate the highest directionality value (rCBV to rCBF) and (rCMRO2 to rCBF) in neonate #2, who was one of the two patients of our study with abnormal EEG (positive rolandic spikes).

Further studies are also required to assess the developmental dynamics of the relationship between rCBF and rCBV (rCBF and rCMRO2) at different postnatal ages. The various treatments administered to preterm infants in this study may have influenced the relationship between rCBF and rCBV (rCBF and rCMRO2). For example, opioids (morphine) may have decreased CMRO2 [START_REF] Uchino | Neuroanesthesia and Cerebrospinal Protection[END_REF]. Moreover, it is widely accepted that neurovascular modulations are highly dependent on sedative treatment including direct cerebral vasodilation and significantly reduce cerebral metabolic demand, which would reduce rCBF in response to neuronal activation during anesthesia [START_REF] Kuroda | Blood flow velocity of middle cerebral artery during prolonged anesthesia with halothane, isoflurane, and sevoflurane in humans[END_REF]. Strict coupling between rCBF and rCMRO2 cannot be expected under such conditions. Nevertheless, the directionality from rCBF to rCBV (rCBF to rCMRO2) was preserved even in lightly sedated preterms.

Conclusions

This study focused on the nonlinear relationship between rCBF and rCBV (rCBF and rCMRO2) in preterm infants recorded before 32 wGA. The mechanisms by which rCBV drives rCBF (rCMRO2 drives rCBF) are already functional at this early age of development regardless of whether or not these two variables are strictly correlated. As the directionality was observed in all preterm infants regardless of the type of anesthesia, it would be interesting to test the A balance was also achieved between signal quality and temporal resolution. The integration time was therefore set 200 ms (sampling period) in the CW-NIRS (Hamamatsu®), and 2.5s in DCS. Due to the low signal-to-noise ratio (SNR), a higher integration time was set for the DCS than for the CW-NIRS. Signal-to-noise ratio and depth of penetration are two interrelated and important experimental parameters.

Larger source-detector separations are required to obtain a sufficient depth of penetration.

However, the use of larger source-detector separation configurations is challenging, since DCS optimally requires single-mode detection fibers to measure the intensity autocorrelation function. The throughput of single-mode fibers is relatively low and leads to a low SNR.

Two approaches were used in this study to resolve the issue of low SNR: 1) Spatial integration and 2) Temporal integration.

1) Spatial integration:

To resolve the issue of low SNR, we implemented a multi-speckle scheme for DCS detection, which substantially improved the DCS signal-to-noise ratio. In this set-up, we employed parallelized detection, e.g. multiple detector fibers bundled together in the same position (4 detectors in the same holder), and the autocorrelation curves from all detectors were then averaged to obtain a single curve.

2) Temporal integration: Additionally, improved SNR were achieved by increasing the amount of light delivered to the tissue by increasing integration time (2.5s). In practice, a low SNR means that repeated measurements of physiologic activity need to be averaged. The effect of averaging over different ranges of measurements constitutes a trade-off between high SNR and high temporal and spatial resolution.

3) Linear correlation plots on measured parameters:

We wanted to detect non-linear correlations between parameters rather than simply linear correlations. The following plots would provide additional information about fluctuations of hemodynamic variables. However, one subject (subject #10) will be presented as an example.

Figure 10 shows the significant linear correlations between z-score-rCMRO2 and z-score-rCBF (p=0.02) and between z-score-SO2 and z-score-rCBF (p=0.00), but the linear correlations between variables (z-score-rCBF, z-score-HbT), (z-score-rCBF, z-score-HR), (zscore-CBF, z-score-BP), (z-score-CMRO2, z-score-HR), (z-score-CMRO2, z-score-BP) were not statistically significant (P = 0.4, 0.9, 0.2, 0.9, 0.4, respectively).

Chapter 4: Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain In the following figure from Roche-Labarbe's study, the first few seconds of stimulation also show that rCBV increased progressively, while rCBF did not change, but started to increase abruptly after 2 seconds while rCBV reached a critical value of 1.005. These results suggest a threshold beyond which CBV triggers CBF dynamics. This part of Figure 3 in Roche-Labarbe's paper is therefore in agreement with our results.

(A) (B) (C) (D) (E) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -4 -3 -2 -

5) The absorption and reduced scattering coefficient (mua, mus), as input for the DCS analysis:

We considered µa = 0.1 cm-1 and µs' = 10 cm-1, which are typical values for biological tissue. Although rCBF is influenced by both tissue absorption and scattering coefficients, μa and μs', respectively, uncertainties in μa lead to relatively small errors in rCBF (<20%), whereas uncertainties in μs' can result in substantial errors in rCBF [START_REF] Mesquita | Influence of probe pressure on the diffuse correlation spectroscopy blood flow signal: extra-cerebral contributions[END_REF]. In neonates, Jain et al. observed a strong correlation between rCBF and CBF in the sagittal sinus despite assuming a fixed μs' across the entire cohort [START_REF] Jain | Cerebral oxygen metabolism in neonates with congenital heart disease quantified by MRI and optics[END_REF], which may have been at least partly due to the homogeneity of the patient cohort, i.e., all subjects were < 1-week-old neonates, which is also the case in the present study (< 34 wGA). Moreover, the effects of uncertainties in μa and μs' on rCBF are decreased when monitoring relative changes in CBF over time, as these tissue parameters change little except in the case of extreme interval blood loss/gain, edema, etc. Clearly, in future studies, we plan to combine DCS with the frequency-NIRS method to determine absolute μa and μs' for the tissue of interest, e.g., in all subjects whenever possible.

6) The linear and non-linear correlations between rCMRO2 and rCBV:

Linear correlations: Although there are high linear correlations between rCMRO2 and rCBV (p-value=0.00), but the figure 12 confirms that the rCMRO2 index does not solely represent fluctuations of HbT (rCBV). Since the data points do not follow the exact linear trend, rCMRO2 does not just represent rCBV.

8) The correlation between CBF and HbT:

The relation between 𝐻𝑏𝑇 and 𝐶𝐵𝐹 is complex and not simply direct. The following figures (14,15) shows the non-significant linear correlation between 𝐻𝑏𝑇 𝑣𝑠. 𝐶𝐵𝐹 (p-value =0.4) and the significant linear correlation of log(𝐻𝑏𝑇) 𝑣𝑠. log(𝐶𝐵𝐹) (p-value=0.01).

Although the linear correlation of log(𝐻𝑏𝑇) 𝑣𝑠. log(𝐶𝐵𝐹) is not significant for subjects 6 and 7. 9) rCBV has a more predominant driving influence on rCBF (with more detail):

Transfer entropy implies to quantify the causal relationship between the variables (i.e., relative CBV and CBF). The causality does not necessarily imply that two variables have a time lag, they also could have taken place simultaneously. Increased volume followed by increased flow with a slight delay (i.e., the time lag between the relative CBV and CBF), direct us to explore for a suitable physiological underlying mechanism.

Although the reports of relative CBV and CBF dynamics have been controversial.

Malonek et al. (Malonek et al., 1997a) reported that CBV increased before CBF, whereas Sheth et al. [START_REF] Sheth | Spatiotemporal evolution of functional hemodynamic changes and their relationship to neuronal activity[END_REF] reported CBV lagged CBF and Jones et al. [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF] reported CBV and CBF had similar onset times and times to peak. Our finding (rCBV followed by rCBF changes) support the assumption of a process of capillary filling (increase in rCBV) followed by a delayed neurovascular regulation of rCBF in the capillary bed (Malonek et al., 1997a).

Functional recruitment of capillaries is the changeover of low blood flow to high blood flow capillaries (Kuschinsky, 1992;[START_REF] Villringer | [END_REF]. An initial phase can be expected when local capillary blood volume increases, but at a time when arterioles have not yet dilated and the blood flow has not yet increased. This type of lagged relationship between blood volume and blood flow is considered to be valid if the outflow from the capillary compartment in the activated regions is briefly lower than the inflow to this capillary compartment (Malonek et al., 1997a). Following the neuronal activation, the capacitance of the capillaries was to raise, and their resistance was to reduce (i.e., the capillary bed might play as a ''sink'' for red blood cells).

This would, in turn, allows the outflow from the compartment to decrease, before the occurrence of upstream arteriolar dilatation that would provoke an increased inflow.

Thereafter, when the arteriolar part has dilated, the increased inflow causes a flow increase in the entire capillary compartment, oxyhemoglobin increases, and deoxyhemoglobin decreases (Malonek et al., 1997a).

Some studies [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF]) also suggested that CBV changes lead to CBF changes.

These findings are discussed in the frame of the most refined model of the vascular response, the "balloon model" (based on the venous balloon the origin of the change in CBV and deoxy-Hb). As mentioned in [START_REF] Vanzetta | Coupling between neuronal activity and microcirculation: implications for functional brain imaging[END_REF]; "Exchanging the roles of CBV and CBF in the Balloon Model equations thus improved the fit of the model predictions to the experimental data, but without attaining satisfactory agreement, probably also because the largest CBV changes occur in arterioles rather than in venules or veins [START_REF] Vanzetta | Compartment-resolved imaging of activity-dependent dynamics of cortical blood volume and oximetry[END_REF].

In any case, it becomes increasingly apparent that CBV and CBF are linked in a more complex way than by a simple power-law CBV=CBF α ("Grubb's law," Grubb et al., 1974), and that they also depend on state of activation, vessel type, and size [START_REF] Hutchinson | Spatial flow-volume dissociation of the cerebral microcirculatory response to mild hypercapnia[END_REF]."

Following figures show different studies in which changes in rCBV leads to changes in rCBF: (Malonek et al., 1997a). [START_REF] Jones | Concurrent optical imaging spectroscopy and laser-Doppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex[END_REF]. The inset shows an enlarged view at the time of stimulation onset [START_REF] Jones | Changes in blood flow, oxygenation, and volume following extended stimulation of rodent barrel cortex[END_REF]. The identification of coupling between the spontaneous physiological neuronal activity with the transient stereotyped hemodynamic pattern in premature infants, consisting of deoxygenation, oxygenation, and cerebral blood flow is a complex issue, which helps to elucidate the principles of neuronal and cortical hemodynamic coupling during development.

We simultaneously recorded (EEG, HbO, HbR, TOI, CBF and estimated CMRO2) in 32 preterms, to determine how the changes in the hemodynamic responses were coupled to the To assess the multi-frequency aspect of dynamic neurovascular coupling wavelet coherence analysis was applied on simultaneously-measured signals. We observed the establishment of neurovascular coupling system as a function of age. High coherence was observed between the cerebral hemodynamic (vascular) and electrical (neuronal) oscillations in the frequency range of 0.003-0.125 Hz in the non-encephalopathic newborns than in two pathological groups (i.e., PDA and IVH). Likewise, NVC coherence (CBF-EEG) was significantly decreased in IVH group vs. normal newborns ], p = 0.03).

Conclusively, different patterns of cerebral hemodynamic response to the neuronal burst of activities coupled with dynamics in neurovascular coupling with ages, reflect the immaturity and complexity of both neonatal vasculature and neuronal networks.

A comprehensive understanding of the variation of the neurovascular patterns could add fresh insights into the clinical assessment of newborn infants. Although maturational differences in early neurovascular coupling may puzzle classical interpretation of functional hemodynamic studies, neurovascular development could provide a biomarker for evaluation of healthy or altered developmental pathways that could be measurable using functional imaging.

Introduction

The dynamic interactions among the components of neurovascular unit balance and control complex brain function. The co-development of neural and vascular networks is more rational, rather than separate maturation or primary blueprint of the arrangement of blood vessels before neural elaboration/refinement. Likewise, embryonic neuronal and vascular networks may serving simillar guidance cues as each is maturing [START_REF] Gelfand | Guidance from above: common cues direct distinct signaling outcomes in vascular and neural patterning[END_REF]. The neuronal and vascular networks constitute the two halves of the same functional unit relying on the neurovascular unit that tightly Coupling (NVC) well characterized in adults by an increase in blood flow in response to neuronal activation (Nourhashemi et al., 2017a). The balance between local consumption and arterial supply related to neuronal activation is much more delicate in the developing brain [START_REF] Kozberg | Neurovascular coupling and energy metabolism in the developing brain[END_REF]. Further, how this NVC is affected by particular metabolic and vascular disorder [START_REF] Attwell | The neural basis of functional brain imaging signals[END_REF][START_REF] Sheth | Linear and nonlinear relationships between neuronal activity, oxygen metabolism, and hemodynamic responses[END_REF], in the immature brain is clinically relevant in respect to the neurodevelopmental consequences of its dysfunction.

Functional hemodynamic imaging research in neonates have determined evidently distinct response in preterm and term new-borns, contrast to canonical adult hemodynamic responses (Arichi et al., 2012). More information indicates that these discrepancies in hemodynamic responses related to the immaturity of neurovascular coupling (Roche-Labarbe et al., 2007a). The massive cortical maturation known to develop after childbirth hence contains the progressive postpartum developing of neurovascular coupling. Structurally, during the last trimester of human gestation, both the neuronal and the vascular system still undergo drastic developments. The processes of neuronal migration, synaptogenesis, short and long-range connectivity, pruning and cell death, neuronal dendritic differentiation, neurochemical maturation, myelination are gradually building the neuronal networks, providing in premature a dual innervation of pyramidal cells by both subplate and thalamic axons [START_REF] Arichi | Somatosensory cortical activation identified by functional MRI in preterm and term infants[END_REF]. Neural networks first experience a potent epoch of axonal prolongation and synaptogenesis [START_REF] Lewis | Cell biology in neuroscience: Cellular and molecular mechanisms underlying axon formation, growth, and branching[END_REF], proceed by wiring refinement with synapse elimination [START_REF] Huttenlocher | Synaptogenesis in human visual cortex--evidence for synapse elimination during normal development[END_REF]. These epochs of elaboration/refinement differ locally, but mostly progress in the human brain well into young adulthood [START_REF] Harris | The physiology of developmental changes in BOLD functional imaging signals[END_REF]. In parallel, the vascular system itself develops remarkably morphologically during the early neonatal period. While neurons and vasculature share guidance cues as each is developing [START_REF] Gelfand | Guidance from above: common cues direct distinct signaling outcomes in vascular and neural patterning[END_REF], the grey matter perforating vessels establish rich intrinsic capillary plexuses that parallel the growth and complexity of the structurally and functionally developing cortical grey matter [START_REF] Marin-Padilla | Structural organization of the human cerebral cortex prior to the appearance of the cortical plate[END_REF]). These vessels constitute the physiological locus of regulation of blood flow in response to change in metabolic demands of local networks [START_REF] Iadecola | Neural mechanisms of blood flow regulation during synaptic activity in cerebellar cortex[END_REF]. The underlying plexus progressively differentiate into the different vascular compartment [START_REF] Herken | Initial development of capillaries in the neuroepithelium of the mouse[END_REF][START_REF] Wang | Development and remodeling of cerebral blood vessels and their flow in postnatal mice observed with in vivo videomicroscopy[END_REF]. This occurs together with capillary bed expansion, remodeling and pruning. Whether this immature network is able to respond to metabolic demands by an increase in blood flow in premature neonate at rest is not entirely elucidated. Functionally, the maturation of the neonatal neuronal network is associated with characteristic age-dependent transient features, high amplitude mixed frequency activities and discontinuous pattern [START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF] reflecting the interaction between genetically encode transient generators of the subplate and cortical plate, permanent generators that progressively built up and exogenous inputs from the external world [START_REF] Routier | Plasticity of neonatal neuronal networks in very premature infants: Source localization of temporal theta activity, the first endogenous neural biomarker, in temporoparietal areas[END_REF]. Some studies has also presented that spontaneous endogenous activity may also be critical to wiring development [START_REF] Feller | Spontaneous correlated activity in developing neural circuits[END_REF] and provoking neural activity which may help in early wiring elaboration and refinement [START_REF] Ackman | Retinal waves coordinate patterned activity throughout the developing visual system[END_REF]. The discontinuous spontaneous EEG bursts of activity constitute discernible events offering the opportunity to monitor non-invasively and passively the hemodynamic responses to endogenous cortical activation in premature neonates, avoiding exogenous stimulation (Roche-Labarbe et al., 2007a).

The adaptation of the immature vascular network to neuronal activation is still a matter of discussion.

fNIRS and fMRI studies in animals have suggested that it develops postnatally [START_REF] Colonnese | Development of hemodynamic responses and functional connectivity in rat somatosensory cortex[END_REF]. In contrast, in premature neonates we observed a neurovascular coupling from 28wGA on, in response to spontaneous endogenous bursts of activity (Roche-Labarbe et al., 2007b) or exogenous phonemes or voices stimulations (Mahmoudzadeh et al., 2013b). While in adult the response of the vascular network is well established as a positive neurovascular coupling, in immature populations, increase-decrease of blood flow or blood volume have been reported in response to exogenous stimulation in neonates or premature (see for example [START_REF] Allievi | Maturation of Sensori-Motor Functional Responses in the Preterm Brain[END_REF][START_REF] Anderson | Neonatal auditory activation detected by functional magnetic resonance imaging[END_REF][START_REF] Born | Functional magnetic resonance imaging of the normal and abnormal visual system in early life[END_REF][START_REF] Erberich | Somatosensory lateralization in the newborn brain[END_REF][START_REF] Heep | Functional magnetic resonance imaging of the sensorimotor system in preterm infants[END_REF][START_REF] Kozberg | Resolving the transition from negative to positive blood oxygen level-dependent responses in the developing brain[END_REF]Mahmoudzadeh et al., 2017a;[START_REF] Martin | Visual processing in infants and children studied using functional MRI[END_REF][START_REF] Sakatani | Cerebral blood oxygenation changes induced by auditory stimulation in newborn infants measured by near infrared spectroscopy[END_REF][START_REF] Sie | Functional MRI of visual cortex in sedated 18 month-old infants with or without periventricular leukomalacia[END_REF][START_REF] Zaramella | Brain auditory activation measured by near-infrared spectroscopy (NIRS) in neonates[END_REF] as well as in immature animals [START_REF] Colonnese | Development of hemodynamic responses and functional connectivity in rat somatosensory cortex[END_REF] pointing to interstudy, intersubject, and even intrasubject regional variability in early development [START_REF] Kozberg | Neurovascular coupling and energy metabolism in the developing brain[END_REF].

The potentiality that neurovascular coupling itself may be matured parallel to neuronal development in the early infancy suggests that in this developmental span the neonatal brain may be undergoing variations in energy supply and demand dynamics in comparison to the adult brain. It makes sense to assume that there is a coupling between hemodynamic and neuronal activity in the premature neonatal brain in resting state (Roche-Labarbe et al., 2007b), but whether the hemodynamic responses to the burst of activities have the same patterns or not has to be analyzed? Is it possible to predict the hemodynamic response of neural activity in resting state in the premature infant considering all the complexity of the immature brain? What is the impact of the different gestational ages and/or pathologic events on the cerebral hemodynamic changes/disturbance in the immature neonatal brain? Is the neurovascular coupling age-dependent at resting state? Does the neonate cerebrum run into a situation of lacking of energy accessiblity that altering the capability of cortical neurons to fire? To answer these questions, in this study, we will mainly focus on the coupling between spontaneous physiological burst of activity with a transient hemodynamic pattern in resting state premature infants, consisting of deoxygenation, oxygenation, cerebral blood flow, cerebral blood volume and cerebral metabolic rate of oxygen, which help to elucidate the principles of neuronal and cortical hemodynamic coupling during development.

The multifaceted progress of neurovascular development prolongs occur after childbirth in natural development, suggesting attention to the potential contribution of this co-developing networks in normal and abnormal pathways of cerebral maturation. Since the early postpartum brain seems to work with a sensitive stability of cortical oxygenation, the establishment of functional hemodynamic response at the right moment in maturation is presumably an essential phase of development. Disconnetion or lags in the onset of neurovascular coupling could promote anomalies in both neural and vascular networks.

To better characterize the dynamics of the vascular network at rest in relation to spontaneous neuronal activity two approaches are considered in premature. The first approach is classic and considers the NVC in response to a neuronal activation. For this we took the opportunity of the spontaneous bursts in the discontinuous cortical activity of prematurity to trigger the analysis of the hemodynamic response. To better explore the different type of hemodynamic responses (direction of changes in [HbO] and [HbR], cerebral blood flow and cerebral oxygenation), a combined simultaneous, multimodal multiscale approach using Electroencephalography (EEG) with Diffuse Correlation Spectroscopy (DCS), Continuous Wave and Frequency Domain (CW and FD) functional Near-infrared spectroscopy (fNIRS) and monitoring of arterial blood pressure at bedside was developed. Another more recent, approach, is to consider the interaction between spontaneous oscillations of the neuronal and the vascular compartments in the time-frequency domain. This approach was applied on our multimodal multiscale data's using wavelet analysis method that has been proved to be adequate in neonates to provide clinical arguments to discriminate healthy neonates from asphyxiated newborns with encephalopathy [START_REF] Grinsted | Application of the cross wavelet transform and wavelet coherence to geophysical time series[END_REF]. Therefore the method was also applied to a subgroup of Patent Ductus Arteriosus (PDA) patients to test if the method might be helpful in situations in which autoregulation is considered to be altered [START_REF] Tian | Wavelet coherence analysis of dynamic cerebral autoregulation in neonatal hypoxic-ischemic encephalopathy[END_REF]. To perform these monitoring's a hybrid EEG-NIRS-DCS patch was built and placed on the infant's forehead (Fig1.A). To define the onset of the burst of spontaneous activity and quantify the neuronal activation at rest, eight EEG channels were recorded at the bedside. To acquire [HbO] and

[HbR] concentration changes and to calculate the cerebral tissue oxygenation index (TOI), a CW near-infrared spectroscopy probe was ls attached. To control spatially the change in HbO and HbR, in depth and at different locations, a multidistance, multichannel frequency-domain-based optical imaging system was used. To control for systemic effects, the peripheral arterial blood pressure was monitored continuously. To non-invasively quantify CBF, a DCS device was connected which further allows an estimate of CMRO2 changes. All the data were acquired simultaneously providing the multimodal and multiscale (neuronal and hemodynamic) approach. To evaluate the effect of the burst on the hemodynamic parameters, the burst onset was defined as the moving average of the EEG envelope-derivative value remaining over a given threshold. This was used to define time =0 for further analysis of the NVC, related to bursts of activity. Then, to extract the directional changes of HbO and HbR, all the trials of hemodynamic responses related to EEG bursts within the time window: [-20 to 30 sec] are passed through a classification algorithm, before grand averaging. The algorithm categorizes the blocks of HbO_HbR if the most samples of the HbO and HbR were over or under the threshold levels of 0.05 or -0.05 after 0 sec, and classifies the HbO_HbR into 3 main conditions; in opposite changes in HbO_HbR (Condition A), increase in both HbO_HbR (Condition B) and decrease in both HbO_HbR (Condition C) (Fig1.B). Condition A was further subdivided into 3 subconditions (i) subcondition A1; bursts are separated by InterBurst Intervals (IBIs) of more than 20s, (ii) subcondition A2; bursts are separated by IBIs of less than 20s, including only one burst in the reference period [-20s to 0s], (iii) subondition A3; bursts are separated by IBIs of less than 20s, including more than one burst in the reference period [-20s to 0s] (Fig1.B). To estimate the linear dynamics between the bursts of activity and the hemodynamic response we compared the root mean quare (rms) of HbO, HbR, TOI, CBF and CMRO2 with the rms of the envelope-derivative of the EEG bursts. To evaluate the nonlinear interactions between EEG and NIRS changes (EEG-HbO) in resting-state preterm infants, as previously (Nourashemi et al., 2017), we used the transfer entropy (TE) method based on information theory [START_REF] Shannon | A Mathematical Theory of Communication[END_REF]. To estimate the directionality in restingstate between spontaneous oscillations in HbO, HbR, TOI, CBF and CMRO2 and the spontaneous EEG oscillations, and to analyse whether it might help to discern between healthy and pathological neonates a new time-frequency domain wavelet analysis was applied to healthy and a subgroup of PDA patients [START_REF] Tian | Wavelet coherence analysis of dynamic cerebral autoregulation in neonatal hypoxic-ischemic encephalopathy[END_REF]. To evaluate the effect of age, the different parameters were evaluated in the course of the development in healthy patients. Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State conditions; in opposite changes in HbO_HbR, increase in both HbO_HbR and decrease in both HbO_HbR.

Classification of Hemodynamic responses

Hemodynamic responses related to EEG bursts were classified into 3 main conditions according to the direction of the changes in HbO and HbR. In condition A, they were further classified according to the number of burst occurring within the reference period [-20s to 0s].

• Condition A; The hemodynamic response consist in opposite changes in HbO and HbR.

-Condition A1; bursts are separated by IBIs of more than 20s (Fig. 2.A1).

-Condition A2; bursts are separated by IBIs of less than 20s, including only one burst in the reference period [-20s to 0s], (Fig. 2.A2).

-Condition A3; bursts are separated by IBIs of less than 20s, including more than one burst in the reference period [-20s to 0s], (Fig. 2.A3).

• Condition B; The hemodynamic response consist in an increase in HbO and HbR, (Fig. 2.B).

• Condition C; The hemodynamic response consists in a decrease in HbO and HbR, (Fig. 2

.C).

Statistical analyses were performed on the amplitude of the hemodynamic signals. For all selected hemodynamic segments [-20 to 30 sec], we used Student's t-test for paired samples to compare the hemodynamic response to the baseline (the first 10 s of each segment). We calculated the mean baseline value by averaging this 10 s of baseline, which provided a reference value for each segment, then compared values for every second of each segment to its own reference. The result is a significance level (p-value) for each comparison.

Wavelet coherence analysis of neurovascular coupling (NVC)

To estimate the cross-correlation in resting state between spontaneous oscillations in CBF, HbO, HbR, TOI and CMRO2 on one side and the spontaneous EEG oscillations on the other side, a new time-frequency domain wavelet analysis was applied [START_REF] Grinsted | Application of the cross wavelet transform and wavelet coherence to geophysical time series[END_REF]. The peak to peak of z-scored EEG amplitudes were first smoothed using a moving average of 0.5 seconds.

The wavelet transform coherence is a method for analyzing the coherence and phase lag, with squared cross-wavelet coherence, R 2 , between two time series as a function of both time and frequency without priori assumptions of linearity and stationarity [START_REF] Chang | Time-frequency dynamics of resting-state brain connectivity measured with fMRI[END_REF][START_REF] Torrence | Interdecadal Changes in the ENSO-Monsoon System[END_REF]. R 2 (squared wavelet coherence) ranges between 0 and 1 (the color scale represents the magnitude of R 2 ) and can be conceptualized as a localized correlation coefficient in the time-frequency domain between the recorded hemodynamic responses and the EEG bursts.

The two variables selected for evaluation of NVC were (i) the amplitude of the hemodynamic responses (either CBF, HbO, HbR, TOI or CMRO2) and (ii) the amplitude of the EEG burst. NVC is represented as the significant in-phase coherence (Δϕ ≈ 0) between the hemodynamics and the EEG bursts oscillations. The percentage of significant coherence is quantified as the percentage of the time-frequency area during which the HbO_EEG burst, HbR_EEG burst, TOI_EEG burst, CBF_EEG burst, CMRO2_EEG burst coherence is statistically significant from the background.

The percentage of significant coherence was further calculated as a function of age and compared between two groups of normal and pathological premature neonates (with IVH and PDA).

Linear and Nonlinear EEG_hemodynamic responses interactions

The linear correlation between rms of EEG and rms of hemodynamic responses and the nonlinear relationship between EEG and NIRS (DCS) data by using transfer entropy (TE) were investigated. The TE was used to define the strength of causality and the coupling between EEG and NIRS (DCS) data. The concept of entropy is related to the degree of uncertainty associated with a signal random variable. In other words, it provides a measure of the average uncertainty in a random variable. The analysis was based on times series with identical probability variables and a flat distribution of quantized values. Because TE is based on transition probabilities, we used TE to determine the dominant direction in the relationship between two variables EEG and NIRS (DCS) data. Statistical analysis with a limit of statistical confidence corresponding to the 95th percentile of the 300 trials was performed according to the surrogate method (Nourashemi et al., 2017).

Results

The discontinuous bursts of EEG activity were first detected by NLEO algorithm and then validated by an experienced neurophysiologist (FW). The percentages of the number of classified hemodynamic responses to EEG bursts in each condition (in all subjects healthy and PDA) are presented in Table 2 (SI).

Cerebral hemodynamic responses to burst of activities in premature neonates

The grand average (n=32) of the changes in the different hemodynamic parameters were calculated (HbO-HbR, TOI, CBF) and estimated (CMRO2) relatively to the onset of the detected burst of activity after grand average of the envelope-derivative of the EEG and a moving average of this envelope over all bursts (Fig. 2). 4 types of responses were observed. They consisted either in a CBF response with either a positive/negative change in CBF (Conditions A1, A2 and A3) or in a CBV response with a positive/negative change in CBV (Conditions B and C). The most frequent responses were observed in condition A during which the hemodynamic CBF response consisted in opposite changes in HbO and HbR. Also more frequent was the condition A1and A2 with a positive neurovascular coupling and increase in CBF. In condition A1 the bursts were separated by interburst intervals (IBI) of more than 20s (Fig. 2.A1). In such condition (A1), the hemodynamic changes started well before the burst onset. It consisted in an initial decrease (starting -12s from the onset of the burst (t0), significant (p<0.001) between -8 and -3s)) followed by an increase in HbO starting from -1s before t0, significant (p<0.001) between -0 and 15s). The following increase is concomitant to the burst of activity (Fig. 2.A1.II). A slight, nonsignificant, increase in HbR was followed by a decrease in HbR starting at -3.5s before t0, being significant (p<0.001) from -0.7s to 19s (Fig. 2.A1.II). The increase in TOI also started before the burst onset (-2s) but is only significant (p<0.001) from 1.2s to 20s (Fig. 2.A1.IV). The decrease in regional CBF (and rCMRO2) also started before the burst onset (-13s and -16s, respectively) and was significant (p<0.001) from -10s to -2.3s and again from 1.7s to 9.6s for CBF and from -9.7s to -1.4s and 6s to 9s for CMRO2. Then rCBF (rCMRO2) starts to increase at the onset (t0) of the EEG burst (Fig. 2.A1.V-VI). CBF and CMRO2 returned to the baseline faster than HbO_HbR. The decrease in CBV (HbT) started before the burst onset (-12s) and was significant (p<0.001) from -7.5s to -5.1s. No significant changes in CBV were observed (Fig. 2.A1.VII). To evaluate the effect of the previous bursts on the hemodynamic responses we considered conditions A2 and A3. In condition A2 the bursts were separated by IBIs of less than 20s and only one burst occurred in the reference period [-20s to 0s], (Fig. 2. A2). As in Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State condition A1, in condition A2 the hemodynamic response started by a significant increase (p<0.001) in HbO, TOI, CBF, CMRO2 and a significant decrease (p<0.001) in HbR beginning at -10s, before the burst onset (Fig. 2. A2). The amplitude of the hemodynamic response was significantly higher (p<0.05) than in condition A1 (Fig. 2.A2 vs. Fig. 2.A1). No significant changes in CBV were observed (Fig. 2. A2.VII). In condition A3; the bursts were also separated by IBIs of less than 20s, but more than one burst occurred in the reference period [-20s to 0s], (Fig. 2.A3). Compared to the previous conditions A1 and A2, the hemodynamic response was utterly inverted, consisting in a significant decrease (p<0.001) in HbO, TOI, CBF, CMRO2 and a simultaneous significant increase (p<0.001) in HbR beginning -10 sec, before the burst onset. A slight nonsignificant decrease in CBV was observed in relation to the burst of activity (Fig. 2.A3.VII). In condition B and C, the hemodynamic responses were strongly different and mainly characterized by changes in CBV. In condition B it consisted in a significant (p<0.001) simultaneous increase in both HbO and HbR (3s to 12s and -1s to 12.4s, respectively) and in CMRO2 (4.8s to 7.2s) with no significant changes in CBF and TOI (Fig. 2.B). In contrast to the previous A conditions, the CBV increased significantly (p<0.001) between 5.1s to 10.5s after the burst of activity (Fig. 2.B.VII). In condition C, the hemodynamic response was opposite to condition B, but still the CBV effect is dominant. The responses consisted in a significant (p<0.001) decreases in HbO (-2.1s to 20.4s), HbR (0.6s to 14.7s), TOI (-10s to 20.8s), CMRO2 (-10s to 17s), with no significant changes in CBF (Fig. 2.C). This resulted in a significant (p<0.001) decreases in CBV from -4.6s to 14.2s around the burst of activity (Fig. 2.C.VII). It must be noted that similar dynamics in HbO and HbR fluctuations were observed whatever a frequency-domain fNIRS or a continuous-wave fNIRS were used (Fig. 2.II and 2.III) and whatever the distance between emitters and detectors. In addition, these burst of activity did not induce any systemic changes in arterial blood pressure (ABP) (Fig. 2.VIII). To identify a nonlinear and causal relationship between EEG and NIRS data, the transfer entropy analysis was used as it detects the relationship between the past of one signal and the present of another signal (Nourashemi et al., 2017).

Linear and Nonlinear interactions between the neuronal and the hemodynamic changes

The effect of age on wavelet real-time analysis

There is positive correlation between age and the percentage of significant coherence (p<0.05) between hemodynamic responses and EEG (R2>0.5 between the frequency range of 0.003-0.125 Hz) whatever the hemodynamic parameters studied (Fig.

Cerebral Hemodynamic patterns

Fine-tuning of neural wiring is subject to the inhibitory trajectories maturation [START_REF] Crook | Evidence for a contribution of lateral inhibition to orientation tuning and direction selectivity in cat visual cortex: reversible inactivation of functionally characterized sites combined with neuroanatomical tracing techniques[END_REF]. GABAergic interneurons establish at various stage after birth related to region-dependent critical periods (Le Magueresse and Monyer, 2013). In particular, there is a maturational shift from the excitatory to inhibitory of the developing brain. This maturational transition happens as a consequence of change of the neurotransmitter GABA from depolarizing to hyperpolarizing at almost day seven postpartum in mouse [START_REF] Amin | Developmental excitatory-to-inhibitory GABA-polarity switch is disrupted in 22q11.2 deletion syndrome: a potential target for clinical therapeutics[END_REF][START_REF] Ben-Ari | The GABA excitatory/inhibitory developmental sequence: a personal journey[END_REF]. This shift have the potential to impact the profile of the brain hemodynamics, since some studies hypothesize that interneurons perform a crucial contribution in neurovascular coupling [START_REF] Cauli | Cortical GABA interneurons in neurovascular coupling: relays for subcortical vasoactive pathways[END_REF].

In addition, the weighting between arterial, venous and capillaries contributions in neurovascular coupling, are significantly different for excitatory and inhibitory task in human brain [START_REF] Huber | Investigation of the neurovascular coupling in positive and negative BOLD responses in human brain at 7 T[END_REF]. The interplay of different vascular compartments in NVC, with their considerable prematurity [START_REF] Miyawaki | Developmental characteristics of vessel density in the human fetal and infant brains[END_REF] consequence of different underlying hemodynamic mechanisms. The different patterns of hemodynamic response we observed might provide some explanations for the divergent hemodynamic responses previously reported in immature neurovascular networks. It further suggests that the strategy developed for the NVC in premature is much more complex than in adults.

Positive hemodynamic response

This response is the most frequent and confirm the ability of the vascular system to couple with neuronal activity in early premature. This response is in total agreement with our previous study (Roche-Labarbe et al., 2007b). The significant initial decrease in HbO (increase in HbR)12s prior to the onset of the EEG burst correspond to an increase in oxygen consumption likely to mimic an initial dip in which the oxygenation is preceded by a brief deoxygenation, related to oxygen consumption preceding a vasoactive response [START_REF] Devor | Coupling of total hemoglobin concentration, oxygenation, and neural activity in rat somatosensory cortex[END_REF][START_REF] Jasdzewski | Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy[END_REF]. The hemodynamic changes (measured with both frequency-domain fNIRS and continuous-wave fNIRS devices) preceded any visible neuronal activity (measured by EEG). These early hemodynamic changes have been related to a low number of synchronized activated neurons or activation of unsynchronized neurons within the first few seconds (Roche-Labarbe et al., 2007b). The origins of the burst recorded by EEG in premature are still unknown. They are likely to be related to intimate mechanisms between the subplate and the cortical plate under development with an interplay between ascending pyramidal neurons and subplate neurons [START_REF] Routier | Plasticity of neonatal neuronal networks in very premature infants: Source localization of temporal theta activity, the first endogenous neural biomarker, in temporoparietal areas[END_REF]. In such condition, an earlier endogenous activation of subplate neurons (Arichi et al., 2012) which electromagnetic field, not orientated perpendicular to the surface of the brain, is not reachable by EEG recordings but might be able to develop a NVC. Despite the possible implication of the subplate neurons, the rms of the neuronal EEG activity is correlated to the rms of the hemodynamic NIRS parameters. But in nonlinear investigation, the predominant driving influence of EEG on NIRS-DCS (or invers) in different preterm newborns were different. The cause for this phenomenon can be multifactorial and might be related to the regulation of brain hemodynamics.

The following increase in HbO (decrease in HbR) starting at the onset of the EEG burst is associated with an increase in cerebral blood flow (CBF) and CMRO2, bringing oxygenated hemoglobin into the brain. A decrease in CBF and CMRO2 before the onset of the burst, supporting the assumption of a recruitment of the capillaries accompanied by a changeover in low blood flow before the onset of the burst to a high blood flow during the burst [START_REF] Kuschinsky | Capillary circulation in the brain[END_REF]Malonek et al., 1997a;Nourhashemi et al., 2017a). The decreased concentration of HbR during the Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State burst further suggests that oxygen delivery exceeds oxygen consumption during spontaneous bursts in premature.

The consequence of considering the hemodynamic response with an IBI of less than 20s (Condition A2) results in a second burst onset occurring during the hemodynamic response of the previous burst. This masks the initial decrease in HbO (increase in HBR) prior to the second burst which is replaced by an earlier onset of the neurovascular coupling in case of short IBI. Whatever these initial differences, the following pattern of hemodynamic changes is similar. Nevertheless, because in short IBIs, the hemodynamic response had a higher amplitude, it is likely that a cumulative effect occurs during the NVC.

The involvement of NVC in positive NIRS response, fitted well with the classical balloon model [START_REF] Buxton | A model for the coupling between cerebral blood flow and oxygen metabolism during neural stimulation[END_REF][START_REF] Buxton | Modeling the hemodynamic response to brain activation[END_REF]. In positive NIRS response, an increase in flow velocity without accompanying either vasodilatation or recruitment might account for the absence of an increase in HbT during activation, which resulted in increases in venous oxygenation.

Negative neurovascular coupling

The negative hemodynamic responses to EEG burst was regularly observed whatever the duration of the IBI. Such negative coupling has been described in many experimental setups not only in fNIRS following peripheral stimulation [START_REF] Maggioni | Investigation of negative BOLD responses in human brain through NIRS technique. A visual stimulation study[END_REF][START_REF] Seiyama | Circulatory basis of fMRI signals: relationship between changes in the hemodynamic parameters and BOLD signal intensity[END_REF], but also in fMRI (visual [START_REF] Born | Functional magnetic resonance imaging of the normal and abnormal visual system in early life[END_REF][START_REF] Martin | Visual processing in infants and children studied using functional MRI[END_REF][START_REF] Sie | Functional MRI of visual cortex in sedated 18 month-old infants with or without periventricular leukomalacia[END_REF], (somatosensory [START_REF] Erberich | Somatosensory lateralization in the newborn brain[END_REF][START_REF] Heep | Functional magnetic resonance imaging of the sensorimotor system in preterm infants[END_REF]). The literature on the negative hemodynamic response is still controversial [START_REF] Colonnese | Development of hemodynamic responses and functional connectivity in rat somatosensory cortex[END_REF][START_REF] Zimmermann | The confounding effect of systemic physiology on the hemodynamic response in newborns[END_REF]. These negative hemodynamic responses could be due to a "negative surround" often characterized as either "vascular steal" or an index of reduced or inhibitory neural activity [START_REF] Boas | A vascular anatomical network model of the spatio-temporal response to brain activation[END_REF][START_REF] Devor | Stimulus-induced changes in blood flow and 2-deoxyglucose uptake dissociate in ipsilateral somatosensory cortex[END_REF]. Nonetheless, this negative hemodynamic response may also be an independent neurovascular coupling potentially linked to cholinergic or noradrenergic-base vasoconstriction to regulate blood flow to activated regions [START_REF] Bekar | The locus coeruleus-norepinephrine network optimizes coupling of cerebral blood volume with oxygen demand[END_REF][START_REF] Takata | Cerebral blood flow modulation by Basal forebrain or whisker stimulation can occur independently of large cytosolic Ca2+ signaling in astrocytes[END_REF]. However, this mechanism is not fully understood, whether this vasoconstriction vail to restrict the degree of functional hemodynamic responses, and its formation in developing brain before neurovascular maturation could provide to preserve frail neonatal vasculature, which is notably predisposed to hemorrhage in premature infants, from immoderate vasodilation and systemic hypertension [START_REF] Volpe | Brain injury in the premature infantfrom pathogenesis to prevention[END_REF].

Alternatively, an inverted NVC related to a situation of anaerobic metabolism has been suggested to explain the hemodynamic response to epileptic spasms associated with metabolic Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State dysfunction treated by a ketogenic diet only [START_REF] Bourel-Ponchel | Non-invasive, multimodal analysis of cortical activity, blood volume and neurovascular coupling in infantile spasms using EEG-fNIRS monitoring[END_REF]. The setting of such anaerobic metabolism [START_REF] Booth | The development of enzymes of energy metabolism in the brain of a precocial (guinea pig) and non-precocial (rat) species[END_REF][START_REF] Rodríguez-Balderrama | Risk factors and the relation of lactic acid to neonatal mortality in the first week of life[END_REF] fits well with the observed decrease in CBF and CMRO2.

In the positive NIRS, the fluctuation of HbO-HbR prior to the onset of EEG burst is concomitant with the decrease in CBF. Likewise, the negative NIRS seems to be driven by the decrease in CBF.

A decrease in rCBF concomitant with a slight increase in HbR, might represent increasing the oxygen extraction, in consequence of the limitations in oxygen transport, the brain switch to anaerobic glucose consumption during activation. This could be explained by the neonatal and early infantile maturation which corresponds to the period of rapid formation of synapses [START_REF] Bourgeois | Synaptogenesis in visual cortex of normal and preterm monkeys: evidence for intrinsic regulation of synaptic overproduction[END_REF][START_REF] Huttenlocher | Regional differences in synaptogenesis in human cerebral cortex[END_REF].

Changes in volume

EEG bursts might also trigger another mechanism of NVC based on changes (increase or decrease) in CBV and in HbO and HbR without any changes in CBF or CMRO2. Considering the different models of NVC [START_REF] Hoshi | Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model[END_REF] increase, decrease in blood volume with no changes in CBF are more likely related to venous constriction or dilatation, respectively. The increases in both HbO and HbR with no significant change in CBF, support the hypothesis that O2-consumption was not fully compensated by the increase in HbO, thus an increase in oxygen supply insufficient to meet the oxygen demand. The similar type of pattern in hemodynamic response was also observed in the visual stimulation of neonates [START_REF] Meek | Regional changes in cerebral haemodynamics as a result of a visual stimulus measured by near infrared spectroscopy[END_REF][START_REF] Meek | Regional hemodynamic responses to visual stimulation in awake infants[END_REF]. The decreases in both HbO and HbR, support the hypothesis that a decrease in HbO during burst of activity linked to an insufficient increase in CBF, but a decrease in HbR reflecting a decrease in venous blood oxygenation and volume [START_REF] Hoshi | Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model[END_REF].

Following our results, in the positive NIRS (Fig. 2.A1-A2), the degree of decreases in HbR during the burst of activity is likely attributed to venous hyperoxia due to overcompensation of the flow. In negative NIRS conditions (Fig. stimuli are accompanied with increases in CBV (in positive BOLD) in cortex and pial vasculature [START_REF] Huber | Investigation of the neurovascular coupling in positive and negative BOLD responses in human brain at 7 T[END_REF].

The different hemodynamic responses that have been observed using the two devices, scanning thus the same area, in the same premature, at different times reflect the complexity of the interactions between the neuronal and vascular networks in premature. We found a correlations between the amplitude or the rms of the bursts and the rms of the hemodynamic response, despite a possible implication of subplate neurons and other non-synchronized or non well-orientated pyramidal cells, which might participate in the elaboration of the type of neurovascular response triggered by the underlying neuronal activity (cortical plate or subplate). In addition, other metabolic nonoxidative mechanisms are like to participate, notably in pathological neonates [START_REF] Bourel-Ponchel | Non-invasive, multimodal analysis of cortical activity, blood volume and neurovascular coupling in infantile spasms using EEG-fNIRS monitoring[END_REF].

Assessment of neurovascular coupling dynamics by Wavelet coherence analysis

Influence of cerebral impairment on NVC

Although the pattern of the hemodynamic response is similar in the PDA and healthy premature, the dynamic of the response is decreased in PDA. In healthy neonates, the coupling in the very lowfrequency range (0.003-0.125 Hz) between the neuronal activation and the hemodynamic response is higher in healthy than in PDA premature. This corresponds to a decrease in the dynamic of the neurovascular coupling as previously described in IVH premature in response to spontaneous bursts (Roche-Labarbe et al., 2007b) or syllable stimulations [START_REF] Mahmoudzadeh | Consequence of intraventricular hemorrhage on neurovascular coupling evoked by speech syllables in preterm neonates[END_REF]. In PDA prematures, it reflects a defect of the vascular network in the functional neuro-vascular coupling (e.g., elasticity) [START_REF] Perlman | Intracerebellar hemorrhage in a premature newborn: diagnosis by real-time ultrasound and correlation with autopsy findings[END_REF][START_REF] Van Bel | Aetiological role of cerebral blood-flow alterations in development and extension of peri-intraventricular haemorrhage[END_REF]. The vascular network in PDA prematures may not be capable of rapid or large local changes in CBF in response to neuronal activation, due to their very low CBF and lack of autoregulation [START_REF] Malamateniou | The effect of preterm birth on neonatal cerebral vasculature studied with magnetic resonance angiography at 3 Tesla[END_REF]. The present results show low NVC is statistically significant, particularly in CBF and CMRO2 (rather than the other hemodynamic responses; HbO, HbR, TOI) in IVH preterms relative to healthy group, which is in good agreement with many studies from different imaging modalities that described altered vascular function consisting in a decrease in CBF in IVH preterms at resting state [START_REF] Meek | Low cerebral blood flow is a risk factor for severe intraventricular haemorrhage[END_REF][START_REF] Osborn | Hemodynamic and antecedent risk factors of early and late periventricular/intraventricular hemorrhage in premature infants[END_REF].

Our results suggest the presence of altered NVC in the group of preterm with PDA and IVH. The slow rhythms have also been shown in adults to synchronize large spatial domains affecting functions [START_REF] Sirota | Communication between neocortex and hippocampus during sleep in rodents[END_REF], and the present study findings would suggest they are also probably to be impaired in the abnormal neonatal brain.

Variability of the NVC as a function of age (Evolution of the NVC with Increasing Age)

The coherence analysis of the hemodynamic responses-EEG activity increased as a function of age demonstrating that oscillatory coupling of the neuronal and the vascular networks mature progressively.

Assessment of the systemic impact as a potential confound

Because autoregulation is not fully mature in the newborn brain [START_REF] Greisen | To autoregulate or not to autoregulate--that is no longer the question[END_REF], variations in systemic blood pressure might be more easily reflected in the hemodynamics of the neonatal brain.

In fact, dynamics and direction of the cortical hemodynamic response might be affected by stimulusevoked increases in systemic blood pressure [START_REF] Kozberg | Resolving the transition from negative to positive blood oxygen level-dependent responses in the developing brain[END_REF]. To evaluate the possible contribution from the blood pressure to the hemodynamic signal, an accurate non-invasive beat-tobeat blood pressure monitoring has been performed. The systemic blood pressure was not significantly correlated with the burst-evoked hemodynamic signal in the resting-state neonatal brain (Fig. 2.VIII), suggesting that the complexity of the observed NVC in resting state was likely not related to the systemic changes.

Conclusion

Noninvasive functional hemodynamic imaging modalities (i.e., fMRI and fNIRS), serve to investigate brain activity, rely on assessment of hemodynamics as a proxy for neural activity. If naturally, there are stages of early brain maturation in which neurovascular coupling is variant than in adults, classical analysis and interpretation of functional hemodynamic data could be misleading.

Contrarily, with reformed insight of how to comprehend functional neuroimaging data in these populations, functional hemodynamic imaging approaches could assert helpful for delineate the development of neurovascular coupling.

This study describes the different pattern of cerebral hemodynamic response to the spontaneous cerebral burst of activities in resting state in premature neonates. This might be related to the immaturity of the neuronal and vascular networks together with the cellular mechanisms of the neurovascular coupling. This study confirms and describes more precisely the abnormal NVC not only in IVH but also in PDA in resting state. The amplitude of the spontaneous NVC is described as being age-dependant on resting-state.

Immaturity of neurovascular coupling suggests that functional hemodynamic data obtained in preterm neonates, and probably term infants need to be interpreted differently from adult signals. Such multimodal study are paving the way for further research which factors should be considered in the analysis of these data. We are confident that our results may improve knowledge about neurovascular development. This multiscale, multimodal non-invasive approach of the neurovascular coupling in spontaneous cerebral burst in premature allows investigating the NVC in the two neuronal and vascular dimension that constitutes the same neurovascular functional system. Moreover, altered neurovascular development is an element in disorders of brain development given neurovascular development is an essential element of neonatal brain development, following alongside with neural development. A more complete understanding of the normal state of neurovascular coupling development could give influential advanced visions into the etiology of neurodevelopmental disorders and may provide novel biomarkers for track and analysis therapeutic objectives. Insights into variations in neurovascular coupling patterns in normal and abnormal will provide brain indicators that could be used for following effective therapies. In fact, such noninvasive approach might be interesting to test in a larger population of premature to evaluate its ability to discriminate between neuronal and vascular pathologies that could help to identify infants at risk of the abnormal outcome. In our view, these results represent an excellent initial step toward providing a unique approach to explore and assess this developmental course and provide new therapeutic biomarkers.

Supplementary Information

Thirty-two preterm neonates (12 females; mean gestational age (GA) at birth: 29.3 weeks GA ) were tested in the supine position (recording age: 31.3 wGA, Table 1). This study is

EEG recording (EEG)

To define the onset of the burst of spontaneous activity and quantify the neuronal activation, eight EEG channels were recorded at the bedside using Ag/AgCl surface electrodes and a Cz reference at a sampling rate of 1024 Hz, amplified by A.N.T® (Enschede, The Netherlands).

Recordings were acquired with a band pass filter of 0.1-100 Hz, and an additional notch filter at 50

Hz. Electrodes impedance were kept below 5 k.

Continous-Wave Spectroscopy (CW NIRS)

To calculate cerebral tissue oxygenation index (TOI), a CW near-infrared spectroscopy probe NIRO-200NX (Hamamatsu Photonics Corp., Tokyo, Japan) was placed on the infant's forehead.

The NIRO 200 NX uses spatially resolved spectroscopy at three wavelengths (λ=735 nm, 810 nm, and 850 nm). It is based on the solution of the diffusion approximation equation for a highly scattering semi-infinite homogeneous medium. The effective light attenuation coefficient can be estimated by measuring the decrease in reflected light as a function of distance. By assuming wavelength dependence of the reduced scattering coefficient, the spectral shape of the absorption coefficient can then be calculated and cerebral tissue oxygen index can be estimated (Matcher et al., 1995a). The average output power of the lasers was less than 2 mW and the CW acquisition rate was fixed to 5 Hz (200 ms).

Frequency-Domain Spectroscopy (FD NIRS)

To acquire [HbO] and [HbR] concentration changes, a multichannel frequency-domain-based optical imaging system (Imagent, ISS Inc., Champaign, IL) was used. Imagent is a frequencydomain tissue spectrometer. We used 8 out of the 32 intensity-modulated laser diodes at two wavelengths (λ=690 nm and 830 nm) coupled to optical fibers, and 1 out of the 4 gain-modulated photomultiplier tube (PMT) detectors to collect the signal at both wavelengths separately. The modulation frequency of laser intensity was 110MHz, and the cross-correlation frequency for heterodyne detection was 5 kHz. Reflected light collected by the PMT was then demodulated. Its mean intensity (DC), modulation amplitude (AC), and phase were determined. The average output power of the lasers was about 0.5 mW and the optical acquisition rate was 9.7656 Hz (about one sample every 100 ms). Oxy (HbO) and deoxyhemoglobin (Hb) are chromophores that absorb light at different wavelengths. To convert signal intensities into relative changes in (de)oxy-hemoglobin concentration, the Modified Beer Lambert Law was applied to the two wavelengths (690 and 830 nm). Each chapter in this thesis describes a combination of techniques applied to preterm neonates in either a healthy or an abnormal brain. It is valuable that most of these approaches can be adapted to a variety of situations to measure different aspects of neurovascular coupling in both normal and pathological brain states in animal as well as human.

This thesis thus presented a framework from which a group of additional studies could be performed as these approaches can be performed to a variety of other species and other areas of the cortex or pathological conditions. What is obvious, is the increasing importance and potency of optical approaches in neurovascular coupling investigation. Moreover, the

Conclusions

In this dissertation, multimodal hybrid EEG-NIRS-DCS and non-invasive blood pressure monitoring techniques were used to measure electro-hemodynamic activities of the premature neonatal brain under resting states (Fig. 1). The differences in functional responses correspond to the immaturity of NVC, support the massive growth and neurogenesis at rest in neonatal brain. The complex process of NVC development continues to occur postnatally in normal development, prompting consideration of the role of this developing system in normal and abnormal trajectories of brain development. Disruptions or delays in NVC could lead to abnormalities in both neural and vascular development. It may have a profound impact on developing neural circuitry. So there is a need to understand the optimal metabolic state of the perinatal brain. At the resting state, data of immature brain can be more challenging to interpret than stimulus-evoked responses: our finding demonstrated the directionality of these slow fluctuations in neural and hemodynamic activity, and the presence of positive, negative, or absent NVC in premature neonatal brain. The main achievements of this thesis can be summarized as follow: 1) Safety issues of optical imaging: There are currently not any major safety problems associated with functional optical imaging measurements. The only safety issue is a potential heating of the light source attached to the scalp. Thus, careful monitoring of the temperature and timely termination of the study will prevent any harmful effect. As there are no substantial medical or ethical constraints associated with functional optical imaging, it can easily be used to study brain processes of normal and healthy subjects.

The photothermal interaction of NIR laser on human tissues (with different laser powers and various spot sizes) were modelled. The results demonstrated the maximum temperature increase was higher in the neonatal brain than in the adult brain, these results can be useful to optimize laser parameters for a variety of laser applications in the brain to avoid any possible tissue damage.

2) Transfer entropy robustly detected the relation between CBF_CBV, CBF_CMRO2, and neuronal-vascular system as a complex non-linear coupling in preterm infants recorded before 32 wGA. The findings of this study suggest that the mechanisms by which rCBV drives rCBF (rCMRO2 drives rCBF) are already functional at this early age of development regardless of whether or not these two variables are strictly correlated. 3) This thesis describes the different pattern of cerebral hemodynamic response to the spontaneous cerebral burst of activities in resting state in premature neonates. This may be a consequence of the immaturity of the neuronal and vascular networks together with the cellular mechanisms of the neurovascular coupling. 4) As wavelet coherence analysis presents the multi-frequency aspect of neurovascular coupling, the results of this study suggest that neurovascular development represents the establishment of neurovascular coupling system as a function of age. The agedependent hemodynamic responses that we observed, could be explained by changes in the underlying neuronal behavior or by changes in the coupling between neural activity and hemodynamic responses.

5) The neurovascular coupling is affected by neonatal encephalopathy in pathological groups (i.e., PDA). Thus, the neurovascular coupling analyzing in the premature neonatal brain at rest, have clinical value as sensitive markers of diseases.

Perspective

This thesis provided an overview of a variety of techniques currently available to investigate neurovascular coupling in both health and disease neonates. Understanding normal neurovascular coupling during sensory and eventually higher order brain functions like memory and language will be essential in the development of novel neuroimaging techniques.

Likewise, the propagation of these approaches to diagnose disease will require a complete understanding of how neurovascular coupling mechanisms fail in disease states to permit accurate interpretation of cortical hemodynamic signals as a proxy for neuronal activity.

A comprehensive understanding of the neurovascular coupling relationship needs the concurrent measurement of neuronal and vascular responses. The value of this approach, is the ability to measure hemodynamics through an intact skull, which provides translational techniques for noninvasive measurements in humans for clinical diagnostic purposes and a new insights into the etiology of developmental disorders. This section contains several suggestions for the future direction that might help in studying neurovascular coupling development in premature neonatal brain and infants.

Investigation of nonlinear NVC in deeper layers and different areas of neonatal brain

The results in Chapter 4, explored a causal relationship between the hemodynamic responses in the frontal area of the premature brain. As the penetration of light is limited in NIRS technique, it is not possible to investigate the nonlinear relation between hemodynamic responses in the deeper layer of the premature neonatal brain. Thus using more technique such as fMRI images can be helpful to investigate nonlinearity of hemodynamic parameters in the deeper layers and more areas of the neonatal brain.

Investigation of impaired cerebral autoregulation in preterm newborns

The immaturity of the cerebral vasculature coupled with unstable cerebral hemodynamic play an essential role in the aetiologies of the major forms of preterm brain injury (du Plessis, 2009a). Hemodynamically significant patent ductus arteriosus (hsPDA) in preterm infants lead to cerebral injury and cerebral autoregulation impairment because of lower cerebral oxygenation and reduced cerebral blood flow due to left-to-right shunting. The pressure of passive cerebral blood flow in distressed preterm infants has been widely accepted as an important aspect within the physiopathological considerations of the hemorrhagic/ischaemic cerebral injury in preterm neonates [START_REF] Vutskits | Cerebral blood flow in the neonate[END_REF]. These patients seem to be exceptionally prone to loss of autoregulation and risk of intraventricular hemorrhage (IVH) under blood pressure changing events like suctioning, pneumothorax, and rapid volume restoration. Roche et al. previously demonstrated that the neurovascular coupling was impaired by IVH grade III and IV (Roche-Labarbe et al., 2007a). In the present study, we evaluate whether PDA and IVH grade I and II, which are less dramatic situations but are likely to impair future neuronal abilities, might impact the neurovascular coupling in response to spontaneous bursts (chapter 5).

As the characteristics of cerebral autoregulation and the ideal range of systemic blood pressure in preterm infants remain unclear, and DCS, Finometer, and NIRS have established techniques for the assessment of cerebral blood flow, systemic blood pressure and cerebral oxygenation respectively. As a future work, the assessment of the correlation between dynamic indexes of cerebral autoregulation in preterm infants, with indices obtained in this study using DCS and Finometer/NIRS will be done. Initial results (in the following part) suggest that

Development of hemodynamic responses function (HRF) in preterm newborns

As the hemodynamic response to brain activity forms the basis for imaging modalities as a surrogate measure of neural activity, it is therefore critical to understand how the coupling between neuronal activity and hemodynamic response is mediated and if the model of Hemodynamic Response Function (HRF) can link hemodynamic and electrophysiological measures of brain activity in resting neonatal brain with varied ages and pathologies.

In the adult human brain, the morphology of the HRF has been well determined and found to be reproducible across different populations [START_REF] Handwerker | Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses[END_REF]. Arichi et al. characterized the morphology of the HRF to neural stimulation during the term and preterm neonates, with hypothesized that the neonatal HRF differs from the canonical adult waveform and considering a systematic maturational trend (Arichi et al., 2012). As presented in chapter 5, because of the different appearances of hemodynamic response to the burst of activities during the preterm newborn period, the morphology of the HRF to burst of activities at rest will be more complex that need a more precise algorithm. Changes in the neonatal brain would complicate the determination of the HRF during development at different gestational age and also pathology cases. As a future work, HRF at different gestational age and pathology cases will be estimated. Initial results for HRF fitting by using Genetic algorithms will be presented in the figure 2.

Somatosensory evoked changes in hemodynamic responses on bald scalp

We combined multiple near-infrared spectroscopy techniques to measure hemodynamic responses in the somatosensory cortex of 6 bald scalp during passive tactile stimulation of the hand (Fig. 3). This experiment was designed to provide a preliminary control condition to evaluate the functional hemodynamic response as a reliable marker of neuronal activity. As a future work, to independently evaluate our multimodal method for studying the pathophysiological cases such as epileptic patient (absence seizure), we obtained event-related optical signals such as HbO, HbR, CBF, and CMRO2 in response to exogenous stimulation of median nerve as a control experiment.

Investigation of multimodal imaging during absence seizure in epileptic children

The present results of this thesis demonstrated the abnormalities of spontaneous neurovascular coupling in IVH premature neonates (chapter 5). In contrast, in infants without impairment of the vascular system (no IVH), the hemodynamic response is still present in response to neuronal "seizure-like" discharges [START_REF] Wallois | Haemodynamic changes during seizure-like activity in a neonate: a simultaneous AC EEG-SPIR and high-resolution DC EEG recording[END_REF]. Childhood absence epilepsy is an idiopathic, generalized non-convulsive epilepsy with a multifactorial genetic etiology. The complex pathophysiological mechanisms of absence seizure in epileptic children require a global approach of the interactions between neural synaptic and non-synaptic, vascular and metabolic systems. As a future work, we will focus on the interaction between synaptic and non-synaptic mechanisms through the simultaneous non-invasive multimodal Je présente les méthodes de calcul du taux de consommation cérébrale en oxygène (CMRO2), de la mesure et de l'estimation de la pression artérielle par le dispositif Finometer® (surveillance de la pression artérielle non invasive). La distribution de la température à l'intérieur du tissu a été modélisée en utilisant des simulations FEM et l'équation de transfert de chaleur biologique pour déterminer la fonction de température transitoire requise pour calculer l'interaction photothermique. Une gamme de différentes puissances laser (1mW-100mW) avec différentes tailles de faisceaux, les différents La cohérence significative de phase entre l'amplitude du paramètre hémodynamique et l'amplitude de la salve EEG a été réalisée par une analyse de cohérence par ondelettes. L'analyse de cohérence basée sur les ondelettes a d'abord été calculée chez un nouveau -né prématuré sains, sur une période de 25-30 minutes équivalente à une très-basse fréquence (VLF) ( 0,003 à 0,125 Hz) puis ensuite comparé aux résultats obtenus chez le prématuré avec un canal artériel persistant (Fig. 9). Réponses NIRS négatives (augmentation de HbR, diminution de HbO avec diminution de CBF et CMRO2), c.

Augmentation et diminution à la fois de HbO-HbR et de CMRO2, sans modification du CBF.

(2) Ces différents types de réponses hémodynamiques aux bouffées EEG se sont produits de manière similaire chez les patients pathologiques et sains, mais la cohérence dynamique entre les réponses hémodynamiques et les bouffées EEG pour évaluer le NVC est plus faible chez les nouveau-nés avec PDA et HIV que chez les sujets sains.

(3) Les mesures en ondelettes de NVC dans le cerveau néonatal dépendent de l'âge, ce qui suggère que la trajectoire développementale des réponses hémodynamiques dans le cerveau postnatal reflète, au moins en partie, le développement progressif du couplage neurovasculaire.

Cette étude décrit les différentes formes de réponse hémodynamique cérébrale aux bouffées d'activités cérébrales spontanées au repos chez les nouveau-nés prématurés. Cela pourrait être lié à l'immaturité des réseaux neuronaux et vasculaires ainsi qu'à l'immaturité des mécanismes cellulaires du couplage neurovasculaire. Cette étude confirme et décrit plus précisément le NVC anormale non seulement dans les HIV mais aussi dans les PDA au repos.

L'amplitude du NVC spontanée est décrite comme étant dépendante de l'âge au repos.

Conclusions générales et perspectives

I

  am indebted to all my friends who have supported me over the last few years. I have enjoyed entertaining discussions with my friends in Inserm_U1105 laboratory and most kind people imaginable in CHU 's clinical team. Above all, I want to thank my family, my father & mother, my sisters & brother: Mitra, Ghazal & Mohamad, for their support and encouragement. Finally, huge thanks, love and appreciation go to Mahdi, for his grace, generosity and presence in my life. GLOSSARY BOLD blood oxygenation level dependent CBF cerebral blood flow CBV cerebral blood volume CSF cerebrospinal fluid CW Continuous wave CPP Cerebral perfusion pressure DCS Diffuse correlation spectroscopy DPF differential pathlength factor EEG electroencephalogram fMRI functional magnetic resonance imaging fNIRS functional near-infrared spectroscopy Hb deoxy-haemoglobin Hb haemoglobin HbO oxy-haemoglobin ICP Intracranial pressure IVH Intra-ventricular hemorrhage MBLL modified Beer-Lambert law MBP arterial mean blood pressure NIR near infrared rCBF relative Cerebral Blood Flow rCBV relative Cerebral Blood Volume rCMRO2 relative Cerebral Metabolic Rate of Oxygen SNR signal-to-noise ratio SPECT single photon emission computed tomography TE Transfer Entropy tHb total hemoglobin TOI tissue oxygenation index StO2 tissue hemoglobin oxygen saturation ΔHb changes in deoxy-hemoglobin concentration ΔHbO changes in oxy-hemoglobin concentration

15

  Chapter 1: Introduction & background connects cerebral blood flow (CBF) to neuronal response and affects oxygen delivery and blood volume.

Fig. 1

 1 Fig.1 Detail of neurovascular unit, A) Neurons and astrocytes are in close proximity and are functionally coupled to smooth muscle cells and endothelial cells.. B) Local and propagated microvascular responses

  ) include local and systemic factors, local factors such as intracranial pressure and resistance, systemic factor such as arterial blood pressure. The arterial

  models of neurovascular coupling Specific dynamic models are currently used for explaining empirical observations in terms of theoretical underlying mechanisms of NVC. These explanatory models are depicting the transient hemodynamic and oxygenation changes in activated cerebral areas. Since the Chapter 1: Introduction & background physiology of NVC (with a large number of unknown parameters) is not yet fully understood, it remains difficult to determine which dynamic model is actually useful for better interpretation of NVC. I explained the physiological assumptions of two common dynamic models; Balloon model and Windkessel model.

Fig. 5

 5 Fig.5 The organization of afferent systems and transient cortical circuitry in preterm infants. (A); the accumulation of afferents in the superficial subplate (i.e. below the cortical plate) in very early preterm (22-23 postconceptional weeks). (B); the penetration of afferents into the cortical plate after 24 postconceptional weeks (C); intra-cortical elaboration of thalamocortical fibers after 29 postconceptional weeks (D). All major pathways 'cross' vulnerable periventricular zone. Note that afferent axons and cells in the subplate zone are involved in all stages of circuitry development and reorganization. Laminar shifts of thalamocortical and basalforebrain afferents together with the laminar development of synapses in the cortical plate cause changes in cortical electric responses[START_REF] Kostovic | The development of the subplate and thalamocortical connections in the human foetal brain[END_REF].

Fig. 6

 6 Fig.6 Burst of activities pattern during sleep, the background is discontinuous with excessive discontinuity more prominent over the right hemisphere 1 .

  At 33 to 35 wCA, discontinuous activity is associated with quiet sleep, and continuous background occurred in active sleep. At 36 to 38 wCA, discontinuous pattern separated by low to medium amplitude background represents quiet sleep.

Fig. 9

 9 Fig.9 Schematic illustration of physiological variables and their interactions in FMRI.

Fig. 10

 10 Fig.10 Diagrams of different types of hemodynamic response to stimulus reported in the developing human brain. (A) Hemodynamic response with an increase in oxygenated (HbO) and total hemoglobin (HbT) and a corresponding decrease in deoxygenated hemoglobin (HbR). (Positive BOLD in fMRI). B and C are negative BOLD in fMRI. (B) The pattern suggests that functional hyperemia is insufficient to meet oxygen demands of the tissue, resulting in an increase in HbT, HbO, and HbR. (C) A decrease in HbT accompanies an increase in HbRsuggesting vasoconstriction amplifying increases in HbR (M.Kozberg, 2016).

Fig. 11 Fig. 12

 1112 Fig.11 Vascular structure in the human temporal cortex obtained by vascular casting and electron scanning microscopy. 1, pial artery; 2, long cortical artery; 3, middle cortical artery; 4, short cortical artery; 5, cortical vein; 6, subpial zone; 7, precapillary vessels with blind endings; 8, superficial capillary zone; 9, middle capillary zone; 10, deep capillary zone. Scale bar=375um (Reina-De La Torre et al., 1998).

Fig. 13

 13 Fig. 13The direction of flow in the PDA in preterm infants 2 .

  Stage I: subependymal hemorrhage, Stage II: intraventricular hemorrhage with normal ventricles, Stage III: intraventricular hemorrhage with dilatation, Stage IV: intraventricular hemorrhage with intraparenchymal extension. 50-60% of children with hemorrhage (lower than 32 wGA) with ventricular dilatation or parenchymal involvement develop cerebral palsy. The primarily imaging technique (such as CT and MRI) used for the diagnosis of IVH in the newborn.

  Fig. 14 Left, Massive intraventricular hemorrhage distending the lateral ventricles (Whitelaw, 2011). Right, IVH grades I-IV (Merestein, 1998).

  Fig. 15 (A) shows one sample fOI channel of grand-average of HbO (red lines), Hb (blue lines) changes for healthy (solid lines) and IVH (dotted lines) neonates during auditory stimulation. Horizontal red thick bars indicate the period of the stimulation (20 seconds). This response was pronounced for the healthy neonates, with a significant increase in HbO. (B) Comparison of the mean AUC changes of Oxy-Hb induced by auditory stimulation between healthy and IVH infants. For each hemisphere, activations were significantly reduced in the IVH group compared to the healthy group.

  Chapter 1: Introduction & background Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State.

  bands: delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), beta (12-30 Hz), and gamma (>30 Hz).

Fig. 1 .

 1 Fig. 1. Absorption spectra (natural logarithm base!) for different chromophores present in human tissue. Shown are the spectra for O2Hb, HHb, proteins, water, collagen, fat, and cytochrome oxidase (CtOx) in the region from 100 nm

  to the tissue blood volume fraction. With these assumptions, the relative change of αD 𝑩 equals the relative change of the cerebral blood flow (CBF).

Fig. 3

 3 Fig.3 (a) Schematic of a diffuse correlation tomography in a turbid medium. Sources and detectors are placed on the "air-side" of the tissue. The photons undergo scattering, absorption and experience Doppler shifts when they scatter from moving particles. The motion of the scatterers leads to fluctuations in intensity which are detected by a photon counting detector. (b) The temporal autocorrelation functions of the intensity are then calculated using an

  CaO2 and CvO2 [mol/dl] are the arteriolar and venous O2 concentrations, where venous oxygenation is SvO 2 = (SO 2 -a × SaO 2 ) b ⁄ (a+b=1), and the arterial: venous (a:b) contribution ratio is 1/4:3/4. In the formula CMRO2i = (HGB × CBFi × (SaO2 -SO2)) / (4 × MWHb × β), the factor 4 implies the four O2 molecules bound to each hemoglobin and b is the percent contribution of the venous compartment to the hemoglobin oxygenation measurement. 4) To assign different fractions of functional changes versus baseline values of HbR and HbT concentrations in the venous compartment with respect to the total volume fractions, the rCMRO2

Fig. 5

 5 Fig.5 Volume clamp setpoint by Physiocal: determine the unloaded volume setpoint from the pressure volume pulsations over a limited number of heartbeats when the counter pressure is gradually varied from zero to suprasystolic. Left panel: intra-arterial pressure (red), counter pressure generated in the cuff (blue) and the volume signal from the plethysmograph (purple) for 15 beats[START_REF] Ehrenfeld | Monitoring Technologies in Acute Care Environments: A Comprehensive Guide to Patient Monitoring Technology[END_REF].

Figure 7 .

 7 Figure 7.A shows the transfer function amplitude (top line), the frequency-dependent filter amplitude (bottom line) and the expected result of the overall transfer function amplitude (middle line) of one subject. It is substantial that the transfer function amplitude should be as close as possible to 1. A deviation from this value will apply amplification or attenuation on the signal and make the distortion on the signal. As a fixed anti-resonance frequency at around 8Hz is used for all subjects, it will create discrepancies in the case subjects having their transfer function resonating at 5 Hz for example.

Fig. 6

 6 Fig.6Site of pressure measurement: because of reflections at the periphery (arterioles, capillaries), the arterial pressure waveform shapes change from rounded at the aortic sites to slightly peaked at the brachial site to more peaked at the more peripheral radial and finger artery sites[START_REF] Ehrenfeld | Monitoring Technologies in Acute Care Environments: A Comprehensive Guide to Patient Monitoring Technology[END_REF].

Fig. 7 A

 7 Fig.7 A) Transfer Function Amplitude Comparison; B) Reconstruction of brachial blood pressure (gray line) from the finger blood pressure (black line) [from FMS website].

  resistance element (RP) refers to the Poiseuille resistance of all vascular beds entirely[Wesseling

Fig. 8

 8 Fig.8 A) Pressure waveform; B) Model flow method; C) Aortic flow waveform

  impact of near-infrared laser in advanced noninvasive optical brain imaging

  ability to perceive changes in skin temperature depends on a number of variables including the location of the simulation, the amplitude and rate of the temperature change, and the baseline temperature of the skin. The rate that skin temperature changes influences how readily people can detect the change in temperature. If the temperature changes very slowly,

  sizes and different head tissue characteristics on neonatal and adult quasirealistic head models, that has been published in Neurophotonics journal; Nourhashemi M, Mahmoudzadeh M, Wallois F. "Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging. Neurophotonics". 2016 Jan;3(1):015001. doi: 10.1117/1.NPh.3.1.015001. Epub 2016 Jan 14.

Fig. 1

 1 Fig. 1 (a) Geometrical structure of 3D-CAD composed of six layers (skin, fat, skull, dura, CSF and brain) (inset shows a zoom up region). The origin was situated immediately under the source. (b) Distributions of the photonfluence rate in the head calculated in the head model.

Figure 2

 2 Figure 2 shows the various temperature change profiles as a function of the radial distance around an optical fiber tip (Laser spot size=1mm) in six different layers of the head models (skin, fat, skull, dura, CSF, brain) under steady-state conditions (Fig. 2a: Adult, Fig. 2b:

Fig. 2

 2 Fig. 2 Temperature changes according to radial distance from the laser source with various powers: 1 mW, 10 mW to 100 mW ten by ten (0.127 W/cm2 < I < 12.73 W/cm2), for a six-layered head model (skin, fat, skull, dura, CSF and brain) obtained from numerical simulations (inset shows a zoom up region). (a) Adult head model. (b) Neonatal head model. (c) Temperature changes at the depth of 0.4mm with various powers: 10 mW to 100 mW in 10 mW increments over time .

Fig. 3

 3 Fig. 3 Temperature changes according to the radial distance from the laser source (I = 3.81 W/cm 2 ) for six layers of adult and neonatal head model (skin, fat, skull, dura, CSF and brain) obtained from numerical simulations.

Fig. 4

 4 Fig. 4 Comparative distributions of the normalized intensity of photons (I/I0) according to the radial distance from the laser source (I = 3.81 W/cm2) for six layers of adult (lower diagram) and neonatal head models (skin, fat, skull, dura, CSF and brain) obtained from numerical simulations.

85

  Fig. 5Comparative temperature changes according to the radial distance from the laser source (I = 3.81 W/cm 2 ) between six layers of the head model (skin, fat, skull, dura, CSF and brain) (a) with blood perfusion and without blood perfusion in adult (b) the effect of different blood perfusion rates and metabolism on induced heat distribution in neonatal brain.

Fig. 7

 7 Fig. 7 The effect of laser spot size on the temperature distribution in (a) adult skin and (b) adult brain tissue.

  Figure. 9 shows the analysis of temperature changes in different tissues due to variations of the thickness of individual layers. Temperature changes were not largely affected by variations of the thickness of each layer: skin

Fig. 9

 9 Fig. 9 Temperature changes in different tissues due to variations in the thickness of individual layers.

Figure 10 .

 10 Figure 10. Curves M are derived from the Monte Carlo method, whereas curve D is derived from the diffusion theory.

92

  Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

Fig. 10

 10 Fig. 10 Comparisons between the Monte Carlo method and the diffusion theory in terms of (a) distribution of fluence rate (b) the diffuse Reflectance, Transmittance. (c) Fluence J/cm2 (inset shows relative errors between the results of the Monte Carlo method and the diffusion theory).

  impact of near-infrared laser in advanced noninvasive optical brain imaging

  impact of near-infrared laser in advanced noninvasive optical brain imaging

  impact of near-infrared laser in advanced noninvasive optical brain imaging combination of simulation and adequate in vitro experiments could help to develop a more effective optical imaging to avoid any possible tissue damage. 100 100 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

  Fig. 11Geometrical structure of 3D-CAD composed of six layers(skin, fat, skull, dura, CSF and brain)

Fig. 12

 12 Fig. 12Geometrical structure of 3D-CAD composed of six layers(skin, fat, skull, dura, CSF and brain)

  impact of near-infrared laser in advanced noninvasive optical brain imaging that the heat transfer occurs in the form of free convection into the air (Heat transfer by radiation at the surface into the air was neglected)[START_REF] Alawadhi | Finite element simulation using ANSYS[END_REF]:

  impact of near-infrared laser in advanced noninvasive optical brain imaging

  𝐽(𝑟, 𝑡) + 3 ∫ 𝑄(𝑟, Ω, 𝑡) Ω 𝑑Ω + 3µ 𝑠 𝑔𝐽(𝑟, 𝑡). (9)Assuming isotropic sources (Q(r,Ω,t) = Q(r,t)), the integral over Q in equation above is zero. Furthermore, if we also assume slow temporal variations in the photon flux J, then (1/v)∂J/∂t in equation above can be neglected compared with (µ 𝑡 -µ 𝑠𝑔 ) 𝐽. results in the photon diffusion equation for the photon fluence rate: ∇. (𝐷(𝑟)∇𝛷(𝑟, 𝑡)) -𝑣µ 𝑎 (𝑟)𝛷(𝑟, 𝑡)

  impact of near-infrared laser in advanced noninvasive optical brain imaging On the other hand, when cautiously applied (in the presence of high absorption for instance, or very close to laser sources) the diffusion approximation has produced experimentally very good results, in most cases better than what was expected.This could be because we are facing with volume averaged quantities measured with real detectors. Thus the question still remains: what are the limits of validity of the diffusion approximation? According to the reference, there is no straight answer to this question. Distances smaller or equivalent to the average distances between particles does not hold much significance neither in the context of the RTE nor the context of the diffusion approximation. Similarly, time scales that confine light propagation to such small volumes should not be considered when dealing with diffuse light.

  Fig.14 (a) Temperature changes at the depth of 0.4mm with various powers: 10 mW to 100 mW in 10 mW increments over time and (b) fluence changes for a constant power over time.

Fig. 15

 15 Fig.15 Eye safety of laser (https://www.laserdentistry.org/uploads/files/conference/2014/Handouts/Benjamin-LeBeau--Laser%20Safety%20Officer%20Training%20Handout.pdf)

  in agreement approximately with our result (both in the shape and attenuation ratio). Following figure (a, on left) shows the delta temperature attenuation is almost one order of magnitude 111 111 Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging per mm for 9.8mw, and figure (b, on right) shows the delta temperature attenuation (from 42°C to 39°C equal to delta temperature=3°C) at 3mm depth from the surface.Ito et al. studied the heating effect of near-infrared irradiation at 789 nm, a 0.101°C/mW temperature elevation was detected at a depth of 0.5 mm in the human forearm (µa(forearm) = 0.2cm -1 (Vo-Dinh, 2014)). Our results are showing temperature increases on the scalp (with µa(skin) =0.2cm -1 ) NIR-light at 800 nm with 30mW power, a 2.7°C temperature elevation was detected at a depth of 0.4 mm in the scalp. On the other hand, for 1 mW power the temperature increase at the depth of 0.4 mm in the scalp (with µa(skin) =0.5cm -1 ) equal to 0.16°C. This has been added to the discussion.

Fig. 16

 16 Fig.16 Interpolated temperature map with overlayed contour map, (a) adapted from Ito et al. for 9.8 mW irradiation in human forearm, (b) Spatial temperature distribution of our model for 30 mW.

  impact of near-infrared laser in advanced noninvasive optical brain imaging ➢ Effect of brain metabolic rate:

  Fig.17 Temperature changes in different tissues due to variations in scattering coefficient of individual layers.

  (It is similar to the temperature changes shown in the following figure, Ashley J. Welch, 2011, page 865 (Welch and van Gemert, 2011)).

Fig. 18

 18 Fig.18Ashley J.[START_REF] Welch | Optical-Thermal Response of Laser-Irradiated Tissue[END_REF]Welch, , page 865. 1989. .

  impact of near-infrared laser in advanced noninvasive optical brain imaging

Fig. 20

 20 Fig.20Relation of temperature, power and spot size with the same irradiance in the skin. (R.Henderson, 2004).

Introduction

  Coupling between cerebral blood flow (CBF), cerebral blood volume (CBV) and cerebral metabolic rate of oxygen (CMRO2) is an important primary function of the microcirculation[START_REF] Kleinman | Hemodynamics and Cardiology: Neonatology Questions and Controversies[END_REF][START_REF] Roy | On the Regulation of the Blood-supply of the Brain[END_REF], as the brain requires a continuous supply of glucose and oxygen (O2) provided by CBF and blood oxygen content to meet cellular oxygen requirements[START_REF] Kleinman | Hemodynamics and Cardiology: Neonatology Questions and Controversies[END_REF]. Identification of a causal relationship between relative cerebral blood volume (rCBV)-relative cerebral blood flow (rCBF) and relative cerebral metabolic rate of oxygen (rCMRO2)-relative cerebral blood flow (rCBF) under resting physiological conditions in the neonatal brain could help to elucidate the principles of cortical hemodynamic function during development.

( 124 Chapter 4 :

 1244 [HbT] ([HbO]+[Hb]) that is equivalent to relative changes in CBV. The relative changes in CBF are proportional to the relative changes in tissue blood flow related to the motion of red blood cells that can be measured by the DCS device(Durduran et al., 2010d).124 Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain Estimation of rCMRO2 by optical imaging requires measurement of rCBF and oxygen extraction fraction (OEF). According to Boas and Payne[START_REF] Boas | Comment on 'Estimating a modified Grubb's exponent in healthy human brains with near infrared spectroscopy and transcranial Doppler[END_REF], CBF can be estimated from CBV by inverting Grubb's equation, which allows CMRO2 to be estimated from CBV.

  Hospital local ethics committee according to the guidelines of the Declaration of Helsinki of 1975 (CPP Nord-Ouest II-France IDRCB-2008-A00704-51). Parents were informed about the study and provided their written informed consent.

126 Chapter 4 :

 1264 near-infrared (NIR) light to noninvasively quantify CBF. The light scattered by moving red blood cells causes temporal fluctuation of the detected light intensity. The time lag of these fluctuations is quantified by the intensity-time autocorrelation function of the detected light.126 Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

127 Chapter 4 :

 1274 Figure 1(b) shows the diagram of the combined DCS-NIRS probe. DCS probe: The tips of the source and detector fibers were angled to 90º and tightly held in place by a flexible rubber material. Four detectors (blue circles) were set up in a multicore arrangement away (dDCS = 2 cm) from the emitter (red circle), creating 4 measuring 127 Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain points (channels) over the frontal area. A special DCS probe made of soft, flexible rubber (3 mm thick) was designed to comfortably hold the source and detector fibers on the infant's head. NIRS probe: The NIRS probe comprising 2 detectors and 1 source and the emitter-detector distance of the continuous-wave optical NIRS probe was 3 cm. The NIRS source contained three wavelength emitters (735, 810 and 850 nm) (bottom right_hand corner) SO2 (tissue oxygenation) was measured by using the Spatially Resolved Spectroscopy(SRS) method. SRS is a method used to calculate concentrations by measuring the change of light attenuation (A) over distance (d), i.e. 𝜕𝐴 𝜕𝑑 , as shown in Figure 1(b). Data processing and statistical analysis Off-line analysis was performed using in-house MATLAB scripts for CBF measured by Neuro-Monitor-FloMo (Hemophotonics SL, Spain), and for CBV (total hemoglobin, HbT=HbO+HbR) and oxygen extraction fraction (OEF) measured by NIRO-200NX (Hamamatsu Photonics Corp, Tokyo, Japan).

  between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

  Fig. 1 (a) The infants were tested with the DCS and CW-NIRS systems, (b) Diagram of the combined DCS-NIRS probe, (c) Diagram of the calculation of rCMRO2 by NIRS data and rCBF by DCS data.

  between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain on times-series with identical probability variables and a flat distribution of quantized values. The original normal distribution of the two variables (rCBF and rCBV) is shown in Figure 2(a).

  between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

Fig. 2

 2 Fig. 2 (a) Distribution histogram of rCBV and rCBF, (b) Time-series of rCBV and rCBF expressed as quantized values to produce time-series with identical probability variables, (c) Flat distribution of rCBV and rCBF, (d)Diagram of the surrogate data approach to the rCBF-rCBV coupling hypothesis.

Chapter 4 :

 4 Fig. 3 (a) Correlation between log(rCBV)_log(rCBF), (b) Amount of information shared between rCBF and rCBV measured by MI, TE indicates the amount of information exchanged from rCBF to rCBV and vice versa and Directionality index(D). (*all values are multiplied by 10 3 ).

  between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

Fig. 5 Chapter 4 :Fig. 6

 546 Fig. 5 Directionality% (rCBV to rCBF ) as a function of (a) GA at the time of the test (weeks), (b) Vascular resistance index, (c) Apgar score at 1 min and (d) Apgar score at 5 min. R 2 and the linear regression equation are indicated in the upper right corner of the graph.

Chapter 4 :

 4 Grubb's equation (β=0.9) (Roche-Labarbe et al., 2010). The effect of different constant β values (0.1, 0.2, 0.3, 0.4, 0.75, 1, 2) on transfer entropy 138 138 Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

Fig. 7 Chapter 4 :Fig. 8

 748 Fig. 7 Impact of time-lagged rCBF on rCMRO2 with different time lags (0.8s, 1.6s, 2.2s, 2.4s) (a) Amount of information shared between rCBF and rCMRO2 measured by mutual information (MI), (b) Transfer entropy (TE) indicates the amount of information exchanged from rCBF to rCMRO2 and vice versa with different time lags, (c) Directionality index D indicates the dominant direction of the transfer, the negative sign indicates the dominance of rCMRO2 over rCBF and vice versa.

Chapter 4 :

 4 Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

Chapter 4 :Fig. 9

 49 Fig.9 Phantom test designed to check the system time-lag. Top: An Arduino ® causes a connected LED to flash off and on at 5-second intervals. Bottom: time lag between the marker and the optical signal in CW-NIRS(200ms)

Fig. 10

 10 Fig.10 Scatterplots of A) z-score-rCMRO2 and z-score-rCBF, (B) z-score-rCBF and z-score-HbT, (C) z-score-SO2 and z-score-rCBF, (D) z-score-rCBF and z-score-HR, (E) z-score-rCMRO2 and z-score-HR, (F) z-score-rCBF and z-score-MBP, (G) z-score-rCMRO2 and z-score-MBP.

  Fig.11 Grand average of relative changes in blood flow, oxy, deoxy and total hemoglobin.

Fig. 13

 13 Fig.13The time traces ofZ-score-beta (subject #2, 10)

Fig. 15

 15 Fig.14 Comparing between the correlation of (HBT-CBF) and (log(HBT)-log(CBF)) (subject #10).

  between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

  Fig.16 Dynamics of various vascular responses. Total hemoglobin concentration (Hbt, green line) leads CBF response (black line) throughout the response cycle for both the short stimulus (A) and the repeated stimuli (B). Each curve is the average response to 24 stimulation periods during a single experiment. Horizontal arrows mark the temporal difference between the curves when they had reached 50% of their maximal amplitude (marked by thin, vertical lines) during the uprising phase and during the decay to baseline.HbR curve appears to lead all other components, and it reaches its peak before all other curves. Notice the delays of both the CBF (marked by arrow) and the HbO2 onsets after the stimulus onsets. At onset, Hbt change is entirely composed of HbR elevation, whereas at the later phase it is predominantly HbO2. Because of fluctuations of HbO2 (and thus Hbt) before stimulation, its onset is determined as time when its rate of change increased. Asterisks mark the maximum of HbO2 and the minimum of HbR(Malonek et al., 1997a).

Fig. 17

 17 Fig.17Correlated dynamics of CBF to HbR and to Hbt for short stimulus. Phase plots show the dependence of CBF changes on HbR and Hbt after 2 sec of stimulation. Along the curves, intervals between the circles represent 0.5 sec, and the first four segments (five circles) are during stimulation. An asterisk marks the stimulus onset, and an arrow marks the onset of CBF, when an observable change in its rate of change is detected. (A) After stimulation onset (pink asterisk), HbR increases, whereas no observable change in CBF is seen for more than a second. As CBF starts to increase (arrow), the rate of change of HbR starts to decrease and becomes negative 1 sec later. At the last phase of the response (red asterisk), an inverse relation between the parameters is seen; an increase in CBF is accompanied by a decrease in HbR and vice versa. (B) An exponential dependence of CBF on Hbt is seen during the first 4.5 sec after stimulus onset. Throughout the response cycle, changes in Hbt lead changes in CBF by about 1-2 sec(Malonek et al., 1997a).

Fig. 19

 19 Fig.19 Comparison of the time series of CBF and Hbt following electrical stimulation of the whisker pad. (b) The mean time series of CBF and Hbt for all stimulation intensities normalized with respect to to the baseline control period and peak. This allows further comparison of the temporal dynamics of flow and volume.

  is an extremely dynamic organization undergoing essential development in connectivity and function. The developmental course of cortical hemodynamics in the neonatal brain reflects, to a certain extent, the gradual maturation of neurovascular coupling. Several functional imaging investigations of the developing brain have found patterns of hemodynamic responses that contrast from adult. This discrepancy is partly due to that neurovascular coupling that is still developing in the neonatal brain. Both neural and vascular organizations spread and are then highly selectively pruned in early brain development. The elaboration and refinement of both neural and vascular networks need exogenous inputs as well as endogenous spontaneous activity within the primary developed wiring. These modifications are presumably to influence early neonatal neurovascular coupling, and likewise may influence functional imaging measurements in this population.

  Coupling in the Developing Neonatal Brain in Resting State occurrence of spontaneous bursts of cerebral electric activity. Data were acquired by using the multimodal EEG-NIRS-DCS technique adapted for neonatal imaging. The bursts of electroencephalographic activity in neonates (<35 wGA) in resting state were found to be coupled to a transient hemodynamic response involving different types of hemodynamic response including (a) positive stereotyped hemodynamic responses (increases in HbO, decreases in HbR together with increases in CBF and CMRO2), (b) negative hemodynamic responses (increases in HbR, decreases in HbO together with decreases in CBF and CMRO2), (c) Increases and decreases in both HbO-HbR and CMRO2 together with no changes in CBF.

  Coupling in the Developing Neonatal Brain in Resting State couple regional blood flow in response to local metabolic demands known as the Neurovascular

  Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

165

  Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

166

  Fig.1 (A) Schematic representation of the location of the EEG and optical probes on an infant's head. (UP) View of the hybrid optical probe constructed with a flexible hypoallergenic material and composed by three sectors, one for the DCS probe (The tips of source and detector fibers were bent 90º and tightly held in place by rigid plastic material), one EEG and the other for the NIRS. Diagram of the frequency-domain multiple-distance (FDMD); the four emitters (red squares) are arranged on multi-distance patch far from detector (Gray square), creating 4 points of measure (channels) over frontal area. (B). Diagram of the hemodynamic responses (HbO, HbR, calculated HbT and TOI by NIRS data, rCBF by DCS data and calculation of rCMRO2 by NIRS data) and Schematic presentation of the algorithm. |NLEO| applied on EEG signal, Classification of Hemodynamic responses to EEG bursts.

  To identify linear relationship between EEG and NIRS data, changes in rms of hemodynamic signals were plotted as a function of rms of EEG. A significant linear correlation was found between the amplitude of the rms of the bursts and the amplitude of the rms of the hemodynamic responses (HbO, HbR, TOI, CBF and CMRO2) (Fig.S.3).

  Figure S.4 shows the values of Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State directionality=(TENIRS→EEG)-(TEEEG→NIRS) for the 31 neonates, resulting in a fluctuating directionality between EEG and NIRS (DCS) with a tendency toward a negative directionality in 23∕31 (21/31) preterms and a positive directionality in the remaining 8 (10) preterms. The negative values of the directionality suggest that EEG was predominant over NIRS. Wavelet real-time analysis of NVC in healthy and PDA premature Significant in-phase coherence between the amplitude of the different hemodynamic parameter and the amplitude of the EEG burst were analysis by wavelet coherence. The Wavelet-based coherence was first calculated in a healthy premature neonate, in the wavelet scale of 25-30 minutes equivalent to a very-low-frequency (VLF) range of 0.003-0.125 Hz and then compared to PDA preemies. Wavelet-based hemodynamic responses (CBF-EEG, CMRO2-EEG, HbO-EEG, HbR-EEG, TOI-EEG) coherence showed decreased NVC for a premature neonate with PDA compared to healthy (Fig.3.A-B). Figure 3.A-B highlights a case example of high NVC in a healthy premature neonate and low NVC in a PDA preemie. According to the boxplot distribution Fig.3.C at the group level, the NVC coherence was lower in PDA prematures (not significant) compared to healthy. Significant differences were observed in CBF-EEG and CMRO2-EEG coherences between normal and IVH groups, (CBF-EEG: median IQR 20.3[17.2-22.8] vs 22.2[21.2-26.9], p = 0.03), (CMRO2-EEG: median IQR 18.8[17-24.3] vs 25[21.7-27.3], p = 0.02) (Fig.S.5). It should be underlined that in contrast to this wavelet analysis, the pattern of the hemodynamic responses to EEG bursts (different conditions) (Fig.S.6-7) in PDA and IVH patients was similar to those in healthy neonates. The boxplot distribution of maximum amplitude of the hemodynamic responses in (Fig.S.8-9) shows that there is no significant difference between PDA (IVH) new-borns compared to healthy.

Figu. 2

 2 Figu.2 The grand average of the regional hemodynamic responses of the onset of EEG bursts at 0s (the time duration was shown 20s before and 30s after the onset of EEG burst, the first 10s was defined as a baseline). The longitudinal panels indicates envelope-derivative of EEG and moving average of envelope-derivative over all EEG bursts in one subject (I), the grand average of changes in HbO_HbR measured by ISS (II), the grand average of changes inHbO_HbR measured by Hamamatsu (III), the grand average of changes in TOI (IV), CBF (V) and CMRO2 (VI). The vertical panels related to the classification of the burst of activities, with no EEG burst during previous 20s (A1), one EEG burst during the first 20s (A2), two EEG bursts during the first 20s (A3) and the vertical panels (B and C) related to the burst of activities that accompanying with increase in both HbO_HbR (B) and decrease in both HbO_HbR (C). The annotations below the signal highlighting the times duration of hemodynamic response were significantly different from the reference period (-20 to -10 s), light stars related to (t-test, p<0.001) and dark stars related to (t-test, p<1.1e-6). Shaded error bars indicate the standard deviations for the corresponding signals at each time-point.

Fig. 3

 3 Fig.3 (A) An enlarged segment of the real-time CMRO2 and EEG data of a sample healthy premature neonate #15 (UP); in a sample premature neonate with Patent ductus arteriosus #28 (Down). (B) Wavelet-based hemodynamic responses (CBF-EEG, CMRO2-EEG, HbO-EEG, HbR-EEG, TOI-EEG) coherence showing intact neurovascular coupling (NVC) in a healthy premature neonate #15. Squared wavelet coherence, R2hemodynamic responses →EEG, where the x-axis represents time in minute, the y-axis represents the range of frequencies, and the color scale represents the magnitude of R2. Significant coherence between the (CBF, CMRO2, HbO, HbR, TOI) and EEG is seen in a very low frequency (VLF) range of 0.0003-0.125 Hz (UP), in a sample premature neonate with Patent ductus arteriosus #28 (DOWN). (C) The boxplot distribution of percentage of area for significant NVC coherence per total considered area over the frequency range of 0.003-0.125Hz between two groups: with PDA(n = 9) and without PDA(n = 23). (D) The percentage of area with high NVC coherence per total considered area for each premature neonate as a function of age.

  2.A3), the increase in HbR mainly reflects venous hypoxia, whereas in volume changes conditions (Fig.2.B-C), the changes in HbR mainly reflects changes in venous blood volume. The increase or decrease in CBV could be related to the different contribution of vascular compartments in NVC. As Huber et al. demonstrated that the inhibitory stimuli are associated with decreases in CBV (in negative BOLD) due to constriction of surface arteries, while the excitatory Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

  Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

  Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

  part of the French public hospital Clinical Research Project (PHRC National). The study was approved by the Amiens University Hospital local ethics committee according to the guidelines of the Declaration of Helsinki of 1975 (CPP Nord-Ouest II-France IDRCB-2008-A00704-51). Parents were informed about the study and provided their written informed consent.

M:

  Male, F: Female, GA: Gestational Age, Brain US: Brain ultrasonography, PAH: pulmonary arterial hypertension, PRS: positive rolandic spikes. Hybrid EEG-NIRS-DCS DCS/NIRS/EEG devices were synchronized and all data were acquired simultaneously from the frontal area of premature neonate at the resting state. The overall measurement duration was between 30 and 40 minutes for each subject including discontinuous activity during quiet and active sleep as required by clinical purposes (du Plessis, 2009b).Because EEG recordings were used for clinical needs, a standard 10-20 montage adapted for neonates were used. Measuring simultaneously the optical properties of the tissue by NIRS and DCS can provide useful information's about blood flow and tissue oxygenation. The optical devices are time-multiplexed (i.e. turn the sources were turned on/off so as the brain tissue is illuminated for either DCS or NIRS at any given time). Any marked events in DCS were also registered by the EEG and NIRS devices.

Fig. S3

 S3 Fig.S3The correlation between rms of the hemodynamic responses and rms of envelope derivative of EEG bursts (IBIs of bursts are more than 20s).

Fig. S5

 S5 Fig.S5The boxplot distribution of percentage of area for significant NVC coherence per total considered area over the frequency range of 0.003-0.125Hz between two groups: with IVH and without IVH.

189

  Fig. S6The grand average of the regional hemodynamic responses of the onset of EEG bursts (5 conditions), compared between two groups of normal and pathological premature neonates (with PDA).

  noninvasive nature of optical approaches renders them useful in the neonatal ICU for use in humans. In addition, multiple techniques are combined in order to measure signals from multiple sources, not just hemodynamic but also neuronal. The combination of multiple approaches allows us to draw conclusions on the coupling dynamics between these different sources of the signals. In our data, it is clear that neurovascular uncoupling may be specific to pathological brain states. This chapter reviews the objectives and contributions that are presented in this thesis. Finally I give an account of future perspectives of this thesis.

Fig. 1

 1 Fig. 1 summery of thesis.

  Fig. 1 (A) Scatterplots of z-score-CBF and z-score-MBP and (z-score-CMRO2, z-score-MBP) (with calculated R and p-value), (B) Autoregulation curve; cerebral blood flow in relation to artery lumen diameter. Dotted lines represent the lower and upper limits of cerebral blood flow autoregulation. The circles in colors represent the mean value of CBF and MBP for each individual premature neonates.

Fig. 2

 2 Fig. 2 HRF, Convolution of envelope-derivative of EEG and estimated HRF is compared with the simultaneously recorded HbO, (sub1).

Fig. 3

 3 Fig. 3 Stimulation somatosensory was applied on the hairless skin.

  multiscale recordings of EEG and optical signal (NIRS, DCS), that evaluate the hemodynamic responses of absence seizure occurring in epileptic children.To evaluate changes in hemodynamic responses in absence seizure area, six children with absence seizure were simultaneously recorded with EEG, NIRS and DCS. Figures4 and 5as initial results, illustrates how the seizure discharges with maximal amplitude in ictal areas induced a change in local hemodynamic parameters characterized by the first decrease in HbO, rCBF followed by an increase in HbO, rCBF and decrease in HbR.

Fig. 4 Fig. 5

 45 Fig. 4 High-resolution EEG in a premature during the recording seizures.

Chapitre 3 :

 3 photothermique du laser NIR d'imagerie optique sur les modèles de tête quasi réalistes néonataaux et adultes. Nous avons modélisé l'effet thermique de différentes puissances de laser avec différentes tailles de fibres et différentes caractéristiques de tissu de tête. Ceci a été réalisé par simulation numérique en développant une analyse par éléments finis. Les résultats du chapitre 3 peuvent permettre d'optimiser les paramètres des lasers pour une variété d'applications cliniques, notamment concernant les études menées sur le cerveau de l'adulte et du nouveau-né.

  photothermiques avec les tissus, provoquées par l'élévation de température due à l'irradiation laser, qui peut endommager les tissus, y compris en provoquant une dénaturation des protéines, une augmentation de la perméabilité de la membrane mitochondriale et finalement la vaporisation. Les augmentations de température peuvent également conduire à des changements dans le métabolisme cellulaire, la capacité de la membrane électrique et, à long terme, peuvent conduire à une nécrose. Cependant, les mécanismes responsables des dommages tissulaires causés par l'exposition à la chaleur sont complexes et encore mal compris.

Fig. 1

 1 Fig. 1 (a) Structure géométrique de la 3D-CAD composée de six couches (peau, graisse, crâne, dure-mère, LCR et cerveau) (l'encart montre une région zoomée). L'origine était située immédiatement sous la source. (b) Les distributions de la vitesse de photon-fluence dans la tête calculée dans le modèle de tête.

Fig. 2

 2 Fig. 2 Variations de température en fonction de la distance radiale de la source laser (I = 3,81 W / cm 2 ) pour six couches de tête adulte et néonatale (peau, graisse, crâne, dure-mère, LCR et cerveau) obtenues à partir de simulations numériques.

Fig. 3 Fig. 4

 34 Fig. 3 Distributions comparatives de l'intensité normalisée des photons ( I / I 0 ) en fonction de la distance radiale de la source laser (I = 3,81 W / cm2) pour six couches de tête adulte (schéma inférieur) et néonatal (peau, graisse, crâne) , dura, CSF et cerveau) obtenus à partir de simulations numériques.

Fig. 5

 5 Fig. 5 (a) Histogramme de distribution de rCBV et de rCBF , (b) les séries temporelles de rCBV et de rCBF exprimées en valeurs quantifiées pour produire des séries chronologiques avec des variables de probabilité identiques , c) Distribution à plat de rCBV et de rCBF , (ré) Diagramme de l'approche des données de substitution de l' hypothèse de couplage rCBF-rCBV .

Fig. 6

 6 Fig. 6 (a) Une partie sélectionnée de rCMRO 2 et rCBF (sujets # 4, # 10), illustrant l'évaluation de TE de rCMRO2 à rCBF, (b) Informations mutuelles partagées entre rCBF_rCMRO2 , (c) Taux d'information (TE) échangé de rCBF à rCMRO 2 et vice versa , (d) Indice de directionnalité (D). (* toutes les valeurs sont multipliées par 10 3 ).

Fig. 7 (Fig. 8

 78 Fig. 7 (A) Représentation schématique de l'emplacement des sondes EEG et optiques sur la tête d'un nourrisson. (UP) (B). Diagramme des réponses hémodynamiques ( HbO , HbR, calculé HbT et TOI par les données NIRS, rCBF par les données DCS et le calcul de rCMRO2 par des données NIRS) et présentation schématique de l'algorithme. | NLEO | appliqué sur le signal EEG, la classification des réponses hémodynamiques aux salves EEG.

  L'ctivité des bouffées neuronales physiologiques spontanées de nouveau-nés prématurés (<35 SAG) au repos est couplée à différents types de réponses hémodynamiques : a. Réponses NIRS positives (augmentation de HbO, diminution de HbR avec augmentation de CBF et CMRO2), b.

Fig. 9

 9 Fig. 9 (A) Un segment agrandi des données CMRO2 et EEG en temps réel d'un échantillon de nouveau-né prématuré sain # 15 (UP); dans un échantillon de nouveau-nés prématurés avec le brevet ductus arteriosus # 28 (Down). (B) les réponses hémodynamiques à base d'ondelettes cohérence (CBF-EEG, CMRO2-EEG, HbO -EEG, HBr-EEG, TOI-EEG) montre un couplage neurovasculaire intact (NVC)

  Plusieurs progrès dans la technologie de neuroimagerie ont largement développé la recherche dans le domaine de la compréhension du couplage neurovasculaire. La neuroimagerie, et notamment «l'imagerie neurovasculaire», peut être considéré comme à l'intersection de différents domaines. Le couplage neurovasculaire est essentiel pour fournir les besoins en énergie du tissu cérébral pendant la fonction physiologique normale et dans les conditions pathologiques. Ainsi, les progrès dans les techniques d'imagerie fonctionnelle ont amélioré notre compréhension de la relation entre l'activité cérébrale et l'apport d'énergie dans le cerveau en développement. Alors qu'au début de l'imagerie cérébrale, chaque méthode d'imagerie cérébrale était utilisée séparément, de plus en plus d'études en recherche comme en clinique soulignent l'intérêt de combiner ces différentes techniques d'imagerie. Chaque chapitre de cette thèse décrit une combinaison de techniques appliquées aux nouveau-nés prématurés dans un cerveau sain ou pathologique. Il est utile que la plupart de ces approches puissent être adaptées à une variété de situations pour mesurer différents aspects du couplage neurovasculaire dans les états cérébraux normaux et pathologiques. Cette thèse a donc présenté un cadre à partir duquel un groupe d'études complémentaires pourrait être réalisé car les approches misent en place dans cette thèse peuvent s'appliquer à d'autres espèces d'autres zones du cortex ou d'autres conditions pathologiques. Ce qu'il faut souigner, c'est l'importance croissante et la puissance des approches optiques dans l'investigation du couplage neurovasculaire. De plus, la nature non invasive des approches optiques les rend adéquates dans les unités de soins intensifs néonatales. Dans cette thèse, plusieurs techniques ont été combinées afin de mesurer les signaux provenant de sources multiples, non seulement hémodynamiques mais aussi neuronales. La combinaison de plusieurs approches de manière simultanée nous permet de tirer des conclusions sur la dynamique du couplage entre ces différentes sources de signaux. Dans nos données, il est clair 225 225 Chapter 7: French Summary que le découplage neurovasculaire peut être spécifique aux états cérébraux pathologiques. Ce chapitre passe en revue les objectifs et les contributions présentés dans cette thèse. Enfin, je rends compte des perspectives futures de cette thèse. Dans cette thèse, une approche multimodale hybride EEG-NIRS-DCS a été utilisée pour mesurer les activités electro-hémodynamique du cerveau néonatal chez le prématuré au repos (Fig.10). Les différences de réponses fonctionnelles correspondent à l'immaturité du NVC, Le processus complexe de développement du NVC continue de se produire au cours de développement, ce qui incite à considérer le rôle de ce système en développement dans les pathologies neurodéveloppementales. Des perturbations ou des retards du NVC pourraient ainsi conduire à des anomalies dans le développement neuronal et vasculaire. Ceci pourrait avoir un impact profond sur le travail de thèse démontre la directionnalité de ces fluctuations lentes dans l'activité neuronale et hémodynamique. LeNVC peut être positif, négatif ou absent dans le cerveau du prématuré en réponse à une bouffée d'activité spontanée. Les principales réalisations de cette thèse ont été résumées sur la Fig. 10. La perspective Cette thèse fournit un aperçu d'une variété de techniques actuellement disponibles pour étudier le couplage neurovasculaire chez les nouveau-nés sains et pathologiques. La compréhension du couplage neurovasculaire normale en relation avec les fonctions sensorielles et les fonctions d'ordre supérieur comme la mémoire et le langage sera essentielle dans le

Fig

  Fig. 10 aperçu de la thèse.

Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain.

	Neurophotonics". 2017 Apr;4(2):021104. doi:
	10.1117/1.NPh.4.2.021104. Epub 2017 Apr 18.

•

Mina Nourhashemi, Mahdi Mahmoudzadeh, Guy Kongolo, Sabrina Goudjil, Fabrice Wallois. "Neurovascular Coupling

in the Developing Neonatal Brain in Resting State", submitted in PNAS. Posters • "Thermal Impact of Functional Near Infrared Optical Brain Imaging

" 2014, SNCLF Congrès de la Société de Neurophysiologie Clinique de Langue Française 25 -27 Juin 2014 ANGERS. • "

Thermal Impact of Functional Near Infrared Optical Brain Imaging

" 2014, FNIRS congress, 10-12 October Montreal.

• "

Multimodal Imaging of Neurovascular Coupling Relationship Between Spontaneous EEG, CMRO2 And Hemodynamic Responses In preterm Infants",ISCBFM congress

, 27-30 June Vancouver, Canada.

• "

rCBF -rCMRO2 Interrelation of Neonatal Premature Brain, A simultaneous NIRS -DCS analysis", OHBM

congress, 26 -30 June 2016 Geneva, Switzerland. • "

rCBF -rCMRO2 Interrelation of Neonatal Premature Brain

", FNIRS congress, 10-12 October 2016 Paris, France.

• "

rCBF -rCMRO2 Interrelation of Neonatal Premature Brain

",

ISCBFM congress, 1-4 April, 2017, Berlin, Germany.

Chapter 1: Introduction & background

Chapter 1: Introduction & background

Table 1 .

 1 INVERSE MATRIX COEFFICIENTS FOR HB, HBO2, AND CYTOCHROME AA3 AT DIFFERENT WAVELENGTHS

Table 1 .

 1 Maximum

	Wavelength (nm)	Exposure time, t (s)	MPE
	400-1400	10 -7 to 10	1.1×CA×t 0.25 (J.cm -2 )
	400-1400	10 to 3.0×10 4	0.2×CA (W.cm -2 )

permissible exposure (MPE) for skin exposure to a laser beam (From ANSI Z136.1-2014), t is the laser exposure duration, CA =10

0.002(λ-700)

: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

Table 2

 2 Tissue thickness (mm) of six-layer adult and neonatal head models

		Skin	Fat	Skull	Dura	CSF	Brain
	Adult	5

Table 3

 3 Thermal

		Thermal conductivity	Density	Heat capacity at
		(W/m.K)		constant pressure
			(kg/m 3 )	(J/(kg.K))
	Skin	0.420	1010	3500
	Fat	0.250	920	2500
	Skull	0.30	1810	1300
	Dura 4	0.44	1174	3364
	CSF 4	0.57	1007	4096

properties of the six layers of the head

(skin, fat, skull, dura, CSF and brain)

[START_REF] Demarco | Computed SAR and thermal elevation in a 0.25-mm 2-D model of the human eye and head in response to an implanted retinal stimulator -part I: models and methods[END_REF]

.

Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

	Brain	0.503	1043	3600

Table 4

 4 Heat equation parameters of the six layers of the head(skin, fat, skull, dura, CSF and brain) (DeMarco

Table 7 .

 7 Tissue thickness (mm) (H.

Table . 11

 . The brain perfusion rate measured in vivo with ASL-fMRI.

Chapter 3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging considering

  , Steve Jacques). By in vivo tissue parameter (table 3, Steve Jacques) and following equation (Steve Jacques):

	a	, a oxy	(1 )	, a deoxy	% [ ]	, a Water	% [ ]	, a Fat	% [ ]	a	,melanosome

Table . 12

 . absorption and scattering coefficients.

Table . 13

 . absorption coefficients.

8 http://omlc.org/news/jan98/skinoptics.html (Oregon Medical Laser Center) 114 114 Chapter

3: Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

Thermal impact of near-infrared laser in advanced noninvasive optical brain imaging

	Chapter 3:														116
		5					5									5
				Skin s =15.09cm -1					Fat s =8.30cm -1		Skull s =8.89cm -1
		4		Skin s =26.75cm -1		4			Fat s =22.12cm -1		4	Skull s =19.24cm	-1
	T°C	3				T°C	3									T°C	3
		2					2									2
		1					1									1
		0					0									0
		Skin	Fat	Skull Dura	CSF	Brain	Skin	Fat	Skull	Dura CSF	Brain	Skin	Fat	Skull	Dura CSF	Brain
		5					5
				CSF s =0.1cm -1					Brain s	=8.74cm -1
		4		CSF s =3.2cm -1		4			Brain s	=12.17cm -1
				CSF s =8cm -1
	T°C	3				T°C	3
		2					2
		1					1
		0					0
		Skin	Fat	Skull Dura	CSF	Brain	Skin	Fat	Skull	Dura CSF	Brain
											s	a		nm	b
																116

-

=

with the parameters of Table

1

in

[START_REF] Jacques | Optical properties of biological tissues: a review[END_REF]

] at a wavelength of 800nm, the brain scattering coefficient

Table . 1

 . Clinical features of the tested infants

			Chapter 4:
															125
	Infant number	Gender	GA at birth (wk)	GA at test (wk)	Birth Weight (g)	Test Weight (g)	Apgar (1 min)	Apgar (5 min)	Multipl e Birth	Delivery	Patent ductus arteriosus	Clinical conditions (Etiology)	Brain US	Drug use	EEG	Vascul ar resista nce index
	1	M	31 1/7	32 1/7	1250	1285	7	8	No	caesarean	Closed ductus	HELLP syndrome preeclampsia	normal	_	normal	0.70
	2	F	25 5/7	28 1/7	750	1110	7	8	No	vaginal	Closed ductus	Multiple pregnancy	bilateral IVH-II +
												-second twin died -	Intraventricular	ibuprofen	PRS	0.84
												chorioamnionitis	cysts
														125

Relationship between relative cerebral blood flow, relative cerebral blood volume, and relative cerebral metabolic rate of oxygen in the preterm neonatal brain

											chorioamnionitis-
	M	26 6/7	30 2/7	900	1350	9	9	Yes	caesarean	Closed ductus at 27 wk	T-T syndrome		expanding precerebral areas	_	normal	0.85
											multi gestation
											Chorioamniotitis-
	M	26 6/7	32	1200	NA	2	5	Yes	caesarean	Closed ductus at 27 1/7 wk	T-T syndrome		normal		_	normal	0.76
											multiple pregnancy
	F	28 4/7	30 5/7	1600	NA	7	8	No	caesarean	Patent ductus	prolapsed cord		suprasystemic PAH	ibuprofen	PRS	0.79
											maternal
	F	29	33 3/7	1000	2180	8	10	Yes	caesarean	Closed ductus at 29 1/7 wk	hypertension, preeclampsia, and	minor edema	cerebral	_	normal	0.77
											twin pregnancy
											maternal
	F	29	34	1249	1690	8	10	Yes	caesarean	Closed ductus at 29 4/7 wk	hypertension, preeclampsia	and	normal		_	normal	0.85
											twin pregnancy
													minor	cerebral
	F	33 3/7	35	1300	1360	10	10	Yes	caesarean	Closed ductus	Birth spontaneous triple	edema_ cardiac congenital	_	normal	0.61
													abnormalities CIV
											Diabetes gravidis;			Dopamin	normal	0.90
	M	26 4/7	29 3/7	790	1150	2	7	No	caesarean	Closed ductus	uterine bleeding;		bilateral IVH-III + hydrocephalus	e-ibuprofen
											Preterm labor				-
															lorazepa
															m
											metrorrhagia+
	F	26 1/7	27	950	1150	7	9	No	vaginal	Patent ductus	threat of premature	bilateral IVH-II
											delivery				ibuprofen	normal	0.69

M: Male, F: Female, GA: Gestational Age, Brain US: Brain ultrasonography, PAH: pulmonary arterial hypertension, PRS: positive rolandic spikes.

5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

  , suggest different hemodynamic patterns Chapter

Table . S1

 . Clinical features of the tested infants

			Chapter
	Infan t numb er	Gender	GA at birth (wk)	GA at test (wk)	Birth Weight (g)	Test Weight (g)	Apgar (1 min)	Apgar (5 min)	Multipl e Birth	Delivery	Patent ductus arteriosus	Clinical conditions (Etiology)	Brain US	Drug use	EEG	Vascula r resistan ce inde
	1	M	31 1/7	32 1/7	1250	1285	7	8	No	caesarean	Closed ductus	HELLP preeclampsia syndrome	normal	_	normal	0.70
												Multiple pregnancy -	bilateral IVH-II +
	2	F	25 5/7	28 1/7	750	1110	7	8	No	vaginal	Closed ductus	second twin died -	Intraventricular	ibuprofen	PRS	0.84
												chorioamnionitis	cysts
	3	M	26 6/7	30 2/7	900	1350	9	9	Yes	caesarean	Closed ductus at 27 wk	chorioamnionitis-T-T syndrome multi gestation	expanding precerebral areas	_	normal	0.85

5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

			Chapter 5:													180
	4	M	6/7	32	1200	NA	2	5	Yes	caesarean	Closed ductus at 27 1/7 wk	Chorioamniotitis-multiple pregnancy T-T syndrome	normal		_	normal	0.76
	5	F	4/7	30 5/7	1600	NA	7	8	No	caesarean	Patent ductus	prolapsed cord		suprasystemic PAH	ibuprofen	PRS	0.79
												maternal
	6	F		33 3/7	1000	2180	8	10	Yes	caesarean	Closed ductus at 29 1/7 wk	hypertension, preeclampsia,	and	minor cerebral edema	_	normal	0.77
												twin pregnancy
												maternal
	7	F		34	1249	1690	8	10	Yes	caesarean	Closed ductus at 29 4/7 wk	hypertension, preeclampsia and twin	normal		_	normal	0.85
												pregnancy
															minor	cerebral
	8	F	3/7	35	1300	1360	10	10	Yes	caesarean	Closed ductus	triple Birth	spontaneous	cardiac congenital edema_	_	normal	0.61
															abnormalities CIV
	9	M	4/7	29 3/7	790	1150	2	7	No	caesarean	Closed ductus	Diabetes Preterm labor uterine bleeding; gravidis;	hydrocephalus bilateral IVH-III +	ibuprofen--Dopamine	normal	0.90
																	lorazepam
												metrorrhagia+
	10	F	1/7	27	950	1150	7	9	No	vaginal	Patent ductus	threat of premature	bilateral IVH-II	ibuprofen	normal	0.69
												delivery
											(Patent ductus)
											Closed ductus
		F		32 2/7	1730	1615	7	10	No	caesarean	at 32 1/7 wk	preeclampsia		normal	_	normal	0.73
																	Dobutamn
	12										Closed ductus	MAP sur pré				/noradrena	0.65
		M	3/7	31 4/7	1505	1350	5	_	No	caesarean	at 29 2/7 wk	eclampsie		normal	line	normal
												Respiratory distress
												secondary to hyaline
		F		31 1/7	1255	1285	8	10	Yes	caesarean	Closed ductus	membrane disease	normal	_	normal	0.69
	14	M		31 1/7	1230	1210	9	9	Yes	caesarean	Closed ductus	Twin pregnancy	normal	_	normal	0.71
	15	M	2/7	33 6/7	1950	1978	10	10	No	vaginal	Closed ductus at 32 4/7 wk	MAP		normal	_	normal	0.7
	16	M		30 6/7	1370	1615	9	10	No	vaginal	Closed ductus at 29 3/7 wk	CPAP-MAP		bilateral IVH-I	cafeine	normal	0.75
											(Patent ductus)	MAP-RCIU
											Closed ductus	triamniotique
		M	4/7	31 6/7	1255	1335	10	10	1	caesarean	at 31 2/7 wk	pregnancy		normal	_	normal	0.7
											Closed ductus	rupture de membrane
	18										at 29 wk	sur MAP et défaut de
		M	4/7	31 6/7	1680	1790	9	9	1	caesarean	(ibuprofen)	progression		normal	ibuprofen	normal	0,75
												Césarienne en
	19										(Patent ductus) Closed ductus	urgence devant persistance
		M	6/7	32 5/7	1775	1760	10	10	0	caesarean	at 32 3/7 wk	metrorragie et ARCF	normal	cafeine	normal	0,6
											Closed ductus
	20										at 28 5/7 wk				IVH-I (in right) +
		M	3/7	30 6/7	1040	1030	8	8	1	vaginal	(ibuprofen)	grossesse gemellaire	bilateral HEPV	ibuprofen	normal
												MAP-RCIU
	21										Closed ductus	grossesse
		M	4/7	32 3/7	805	900	10	10	1	caesarean	at 31 2/7 wk	triamniotique		bilateral IVH-I	_	normal	0.7
												MAP-grossesse
												gemellaire-Detresse
												respiratoire
											Closed ductus	secondaire sur
											at 28 5/7 wk	maladie des		Ventricle slightly
		F	3/7	31 5/7	1195	1490	3	6	1	vaginal	(ibuprofen)	membranes hyalines	enlarged	ibuprofen	normal	0.7
											canal artériel
											bidirectionnel	MAP-Birth
		M		30 5/7	1060	1055	7	9	1	caesarean	at 30 wk	spontaneous triple	normal	_	normal	0.65

Neurovascular Coupling in the Developing Neonatal Brain in Resting State

											rupture prématuré des
											membranes apres
											fissuration des
										Closed ductus	membranes à 17SA
										at 28 1/7 wk	secondaire à une
	M	27 2/7	30	950	965	2	4	0	vaginal	(significant)	amniocentèse	normale	_	normal	0,7
											MAP-infection
											materno-foetale
											confirmé-grossesses
	M	32	33	1800	1890	6	9	1	vaginal	Closed ductus	gemellaire	normale	_	normal
											MAP-infection	confirmation
											materno-foetale	agenesie du corps
											confirmé-grossesses	calleus à j4
	F	32	33	1530	1685	1	6	1	vaginal	Closed ductus	gemellaire	(abnormal)	_	normal	0.75
										Closed ductus	Suspicion d'infection
										at 31 1/7 wk	materno-foetale-
	F	31	33 5/7	1435	1820	10	10	0	vaginal	(no significant)	grossesses gemellaire	normal	_	normal	0.75
												bilateral IVH-II,
												corps calleux
	M	27 2/7	29	1055	1115	5	7	0	caesarean	Patent ductus	MAP	présent.	Dopamine	normal
												bilateral IVH-II (in
												left), IVH-III and	Sufenta -
	F	27 1/7	27 4/7	900	955	5	9	0	vaginal	Patent ductus	MAP spontanée	IVH-IIII (in right)	Hypnovel	normal	0,79
										(Patent ductus)
										Closed ductus	GRossesse gemelaire
	M	29 3/7	30 1/7	1180	1060	8	10	1	caesarean	at 29 4/7 wk	-Présence ARCF	normal	_	normal	0.6
										Closed ductus
										at 29 2/7 wk	Grossesse gemelaire -
	M	29	30 4/7	1050	1350	10	10	1	caesarean	(ibuprofen)	MAP-métrorragie	normal	ibuprofen	normal	0.65
	M	28 4/7	30 5/7	1100	1290	10	10	1	caesarean	Patent ductus	MAP-metrorragies	normal	_	normal	0,75

185 Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

	Sub16 (IVH;I)	51.5%	12.6%	9.4%	10.5%	15.7%
	Sub17 (PDA)	34.5%	9.7%	28.3%	15.9%	11.5%
	Sub18	22%	8%	33%	26%	11%
	Sub19 (PDA)	26%	18.2%	30.4%	13.9%	11.3%
	Sub20 (IVH;I)	29.5%	20%	24.3%	16.5%	9.5%
	Sub21 (IVH;I)	30%	13.3%	28.3%	20%	8.3%
	Sub22	37%	21.3%	20.3%	14.8%	6.4%
	Sub23	26.4%	9.4%	33.3%	20.1%	10.6%
	Sub24	24.2%	24.2%	24.2%	15.1%	12.1%
	Sub25	25.8%	22.4%	25.8%	18.9%	6.9%
	Sub26	27%	20%	32%	12%	9%
	Sub27	32.2%	17.7%	24.4%	16.6%	8.8%
	Sub28 (PDA-IVH;II)	23.8%	23%	30.1%	14.2%	8.7%
	Sub29 (PDA-IVH;III)	70.7%	0%	29.2%	0%	0%
	Sub30 (PDA)	30.2%	18.6%	18.6%	23.2%	9.3%
	Sub31	33%	12.2%	22.6%	25.4%	6.6%
	Sub32 (PDA)	27.6%	16.9%	28.5%	18.7%	8%
	Total PDA	49.3%	11.4%	24.2%	9.5%	5.4%
	Total IVH (I,II,III,IV)	47.7%	12.5%	22%	11.8%	5.8%

Total IVH (III,IV) 58.9% 15.8% 25.1% 0% 0% Total 39.04% 17.18% 24.15% 12.92% 6.71% 186 Chapter 5: Neurovascular Coupling in the Developing Neonatal Brain in Resting State

http://www.demosmedical.com/media/samplechapters/9781620700457/mobile/9781620700457_Chapter1.html

https://www.mayoclinic.org/diseases-conditions/patent-ductus-arteriosus/symptoms-causes/syc-20376145

https://www.rli.com/resources/articles/classification.aspx

Taken from: www.itis.ethz.ch/itis-for-health/tissue-properties/database/database-summary/

https://www.laserdentistry.org/uploads/files/conference/2014/Handouts/Benjamin-LeBeau Laser%20Safety%20Officer%20Training%20Handout.pdf

https://www.rli.com/resources/articles/classification.aspx

ACKNOWLEDGEMENTS

There are many people to whom I am indebted to in helping me to complete this thesis.

First of all, I would like to express my deepest and sincerest thanks to my supervisor, Prof. Dr. Fabrice Wallois, for giving me the opportunity to work on this thesis in his laboratory. I am

Supplementary

In the following we explained some parts of study in more details:

2) The different time constant of the NIR measurements (CBFi and Hb changes were measured with two separate devices):

The first part concerns how we synchronized the various acquisition devices. The second part evaluates the maximum time lags between the two systems. The third part that explained in above part evaluates to what degree this time lag may affect our analysis.

I) Measuring instrument synchronization

To simultaneously measure hemodynamic activities, the various measuring systems must be accurately synchronized. Synchronization was achieved by an external event trigger that produces TTL signals via a parallel port (LPT) using an in-house Matlab ® code. This system produces markers simultaneously on both systems to precisely indicate the beginning and the end of data acquisitions. Synchronization was performed using the Level triggering mode. In this mode, a device monitors the A/D converter for an increase in the voltage level applied to the marker/trigger pins. When the appropriate increase in voltage is reached (TTL "high" signal), the measuring system records the event.

II) Phantom test

The Instruction Manual of NIRO-200NX (page 99) noted that maximum pulse duration of the NIR-light sources is 18µs. In addition, the Non-linear relationship: Moreover, the non-linear relationship was investigated by the entropy (H). The entropy (H) of rCMRO2 and rCBV for each subject was equal to 2000. For each subject, the mutual information MI of rCMRO2 and rCBV was less than the entropy (H) of rCMRO2 and rCBV (MI (rCMRO2, rCBV) < H (rCBV) and MI(rCMRO2, rCBV) < H(rCMRO2)). rCMRO2 and rCBV can, therefore, be considered to be dependent variables but not totally dependent, (i.e., rCMRO2 index is related to signal fluctuation of HbT but not solely represents fluctuations of HbT). The following figure 13 shows the time trace plots of beta in two sample subjects. To validate the constant beta over the measured periods, a t-test was used to determine whether data are significantly fluctuate. The t-test does not reject the null hypothesis at 5% significance level for each subject. Thus we accept the null hypothesis that the beta is constant over the time traces of the measured CBF and CBV.

EEG data processing

Off-line analysis was performed using in-house MATLAB scripts for all signals. The artifacts from EEG data detected and rejected visually by trained an experimented clinical neurophysiologist (FW).

Automated detection of spontaneous burst of activity

In order to detect EEG burst of activity, we used a non-linear energy operator (NLEO)

algorithm. The NLEO combines information's from both the amplitude and the frequency content of the signal, which makes it more sensitive for detection of preterm bursts rather than other estimators of signal energy with information's extracted from amplitude or frequency only [START_REF] Vanhatalo | Slow endogenous activity transients and developmental expression of K+-Cl-cotransporter 2 in the immature human cortex[END_REF].

To provide a moving average signal, the absolute value of NLEO output was then smoothed by calculating the average in a sliding window with a length of 1.5 seconds. In order to better detect the interburst intervals (IBIs), a baseline correction was applied; the value of each EEG sample was subtracted by the minimum value of the moving averaged calculated from 1 min prior each considered sample. Then EEG bursts of activity was extracted from the discontinuous trace when the moving average of the EEG envelope-derivative value remains over a given threshold (1.5 μV 2 ) for longer than a defined duration as a time limit (1s). The optimal values for the threshold level, the

Hemodynamic data processing; HbO, HbR, TOI, HbT, CBF, and CMRO2

A z-score-based algorithm was used to reject artifact from optical signals [START_REF] Born | Functional magnetic resonance imaging of the normal and abnormal visual system in early life[END_REF].

As individual features, such as skull thickness and hair color, influence signal strength, the signal was first homogenized in each participant by computing a z-score across all measurement periods for each channel. A z-score greater than 4 in any channel was considered to be an artifact, in which case, the entire artifact time-window was excised from the data for all channels [START_REF] Born | Functional magnetic resonance imaging of the normal and abnormal visual system in early life[END_REF].

The mean value of rCBF signals recorded from 4 paired source-detectors was calculated. The remaining cleaned hemodynamic signals were band-pass filtered [0.03-0.5 Hz] using a zero phase filter (Butterworth, order 3) to eliminate physiologic noise (e.g., slow drifts, arterial pulse oscillations).

While CBF can be independently measured by DCS, it has been proposed that the relative cerebral metabolic rate of oxygen (CMRO2) can be theoretically estimated by combining relative changes in CBF and oxygen extraction fraction [START_REF] Culver | Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia[END_REF]:

Where rOEF is defined as:

With venous oxygenation 𝑆𝑣𝑂 2 = (𝑆𝑂 2 -𝑎 × 𝑆𝑎𝑂 2 ) 𝑏 ⁄ , where a+b=1, a and b are the arterial and venous contributions that are constant over time [START_REF] Watzman | Arterial and venous contributions to near-infrared cerebral oximetry[END_REF], and arterial oxygenation SaO2=100%. Mechanical ventilation parameters and inspired oxygen concentrations were maintained constant at sufficiently high levels to saturate arterial hemoglobin (SaO2 ≈ 100%). SO2

is the microvascular tissue oxygen saturation [START_REF] Wray | Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation[END_REF] (𝑆𝑂 2 = 𝐻𝑏𝑂 2 /𝐻𝑏𝑇). The control state at time t0 was defined as the mean value of the signal and was considered to be the reference value.

Hemodynamic analysis

The hemodynamic responses (i.e. HbO, HbR, TOI, CBF and CMRO2) time-locked to the EEG signal were averaged (time window: [-20 to 30 sec]). Because the hemodynamic responses to EEG bursts last around 15s, we defined a reference period of -20s to 0s, to be able to define a reference (condition.A1, see below), during which hemodynamic changes are unlikely to be related to the previous burst. The first 10 sec period [-20 to -10 sec] was defined as the baseline for further analysis. The DCS part of the probe is made off one series of source (light emitting) fiber-optics (400 μm core diameter), and one fibre-optic (light collecting) detector bundle (3 mm diameter) placed at the end of the rows of emitters fibres, creating 4 measuring points (channels) over the frontal area.

The FD NIRS part of the probe is made off four emitters fibres (one row) that were connected to 690 nm and 830 nm lasers (see Figure 2.b). The emitting tips were 'clad' with plastic tubing and slid into holes in rubber block. The input tip of the detector bundle was fixed in place of well contact with prisms. The probe was held in place by a headband to wrap the probe, to minimize any light interference. Special care was considered to ensure that the light from the source of one modality do not saturate the detectors of the other modality.

The CW-NIRS part of the probe is made off 2 detectors and 1 source. The emitter-detector distance was 3 cm. The NIRS source contained three wavelength emitters (735, 810 and 850 nm) (bottom right-hand corner). SO2 (tissue oxygenation) was measured by using the Spatially Resolved Spectroscopy (SRS) method (Nourhashemi et al., 2017a). Une compréhension globale de la relation de couplage neurovasculaire nécessite la mesure simultanée des réponses neuronales et vasculaires. La valeur de cette approche est la capacité de mesurer l'hémodynamique à travers un crâne intact, qui fournit des mesures non invasives chez l'homme à des fins de diagnostic et clinique et qui ouvre de nouvelles perspectives sur l'étiologie des troubles du neurodéveloppement.

Table.S2 The percentages of the number of the classified hemodynamic responses to EEG bursts in each condition