PhD / When modeling a system as complex as the brain, considerable simplifications are inevitable. The nature of these simplifications depends on the available experimental evidence, and the desired form of model predictions. A focus on the former often inspires models of networks of individual neurons, since properties of single cells are more easily measured than those of entire populations. However, if the goal is to describe the processes responsible for the electroencephalogram (EEG), such models can become unmanageable due to the large numbers of neurons involved. Mean-field models in which assemblies of neurons are represented by their average properties allow activity underlying the EEG to be captured in a tractable manner. The starting point of the results presented here is a recent physiologically-based mean-field model of the corticothalamic system, which includes populations of excitatory and inhibitory cortical neurons, and an excitatory population representing the thalamic relay nuclei, reciprocally connected with the cortex and the inhibitory thalamic reticular nucleus. The average firing rates of these populations depend nonlinearly on their membrane potentials, which are determined by afferent inputs after axonal propagation and dendritic and synaptic delays. It has been found that neuronal activity spreads in an approximately wavelike fashion across the cortex, which is modeled as a two-dimensional surface. On the basis of the literature, the EEG signal is assumed to be roughly proportional to the activity of cortical excitatory neurons, allowing physiological parameters to be extracted by inverse modeling of empirical EEG spectra. One objective of the present work is to characterize the statistical distributions of fitted model parameters in the healthy population. Variability of model parameters within and between individuals is assessed over time scales of minutes to more than a year, and compared with the variability of classical quantitative EEG (qEEG) parameters. These parameters are generally not normally distributed, and transformations toward the normal distribution are often used to facilitate statistical analysis. However, no single optimal transformation exists to render data distributions approximately normal. A uniformly applicable solution that not only yields data following the normal distribution as closely as possible, but also increases test-retest reliability, is described in Chapter 2. Specialized versions of this transformation have been known for some time in the statistical literature, but it has not previously found its way to the empirical sciences. Chapter 3 contains the study of intra-individual and inter-individual variability in model parameters, also providing a comparison of test-retest reliability with that of commonly used EEG spectral measures such as band powers and the frequency of the alpha peak. It is found that the combined model parameters provide a reliable characterization of an individual's EEG spectrum, where some parameters are more informative than others. Classical quantitative EEG measures are found to be somewhat more reproducible than model parameters. However, the latter have the advantage of providing direct connections with the underlying physiology. In addition, model parameters are complementary to classical measures in that they capture more information about spectral structure. Another conclusion from this work was that a few minutes of alert eyes-closed EEG already contain most of the individual variability likely to occur in this state on the scale of years. In Chapter 4, age trends in model parameters are investigated for a large sample of healthy subjects aged 6-86 years. Sex differences in parameter distributions and trends are considered in three age ranges, and related to the relevant literature. We also look at changes in inter-individual variance across age, and find that subjects are in many respects maximally different around adolescence. This study forms the basis for prospective comparisons with age trends in evoked response potentials (ERPs) and alpha peak morphology, besides providing a standard for the assessment of clinical data. It is the first study to report physiologically-based parameters for such a large sample of EEG data. The second main thrust of this work is toward incorporating the thalamocortical system and the basal ganglia in a unified framework. The basal ganglia are a group of gray matter structures reciprocally connected with the thalamus and cortex, both significantly influencing, and influenced by, their activity. Abnormalities in the basal ganglia are associated with various disorders, including schizophrenia, Huntington's disease, and Parkinson's disease. A model of the basal ganglia-thalamocortical system is presented in Chapter 5, and used to investigate changes in average firing rates often measured in parkinsonian patients and animal models of Parkinson's disease. Modeling results support the hypothesis that two pathways through the basal ganglia (the so-called direct and indirect pathways) are differentially affected by the dopamine depletion that is the hallmark of Parkinson's disease. However, alterations in other components of the system are also suggested by matching model predictions to experimental data. The dynamics of the model are explored in detail in Chapter 6. Electrophysiological aspects of Parkinson's disease include frequency reduction of the alpha peak, increased relative power at lower frequencies, and abnormal synchronized fluctuations in firing rates. It is shown that the same parameter variations that reproduce realistic changes in mean firing rates can also account for EEG frequency reduction by increasing the strength of the indirect pathway, which exerts an inhibitory effect on the cortex. Furthermore, even more strongly connected subcircuits in the indirect pathway can sustain limit cycle oscillations around 5 Hz, in accord with oscillations at this frequency often observed in tremulous patients. Additionally, oscillations around 20 Hz that are normally present in corticothalamic circuits can spread to the basal ganglia when both corticothalamic and indirect circuits have large gains. The model also accounts for changes in the responsiveness of the components of the basal ganglia-thalamocortical system, and increased synchronization upon dopamine depletion, which plausibly reflect the loss of specificity of neuronal signaling pathways in the parkinsonian basal ganglia. Thus, a parsimonious explanation is provided for many electrophysiological correlates of Parkinson's disease using a single set of parameter changes with respect to the healthy state. Overall, we conclude that mean-field models of brain electrophysiology possess a versatility that allows them to be usefully applied in a variety of scenarios. Such models allow information about underlying physiology to be extracted from the experimental EEG, complementing traditional measures that may be more statistically robust but do not provide a direct link with physiology. Furthermore, there is ample opportunity for future developments, extending the basic model to encompass different neuronal systems, connections, and mechanisms. The basal ganglia are an important addition, not only leading to unified explanations for many hitherto disparate phenomena, but also contributing to the validation of this form of modeling.

PhD / When modeling a system as complex as the brain, considerable simplifications are inevitable. The nature of these simplifications depends on the available experimental evidence, and the desired form of model predictions. A focus on the former often inspires models of networks of individual neurons, since properties of single cells are more easily measured than those of entire populations. However, if the goal is to describe the processes responsible for the electroencephalogram (EEG), such models can become unmanageable due to the large numbers of neurons involved. Mean-field models in which assemblies of neurons are represented by their average properties allow activity underlying the EEG to be captured in a tractable manner. The starting point of the results presented here is a recent physiologically-based mean-field model of the corticothalamic system, which includes populations of excitatory and inhibitory cortical neurons, and an excitatory population representing the thalamic relay nuclei, reciprocally connected with the cortex and the inhibitory thalamic reticular nucleus. The average firing rates of these populations depend nonlinearly on their membrane potentials, which are determined by afferent inputs after axonal propagation and dendritic and synaptic delays. It has been found that neuronal activity spreads in an approximately wavelike fashion across the cortex, which is modeled as a two-dimensional surface. On the basis of the literature, the EEG signal is assumed to be roughly proportional to the activity of cortical excitatory neurons, allowing physiological parameters to be extracted by inverse modeling of empirical EEG spectra. One objective of the present work is to characterize the statistical distributions of fitted model parameters in the healthy population. Variability of model parameters within and between individuals is assessed over time scales of minutes to more than a year, and compared with the variability of classical quantitative EEG (qEEG) parameters. These parameters are generally not normally distributed, and transformations toward the normal distribution are often used to facilitate statistical analysis. However, no single optimal transformation exists to render data distributions approximately normal. A uniformly applicable solution that not only yields data following the normal distribution as closely as possible, but also increases test-retest reliability, is described in Chapter 2. Specialized versions of this transformation have been known for some time in the statistical literature, but it has not previously found its way to the empirical sciences. Chapter 3 contains the study of intra-individual and inter-individual variability in model parameters, also providing a comparison of test-retest reliability with that of commonly used EEG spectral measures such as band powers and the frequency of the alpha peak. It is found that the combined model parameters provide a reliable characterization of an individual's EEG spectrum, where some parameters are more informative than others. Classical quantitative EEG measures are found to be somewhat more reproducible than model parameters. However, the latter have the advantage of providing direct connections with the underlying physiology. In addition, model parameters are complementary to classical measures in that they capture more information about spectral structure. Another conclusion from this work was that a few minutes of alert eyes-closed EEG already contain most of the individual variability likely to occur in this state on the scale of years. In Chapter 4, age trends in model parameters are investigated for a large sample of healthy subjects aged 6-86 years. Sex differences in parameter distributions and trends are considered in three age ranges, and related to the relevant literature. We also look at changes in inter-individual variance across age, and find that subjects are in many respects maximally different around adolescence. This study forms the basis for prospective comparisons with age trends in evoked response potentials (ERPs) and alpha peak morphology, besides providing a standard for the assessment of clinical data. It is the first study to report physiologically-based parameters for such a large sample of EEG data. The second main thrust of this work is toward incorporating the thalamocortical system and the basal ganglia in a unified framework. The basal ganglia are a group of gray matter structures reciprocally connected with the thalamus and cortex, both significantly influencing, and influenced by, their activity. Abnormalities in the basal ganglia are associated with various disorders, including schizophrenia, Huntington's disease, and Parkinson's disease. A model of the basal ganglia-thalamocortical system is presented in Chapter 5, and used to investigate changes in average firing rates often measured in parkinsonian patients and animal models of Parkinson's disease. Modeling results support the hypothesis that two pathways through the basal ganglia (the so-called direct and indirect pathways) are differentially affected by the dopamine depletion that is the hallmark of Parkinson's disease. However, alterations in other components of the system are also suggested by matching model predictions to experimental data. The dynamics of the model are explored in detail in Chapter 6. Electrophysiological aspects of Parkinson's disease include frequency reduction of the alpha peak, increased relative power at lower frequencies, and abnormal synchronized fluctuations in firing rates. It is shown that the same parameter variations that reproduce realistic changes in mean firing rates can also account for EEG frequency reduction by increasing the strength of the indirect pathway, which exerts an inhibitory effect on the cortex. Furthermore, even more strongly connected subcircuits in the indirect pathway can sustain limit cycle oscillations around 5 Hz, in accord with oscillations at this frequency often observed in tremulous patients. Additionally, oscillations around 20 Hz that are normally present in corticothalamic circuits can spread to the basal ganglia when both corticothalamic and indirect circuits have large gains. The model also accounts for changes in the responsiveness of the components of the basal ganglia-thalamocortical system, and increased synchronization upon dopamine depletion, which plausibly reflect the loss of specificity of neuronal signaling pathways in the parkinsonian basal ganglia. Thus, a parsimonious explanation is provided for many electrophysiological correlates of Parkinson's disease using a single set of parameter changes with respect to the healthy state. Overall, we conclude that mean-field models of brain electrophysiology possess a versatility that allows them to be usefully applied in a variety of scenarios. Such models allow information about underlying physiology to be extracted from the experimental EEG, complementing traditional measures that may be more statistically robust but do not provide a direct link with physiology. Furthermore, there is ample opportunity for future developments, extending the basic model to encompass different neuronal systems, connections, and mechanisms. The basal ganglia are an important addition, not only leading to unified explanations for many hitherto disparate phenomena, but also contributing to the validation of this form of modeling.

L'objectif de ce travail est de prédire les évolutions microstructurales se produisant dans le tantale pur lors d'un traitement thermique en fonction de son état microstructural initial. La restauration, la recristallisation et la croissance de grains sont décrites à l'aide d'un modèle en champ moyen qui nécessite une description adéquate de la microstructure, en termes de distributions de tailles de grains et de densités de dislocations équivalentes. La densité de dislocation équivalente moyenne peut être évaluée par une simple mesure de dureté Vickers. L'établissement de la relation dureté-densité de dislocations nécessite l'utilisation d'une loi de comportement basée sur la densité de dislocations équivalente. Les évolutions microstructurales au cours d'un traitement thermique ont été observées et les paramètres pilotant ces phénomènes ont été identifiés à l'aide d'essais originaux comme l'observation in situ de la recristallisation ou l'utilisation d'essais à gradient de déformation pour déterminer le seuil de densité de dislocations équivalente pour déclencher la recristallisation. Des essais plus classiques ont permis d'obtenir des cinétiques de recristallisation dans la gamme 1000°C-1100°C pour différentes microstructures initiales. Les simulations des différents traitements thermiques à l'aide du modèle à champ moyen rendent bien compte des évolutions microstructurales en termes de fraction recristallisée et de taille des grains recristallisés pour des microstructures faiblement déformées ou fortement déformées et fragmentées, en utilisant une description adéquate du type de microstructure initiale. Le modèle devra en revanche être adapté pour traiter le cas de microstructures intermédiaires, en enrichissant non seulement la description de la microstructure initiale mais également celle de l'étape de germination des grains recristallisés. Il deviendra alors capable de prédire les évolutions de microstructures pour tout type de microstructure initiale de tantale. / This study aims at predicting the microstructural evolution of pure tantalum during annealing according the initial microstructural state. Static recovery and discontinuous recrystallization as well as grain growth are described using a mean-field model requiring an appropriate description of the microstructure, using both equivalent dislocation densities and grain sizes distributions. The average equivalent dislocation density can be assessed from Vickers microhardness measurements. The calibration of such a relation between microhardness and dislocation density involves the use of a dislocation density-based constitutive law. Microstructural evolutions during annealing have been observed and control parameters of these phenomena have been determined using original tests such as in situ observation of the recrystallization process or the use of strain gradient samples to assess the critical dislocation density for the onset of recrystallization. More classical tests have been carried out to get recrystallization kinetics in the range 1000-1100°C for different initial microstructures. Simulations of annealing using the mean-field model adapted for tantalum match the experimental evolution of both recrystallized fraction and recrystallized grain size, in either weakly deformed or severely deformed and fragmented microstructures. On the other hand, the model needs to be further adapted for intermediate microstructures, with both a more elaborate description of the initial microstructure and of the nucleation stage of the recrystallized grains. It will then be suitable to predict evolutions of any initial tantalum microstructure during annealing.

Les pièces métalliques constituant le circuit primaire des installations nucléaires sont élaborées par forgeage à chaud. Pendant ce procédé, les transformations microstructurales induites par la déformation et les recuits déterminent une partie des propriétés mécaniques des produits finaux. L’orientation de la microstructure lors du processus de fabrication nécessite une connaissance précise des mécanismes physiques qui opèrent dans le matériau. Dans le cas de la déformation à chaud de l’acier austénitique 304L, ces modifications microstructurales dépendent de la recristallisation dynamique discontinue (DDRX) et de la recristallisation post-dynamique (PDRX). L’objet de ce projet est : (i) l’étude de la DDRX et de la PDRX dans les conditions de déformation du procédé de forgeage, (ii) l’étude de l’influence d’un ajout de niobium sur ces mécanismes, (iii) la modélisation de ces mécanismes afin de prédire les caractéristiques de la microstructure (moyenne et distribution de la taille des grains) à l’issue d’un procédé multipasses. Dans le cadre de l’étude, les conditions de déformation rencontrées lors du forgeage à chaud sont reproduites à l’aide d’essais de torsion sur des matériaux modèles contenant des teneurs en niobium différentes. La caractérisation et la modélisation des microstructures a permis de comprendre les effets respectifs de la température, de la vitesse de déformation ainsi que de l’ajout de niobium sur les mécanismes de la DDRX et de la PDRX. Dans cette étude, une nouvelle approche semi-topologique de l’hypothèse champs moyens est développée afin de permettre la prédiction de distributions de la taille de grain cohérentes avec les données expérimentales. / Cooling system of nuclear power plants is constituted of metallic parts obtained by hot forging. Thus during the manufacturing process, the microstructural trans- formations induced by the deformation and annealing process define partially the mechanical properties of the final products. A sharp knowledge of the physical mechanisms generated within the material is required to handle the microstructure. In the case of hot deformation of 304L austenitic stainless steel, the microstructural modifications depend on the discontinuous dynamic recrystallization (DDRX) and the post-dynamic recrystallization (PDRX). The aim of this project is: (i) the study of the DDRX and the PDRX under the conditions of deformation inherent in the forging process, (ii) the study of the influence of niobium addition on these mechanisms, (iii) the modeling of these me- chanisms in order to predict the microstructure characteristics (mean grain size and distribution) following a multipass process. As part of the research, the deformation conditions experienced during the hot forging process are replicated through torsion tests with model materials containing various niobium concentrations. Characterization and modeling of microstructures enable to understand the respective e ects of temperature, strain rate as well as niobium addittion on the DDRX and PDRX mechanisms. In this study, a new topological approach of mean-field hypothesis is developed in order to allow the prediction of realistic grain size distributions.