La tomographie par émission de positons (TEP) est une méthode d’imagerie fonctionnelle, utilisée en particulier lors du développement de nouveaux médicaments et pour imager les tumeurs. En TEP, l’estimation de la concentration plasmatique artérielle d’activité du traceur non métabolisé (nommée « fonction d’entrée ») est nécessaire pour l’extraction des paramètres pharmacocinétiques. Ceux-ci permettent de quantifier le comportement du traceur dans les tissus, ou plus précisément le traitement du traceur par les tissus. Cette thèse constitue une contribution à l’étude de la fonction d’entrée, par l’élaboration d’une méthode d’estimation de la fonction d’entrée peu invasive à partir des images TEP et de prélèvements veineux. L’exemple du traceur FDG (analogue du glucose) dans le cerveau humain a été choisi. La méthode proposée repose sur la modélisation compartimentale de l’organisme : elle déconvolue le modèle à trois compartiments utilisé pour le FDG. L’originalité de la méthode repose sur trois points : l’utilisation d’un grand nombre de régions d’intérêt ; l’utilisation d’un grand nombre de jeux de trois régions d’intérêt différentes; une estimation itérative. Pour la validation de la méthode, un soin particulier a été porté à la simulation d’images TEP (simulation d’acquisition, reconstruction, corrections) de plus en plus réalistes, depuis une image simple simulée avec un simulateur analytique jusqu’à une image la plus proche possible de la réalité, simulée avec simulateur Monte-Carlo. Une chaîne de pré-traitement (segmentation des IRM associés, recalage entre images TEP et IRM et correction de l’effet de volume partiel par une variante de la méthode de Rousset) a ensuite été appliquée à ces images afin d’extraire les cinétiques des régions d’intérêt, données d’entrée de la méthode d’estimation de la fonction d’entrée. L’évaluation de la méthode sur différentes données, simulées et réelles, est présentée, ainsi que l’étude de la sensibilité de la méthode à différents facteurs tels que les erreurs de segmentation, de recalage, de mesure de l’activité des prélèvements sanguins. / Positron Emission Tomography (PET) is a method of functional imaging, used in particular for drug development and tumor imaging. In PET, the estimation of the arterial plasmatic activity concentration of the non-metabolized compound (the "input function") is necessary for the extraction of the pharmacokinetic parameters. These parameters enable the quantification of the compound dynamics in the tissues. This PhD thesis contributes to the study of the input function by the development of a minimally invasive method to estimate the input function. This method uses the PET image and a few blood samples. In this work, the example of the FDG tracer is chosen. The proposed method relies on compartmental modeling: it deconvoluates the three-compartment-model. The originality of the method consists in using a large number of regions of interest (ROIs), a large number of sets of three ROIs, and an iterative process. To validate the method, simulations of PET images of increasing complexity have been performed, from a simple image simulated with an analytic simulator to a complex image simulated with a Monte-Carlo simulator. After simulation of the acquisition, reconstruction and corrections, the images were segmented (through segmentation of an IRM image and registration between PET and IRM images) and corrected for partial volume effect by a variant of Rousset’s method, to obtain the kinetics in the ROIs, which are the input data of the estimation method. The evaluation of the method on simulated and real data is presented, as well as a study of the method robustness to different error sources, for example in the segmentation, in the registration or in the activity of the used blood samples.

Recentes estudos sugerem a existência de sinapses elétricas mediadas por junções gap entre fotorreceptores na retina de vertebrados. Neste trabalho, descrevemos um modelo computacional dos circuitos primário e secundário mediados pelos bastonetes da retina de vertebrados. O modelo é composto pelas seguintes populações de células: bastonetes, cones, células bipolares dos bastonetes, células bipolares dos cones, células amácrinas do tipo AII e células ganglionares. As células do modelo estão acopladas entre si por sinapses químicas e elétricas segundo padrões realísticos de convergência e divergência. As sinapses elétricas ocorrem entre os bastonetes, entre os bastonetes e os cones, entre as células amácrinas AII e entre as células bipolares dos cones e a células amácrinas AII. O modelo assume que um estímulo luminoso de baixa intensidade, simulando condições escotópicas, atinge todos os bastonetes da camada receptora, porém menos da metade deles é excitada. A resposta dos bastonetes excitados é controlada por uma fotocorrente cuja amplitude pode ser alterada para simular estímulos de diferentes intensidades dentro da faixa escotópica. O modelo é utilizado para investigar os efeitos dos diferentes graus de acoplamento elétrico entre as células receptoras e entre as células amácrinas AII, além do efeito de diferentes valores de condutância do canal Ih ativado pela hiperpolarização nos bastonetes, sobre a faixa dinâmica da retina. Os resultados das simulações mostram que, para valores realísticos da condutância do canal Ih, a faixa dinâmica medida na camada receptora é maximizada para o índice de conectividade crítico para que haja percolação de ligação. No entanto, quando a faixa dinâmica é medida para as células bipolares ou ganglionares o valor máximo é obtido para um índice de conectividade subcrítico. Este resultado é conseqüência da alta convergência de sinapses químicas entre os bastonetes e células bipolares. / Recent studies suggest the existence of electrical synapses (gap junctions) connecting photoreceptors in the vertebrate retina. In this work we describe a computer model of the primary and secondary rod pathways in the vertebrate retina. The model is composed of the following cell populations: rods, cones, rod bipolar cells, cone bipolar cells, AII amacrine cells and ganglion cells. Cells of the model are connected via chemical as well as electrical synapses according to realistic convergence and divergence factors. There are electrical synapses between rods, rods and cones, AII amacrine cells, and cone bipolar cells and AII amacrine cells. The model assumes that low intensity stimuli simulating scotopic conditions reach all rods in the receptor array but less than half of them are excited. The excited rods response is controlled by a photocurrent waveform whose amplitude can be manipulated to simulate stimuli of different intensities within the scotopic range. The model is used to investigate the effects of different degrees of coupling among photoreceptors and among AII amacrine cells, as well as values of rod hyperpolarization activated current Ih on the dynamic range of the retina. Results show that for realistic values of Ih conductance the dynamic range of the rod array is maximized at the critical connectivity degree for bond percolation. However, the dynamic range of the rod bipolar and ganglion cells is maximized for a photoreceptor connectivity degree below the critical value. The latter result is a consequence of the high convergence of chemical synapses from rods to rod bipolar cells.

Ce travail de thèse s'articule autour de trois parties distinctes abordant chacune un thème précis lié à l'épidémiologie. La première partie de ces travaux s'inscrit dans le cadre de la propagation de virus via l'utilisation de modèles épidémiques. Dans cette partie, sont analysées différentes méthodes d'estimations paramétriques et y sont étudiés la qualité de ces estimateurs. Une application à des virus informatiques est proposée. La deuxième partie de cette thèse propose une méthode d'estimation de la prévalence actuelle du virus de l'hépatite C en France par l'intermédiaire d'un modèle de rétro-calcul associé à un modèle de Markov modélisant l'histoire naturelle de la maladie. Cette méthode et les résultats qui en découlent sont comparés avec les résultats obtenus via l'approche de référence en France. Enfin, la dernière partie s'intéresse à l'étude de l'impact des nouvelles thérapeutiques anti-hépatite C susceptible d'éradiquer le virus à moyen terme. En assimilant la population d'intérêt à un groupement de graphes aléatoires, la propagation du virus est modélisée à partir d'un modèle de métapopulation construit sur la base de données migratoires où les dynamiques de chaque sous-population sont régies par un ensemble d'équations différentielles déterministes. Ce travail doctoral a été réalisé dans le cadre d'une convention CIFRE avec les laboratoires Bristol-Myers Squibb. / The works undertaken in this doctoral thesis are conducted in three parts, each one dealing with a specific epidemiology-related domain. The first part of this work deals with the propagation of viruses by using well-known epidemic models. It is mainly focused on the analyze of different estimation methods and on their performance. An application on computer virus is proposed. The second part of this thesis gives an estimation method of the hepatitis C virus prevalence in France based on a back-calculation model in association with a Markov model of the disease's natural history. This method and its results are compared with those generated by the reference approach in France. The last part is focused on the study of the recent anti-hepatitis C therapeutics impact on the population since is has been stated that those could eradicate the virus at middle term. In that optic, based on published migration data and assuming that the population of interest is organized into a set of specific contact networks, a metapopulation is computed in which the dynamics of each sub-population is governed by a set of deterministic differential equations. This doctoral research has been conducted through a CIFRE industrial research agreement with the Bristol-Myers Squibb pharmaceutical company.

L’objet de cette thèse est l’étude de certains problèmes liés à l’ingénierie des bioprocédés, en particulier l’analyse du comportement et de la culture optimale des microalgues et la connexion de plusieurs bioréacteurs. Trois problèmes sont proposés et analysés. Le première est basé sur une étude récente dans laquelle les auteurs modifient le modèle classique du Monod en incorporant l’incidence de la lumière sur la dynamique à travers le rôle de la croissance de la biomasse. L’idée est d’étudier un problème plus général de l’optimisation non linéaire qui considère maximisation de la biomasse moyenne de microalgues en fonction du temps, pour des intervalles de temps différents. La difficulté mathématique qui se pose est lié à la discontinuité des intervalles de temps qui rend la fonction à optimiser non différentiable. Ce manque de régularité comprend la formulation d’un problème d’optimisation non-lisse. Dans le deuxième problème, un modèle réduit du réservoir microalgues avec nitrification est analysé, en supposant que les microalgues peuvent se développer à partir de la consommation de nitrate et d’ammonium, de préférence par l’ammonium. La limitation de la lumière par l’auto-ombrage est également inclus dans le taux de croissance du microalgues comme inhibition non compétitive. En réduisant le système en utilisant la théorie des systèmes asymptotiquement autonomes, il peut être considéré comme une perturbation d’un système de deux espèces en compétition pour un substrat. Par conséquent, nous utilisons un résultat de systèmes perturbés non-évanescentes pour obtenir un théorème de stabilité pour la coexistence.Le dernier problème est lié aux systèmes compartimentés. Il est prouvé que pour une grande classe de systèmes entrées-sorties positifs de dimension finie, représentant transport et diffusion de soluté entre des compartiments mobiles et immobiles, il existe des représentations MINC (multiple interacting continua) et MRMT (multi-rate mass transfer) algébriquement équivalentes. En outre, des méthodes explicites sont donnés pour construire ces représentations équivalentes, où la contrôlabilité des systèmes joue un rôle important. / The purpose of this thesis is to study some problems that arise from bioprocess engineering, in particular the behaviour analysis and optimal cultivation of microalgae and the connection of multiple bioreactors. The thesis consists of three problems. The first is based on a recent study in which the authors extend the classical Monod model incorporating light incidence on the dynamics through the role of biomass growth. The idea is to study a more general problem of nonlinear optimization which considers maximization average biomass of microalgae versus time, for different time intervals. The mathematical difficulty that arises is related to that discontinuity of the time intervals which causes non differentiability in some domain points. This lack of regularity involves the formulation of a non-smooth optimization problem. In the second problem, a reduced mathematical model of a microalgal pond with nitrification is analyzed, assuming that microalgae can grow either by ammonium consumption or by nitrate consuming, with preference for ammonium. Light limitation by self-shading is also included in the growth rate of microalgae as a noncompetitive inhibition.It is feasible to reduce the system using the theory of asymptotically autonomous systems and the limiting system obtained can be considered as a perturbation of a system of two species competing for a substrate. So, we use a result of non-vanishing perturbated systems to obtain a strong stability theorem for equilibrium coexistence. The last problem is related to compartmental systems. It is proved that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in mobile and immobile compartments, there exist MINC (multiple interacting continua) and MRMT (multirate mass transfer) algebraically equivalent representations. Moreover, we provide explicit methods to construct these representations, where controllability property is playing a crucial role.

[pt] Ligantes compartimentais são aqueles possuindo dois ou mais sítios polidentados de coordenação próximos, podendo fornecer um bom reconhecimento seletivo de íons metálicos em suas câmaras adjacentes. Neste contexto, o composto BPMAMFF {3-[N,N-bis(2-piridilmetil)aminometil]-5-metilsalicilaldeído} e o seu análogo HBPAMFF {3-[N,N-(2-piridilmetil)(2-hidroxibenzil)aminometil]-5-metilsalicilaldeído}, são ligantes compartimentais cujas características de reatividade os ressaltam como compostos de interesse para a Química de Materiais, a Nanotecnologia, a Química Bioinorgânica e outras áreas. Neste trabalho, BPMAMFF e HBPAMFF foram sintetizados, assim como seus respectivos derivados oxímicos BPMAMFF-ox e HBPAMFF-ox, visto que a adição do grupamento oxima pode potencializar algumas de suas propriedades. Assim, obteve-se 4 ligantes compartimentais, que foram caracterizados através de seus pontos de fusão, espectroscopia vibracional no IV e RMN de 1H. Além disto, 6 complexos de coordenação, sendo 5 deles inéditos, foram preparados a partir destes ligantes, sendo os complexos de cobre(II) obtidos para todos eles e os de zinco(II) sintetizados apenas para os derivados de BPMA. Todos os compostos de coordenação foram caracterizados no estado sólido através de espectroscopia vibracional no IV, termogravimetria e, quando possível, através de difração de raios X em monocristais. Os complexos diamagnéticos de zinco(II) também foram estudados através de RMN de 1H. Os resultados aqui apresentados mostram que a porção oxímica, diferentemente do esperado ao começo do projeto, não participa da coordenação a esses íons metálicos nas espécies mononucleares, ficando assim disponível para a coordenação de outros centros metálicos. Assim, estes complexos podem servir como blocos construtores na síntese de estruturas supramoleculares e polímeros de coordenação com as mais diversas aplicações. Por fim, a obtenção do complexo inédito [Cu(HBPAMFF)Cl2]·0,25 H2O, no qual observou-se pela primeira vez que o fenol terminal do ligante tripodal HBPAMFF não participa ativamente da coordenação, foi descrita por nós em um artigo publicado na revista Journal of Molecular Structure. / [en] Compartmental ligands are those that have two or more polydentate coordination sites close together , which can provide good recognition of metal ions in their adjacent chambers. In this context, the BPMAMFF {3 N N bis(2 pyridylmethyl)aminomethyl] 5 methylsalicylaldehyde} ligand and its analog ue, namely HBPAMFF {3 N N --(2 pyridylmethyl)(2 hydroxybenzyl)aminomethyl] 5 methylsalicylaldehyde}, are compartmental ligands whose reactivity features highlight them as compou nds of interest for Materials Chemistry, Nanotechnology, Bioinorganic Chemistry and other areas. In this work, BPMAMFF and HBPAMFF were synthesized, as well as their respective oximic derivatives BPMAMFF ox and HBPAMFF ox , since the addition of th is group can potentiate some of their properties. Thus, 4 compartmental ligands were obtained, which were characterized through their melting points, vibrational IR spectroscopy and 1 H NMR. Furthermore , 6 coordination complexes, 5 of them new , were prepared from th ese ligands, being the copper(II) complexes obtained for all of them and the zinc(II) complexes synthesized only for BPMA derivatives. All coordination compounds were characterized in the solid state by vibrational IR spectroscopy, thermogravimetry and, wh en possible, by X ray diffraction in single crystals. Zinc(II) diamagnetic complexes were also studied by 1 H NMR. The results presented here in show that the oximic moiety , unlike what was expected at the beginning of the project, does not participate in th e coordination of these metal ions in the mononuclear species, thus becoming available for the coordination of other metal centers. Hence , the se complexes can be used as building blocks in the synthesis of supramolecular structures and coordination polymer s with the most diverse applications. Finally, the obtention of the novel complex [Cu( HBPAMFF )Cl 2 ]·0.25 H 2 O, in which it was observed, for the first time, that the terminal phenol of the tripodal ligand HBPAMFF does not actively participate in coordination, was described by us in a p a per published in the Journal of Molecular Structure.

With the algorithm’s suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. In this dissertation, summation-by-parts (SBP) operators and a new relaxation Runge–Kutta (RRK) scheme are used to construct mimetic and structure-preserving full discretization for non-reactive compressible computational fluid dynamics (CFD) and reaction-diffusion models. In the first chapter, we provide the necessary background and a literature survey that forms the basis of this dissertation. Next, we provide a short overview of entropy stability for general conservation laws. The second chapter covers the analysis of the Eulerian model for compressible and heat-conducting flows. We provide the necessary background of the new system of parabolic partial differential equation (PDE). Then, we present the entropy stability analysis of the model at the continuous level. Subsequently, using the SBP, we construct an entropy-stable discretization of any order for unstructured grids with tensor-product elements. The third chapter discusses the implementation of RRK methods. We start by reviewing the RRK scheme constructed to guarantee conservation or stability with respect to any inner-product norm. Then, we present the extension and generalization of RRK schemes to general convex functionals and their application to compressible fluid flow problems. The final chapter demonstrates the far-reaching capabilities of the SBP operators and RRK schemes presenting the development of a novel fully discrete Lyapunov stable discretization for reaction models with spatial diffusion. Finally, we conclude this dissertation with an overview of our achievements and future research directions.

Il est rapporté que la biodisponibilité orale de l’amoxicilline chez le porc est environ trois fois moindre que chez l’homme. Pour élucider les raisons de cette différence, la pharmacocinétique artérielle, veineuse porte et urinaire de cet antibiotique a été caractérisée à des doses intragastriques de 4 à 30 mg/kg et différents modèles compartimentaux physiologiques ont été conçus pour l’analyse des données. La biodisponibilité orale de l’amoxicilline est maximale à 4 mg/kg, avec une valeur moyenne de 52%. Les différences porto-systémiques de concentrations plasmatiques d’amoxicilline et la clairance urinaire ont permis de démontrer une augmentation de la clairance hépatique jusqu’à la dose de 30 mg/kg. Un modèle compartimental comprenant deux voies parallèles d’absorption (de type Michaelis- Menten d’accessibilité limitée dans le temps et d’ordre 1), deux compartiments de distribution (central et périphérique) deux voies d’élimination (excrétions urinaire et biliaire) est celui qui prédit le mieux les données observées. Ces résultats mettent en évidence le rôle prépondérant du transporteur saturable PepT1 dans l’absorption orale de l’amoxicilline administrée à faible dose, ainsi que l’importance croissante de l’absorption passive lors d’administration à forte dose. / It was reported that the oral bioavailability of amoxicillin in swine is about three times lower than in human beings. To elucidate the reasons for this difference, arterial, portal venous and urinary pharmacokinetics was documented at intragastric dose amounts ranging between 4 and 30 mg/kg, and several physiologic compartmental models were developed for data analysis. The maximum oral bioavailability of amoxicillin was recorded at 4mg/kg with a mean value of 52%. The portal-systemic plasma concentration differences of amoxicillin and its urinary clearance revealed an increase in hepatic clearance up to the 30 mg/kg dose. A compartmental model with two parallel absorption route (time-constrained Michaelis- Menten and first-order processes), two distribution compartments (central and peripheral) two elimination pathways (urinary and biliary excretions) best fitted the experimental data. These results highlight the paramount role of the PepT1 carriermediated, saturable absorption at low oral amoxicillin doses, as well as the increasing role of passive absorption at high doses.

Les études non destructives des processus physiologiques dans les produits agronomiques exigent des résolutions spatiales et temporelles de plus en plus élevées. L'imagerie par résonance magnétique nucléaire (RMN) est une technique totalement non-invasive qui permet d'accéder à plusieurs types de variables (architecture des tissus, variabilités spatiales de la composition, flux entrants et internes au cours de la croissance du fruit) plus difficilement quantifiables avec des méthodes destructives classiques. Un des enjeux majeur également réside dans la faculté de localiser spatialement ces transformations physiologiques et morphologiques dans les produits agronomiques. Les travaux de recherches réalisés dans le cadre de cette thèse ont pour objectif principal, la mise en œuvre d'une méthodologie de calcul et d'analyse quantitative en imagerie RMN appliquée à l'agronomie. L'implémentation, l'optimisation et la validation de la séquence FLASH combinée avec des agents de contraste efficaces en terme de relaxivité et bio-compatibles a permis d'une part, la cartographie des paramètres de relaxation et d'autre part, la quantification du transport de l'eau in vivo d'un système agronomique modèle au cours de sa croissance. Les nanoparticules de l'agent de contraste Gd3+[Fe(CN)6]3-/Mannitol ont été utilisées comme des marqueurs afin de localiser les flux hydriques dans le fruit. Le choix de la séquence d'imagerie FLASH a été motivé par la nécessite d'atteindre des résolutions temporelles suffisante pour suivre la dynamique des changements physiologiques liés au transport de l'eau dans ce type de matériau. La validation de la méthode de calcul du T1 menée sur le fantôme a révélé un bon accord par rapport aux T1 mesurés par relaxométrie. Nous avons également mis au point une procédure d'évaluation du rapport signal sur bruit et des incertitudes commises dans chaque voxel des images paramétriques M0 et T1. L'évaluation de ces incertitudes est un élément fondamental de cette analyse quantitative, afin d'assurer des interprétations fiables des images RMN. La segmentation des images nous a permis de localiser précisément les tissus où règne une forte activité cellulaire. Enfin, la modélisation compartimentale mis en oeuvre nous a permis de quantifier les paramètres cinétiques liés au transport de l'eau dans le fruit.Mots-clés: Imagerie RMN quantitative, paramètres intrinsèques, segmentation, modélisation compartimentale, agents de contraste, tissus végétaux / Non destructive studies of physiological processes in agronomic products require increasingly higher spatial and temporal resolutions. Nuclear Magnetic Resonance (NMR) imaging is a completely non-invasive technique providing access to several types of variables (tissue architecture, spatial variability of the composition, external and internal flow during fruit growth) more difficult to quantify with conventional destructive methods. One of major challenge lies in the ability to spatially localize the physiological and morphological changes in the agricultural products. The main objective of the research work in this thesis is to carry out a methodology in order to calculate and analyze quantitative NMR imaging applied to agronomy. The implementation, optimization and validation of the FLASH imaging sequence is performed in combination with innovative biocompatible contrast agents efficient in terms of relativity which allow to map in vivo relaxation parameters and then to explore water transportation in an agronomic model : the tomato during its growth. Nanoparticles of Gd3+[Fe(CN)6]3-/Mannitol contrast agents have been used as markers to localize the water flow in the fruit. The choice of the FLASH imaging sequence is motivated by the necessity to achieve sufficient high temporal resolution for monitoring the dynamics of physiological changes related to the water transport. The validation of the T1 calculation method performed on a phantom shows a good agreement compared to T1 measured by relaxometry. A systematic procedure for the estimation of the signal to noise ratio on the parametric images is also proposed which ensures a carefull determination of the intrinsic parameters of living tissues (M0 and T1) and their uncertainties. This step in the analysis ensures reliable interpretation of NMR images and permits image segmentation in order to precisely localize the tissues where there is a high cellular activity. Finally, the time dependance and the compartmental modeling allow to quantify the kinetic parameters associated with the water transport in the fruit.Keywords: Quantitative NMR imaging, intrinsic parameters, segmentation, compartmental modeling, contrast agents, plant tissues

L'objectif de cette thèse est d’étudier temporellement des phénomènes évolutifs à l'aide de la tomographie d'émission monophotonique (TEMP). La première partie de cette thèse traite le problème du mouvement respiratoire dans les images TEMP de souris. Nous présentons ici une méthode permettant de détecter ce mouvement respiratoire dans les images TEMP 4D, d'extraire un signal respiratoire intrinsèque, et de déterminer la phase du cycle respiratoire sans mouvement la plus large possible. Les données enregistrées durant ces phases sans mouvement sont alors utilisées pour reconstruire une seule image TEMP 3D sans artefact de mouvement par acquisition. Les images ainsi reconstruites présentent un bon compromis en terme de statistiques et de précision des mesures par rapport aux images TEMP 3D de base et TEMP 4D. Dans la deuxième partie, nous étudions la cinétique d'incorporation de l'iode dans l'estomac de souris à partir d'images TEMP 4D. Afin de comprendre le rôle biologique de cette accumulation dans l'estomac, nous avons modélisé le phénomène par une approche d'analyse compartimentale avec un modèle simplifiée à deux compartiments (paroi et cavité stomacale) et une entrée (sang). Les courbes temps-activité (TAC) de chaque compartiment sont déduites des observations et une première estimation des paramètres a été obtenue. / The aim of this thesis is to investigate temporally evolving phenomena with the use of single photon emission computed tomography (SPECT).The first part of this thesis addresses the problem of respiratory motion in SPECT images of mice. The presented method permits us to detect the respiratory motion in 4D SPECT images, to extract an intrinsic respiratory signal and to determine the widest possible phase of the respiratory cycle without movement. The data recorded during these motionless phases are then used to reconstruct a single 3D SPECT image without motion artefacts per acquisition. Reconstructed motionless SPECT images present a good compromise in terms of statistics and accuracy of the measurements with respect to basic 3D SPECT and 4D SPECT images. In the second part, we study the iodide uptake kinetics in the stomach 99mTc-pertechnetate biodistribution with the of mice through the study of use of 4D SPECT images. To understand the biological role of the iodide accumulation in the stomach, we modelled the phenomenon with a compartmental analysis approach using a simplified two-compartment (stomach wall and cavity) model with one input (blood). Time activity curves (TAC) of each compartment are deduced from observations and a first estimation of the parameters was obtained.

O presente trabalho possui como metas o estudo, simulação, identificação de parâmetros e comparação estatística de modelos compartimentais utilizados em tomografia por emissão de pósitrons (PET). Para tanto, propõe-se utilizar a metodologia de equações de sensibilidade e o método de Levenberg-Marquardt para a tarefa de estimação de parâmetros característicos das equações diferenciais descritoras dos referidos sistemas. Para comparação entre modelos, foi empregado o critério de informação de Akaike. São consideradas três estruturas compartimentais compostas, respectivamente, por dois compartimentos e duas constantes características, três compartimentos e quatro constantes características e quatro compartimentos e seis constantes características. Os dados considerados neste texto foram sintetizados preocupando-se em reunir as principais características de um exame de tomografia real, tais como tipo e nível de ruído e morfologia de função de excitação do sistema. Para tanto, foram utilizados exames de pacientes do setor de Medicina Nuclear do Instituto do Coração da Faculdade de Medicina da Universidade de São Paulo. Aplicando-se a metodologia proposta em três níveis de ruído (baixo, médio e alto), obteve-se concordância do melhor modelo em graus forte e considerável (com índices de Kappa iguais a 0.95, 0.93 e 0.63, respectivamente). Observou-se que, com elevado nível de ruído e modelos mais complexos (quatro compartimentos), a classificação se deteriora devido ao pequeno número de dados para a decisão. Foram desenvolvidos programas e uma interface gráfica que podem ser utilizadas na investigação, elaboração, simulação e identificação de parâmetros de modelos compartimentais para apoio e análise de diagnósticos clínicos e práticas científicas. / This work has as goals the study, simulation, parameter identification and statistical comparison of compartmental models used in positron emission tomography (PET). We propose to use the methodology of sensitivity equations and the method of Levenberg-Marquardt for the task of estimating the characteristic parameters of the differential equations describing such systems. For model comparison, Akaikes information criterion is applied. We have considered three compartmental structures represented, respectively, by two compartments and two characteristic constants, three compartments and four characteristic constants and four compartments and six characteristics constants. The data considered in this work were synthesized taking into account key features of a real tomography exam, such as type and level of noise and morphology of the input function of the system. To this end, we used tests of patients in the sector of Nuclear Medicine of the Heart Institute of the Faculty of Medicine, University of São Paulo. Applying the proposed methodology with three noise levels (low, medium and high), we obtained agreement of the best model with strong and considerable degrees (with Kappa indexes equal to 0.95, 0.93 and 0.63, respectively). It was observed that, with high noise level and more complex models (four compartments), the classification is deteriorated due to lack of data for the decision. Programs have been developed and a graphical interface that can be used in research, development, simulation and parameter identification of compartmental models, supporting analysis of clinical diagnostics and scientific practices.