Cette thèse est consacrée à la modélisation mathématique de la coagulation sanguine et de la formation de thrombus dans des conditions normales et pathologiques. La coagulation sanguine est un mécanisme défensif qui empêche la perte de sang suite à la rupture des tissus endothéliaux. C'est un processus complexe qui est règlementé par différents mécanismes mécaniques et biochimiques. La formation du caillot sanguin a lieu dans l'écoulement sanguin. Dans ce contexte, l'écoulement à faible taux de cisaillement stimule la croissance du caillot tandis que la circulation sanguine à fort taux de cisaillement la limite. Les désordres qui affectent le système de coagulation du sang peuvent provoquer différentes anomalies telles que la thrombose (coagulation exagérée) ou les saignements (insuffisance de coagulation). Dans la première partie de la thèse, nous présentons un modèle mathématique de coagulation sanguine. Le modèle capture la dynamique essentielle de la croissance du caillot dans le plasma et le flux sanguin quiescent. Ce modèle peut être réduit à un modèle qui consiste en une équation de génération de thrombine et qui donne approximativement les mêmes résultats. Nous avons utilisé des simulations numériques en plus de l'analyse mathématique pour montrer l'existence de différents régimes de coagulation sanguine. Nous spécifions les conditions pour ces régimes sur différents paramètres pathophysiologiques du modèle. Ensuite, nous quantifions les effets de divers mécanismes sur la croissance du caillot comme le flux sanguin et l'agrégation plaquettaire. La partie suivante de la thèse étudie certaines des anomalies du système de coagulation sanguine. Nous commençons par étudier le développement de la thrombose chez les patients présentant une carence en antihrombine ou l'une des maladies inflammatoires. Nous déterminons le seuil de l'antithrombine qui provoque la thrombose et nous quantifions l'effet des cytokines inflammatoires sur le processus de coagulation. Puis, nous étudions la compensation de la perte du sang après un saignement en utilisant un modèle multi-échelles qui décrit en particulier l'érythropoïèse et la production de l'hémoglobine. Ensuite, nous évaluons le risque de thrombose chez les patients atteints de cancer (le myélome multiple en particulier) et le VIH en combinant les résultats du modèle de coagulation sanguine avec les produits des modèles hybrides (discret-continues) multi-échelles des systèmes physiologiques correspondants. Finalement, quelques applications cliniques possibles de la modélisation de la coagulation sanguine sont présentées. En combinant le modèle de formation du caillot avec les modèles pharmacocinétiques pharmacodynamiques (PK-PD) des médicaments anticoagulants, nous quantifions l'action de ces traitements et nous prédisons leur effet sur des patients individuels / This thesis is devoted to the mathematical modelling of blood coagulation and clot formation under flow in normal and pathological conditions. Blood coagulation is a defensive mechanism that prevents the loss of blood upon the rupture of endothelial tissues. It is a complex process that is regulated by different mechanical and biochemical mechanisms. The formation of the blood clot takes place in blood flow. In this context, low-shear flow stimulates clot growth while high-shear blood circulation limits it. The disorders that affect the blood clotting system can provoke different abnormalities such thrombosis (exaggerated clotting) or bleeding (insufficient clotting). In the first part of the thesis, we introduce a mathematical model of blood coagulation. The model captures the essential dynamics of clot growth in quiescent plasma and blood flow. The model can be reduced to a one equation model of thrombin generation that gives approximately the same results. We used both numerical simulations and mathematical investigation to show the existence of different regimes of blood coagulation. We specify the conditions of these regimes on various pathophysiological parameters of the model. Then, we quantify the effects of various mechanisms on clot growth such as blood flow and platelet aggregation. The next part of the thesis studies some of the abnormalities of the blood clotting system. We begin by investigating the development of thrombosis in patients with antihrombin deficiency and inflammatory diseases. We determine the thrombosis threshold on antithrombin and quantify the effect of inflammatory cytokines on the coagulation process. Next, we study the recovery from blood loss following bleeding using a multiscale model which focuses on erythropoiesis and hemoglobin production. Then, we evaluate the risk of thrombosis in patients with cancer (multiple myeloma in particular) and HIV by combining the blood coagulation model results with the output of hybrid multiscale models of the corresponding physiological system. Finally, possible clinical applications of the blood coagulation modelling are provided. By combining clot formation model with pharmacokinetics-pharmacodynamics (PK-PD) models of anticoagulant drugs, we quantify the action of these treatments and predict their effect on individual patients

Durante a cirurgia de revascularização do miocárdio com circulação extracorpórea e hipotermia (CEC-H) ocorre alteração na efetividade do propofol e na sua farmacocinética realizada a partir das concentrações plasmáticas do propofol total no decurso do tempo. A ligação do propofol à proteína plasmática parece estar alterada em consequência de diversos fatores incluindo a hemodiluição e a heparinização que ocorre no início da circulação extracorpórea, uma vez que se reportou anteriormente que a concentração plasmática do propofol livre aumentou durante a realização da circulação extracorpórea normotérmica. Por outro lado, a infusão alvo controlada é recomendada para manter a concentração plasmática do propofol equivalente ao alvo de 2 &#181g/mL durante a intervenção cirúrgica com CEC-H. Se alterações significativas na hipnose do propofol ocorrem nesses pacientes, então o efeito aumentado desse agente hipnótico poderia estar relacionado à redução na extensão da ligação do fármaco as proteínas plasmáticas; entretanto, o assunto ainda permanece em discussão e necessita de investigações adicionais. Assim, o objetivo do estudo foi investigar as concentrações plasmáticas de propofol livre em pacientes durante a revascularização do miocárdio com e sem o procedimento de CEC-H através da abordagem PK-PD. Dezenove pacientes foram alocados e estratificados para realização de cirurgia de revascularização do miocárdio com circulação extracorpórea (CEC-H, n=10) ou sem circulação extracorpórea (NCEC, n=9). Os pacientes foram anestesiados com sufentanil e propofol alvo de 2 &#181g/mL. Realizou-se coleta seriada de sangue para estudo farmacocinético e o efeito foi monitorado através do índice bispectral (BIS) para medida da profundidade da hipnose no período desde a indução da anestesia até 12 horas após o término da infusão de propofol, em intervalos de tempo pré-determinados no protocolo de estudo. As concentrações plasmáticas foram determinadas através de método bioanalítico pela técnica de cromatografia líquida de alta eficiência. A farmacocinética foi investigada a partir da aplicação do modelo aberto de dois compartimentos, PK Solutions v. 2. A análise PK-PD foi realizada no Graph Pad Prisma v.5.0 após a escolha do modelo do efeito máximo (EMAX sigmóide, slope variável). Os dados foram analisados utilizando o Prisma v. 5.0, p<0,05, significância estatística. As concentrações plasmáticas de propofol total foram comparáveis nos dois grupos (CEC-H e NCEC); entretanto o grupo CEC-H evidenciou aumento na concentração do propofol livre de 2 a 5 vezes em função da redução na ligação do fármaco às proteínas plasmáticas. A farmacocinética do propofol livre mostrou diferença significativa entre os grupos no processo de distribuição pelo prolongamento da meia vida e aumento do volume aparente, e no processo de eliminação em função do aumento na depuração plasmática e redução na meia vida biológica no grupo CEC-H. A escolha do modelo EMAX sigmóide, slope variável foi adequada uma vez que se evidenciou alta correlação entre os valores do índice bispectral e as concentrações plasmáticas do propofol livre (r2>0.90, P<0.001) para os pacientes investigados. / During coronary artery bypass grafting (CABG) surgery with cardiopulmonary bypass (CPB) profound changes occur on propofol effect and on kinetic disposition related to total drug plasma measurements in these patients. It was reported that drug plasma binding could be altered as a consequence of hemodilution and heparinization before starts CPB since free propofol plasma levels was increased by twice under normothermic procedure. In addition, the target controlled infusion (TCI) is recommended to maintain propofol plasma concentration (2 &#181g/mL) during CABG CPB-H intervention. However, whether significant changes that occur in propofol hypnosis in these patients could be related to the reduction on the extension of drug plasma binding remain unclear and under discussion until now. Then, the objective of this study was to investigate propofol free plasma levels in patients undergoing CABG with and without CPB by a pharmacokinetics-pharmacodynamics (PK-PD) approach. Nineteen patients were scheduled for on-pump coronary artery bypass grafting (CABG-CPB, n=10) or off-pump coronary artery bypass grafting (OPCABG, n=9) were anesthetized with sufentanil and propofol TCI (2 &#181g/mL). Blood samples were collected for drug plasma measurements and BIS were applied to access the depth of hypnosis from the induction of anesthesia up to 12 hours after the end of propofol infusion, at predetermined intervals. Plasma drug concentrations were measured using high-performance liquid chromatography, followed by a propofol pharmacokinetic analysis based on two compartment open model, PK Solutions v.2; PK-PD analysis was performed by applying EMAX model, sigmoid shape-variable slope and data were analyzed using Prisma v. 5.0, considering p<0.05 as significant difference between groups. The total propofol plasma concentrations were comparable in both groups during CABG; however it was shown in CPB-group significant increases in propofol free plasma concentration by twice to fivefold occur as a consequence of drug plasma protein binding reduced in these patients. Pharmacokinetics of free propofol in CPB-H group compared to OPCAB group based on two compartment open model was significantly different by the prolongation of distribution half-life, increases on plasma clearance, and biological half-life shortened. In addition, the kinetic disposition of propofol changes in a different manner considering free drug levels in the CPB-H group against OPCAB group as follows: prolongation of distribution half-life and increases on volume of distribution, remaining unchanged biological half-life in spite of plasma clearance increased. BIS values showed a strong correlation with free drug levels (r2>0.90, P<0.001) in CPB-H group and also in OPCAB group by the chosen EMAX model sigmoid shape-variable slope analyzed by GraphPad Prisma v.5.0.

Cette thèse est consacrée à la modélisation mathématique de l'hématopoïèse et des maladies sanguines. Plusieurs modèles traitant d'aspects différents et complémentaires de l'hématopoïèse y sont étudiés.Tout d'abord, un modèle multi-échelle de l'érythropoïèse est analysé, dans lequel sont décrits à la fois le réseau intracellulaire, qui détermine le comportement individuel des cellules, et la dynamique des populations de cellules. En utilisant des données expérimentales sur les souris, nous évaluons les rôles des divers mécanismes de retro-contrôle en réponse aux situations de stress.Ensuite, nous tenons compte de la distribution spatiale des cellules dans la moelle osseuse, question qui n'avait pas été étudiée auparavant. Nous décrivons l'hématopoïèse normale à l'aide d'un système d'équations de réaction-diffusion-convection et nous démontrons l'existence d'une distribution stationnaire des cellules. Puis, nous introduisons dans le modèle les cellules malignes. Pour certaines valeurs des paramètres, la solution "disease-free" devient instable et une autre solution, qui correspond à la leucémie, apparaît. Cela mène à la formation d'une tumeur qui se propage dans la moelle osseuse comme une onde progressive. La vitesse de cette propagation est étudiée analytiquement et numériquement. Les cellules de la moelle osseuse échangent des signaux qui régulent le comportement cellulaire. Nous étudions ensuite une équation integro-différentielle qui décrit la communication cellulaire et nous prouvons l'existence d'une solution du type onde progressive en utilisant la théorie du degré topologique et la méthode de Leray et Schauder. L'approche multi-agent est utilisée afin d'étudier la distribution des différents types de cellules dans la moelle osseuse.Finalement, nous étudions un modèle de type "Physiologically Based Pharmacokinetics-Pharmacodynamics" du traitement de la leucémie par l'AraC. L'AraC agit comme chimiothérapie et induit l'apoptose de toutes les cellules proliférantes, saines et malignes. La pharmacocinétique donne accès à la concentration intracellulaire d'AraC. Cette dernière, à son tour, détermine la dynamique des populations cellulaires et, par conséquent, l'efficacité de différents protocoles de traitement.

Durante a cirurgia de revascularização do miocárdio com circulação extracorpórea e hipotermia (CEC-H) ocorre alteração na efetividade do propofol e na sua farmacocinética realizada a partir das concentrações plasmáticas do propofol total no decurso do tempo. A ligação do propofol à proteína plasmática parece estar alterada em consequência de diversos fatores incluindo a hemodiluição e a heparinização que ocorre no início da circulação extracorpórea, uma vez que se reportou anteriormente que a concentração plasmática do propofol livre aumentou durante a realização da circulação extracorpórea normotérmica. Por outro lado, a infusão alvo controlada é recomendada para manter a concentração plasmática do propofol equivalente ao alvo de 2 &#181g/mL durante a intervenção cirúrgica com CEC-H. Se alterações significativas na hipnose do propofol ocorrem nesses pacientes, então o efeito aumentado desse agente hipnótico poderia estar relacionado à redução na extensão da ligação do fármaco as proteínas plasmáticas; entretanto, o assunto ainda permanece em discussão e necessita de investigações adicionais. Assim, o objetivo do estudo foi investigar as concentrações plasmáticas de propofol livre em pacientes durante a revascularização do miocárdio com e sem o procedimento de CEC-H através da abordagem PK-PD. Dezenove pacientes foram alocados e estratificados para realização de cirurgia de revascularização do miocárdio com circulação extracorpórea (CEC-H, n=10) ou sem circulação extracorpórea (NCEC, n=9). Os pacientes foram anestesiados com sufentanil e propofol alvo de 2 &#181g/mL. Realizou-se coleta seriada de sangue para estudo farmacocinético e o efeito foi monitorado através do índice bispectral (BIS) para medida da profundidade da hipnose no período desde a indução da anestesia até 12 horas após o término da infusão de propofol, em intervalos de tempo pré-determinados no protocolo de estudo. As concentrações plasmáticas foram determinadas através de método bioanalítico pela técnica de cromatografia líquida de alta eficiência. A farmacocinética foi investigada a partir da aplicação do modelo aberto de dois compartimentos, PK Solutions v. 2. A análise PK-PD foi realizada no Graph Pad Prisma v.5.0 após a escolha do modelo do efeito máximo (EMAX sigmóide, slope variável). Os dados foram analisados utilizando o Prisma v. 5.0, p<0,05, significância estatística. As concentrações plasmáticas de propofol total foram comparáveis nos dois grupos (CEC-H e NCEC); entretanto o grupo CEC-H evidenciou aumento na concentração do propofol livre de 2 a 5 vezes em função da redução na ligação do fármaco às proteínas plasmáticas. A farmacocinética do propofol livre mostrou diferença significativa entre os grupos no processo de distribuição pelo prolongamento da meia vida e aumento do volume aparente, e no processo de eliminação em função do aumento na depuração plasmática e redução na meia vida biológica no grupo CEC-H. A escolha do modelo EMAX sigmóide, slope variável foi adequada uma vez que se evidenciou alta correlação entre os valores do índice bispectral e as concentrações plasmáticas do propofol livre (r2>0.90, P<0.001) para os pacientes investigados. / During coronary artery bypass grafting (CABG) surgery with cardiopulmonary bypass (CPB) profound changes occur on propofol effect and on kinetic disposition related to total drug plasma measurements in these patients. It was reported that drug plasma binding could be altered as a consequence of hemodilution and heparinization before starts CPB since free propofol plasma levels was increased by twice under normothermic procedure. In addition, the target controlled infusion (TCI) is recommended to maintain propofol plasma concentration (2 &#181g/mL) during CABG CPB-H intervention. However, whether significant changes that occur in propofol hypnosis in these patients could be related to the reduction on the extension of drug plasma binding remain unclear and under discussion until now. Then, the objective of this study was to investigate propofol free plasma levels in patients undergoing CABG with and without CPB by a pharmacokinetics-pharmacodynamics (PK-PD) approach. Nineteen patients were scheduled for on-pump coronary artery bypass grafting (CABG-CPB, n=10) or off-pump coronary artery bypass grafting (OPCABG, n=9) were anesthetized with sufentanil and propofol TCI (2 &#181g/mL). Blood samples were collected for drug plasma measurements and BIS were applied to access the depth of hypnosis from the induction of anesthesia up to 12 hours after the end of propofol infusion, at predetermined intervals. Plasma drug concentrations were measured using high-performance liquid chromatography, followed by a propofol pharmacokinetic analysis based on two compartment open model, PK Solutions v.2; PK-PD analysis was performed by applying EMAX model, sigmoid shape-variable slope and data were analyzed using Prisma v. 5.0, considering p<0.05 as significant difference between groups. The total propofol plasma concentrations were comparable in both groups during CABG; however it was shown in CPB-group significant increases in propofol free plasma concentration by twice to fivefold occur as a consequence of drug plasma protein binding reduced in these patients. Pharmacokinetics of free propofol in CPB-H group compared to OPCAB group based on two compartment open model was significantly different by the prolongation of distribution half-life, increases on plasma clearance, and biological half-life shortened. In addition, the kinetic disposition of propofol changes in a different manner considering free drug levels in the CPB-H group against OPCAB group as follows: prolongation of distribution half-life and increases on volume of distribution, remaining unchanged biological half-life in spite of plasma clearance increased. BIS values showed a strong correlation with free drug levels (r2>0.90, P<0.001) in CPB-H group and also in OPCAB group by the chosen EMAX model sigmoid shape-variable slope analyzed by GraphPad Prisma v.5.0.

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