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Dans les dernières décennies, l'impact dû à l'altération de la microstructure du tissu cardiaque dans la survenue de troubles arythmiques (syndrome de Brugada, fibrillation auriculaire, syndromes de repolarisation précoce…) est de plus en plus étudié. Les données expérimentales relatives au fonctionnement et aux régulations intervenant aux échelles cellulaires et subcellulaires (jonctions communiquantes, rôle de certains canaux ioniques) sont de plus en plus nombreuses, et fournissent un cadre adapté aux numériciens pour développer ou affiner des modèles et en valider les comportements. Dans cette thèse, nous proposons le développement et l'étude d'un modèle « microscopique » prenant en compte la géométrie individuelle des cellules et les jonctions communiquantes entre elles. Le modèle vise à comprendre la propagation du potentiel d'action au sein d'un réseau de cellules. Nous établissons ce modèle via une étude du comportement des ions dans les cellules. Ce comportement, décrit par diverses équations de la physique microscopique (électrostatique...), fournit un cadre à partir duquel, en effectuant quelques analyses dimensionnelles et une étude asymptotique, nous dérivons le modèle susmentionné. Puis, nous démontrons l'existence d'une solution à ce modèle à l'aide d'un processus de discrétisation en temps « semi-implicite » et de théorèmes de compacité. Nous proposons ensuite un ensemble de simulations dont l'objet est de comprendre la propagation des potentiels d'action entres cellules au sein d'un réseau, et en particulier le rôle des jonctions communiquantes. Nous étudions différents modèles de jonctions communiquantes, dont un non-linéaire et dépendant du temps. Cette thèse ouvre de nombreuses perspectives, à courte échéance des comparaisons à des observations expérimentales chez la souris, et à plus long terme de recherche sur les mécanismes de propagation à l'échelle cellulaire et leurs impact sur les troubles du rythme cardiaque. / During the last decades, studies regarding the prospective impact of the alterations at the microscopic scale of the heart tissue in the appearance of arrhythmias (Brugada's syndrome, atrial fibrillation, early repolarization syndrome...) have been more numerous. The amount of experimental data regarding the behaviors and regulations that occur at a cellular and a subcellular (gap junctions, role of specific ionic channels) is increasing and these data provide an adapted frame for the computational mathematicians to develop or improve models and confirm their behaviour. In this thesis, we developed and studied a ``microscopic'' model taking into account the individual geometry of the cells and the gap junctions between them. This model is designed to enhance our understanding of the action potential propagation in a network of cells. We extracted this model using a study of the ions movements in the cells. These movements, described by various microscopic physics equations (electrostatic...), and some dimensional analysis, including an asymptotic study, allow us to derive the model. We then show that the problem described by such a model has a solution, via a semi-implicit time discretization process and compacity arguments. Afterwards, we offer numerous simulations in order to enhance our understanding of the action potential propagation between the cells of various networks. We specifically customize the gap junction models we use (a geometric one, a linear one and a non-linear one) to enhance our comprehension. This thesis introduces many questions. On the short-term, on the comparison between experimental data observed on mice cells and our results. On the long-term regarding the mechanisms regulating the action potential propagation, and their impact on the alterations of the cardiac rhythm.

Orientadores: Jose Wilson Magalhães Bassani, Rosana Almada Bassani / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-06T07:47:18Z (GMT). No. of bitstreams: 1 Boer_DenileCominato_M.pdf: 557480 bytes, checksum: e378c01e865d04a595d3f0e7ad3c60dd (MD5) Previous issue date: 2006 / Resumo: Embora haja demonstração de que a estimulação simpática tenha efeito facilitatório sobre a indução de atividade espontânea em miocárdio há controvérsia sobre a participação dos tipos de adrenoceptores na mediação deste efeito. No presente trabalho, descrevemos um método desenvolvido para determinação, em átrio esquerdo isolado (AE) de rato, da relação concentração-efeito para agentes que exercem efeito arritmogênico por aumento da mobilização celular de 'Ca POT. 2+¿. O método baseou-se na interposição de pausas estimulatórias, durante as quais registraram-se contrações espontâneas (CE), precedidas ou não por trens estimulatórios de alta freqüência (5 Hz). O protocolo estimulatório foi repetido na presença de diferentes concentrações de agonistas. Para cada concentração de agonista, a resposta arrítmica foi considerada como a soma dos números de CE/min, no total de preparações. Foi analisada também a resposta inotrópica, como sendo o incremento de força ou encurtamento de pico, desenvolvidos em AE e miócitos ventriculares (MV), respectivamente. A relação foi ajustada por uma função sigmóide para cálculo de Min (i.e., valor da variável na ausência do agonista), Rmax (resposta máxima) e pD2 (-log da concentração do agonista que produziu uma resposta igual a 50% de Rmax). Este método foi aplicado no estudo dos tipos de adrenoceptores envolvidos na resposta arrítmica a catecolaminas em AE e MV. A Rmax inotrópica à ativação de adrenoceptores 'alfa IND. 1¿ + 'beta IND. 1¿ foi comparável àquela por ativação de apenas receptores 'beta IND. 1¿, em ambos AE e MV. Já a ativação de adrenoceptores 'alfa IND. 1¿ produziu uma Rmax inotrópica de apenas metade daquela observada pela estimulação 'alfa IND. 1¿ + 'beta IND. 1¿. Da mesma forma, a resposta arrítmica foi semelhante para estimulação de adrenoceptores a1+ß1 e de apenas receptores 'beta IND. 1¿. Entretanto, nenhuma resposta foi obtida pela estimulação de receptores adrenérgico do tipo 'alfa IND. 1¿. Estes resultados indicam que a estimulação de adrenoceptores 'alfa IND. 1¿, apesar de evocar uma resposta inotrópica positiva em ambos AE e MV, não é arritmogênica. A ativação do tipo 'beta¿, por outro lado, parece ser a principal via para estimulação inotrópica simpática e na indução de arritmias. Além disso, concluímos que parece existir antagonismo funcional entre os subtipos de adrenoceptores 'beta¿, manifestado por ações pró- e anti-arrítmicas dos subtipos 'beta IND. 1¿ e 'beta IND. 2¿, respectivamente, em miocárdio (tanto atrial, quanto ventricular) de rato / Abstract: Although it has been shown that sympathetic stimulation facilitates the appearance of myocardial spontaneous activity, it is still not clear which types of adrenoceptors mediate this effect. In this study, we describe a method developed for determination, in isolated rat atria (AE), of the concentration-effect relationship for arrhythmogenic agents that act via promotion of cell 'Ca POT. 2+¿ overload. The method was based on the interposition of stimulatory rest periods, during which spontaneous contractions (CE) were recorded, preceded or not by high frequency (5 Hz) stimulus trains. The stimulation protocol was applied at each agonist concentration, and the arrhythmic response was taken as the sum of the number of CE/min in all preparations. The positive inotropic response was considered as the agonist-dependent increment of developed force or peak shortening in AE and isolated ventricular myocytes (MV), respectively. Concentration-effect curves were determined by fitting a sigmoid function, from which the following parameters were estimated: Min (i.e., value of the variable in the absence of the agonist), Rmax (maximal response) e 'pD IND. 2¿ (-log of the molar agonist concentration that evokes a response equal to 50% of Rmax). This method was applied to investigate the adrenoceptor types involved in the mediation of catecholamine-induced arrhythmogenesis in AE and MV. Inotropic Rmax to activation of 'alfa IND. 1¿ + 'beta IND. 1¿ adrenoceptors was comparable to that of activation of solely 'beta IND. 1¿ adrenoceptors in both AE and MV. However, Rmax to selective 'alfa IND. 1¿ adrenoceptor activation was only half of that produced by 'alfa IND. 1¿ + 'beta IND. 1¿ adrenoceptor stimulation. The arrhythmic responses to 'alfa IND. 1¿ + 'beta IND. 1¿ and 'beta IND.1¿ receptor stimulation were similar, but selective a1 adrenoceptor activation was unable to evoke any spontaneous activity. The results indicate that a1 adrenoceptors, although able to mediate stimulation in both AE and MV, are not involved in arrhythmogenesis. 'beta¿-adrenoceptor activation, thus, seems the main type involved in both inotropic and arrhythmic responses to catecholamines. In addition, our results point out a functional antagonism between 'beta¿-adrenoceptor subtypes: i.e., pro- and anti-arrhythmic effects mediated by 'beta IND. 1¿ and 'beta IND. 2¿-adrenoceptors, respectively in both atrial and ventricular rat myocardium / Mestrado / Engenharia Biomedica / Mestre em Engenharia Elétrica