The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

Plusieurs maladies entraînent soit une augmentation soit une diminution du taux des acides gras (AG) et de leurs dérivés circulants, notamment les acyl-carnitines (AC). Ce changement a été soupçonné comme étant la cause de importants dérangements électriques. Nous avons montré que les AC à chaine longue (LCAC) du côté extracellulaire modulent le canal hERG de façon spécifique, modulant sa amplitude de courant et sa cinétique. Aucun AC testé n’a eu d’effet en intracellulaire. La CAR et les MCAC n’ont eu aucun effet. Les AC ne modulent pas les courants IKS et IK1. Le canal Cav1.2 est modulé par C16-CAR et le C16 dans la lignée HEK293-ICaL et dans des cardiomyocytes de rat. En condition physiologique il existe donc un lien strict entre le métabolisme énergétique et activité électrique cardiaque qui entraine une modulation permanente du canal hERG par les LCAC. La régulation par les LCAC du canal hERG et peut être celle du canal ICaL, pourraient participer au dérangement électrique à l’origine du déclenchement de troubles du rythme cardiaque retrouvé dans certaines maladies. / Several diseases can cause either an increase or a decrease in the rate of fatty acids (FAs) and their derivatives circulating, including acyl-carnitines (AC). This change is suspected as being the cause of major cardiac electrical perturbations. We have shown that long-chain AC (LCAC) modulate specifically by the extracellular side the hERG channel, regulating its current amplitude and kinetics. All AC tested had no effect when applied intracellularly. Carnitine and medium chain AC had no effect on hERG. LCAC does not modulate IK1 and IKS. Cav1.2 channel is modulated by C16 and C16-CAR in line HEK293-ICaL and rat cardiomyocytes. In physiological conditions there exists a strict link between energy metabolism and cardiac electrical activity which causes a permanent modulation of hERG channel by the LCAC. Regulation by the LCAC of the hERG channel and maybe ICaL, could participate in the electrical disturbance causing the onset of cardiac arrhythmia found in certain diseases.

The underlying causes of variability in the electrical activity of hearts from individuals of the same species are not well understood. Understanding this variability is important to enable prediction of the response of individual hearts to diseases and therapies. Current experimental and computational methods for investigating the behaviour of the heart do not incorporate biological variation between individuals. In experimental studies, experimental results are averaged together to control errors and determine the average behaviour of the studied organism. In computational studies, averaged experimental data is usually used to develop models, and these models therefore represent a 'typical' organism, with all information on variability within the species having been lost. In this thesis we develop a methodology for modelling variability between individuals of the same species in cardiac cellular electrophysiology, motivated by the inability of traditional computational modelling approaches to capture experimental variability. A first study is conducted using traditional modelling approaches to investigate potentially pro-arrhythmic abnormalities in rabbit Purkinje fibres. A comparison with experimental recordings highlights their wide variability and the inability of existing computer modelling approaches to capture it. This leads to the development of a novel methodology that integrates the variability observed in experimental data with computational modelling and simulation, by building experimentally-calibrated populations of computational models, that collectively span the variability seen in experimental data. We apply this methodology to construct a population of rabbit Purkinje cell models. We show that our population of models can quantitatively predict the range of responses, not just the average response, to application of the potassium channel blocking drug dofetilide. This demonstrates an important potential application of our methodology, for predicting pro-arrhythmic drug effects in safety pharmacology. We then analyse a data set of experimental recordings from human ventricular tissue preparations, and use this data to develop a population of human ventricular cell models. We apply this population to study how variability between individuals alters the susceptibility of cardiac cells to developing drug-induced repolarisation abnormalities. These abnormalities can increase the chance of fatal arrhythmias, but the mechanisms that determine individual susceptibility are not well-understood.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T14:38:55Z No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:42:47Z (GMT) No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Made available in DSpace on 2018-01-23T13:42:47Z (GMT). No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) Previous issue date: 2017-08-28 / A fibrilação ventricular é uma arritmia cardíaca listada como uma das principais causas de morte no mundo industrializado, por isso, a importância do estudo do comportamento elétrico cardíaco. O equipamento mais indicado para tentar reverter este quadro de arritmia é o desfibrilador, que submete o tórax do paciente a um campo elétrico de alta energia. Entretanto essa técnica pode causar efeitos graves como queimaduras e dor intensa. Técnicas menos agressivas vêm sendo estudadas e consideram, por exemplo, protocolos com múltiplos estímulos de baixa energia. Observou-se que, nessas estratégias alternativas, a rede vascular cardíaca pode ter papel importante com relação ao padrões espaço-temporais gerados pelos estímulos. Nesta mesma direção, este trabalho apresenta um estudo computacional sobre a influência da rede vascular durante estímulos por campo elétrico em tecidos cardíacos. O fenômeno é capturado por um sistema não-linear de equações diferenciais parciais. Para resolver este modelo numericamente os Métodos de Volumes Finitos (MVF) e de Phase-Field (MPF) foram combinados buscando assim a caracterização geométrica de vasos arteriais durante simulações de desfibrilação de tecido cardíaco. Os resultados obtidos sugerem que os métodos usados (MVF+MPF) são adequados para o estudo de protocolo para desfibrilação cardíaca. / The ventricular fibrillation is a cardiac arrhythmia listed as one of the leading causes of death within the industrialized world, hence the study of cardiac electrical behavior is an important research area. The most used equipment for the reversal of this condition is the defibrillator, which subjects the patient's chest to a high-energy electric field. However, it can have serious effects such as burns and severe pain. Less aggressive techniques have been studied and considered, for example, protocols with multiple low energy stimuli. It was observed that, in this alternative technique, the cardiac vascular network may play an important role in relation to the spatial-temporal patterns generated by the stimuli. This work presents a computational study about the influence of the vascular network during electrical field stimuli in cardiac tissues. The phenomenon is described by a nonlinear system of partial differential equations. To solve this model numerically the Finite Volume Method (FVM) and the Phase-Field Method (PFM) were combined, thus seeking a better geometric characterization of arterial vessels during simulations of cardiac tissue defibrillation. The results obtained in this work suggest that these methods (FVM + PFM) are suitable for the protocol study for cardiac defibrillation.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-03T17:31:40Z No. of bitstreams: 1 carolinemendoncacosta.pdf: 8702151 bytes, checksum: 71f420415d76b4959dd71a63dd2b39ad (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T20:17:19Z (GMT) No. of bitstreams: 1 carolinemendoncacosta.pdf: 8702151 bytes, checksum: 71f420415d76b4959dd71a63dd2b39ad (MD5) / Made available in DSpace on 2017-03-06T20:17:19Z (GMT). No. of bitstreams: 1 carolinemendoncacosta.pdf: 8702151 bytes, checksum: 71f420415d76b4959dd71a63dd2b39ad (MD5) Previous issue date: 2011-02-28 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / Há algumas décadas atrás acreditava-se que o tecido cardíaco era contínuo e uniformemente conectado. Atualmente, sabe-se que as células do tecido cardíaco são conectadas umas às outras por canais especiais chamados junções gap, por onde há fluxo de corrente entre células vizinhas. Estas células por sua vez estão arranjadas em distintas camadas formando fibras de músculo cercadas por espaços extracelulares e tecido conectivo. A modelagem da eletrofisiologia cardíaca é uma importante ferramenta na compreensão de fenômenos cardíacos, como arritmias e outras doenças. Um dos modelos mais utilizados para descrever a atividade elétrica no coração é o modelo Monodomínio, no qual considera-se um tecido contínuo e uniformemente conectado obtido através da técnica de homogeneização. Em condições normais esta é uma aproximação adequada, uma vez que a influência da microestrutura do tecido não é tão evidente. Por outro lado, sabe-se que algumas condições patológicas alteram a conectividade do tecido, como em casos de infarto do miocárdio, onde é observada uma redução no acoplamento intercelular formando uma barreira parcial à propagação elétrica e no caso de fibrose, onde é observado um aumento do tecido conectivo formando uma barreira total à propagação. Nestas circunstâncias, estudos mostram que o modelo Monodomínio não é capaz de reproduzir os efeitos destas barreiras microscópicas na propagação elétrica. Sendo assim, neste trabalho serão apresentadas algumas das limitações deste modelo em casos de acoplamento intercelular reduzido e também uma técnica numérica baseada no método dos elementos finitos para reproduzir barreiras microscópicas causadas pela presença de espaços extracelulares e tecido conectivo no tecido cardíaco. / A few decades ago the cardiac tissue was believed to be an uniformly connected continumm. Currently, it is known that the cardiac cells are connected to each other via special protein channels called gap junctions, through which the ionic current flows between neighboring cells. The cardiac cells are arranged in distinct layers of muscle fibers surrounded by extracellular space and connective tissue. The cardiac electrophysiology modeling is an important tool in understanding cardiac phenomena, such as arrythmias and other cardiac diseases. The Monodomain model is extensively used to describe the electrical activity in the heart. In this model the cardiac tissue is considered an uniformly connected continumm obtained by the application the homogenization technique. This is a reasonably approximation for normal physiological conditions, as in this case the cardiac microstructure is not so evident. On the other hand, some pathological conditions are known to modify the connectivity of the tissue. In isquemic and infarcted tissue it is observed a reduction in the intercellular coupling representing a partial barrier to the electrical propagation. In adittion, during fibrosis it is observed an excessive growth of the conective tissue, representing a total barrier to the electrical propagation. In such cases, recent simulation studies show that the Monodomain model can not reproduce such microscopic barrier effect on the electrical propagation. In this work we present some limitations of this model for the case of low intercellular coupling and also a numerical technique based on the finite element method to reproduce microscopic barrier caused by the presence of extracellular spaces and connective tissue in the cardiac tissue

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-06T19:49:56Z No. of bitstreams: 1 johnnymoreiragomes.pdf: 4938794 bytes, checksum: fb03990a45c2c77e8ff60eae73a2d21d (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T20:27:17Z (GMT) No. of bitstreams: 1 johnnymoreiragomes.pdf: 4938794 bytes, checksum: fb03990a45c2c77e8ff60eae73a2d21d (MD5) / Made available in DSpace on 2017-03-06T20:27:17Z (GMT). No. of bitstreams: 1 johnnymoreiragomes.pdf: 4938794 bytes, checksum: fb03990a45c2c77e8ff60eae73a2d21d (MD5) Previous issue date: 2015-02-24 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / Este trabalho compara diferentes esquemas numéricos para a solução de modelos modernos para a eletrofisiologia de miócitos cardíacos. Apresentamos o Método de Uniformização - amplamente utilizado para a solução de problemas estocásticos em ciência da computação - e mostramos que, quando aplicado na resolução numérica de modelos cardíacos baseados em Cadeias de Markov de Tempo contínuo, aumenta substancialmente a estabilidade numérica em relação a métodos explícitos tradicionalmente utilizados, como o Método de Rush-Larsen e o Método de Euler Explícito. A formulação em Cadeias de Markov para estruturas subcelulares - como os canais iônicos - permite a descrição detalhada do comportamento elétrico de células cardíacas para importantes aplicações experimentais, como a simulação dos efeitos de drogas e toxinas sobre a atividade elétrica da membrana celular. No entanto, as equações diferenciais associadas às Cadeias de Markov para canais iônicos frequentemente trazem problemas de estabilidade numérica, que limitam fortemente o passo de tempo utilizado por esquemas explícitos. Com a utilização do Método de Uniformização foi possível aumentar significativamente a magnitude dos passos de tempo utilizados em simulações de três modelos da eletrofisiologia cardíaca baseados em Cadeias de Markov. Neste trabalho mostramos como é possível associar o Método de Uniformização a outros esquemas explícitos para a solução numérica de tais modelos, e como tais técnicas melhoram significativamente o desempenho computacional em relação a métodos explícitos tradicionais. Além disso, propomos extensões do método de Rush-Larsen e do método de Uniformização com segunda ordem de precisão para o desenvolvimento de esquemas explícitos de passo de tempo adaptativo, visando reduzir ainda mais o custo computacional em simulações com tolerância numérica estrita. / This work compares different numerical schemes for the solution of modern electrophysiology models for cardiac myocytes. We present the Uniformization Method - frequently applied to stochastic problems in computer science - which significantly increase the numerical stability when used for the solution of cardiac models based on Continuous Time Markov Chains, with respect to traditional explicit schemes such as Rush-Larsen Method and Foward Euler Method. The Markov Chains formulation for subcellular structures, e.g. ionic channels, enables an accurate description of the electrical behaviour of cardiac cells for important experimental applications, for instance the simulation of the effects of drugs or toxins on the electrical activity of the cell's membrane. However, the differential equations associated with the Markov Chains for ionic channels frequently cause problems of numerical stability, which severely limits the time step used by explicit schemes. By using the Uniformization Method we could significantly increase the time steps size in simulations of three models of cardiac electrophysiology based on Markov Chains. In this work we show how the Uniformization Method can be used along with other foward numerical schemes for the solution of these models, and how these techniques significantly improve the computational performance with respect to traditional numerical methods. In adition, we propose extensions of the Rush-Larsen method and the Uniformization method with second-order accuracy for developing foward time-adaptive techniques, aiming to reduce the computational cost of simulations with strict numerical tolerances.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-07-04T17:30:00Z No. of bitstreams: 1 raphaelpereiracordeiro.pdf: 17027543 bytes, checksum: 91ef68c2021ff4c93dc8b4fe66217cf2 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-08T13:42:41Z (GMT) No. of bitstreams: 1 raphaelpereiracordeiro.pdf: 17027543 bytes, checksum: 91ef68c2021ff4c93dc8b4fe66217cf2 (MD5) / Made available in DSpace on 2017-08-08T13:42:41Z (GMT). No. of bitstreams: 1 raphaelpereiracordeiro.pdf: 17027543 bytes, checksum: 91ef68c2021ff4c93dc8b4fe66217cf2 (MD5) Previous issue date: 2017-03-10 / A modelagem computacional é uma ferramenta útil no estudo de diversos fenômenos complexos, como o comportamento eletro-mecânico do coração em condições normais e patológicas, sendo importante para o desenvolvimento de novos medicamentos e métodos de combate às doenças cardíacas. A alta complexidade de processos biofísicos se traduz em complexos modelos matemáticos e computacionais, o que faz com que simulações cardíacas necessitem de um grande poder computacional para serem executadas. Logo, o estado da arte em simuladores cardíacos é implementado para ser executado em arquiteturas paralelas. Este trabalho apresenta a implementação e avaliação de um método com dados e kernel agregados, método este utilizado para reduzir o tempo de computação de códigos que executam em ambientes computacionais compostos de múltiplas unidades de processamento gráfico (Graphics Processing Unit ou simplesmente GPUs). Este método foi testado na computação de uma importante parte da simulação da eletrofisiologia do coração, a resolução das equações diferenciais ordinárias (EDOs), resultando em uma redução pela metade do tempo necessário para a sua resolução, quando comparado com o esquema onde este método não foi implementado. Com o uso da técnica proposta neste trabalho, o tempo total de execução das simulações cardíacas foi reduzido em até 25%. / Computational modeling is a useful tool to study many distinct and complex phenomena, such as to describe the electrical and mechanical behavior of the heart, under normal and pathological conditions. The high complexity of the associated biophysical processes translates into complex mathematical and computational models. This, in turn, translates to cardiac simulators that demand a lot of computational power to be executed. Therefore, most of the state-of-the-art cardiac simulators are implemented to run in parallel architectures. In this work a new coalesced data and kernel scheme is evaluated. Its objective is to reduce the execution costs of cardiac simulations that run on multi-GPU environments. The new scheme was tested for an important part of the simulator, the solution of the systems of Ordinary Differential Equations (ODEs). The results have shown that the proposed scheme is very effective. The execution time to solve the systems of ODEs on the multi-GPU environment was reduced by half, when compared to a scheme that does not implemented the proposed data and kernel coalescing. As a result, the total execution time of cardiac simulations was 25% faster.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.