Fluid-electro-mechanical model of the human heart for supercomputers

The heart is a complex system. From the transmembrane cell activity to the spatial organization in helicoidal fibers, it includes several spatial and temporal scales. The heart muscle is surrounded by two main tissues that modulate how it deforms: the pericardium and the blood. The former constrains the epicardial surface and the latter exerts a force in the endocardium. The main function of this peculiar muscle is to pump blood to the pulmonary and systemic circulations. In this way, solid dynamics of the heart is as important as the induced fluid dynamics. Despite the work done in computational research of multiphysics heart modelling, there is no reference of a tightly-coupled scheme that includes electrophysiology, solid and fluid mechanics in a whole human heart. In this work, we propose, develop and test a fluid-electro-mechanical model of the human heart. To start, the heartbeat phenomenon is disassembled in the different composing problems. The first building block is the electrical activity of the myocytes, that induces the mechanical deformation of the myocardium. The contraction of the muscle reduces the intracavitary space, that pushes out the contained blood. At the same time, the inertia, pressure and viscous stresses in this fluid exerts a force on the solid wall. In this way, we can understand the heart as a fluid-electro-mechanical problem. All the models are implemented in Alya, the Barcelona Supercomputing Center simulation software. A multi-code approach is used, splitting the problem in a solid and a fluid domain. In the former, electrophysiology coupled with solid mechanics are solved. In the later, fluid dynamics in an arbitrary Lagrangian-Eulerian domain are computed. The equations are spatially discretized using the finite element method and temporally discretized using finite differences. Facilitated by the multi-code approach, a novel high performance quasi-Newton method is developed to deal with the intrinsic issues of fluid-structure interaction problems in iomechanics. All the schemes are optimized to run in massively parallel computers. A wide range of experiments are shown to validate, test and tune the numerical model. The different hypothesis proposed — as the critical effect of the atrium or the presence of pericardium — are also tested in these experiments. Finally, a normal heartbeat is simulated and deeply analyzed. This healthy computational heart is first diseased with a left bundle branch block. After this, its function is restored simulating a cardiac resynchronization therapy. Then, a third grade atrioventricular block is simulated in the healthy heart. In this case, the pathologic model is treated with a minimally invasive leadless intracardiac pacemaker. This requires to include the device in the geometrical description of the problem, solve the structural problem with the tissue, and the fluid-structure interaction problem with the blood. As final experiment, we test the parallel performance of the coupled solver. In the cases mentioned above, the results are qualitatively compared against experimental measurements, when possible. Finally, a first glance in a coupled fluid-electro-mechanical cardiovascular system is shown. This model is build adding a one dimensional model of the arterial network created by the Laboratório Nacional de Computação Científica in Petropolis, Brasil. Despite the artificial geometries used, the outflow curves are comparable with physiological observations. The model presented in this thesis is a step towards the virtual human heart. In a near future computational models like the presented in this thesis will change how pathologies are understood and treated, and the way biomedical devices are designed.El corazón es un sistema complejo. Desde la actividad celular hasta la organización espacial en fibras helicoidales, incluye gran cantidad de escalas espaciales y temporales. El corazón está rodeado principalmente por dos tejidos que modulan su deformación: el pericardio y la sangre. El primero restringe el movimiento del epicardio, mientras el segundo ejerce fuerza sobre el endocardio. La función principal de este músculo es bombear sangre a la circulación sistémica y a la pulmonar. Así, la deformación del miocardio es tan importante como la fluidodinámica inducida. Al día de hoy, solo se han propuesto modelos parciales del corazón. Ninguno de los modelos publicados resuelve electrofisiología, mecánica del sólido, y dinámica de fluidos en una geometría completa del corazón. En esta tesis, proponemos, desarrollamos y probamos un modelo fluido -electro -mecánico del corazón. Primero, el problema del latido cardíaco es descompuesto en los distintos subproblemas. El primer bloque componente es la actividad eléctrica de los miocitos, que inducen la deformación mecánica del miocardio. La contratación de este músculo, reduce el espacio intracavitario, que empuja la sangre contenida. Al mismo tiempo, la inercia, presión y fuerzas viscosas del fluido inducen una presión sobre la pared del sólido. De esta manera, podemos entender el latido cardíaco como un problema fluido-electro-mecánico. Los modelos son implementados en Alya, el software de simulación del Barcelona Supercomputing Center. Se utiliza un diseño multi-código, separando el problema según el dominio en sólido y fluido. En el primero, se resuelve electrofisiología acoplado con mecánica del sólido. En el segundo, fluido dinámica en un dominio arbitrario Lagrangiano-Euleriano. Las ecuaciones son discretizadas espacial y temporalmente utilizando elementos finitos y diferencias finitas respectivamente. Facilitado por el diseño multi-codigo, se desarrolló un novedoso método quasi-Newton de alta performance, pensado específicamente para lidiar con los problemas intrínsecos de interacción fluido-estructura en biomecánica. Todos los esquemas fueron optimizados para correr en ordenadores masivamente paralelos.Se presenta un amplio espectro de experimentos con el fin de validar, probar y ajustar el modelo numérico. Las diferentes hipótesis propuestas tales como el efecto producido por la presencia de las aurículas o el pericardio son también demostradas en estos experimentos. Finalmente un latido normal es simulado y sus resultados son analizados con profundidad. El corazón computacional sano es, primeramente enfermado de un bloqueo de rama izquierda. Posteriormente se restaura la función normal mediante la terapia de resincronización cardíaca. Luego se afecta al corazón de un bloqueo atrioventricular de tercer grado. Esta patología es tratada mediante la implantación de un marcapasos intracardíaco. Para esto, se requiere incluir el dispositivo en la descripción geométrica, resolver el problema estructural con el tejido y la interacción fluido-estructura con la sangre. Como experimento numérico final, se prueba el desempeño paralelo del modelo acoplado.Finalmente, se muestran resultados preliminares para un modelo fluido-electro-mecánico del sistema cardiovascular. Este modelo se construye agregando un modelo unidimensional del árbol arterial. A pesar de las geometrías artificiales usadas, la curva de flujo en la raíz aórtica es comparable con observaciones experimentales. El modelo presentado aquí representa un avance hacia el humano virtual. En un futuro, modelos similares, cambiarán la forma en la que se entienden y tratan las enfermedades y la forma en la que los dispositivos biomédicos son diseñados.Postprint (published version

Marta María Magdalena Huertas, El modelo constitucional norteamericano en los fallos de la Corte Suprema de Justicia de la Nación (1863-1903), Buenos Aires, Instituto de Investigaciones de Historia del Derecho, 2001.

Fil: Santiago, Alfonso (h). Universidad Nacional de Cuyo. Facultad de Filosofía y Letra

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