ABSTRACT
Introducción: la fibrilación auricular (AF), es la más común de la arritmia cardiaca sostenida y un factor de riesgo para el accidente cerebro vascular y otras morbilidades, si no es tratada. Estudios epidemiológicos muestran que la AF tiende a perpetuarse con el tiempo, generando cambios electrofisiológicos y anatómicos denominados: remodelados auriculares. Se ha demostrado que estos cambios provocan variaciones de la velocidad de conducción (CV), en el tejido auricular. Objetivo: estudiar el efecto del remodelado de gap junctions en la propagación del potencial de acción, implementando un modelo 3D de aurícula humana altamente realista. Materiales y Métodos: se incorporaron los cambios generados por el remodelado eléctrico a un modelo de potencial de acción (AP) de miocito auricular, acoplado con un modelo tridimensional anatómicamente realista de aurícula humana dilatada. Mediante simulaciones de la propagación del AP en condiciones de remodelado eléctrico y anatómico, y de remodelado de gap junctions, se midieron las ventanas vulnerables de generación de reentradas en la base de las venas pulmonares izquierdas de la aurícula. Resultados: los resultados obtenidos indican que la ventana vulnerable en el remodelado de gap junctions, se desplazó 38 ms con relación al modelo dilatado, lo que nos muestra el impacto de la dilatación con remodelado de gap junction. Conclusiones: el remodelado eléctrico generó una disminución del 70 % en la duración del potencial de acción y una disminución de las velocidades de conducción entre un 14.6 y un 26 %, que fueron medidas en diferentes regiones de la aurícula dilatada. El foco disparado en la base de las venas pulmonares izquierdas, generó un frente de onda que mantiene una actividad reentrante debido a la anatomía subyacente de las venas pulmonares.
Introduction: Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia and a significant risk factor for cerebrovascular accident and other morbidities if left untreated. Epidemiological studies show that AF tends to persist over time, creating electrophysiological and anatomical changes called atrial remodeling. It has been shown that these changes result in variations in conduction velocity (CV) in the atrial tissue. Objective: to study the effect of remodeling of gap junctions in the propagation of the action potential by implementing a highly realistic 3D human atrial model. Materials and methods: the changes caused by electrical remodeling were incorporated in an atrial myocyte action potential (AP) model coupled with an anatomically realistic three-dimensional model of dilated human atria. Through simulations of the AP spread in variations of anatomical and electrical remodeling and of gap junctions remodeling, vulnerable windows of reentry generation were measured at the base of the atrium left pulmonary veins. Results: the results obtained indicate that vulnerable window in the gap junctions remodeling moved 38 ms in relation with the expanded model which shows the impact of the dilatation gap junction remodeling. Conclusions: the electrical remodeling produced 70% decrease in action potential duration and decreased conduction velocities between 14.6 and 26 %, which were measured in different regions of the dilated atrium. The focus shot at the base of the left pulmonary veins created a wave which maintains a reentering activity due to the underlying anatomy of the pulmonary veins.
ABSTRACT
Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.
