Un metodo adaptativo para el modelo Bidominio en electrocardiologia

TL;DR

This paper introduces an adaptive finite-volume method with multi-resolution and variable time-stepping schemes to efficiently solve bidomain equations modeling cardiac electrical activity, demonstrating improved accuracy and computational efficiency.

Contribution

The paper presents a novel combination of adaptive multi-resolution and variable time-stepping methods for bidomain equations, with proven convergence and optimized noise reduction thresholds.

Findings

Reduces computational time and memory usage.

Achieves high accuracy with adaptive schemes.

Demonstrates convergence to weak solutions.

Abstract

This paper presents a finite-volume method, together with fully adaptive multi-resolution scheme to obtain spatial adaptation, and a Runge-Kutta-Fehlberg scheme with a local time-varying step to obtain temporal adaptation, to solve numerically the known "bidominio" equations that model the electrical activity of the tissue in the myocardium. Two simple models are considered for membrane flows and ionic currents. First we define an approximate solution and we verify its convergence to the corresponding weak solution of the continuum problem, obtaining in this way an alternative demonstration that the continuum problem is well-posed. Next we introduce the multiresolution technique and derive an optimal noise reduction threshold. The efficiency and precision of our method is seen in the reduction of machine time, memory usage, and errors in comparison to other methods. ----- En este trabajo se presenta un metodo de volumenes finitos enriquecido con un esquema de multiresolucion completamente adaptativo para obtener adaptatividad espacial, y un esquema Runge-Kutta-Fehlberg con paso temporal de variacion local para obtener adaptatividad temporal, para resolver numericamente las conocidas ecuaciones "bidominio" que modelan la actividad electrica del tejido en el miocardio. Se consideran dos modelos simples para las corrientes de membrana y corrientes ionicas. En primer lugar definimos una solucion aproximada y nos referimos a su convergencia a la correspondiente solucion debil del problema continuo, obteniendo de este modo una demostracion alternativa de que el problema continuo es bien puesto. Luego de introducir la tecnica de multiresolucion, se deriva un umbral optimo para descartar la informacion no significativa, y tanto la eficiencia como la precision de nuestro metodo es vista en terminos de la aceleracion de tiempo de maquina, compresion de memoria computacional y errores en diferentes normas.