Adaptive Time Step for Cardiac Myocyte Models

The modeling of the electrical activity of the heart is of great medical and scientific interest as it provides a way to better understand the underlying biophysical phenomena, supports the development of new techniques for diagnoses and serves as a platform for drug tests. At cellular level, the electrical activity of cardiac myocytes may be simulated by solving a system of ordinary di_erential equations (ODEs) describing the electrical behavior of the cell membrane. Because the biophysical processes underlying this phenomenon are non-linear and change very rapidly, the ODE system is challenging to solve numerically. Furthermore, the implementation of these models is a hard task. This paper presents a tool to describe models using Ordinary Differential Equations. It is based on CellML standard and automatically generates C++ source-code, with numerical methods to solve the model's equations. The aim of this work is to present a numerical method with adaptive time step based on the Euler Method and Second Order Runge-Kutta method. The proposed method accelerated the execution and kept numerical errors under control. Preliminary results suggest this adaptive method is up to 25 times faster than the explicit Euler method with fixed time step