A discrete model of the dynamic behavior of the cardiac muscle
The objective of this study is to construct a discrete finite state model of the electrical activity of the heart, which is directly related to the FitzHugh-Nagumo equations, but offers both a faster and more stable solution. The authors set up a 2D two variable model with non-nearest neighbor interactions to include curvature dependence of the wave front. For better approximation of the electrotonic propagation, a hexagonal grid and distance-dependent weighting coefficients are used. Despite its simplicity the model follows the local dynamics prescribed by the modified FitzHugh-Nagumo equations and its parameters are directly derived from the original ones. The model was validated by comparison to existing experimental data for the propagation velocity, curvature velocity relationship, rotation speed and core size. It was successfully used to study spiral wave interactions with nonexcitable obstacles of different shapes.
Abstract The variational Monte Carlo (VMC) method, which evaluates multi-dimensional integrals by random walk sampling based on the Metropolis algorithm, has been implemented in the connected moments expansion (CMX). The Hartree-Fock single determinant multiplied by the Jastrow function has been employed for a trial function. Pilot calculations on the hydrogen molecule at various internuclear separations have been performed. The results are found to be in good agreement with those by Kolos and Wolniewicz.