Rogers, McCulloch, 1994
This is a CellML version of the modified FitzHugh-Nagumo model, published by Rogers and McCulloch in 1994. While the original two-variable model described a non-dimensional activation variable (u) and a non-dimensional recovery variable (v), here we formulate the model in terms of the `real' action potential given by the time course of the transmembrane potential (Vm). In so doing, the time rate of change of the activation variable describes the total `ionic current' through the membrane with the original model parameters adjusted to give the correct dimensionality.
Abstract: A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.
The original paper reference is cited below:
A collocation--Galerkin finite element model of cardiac action potential propagation, J.M. Rogers and A.D. McCulloch, 1994, IEEE Transactions on Biomedical Engineering, 41, (8), 743-757. PubMed ID: 7927397