Increasing the computational efficiency of a bidomain model of defibrillation using a time-dependent activating...

Realistic simulations of the effects of strong shocks on cardiac muscle require solving the bidomain model, a continuum representation of cardiac tissue by a system of two reaction-diffusion equations. For two- and three-dimensional problems, the computations tend to take a prohibitively long time. This study develops a computationally efficient and accurate approximation of the bidomain model: a "reduced bidomain" model. The approximation is based on the fact that during a strong shock, the extracellular field in the muscle changes only slightly and, therefore, can be approximated by an activating function, following the concept introduced by Rattay (Rattay, F. Analysis of models for external stimulation of axons. IEEE Trans. Biomed. Eng. 33:974-977, 1986). The activating function used here is time-dependent and is computed using an iterative algorithm. The results show that in two spatial dimensions, the "reduced bidomain" model, as implemented in this study, cuts the computational cost by two orders of magnitude while preserving most properties of the "full bidomain" model. It faithfully represents the spatial pattern and the temporal development of the muscle polarization. Consequently, relative errors in the "defibrillation" threshold, the strength of the weakest shock that terminates all electrical activity within 100 ms, are below 10%.