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

Realistic simulations of the effects of strong shocks on cardiac muscle req uire solving the bidomain model, a continuum representation of cardiac tiss ue by a system of two reaction-diffusion equations. For two- and three-dime nsional 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 bas ed on the fact that during a strong shock, the extracellular field in the m uscle changes only slightly and, therefore, can be approximated by an activ ating function, following the concept introduced by Rattay (Rattay, F. Anal ysis 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 spat ial dimensions, the "reduced bidomain" model, as implemented in this study, cuts the computational cost by two orders of magnitude while preserving mo st properties of the "full bidomain" model. It faithfully represents the sp atial pattern and the temporal development of the muscle polarization. Cons equently, relative errors in the "defibrillation" threshold, the strength o f the weakest shock that terminates all electrical activity within 100 ms, are below 10%. (C) 2000 Biomedical Engineering Society. [S0090-6964(00)0100 7-9].