An algorithm for fitting local membrane parameters to an action potential duration map in a tissue with electrotonic interactions

Repolarization gradients contribute to arrhythmogenicity. They can be introduced in computer models of cardiac tissue by locally adjusting an intrinsic parameter of the membrane model. Electronic coupling, however, modulates the dispersion of action potential duration (APD). We developed an algorithm based on a modified Newton method to iteratively adjust the spatial distribution of a membrane parameter in order to reproduce a given APD map in a coupled tissue. The method was applied to an atrial model with randomly generated APD maps with controllable maximum APD gradient. The adjustable local parameter was the conductance of the I
K
,
ACh
current. Convergence was found to be faster when the maximal gradient was less steep and when tissue conductivity was reduced. This algorithm provides a tool to automatically generate arrhythmogenic substrates with controllable repolarization gradients and possibly incorporate experimental APD maps into computer models.