Fitting local repolarization parameters in cardiac reaction-diffusion models in the presence of electrotonic coupling

Repolarization gradients contribute to arrhythmogenicity. In reaction-diffusion models of cardiac tissue, heterogeneities in action potential duration (APD) can be created by locally modifying an intrinsic membrane kinetics parameter. Electrotonic coupling, however, acts as a confounding factor that modulates APD dispersion.

We developed an algorithm based on a quasi-Newton method that iteratively adjusts the spatial distribution of a membrane parameter to reproduce a pre-defined target APD map in a coupled tissue. The method assumes that the relation between the adjustable parameter and APD is bijective in an isolated cell. Each iteration of the algorithm involved simulating the cardiac reaction-diffusion system with the updated parameter profile for one beat and extracting the APD map. The algorithm was extended to simultaneous estimation of two parameter profiles based on two APD maps at different repolarization thresholds.

The method was validated in 1D, 2D and 3D atrial tissues using synthetic target APD maps with controllable total variation and maximum APD gradient. The adjustable parameter was local acetylcholine concentration. The iterations converged provided that APD gradients were not too steep. Convergence was found to be faster 2-5 iterations) when the maximal gradient was less steep, when APD range was smaller 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.