Mathematical models of cardiac arrhythmias derived from experimental recordings

Traditionally, the kinetics of transmembrane potential of cardiac cells are represented by a number of variables that control the dynamics of various ionic species. These kinetics are derived from patch-clamp experiments on isolated cardiac cells or membrane patches. These models have increased in complexity over the years and reproduce many phenomenon of cardiac cells. They have been used to study reentry and fibrillation in the heart, yet it is not clear if models derived from single cells are appropriate to study reentry and fibrillation. These ionic models have been simplified to two-state variable models using generic equations for excitable cells, but selecting parameter values to correspond to cardiac tissue has proven problematic. Here, the authors show that it is possible to derive mathematical models directly from experimental data recorded during cardiac arrhythmias. They demonstrate that the spatio-temporal patterns recorded from the heart surface during arrhythmias are well represented by a generalized complex Ginzburg-Landau (CGL) equation. The CGL equation represents many partial differential equations and exhibits both stable reentrant patterns and turbulent patterns not unlike the heart. A high speed CCD video camera was used in combination with a voltage-sensitive dye (di-4-ANMEPPS) to record transmembrane activity from isolated rabbit hearts. Video frames (64/spl times/64 pixels) were acquired from the ventricular surface at a rate of 480 frames per second during stable reentry (i.e., monomorphic ventricular tachycardia or MVT) and ventricular fibrillation.