The dynamics of vortex-like reentry wave filaments in three-dimensional computer models

Abstract

Recent studies using computer simulation and biological studies in 2-dimensional excitable media have suggested that spiral wave reentrant activation and its core dynamics are important elements in the mechanism of functional reentrant tachyarrhythmias, such as atrial and ventricular fibrillation. However, vortex-like reentry has been observed in homogeneous 3-dimensional excitable media, and the dynamics of the related “filaments,” which have 3-dimensionally connected “cores” in 2 dimensions, have not been clarified. In order to determine whether the filaments of vortex-like reentry waves can be observed in 3-dimensional media using a mathematical ionic current heart model and whether the abnormal ionic currents in myocardium affect the complexity of the filaments, we studied the qualitative features of vortex-like reentry dynamics using mathematical models in computer simulations. We employed the Luo-Rudy Phase I and the FitzHugh-Nagumo models for our heart media, which were cubic and ventricular shaped, and consisted of 8,000,000 and 5,636,654 myocardial units, respectively. Functional reentry, in the form of vortex waves, was induced in the media by the S1–S2 method. The vortex-like reentry waves and their filaments were displayed by computer graphics. Computations were performed on an NEC SX-4 supercomputer (NEC, Tokyo, Japan) using programs written in C language. Computer simulation studies have shown that the filament dynamics of vortex-like reentry in the original Luo-Rudy model is considerably more complex than that in the FitzHugh-Nagumo model. However, when we mathematically modified the L-type calcium current and shortened the action potential duration, just as occurs with sustained rapid ventricular pacing, the dynamics of the vortex-like reentrant wave fronts and the filaments were similar in both models. Our results suggested that the original character of myocardium causes drastic changes in filament shape and location, resulting in intricate functional reentrant waves, and that if the L-type calcium current is depressed, the complexity of the dynamics of the filaments are decreased to some degree.