Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities

Abstract

Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This novel result shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.

The physics of heart rhythm disorders

“…This extended SP model was able to qualitatively reproduce the results of the full model, as can seen in the phase diagram presented in Fig. 14C [221]. As in the full model, for small spacing, the trajectory migrates around both heterogeneities and for large spacing the particle migrates around one of the two heterogeneities.…”

“…Both the simple circular trajectory as well as the meandering trajectory (middle column) are reproduced by the SP model. The SP model can also reproduce tip trajectories obtained using more complicated electrophysiological models [221]. An example of this is shown in the right-most trajectory in Fig.…”

“…Specifically, when the conductance inside these heterogeneities was decreased, trajectories in both the simple FK model and the detailed KKT model were found to display chaotic tip trajectories. Simulations revealed that the size of the heterogeneities and their spacing critically determined the tip dynamics [221]. This is quantified in the phase diagram shown in Fig.…”

“…These two possibilities are presented in Fig. 13C and D where a change in one parameter of the FK model dramatically alters the trajectory [221]. More complicated trajectories, including ones in which the path contains large linear segments, are also possible.…”

“…and where the third term represents a damping that prevents the model from drifting and allows it to converge to a steady state quickly. This SP model can be trivially solved and the parameters can be immediately determined from the tip trajectory computed using the spatially extended electrophysiological models [221]. Specifically, the angular frequencies are obtained from the power spectrum of the trajectory, with ω 1 corresponding to the overall period of the spiral and ω 2 , corresponding to the angular frequency of the petals in the flower patterns.…”