Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium

Abstract

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär–Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed. Understanding the mechanisms that govern the onset, development, and termination of cardiac arrhythmias is essential to develop and further refine novel strategies for controlling them. However, cardiac tissue is inherently heterogeneous, and heterogeneity might be exacerbated in diseased hearts. In a generic model of excitable media, we investigate how patches of lower excitability change the characteristics of spatio-temporal chaos, which is related to lethal cardiac fibrillation. Surprisingly, the presence of multiple discrete heterogeneities may lead to the complete cessation of chaos, even though lower excitability increases complexity in a homogeneous medium. In other cases, the complexity of spatio-temporal chaos increases beyond the values expected from homogeneous behavior. Our results show that spatial variations in local parameters may have truly emergent effects and information about the distribution of natural heterogeneity in the cardiac muscle as well as the spatial scale and strength of pathological heterogeneities is an indispensable prerequisite for understanding the stability properties of cardiac arrhythmias and developing control strategies tailored to specific types of dynamics.