Paradoxical Onset of Arrhythmic Waves from Depolarized Areas in Cardiac Tissue Due to Curvature-Dependent Instability

Abstract

The generation of abnormal excitations in pathological regions of the heart is a main trigger for lethal cardiac arrhythmias. Such abnormal excitations, also called ectopic activity, often arise from areas with local tissue heterogeneity or damage accompanied by localized depolarization. Finding the conditions that lead to ectopy is important to understand the basic biophysical principles underlying arrhythmia initiation and might further refine clinical procedures. In this study, we are the first to address the question of how geometry of the abnormal region affects the onset of ectopy using a combination of experimental, in silico, and theoretical approaches. We paradoxically find that, for any studied geometry of the depolarized region in optogenetically modified monolayers of cardiac cells, primary ectopic excitation originates at areas of maximal curvature of the boundary, where the stimulating electrotonic currents are minimal. It contradicts the standard critical nucleation theory applied to nonlinear waves in reaction-diffusion systems, where a higher stimulus is expected to produce excitation more easily. Our in silico studies reveal that the nonconventional ectopic activity is caused by an oscillatory instability at the boundary of the damaged region, the occurrence of which depends on the curvature of that boundary. The onset of this instability is confirmed using the Schrödinger equation methodology proposed by Rinzel and Keener [SIAM J. Appl. Math. 43, 907 (1983)]. Overall, we show distinctively novel insight into how the geometry of a heterogeneous cardiac region determines ectopic activity, which can be used in the future to predict the conditions that can trigger cardiac arrhythmias.

(INVITED) Reaction–diffusion waves in cardiovascular diseases

“…The presence of depolarized regions can also produce a pathological local periodic electrical activity which was recently confirmed in experimental and modeling studies [206]. There are also many other types of multi-stability at the level of the excitation patterns in the heart.…”

Simulation of ectopic activity onset in border zones between normal and damaged myocardium with minimal ionic models

“…In this study, we use two-variable Mitchell-Schaeffer (MS) model [2], its modification by Corrado and Niederer (CN) [3], and four-variable Bueno-Orovio-Cherry-Fenton (BOCF) model [4] to investigate the possibility to obtain the paradoxical effect mentioned above in these popular minimal ionic models. We also reproduce as a reference the results for simulations with FitzHugh-Nagumo (FHN) model [5] demonstrated in [1].…”

“…Excitation front propagates from the right side of the normal area and, upon passing through the DR, eventually spontaneous depolarizations may appear near the borders of the normal and damaged tissue due to the electrotonic interactions in the presence of large gradients of the trans-membrane potentials. Similar to [1], we implemented two variants of damaged tissue -with bistable (subscript B) and ultra-long (subscript L) APs for all models considered.…”

“…is the diffusion term, and D is the diffusion coefficient. The parameters were taken similar to that in [1]: a = 0.13 for all AP variants, for normal AP -F HN = 0.004 and γ = 1.5, for bistable AP F HN = 0.004 and γ = 13, and for long AP F HN = 0.00005 and γ = 3.12.…”

“…Ectopic activity, which is an abnormal excitation in cardiac tissue, is one of the triggers for dangerous arrhythmia initiation. Recently, the paradoxical onset of ectopic sources in the border zones between normal and damaged myocardium was reported in experiments with optogenetically modified monolayers of cardiomyocytes, accompanied by computer simulations and theoretical explanations [1]. The study claims that primary ectopic excitation takes place at the areas of maximal curvature, such as corners of damaged tissue regions (DR) with ultra-long action potentials (AP), in which, as stipulated in the paper, the stimulating coupling currents between cells do not correspond to classical source-sink relationship for successful excitation of the neighboring tissue.…”