Vulnerability in an excitable medium: analytical and numerical studies of initiating unidirectional propagation

Abstract

Cardiac tissue can display unusual responses to certain stimulation protocols. In the wake of a conditioning wave of excitation, spiral waves can be initiated by applying stimuli timed to occur during a period of vulnerability (VP). Although vulnerability is well known in cardiac and chemical media, the determinants of the VP and its boundaries have received little theoretical and analytical study. From numerical and analytical studies of reaction-diffusion equations, we have found that 1) vulnerability is an inherent property of Beeler-Reuter and FitzHugh-Nagumo models of excitable media; 2) the duration of the vulnerable window (VW) the one-dimensional analog of the VP, is sensitive to the medium properties and the size of the stimulus field; and 3) the amplitudes of the excitatory and recovery processes modulate the duration of the VW. The analytical results reveal macroscopic behavior (vulnerability) derived from the diffusion of excitation that is not observable at the level of isolated cells or single reaction units.

Theoretical perspective on the route to turbulence in a pipe

“…The literature on excitable media is filled with studies of these effects (e.g. Winfree 1991;Starmer et al 1993;Jalife 2000;Keener & Sneyd 2008), because the issues of how action potentials affect one other and how closely they can be spaced are fundamental to the field. Here the main message is that the recovery of the blunted shear profile dictates the refractory region.…”

Re-entrant Cardiac Arrhythmias in Computational Models of Long QT Myocardium

“…S2 stimuli delivered prematurely in the wake of a conditioning wave can initiate re-entry in two or three dimensions, and in a one-dimensional model the vulnerability can be quanti"ed from the range of coupling intervals and strengths of a premature S2 stimulus that initiate retrograde unidirectional propagation (Starmer et al, 1993) as shown in Fig. 2.…”

Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture

“…One of the classic mechanisms for the initiation of reentry is the initiation of an activation in the refractory tail of a propagating pulse. 7 In contrast, the spontaneous initiation of spiral waves here arises as a consequence of wave break over a refractory pacemaker. In this regard, the blockage of excitation by the pacemaker, evident in Figs.…”

“…4,5 A variety of mechanisms lead to the initiation of reentrant waves in both experimental and theoretical models. These mechanisms include stimuli delivered during a short time interval (called the vulnerable period) following the excitation; [6][7][8] instabilities in propagation during rapid excitation frequencies leading to fluctuations in excitation properties and eventual formation of reentrant waves; 9-13 blocked propagation by large inexcitable heterogeneities in cardiac tissue; [14][15][16] and blocked propagation due to small but dispersed heterogeneities leading to wave break. [17][18][19][20][21] Experimental studies in intact cardiac tissue 2,3,22-24 and cardiac tissue culture 11,13,17,18,[24][25][26][27][28][29][30][31][32] represent important approaches to study both the properties of reentrant waves and the mechanisms that lead to their initiation.…”