Reentrant Waves Induced by Local Bistabilities in a Cardiac Model

Rate-dependent bistability and hysteresis have recently been observed to be highly prevalent in periodically stimulated bullfrog ventricular muscle. Similar bistabilities have been found in in vivo sheep atria at interstimulus intervals for which spatiotemporally complex behaviors, possibly atrial flutter and fibrillation, are observed. Might bistability play a role in the onset of spatiotemporal disorganization in the whole heart? We investigate the role of local bistability in a coupled map/cellular automaton model of cardiac dynamics. This two-dimensional model is based on a simple mapping which gives good qualitative agreement with many of the local features of cardiac dynamics. Under some conditions, local regions of bistability are found to result in phase singularities and rotors in the spatially extended model presented here. Introduction and Background Different patterns of dynamical response can be elicited under different conditions in cardiac tissue. For example, when stimuli are delivered at a slow rate, one action potential response is elicited for every stimulus (denoted as a 1:1 state). As the stimulus rate (basic cycle length, or BCL) is increased, the action potential duration (APD) begins to oscillate, entering a state called “alternans”, in which every stimulus elicits a response but the responses are of alternating duration (2:2 state) [1,2,3]. As the stimulus rate is increased further, the tissue becomes unable to recover fast enough to respond to every applied stimulus, resulting in a pattern of “skipped beats”, where every other stimulus elicits a response (2:1 pattern). Under other conditions (e.g., different range of applied current amplitude), more complicated behaviors arise [4,5,6]. As pointed out by Guevara et al. [2], rate-dependent bistability and hysteresis between 1:1 (or 2:2) and 2:1 states can occur in simple models of cardiac dynamics as the interstimulus interval (here called BCL, or basic cycle length) is swept up and down. Bistability between the 1:1 branch and the 2:1 branch of APD response was first observed experimentally by Mines in 1913 in a bullfrog cardiac preparation [7], and later by Guevara et al. [4] in an aggregate of spontaneously beating chick embryonic ventricular myocytes. Recently it has been shown that bistability is a highly prevalent local behavior in bullfrog ventricular myocardium, occurring in 74% of preparations studied [8]. Bistability was subsequently observed in in vivo sheep atrium for BCL values over which arrhythmias and spatiotemporal disorganization (possibly flutter or fibrillation) also occurred [9]. Can local bistabilities play a role in the onset of spatial disorganization in excitable media? We investigate this question using a simple cardiac model.