Conduction Block and Chaotic Dynamics in an Asymmetrical Model of Coupled Cardiac Cells

Abstract

The initiation and propagation of the cardiac impulse depends on intrinsic properties of cells, geometrical arrangements, and intracellular coupling resistances. To address the issue of the interplay between these factors in a simple way, we have used a system, based on the van Capelle and Dürrer model, including a pacemaker and a non-pacemaker cell linked by an ohmic coupling resistance. The influence of asymmetrical cell sizes and electrotonic load was investigated by using numerical simulations and continuation-bifurcation techniques. The loading of a small pacemaker cell by a large non-pacemaker one (pacemaker: non-pacemaker size ratio=0.3) was expressed as a pronounced early repolarization in the pacemaker cell and a quite long latency for the impulse propagation. Using coupling resistance as the continuation parameter, three behavioral zones were detected from low to high coupling resistance values: a zone of total quiescence (0:0), a zone of effective entrainment (1:1), and a zone of total block (1:0 pattern). At boundary between 1:1 and 1:0 patterns, for relatively high coupling resistance values, a cascade of period doubling bifurcations emerged, corresponding to discrete changes of propagation patterns leading into irregular dynamics. Another route to irregular dynamics was also observed in the parameter space. The high sensitivity of the detected irregular dynamics to initial conditions and the positive value of the maximum Lyapunov exponent allowed us to identify these dynamics as being chaotic. Since neither intermediate block patterns nor irregular dynamics were observed with larger size ratios, we suggest that the interplay between resting membrane conductance of the non-pacemaker cell and intercellular coupling may bring about these rhythmic disturbances.