Periodic behaviour in automatic and non-automatic cardiac cells

We have investigated the oscillatory behaviour of a cardiac electrophysiological system model including coupled pacemaker and non-pacemaker cells. A previously reported version of the van Capelle and Dürrer model was used for both the pacemaker and the non-pacemaker cells, which were linked by an Ohmic coupling resistance (CR). In order to investigate the influence of respective cell sizes and electrotonic load, we examined the oscillatory behaviour of the system by using a pacemaker: non-pacemaker size ratio ranging from 0.1 to 0.5. Numerical simulations and continuation techniques disclosed three zones from low to high CR values: a zone of quiescence (0:0 pattern), a zone of effective entrainment (1:1 pattern), and a zone of total block (1:0) pattern. At the boundary between 1:1 and 1:0 patterns, for relatively CR values, period-doubling bifurcation points emerged as a cascade of nested bifurcations corresponding to discrete decreases of propagation patterns. The major issues were the finding of multistabilities between different patterns and above all the presence in the parameter space of irregular chaotic dynamics. This suggest that the interplay between loading and cellular coupling might be the underlying mechanism of the propagation patterns detected in the system under study.