Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells.
The transmembrane potential of a single quiescent cell isolated from rabbit ventricular muscle was recorded using a suction electrode in whole-cell recording mode. The cell was then driven with a periodic train of current pulses injected into the cell through the same recording electrode. When the interpulse interval or basic cycle length (BCL) was sufficiently long, 1:1 rhythm resulted, with each stimulus pulse producing an action potential. Gradual decrease in BCL invariably resulted in loss of 1:1 synchronization at some point. When the pulse amplitude was set to a fixed low level and BCL gradually decreased, N+1:N rhythms (N>/=2) reminiscent of clinically observed Wenckebach rhythms were seen. Further decrease in BCL then yielded a 2:1 rhythm. In contrast, when the pulse amplitude was set to a fixed high level, a period-doubled 2:2 rhythm resembling alternans rhythm was seen before a 2:1 rhythm occurred. With the pulse amplitude set to an intermediate level (i.e., to a level between those at which Wenckebach and alternans rhythms were seen), there was a direct transition from 1:1 to 2:1 rhythm as the BCL was decreased: Wenckebach and alternans rhythms were not seen. When at that point the BCL was increased, the transition back to 1:1 rhythm occurred at a longer BCL than that at which the {1:1-->2:1} transition had initially occurred, demonstrating hysteresis. With the BCL set to a value within the hysteresis range, injection of a single well-timed extrastimulus converted 1:1 rhythm into 2:1 rhythm or vice versa, providing incontrovertible evidence of bistability (the coexistence of two different periodic rhythms at a fixed set of stimulation parameters). Hysteresis between 1:1 and 2:1 rhythms was also seen when the stimulus amplitude, rather than the BCL, was changed. Simulations using numerical integration of an ionic model of a single ventricular cell formulated as a nonlinear system of differential equations provided results that were very similar to those found in the experiments. The steady-state action potential duration restitution curve, which is a plot of the duration of the action potential during 1:1 rhythm as a function of the recovery time or diastolic interval immediately preceding that action potential, was determined. Iteration of a finite-difference equation derived using the restitution curve predicted the direct {1:1<-->2:1} transition, as well as bistability, in both the experimental and modeling work. However, prediction of the action potential duration during 2:1 rhythm was not as accurate in the experiments as in the model. Finally, we point out a few implications of our findings for cardiac arrhythmias (e.g., Mobitz type II block, ischemic alternans). (c) 1999 American Institute of Physics.
Yehia
Ali R.
AR
Department of Physiology and Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montreal, Quebec H3G 1Y6, Canada.
Jeandupeux
Dominique
D
Alonso
Francisco
F
Guevara
Michael R.
MR