Bursting behavior during fixed-delay stimulation of spontaneously beating chick heart cell aggregates ARKADY M. KUNYSZ,l ALVIN SHRIER,2 AND LEON GLASS2 Tentre for Nonlinear Dynamics in Physiology and Medicine, Departments of Physiology and Physics, and 2Department of Physiology, McGill University, Montreal, Quebec, Canada H3G lY6 Kunysz, Arkady M., Alvin Shrier, and Leon Glass. Bursting behavior during fixed-delay stimulation of spontane- ously beating chick heart cell aggregates. Am. J. Physiol. 273 (CeZZ Physiol. 42): C33LC346, 1997. -Spontaneously beat- ing embryonic chick atria1 heart cell aggregates were stimu- lated with depolarizing current pulses delivered at a fixed delay after each action potential. This preparation is an experimental model of a reentrant tachycardia. During fixed- delay stimulation, bursting behavior was typically observed for a wide range of delays. Episodes of bursting at a rate faster (slower) than control were followed by overdrive sup- pression (underdrive acceleration). We use a simple nonlinear model, based on the interaction between excitability and overdrive suppression, to describe these dynamics. A modified version of the Shrier-Clay ionic model of electrical activity of the embryonic chick heart cell aggregates that includes a simplified Na+ pump term is also presented. We show that the complex patterns during fixed-delay stimulation arise as a result of delicate interactions between overdrive suppres- sion and phase resetting, which can be described in terms of the underlying ionic mechanisms. This study may provide a basis for understanding incessant tachycardias in the intact heart, as well as an alternative mechanism for the emergence of bursting activity in other biologic tissue. reentry; overdrive suppression; phase resetting; ionic models BURSTING RHYTHMS ARE COMMON in endocrine (4, 6, 27), neural (22, 25, 32), and cardiac systems (7, 8, 20). Extensive experimental and theoretical studies indi- cate that bursting discharges may arise as a conse- quence of the interaction between mechanisms operat- ing on markedly different time scales (22,24). Bursting activity has been associated with several mechanisms that include ionic currents such as the Ca2+-dependent K+ current (4, 22) and an adenosine triphosphate- dependent conductance (6, 27), as well as the interac- tion between weakly coupled pacemakers (25). Bursting rhythms may also arise during a class of cardiac arrhythmias called reentrant tachycardias. In reentrant tachycardia, a wave of excitation travels in a circuitous pathway in the myocardium with a period that is shorter than the normal interval between heartbeats. The conditions that lead to the onset and termination of reentrant tachycardias have been inves- tigated in models of intact myocardium that employ the concepts of conduction, refractoriness, and action poten- tial (AP) duration (APD) (5,7,10,26,29). We examine complex bursting behavior in a highly simplified model of reentrant tachycardia that employs embryonic chick heart cell aggregates. Under normal experimental conditions, the embryonic heart cell aggre- gates beat spontaneously with a regular rhythm. This experimental system has been well characterized with respect to ionic mechanisms as well as complex dynam- ics that arise during periodic stimulation (13, 14, 16, 17, 34). Key concepts to understand the dynamics are phase resetting and overdrive suppression. Phase reset- ting refers to the shifting of the timing of an oscillation as a consequence of its perturbation by an external stimulus (12-14, 16, 34). Overdrive suppression is the slowing of the frequency of an oscillation after rapid stimulation (11,17,19,21,30,31,34). The bursting behavior studied here arises in a simu- lated reentrant loop that is generated by imposing a current pulse with a fixed delay after the AP upstroke. In this paradigm the delay represents the conduction time around a hypothetical reentrant pathway, the length of which can be varied by modifying the fixed- delay interval. This preparation is similar to experimen- tal models of atrioventricular conduction in which atria are stimulated at a fixed delay after ventricular activa- tion (10,26,29). We use a nonlinear theoretical model, describing the interaction between time-dependent ef- fects and the excitability of the preparation, to under- stand the experimentally observed dynamics. The com- plex bursting patterns that are observed emerge naturally from a consideration of the interplay of these factors. Previous studies have shown that the Shrier- Clay ionic model can reproduce qualitative aspects of phase resetting due to electrical stimulation (16). To help understand the ionic basis of the bursting phenom- ena, we further develop this ionic model by incorporat- ing a simplified model of the Na+-K+ pump, which is primarily responsible for generating overdrive suppres- sion in this preparation (21). This study demonstrates how phase resetting and overdrive suppression can lead to paroxysmal bursting behaviors. The interplay between resetting mecha- nisms and slow time-dependent processes may have general implications, since similar bursting patterns are observed in a variety of other preparations, includ- ing clinically relevant arrhythmias. 0363-6143/97 $5.00 Copyright o 1997 the American Physiological Society c331