1108 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 48, NO. 10, OCTOBER 2001 Inhomogeneity of Action Potential Waveshape Assists Frequency Entrainment of Cardiac Pacemaker Cells Shaun L. Cloherty*, Nigel H. Lovell, Senior Member, IEEE, Branko G. Celler, Member, IEEE, and Socrates Dokos, Member, IEEE Abstract—In this paper, we have employed ionic models of sinoa- trial node cells to investigate the synchronization of a pair of cou- pled cardiac pacemaker cells from central and peripheral regions of the sinoatrial node. The free-running cycle length of the cell models was perturbed using two independent techniques and the minimum coupling conductance required to achieve frequency en- trainment was used to assess the relative ease with which various cell pairs achieve entrainment. The factors effecting entrainment were further investigated using single-cell models paced with an artificial biphasic coupling current. Our simulation results suggest that dissimilar cell types, those with largely different upstroke velocities entrain more easily, that is, they require less coupling conductance to achieve 1 : 1 frequency entrainment. We, therefore, propose that regional variation in action-potential waveshape within the sinoatrial node assists frequency synchronization in vivo. Index Terms—Action-potential waveshape, frequency entrain- ment, mathematical modeling, sinoatrial node. I. INTRODUCTION T HE NORMAL electrical activity of the heart is initiated by a small region of specialized pacemaker cells, known as the sinoatrial node, located in the wall of the right atrium near the opening of the superior vena cava. The pacemaker cells are spontaneously active, exhibiting a slow depolarization to threshold (pacemaker potential) rather than a stable resting po- tential. The sinoatrial node is known to consist of a large number of heterogeneous cells with at least a moderate degree of electro- tonic interconnection [1]. Microelectrode recordings from the intact sinus node reveal a marked change in action-potential characteristics from the center to the periphery of the sinus node, including an increase (hyperpolarization) in the maximum dias- tolic potential (MDP), an increase in overshoot potential (OS), upstroke velocity (UV) and a decrease in intrinsic cycle length (CL) [2]. Kodama and Boyett [3] observed this same variation in action-potential characteristics in small electrically isolated tissue specimens ( mm in diameter). They concluded that Manuscript received September 28, 2000; revised June 24, 2001. This work was supported by the Australian Research Council. Asterisk indicates corre- sponding author. *S. L. Cloherty is with the Graduate School of Biomedical Engineering, University of New South Wales, Sydney 2052, Australia. (e-mail: s.clo- herty@gsbme.unsw.edu.au) N. H. Lovell and S. Dokos are with the Graduate School of Biomedical En- gineering, University of New South Wales, Sydney 2052, Australia. B. G. Celler is with the Biomedical Systems Laboratory, School of Electrical Engineering, University of New South Wales, Sydney 2052, Australia. Publisher Item Identifier S 0018-9294(01)08275-1. action-potential heterogeneity, including variation in intrinsic CL, was the result of a genuine transition in cell membrane elec- trophysiological characteristics. Despite the variation in action-potential characteristics, cells of the sinus node synchronize their firing rate and drive contrac- tion of the entire myocardium in a robust synchronous rhythm. This synchronization of cells, despite differences in intrinsic CL, has been attributed to the electrical coupling of neighboring cells via gap junctions, a hypothesis supported both experimen- tally and via simulation studies [4], [5]. In the present study, we investigate the possible role of regional variation in action-po- tential characteristics in frequency synchronization of the sinoa- trial node. Cai et al. [6] attempted to model the central–peripheral variation in action-potential characteristics and coupled pairs of central and peripheral cells via a constant conductance. They reported that the minimum coupling conductance required for frequency entrainment decreased as the difference in intrinsic CL was reduced. Our simulations of coupled cell pairs suggest that in addition to intrinsic CL, action-potential waveshape also influences entrainment. We find that cells with largely different action-potential characteristics require less coupling conductance to achieve frequency entrainment and, thus, entrain more easily. Our simulation results suggest that the observed variation in action-potential characteristics of cells of the sinus node may well aid in the synchronization of their firing rate. II. METHODS A. The Single-Cell Model Single sinoatrial node cells were modeled using a modified version of the equations of Dokos et al. [7]. These modifications were the addition of both rapid and slow components of the de- layed rectifier potassium current and , and setting the reversal potential of the and type calcium currents, and to a constant value of 40 mV (See Appendix A). A set of 38 model parameters was identified which determined the action-potential characteristics of the model. Values of these parameters were chosen to accurately reproduce the central–pe- ripheral variation in action-potential characteristics observed by Kodama et al. [8]. An additional parameter specifying a voltage offset was applied to the experimental recordings to minimize the disparity between the experimental recording and the sim- ulated membrane potential. This offset is analogous to the un- 0018–9294/01$10.00 © 2001 IEEE