A single pacemaker cell model based on the phase response curve

Abstract

A single pacemaker cell model and its response to repetitive external depolarization stimulations is described in this paper. This model is a simple model based on the two most important functional properties of the cardiac pacemaker cells. The first property is the intrinsic pacemaker cycle length, which is an `internal' parameter of the cell, describing the most important feature of a pacemaker cell. The second functional property is the phase response curve (PRC), which is an `overall collective' function: it contains all the `information' about the possible interactions of the pacemaker cell with the outside world (external stimulus, interaction with surrounding cells, etc.). This study demonstrates that by representing the pacemaker cell only by two fundamental features, and by applying a simple physical-mathematical model, a global picture of the system can be achieved, allowing us to explore qualitatively various physiological phenomena related to the pacemaker function. For example, we demonstrated that the PRC is a crucial parameter in the prediction of the entrainment phenomena of a single pacemaker cell in response to a periodic train of depolarization pulses. Specifically, the PRC permits a quantitative determination of the 1:1 synchronization range for a single pacemaker cell and an external depolarization pulse. Moreover, we show that the PRC can be used to represent the type of external stimulus applied to the pacemaker (e.g. depolarization pulse) and its intensity. Therefore, the PRC emerges as an important determinant and a useful `tool' for the understanding of the dynamic interaction of pacemaker cells with the outside world. As a result of our simulations, we unveil a new important parameter: the `degree of influence', which determines the range of 1:1 synchronization between an external depolarization pulse and a pacemaker cell. This interaction parameter is a direct function of the PRC parameters. It appears to be a helpful `tool' for the understanding of synchronization and mutual entrainment mechanisms between the pacemaker cell and an external stimulus, and therefore it supports the basic importance of the PRC in the description and determination of these mechanisms.