Simulation of atrial activity by a phase response curve based model of a two-dimensional pacemaker cells array: the transition from a normal activation pattern to atrial fibrillation.

In this paper, we present an original model of the atria, based on our hypothesis that atrial cells have features of pacemaker cells, characterized by their normally longer intrinsic cycle lengths and different type of connection (stronger) than the, sino-atrial (SA) node pacemaker cells. The atrium is simulated by a two-dimensional array of pacemaker cells (25 x 25), composed of a region of SA node pacemaker cells (11 x 11) surrounded by atrial pacemaker cells. All pacemakers cells are characterized by only the most relevant functional properties, those which play the most direct role in the determination of the cardiac rate and in the mechanism of arrhythmias. These properties are: the intrinsic cycle length, tau, an 'internal' feature of each pacemaker cell, and the phase-response curve (PRC), an 'overall collective' function. The PRC embodies the interactions of each pacemaker cell with its neighboring cells, and thus represents the type of connection (strong, weak, etc.) of the pacemaker cell with its surroundings. In our model, the SA node region differs from the atrial region by cycle length distribution and PRCs. We studied the spatial interaction between SA node pacemaker cells and atrial pacemaker cells as a function of the regional variation of cells properties and as a function of the "electrical" coupling between cells (the PRC), in the SA node region, in the atrial region, and in a border zone between them. We investigated the influence of those parameters on the activation pattern, on the conduction time of the array, and on a pseudo-ECG signal. This study demonstrates that by representing the atrial cells as a population of 'pacemaker-like' cells, similar to the SA node pacemaker cells, but differing markedly in their cycle lengths and cell-to-cell interaction (PRC), we can create a global picture of the atrial system by applying a simple physical-mathematical model. This approach enables us to explore physiological phenomena related to the genesis and maintenance of atrial activity. It also reveals the conditions which predispose to atrial arrhythmias and conduction disturbances (e.g. tachycardia, pacemaker shift, re-entry, fibrillation). In particular, it yields insight into the mechanism of transition from normal atrial activity to the disordered state of atrial fibrillation. Therefore, this study suggests a new way of looking at the development of cardiac arrhythmias of atrial origin.