The Fourier series approach to investigate phase-locking behaviors of the sinoatrial node cell

Abstract

Phase-locking behaviors are closely relevant to arrhythmias. The traditional approach to investigate the subject is the phase resetting map, which interprets phase-locking via the view point of nonlinear mapping dynamics. In the present paper, the Fourier series approach is developed. By decomposing the traces of the transmembrane voltage and total ionic current into Fourier series, the effect of the stimulations on the oscillation period could be revealed analytically. The following well-studied problems are reinvestigated: i) the phase resetting property of the cell; ii) the bifurcations between phase-locking zones; iii) phase-locking behaviors of a pair of coupled cells, which is relevant to behaviors of the sinoatrial node tissue. The work may provide a deeper insight into the subject and a simple method to predict sinoatrial node phase-locking dynamics.