Phase-locking behaviors in sinoatrial node (SAN) are closely related to cardiac arrhythmias. An ionic model considering structural heterogeneity of SAN is numerically investigated. The bifurcations between phase-locking zones are interpreted by the map derived from the phase resetting curve. Furthermore, the validity of the circle map in describing phase locking of the actual SAN system is evaluated and explained. We reveal also how the phase-locking behaviors in heterogeneous tissue depend on the location of stimulating site and the coupling strength of the tissue. All these results may be of suggestive uses for understanding and controlling practical SAN dynamics.
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.
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