Abstract

We characterize the effects of external stimulation on central and peripheral sinoatrial node (SAN) cells using the Zhang et al. model [1]. Phase transition curves (PTCs) for brief (0.5ms) depolarizing and hyperpolarising electrical current pulses of varying amplitude and of timing spanning the whole period are obtained. The application of a critical depolarizing stimulus (about 0.4 nA) during the late repolarization phase of the action potential resulted in annihilation of activity in central SAN cells, revealing the existence of a stable singularity in the corresponding model configuration. The peripheral SAN cell does not exhibit a similar singularity and annihilation of the normal activity. Sinoatrial node (SAN), the natural pacemaker of the heart, is subjected to external stimuli under both clinical interventions (defibrillation) and physiological autonomic control. Results from extensive experimental and theoretical studies [2] on the response of biological oscillators to external perturbations indicate that, in the cardiac tissue, such responses play an important role in the generation of arrhythmias [3]. Stimuli of critical amplitude and phase can lead to annihilation of normal rhythmic activity. The analysis of phase response characteristics provides new insight into the dynamics of the models, as well as an experimentally verifiable test for the accurate reconstruction of SAN tissue dynamics. Simulation of the spatial variation in the electrical properties of SAN cells and their phase response profiles is an important step for the reconstruction of the complex dynamics of the sinoatrial node tissue. In this work, we characterize the effects of external stimulation on central and peripheral SAN cells using the Zhang et al. SAN-model [1]. A Runge-Kutta method is used for the numerical solution of the differential equations describing the model. Brief (0.5ms) depolarising and hyperpolarising electrical current pulses of varying amplitude and of timing spanning the whole period are applied and phase transition curves (PTC) are obtained [4]. Three dimensional PTCs [5], relating old phase and stimulus amplitude to the new phase after stimulation, are generated in order to locate critical stimuli and singularities in the models. Numerical simulations for transitional cells lying between the center and periphery of the SAN [1], as well as under modulation of specific ionic currents are also conducted.

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