Abstract
Sinus node arrest is a dangerous disease, which is associated with the annihilation of the cardiac biological oscillators. The present work investigates in detail the pacemaking annihilation of the modeled single SAN cell and heterogeneous tissue by the conventional nonlinear dynamics approach. It is found that annihilation should generally exist in the SAN system, which is due to the subcritical Hopf bifurcation. However, the annihilation is strict with the stimulus and the physiological parameters, for which the difficulty is estimated. Intracellular calcium cycling makes the pacemaking more robust against annihilation. Furthermore, some general methods for exploring the annihilation dynamics are demonstrated, which may be helpful for the investigations of the other complex biological oscillators. The present work may provide suggestive ideas for the treatments of the sinus arrest and the relevant arrhythmogenesis.
Highlights
Hyperkalemia, drug toxicity such as digitalis, and even the suppression from the surrounding nonoscillatory cells may cause sinus node arrest.[11,12,13,14,15] Besides the physiological suppressing factors, annihilation is found to be an inherent property of the normally pacing sinoatrial node (SAN) system, which can be caused by a single stimulus of proper timing.[16]
We are going to study the following problems: (1) What are the general rules for annihilation in the modeled SAN cell and tissue; (2) What are the effects of the conductances and kinetics of the ionic channels; (3) What is the condition and how difficult it is for inducing the annihilation in an normally pacing SAN cell and tissue by a single stimulus
We study the human model developed by Maltsev and Lakatta[41] in 2013 which is a modified version of their rabbit SAN model in 2010.47 This model incorporates the intracellular calcium cycling into the conventional membrane-delimited model
Summary
Hyperkalemia, drug toxicity such as digitalis, and even the suppression from the surrounding nonoscillatory cells (the atrial cells and the fibroblast cells) may cause sinus node arrest.[11,12,13,14,15] Besides the physiological suppressing factors, annihilation is found to be an inherent property of the normally pacing SAN system, which can be caused by a single stimulus of proper timing.[16]. We mainly explored the rabbit SAN model developed by Zhang et al.[40] The conventional methods of nonlinear physics are applied This model simulates the practical electrophysiological behaviors of the rabbit SAN, and takes into account the spatial heterogeneity of the sinus node tissue. We study a more recent and detailed SAN model which incorporates the intracellular calcium cycling dynamics.[41] It serves as a support for the basic knowledge from Zhang’s model, convincing people that the mechanism of annihilation revealed by the present work should generally exist in the practical SAN system
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