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Mathematical Modeling of Sinoatrial Node Dynamics at the Subcellular, Cellular, and Tissue Scales


Cardiac pacing is an important area of scientific inquiry, and provides a rich opportunity for mathematical study due to the dynamic interplay of robustness and flexibility required for healthy function. The sinoatrial node (SAN) is key to understanding pacing, since the spontaneous periodic action potentials in the SAN pace the action potentials -- and thus mechanical contraction -- in the cardiac muscle tissue. However, several components of SAN function remain unclear; in the present work, we address three questions related to the rhythmicity and pacing activity of the SAN at multiple scales. First, we use model reduction and dynamical systems analysis to elucidate the rate-limiting steps in the subcellular kinetics of changes in SAN cell firing frequency resulting from sympathetic nervous system activity. This sheds light on the key biochemical factors involved in the potential arrhythmogenicity of sympathetic surges, and generates implications for pharmaceutical interventions for pathologies involving cardiac sympathetic dysregulation. Next, we apply the theory of weakly coupled oscillators to analyze the role of voltage-dependent gap junction gating on phase-locking in a differential equation model of SAN cell electrophysiology. This approach explores the potential effects of the distinct type of gap junctions in the SAN on synchrony. Finally, we use a combination of bifurcation analysis, spectral analysis, and simulations to investigate the role of size and curvature of the SAN or an ischemic region on its ability to drive action potentials in a neighboring excitable region of tissue. This elucidates how emergent properties of the physiology and geometry of a spontaneously active region impact threshold behavior for periodic propagating waves. Taken together, our results provide insight into the theoretical underpinnings for several complex processes involved in cardiac pacing, and inspiration for future computational and experimental work to apply the predictions made by our models.

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