Modelling and analysis of the sinoatrial node

Abstract

The contraction of the heart is achieved by the regulation of the sinoatrial node (SAN), the natural pacemaker. The SAN cells are capable of initiating action potentials, i.e. the electrical signals which produce the contraction of cardiac muscle. The generation of action potentials are governed by ion channels where various types of ion currents flow through. Computational models characterized by ordinary differential equations (ODE) have been published to explain the deterministic behavior of SAN cells.

In this thesis, we investigate the effects of the ion channels of these models by both local and global sensitivity analysis. The local sensitivity analysis identifies the impact of ion channels by means of partial derivatives. The global sensitivity analysis uses the variance of model outputs as an indicator to investigate the influence of ion channels. The results show that there are common roles of ion channels on action potentials among several models. Additionally, we propose stochastic single cell SAN models to explain the cellular-level variability in action potentials. Novel one-dimensional SAN models of coupled SAN cells are developed to explain the action potential variability at a tissue level. These models capture the stochastic behavior of ion channels, cell-to-cell coupling and SAN cell heterogeneity. By this analysis we are able to computationally compare two models of coupled cells (heterogeneity of cell population versus identical cells with graded coupling strength), regarded as an open problem in the literature. Our results suggest that the SAN heterogeneity decreases the tissue level variability of action potentials. Based on the experimental observation that the variability of intact SAN is greatly smaller than the variability of single cell, our results support the hypothesis of the SAN cell heterogeneity. New insights are provided by the models to further understand the influence of heterogeneity and the coupling strength on determining the stochastic behavior of the intact SAN.

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Identifiers

ORCID for Mahesan Niranjan: orcid.org/0000-0001-7021-140X

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