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Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells

Author

Listed:
  • Guanyu Zhou

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Tatsuya Hayashi

    (Faculty of Science and Engineering, Yamato University, Osaka 564-0082, Japan
    Research and Development Initiative, Chuo University, Tokyo 192-0393, Japan)

  • Tetsuji Tokihiro

    (Department of Mathematical Engineering, Faculty of Engineering, Musashino University, Tokyo 135-8181, Japan)

Abstract

We examine stochastic phase models for the community effect of cardiac muscle cells. Our model extends the stochastic integrate-and-fire model by incorporating irreversibility after beating, induced beating, and refractoriness. We focus on investigating the expectation and variance in the synchronized beating interval. Specifically, for a single isolated cell, we obtain the closed-form expectation and variance in the beating interval, discovering that the coefficient of variation has an upper limit of 2 / 3 . For two coupled cells, we derive the partial differential equations for the expected synchronized beating intervals and the distribution density of phases. Furthermore, we consider the conventional Kuramoto model for both two- and N -cell models. We establish a new analysis using stochastic calculus to obtain the coefficient of variation in the synchronized beating interval, thereby improving upon existing literature.

Suggested Citation

  • Guanyu Zhou & Tatsuya Hayashi & Tetsuji Tokihiro, 2024. "Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells," Mathematics, MDPI, vol. 12(19), pages 1-30, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:2964-:d:1484786
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