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

Guanyu Zhou (), Tatsuya Hayashi and Tetsuji Tokihiro
Additional contact information
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
Tetsuji Tokihiro: Department of Mathematical Engineering, Faculty of Engineering, Musashino University, Tokyo 135-8181, Japan

Mathematics, 2024, vol. 12, issue 19, 1-30

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.

Keywords: stochastic phase model; cardiac muscle cells; synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/2964/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/2964/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:2964-:d:1484786

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().