Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells
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 synchroniz...
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MDPI AG
2024-09-01
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| author | Guanyu Zhou Tatsuya Hayashi Tetsuji Tokihiro |
| author_facet | Guanyu Zhou Tatsuya Hayashi Tetsuji Tokihiro |
| author_sort | Guanyu Zhou |
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| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msqrt></semantics></math></inline-formula>. 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 <i>N</i>-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. |
| format | Article |
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| issn | 2227-7390 |
| language | English |
| publishDate | 2024-09-01 |
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| spelling | doaj-art-0f2f3a633882422a963d3202c8f45d8a2025-08-20T02:16:50ZengMDPI AGMathematics2227-73902024-09-011219296410.3390/math12192964Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle CellsGuanyu Zhou0Tatsuya Hayashi1Tetsuji Tokihiro2Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaFaculty of Science and Engineering, Yamato University, Osaka 564-0082, JapanDepartment of Mathematical Engineering, Faculty of Engineering, Musashino University, Tokyo 135-8181, JapanWe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msqrt></semantics></math></inline-formula>. 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 <i>N</i>-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.https://www.mdpi.com/2227-7390/12/19/2964stochastic phase modelcardiac muscle cellssynchronization |
| spellingShingle | Guanyu Zhou Tatsuya Hayashi Tetsuji Tokihiro Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells Mathematics stochastic phase model cardiac muscle cells synchronization |
| title | Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells |
| title_full | Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells |
| title_fullStr | Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells |
| title_full_unstemmed | Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells |
| title_short | Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells |
| title_sort | stochastic phase model with reflective boundary and induced beating an approach for cardiac muscle cells |
| topic | stochastic phase model cardiac muscle cells synchronization |
| url | https://www.mdpi.com/2227-7390/12/19/2964 |
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