Mortensen, P., Gao, H. , Smith, G. and Simitev, R. D. (2021) Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling. Mathematical Medicine and Biology, 38(1), pp. 106-131. (doi: 10.1093/imammb/dqaa014) (PMID:33412587)
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Abstract
The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias, but their roles are poorly understood. This article describes both direct numerical simulations and an asymptotic theory of propagation and block of electrical excitation in a model of atrial tissue with myocyte–fibroblast coupling. In particular, three idealized fibroblast distributions are introduced: uniform distribution, fibroblast barrier and myocyte strait—all believed to be constituent blocks of realistic fibroblast distributions. Primary action potential biomarkers including conduction velocity, peak potential and triangulation index are estimated from direct simulations in all cases. Propagation block is found to occur at certain critical values of the parameters defining each idealized fibroblast distribution, and these critical values are accurately determined. An asymptotic theory proposed earlier is extended and applied to the case of a uniform fibroblast distribution. Biomarker values are obtained from hybrid analytical-numerical solutions of coupled fast-time and slow-time periodic boundary value problems and compare well to direct numerical simulations. The boundary of absolute refractoriness is determined solely by the fast-time problem and is found to depend on the values of the myocyte potential and on the slow inactivation variable of the sodium current ahead of the propagating pulse. In turn, these quantities are estimated from the slow-time problem using a regular perturbation expansion to find the steady state of the coupled myocyte–fibroblast kinetics. The asymptotic theory gives a simple analytical expression that captures with remarkable accuracy the block of propagation in the presence of fibroblasts.
| Item Type: | Articles |
|---|---|
| Additional Information: | This work was supported by the UK Engineering and Physical Sciences Research Council (EP/N014642/1). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Simitev, Professor Radostin and Smith, Professor Godfrey and Gao, Dr Hao and Mortensen, Mr Peter |
| Authors: | Mortensen, P., Gao, H., Smith, G., and Simitev, R. D. |
| College/School: | College of Medical Veterinary and Life Sciences > School of Cardiovascular & Metabolic Health College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Mathematical Medicine and Biology |
| Publisher: | Oxford University Press |
| ISSN: | 1477-8599 |
| ISSN (Online): | 1477-8602 |
| Published Online: | 08 January 2021 |
| Copyright Holders: | Copyright © 2021 The Authors |
| First Published: | First published in Mathematical Medicine and Biology 38(1): 106-131 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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