Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling

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, Dr 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 > Institute of Cardiovascular and Medical Sciences
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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
172141EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - Mathematics