Abstract
The analytical theory of our earlier study (Mortensen et al., 2021, Math. Med. Biol., 38, 106-131) is extended to address the outstanding cases of fibroblast barrier distribution and myocyte strait distribution. In particular, closed-form approximations to the resting membrane potential and to the critical parameter values for propagation are derived for these two non-uniform fibroblast distributions and are in good agreement with numerical estimates.
Highlights
The spatial distribution of fibroblasts within the myocardial tissue and the electrical coupling between the fibroblasts and cardiomyocytes are significant but poorly understood factors in triggering and sustaining cardiac arrhythmias
Based on a fast-slow scale analysis (Biktashev et al, 2008; Simitev & Biktashev, 2006, 2011), we demonstrated that the boundary of absolute refractoriness in the myocyte–fibroblast tissue is determined primarily by the value of the myocyte potential ahead of a propagating pulse and used this to obtain a simple analytic expression that captures with remarkable accuracy the block of propagation in the case of a uniform fibroblast distribution (C1)
ADDENDUM: PROPAGATION AND BLOCK IN A MYOCYTE–FIBROBLAST MODEL. The purpose of this addendum is to extend the analytical theory of MGSS to the remaining two elementary fibroblast distribution cases—(C2) fibroblast barriers and (C3) myocyte straits
Summary
The spatial distribution of fibroblasts within the myocardial tissue and the electrical coupling between the fibroblasts and cardiomyocytes are significant but poorly understood factors in triggering and sustaining cardiac arrhythmias. Based on a fast-slow scale analysis (Biktashev et al, 2008; Simitev & Biktashev, 2006, 2011), we demonstrated that the boundary of absolute refractoriness in the myocyte–fibroblast tissue is determined primarily by the value of the myocyte potential ahead of a propagating pulse and used this to obtain a simple analytic expression that captures with remarkable accuracy the block of propagation in the case of a uniform fibroblast distribution (C1).
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