Abstract
Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.
Highlights
Excitable biological tissues, such as neural, cortical, gastric muscle or cardiac cells, are characterized by the generation and spread of timed electrical impulses that regulate their function, such as vision or contraction
We propose a family of fractional diffusion models to describe electrical propagation in heterogeneous excitable media, analysing their application to cardiac muscle as a representative case of composite biological tissue
The new modelling framework presented in this contribution aims to probe mathematical descriptions of cardiac tissue with the macroscopic effects of structural heterogeneity on impulse propagation
Summary
Excitable biological tissues, such as neural, cortical, gastric muscle or cardiac cells, are characterized by the generation and spread of timed electrical impulses that regulate their function, such as vision or contraction. The action potential (AP) represents changes over time in the electric potential of these cells that are the result of currents flowing across the membrane via the movement of ions. The extent to which electrical propagation is influenced by the highly complex, and heterogeneous nature of these tissues remains unclear. Conventional modelling techniques represent these tissues as continuum media with spaced averaged properties, assuming a negligible contribution of their composite microstructure in modulating electrical conduction. New mathematical modelling techniques are needed to capture and explain the influence of tissue heterogeneity on cardiac wavefront propagation
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