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J R Soc Interface. 2014 Aug 6;11(97):20140352. doi: 10.1098/rsif.2014.0352.

Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization.

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Oxford Centre for Collaborative Applied Mathematics, University of Oxford, Oxford OX1 3LB, UK Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK
Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK.
Department of Engineering Science, Institute of Biomedical Engineering, University of Oxford, Oxford OX3 7DQ, UK.
Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland 4001, Australia.


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.


Riesz potential; cardiac tissue; dispersion of repolarization; electrotonic effects; fractional diffusion; structural heterogeneity

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