title: On the Order of the Fractional Laplacian in Determining the Spatio-Temporal Evolution of a Space-Fractional Model of Cardiac Electrophysiology.
abstract: Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.
authors.affiliation: Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Queensland, Australia.
authors.forename: Nicole
authors.initials: N
authors.lastname: Cusimano
authors.affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom.
authors.forename: Alfonso
authors.initials: A
authors.lastname: Bueno-Orovio
authors.affiliation: Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Queensland, Australia.
authors.forename: Ian
authors.initials: I
authors.lastname: Turner
authors.affiliation: Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Queensland, Australia.|Department of Computer Science, University of Oxford, Oxford, United Kingdom.
authors.forename: Kevin
authors.initials: K
authors.lastname: Burrage
mesh_terms: D000200:Action Potentials; D054849:Cardiac Electrophysiology; D008955:Models, Cardiovascular; D062211:Spatio-Temporal Analysis