On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology
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Description
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.
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ID Code: | 91104 | ||||
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Item Type: | Contribution to Journal (Journal Article) | ||||
Refereed: | Yes | ||||
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Measurements or Duration: | 16 pages | ||||
DOI: | 10.1371/journal.pone.0143938 | ||||
ISSN: | 1932-6203 | ||||
Pure ID: | 32922040 | ||||
Divisions: | Past > Institutes > Institute for Future Environments Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Schools > School of Mathematical Sciences Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS) |
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Copyright Owner: | Consult author(s) regarding copyright matters | ||||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||
Deposited On: | 09 Dec 2015 01:56 | ||||
Last Modified: | 15 May 2024 11:05 |
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