Fractional pennes' bioheat equation: Theoretical and numerical studies
AffiliationUniversity of Minho & University of Chester, University of Chester, UTAD, UNL Lisboa, University of Minho
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AbstractIn this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bio heat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.
CitationFerrás, L., Ford, N., Morgado, M., Rebelo, M. S., & Nobrega, J. M. (2015). Fractional Pennes’ bioheat equation: Theoretical and numerical studies. Fractional Calculus and Applied Analysis, 18(4), pp. 1080-1106. doi:10.1515/fca-2015-0062
DescriptionAccepted for publication in Fractional calculus and applied analysis
Originally published in the journal Fract. Cal. Appl. Anal. Vol. 18 No. 4 / 2015 / pp.1080–1106 / DOI 10.1515/fca-2015-0062. The original publication is available at: http://www.degruyter.com/view/j/fca.2015.18.issue-4/fca-2015-0062/fca-2015-0062.xml?rskey=sWWcn0&result=1
SponsorsThe authors L.L. Ferras and J. M. Nobrega acknowledge financial funding by FEDER through the COMPETE 2020 Programme and by FCT- Portuguese Foundation for Science and Technology under the projects UID/CTM/50025/2013 and EXPL/CTM-POL/1299/2013. L.L. Ferras acknowledges financial funding by the Portuguese Foundation for Science and Technology through the scholarship SFRH/BPD/100353/2014. M. Rebelo acknowledges financial funding by the Portuguese Foundation for Science and Technology through the project UID/MAT/00297/2013.
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