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Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies

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Abstract

In 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 bioheat 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.

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Author information

Authors and Affiliations

  1. Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058, Guimares, Portugal

    Luis L. Ferrás & João M. Nóbrega

  2. Department of Mathematics, University of Chester, CH1 4BJ, UK

    Luis L. Ferrás & Neville J. Ford

  3. Department of Mathematics, University of Trás-os-Montes e Alto Douro, UTAD Quinta de Prados, 5001-801, Vila Real, Portugal

    Maria L. Morgado

  4. Departamento de Matemática and Centro de Matemática e Aplicacões Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

    Magda S. Rebelo

Authors
  1. Luis L. Ferrás
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  2. Neville J. Ford
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  4. João M. Nóbrega
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  5. Magda S. Rebelo
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Correspondence to Luis L. Ferrás.

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Ferrás, L.L., Ford, N.J., Morgado, M.L. et al. Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies. FCAA 18, 1080–1106 (2015). https://doi.org/10.1515/fca-2015-0062

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