Fractional Pennes' Bioheat Equation: Theoretical and Numerical Studies

Luis L. Ferras, Neville J. Ford, Maria L. Morgado, João Miguel Nóbrega, Magda S. Rebelo

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1080-1106
Number of pages27
JournalFractional Calculus and Applied Analysis
Volume18
Issue number4
DOIs
Publication statusPublished - Aug 2015

Keywords

  • fractional differential equations
  • Caputo derivative
  • bioheat equation
  • stability
  • convergence
  • HEAT TRANSFER EQUATION
  • DIFFUSION-EQUATIONS
  • DIFFERENCE SCHEME
  • GENERAL-THEORY
  • TISSUE
  • TEMPERATURE
  • MODEL
  • APPROXIMATION
  • CONDUCTION
  • SURFACE

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