FRACTIONAL PENNES' BIOHEAT EQUATION: THEORETICAL AND NUMERICAL STUDIES

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Ferras, LL (Author) Other; Ford, NJ (Author) Other; Morgado, ML (Author) Other; Nobrega, JAM (Author) Other; Rebelo, MS (Author) Other

Journal

Title: Fractional Calculus and Applied Analysis

Vol. 18

Pages: 1080-1106

ISSN: 1311-0454

Publisher: Walter De Gruyter

Indexing

ISI Web of Knowledge - 33 Citations

Scopus - 45 Citations

Other information

Authenticus ID: P-00G-FHF

DOI: 10.1515/fca-2015-0062

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27