Fractional pennes' bioheat equation: theoretical and numerical studies

• Autor(a) principal: Ferrás, Luís Jorge Lima
• Data de Publicação: 2015
• Outros Autores: Ford, N. J., Morgado, M. L., Nóbrega, J. M., Rebelo, M. S.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/38378
• topic: Fractional differential equations; Caputo derivative; Bioheat equation; Stability; Convergence; fractional differential equations; Engenharia e Tecnologia::Engenharia dos Materiais; Science & Technology

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.