Heat treatment modelling using strongly continuous semigroups.
In this paper, mathematical simulation of bioheat transfer phenomenon within the living tissue is studied using the thermal wave model. Three different sources that have therapeutic applications in laser surgery, cornea laser heating and cancer hyperthermia are used. Spatial and transient heating source, on the skin surface and inside biological body, are considered by using step heating, sinusoidal and constant heating. Mathematical simulations describe a non-Fourier process. Exact solution for the corresponding non-Fourier bioheat transfer model that has time lag in its heat flux is proposed using strongly continuous semigroup theory in conjunction with variational methods. The abstract differential equation, infinitesimal generator and corresponding strongly continuous semigroup are proposed. It is proved that related semigroup is a contraction semigroup and is exponentially stable. Mathematical simulations are done for skin burning and thermal therapy in 10 different models and the related solutions are depicted. Unlike numerical solutions, which suffer from uncertain physical results, proposed analytical solutions do not have unwanted numerical oscillations.
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran. Electronic address: mala@modares.ac.ir.
Alaeddin
A
Malek
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran. Electronic address: g.abbasi@modares.ac.ir.
Ghasem
G
Abbasi
D000818:Animals; D006358:Hot Temperature; D006801:Humans; D006979:Hyperthermia, Induced; D008954:Models, Biological; D009369:Neoplasms / Q000378:metabolism / Q000473:pathology / Q000628:therapy
Analytical solution; Semigroup theory; Temperature control; Thermal therapy; Thermal wave