title: Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface.
abstract: This study focuses on the effect of the temperature response of a semi-infinite biological tissue due to a sinusoidal heat flux at the skin. The Pennes bioheat transfer equation such as rho(t)c(t)( partial differentialT/ partial differentialt)+W(b)c(b)(T-T(a))=k partial differential(2)T/ partial differentialx(2) with the oscillatory heat flux boundary condition such as q(0,t)=q(0)e(iomegat) was investigated. By using the Laplace transform, the analytical solution of the Pennes bioheat transfer equation with surface sinusoidal heating condition is found. This analytical expression is suitable for describing the transient temperature response of tissue for the whole time domain from the starting periodic oscillation to the final steady periodic oscillation. The results show that the temperature oscillation due to the sinusoidal heating on the skin surface is unstable in the initial period. Further, it is unavailable to predict the blood perfusion rate via the phase shifting between the surface heat flux and the surface temperature. Moreover, the lower frequency of sinusoidal heat flux on the skin surface induces a more sensitive phase shift response to the blood perfusion rate change, but extends the beginning time of sampling because of the avoidance of the unavailable first cyclic oscillation.
authors.affiliation: Department of Medical Radiology Technology, China Medical University, Taiwan.
authors.forename: Tzu-Ching
authors.initials: TC
authors.lastname: Shih
authors.forename: Ping
authors.initials: P
authors.lastname: Yuan
authors.forename: Win-Li
authors.initials: WL
authors.lastname: Lin
authors.forename: Hong-Sen
authors.initials: HS
authors.lastname: Kou
mesh_terms: D001783:Blood Flow Velocity; D001833:Body Temperature Regulation / Q000502:physiology; D003198:Computer Simulation; D004735:Energy Transfer / Q000502:physiology*; D006358:Hot Temperature; D008954:Models, Biological; D012867:Skin / Q000098:blood supply; D012881:Skin Temperature / Q000502:physiology*; D013814:Thermal Conductivity; D013997:Time Factors