Numerical analysis of coupled effects of pulsatile blood flow and thermal relaxation time during thermal therapy

Abstract

The main purpose of this study is to investigate the coupled effects of the pulsatile blood flow in thermally significant blood vessels and the thermal relaxation time in living tissues on temperature distributions during thermal treatments. Considering the fact that propagation speed of heat transfer in solid tissues is actually finite according to experiments, the traditional Pennes bioheat transfer equation (PBTE) was modified to a wave bioheat transfer equation (WBTE) that contains both wave transportation and diffusion competing with each other and characterized by the thermal relaxation time. The wave behavior will be more dominant when the relaxation time is large. WBTE together with a coupled energy transport equation for blood vessel flow was used to describe the temperature evolution of our current tumor–blood vessel system, and the equations were numerically solved by the highly accurate multi-block Chebyshev pseudospectral method. Numerical results showed that temperature evolution from WBTE was quite different from their counterparts from PBTE due to the dominant wave feature under large relaxation time. For example, larger relaxation time would preserve high temperature longer and this effect is even more pronounced when heating is fast. It further implies that heat is drained more slowly when relaxation time is large, and would make thermal lesion region cover the tumor tissue, the heating target, better. This phenomenon would therefore hint that the traditional PBTE simulations might under-estimate the thermal dose exerted on tumor. As to the pulsation frequency of blood flow from heart beat which was originally predicted to be important here, it turned out that the thermal behavior is quite insensitive to pulsation frequency in the current study.