Theoretical analysis on thermal effect of weakly nonlinear propagation of focused ultrasound toward medical applications

Abstract

Toward medical applications such as a tumor ablation therapy by High-Intensity Focused Ultrasound (HIFU), weakly nonlinear propagation of quasi-planar focused ultrasound in a liquid containing many spherical microbubbles is theoretically investigated, especially focusing on thermal effects of microbubble oscillations. We shall derive a Khokhlov–Zabolotskaya–Kuznetsov (KZK) type equation incorporating the thermal effects of the microbubble oscillations by introducing the energy equation proposed by Prosperetti [J. Fluid Mech. (1991)] into the set of basic equations based on mixture and two-fluid models. Moreover, the phase difference between the temperature gradient and the average temperature inside bubble is considered in the energy equation. As a result, we found that (i) the thermal conduction of gas inside bubbles strongly affects the dissipation of ultrasound and (ii) the phase difference affects the advection of ultrasound.