マイクロバブル増強型の強力集束超音波を用いた腫瘍焼灼治療のための非線形理論解析

抄録

Weakly nonlinear propagation of focused ultrasound in liquids containing many spherical microbubbles is theoretically and numerically investigated, especially focusing on the thermal conductivity of gas inside bubbles toward medical applications such as HIFU treatment. A Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation for the weakly nonlinear propagation of quasi-plane waves in pure liquid has been widely used as the mathematical model for HIFU treatment. Our previous study [Kagami & Kanagawa, Jpn. J. Multiphase Flow, 35(2) (2021), 346] derived a KZK equation for bubbly liquids incorporating the thermal conductivity of gas inside bubbles by utilizing the energy equation for gas inside bubbles and then we found that the thermal conductivity strongly contributes the dissipation effect, however, basic equations based on the mixture model of bubbly liquids were used. In the present study, a KZK equation incorporating the thermal conductivity of gas inside bubbles is re-derived by using basic equations based on the two-fluid model of bubbly liquids. Furthermore, we numerically solve the newly obtained KZK equation, and we then found temperature rise near the focus.