マイクロバブルを利用した集束超音波治療における 非線形効果と熱的効果に関する基礎理論の構築

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  • Basic Theoretical Study on Nonlinear and Thermal Effects in Microbubble-Enhanced Focused Ultrasound Treatment

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Weakly nonlinear propagation of ultrasound in an initially quiescent liquids uniformly containing many spherical microbubbles is theoretically investigated, especially focusing on the thermal conductivity and liquid viscosity toward medical application such as HIFU treatment. Although our group has derived a Khokhlov–abolotskaya–Kuznetsov (KZK) equation for the description of quasi-plane propagation of ultrasound with a long wavelength and a low frequency in bubbly liquids with a nonuniformity of the number density of bubbles, the effects of the thermal conductivity and liquid viscosity has been ignored. The present study re-derived a KZK equation incorporating the thermal conductivity and liquid viscosity. As a result, the nonlinear, dissipation, dispersion, and diffraction effects of ultrasound are expressed as a linear combination. Especially, the dissipation effect is divided into two terms, i.e., the second partial derivative and the term without differentiation with respect to a retarded time: the former is owing to the liquid viscosity and the liquid compressibility (i.e., acoustic radiation damping) and the latter is to the thermal conduction. Three types of dissipations (i.e., the liquid viscosity, liquid compressibility, and thermal conduction) are also expressed as the linear combination.

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