Comparison of Gilmore-Akulichev’s, Keller-Miksis’s and Rayleigh-Plesset’s equations on therapeutic ultrasound bubble cavitation

Abstract

Many models have been utilized to simulate inertial cavitation for ultrasound therapies such as histotripsy. The models range from the very simple Rayleigh-Plesset model to the complex Gilmore-Akulichev model. The computational time increases with the complexity of the model, so it is important to know when the results from the simpler models are sufficient. In this paper the simulation performance of the widely used Rayleigh-Plesset model, Keller-Miksis model, and Gilmore-Akulichev model both with and without gas diffusion are compared by calculating the bubble radius response and bubble wall velocity as a function the ultrasonic pressure and frequency. The bubble oscillates similarly with the three models within the first collapse for small pressures (<3MPa), but the Keller-Miksis model diverges at higher pressures. In contrast, the maximum expansion radius of the bubble is similar at all pressures with Rayleigh-Plesset and Gilmore-AKulichev although the collapse velocity is unrealistically high with Rayleigh-Plesset model. After multiple cycles, the Rayleigh-Plesset model starts to behave disparately both in the expansion and collapse stages. The inclusion of rectified gas diffusion lengthens the collapse time and increases the expansion radius. However, for frequency smaller than 1 MHz, the impact of gas diffusion is not significant.