A semi-analytical model of a time reversal cavity for high-amplitude focused ultrasound applications

Time reversal cavities (TRC) have been proposed as an efficient approach for 3D ultrasound therapy. They allow the precise spatio-temporal focusing of high-power ultrasound pulses within a large region of interest with a low number of transducers. Leaky TRCs are usually built by placing a multiple scattering medium, such as a random rod forest, in a reverberating cavity, and the final peak pressure gain of the device only depends on the temporal length of its impulse response. Such multiple scattering in a reverberating cavity is a complex phenomenon, and optimisation of the device's gain is usually a cumbersome process, mostly empirical, and requiring numerical simulations with extremely long computation times. In this paper, we present a semi-analytical model for the fast optimisation of a TRC. This model decouples ultrasound propagation in an empty cavity and multiple scattering in a multiple scattering medium. It was validated numerically and experimentally using a 2D-TRC and numerically using a 3D-TRC. Finally, the model was used to determine rapidly the optimal parameters of the 3D-TRC which had been confirmed by numerical simulations.