Optimal Control of Phased-Array Ultrasound Transducer for Lithotripsy Using Input-Output Analysis*

Burst-wave lithotripsy is a non-invasive treatment of kidney stones using short pulses of focused ultrasound. In this talk, we present the use of input-output analysis (a frequency domain approach) to optimize the design and control of a multi-element array transducer to optimize stone breakage. The analysis is based on a linear fluid-structure coupled system that maps the acoustic forcing from individual elements to the stress in a stone of assumed shape, size, and composition. We determine the optimal frequency and optimal distribution of the phase and amplitude across the aperture by maximizing a cost function that represents the strain energy in stone. The optimal parameters are obtained by applying a state-of-the-art, randomized singular value decomposition to the discrete linear operator. The results show that under the same input energy, carefully controlling the relative phase and amplitude between elements can increase strain energy (by 2-3 times in certain cases) compared to a uniform distribution. This suggests that stone fragmentation can be accelerated or performed with lower energy for safer treatment. The improvement is validated by combining high-fidelity simulations with high-speed camera images of crack formation in model stones from in-vitro experiments.