Acoustic Field Optimization for an Ultrasound Phased Array in Sonodynamic Therapy Based on an Improved Multi-Objective Particle Swarm Optimization Algorithm

Sonodynamic therapy (SDT) for atherosclerotic plaque-related diseases requires the formation of a precise and controllable ultrasound field within the lesion region, placing high demands on the acoustic field steering capability of ultrasound phased arrays. To address insufficient focusing accuracy, incomplete plaque coverage, and sidelobe leakage in SDT phased arrays, this study proposes a hierarchical cooperative adaptive multi-objective particle swarm optimization algorithm (HC-AMOPSO) for the joint optimization of phased-array amplitudes and phases. First, a physics-prior-guided hierarchical excitation coding mechanism is developed, in which base excitation, group-wise modulation, and local residuals are used to establish structured relationships among the element amplitudes and phases, thereby improving search stability and cooperative focusing capability among array elements. Second, an adaptive hierarchical cooperative evolution mechanism is introduced, combining error-feedback adjustment with hierarchical particle updating to balance global exploration and local convergence.Finally, an acoustic field shape deviation (AFSD) metric is proposed to quantify the overall quality of the acoustic field and improve the multi-objective acoustic field evaluation framework for SDT. Numerical optimization results show that the focal shift is controlled within 0.10 mm and the coverage rate reaches 93.85%. The overall performance is superior to that of comparable algorithms, demonstrating the feasibility of the acoustic field model, optimization algorithm, and evaluation metrics, while maintaining good adaptability at different focal positions. The hydrophone-measured acoustic fields are generally consistent with the corresponding homogeneous-water simulation results, providing a reference for personalized acoustic field optimization in the SDT of atherosclerotic plaques.