Differential evolution method to find optimal location of a single-element transducer for transcranial focused ultrasound therapy

Background and objective: Focused ultrasound (FUS) has been receiving growing attention as a noninvasive brain stimulation tool because of its superior spatial specificity and depth penetrability. However, the large mismatch of acoustic properties between the skull and water can disrupt and shift the acoustic focus in the brain. In this paper, we present a numerical method to find the optimal location of a single-element FUS transducer, which creates focus on the target region. Methods: The score function, representing the superposition of acoustic waves according to the relative phase difference and transmissibility, was defined based on time-reversal invariance of acoustic waves and depending on the spatial location of the transducer. The optimal location of the transducer was then determined using a differential evolution algorithm. To assess the proposed method, we conducted a forward simulation and compared the resulting focal location to the desired target point. We also performed experimental validation by measuring the acoustic pressure field through an ex vivo human skull in a water tank. Results: The numerical results indicated that the score function had a positive proportional relationship with the acoustic pressure at the target. Moreover, for the optimized transducer location, both the numerical and experimental results showed that the normalized acoustic pressure at the target was higher than 0.9. Conclusions: In this study, we developed an optimization method to place a single-element transducer that effectively transmits acoustic energy to the targeted region in the brain. Our numerical and experimental results demonstrate that the proposed method can provide an optimal transducer location for safe and efficient FUS treatment.