Optimization of acoustic lens design for transcranial holographic ultrasound using an active learning-based genetic algorithm

Transcranial focused ultrasound (tFUS) is a promising non-invasive brain stimulation modality; however, achieving precise volumetric focusing remains challenging due to skull-induced distortion of acoustic field propagation. Acoustic holography (AH) has been proposed to compensate for the distortion, yet conventional AH lens design methods remain limited in accurately engaging volumetric targets due to complex, subject-specific skull geometries. Here, we propose an AH lens optimization framework for transcranial holographic ultrasound (THUS) that integrates deep learning-based surrogate modeling and an active learning-guided genetic algorithm. A deep learning surrogate model was constructed to capture the relationship between lens geometries, parameterized by Bézier surfaces, and the resulting volumetric acoustic focusing performance. Through active learning–guided genetic optimization, the surrogate model was iteratively refined across multiple generations, enabling efficient and comprehensive exploration of the lens design space. The proposed framework was evaluated across four volumetric target regions in three human skull models, including deep brain structures such as the thalamus and putamen. Overall, the proposed approach consistently outperformed the conventional time-reversal-based method in volumetric target engagement. For clinically relevant deep brain targets, the average volumetric overlap increased from approximately 0.28–0.33 to 0.37–0.48, corresponding to relative improvements of approximately 50%. These results demonstrate that active learning–guided AH lens design optimization substantially enhances precise volumetric target engagement in THUS and provides an efficient optimization framework for subject-specific transcranial ultrasound neuromodulation.