Low-intensity focused ultrasound (LIFU) has been shown to modulate neural activity, with potential applications in treating neuropsychiatric disorders like depression. Recent experiments suggest that the stimulation effect is highly target-specific, which emphasizes the necessity of high neuromodulation resolution. Although the ultrasound beam profile resolution has been well investigated, the neuromodulation resolution, dependent on neural responses, is not strictly defined yet. Therefore, in this work, we aim to numerically define and evaluate the neuromodulation resolution of different beam focusing methods for ultrasound phased array transducers. In this work, we introduce an ultrasound neuromodulation resolution metric, Off-Target Activation Area (OTAA). OTAA measures the off-target area with potential unintended neuron activation according to the dependence of neuromodulation effects on sonication pressure. To minimize OTAA, a phased-array beamforming scheme, Constrained Optimal Resolution (COR) beamforming, is proposed to minimize the off-target region sonications while ensuring effective stimulation in the target brain region. A lower bound of OTAA is also analytically approximated in a simplified homogeneous medium, which can serve as guidelines for the selection of transducer parameters like aperture size and operating frequency. Numerical evaluations of OTAA in a human head model are conducted with different array setups and beamforming algorithms. Results show that COR beamforming is able to significantly improve the OTAA-based neuromodulation resolution compared to benchmark methods by reducing the degree of possible off-target neuromodulation experienced. The numerical evaluation of neuromodulation resolution is necessary to understand how brain circuits are influenced by stimulation. An appropriate neuromodulation resolution can also help to avoid potential side effects in future treatment applications caused by off-target activation.

Although the ultrasound energy can be precisely focused on the target with beamforming methods we designed to achieve high neuromodulation resolution, the focusing beam design is usually based on measurements or simulations of the ultrasound propagation in the human head. Model inaccuracies can hence be involved that can potentially degrade the neuromodulation resolution. Therefore, in this work, we aim to numerically evaluate how the neuromodulation resolution is sensitive to the inaccuracy of acoustic parameters, like the sound speed, and address the potential sensitivity issue with beamforming methods. In this research, we propose a phased array beamforming technique, Robust Optimal Resolution (ROR) beamforming method, that preserves a high neuromodulation resolution while tolerating inaccuracies in brain tissue sound speeds. A min-max optimization problem is formulated to minimize the worst-case OTAA with restricted sound speed inaccuracy. An ultrasound propagation model is designed to predict the propagation channel with arbitrary sound speed values in a feasible range, which can be highly invasive to measure in experiments and computationally inefficient to simulate. Numerical evaluation results show that our propagation model can predict the change of propagation channel with limited errors. The proposed ROR beamforming method can significantly reduce the worst-case OTAA compared to benchmark methods, which implies that the robustness of stimulation is improved and the sensitivity is addressed. The proposed beamforming scheme allows the high neuromodulation resolution to be robust in future applications, while reducing the potential invasiveness and challenges to acquire the necessary propagation information for ultrasound focusing.