Gaussian Process-Based Surrogate Models for Optimizing Electrode Configurations in HD-tDCS

High-definition transcranial direct current stimulation (HD-tDCS) is a promising noninvasive neurostimulation technique used in therapeutic applications and brain-machine interfaces. It delivers direct current via multiple scalp electrodes, generating targeted electrical fields to modulate specific brain areas. In the context of HD-tDCS, optimizing electrode placements is challenging due to the complexity of brain anatomy and the vast number of possible configurations. While simulation models enable model-based optimization, continuous electrode positioning is generally computationally prohibitive. We propose Gaussian Process (GP)-based framework for optimizing HD-tDCS, allowing continuous prediction of electric field distributions. Unlike traditional leadfield-based methods, which restrict electrode placement, our approach expands the search space for greater precision. We employ a Sparse Gaussian Process (SGP) approximation, optimized using Block-Coordinate Descent and Subset of Data techniques, to efficiently handle large datasets. Results demonstrate that the SGP-based model significantly enhanced focality for superficial and mid-brain regions, achieving performance comparable to leadfield-based methods for deep brain targets. Overall, this framework offers enhanced stimulation precision and flexibility, supporting the advancement of tDCS in research and clinical contexts.