Optimizing stimulus patterns for dense array TDCS with fewer sources than electrodes using a branch and bound algorithm

Dense array transcranial direct current stimulation (tDCS) has become of increasing interest as a noninvasive modality to modulate brain function. To target a particular brain region of interest (ROI), using a dense electrode array placed on the scalp, the current injection pattern can be appropriately optimized. Previous optimization methods have assumed availability of individually controlled current sources for each non-reference electrode. This may be costly and impractical in a clinical setting. However, using fewer current sources than electrodes results in a non-convex combinatorial optimization problem. In this paper, we present a novel use of the branch and bound (BB) algorithm to find sub-optimal stimulus patterns with fewer current sources than electrodes. We present simulation results for both focal and spatially extended cortical ROIs. Our results suggest that only a few (2–3) independently controlled current sources can achieve comparable results to a full set (125 sources) to a tolerance of 5%. BB is computationally 3–5 orders of magnitude less demanding than exhaustive search.