An efficient algorithm for electrode optimization of transcranial temporal interference stimulation

Transcranial current stimulation (tCS) has been used extensively to noninvasively investigate and influence brain function in both healthy volunteers and clinical populations. Though positive results have been obtained with current methods, accurate targeting, high focality and deep stimulation are yet to be achieved. Transcranial temporal interference stimulation (tTIS) offers a potential solution to these issues by combining two alternating currents to create an amplitude-modulated electric field that can peak deep in the brain (Fig. 1A). Simulations of electric field in human models indicated the potential of tTIS for subthreshold neuromodulation similar to tACS, but with maximal effects in deep brain areas and greater focality. For tTIS to become practical, optimization methods are needed that can selectively stimulate a region of interest (ROI) while meeting safety constraints. Because conventional tCS presents a linear optimization problem, existing optimization methods for tCS cannot be used for tTIS. Previously proposed solutions for tTIS optimization included exhaustive search (Rampersad et al., 2019) and reformulations of existing tCS methods (Huang et al., 2020). These methods take hours to complete, making them inefficient for practical use in research or in the clinic. As an alternative we posed tTIS targeting as a non-convex optimization problem and exploit its associated mathematical model using convex relaxations and tailored heuristics. We tested our algorithm on multiple realistic human head models with 88 electrodes for a large set of ROIs spread throughout the brain (Fig. 1B). Our method was able to find current patterns that deliver maximal tTIS fields to any ROI in seconds. We combined this method with Pareto optimization, which allowed maximizing focality in addition to ROI effects, but significantly increases the runtime. Optimization outcomes were evaluated on ROI effects, focality and efficiency, and compared to the two previously proposed methods (Fig. 1C), demonstrating a tradeoff dependent on ROI location. Keywords: temporal interference, transcranial stimulation, optimization, simulation