Optimization of interferential stimulation of the human brain with electrode arrays

Abstract Objective. Interferential stimulation (IFS) has generated considerable interest recently because of its potential to achieve focal electric fields in deep brain areas with transcranial currents. Conventionally, IFS applies sinusoidal currents through two electrode pairs with close-by frequencies. Here we propose to use an array of electrodes instead of just two electrode pairs; and to use algorithmic optimization to identify the currents required at each electrode to target a desired location in the brain. Approach. We formulate rigorous optimization criteria for IFS to achieve either maximal modulation-depth or maximally focal stimulation. We find the solution for optimal modulation-depth analytically and maximize for focal stimulation numerically. Main results. Maximal modulation is achieved when IFS equals conventional high-definition multi-electrode transcranial electrical stimulation (HD-TES) with a modulated current source. This optimal solution can be found directly from a current-flow model, i.e. the ‘lead field’ without the need for algorithmic optimization. Once currents are optimized numerically to achieve optimal focal stimulation, we find that IFS can indeed be more focal than conventional HD-TES, both at the cortical surface and deep in the brain. Generally, however, stimulation intensity of IFS is weak and the locus of highest intensity does not match the locus of highest modulation. Significance. This proof-of-principle study shows the potential of IFS over HD-TES for focal non-invasive deep brain stimulation. Future work will be needed to improve on intensity of stimulation and convergence of the optimization procedure.