One placement, many fields: robust voxel-wise mapping with multichannel TMS

Understanding the human brain at the individual level is central to understanding its function and a prerequisite for personalized therapy. Transcranial magnetic stimulation (TMS) can map structure-function relationships at high resolution by regressing trial-wise variation in the TMS-induced electric field (E-field) against a response such as motor evoked potentials (MEPs). This requires distinct E-fields across pulses at different cortical locations, which single-coil TMS (sTMS) achieves by physically repositioning the coil (typically supported by neuronavigation software such as InVesalius Navigator; Souza et al., 2018)--increasingly reliant on robotic guidance and capped by the coil geometry. Multichannel TMS (mTMS) instead steers the E-field electronically via independent currents in several coils, opening a design space of high variability without physical repositioning. We adapt determinant-based sequence optimization from discrete sTMS coil-placement sets to the continuous mTMS current space (D-optimal design), identifying pulse sequences whose induced cortical E-fields are as mutually dissimilar as biophysical constraints allow. We benchmarked optimized mTMS sequences against random baselines and optimized sTMS placements in virtual motor mapping across multiple head models, assessing three mTMS array geometries (5-channel planar, 6- and 12-channel spherical), two figure-of-eight sTMS coils, and varying pulse counts, response noise, and cortical depth. D-optimal mTMS currents substantially outperformed random currents and optimized sTMS at matched pulse counts. The gain was modest without noise but increased significantly with it: at the highest noise level, optimized sTMS failed to converge after 100 pulses (~20-22 mm error), whereas all mTMS arrays reached median errors at or below 6 mm. mTMS also recovered deep targets better than sTMS (up to 35 mm skin-cortex distance, versus 25 mm) and performed uniformly across the region of interest. A coil-space scheme based only on the magnetic vector potential, precomputable once per array without per-subject MRI, captured most of the benefit, matching subject-specific optimization at 100 pulses. mTMS thus makes voxel-wise mapping robust throughout a region of interest without coil repositioning.