Optimal Pre-Experimental Coil Sequence Selection for TMS Motor Mapping

Transcranial magnetic stimulation (TMS) motor mapping increasingly relies on electric-field (E-field) modeling to localize cortical targets, but many candidate coil placements induce highly redundant cortical patterns. We frame prospective coil-sequence design as a subset-selection problem and compare farthest-point sampling, determinant-based objectives, and related controls in virtual mapping experiments across 12 realistic head models. Across convergence, matrix-diagnostic, and manifold-coverage analyses, the best-performing objectives combined low between-stimulation redundancy with preserved inter-element separability on the cortex; objectives that maximized one of these at the expense of the other fell below random sampling. An RBF-kernelized D-optimal objective matched FPS in mapping accuracy while using [~]15 fewer unique scalp positions per 100 pulses, suggesting reduced arm-reconfiguration cost on robotic TMS platforms. A singular-spectrum analysis of the candidate library provides a low-cost a-priori indicator that predicts when discretization choices fall below the diversity floor required for stable mapping. These results recast prospective TMS mapping as a limited manifold-coverage problem and offer concrete design rules for sample-efficient, robotically efficient sequence planning. Algorithm implementations are available as part of the open-source pynibs tool-box at https://gitlab.gwdg.de/tms-localization/pynibs/-/tree/dev/pynibs/optimization.