Projection-based numerical optimization of transcranial magnetic coil placement for nonconvex target surfaces and double-cone coil geometries.

Objective.To develop a coil placement optimization pipeline for transcranial magnetic stimulation (TMS) that improves over existing solutions by guaranteeing the feasibility of the solution when double-cone coils are used and/or targets are placed over nonconvex scalp areas like the occipital region.Approach.Our proposed pipeline estimates feasible candidate coil locations by projecting the coil's geometry over the scalp around the target site and optimizing the coil's orientation to maximize scalp exposure to coil while avoiding coil-scalp collision. Then, the reciprocity principle is used to select the best position/orientation among candidates and maximize the average electric field (E-field) intensity at the target site. Our pipeline was tested on five magnetic resonance imaging-derived human head models for three different targets (motor cortex, lateral cerebellum, and cerebellar inion) and four coil models (planar coil: MagStim D70; double-cone coils: MagStim DCC, MagVenture Cool-D-B80, and Deymed 120BFV).Main results.Our pipeline returned several feasible solutions for any combination of anatomical target and coil, calculated and screened over 2000 candidates in minutes, and resulted in optimal locations that satisfy the minimum coil-scalp distance, whereas the direct method returned feasible candidates for just one combination of target and coil, i.e. planar coil and convex target over the motor cortex. We also found that, when the objective is to maximize the E-field magnitude, the target-to-scalp extension line is a better axis for coil translation compared to the normal vector at the scalp's surface, which is commonly used in existing approaches.Significance.We expand the use of numerical optimization for coil placement to double-cone coils, which are rapidly diffusing in research and clinical settings, and novel application domains, e.g. cerebellar TMS and ataxia treatment.