Background. Transcranial magnetic stimulation (TMS) is a noninvasive brain stimulation technique used for research and clinical applications. Existent TMS coils are limited in their precision of spatial targeting (focality), especially for deeper targets.

 

Objective. This project presents a methodology for designing and fabricating TMS coils that achieve optimal trade-off between the depth and focality of the induced electric field (E-field), as well as the energy required by the coil. 

 

Approach. A multi-objective optimization technique is used for computationally designing TMS coils that achieve optimal trade-offs between E-field focality, depth, and energy (fdTMS coils). The fdTMS coil winding(s) maximize focality (minimize the volume of the brain region with E-field above a given threshold) while reaching a target at a specified depth and not exceeding predefined peak E-field strength and required coil energy. Spherical and MRI-derived head models are used to compute the fundamental depth–focality trade-off as well as focality–energy trade-offs for specific target depths. 

 

Main results. Across stimulation target depths of 1.0–3.4 cm from the brain surface, the suprathreshold volume can be theoretically decreased by 42%–55% compared to existing TMS coil designs. The suprathreshold volume of a figure-8 coil can be decreased by 36%, 44%, or 46%, for matched, doubled, or quadrupled energy. For matched focality and energy, the depth of a figure-8 coil can be increased by 22%. 

 

Significance. Computational design of TMS coils could enable more selective targeting of the induced E-field. The presented results are the first significant advancement in the depth–focality trade-off of TMS coils since the introduction of the figure-8 coil three decades ago, and likely represent the fundamental physical limit.