Optimization, implementation, and performance of TMS coils with maximum focality and various stimulation depths

<i>Objective.</i>Conventional transcranial magnetic stimulation (TMS) coils generate a diffuse and shallow electric field (E-field) in the brain, resulting in limited spatial targeting precision (focality). Previously, we developed a methodology for designing theoretical TMS coils to achieve maximal focality for a given E-field penetration depth and minimize the required energy. This paper presents the practical design, implementation, and characterization of such focal-deep TMS (fdTMS) coils.<i>Approach.</i>We considered how the coil's shape affects energy requirements and designed a curved 'hat' former that enables a wide range of coil placements while improving energy efficiency compared to flat formers. To improve energy efficiency, we introduced optimized-coverage partial-multi-layer windings of the coil. Through simulations with a spherical head model, we benchmarked the focality of the fdTMS E-field in the brain and the scalp, as well as the required energy, against conventional TMS coils. We then implemented two fdTMS coil designs with copper wire wound inside a 3d-printed plastic former.<i>Main results.</i>The E-field of the prototype fdTMS coils and conventional figure-8 counterparts were simulated in spherical and realistic head models and measured with a robotic probe, confirming a more compact fdTMS E-field. The fdTMS coils were also compared to two commercial coils with motor mapping in nine human subjects, which confirmed improved focality of fdTMS at the cost of greater E-field spread, increased energy loss and heating from the smaller wire diameter positioning constraints of the curved coil surface.<i>Significance.</i>The study findings inform TMS coil implementation for precise mapping and targeting applications, and the design framework can be leveraged for future coil optimizations.