Trade-off between stimulation focality and the number of coils in multi-locus transcranial magnetic stimulation

Objective. Coils designed for transcranial magnetic stimulation (TMS) must incorporate trade-offs between the required electrical power or energy, focality and depth penetration of the induced electric field (E-field), coil size, and mechanical properties of the coil, as all of them cannot be optimally met at the same time. In multi-locus TMS (mTMS), a transducer consisting of several coils allows electronically targeted stimulation of the cortex without physically moving a coil. In this study, we aimed to investigate the relationship between the number of coils in an mTMS transducer, the focality of the induced E-field, and the extent of the cortical region within which the location and orientation of the maximum of the induced E-field can be controlled. Approach. We applied convex optimization to design planar and spherically curved mTMS transducers of different E-field focalities and analyzed their properties. We characterized the trade-off between the focality of the induced E-field and the extent of the cortical region that can be stimulated with an mTMS transducer with a given number of coils. Main results. At the expense of the E-field focality, one can, with the same number of coils, design an mTMS transducer that can control the location and orientation of the peak of the induced E-field within a wider cortical region. Significance. With E-fields of moderate focality, the problem of electronically targeted TMS becomes considerably easier compared with highly focal E-fields; this may speed up the development of mTMS and the emergence of new clinical and research applications.