Development of Transcranial Magnetic Stimulator Coils that Physically Achieve the Deepest Stimulation Based on the Inverse Problem Approach

The stimulation of deeper brain regions with transcranial magnetic stimulation (TMS) is a promising treatment for depression with higher remission rates. The focality of the stimulation area is essential to reduce the risk of side effects; however, there is a physical trade-off between depth and focality. Because existent studies have searched for depth by iteratively designing a coil and then calculating the electric field in the brain, the theoretical maximum depth has not yet been determined. In this study, we propose a methodology to derive the coil based on an inverse problem approach from an analytical description of the desired electric field in the brain. This new method has allowed us to theoretically derive the maximum depth of the electric field, which was previously only determined empirically. Based on this, we designed and built a coil that can deliver the electric field to the deepest depth. Numerical simulations of the proposed coils derived show that they have the highest electric field depth of any coil feasible in the existing medical field. Moreover, the balance between depth and focality was also the best of the existing coils.