Numerical optimization of electrically focal transcranial magnetic stimulation coils

The objective of this paper is to numerically investigate novel coil designs that have an improved electric field focality compared to the standard figure-of-eight coil and other variations on such a design. The induced electric field was calculated on homogeneous conducting sphere representing a simplified head model. In the presented models, skin effect is neglected, due to the low frequencies in transcranial magnetic stimulation. Field focality is described by an equivalent area where the field drops below 50% of its maximal value. In order to provide comparison, the coils were designed to have the same or similar dimensions as the figure-of-eight coil. The electric field of the proposed coils is more focal with values from 5.5 cm² to 9.5 cm². However, the penetration depth of these coils is smaller compared to traditional figure-of-8 coils, ranging from 0.9 cm to 1.2 cm. It is observed, that for every proposed coil design an improvement in focality is paid by penetration depth and vice versa. In this way, the application of smaller coils and windings improves focality but decreases maximum induction field and penetration depth.