Adopting reciprocity theorem in deep transcranial magnetic stimulation problem to design an efficient single source coil array based on nerve cell direction.

Deep transcranial magnetic stimulation (dTMS) plays an important role in the treatment of many diseases. Previous designs rarely considered the direction of the induced electric field (E) with respect to nerve fibers. However, it can be observed from related formulae that the tangential component of E (E effective) has a more significant role in the stimulation of nerve cells. In this paper, a new approach is proposed for designing a single-source coil array (CA) by combining tractography and the reciprocity theorem (RT). This method is a non-iterative procedure that can directly design CAs for the stimulation of each desired target zone without any complicated and slow iterative algorithm. Specifications of CA such as the optimum spatial angle and the best placement of coils are important because the location of the coil around the head and its spatial angle have been shown to have a major effect on induced E. Adoption of the RT yields the optimum specifications of CA and maximum E effective at the stimulation zone. This novel technique can introduce a new approach for the application of CA since it entails a high flexibility, high speed, and good accuracy.