A parallel solution for the numerical study of transcranial magnetic stimulation using the scalar potential finite differences method

Abstract

Introduction In transcranial magnetic stimulation (TMS) coils are used for the stimulation of human brain cortex. Numerous coil designs have been proposed and tested for different applications, both diagnostic and therapeutic. Purpose The objective of the current study is the fast and accurate calculation of the induced electric field and current density distribution inside the human head, in order to allow for the design of coils fulfilling specific treatment requirements. Materials and methods In order to avoid the intense computation of finite and boundary element meshes we developed a parallel in-house code, which implements a finite difference method. It calculates the magnetic scalar potential inside a human head model, given the electric conductivity distribution and the magnetic vector potential from 3D thin-wire coils. Tissue conductivity values can be derived either from volumetric data of realistic, voxelized human models, or from DICOM data segmentation. The numerical code was validated using analytical solutions of induced electric field in homogeneous conductive spherical models. Results The simulation gives information on focality, depth of stimulus, peak value and orientation of the induced electric field for different coil topologies. These characteristics of the TMS are different for various areas of the brain cortex. Furthermore, they show not only intra- but also inter-subject changes that can easily be quantified. Conclusion Our code can calculate the induced electric fields from TMS coils in the tissues of a human head model. The results can be derived within reasonable computational times and, therefore, the code can be used in the future to design coils with given specifications. Disclosure Authors declare that they have no competing interests.