The Electric Field Induced by Transcranial Magnetic Stimulation: A Comparison Between Analytic and FEM Solutions

Abstract: The induced electric field profiles in a homogeneous isotropic sphere, were calculated and compared between an analytic and a finite-element method in the framework of transcranial magnetic stimulation (TMS). This model can also be applied for concentric spheres in the framework of magnetic induction tomography (MIT), non destructive testing (NDT) or to calculate the lead field in magnetoencephalography (MEG). The calculations were performed using Eaton’s method as well as the finite-element program Comsol Multiphysics 4.2a (COMSOL Inc., Burlington, USA). A circular- and a figure-of-8 coil were used to operate as the sources of excitation. In our study the spherical volume conductor represents the human head consisting of grey matter. In order to quantify the differences between both methods an intense parameter study was performed. A comparison between both methods show a higher conformity than reported in previous studies. Regarding Eaton’s method, the influence of the maximum order of approximation L and the number of elements per winding K was investigated. The maximum relative difference was approximately 0.3 % for L = 20 and K> 16. Furthermore the relative efficiency of the algorithm was calculated to save computational time. With the presented results it is possible to use Eaton’s method efficiently to compute the induced electric field profiles very quickly for example while searching for specific coil arrangements around the humans head, as in the case of deep brain transcranial magnetic stimulation (dTMS)