Numerical Analyses of Transcranial Magnetic Stimulation Based on Individual Brain Models by Using a Scalar-Potential Finite-Difference Method

Recent studies show that transcranial magnetic stimulation (TMS) is effective for the treatment of neurological and psychiatric diseases and that the therapeutic effect varies significantly among patients. The distribution of the electric fields induced by TMS is affected by individual variability in the shape of the brain. Numerical analyses of the electric fields in each patient performed by using individual brain models are potentially valuable for maximizing the therapeutic effect if the calculated fields are correlated with the effect of TMS. However, most of the numerical simulations of TMS are carried out by using standard human models. In this paper, we develop a new TMS simulation system, which is able to calculate the electric field induced in the brain with consideration of a complex gyral folding pattern, based on a scalar-potential finite-difference (SPFD) method. An easy implementation and a high efficiency of calculation resulting in a reduced computation time are the advantages of the SPFD method. The simulation is first performed on a sphere conductor model and a cube conductor model with 0.75 mm voxels, and we evaluate its accuracy through comparison with a finite-element method simulation. Second, we perform the simulations using six individual brain models constructed by segmenting magnetic resonance images and calculate the intensity of the field induced in each subject when they are stimulated with the intensity of their resting motor threshold (RMT). As a result, we find that there is a diversity of not only the intensity of the RMT but also the induced electric field in their brain tissues; the difference between the maximum and minimum values of the induced field on the stimulation spot among the subjects is 97 V/m, while the average value of the induced field is 203 V/m. Finally, we discuss the potential of this software in practical use and in the research of TMS.