Obtaining accurate and calibrated coil models for transcranial magnetic stimulation using magnetic field measurements

Currently, simulations of the induced currents in the brain produced by transcranial magnetic stimulation (TMS) are used to elucidate the regions reached by stimuli. However, models commonly found in the literature are too general and neglect imperfections in the windings. Aiming to predict the stimulation sites in patients requires precise modeling of the electric field (E-field), and a proper calibration to adequate to the empirical data of the particular coil employed. Furthermore, most fabricators do not provide precise information about the coil geometries, and even using X-ray images may lead to subjective interpretations. We measured the three components of the vector magnetic field induced by a TMS figure-8 coil with spatial resolutions of up to 1 mm. Starting from a computerized tomography-based coil model, we applied a multivariate optimization algorithm to automatically modify the original model and obtain one that optimally fits the measurements. Differences between models were assessed in a human brain mesh using the finite-elements method showing up to 6% variations in the E-field magnitude. Our calibrated model could increase the precision of the estimated E-field induced in the brain during TMS, enhance the accuracy of delivered stimulation during functional brain mapping, and improve dosimetry for repetitive TMS.