Real-time computation of the TMS-induced electric field in a realistic head model

Abstract

BackgroundTranscranial magnetic stimulation (TMS) is often targeted using a model of TMS-induced electric field (E). In such navigated TMS, the E-field models have been based on spherical approximation of the head. Such models omit the effects of cerebrospinal fluid (CSF) on the E-field, leading to potentially large errors in the computed field. So far, realistic models have been too slow for interactive TMS navigation. ObjectiveWe present computational methods that enable real-time solving of the E-field in a realistic head model that contains the CSF. MethodsUsing reciprocity and Geselowitz integral equation, we separate the computations to coil-dependent and -independent parts. For the coil-dependent part of Geselowitz integrals, we present a fast numerical quadrature. Further, we present a moment-matching approach for optimizing dipole-based coil models. We verify the new methods using simulations in a realistic head model that contains the brain, CSF, skull, and scalp. ResultsThe new quadrature introduces a relative error of 1.1%. The total error of the quadrature and coil model was 1.43% and 1.15% for coils with 38 and 76 dipoles, respectively. The difference between our head model and a simpler realistic model that omits the CSF was 29%. Using a standard PC and a 38-dipole coil, our solver computed the E-field in 84 coil positions per second in 20000 points on the cortex. ConclusionThe presented methods enable real-time solving of the TMS-induced E-field in a realistic head model that contains the CSF. The new methodology allows more accurate targeting and precise adjustment of intensity during experimental or clinical TMS mapping.