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

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.

Can transcranial electric stimulation with multiple electrodes reach deep targets?

To reach a deep target in the brain with transcranial electric stimulation (TES), currents have to pass also through the cortical surface. Thus, it is generally thought that TES cannot achieve focal deep brain stimulation. Recent efforts with interfering waveforms and pulsed stimulation have argued that one can achieve deeper or more intense stimulation in the brain. Here we argue that conventional transcranial stimulation with multiple current sources is just as effective as these new approaches. The conventional multi-electrode approach can be numerically optimized to maximize intensity or focality at a desired target location. Using such optimal electrode configurations we find in a detailed and realistic head model that deep targets may in fact be strongly stimulated, with cerebrospinal fluid guiding currents deep into the brain.