Published Paper Details:

The placement of Transcranial Magnetic Stimulation (TMS) coils and the selection of pulse waveform currents are typically optimized to achieve a precise electric (E) field dosage in targeted brain regions. Enhancing TMS neuronavigation requires real-time, accurate visualization of E-field distributions on the cortex. In this study, we introduce a novel computational method and develop software that enables real-time E-field mapping with accuracy comparable to first-order finite element method (FEM) solvers. Our approach begins by generating a basis set (<400) of E-field distributions using white noise-induced magnetic currents on a boundary surface separating the head from allowable coil placements. These basis fields are orthogonalized to form computational modes. We then apply Reciprocity and Huygens' principles to calculate the fields induced by these modes using FEM, which are combined with real-time computed primary fields to construct the mode expansion. To validate our method, we compared real-time E-field computations with FEM-based simulations across eight subjects. We tested two head modeling pipelines (SimNIBS's 'headreco' and 'mri2mesh'), three coil configurations (circular, double-cone, and Figure-8), and 1,000 coil placements, resulting in a total of 48,000 simulations. Our solver achieves real-time E-field calculations in under 4 milliseconds (ms) using 400 modes, requiring less than 4 GB of GPU memory. This efficient solver facilitates seamless integration of E-field data into neuronavigation systems without introducing significant computational overhead. The software is publicly available at: GitHub Repository.