Abstract

ObjectiveTranscranial magnetic stimulation (TMS) and transcranial electric stimulation (TES) modulate brain activity non-invasively by generating electric fields either by electromagnetic induction or by injecting currents via skin electrodes. Numerical simulations based on anatomically detailed head models of the TMS and TES electric fields can help us to understand and optimize the spatial stimulation pattern in the brain. However, most realistic simulations are still slow, and their numerical accuracy and the factors that influence it have not been evaluated in detail so far. ApproachWe present and validate a new implementation of the Finite Element Method (FEM) for TMS and TES that is based on modern algorithms and libraries. We also evaluate the convergence of the simulations and give estimates for the discretization errors. Main resultsComparisons with analytical solutions for spherical head models validate our new FEM implementation. It is five to ten times faster than previous implementations. The convergence results suggest that accurately capturing the tissue geometry in addition to choosing a sufficiently high mesh density is of fundamental importance for accurate simulations. SignificanceThe new implementation allows for a substantial increase in computational efficiency of TMS and TES simulations. This is especially relevant for applications such as the systematic assessment of model uncertainty and the optimization of multi-electrode TES montages. The results of our systematic error analysis allow the user to select the best tradeoff between model resolution and simulation speed for a specific application. The new FEM code will be made openly available as a part of our open-source software SimNIBS 3.0.