Computational Electromagnetic Tools for Transcranial Magnetic Stimulation

Transcranial magnetic stimulation (TMS) is a noninvasive technique used both as a research tool for cognitive neuroscience and as a FDA approved treatment for depression. During TMS, one or more coils positioned near the scalp are used to generate electric fields and activate targeted functional brain regions. In this work, several computational electromagnetics tools for the analysis and improvement of TMS systems were developed.
(i) Coil design: Many TMS applications call for electric fields to be sharply focused on regions that lie deep inside the brain. The fields generated by present-day TMS coils stimulate relatively large regions near the brain surface. A optimization tool for the design of TMS coils capable of producing more localized and deeper brain stimulation has been developed.
(ii) Uncertainty quantification: The location/volume/depth of the stimulated region during TMS is often strongly affected by variability of the position and orientation of the TMS coils, as well as anatomical differences between patients. A surrogate model assisted uncertainty quantification framework was developed and used to statistically characterize TMS depression therapy.
(iii) Real-time TMS analysis: The electric fields generated during TMS are currently analyzed using quasi-static Finite-difference (FD)/Finite-element methods. These methods require the solution of a sparse linear system of equations having millions of unknowns. This is typically done by iterative techniques that require CPU run-times of minutes, preventing their use in real-time applications. A fast direct solver able to solve the FD linear system of equations in seconds after a single factorization step"”enabling its use for real-time TMS applications"”was developed.
(iv) Integral equation for TMS (and negative permittivity plasmas): The human head is highly-heterogeneous and has high-permittivities (107 times larger than the free-space permittivity). Integral equation based tools for electromagnetic (EM) analysis of highly-heterogeneous media breakdown for the high-permittivities and the low operating frequencies (1-10KHz) of TMS. A novel high-permittivity/low-frequency stable internally combined volume-surface integral equation (ICVSIE) for TMS EM analysis has been developed. The ICVSIE is not only applicable to high-permittivity objects but it is also useful for analysis of negative permittivity plasmas making it a robust and accurate tool for general EM analysis.