Computational Electromagnetic Methods for Transcranial Magnetic Stimulation.

Abstract

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, coils positioned near the scalp generate electric fields and activate targeted brain regions. In this thesis, several computational electromagnetics methods that improve the analysis, design, and uncertainty quantification of TMS systems were developed.

Analysis: A new fast direct technique for solving the large and sparse linear system of equations (LSEs) arising from the finite difference (FD) discretization of Maxwell’s quasi-static equations was developed. Following a factorization step, the solver permits computation of TMS fields inside realistic brain models in seconds, allowing for patient-specific real-time usage during TMS. The solver is an alternative to iterative methods for solving FD LSEs, often requiring run-times of minutes. A new integral equation (IE) method for analyzing TMS fields was developed. The human head is highly-heterogeneous and characterized by high-relative permittivities (10^7). IE techniques for analyzing electromagnetic interactions with such media suffer from high-contrast and low-frequency breakdowns. The novel high-permittivity and low-frequency stable internally combined volume-surface IE method developed. The method not only applies to the analysis of high-permittivity objects, but it is also the first IE tool that is stable when analyzing highly-inhomogeneous negative permittivity plasmas.

Design: TMS applications call for electric fields to be sharply focused on regions that lie deep inside the brain. Unfortunately, fields generated by present-day Figure-8 coils stimulate relatively large regions near the brain surface. An optimization method for designing single feed TMS coil-arrays capable of producing more localized and deeper stimulation was developed. Results show that the coil-arrays stimulate 2.4 cm into the head while stimulating 3.0 times less volume than Figure-8 coils.

Uncertainty quantification (UQ): The location/volume/depth of the stimulated region during TMS is often strongly affected by variability in the position and orientation of TMS coils, as well as anatomical differences between patients. A surrogate model-assisted UQ framework was developed and used to statistically characterize TMS depression therapy. The framework identifies key parameters that strongly affect TMS fields, and partially explains variations in TMS treatment responses.