Development of the Boundary Element Fast Multipole Method for Quasistatic Electromagnetic Modeling of the Brain

Wartman, William A.

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Development of the Boundary Element Fast Multipole Method for Quasistatic Electromagnetic Modeling of the Brain

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In this thesis, several algorithmic improvements of the Boundary Element Fast Multipole Method (BEM-FMM) for quasistatic electromagnetic modeling of multi-tissue anatomical human models have been suggested and implemented. These improvements include: - Fast solid-angle approach for neighbor E-field integral calculations – FMM implementation - Fast cubatures for neighbor potential and E-field integral calculations – FMM implementation In addition, several pre/post-processing improvements of the modeling pipeline have been suggested and implemented. They include: - Automated detection and removal of coincident faces for meshes with duplicated boundaries; - Approach for automated volumetric labeling for BEM problems with large surface meshes; The application examples discussed in this thesis include: - Simulation of the MIDA head model (with 11 M triangular surface elements and 100+ tissue compartments) - Transcranial magnetic stimulation, transcranial electrical stimulation, and electroencephalography/magnetoencephalography modeling toolkits with the BEM-FMM Appropriate MATLAB scripts are given in the text. The corresponding BEM-FMM modeling toolkits, along with the documentation and application examples (MATLAB platform), are available at the following locations: Transcranial Magnetic Stimulation: https://tmscorelab.github.io/TMS-Modeling-Website/ Transcranial Electrical Stimulation: https://tmscorelab.github.io/TES-Modeling-Website/ EEG/MEG Forward Solver: https://tmscorelab.github.io/EEG_MEG-Modeling-Website/ The software should run as is on Windows systems running MATLAB r2019a or newer.

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