FAST METHODS FOR ELECTRIC FIELD DOSIMETRY AND NEURON CELL RESPONSE ESTIMATION IN NON-INVASIVE ELECTROMAGNETIC BRAIN STIMULATION

Transcranial Magnetic Stimulation (TMS) is a non-invasive neuromodulation technique that induces electric fields (E-fields) in the brain to modulate neural activity. Accurate modeling of these E-fields is essential for effective stimulation targeting. However, existing numerical solvers—such as the Finite Element Method (FEM) and Boundary Element Method (BEM)—are computationally expensive, limiting their applicability in large-scale or real-time settings. This thesis addresses the need for fast, high-fidelity E-field solvers from two complementary perspectives: 1) High-throughput simulation across numerous coil configurations to support population-level analysis and inform clinically effective TMS dosing strategies. 2) Real-time E-field estimation to enable adaptive, subject-specific dosing during neuronavigated TMS sessions. To address the first challenge, we introduce the Probabilistic Matrix Decomposition with Auxiliary Dipole Method (PMD-ADM), which significantly accelerates E-field computations in large-scale coil placement scenarios. For the second, we present a real-time solution strategy based on electromagnetic equivalence principles, capable of computing E-fields from coil specifications in under 4 milliseconds—fast enough to support live E-field superposition on head models during neuronavigation. Beyond macroscopic field modeling, we also develop the first fast direct solver for simulating bidirectional coupling between morphologically realistic neurons and extracellular E-fields. This solver enables efficient, high-resolution multi-scale modeling using boundary integral equations—an approach previously impractical for realistic neural populations. Together, these advances establish a comprehensive and scalable framework for TMS E-field dosimetry in both clinical and research contexts, and open new avenues for studying the effects of brain stimulation on individual neurons.