Integral equation models in some biomedical applications of electromagnetic fields: Transcranial magnetic stimulation (TMS), nerve fiber stimulation

The paper reviews certain integral equation formulations and related numerical solution methods used in studies of biomedical applications of electromagnetic fields related to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is modeled via the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is undertaken via an efficient Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current generator, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-diferential equation numerically solved via the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, is obtained.