On the Use of Integral Equation Approach for Low Frequency Bioelectromagnetics Problems

This paper deals with the use of boundary integral approach to the solution of problems arising in low-frequency bioelectromagnetics. To this end, two formulations are considered, based on the full-wave approach and the quasi-static approximation, respectively. The former is related to the use of electric field integral equation (EFIE) formulation for dielectric bodies where the unknowns are expressed in terms of equivalent surface current density - here termed J-formulation. The latter is the surface integral equation formulation for the poorly conducting bodies based on the quasi-static eddy current approximation with unknowns being the surface charge density - here termed ρ-formulation. The two formulations usually find their application in high-frequency and low-frequency related problems, respectively. This work considers their use in modelling low-frequency electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and magneto-therapy. Numerical solution of governing integral expressions is carried out by means of Method of Moments (MoM). The results for the induced field indicate up to 25% discrepancy between two considered approaches.Clinical relevance-The obtained numerical results could be found useful for improving the precision and effectiveness of TMS therapies in clinical applications.