Probe Design for Measurement and Verification of Electric Field Induced by Figure-8 Coil in Transcranial Magnetic Stimulation

Transcranial magnetic stimulation (TMS) efficiency relies on the electric field (EF) delivered to the stimulation target. Due to lack of intracranial EF measurement methods, the induced EF is often calculated using simulation models. However, the difference between simulation and practice is still unknown. Our objective is to provide a novel and feasible method of measuring induced EF in the air domain and verify the consistency between simulation and measurement. Coil voltage inside the stimulator was measured to derive the ratio of coil voltage to coil inductance, representing the current change rate (di/dt). The calculated induced EF was obtained by multiplying di/dt values with magnetic vector potentials acquired through numerical and analytical calculations. A measurement probe based on concentric circular loops measured induced electromotive force (EMF) from a figure-8 coil, validating the presented method by comparing measurement and calculation results. Using this approach, we calculated and measured the spatial distribution of induced EF generated by a self-made figure-8 coil, demonstrating consistency with relative errors below 5% in the volume of interest (VOI). Spatial distributions of induced EF from a commercial figure-8 coil, identical in outer dimensions and turns to the self-made coil, were also measured, showing agreement despite differences in pulse widths and amplitudes. The presented measurement probe allows a feasible characterization of the TMS-induced EF. The measured values are consistent with calculated values. The proposed method may provide experimental data rather than coil geometry model for intracranial EF simulation software.