Evaluating Human Perception Thresholds in Magnetic Stimulation Using Experimental Measurements and Modelling

This preregistered study investigated whether induced electric fields alone could predict human perception thresholds in magnetic stimulation. Using a figure-of-eight magnetic coil placed on the forearm, perception thresholds were collected from 24 healthy participants using the method of adjustment in 12 stimulation conditions. Subject-fitted, anatomically realistic forearm models were constructed from a set of 10 MRI-based models. Induced electric fields were computed using the finite element method with probabilistic tissue conductivities and post-processed using spatial averaging and percentiles. Linear mixed-effects modelling showed that the perception threshold was 32.2 V/m (SD between subjects 5.2 V/m) for a damped sinusoidal magnetic pulse with 83  $\mu$ s phase duration. This threshold value was determined by spatial averaging over a cube with a side length of 2 mm and taking the 99th percentile of the electric field within the modelled forearms. However, the induced electric field did not fully explain the perception threshold (adjusted $R^2$  = 0.48; permutation testing, p  $<$  0.001). We also conducted a supplementary modelling study, retrospectively analysing previous literature results to allow for direct comparison with our findings. These results showed that simplified calculations of the threshold electric field, obtained by modelling the forearm as a uniform cylinder, need to be scaled by a factor of 1.4 to align with the 99th percentile electric field calculated with anatomically realistic models. Both our experimental results and the modelling provide data to inform the refinement of safety guidelines.