Variation of stimulation intensity in transcranial magnetic stimulation with depth

The quantification of stimulation intensity in transcranial magnetic stimulation (TMS) as a function of depth is of interest in order to adjust stimulator output when non-motor regions are stimulated. Currently, a linear increase of stimulator output to correct for depth has been suggested. This is contrary to the physical properties of the electric field that is induced by the stimulation coil as measured in vitro. For two stimulation coils, we determined the characteristics of their field in air. We then measured motor thresholds for the abductor hallucis muscle of 10 healthy subjects. Coil position, distance from the scalp, and orientation were controlled with a head tracking robotic system that corrected for head movements. In both coils an approximately exponential increase, rather than a linear increase, of the threshold with the scalp-coil distance was measured. The slope of the increase was slightly smaller than expected from the field characteristic, but overall in good agreement. With respect to the depth of the TMS target, different results were obtained from the threshold ratios of the coils and from the slopes of the threshold increase with distance. For the adjustment of stimulator output to scalp-to-cortex distances exponential functions with parameters motivated by physical properties of the coils should be used. Estimation of the target depth from the thresholds, with different coils, is not reliable. Our results resolve a conflict between physiological data and physical properties of TMS coils. They provide a more reliable base for depth dependent corrections for TMS stimulator output.