Spatial distribution of the electric field induced in volume by round and figure ‘8’ magnetic coils: relevance to activation of sensory nerve fibers

Abstract

The electric fields induced in finite homogeneous volume conductors by a round and a figure ‘8’ magnetic coil (MC) were measured and related to MC stimulation of the median nerve. The volume conductors, filled with isotonic saline, consisted of a large rectangular trough (‘unrestricted’) and a smaller trough, whose dimensions approximated human forearm (‘restricted’). Various MC orientations were applied to the volume conductor. Bipolar recordings were obtained with a coaxial electrode, which measured the voltage gradient between the exposed edge of the cable shield and the central wire at its tip, 1 cm distant (a linear probe). The probe was moved in 3 dimensions, allowing computer reconstruction of the electric field as a function of the 3 spatial axes. When the probe was parallel to the plane of the round MC and tangential to the direction of current in its windings, the induced electric field was maximal; it tended towards zero when the probe was over the center of the MC, or when the probe, remaining parallel to the plane of the MC, was radial (i.e., perpendicular) to the direction of the current in the windings. For a variety of MC orientations, the electric field was consistently increased when the probe was adjacent and parallel to the edge of the trough, indicating the important effect of boundaries. The electric field was greatly increased focally when the round MC was applied orthogonally to the volume conductor, or when the figure ‘8’ MC was applied tangentially (i.e., flat) to the volume conductor. With the figure ‘8’ MC, a sharp central peak parallel to the long axis was bounded on each side by smaller (less than half amplitude) peaks. The findings from physical modeling led to correct predictions as to the most effective orientations of round and figure ‘8’ MCs for eliciting sensory nerve action potentials (SNAPs) from the median nerve.