A theoretical calculation of the electric field induced by magnetic stimulation of a peripheral nerve

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Abstract
A mathematical model is presented that predicts the electric field induced in the arm during magnetic stimulation of a peripheral nerve. The arm is represented as a homogeneous, cylindrical volume conductor. The electric field arises from two sources: the time-varying magnetic field and the accumulation of charge on the arm surface. In magnetic stimulation both of these contributions are significant. The magnitude of the electric field is greatest near the surface of the arm, and is well localized. Various coil orientations are examined; the smallest electric fields are induced when the coil is perpendicular to the arm surface, the largest when the coil is parallel. These results are consistent with many experimental observations in the literature, and aid in the basic understanding of magnetic stimulation of the peripheral nervous system.