A model of the stimulation of a nerve fiber by electromagnetic induction

Abstract

A model is presented to explain the physics of nerve stimulation by electromagnetic induction. Maxwell's equations predict the induced electric field distribution that is produced when a capacitor is discharged through a stimulating coil. A nonlinear Hodgkin-Huxley cable model describes the response of the nerve fiber to this induced electric field. Once the coil's position, orientation, and shape are given and the resistance, capacitance, and initial voltage of the stimulating circuit are specified, this model predicts the resulting transmembrane potential of the fiber as a function of distance and time. It is shown that the nerve fiber is stimulated by the gradient of the component of the induced electric field that is parallel to the fiber, which hyperpolarizes or depolarizes the membrane and may stimulate an action potential. Finally, it predicts complicated dynamics such as action potential annihilation and dispersion.

A model of magnetic stimulation of neocortical neurons

“…TMS exerts its e!ect on cortical neurons through a mechanism di!erent from its action on a straight axonal "ber in which transmembrane current is induced by the spatial gradient of induced electric "eld [10]. For cortical neurons, the induced electric "eld is nearly uniform because of the small size of neurons as compared to the size of coils used in TMS.…”

“…Biophysical mechanism underlying its e!ect is, however, largely unknown. Previous theoretical studies [10,8] have demonstrated that a brief magnetic pulse (less than 1 ms duration), commonly used in TMS, can generate an action potential in a straight axonal "ber. Nevertheless, TMS typically demonstrates e!ects including a long inhibitory period (a few hundred ms) as observed in EMG [3] and visual perception [1,5].…”

Mathematical models and reconstruction methods in magneto-acoustic imaging

“…Similarly to MAT-MI, it is possible to detect a pressure signal created in the presence of a magnetic field by electrically active tissues [8,15,16]. A magneto-acoustic technique has been developed to image electrical activity in biological tissue.…”

“…We refer the reader to [14,12,13,17,18,8,15,16] for physical basic principles of vibration potential tomography, magneto-acoustic tomography with magnetic induction, and magneto-acoustic current imaging.…”

Magnetic stimulation coil and circuit design

“…Many authors have attempted to offer guidelines for producing energy efficient stimulation coils [5]- [7], as well in the modeling of these coils [8]. Roth and Basser were among the first to actually model the stimulation of a single fiber by electromagnetic induction [9].…”