Calculation of electric fields in a multiple cylindrical volume conductor induced by magnetic coils

Abstract

A method is presented for calculating the electric field, that is induced in a cylindrical volume conductor by an alternating electrical current through a magnetic coil of arbitrary shape and position. The volume conductor is modeled as a set of concentric, infinitely long, homogeneous cylinders embedded in an outer space that extends to infinity. An analytic expression of the primary electric field induced by the magnetic coil, assuming quasi-static conditions, is combined with the analytic solution of the induced electric scalar potential due to the inhomogeneities of the volume conductor at the cylindrical interfaces. The latter is obtained by the method of separation of variables based on expansion with modified Bessel functions. Numerical results are presented for the case of two cylinders representing a nerve bundle with perineurium. An active cable model of a myelinated nerve fiber is included, and the effect of the nerve fiber's undulation is shown.