IEEE transactions on bio-medical engineering
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During magnetic stimulation, electric fields are induced both on the inside (intracellular region) and the outside (extracellular region) of nerve fibers. The induced electric fields in each region can be expressed as the sum of a primary and a secondary component. The primary component arises due to an applied time varying magnetic field and is the time derivative of a vector potential. ⋯ An earlier form of the cable equation for magnetic stimulation has been shown to result in solutions identical to three-dimensional (3-D) volume-conductor model for the specific configuration of an isolated axon in a located in an infinite homogenous conducting medium. In this paper, we extend and generalize this result by demonstrating that our generalized cable equation results in solutions identical to 3-D volume conductor models even for complex geometries of volume conductors surrounding axons such as a nerve bundle of different conductivity surrounding axons. This equivalence in the solutions is valid for several representations of a nerve bundle such as anisotropic monodomain and bidomain models.