A general theory for predicting subthreshold transmembrane response to electric and magnetic fields

The authors present a general theory for predicting transmembrane response along uniform finite length axons with arbitrary geometries and finite terminating impedances due to applied electric and magnetic fields. The transmembrane potential due to subthreshold applied electric and magnetic fields can be described using a generalized cable equation. The authors derive an integral expression for the subthreshold transmembrane potential by choosing a Green´s function appropriate to the boundary conditions and configuration of the neuronal structure. Numerical evaluation of this integral expression can then be used to predict transmembrane response during electric and magnetic stimulation. The authors illustrate the usefulness of the theory with specific examples of stimulation of finite axons with arbitrary geometries, by electric and magnetic fields