Cable equation for a myelinated axon derived from its microstructure

A simplified cable equation that describes the subthreshold behaviour of a myelinated axon is derived from its microstructure. Specifically, a microcontinuum cable model of a composite axon is homogenised, yielding a familiar macrocontinuum cable equation of electrotonus, for which the space and time constants depend on microstructural electrical parameters. Activating functions for magnetic and electrical stimulation can be incorporated into this homogenised cable equation as sources or sinks of transmembrane potential. An integral solution to the forced cable equation is also presented for the subthreshold regime. Errors are introduced when myelin membrane resistance is assumed to be infinite.