Abstract
The unmyelinated axon of negligibly thin axolemma is idealized as a right circular cylinder of infinite length imbedded in an unbounded aqueous electrolyte. The scalar wave equation is solved in this geometry subject to the boundary conditions (i) that the electric scalar potential vanish at infinity and be a known function along the cylinder axis, and (ii) that the radial current be continuous across the axolemma. Exact solutions for the infinite reluctivity limit are obtained for the interior potential, the total axial current, and the radial current at the axolemma; an approximate solution is obtained for the exterior potential. These solutions are compared with predictions of the classical transmission line theory commonly employed in describing the electrical properties of axons.
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