Numerical implementation of sealed-end boundary conditions in cable theory

The cable theory used for modeling voltage distributions in spatially extended neurons or other excitable cells, such as cells found in cardiac tissue, is reviewed. The theory is based on the observation that the intracellular electrical potential varies much more along a long nerve fiber than between points inside the fiber in a plane perpendicular to the fiber axis. This facilitates the mathematical analysis, since the spatial dimension of the differential equations for the intracellular voltage is reduced from three to one. It is shown that a frequently used numerical implementation of von Neumann boundary conditions (zero inflowing current) in cable theory is incorrect. Correct implementations are given, and it is shown that they yield results in good agreement with known analytical solutions.