Analysis of a model of membrane potential for a skin receptor

A linear model for the membrane potential of a nerve ending associated with a sense-of-touch skin receptor is formulated and analyzed. Because the nerve has cytoplasmic extensions and is stimulated through a membrane strain mechanism, the model is a generalized cable equation with linear oblique boundary conditions (i.e. boundary conditions involving both time and space derivatives). The model is stimulated through a certain conductance parameter. We establish solutions for the problem and we consider a particular physiological question, both analytically and computationally, of determining conditions on parameters and stimulus which give threshold level potential values at a particular boundary point.