Application of Phase Analysis of the Frankenhaeuser - Huxley Equations to Determine Threshold Stimulus Amplitudes

Applications of the Frankenhaeuser-Huxley model of myelinated nerve have been presented in the literature which involve the determination of threshold amplitudes of current stimuli as a function of various physical parameters. There is no known analytic solution to the equations describing the model, and so threshold amplitudes must be determined by repeated numerical solution of the five-equation model. Previous definitions of threshold rely upon a stimulus-response curve to define threshold stimulus amplitude. It is shown that knowledge of the phase behavior of the model leads to a threshold definition based upon the phase trajectories in a reduced phase plane. This phase-based definition is shown to have advantages in terms of lack of ambiguity and markedly increased computational efficiency. The model is shown to be a member of the quasi-threshold phenomenon class of excitable systems.