Stimulus-dependent refractoriness in the Frankenhaeuser-Huxley model

Phenomenological neural models, such as the leaky integrate-and-fire model, normally have a fixed refractory time-course that is independent of the stimulus. The recovery of threshold following an action potential is typically based on physiological experiments that use a two-pulse paradigm in which the first pulse is suprathreshold and causes excitation and the second pulse is used to determine the threshold at various intervals following the first. In such experiments, the nerve is completely unstimulated between the two pulses. This contrasts the receptor stimuli in normal physiological systems and the electrical stimuli used by cochlear implants and other neural prostheses. A numerical study of the Frankenhaeuser-Huxley conductance-based model of nerve fibre was therefore undertaken to investigate the effect of stimulation on refractoriness. We found that the application of a depolarizing stimulus during the later part of what is classically regarded as the absolute refractory period could effectively prolong the absolute refractory period, while leaving the refractory time-constants and other refractory parameters largely unaffected. Indeed, long depolarizing pulses, which would have been suprathreshold if presented to a resting nerve fibre, appeared to block excitation indefinitely. Stimulation during what is classically regarded as the absolute refractory period can therefore greatly affect the temporal response of a nerve. We conclude that the classical definition of absolute refractory period should be refined to include only the initial period following an action potential when an ongoing stimulus would not affect threshold; this period was found to be about half as long as the classical absolute refractory period. We further conclude that the stimulus-dependent nature of the relative refractory period must be considered when developing a phenomenological nerve model for complex stimuli.