The distribution of quick phase interval durations in human optokinetic nystagmus

There is an interesting dichotomy between models that predict the quick phase interval durations (QPIDs) of human optokinetic nystagmus (OKN). Accumulator models describe a stochastic signal in a neural network that triggers a response once the signal reaches a fixed threshold value. However, it is also possible that quick phases are triggered after eye position reaches a variable amplitude threshold. In this study, we fitted a range of probability density functions previously predicted by stochastic models of OKN (including those of the reciprocal truncated Normal, inverse Gaussian, gamma, lognormal and the mixture of two reciprocal truncated Normal distributions) to individual QPID histograms. We compared the goodness of fit between these models, and a model where the distribution of QPIDs is determined by the ratio of two correlated and truncated Normal random variables. The ratio distribution gave the best fit to the data, and we propose this is due to the approximately linear trajectory of slow phases (SPs) and that QPIDs are given by the ratio of a variable SP amplitude threshold and variable SP velocity.