Parametric Covariability in the Standard Model of the Saccadic Main Sequence

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Abstract

SIGNIFICANCE

Saccades present a direct relationship between the size of the movement (SACSIZE) and its peak velocity (SACPEAK), the main sequence, which is traditionally quantified using the model SACPEAK = Vmax × (1 − e−SACSIZE/SAT). This study shows that Vmax and SAT are not veridical indicators of saccadic dynamics.

PURPOSE

Alterations in saccadic dynamics are used as a diagnostic tool. Are the 95% reference ranges (RRs) of Vmax and SAT correctly quantifying the variability in saccadic dynamics of a population?

METHODS

Visually driven horizontal and vertical saccades were acquired from 116 normal subjects using the Neuro Kinetics Inc. Concussion Protocol with a 100-Hz I-Portal NOTC Vestibular System, and the main sequence models were computed.

RESULTS

The 95% RRs of Vmax, the asymptotic peak velocity, and SAT, the speed of the exponential rise toward Vmax, were quite large. The finding of a strong correlation between Vmax and SAT suggests that their variability might be, in part, a computational interaction. In fact, the interplay between the two parameters greatly reduced the actual peak velocity variability for saccades less than 15°. This correlation was not strong enough to support the adoption of a one-parameter model, where Vmax is estimated from SAT using the regression parameters. We also evaluated the effects of interpolating the position data to a simulated acquisition rate of 1 kHz. Interpolation had no effect on the population average of Vmax and brought a decrease of the average SAT by roughly 8%.

CONCLUSIONS

The 95% RRs of Vmax and SAT, treated as independent entities, are not a veridical representation of the variability in saccadic dynamics inside a population, especially for small saccades. We introduce a novel three-step method to determine if a data set is inside or outside a reference population that takes into account the correlation between Vmax and SAT.

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