Parametric Co-Variability in the Standard Model of the Saccadic Main Sequence

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 = V _max × (1 – e ^{−SACSIZE/SAT}). This study shows that V _max and SAT are not veridical indicators of saccadic dynamics.

Purpose:

Alterations in saccadic dynamics are used as a diagnostic tool. Are the 95% confidence intervals of V _max 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% confidence intervals of V _max, the asymptotic peak-velocity, and SAT, the speed of the exponential rise towards V _max, were quite large. The finding of a strong correlation between V _max 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 1-parameter model, where V _max 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 V _max and brought a decrease of the average SAT by roughly 8%.

Conclusions:

The 95% confidence intervals of V _max 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 3-step method to determine if a data set is inside or outside a reference population that takes into account the correlation between V _max and SAT