Square-root relations between main saccadic parameters

Purpose. To derive and evaluate two equations in which saccade duration and peak velocity are proportional to the square root of saccade amplitude. Methods. A population of horizontal visually guided saccades in a range of amplitudes from 1.5 degrees to 30 degrees was recorded by means of electro-oculography in eight normal adult subjects. The peak velocity-amplitude data of this population were fitted to four models: inverse linear, exponential, power la-v, and square root. To approximate the duration-amplitude relation, the square root was tested against the linear and power law models. For each model, the best-fit values of its parameters were estimated by the method of least squares. Results. When the entire population was used, all tested models displayed comparable goodness of fit, but when different subranges of this population were used, only the square root equations appeared to be robust and acceptably accurate. Conclusions. In a restricted range of saccade amplitudes from 1.5 degrees to 30 degrees, the square root model has some advantages over the others commonly used: to express peak velocity and duration as functions of amplitude, it requires the estimation of only mio parameters, whereas the others require four. Because of its robustness, this model can be used to evaluate populations of saccadic eye movements with different ranges of amplitudes. The two parameters of the model equations allow a simple and clear physical interpretation.