Unified modelling of gaze and pupil dynamics in saccadic tasks

This study introduces a unified phenomenological framework to characterize the interconnected dynamics of gaze displacement and pupillary area variation during large-amplitude (30°) horizontal saccades. Using a high-resolution dataset from 242 healthy participants, we modeled primary saccadic shifts and post-saccadic oscillations (PSO) using a combined sigmoidal Boltzmann and damped harmonic oscillator approach. Our framework demonstrates that even after correcting for pupil foreshortening error, the pupillary signal contains physiological PSO-like oscillations that mirror gaze dynamics-a phenomenon previously uncharacterized in the literature. To account for the non-normal, heavy-tailed distribution of oculomotor parameters, population characteristics were defined using t location-scale modeling. Non-parametric Wilcoxon signed-rank tests revealed significant directional asymmetries; specifically, leftward movements exhibited longer total durations (∆t) and slower stabilization compared to rightward shifts. However, mechanical parameters such as oscillation amplitude and gaze baseline offsets remained directionally invariant (p > 0.01), suggesting a decoupling between asymmetric neural motor preparation and symmetrical biomechanical constraints. By establishing high-precision baseline parameters in an extensive population, this model provides a foundation for using joint gaze-pupil signatures as sensitive biomarkers for detecting subtle oculomotor and autonomic dysfunctions.