Models for saccadic motion and postsaccadic oscillations

J. A. DEL PUNTA; K V RODRIGUEZ; G GASANEO; S BOUZAT

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2019 vol. 99

1539-3755

In a recent letter [S. Bouzat et al., Phys. Rev. Lett. 120, 178101 (2018)], a mathematical model for eyeballand pupil motion was developed allowing for the understanding of the postsaccadic oscillations (PSO) as inertialeffects. The model assumes that the inner part of the iris, which defines the pupil, moves driven by inertial forcesinduced by the eyeball rotation, in addition to viscous and elastic forces. Among other achievements, the modelcorrectly reproduces eye-tracking experiments concerning PSO profiles and their dependence on the saccadesize. In this paper we propose various extensions of thementioned model, we provide analytical solutions, and weperform an exhaustive analysis of the dynamics. In particular, we consider a more general time dependence forthe eyeball velocity enabling the description of saccades with vanishing initial acceleration. Moreover, we givethe analytical solution in terms of hypergeometric functions for the constant parameter version of the model andwe provide particular expressions for some cases of interest. We also introduce a new version of the model withinhomogeneous viscosity that can improve the fitting of the experimental results. Our analysis of the solutionsexplores the dependence of the PSO profiles on the system parameters for varying saccade sizes. We show thatthe PSO emerge in critical-like ways when parameters such as the elasticity of the iris, the global eyeball velocity,or the saccade size vary. Moreover, we find that the PSO profiles with the first overshoot smaller than the secondone, which are usually observed in experiments, can be associated to parameter regions close to criticality.