A Cross-Recurrence Analysis of the Pupil Size Fluctuations in Steady Scotopic Conditions

Pupil size fluctuations during stationary scotopic conditions may convey information about the cortical state activity at rest. An important link between neuronal network state modulation and pupil fluctuations is the cholinergic and noradrenergic neuromodulatory tone, which is active at cortical level and in the peripheral terminals of the autonomic nervous system (ANS). This work aimed at studying the low- and high-frequency coupled oscillators in the autonomic spectrum (0-0.45 Hz) which, reportedly, drive the spontaneous pupillary fluctuations. To assess the interaction between the oscillators, we focused on the patterns of their trajectories in the phase-space. Firstly, the frequency spectrum of the pupil signal was determined by empirical mode decomposition. Secondly, cross-recurrence quantification analysis was used to unfold the non-linear dynamics. The global and local patterns of recurrence of the trajectories were estimated by two parameters: determinism and entropy. An elliptic region in the entropy-determinism plane (95% prediction area) yielded health-related values of entropy and determinism. We hypothesize that the data points inside the ellipse would likely represent balanced activity in the ANS. Interestingly, the Epworth Sleepiness Scale scores scaled up along with the entropy and determinism parameters. Although other non-linear methods like Short Time Fourier Transform and wavelets are usually applied for analyzing the pupillary oscillations, they rely on strong assumptions like the stationarity of the signal or the a priori knowledge of the shape of the single basis wave. Instead, the cross-recurrence analysis of the non-linear dynamics of the pupil size oscillations is an adaptable diagnostic tool for identifying the different weight of the autonomic nervous system components in the modulation of pupil size changes at rest in non-luminance conditions.