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

Abstract

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.

Pupillometric Complexity and Symmetricity Follow Inverted-U Curves Against Baseline Diameter Due to Crossed Locus Coeruleus Projections to the Edinger-Westphal Nucleus

“…The complexity and temporal patterns of pupil-diameter changes reflect LC activity, sleepiness, cognitive processes, autonomic nerve activity, and psychiatric disorders (Usui and Stark, 1982 ; Schumann et al, 2015 ; Artoni et al, 2019 ; Nakamura et al, 2019 ; Piu et al, 2019 ). Sleepiness in particular decreases the temporal complexity and determinicity of pupil diameter (Piu et al, 2019 ). Nakamura et al reported that at the discrimination stage of the cognitive process, the complexity of pupil-diameter changes is reduced and pupil dilation occurs (Nakamura et al, 2019 ).…”

“…The advantages of evaluating complexity and symmetricity as SampEn and TranEn, respectively, requires further discussion. Conventional evaluation methods for pupil complexity and symmetricity utilize temporal standard deviation, Shannon entropy, and the difference between right and left pupil diameters (Usui and Stark, 1982 ; Poynter, 2017 ; Wahn et al, 2017 ; Piu et al, 2019 ). Moreover, Piu et al showed that the combination of complexity estimation by Shannon entropy and determinism is an effective diagnostic tool for identifying the states of neural systems (Piu et al, 2019 ).…”

“…Conventional evaluation methods for pupil complexity and symmetricity utilize temporal standard deviation, Shannon entropy, and the difference between right and left pupil diameters (Usui and Stark, 1982 ; Poynter, 2017 ; Wahn et al, 2017 ; Piu et al, 2019 ). Moreover, Piu et al showed that the combination of complexity estimation by Shannon entropy and determinism is an effective diagnostic tool for identifying the states of neural systems (Piu et al, 2019 ). The importance of determinism for evaluation is supported by the fact that changes in pupil diameter are produced by multiple non-linear neural pathways (Usui and Stark, 1982 ; Liu et al, 2017 ).…”

“…Furthermore, recent progress in research on pupil diameter has provided new insights into the temporal patterns of pupil diameter and its controlling neural pathways (Liu et al, 2017 ; Poynter, 2017 ; Wahn et al, 2017 ; Artoni et al, 2019 ; Nakamura et al, 2019 ; Piu et al, 2019 ). In particular, it has been discovered that the parasympathetic pathways from the LC project are inhibitory to both the ipsilateral and contralateral parts of the Edinger-Westphal nucleus (EWN) to control the pupil sphincter muscles, not only to the ipsilateral parts as previously thought (Liu et al, 2017 ).…”

“…Nakamura et al and Artoni et al demonstrated that the temporal hippus patterns reflect several stages of cognitive processing (Nakamura et al, 2019 ) and are affected by psychiatric disorders (Artoni et al, 2019 ). Piu et al showed that the hippus fluctuation reflects the non-linear dynamics of autonomous neural activity; this determinism and non-linear complexity might be utilized as a diagnostic tool for detecting the states of neural systems (Piu et al, 2019 ). In addition to the temporal pattern of pupil diameter, the asymmetricity between the right and left pupil diameters is informative, reflecting the attention function (Poynter, 2017 ; Wahn et al, 2017 ).…”