Spontaneous fluctuations in pupil size are not triggered by lens accommodation

From pre-processing to advanced dynamic modeling of pupil data

The pupil of the eye provides a rich source of information for cognitive scientists, as it can index a variety of bodily states (e.g., arousal, fatigue) and cognitive processes (e.g., attention, decision-making). As pupillometry becomes a more accessible and popular methodology, researchers have proposed a variety of techniques for analyzing pupil data. Here, we focus on time series-based, signal-to-signal approaches that enable one to relate dynamic changes in pupil size over time with dynamic changes in a stimulus time series, continuous behavioral outcome measures, or other participants' pupil traces. We first introduce pupillometry, its neural underpinnings, and the relation between pupil measurements and other oculomotor behaviors (e.g., blinks, saccades), to stress the importance of understanding what is being measured and what can be inferred from changes in pupillary activity. Next, we discuss possible pre-processing steps, and the contexts in which they may be necessary. Finally, we turn to signal-to-signal analytic techniques, including regression-based approaches, dynamic time-warping, phase clustering, detrended fluctuation analysis, and recurrence quantification analysis. Assumptions of these techniques, and examples of the scientific questions each can address, are outlined, with references to key papers and software packages. Additionally, we provide a detailed code tutorial that steps through the key examples and figures in this paper. Ultimately, we contend that the insights gained from pupillometry are constrained by the analysis techniques used, and that signal-to-signal approaches offer a means to generate novel scientific insights by taking into account understudied spectro-temporal relationships between the pupil signal and other signals of interest.

Predictor feedback models for stick balancing with delay mismatch and sensory dead zones

Human stick balancing is investigated in terms of reaction time delay and sensory dead zones for position and velocity perception using a special combination of delayed state feedback and mismatched predictor feedback as a control model. The corresponding mathematical model is a delay-differential equation with event-driven switching in the control action. Due to the sensory dead zones, initial conditions of the actual state cannot always be provided for an internal-model-based prediction, which indicates that (1) perfect prediction is not possible and (2) the delay in the switching condition cannot be compensated. The imperfection of the predictor is described by the delay mismatch, which is treated as a lumped parameter that creates a transition between perfect predictor feedback (zero delay mismatch) and delayed state feedback (mismatch equal to switching delay). The maximum admissible switching delay (critical delay) is determined numerically based on a practical stabilizability concept. This critical delay is compared to a realistic reference value of 230 ms in order to assess the possible regions of the threshold values for position and velocity perception. The ratio of the angular position and angular velocity for 44 successful balancing trials by 8 human subjects was used to validate the numerical results. Comparison of actual human stick balancing data and numerical simulations based on the mismatched predictor feedback model provided a plausible range of parameters: position detection threshold 1°, velocity detection threshold between 4.24 and 9.35°/s, and delay mismatch around 100-150 ms.

A unified model of the task-evoked pupil response

The pupil dilates and reconstricts following task events. It is popular to model this task-evoked pupil response as a linear transformation of event-locked impulses, whose amplitudes are used as estimates of arousal. We show that this model is incorrect and propose an alternative model based on the physiological finding that a common neural input drives saccades and pupil size. The estimates of arousal from our model agreed with key predictions: Arousal scaled with task difficulty and behavioral performance but was invariant to small differences in trial duration. Moreover, the model offers a unified explanation for a wide range of phenomena: entrainment of pupil size and saccades to task timing, modulation of pupil response amplitude and noise with task difficulty, reaction time-dependent modulation of pupil response timing and amplitude, a constrictory pupil response time-locked to saccades, and task-dependent distortion of this saccade-locked pupil response.

Pupillometric recordings to detect glaucoma

Objective. Glaucoma is the second cause of vision loss with early diagnosis having significantly better prognosis. We propose the use of hippus, the steady-state pupil oscillations, obtained from an eye-tracker for computerised detection of glaucoma.Approach. Pupillary data were recorded using a commercial eye-tracker device directly to the laptop. A total of 40 glaucoma patients and 30 age-matched controls were recruited for the study. The signals were de-noised, and the entropy of the steady-state oscillations was obtained for two light intensities, 34 and 100 cd m^-2.Main results. The results show that at 100 cd m^-2, there was significant difference (p < 0.05) between the sample entropy of the healthy eyes (0.55 ± 0.017) and glaucoma eyes (0.7 ± 0.034). The results at 34 cd m^-2were also significantly different, though to a lesser extent.Significance. Entropy of the pupillary oscillations, or hippus, obtained using an eye-tracking device showed a significant difference between glaucoma and healthy eyes. The method used commercially available inexpensive hardware and thus has the potential for wide-scale deployment for computerized detection of glaucoma.

Is accommodation a confounder in pupillometry research?

Much psychological research uses pupil diameter measurements to investigate the cognitive and emotional effects of visual stimuli. A potential problem is that accommodating at a nearby point causes the pupil to constrict. This study examined to what extent accommodation is a confounder in pupillometry research. Participants solved multiplication problems at different distances (Experiment 1) and looked at line drawings with different monocular depth cues (Experiment 2) while their pupil diameter, refraction, and vergence angle were recorded using a photorefractor. Experiment 1 showed that the pupils dilated while performing the multiplications, for all presentation distances. Pupillary constriction due to accommodation was not strong enough to override pupil dilation due to cognitive load. Experiment 2 showed that monocular depth cues caused a small shift in refraction in the expected direction. We conclude that, for the young student sample we used, pupil diameter measurements are not substantially affected by accommodation.

Assessing Pain Using the Variation Coefficient of Pupillary Diameter

Pupillary diameter (PD) varies under the influence of the sympathetic as well as parasympathetic systems, increasing proportionally with pain intensity. Such variations however, should not be confused with pupillary fluctuations, which refer to the fast and permanent PD fluctuations induced by the ongoing interplay between the sympathetic and parasympathetic systems, which we propose to measure using the variation coefficient of PD (VCPD). This study aimed first at correlating PD, PD increase during a contraction, and VCPD, with pain rated using a numeric rating scale (NRS) during obstetrical labor, and then at comparing such correlations with each other. Forty patients were included in the study, and 160 simultaneous ratings (NRS, PD, and VCPD) were taken: 40 in the presence of uterine contractions and 40 in the absence of such contractions, before and 20 minutes after epidural analgesia. VCPD correlates more strongly (r = .77) than PD increase (r = .42) with pain rated using a NRS. The ability of VCPD to predict the occurrence of NRS scores ≥4 during obstetrical labor is .97 (confidence interval, .93-1.0). When measured over 10 seconds during contraction, VCPD correlates more strongly than PD increase with pain rated using the NRS. Such stronger correlation allows for an easy assessment of antinociception-nociception balance.

PERSPECTIVE

The VCPD allows for an objective assessment of pain in laboring women. It could allow for an easy assessment of pain in noncommunicating patients: newborns or very old patients, patients with serious psychological conditions, assessment during the immediate postoperative period, or in intensive care units.

Relationships between Pupil Diameter and Neuronal Activity in the Locus Coeruleus, Colliculi, and Cingulate Cortex

Changes in pupil diameter that reflect effort and other cognitive factors are often interpreted in terms of the activity of norepinephrine-containing neurons in the brainstem nucleus locus coeruleus (LC), but there is little direct evidence for such a relationship. Here, we show that LC activation reliably anticipates changes in pupil diameter that either fluctuate naturally or are driven by external events during near fixation, as in many psychophysical tasks. This relationship occurs on as fine a temporal and spatial scale as single spikes from single units. However, this relationship is not specific to the LC. Similar relationships, albeit with delayed timing and different reliabilities across sites, are evident in the inferior and superior colliculus and anterior and posterior cingulate cortex. Because these regions are interconnected with the LC, the results suggest that non-luminance-mediated changes in pupil diameter might reflect LC-mediated coordination of neuronal activity throughout some parts of the brain.

Fentanyl, an agonist at the mu opioid receptor, depresses pupillary unrest

Pupillary unrest is a chaotic fluctuation in pupil size that is observed in darkness with the onset of drowsiness, and in ambient light. The mechanism of pupillary unrest in darkness as well as in ambient light is unknown but studies suggest that it is caused by fluctuating activity in the Edinger-Westphal (E.W.) nucleus. Neurons in the periaqueductal gray with oscillating firing patterns that are inhibitory to the E.W. nucleus have been described in the cat. We theorized that such oscillating neurons produce pupillary unrest in light and would be depressed by agents, such as opioids, known to depress inhibitory pathways in the midbrain. An infrared pupillometer was used to measure the effect of light on pupillary unrest in eight volunteer subjects, and on 20 patients scheduled for knee arthroscopy who received fentanyl as premedication. Pupillary unrest was quantified through spectral analysis of fast Fourier transforms. Sixteen-second measurements of pupil size at 33 Hz were filtered to eliminate blink artifacts and baseline drift. Pupillary unrest was augmented by excitation of the E.W. nucleus by light and was depressed by 40 ± 20% after the administration of the moderate dose of 1 mcg/kg of fentanyl. Recovery from the drug effect was observed. Based upon the data from this study we propose that pupillary unrest in light originates within oscillating inhibitory neurons that intermittently depress the E. W. nucleus.

Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing

Linear Time Invariant (LTI) processes can be modelled by means of Auto-Regressive Moving Average (ARMA) model systems. In this paper, we examine whether an ARMA model can be fitted to a process characterised by switched nonlinearities. In particular, we conduct the following test: we generate data from known LTI and nonlinear (threshold/dead-zone) models of human balance and analyse the output using ARMA. We show that both these known systems can be fitted, according to standard criteria, with low order ARMA models. To check if there are some obvious effects of the dead-zone, we compare the power spectra of both systems with the power spectra of their ARMA models. We then examine spectral properties of three posturographic data sets and their ARMA models and compare them with the power spectra of our model systems. Finally, we examine the dynamics of our model systems in the absence of noise to determine what is the effect of the switching threshold (dead-zone) on the asymptotic dynamics.

How do spontaneous pupillary oscillations in light relate to light intensity?

Characteristics of light-induced pupillary oscillations at constant light intensities have been investigated sparsely compared to sleepiness-related pupillary oscillations in darkness. This study presents the first controlled analysis of light-induced pupillary oscillations and their relationship to illumination. Pupillary oscillations of alert subjects were recorded by infrared video pupillography in different background lighting. Although showing obvious relationships of mean frequency and amplitude to light intensity, there were considerable inter- and intra-individual differences in the appearance of light-induced oscillations. As they looked rather similar to sleepiness waves, the question remains to identify light-induced oscillations in day light and to differentiate them from sleepiness-related oscillations.

Age related changes in the characteristics of the near pupil response

Static and dynamic aspects of the near pupil response were studied in human subjects in the age range when accommodative amplitude steadily declines. Dynamic accommodative and pupillary responses to step stimuli were recorded in 66 subjects (ages: 14-45 years). Exponential fits to data provided amplitude, peak velocity and time constants. Accommodative amplitude decreased linearly with age (p < 0.05). Pupil constriction per diopter of accommodative response increased exponentially with age (p < 0.05). The amplitude of pupil constriction for a 2D stimulus decreased linearly with age (p < 0.05) and for a 5D stimulus did not change with age (p = 0.90). The latency of pupil constriction did not change with age (p = 0.65), while the mean peak velocity decreased linearly with age (p < 0.05). An increase in the amount of pupil constriction per diopter of accommodative response, but not per diopter of stimulus amplitude, suggests that the near effort per se does not increase with age. There is a slight reduction in the speed of near pupil response with age.

Characteristics of pupil responses during far-to-near and near-to-far accommodation

The static and dynamic aspects of the pupil response associated with various amplitudes of far-to-near (accommodation) and near-to-far (disaccommodation) focusing responses were evaluated in this study. Dynamic refractive and pupillary changes were measured simultaneously during focusing responses to targets at real distances in 12 young (23-26 years) emmetropic subjects. The targets were presented alternately at far (6 m) and at one of six near positions from 1 D (1 m) to 6 D (16.7 cm) in 1 D steps. The latency, magnitude and peak velocity of pupil changes associated with accommodation and disaccommodation responses were calculated. The latency of refractive changes was shorter than that of pupillary changes. In general, the pupil constricted with accommodation and started dilating while accommodation was still maintained, resulting in reduced pupil dilation with disaccommodation. The magnitude of the pupil response increased linearly with that of accommodation and disaccommodation. The amount of pupil change per dioptre of refractive change was invariant with various amplitudes of refractive change. The peak velocity of pupil constriction was greater than that of pupil dilation for corresponding amplitudes. The pupil response is more closely associated with accommodation than with disaccommodation.

Pupil staging and EEG measurement of sleepiness

The goal of this multi-method study was to examine the validity (accuracy) of the pupillometric Alertness Level Test (ALT) as a physiologic measure of sleepiness. The study used a pooled-time series-correlation design with 16 untreated narcolepsy (8 F, 8 M), 16 untreated obstructive sleep apnea (OSA) (7 F, 9 M) and 16 healthy control (8 F, 8 M) subjects. Participants underwent EEG/polysomnography testing using standard Multiple Sleep Latency Test electrode placement concurrent with the 15 min pupillometric ALT. EEG data were examined to determine if theta power (4-7 Hz) increased during 2-s periods of proportional pupil size decreases (pupil Stage 1, 95% or more of maximal pupil size to Stage 4, 65-74% of maximal size). Printed EEG records also were visually scored. Self-report sleepiness measures included the Pittsburgh Sleep Quality Index, the Profile of Mood States and the Epworth Sleepiness Scale. Within subject groups, theta power ratios significantly increased across pupil stages for the sleep disorder groups but not for controls (theta activity increased 42% for narcoleptic and 36% for OSA subjects). Between subject groups, the amount of theta activity was significantly greater for narcoleptic and OSA subjects than that for controls. Visual EEG scoring and self-report measures were usually consistent with objective findings. The ALT is convenient, easily repeatable and less technically demanding than EEG sleepiness measures, and it deserves more comprehensive testing as a valid measure of sleepiness.

The effect of bright light exposure on pupillary fluctuations in healthy subjects

BACKGROUND

Light therapy is thought to be the first choice treatment of winter depression. However, its way of action is poorly understood. In order to find a solid effect of bright artificial light, we studied its possible alerting action through the spontaneous fluctuations of the pupil, considered to be an objective measurement of vigilance.

METHODS

Pupillary fluctuations of 10 healthy subjects (mean age: 22+/-1 S.D. years) were measured for 60 s before and 15 min after 0.5 h, 10000-lux light exposure. The cumulative change in pupil size, characterised by the pupillary unrest index (PUI) decreased at each subject, and this decrease was in average 35+/-4.4% S.E.M. The average pupillary diameters were unchanged (101+/-2.2% S.E.M.). This analysis revealed that the slow components of the pupillary fluctuations also decreased considerably.

LIMITATIONS

There was no dim light or other placebo control of the light treatment.

CONCLUSIONS

Bright light exposure significantly influenced the pupillary fluctuations. We suppose that bright light exposure increases the level of alertness, and this could be a possible way by which bright artificial light exerts a beneficial effect also in affective disorders.