Modeling pupil responses to rapid sequential events

Abstract

Pupil size is an easily accessible, noninvasive online indicator of various perceptual and cognitive processes. Pupil measurements have the potential to reveal continuous processing dynamics throughout an experimental trial, including anticipatory responses. However, the relatively sluggish (∼2 s) response dynamics of pupil dilation make it challenging to connect changes in pupil size to events occurring close together in time. Researchers have used models to link changes in pupil size to specific trial events, but such methods have not been systematically evaluated. Here we developed and evaluated a general linear model (GLM) pipeline that estimates pupillary responses to multiple rapid events within an experimental trial. We evaluated the modeling approach using a sample dataset in which multiple sequential stimuli were presented within 2-s trials. We found: (1) Model fits improved when the pupil impulse response function (puRF) was fit for each observer. PuRFs varied substantially across individuals but were consistent for each individual. (2) Model fits also improved when pupil responses were not assumed to occur simultaneously with their associated trial events, but could have non-zero latencies. For example, pupil responses could anticipate predictable trial events. (3) Parameter recovery confirmed the validity of the fitting procedures, and we quantified the reliability of the parameter estimates for our sample dataset. (4) A cognitive task manipulation modulated pupil response amplitude. We provide our pupil analysis pipeline as open-source software (Pupil Response Estimation Toolbox: PRET) to facilitate the estimation of pupil responses and the evaluation of the estimates in other datasets.

Pupil dilation indexes automatic and dynamic inference about the precision of stimulus distributions

“…This also showed a good fit with the data (  = 0.848, range: 0.154 -0.990), as illustrated by Figures 4 and 5. Inspection of the convolution kernels derived from our modelling suggested that these provided plausible pupil dilation responses both when compared with existing literature (Denison et al, 2019;Hong et al, 2014;Knapen et al, 2016;Korn & Bach, 2016;Murphy et al, 2011), and when compared with the waveform generated when regressing estimated beliefs about surprise onto epoched data ( Figure 5). This suggests that our GLM-AR modelling approach was appropriate for analysing these data, and supports its use in future studies.…”

“…The design matrix X is generated by convolving a   TK  input matrix U with a gamma kernel to model the slow time course of pupil responses (Denison et al, 2019;Hoeks & Levelt, 1993;Korn & Bach, 2016). The kernel is parameterised using three parameters: shape ( h ) and scale ( l ) parameters governing the properties of the Gamma distribution, and a delay parameter ( d ) introducing a temporal delay.…”

“…where Gamma indicates the probability density function of the gamma distribution. Our approach thus naturally accounts for between-subject variability in the time course of pupil responses, since the shape of the gamma distribution is fitted to individual responses (Denison et al, 2019) (Note that in our experiment there were no luminance changes, and we thus needed only to model pupil dilation responses. The GLM-AR approach is equally applicable to data involving pupil constriction (Korn & Bach, 2016), and we will consider this in future work).…”

“…Our main hypothesis was that a deviant sound (probe tones at 2000 Hz) would be more surprising, and therefore elicit a bigger pupil dilation, in high precision compared to low precision blocks, as the associated probability density would be lower (Figure 1). In the second we combined agent-based modelling (O'Doherty, Hampton, & Kim, 2007) with a novel convolution-based approach to analysing pupillometry data (Denison, Parker, & Carrasco, 2019;Zénon, 2017), which we believe has considerable promise for exploring automatic statistical learning in humans. We hypothesised that pupil dilation responses would reflect dynamic updating of beliefs about the precision of the stimulus distribution.…”

Eyes wide open: regulation of arousal by temporal expectations

“…The raw pupil data were converted to a data matrix using a MATLAB script, excluding data from practice and breaks between blocks. Blinks were interpolated using a cubic spline interpolation (Mathôt et al, 2013), using a dedicated Matlab function available as part of the Pupil Response Estimation Toolbox (PRET) (Denison, Parker, & Carrasco, 2019). Data were smoothed using a 20-ms moving time window, which corresponded to two refresh cycles of the LCD monitor.…”