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Supplementary Online Material for M. Vidal, K. E. Onderdijk, A. M. Aguilera, J. Six, P-J. Maes and T. H. Fritz, M. Leman. "Cholinergic-related pupil activity reflects level of emotionality during motor performance", 2023. (Accepted at the European Journal of Neuroscience)

Removal of turbulent flows in the pupil signal

This repository contains a set of routines written in R for pupilometry artifact removal. The main algorithm, described in [1], detects and removes slow and high-frequency turbulences produced by changes in retinal luminance (e.g. due to blinks). We call this turbulent activity “responses to ocular events” (ROE). The algorithm is unsupervised, meaning that it does not rely on any artifact benchmark. It was specifically designed to enhance the estimation of cognitive-related pupil activity during complex motor tasks.

To show the performance of our methods, we recorded a participant who was asked to blink four times synchronised with an auditory beat (of 2 s duration) in two time frames (shaded in red, see Fig. 1) separated by pauses. The beat appeared 4 times with a different sound during the pauses to alert the participant of the beginning/end of the blinking task. Blinks were intentionally performed longer to see their effect on the signal. During the pauses, eventual (faster) blinks also occurred. We recorded pupil activity in a dark environment where, a time before the beginning of the blinking task, a white cross was projected to the scene until the end of the recording. This produced a slow ROE not related to blinking activity, rather to a change in constant luminance.

Blinks/pupil occlusions are recorded as NA, 0 or even negative time observations in the raw signal. Partial occlusions of the pupil are not easily detectable and one should examine the data after the removal of these points to check for other unusual activity. All these observations are usually removed from 100 ms before the presumed rapid closing of the eyelid until 200 ms after. We implemented this procedure in the R function pup.med with three different kinds of data imputation: Gaussian [3], t-Student [2] and Kalman filtering [3]. Their stochastic performance is shown in Fig. 1.

Fig. 1

Fig. 1. Raw pupil signal and reconstructed signal using data imputation.

The removal of ROE is conducted in two steps, which allows to detect different kinds of ROE (see [1] for further details). Results of this procedure are available by running the R script bellow.

Methods in practice

#Download the repository and copy this code chunk to a new R script
#setwd(~/pupil-turbulence-removal) #set the working directory 
#Uncomment to install the packages if necessary
#install.packages('signal')
#install.packages('imputeFin')
#install.packages('imputeTS')
source('fn.R') #load functions to the environment
y <- read.csv('blinks.csv')$x #read the data
ry <- pup.med(y, ant=0.1, post=0.2, method="t-Student")
y <- ry$Pupildata #reconstructed pupil signal

#Plot the ROE corrected pupil data
duration <- length(y)/30
arg <- seq(0,duration,duration/length(y))[1:length(y)]
plot(arg, y, ylab='Pupil diameter', xlab='Time (s)', type='l', main='ROE correction')
lines(arg, pup.turbulence(y, sd.factor.high=3*exp(-ry$Blink_rate), LPF=NA), col='orange')
lines(arg, pup.turbulence(y, sd.factor.high=3*exp(-ry$Blink_rate), LPF=1.6), col='darkgreen', lwd=2)
legend('topright',legend=c('Artifact corrected signal', 'ROE corrected signal', 'Final smoothing'),
       col=c('black', 'orange', 'darkgreen'), lwd=c(1,1,2), cex=0.8, bg='lightblue')

y <- pup.turbulence(y, sd.factor.high=3*exp(-ry$Blink_rate), LPF=1.6, Nf=15) #Nf is the Nyquist frequency

The R function pup.turbulence removes pupil turbulences according to [1]. The dispersion hyperparameter for slow turbulences is set by default to 3 (sd.factor.low=3); we observed that between 3-5 provides optimal results under constant luminance conditions. For high-frequency turbulences, such as ROE due to blinks, we recommend modeling the hyperparameter as the exponential 3*exp(-ry$Blink_rate), where ry$Blink_rate is an estimation of the blink rate calculated in the function pup.med. By default, the parameter is set to 3. We recommend to perform the final smoothing step using a cutoff frequency between 1 Hz (LPF=1) and 4 Hz (LPF=4). If LPF=NA (default) no smoothing is conducted. The function pup.turbulence is configured for a 30 Hz sampling frequency.

References

[1] M. Vidal, K. E. Onderdijk, A. M. Aguilera, J. Six, P-J. Maes and T. H. Fritz, M. Leman. "Cholinergic-related pupil activity reflects level of emotionality during motor performance", 2022.

[2] J. Liu, S. Kumar and D. P. Palomar, "Parameter Estimation of Heavy-Tailed AR Model With Missing Data Via Stochastic EM," in IEEE Transactions on Signal Processing, vol. 67, no. 8, pp. 2159-2172, 2019, doi: 10.1109/TSP.2019.2899816.

[3] R. Zhou, J. Liu, S. Kumar and D. P. Palomar, "Student's t VAR Modeling With Missing Data Via Stochastic EM and Gibbs Sampling," in IEEE Transactions on Signal Processing, vol. 68, pp. 6198-6211, 2020, doi: 10.1109/TSP.2020.3033378.

[4] R. J. Hyndman and Y. Khandakar (2008). "Automatic time series forecasting: the forecast package for R". Journal of Statistical Software, 26(3).