Time-frequency analysis of pupil size modulated by global luminance, arousal, and saccade preparation signals using Hilbert-Huang transform.

Pupil size changes constantly and is mainly determined by global luminance signals. In addition, the pupil responds to various cognitive and arousal processes, with larger pupil dilation observed in higher levels of cognitive or arousal processing. Although these task-evoked pupillary responses are extensively used in the pupil research, pupil analysis focusing on the frequency domain, particularly in the context of arousal and cognitive modulations, is less established. Fourier Transform method (FFT) has been used to understand the modulation of task difficulty on pupil oscillations. However, physiological signals are often characterized as non-linear and non-stationary waves, and the conventional spectral analytical method with linearity presumption is less appropriate to reveal modulation dynamics between time and frequency. Here, we used Hilbert-Huang Transform (HHT) to examine the time-frequency modulations on pupil size regulated by arousal, cognitive, and global luminance signals. Consistent with previous research, using FFT, higher spectral densities were obtained with lower luminance background. Moreover, higher spectral densities were found in the high emotional arousal condition. With HHT, we further demonstrated temporal changes on amplitude spectrum and inter-trial phase coherence (ITPC) in each intrinsic mode function (IMF), with stronger amplitudes in higher IMFs (i.e., low frequencies). Moreover, although global luminance, arousal and saccade preparation modulated pupil oscillatory responses, the modulation pattern in different IMFs was different. Together, our results demonstrated dynamics between the time and frequency domain on pupil oscillatory responses, highlighting the importance of examining the time-frequency interactions in the context of various pupil modulations.