Temporal dynamics of saccades explained by a self-paced process

Abstract

Sensory organs are thought to sample the environment rhythmically thereby providing periodic perceptual input. Whisking and sniffing are governed by oscillators which impose rhythms on the motor-control of sensory acquisition and consequently on sensory input. Saccadic eye movements are the main visual sampling mechanism in primates, and were suggested to constitute part of such a rhythmic exploration system. In this study we characterized saccadic rhythmicity, and examined whether it is consistent with autonomous oscillatory generator or with self-paced generation. Eye movements were tracked while observers were either free-viewing a movie or fixating a static stimulus. We inspected the temporal dynamics of exploratory and fixational saccades and quantified their first-order and high-order dependencies. Data were analyzed using methods derived from spike-train analysis, and tested against mathematical models and simulations. The findings show that saccade timings are explained by first-order dependencies, specifically by their refractory period. Saccade-timings are inconsistent with an autonomous pace-maker but are consistent with a "self-paced" generator, where each saccade is a link in a chain of neural processes that depend on the outcome of the saccade itself. We propose a mathematical model parsimoniously capturing various facets of saccade-timings, and suggest a possible neural mechanism producing the observed dynamics.

Figure 1

Spectra of saccade sequences. (A) Power spectra of saccade sequences. Each row represents the 1–20 Hz normalized power spectrum density of an individual observer. For convenience of presentation, we normalized each data-set’s power spectrum to the fraction of the overall power. (B) Same data for two selected observers. While one (S3-red line) has a distinctive spectral peak, the other’s spectrum is nearly flat (S2-black line). With different parameters, our first-order model can fit both types of data-sets (purple and gray lines).

Figure 2

Statistical properties of single-subject saccade sequences during free-view (Exp 1). (A–E) Subjects ordered from left to right according to their level of rhythmicity as indicated by their modulation index. (A) Inter-saccade intervals distributions of 4 subjects (black) and their fitted first-order model (gray). (B) Autocorrelation functions of saccade events normalized to represent post-saccadic saccade rate. (C) Hazard Functions. (D) Power spectra of saccade sequences. (E) Histograms of modulation indices calculated on 1000 shuffles of intervals of either real data (blue) or simulated oscillatory data (green). The red bar indicates the original modulation index.

Figure 3

Statistical properties of single-subject saccade sequences during fixation (Exp 2). (A–E) Subjects ordered from left to right according to their level of rhythmicity as indicated by their modulation index. (A) Inter-saccade intervals distributions of 4 subjects (black) and their fitted first-order model (gray). (B) Autocorrelation functions of saccade events normalized to represent post-saccadic saccade rate. (C) Hazard Functions. (D) Power spectra of saccade sequences. (E) Histograms of modulation indices calculated on 1000 shuffles of intervals of either experimental data (blue) or simulated oscillatory data (green). The red bar indicates the original modulation index.

Figure 4

Comparison of saccade data and an oscillatory simulation model. (A) Autocorrelation function of subject 3 who participated in Exp. 2, normalized to represent post-saccadic saccade rate in Hz (black). The autocorrelation function of an oscillatory model matched in modulation index (gray). (B) Hazard function of the same data-set (black) and of its matched oscillatory model (gray).

Figure 5

Effects of first-order model parameters on spectra and modulation indices. PSD (A), and modulation index (C), modulated by the duration of inhibition (rebound is fixed at 0). PSD (B) and modulation index (D) modulated by the magnitude of rebound (duration of inhibition is fixed at 200 ms).

Figure 6

Modulation of the power spectra by shuffling. (A) Spectra of oscillatory model and first-order model matched in spectral peak magnitude. (B) After shuffling, the spectrum of the oscillatory model is flattened while the spectrum of the first-order model is preserved.

Figure 7

Modulation indices of individual subjects and groups. (A) For each subject, the shuffled sequence modulation index is plotted as a function of experimental modulation index (black circles). As a baseline for this analysis, the shuffled simulated oscillatory sequence modulation index is plotted as a function of the original modulation index (gray Xs). (B) For each experiment, the mean modulation index before and after shuffling is given, both for experimental data (black) and oscillatory model (Gray). Data are represented as mean ± SEM, N = 12,11,12 for Exp 1–3 respectively.

Figure 8

Modulation indices of individual subjects and groups (surrogate blink-free data). This figure is equivalent to Fig. 7 remade using blink-free saccade sequences. (A) For each subject, the shuffled sequence modulation index is plotted as a function of real modulation index (black circles). As a baseline for this analysis, the shuffled oscillatory sequence modulation index is plotted as a function of the original modulation index (gray Xs). (B) For each experiment, the mean modulation index before and after shuffling is given, both for real data (black) and oscillatory model (Gray). Data are represented as mean ± SEM, N = 12,11,12 for Exp 1–3 respectively.

Figure 9

Alternative models explaining visual exploration dynamics. Hypothesis A Central theta oscillations drive saccades and the visual cortex independently; Hypothesis B, Central theta oscillations drive saccades. Saccades then drive visual activity through retinal image shifts or efferent activity; Hypothesis C, Saccades are generated by a self-paced mechanism and drive cortical rhythmicity through retinal image shifts or afferent activity. The visual transient caused by saccades’ first-order statistics constitutes the observed cortical theta rhythm (solid arrows).Visual cortex activity then drives saccades (dashed arrows).