The results for the two experiments dealing with contrast and spatial frequency obtained with the FET eye tracker are summarized below (see the Methods). We first show the effect of the stimulus on microsaccade inhibition (OMI) for FET data, compared to results from previous studies. We then show the results for the overall effect of a transient stimulus on the drift in both experiments, and finally the stimulus dependency.
Microsaccade inhibition with FET
The microsaccade inhibition results for both experiments are shown in Fig. 3. The rate modulation functions (Fig. 3a, 3d) show the typical inhibition effect, with minima around 200ms and maxima around 400ms for the inhibition onset and release, respectively. The stimulus dependency was then quantified via the microsaccade response time (msRT) computed as the latency of the first microsaccade in the inhibition release time window of 200-800ms post-stimulus onset. The results are shown in Figs. 3b and 3e, showing stimulus-dependent latencies with a faster inhibition release for the more salient stimuli (i.e., 1cpd and 50% contrast). The effects were statistically significant, as assessed using the linear mix model (LMM) with β1 = 5.2 (2.7,7.7), SE = 1.2, t(63) = 4.2, and p = 8.2e-05 in the spatial frequency results (Fig. 3b), and β1=-32 (-50,-14), SE = 9.2, t(58)=-3.5, p = 0.001 in the contrast results (Fig. 3e). The inhibition onset time window (0-200ms) showed a non-significant LMM effect for msRT (p = 0.16 for spatial frequency and p = 0.71 for contrast). In addition, we compared our FET results to previous publications using EyeLink 4,5 and obtained very similar results for spatial frequency (Fig. 3c). In the contrast experiment we found a similar trend, but a faster inhibition release (~ 70ms ahead) in the FET (Fig. 3f) that persisted (~ 55ms ahead) when the time window was equalized to previous work (200-950ms). This difference could possibly stem from a higher sensitivity of the FET in the detection of microsaccades.
Drift inhibition in response to a transient stimulus
The results for the average drift modulation functions in response to a Gabor flash (100ms at 0.9Hz) in the spatial frequency and contrast experiments are shown in Fig. 4. The results were obtained by pooling all stimulus conditions within the experiment. Three measures were computed: Area (4a), Velocity (4b), and Diffusion (4c) averaged across the different spatial frequencies and contrasts (see the Methods). All three measures show an OMI pattern with the inhibition onset shown as the minimum point ~ 240ms post-stimulus onset in the spatial frequency trials and ~ 220ms in the contrast trials, followed by inhibition release shown as the maximum point ~ 360ms in the spatial frequency trials and ~ 380ms in the contrast trials. When compared to the saccade rate modulation in the spatial frequency trials (Z-values, Fig. 4d), the drift minima appeared ~ 65ms after the microsaccade rate minima, and the drift maxima (inhibition release latencies) appeared ~ 25ms after the saccade maximum. The contrast trials (Z-values, Fig. 4e) show both the drift minima (~ 75ms) and maxima (~ 65ms) after the saccade minimum and maximum peaks. Overall, drift modulation resembles other types of OMI such as saccades, however, with a shift in the time course and a later inhibition pattern of the drift compared to microsaccades. In addition, the overall drift modulation in the spatial frequency experiment was larger than the modulation in the contrast experiment (see Fig. 4a-c), presumably reflecting the difference in the average saliency of the stimuli.
The effect of spatial frequency on drift inhibition
The results for the spatial frequency dependence of the drift modulation for the area, velocity, and diffusion measures are shown in Fig. 5. All measures were computed after saccades and blink removal, with additional margins to avoid their impact on the results, and trace alignment (see the Methods). In addition to the time course plots (Fig. 5, left column), there are 2 measures for each drift method: (1) inhibition onset (Fig. 5, middle column) computed as the drift minima latency in an early time window (100-300ms), and (2) inhibition release (Fig. 5, right column), computed as the drift maxima latency in a late time window (200-600ms for Area, 100-600ms for Diffusion and Velocity). All measures showed a roughly linear relationship to the spatial frequency (1-8cpd). All plots showed significant LMM: The drift area inhibition onset showed β1 = 2 (0.93,3.1), SE = 0.54, t(63) = 3.7, and p = 0.00044 (5b), and the inhibition release showed β1=-3.2 (-5.8,-0.58), SE = 1.3, t(63)=-2.4 with p = 0.017 (5c). The drift diffusion inhibition onset showed β1 = 1.9 (0.94,2.9), SE = 0.49, t(63) = 3.9 with p = 0.00024 (5e), and the inhibition release showed β1=-4.4 (-8.2,-0.62), SE = 1.9, t(63)=-2.3 and p = 0.023 (5f). The drift velocity inhibition onset showed β1 = 1.6 (0.44,2.8), SE = 0.59, t(63) = 2.7, and p = 0.0081 (5h), and the inhibition release showed β1=-4.2 (-7.7,-0.69), SE = 1.7, t(63)=-2.4, and p = 0.02 (5i). The drift latencies showed slopes of 1.6 to 2ms per spatial frequency in the inhibition onset window and − 4.4 to -3.2ms per spatial frequency in the inhibition release time windows, which implies that in all measures, the drift minima latency (inhibition onset) increased, and the drift maxima latency (inhibition release) decreased with increasing spatial frequency.
In addition to the velocity results shown in Fig. 5g, we noted early velocity peaks of ~ 100ms. We calculated the latencies of the local maxima in a time window of 0-200ms, and showed a stimulus-dependent pattern with a decrease in latencies with spatial frequency increase, i.e., shorter latencies and an earlier peak at 8cpd (~ 96ms) and longer at 1cpd (~ 103ms). The early time window showed significant LMM with β1=-0.98 (-1.9,-0.058), SE = 0.46, t(63)=-2.1, and p = 0.038 (Figure S1).
A graphical demonstration of the drift spatiotemporal modulation in terms of heat maps and Area is shown in Fig. 6. The data were analyzed in time segments of 100ms, excluding segments containing blinks or saccades. As shown, the drift was dispersed before stimulus onset with a wide area and low heat map peaks (HMP); then its area became smaller (inhibition) with a higher heat map peak at 0.2-0.3s following stimulus onset, and later it became dispersed again. Figure 6 also shows that a difference exists between 1 and 8cpd, with the drift spreading earlier and showing a larger area, i.e., earlier release from inhibition at 8cpd (Fig. 6b), compared to 1cpd (Fig. 6a).
Overall, the heat map peak (HMP) shows the opposite modulation compared to the drift area, diffusion, and velocity (from Fig. 5), where drift inhibition is associated with a lower velocity, smaller area, and higher heat map peaks. To quantify the effect of spatial frequency on the HMP, we conducted a similar analysis for inhibition onset and release, as was done for the other measures from Fig. 5, except for assessing the maxima for onset and the minima for release due to the opposite trend of the HM (data not shown). We found both measures to be significantly associated with the spatial frequency using LMM (see the Methods). Inhibition onset, calculated as the local maxima in a time window of 100-400ms, shows a slope of β1 = 1.7 (0.28,3), with SE = 0.69, t(63) = 2.4, and p = 0.02. Inhibition release, calculated as the local minima in a time window of 200-600ms window, shows β1=-2.8 (-5,-0.47), SE = 1.1, t(63)=-2.4, and p = 0.019. The peak heat map measure was found to be sensitive to saccades and the margins around saccades; however, as long as the margins were large enough, we could notice a general pattern; when the stimulus flashes, the drift area decreased (Figs. 6a, 6b, 5b) with higher heat map peaks (Figs. 6a, 6b: time range 0.2-0.3sec), lower diffusion (5e), and lower velocity (5h).
The effect of contrast on drift inhibition
In the contrast experiment, we tested the effect of contrast on the drift, with a fixed spatial frequency (3cpd). The analysis was similar to the spatial frequency (Fig. 5). The results are shown in Fig. 7. All measures were computed after saccade removal and trace alignment, whereas time bins containing saccades or blinks were excluded from the area and the diffusion calculations (see the Methods). In addition to the time course plots shown (Fig. 7, left column), there were two measures for each drift method: (1) the inhibition onset (Fig. 7, middle column), assessed by the drift minima latency in an early time window (100-400ms, except Velocity at 200-300ms), and (2) inhibition release (Fig. 7, right column), assessed by the drift maxima latency in a late time window (300-600ms). All measures showed a roughly linear relationship to the stimulus contrast (log scale), and a significant linear mixed model (LMM), with statistical details appearing in Fig. 7 plots: Drift area inhibition onset β1=-21 (-30,-11), SE = 4.8, t(58)=-4.3, and p = 7.1e-05 (8b), and inhibition release β1 = 31 (18,44), SE = 6.6, t(58) = 4.7, with p = 1.4e-05 (8c). Drift diffusion inhibition onset β1=-15 (-29,-0.96), SE = 7, t(58)=-2.1 and p = 0.037 (8e), and inhibition release β1 = 37(22,52), SE = 7.5, t(58) = 5, and p = 5.8e-06 (8f). Drift velocity inhibition onset β1=-5.9 (-9.6,-2.2), SE = 1.8, t(58)=-3.2, and p = 0.0021 (8h), and inhibition release β1 = 29 (15,43), SE = 7.1, t(58) = 4.1, and p = 0.00013 (8i). In all measures, the drift minima latency decreased (5.9-21ms per log unit), and the drift maxima increased (29-37ms per log unit) with increasing contrast. Analysis of the heat map peaks produced ambiguous results for contrast and therefore, they were not included.
Drift inhibition in epochs without saccades
To rule out the possibility that the drift inhibition effect is a side effect of saccades or their inhibition, we analyzed epochs without saccades in the time range − 100 to 600ms around stimulus onset; the results are shown in Fig. 8. Both spatial frequency (8a-b) and contrast (8c-d) show drift inhibition patterns for Area, with only 270 − 240 epochs per condition. However, a significant stimulus-dependent drift inhibition was only found in the inhibition onset stage (100-300ms) of the spatial frequency trials (Fig. 8b), with LMM results of β1 = 1.7 (0.29,3.1), SE = 0.71, t(63) = 2.4, and p = 0.019. The drift inhibition onset of the contrast results (8d) in a time window of 100-400ms did not show significant LMM (β1=-8.2 (-23,6.9), SE = 7.5, t(57)=-1.1, and p = 0.28). This insignificant result could have resulted from a small number of repetitions in each condition. Without saccades, the drift showed a trend similar to our previous findings, with longer latencies of the inhibition onset by ~ 15ms for spatial frequency (Fig. 5b), and by ~ 20ms for contrast (Fig. 7b). The drift inhibition release did not show significant stimulus-dependent latencies of the maxima peaks.
Inter-relationships and consistency across drift inhibition measures
Since this study involved complex measures with some tuning of parameters, we sought to validate these measures by testing their consistency via correlations. In addition to correlations between the different drift measures, we included microsaccade inhibition to further investigate the inter-relationships between drift and saccades, and the validity of the general oculomotor inhibition (OMI) concept. The results are shown in Figs. 9 and 10 for spatial frequency and contrast, respectively, each for both the inhibition onset and the inhibition release measures, with details included in the figures and captions. All correlations were performed on observers per stimuli, i.e., a dot per observer in one spatial frequency (Fig. 9) or one contrast (Fig. 10), thus capturing both the stimulus dependency and the inter-subject variability. The correlations were computed after data demeaning to remove the individual speed effect of fast or slow observers. For comparison, the raw data are shown in supplementary data Figures S2 and S3, demonstrating large individual differences which are correlated across measures, in addition to the differences induced by changes in the stimulus. To compensate for the multiple comparisons, we used the False Discovery Rate (FDR) procedure 33 to adjust the p-values, per experiment and time window (inhibition onset or release).
Overall, many correlations were significant after correcting for multiple comparisons, both between the different drift inhibition measures as well as the microsaccade inhibition. In the spatial frequency inhibition onset analysis (Fig. 9a) all measures were significantly positively correlated. In the spatial frequency inhibition release analysis (Fig. 9b) only some correlations were significant: Velocity-Diffusion, Area-Diffusion, and Velocity-Area. In the contrast inhibition-onset analysis (Fig. 10a) only the Area-msRT and Area-Diffusion correlations were significant after FDR correction. On the other hand, in the contrast inhibition release analysis (Fig. 10b) all measures showed significant correlations, positive between drift measures and negative between msRT and drift measures. It is noteworthy that this last analysis (inhibition release for contrast, Fig. 10b) showed some very high correlations (R = ~ 0.8) and all correlations were highly significant including negative correlations between msRT and drift-measures (R≈-0.41, p < 0.01). These correlations strengthen the finding that saccade and drift inhibitions differ in their stimulus dependency in terms of inhibition release latency.