Fast cyclic stimulus flashing modulates perception of bi-stable figure

Participants

Eight subjects (seven males, one female) participated in the experiments. Three subjects (RB, AS, and MK; 32, 66, and 22 years old, respectively) had experience in psychophysical research. The other five (AV, IS, GS, MR, and AS2; 19, 20, 21, 22, and 49 years old, respectively) were naive. Two experienced subjects participated in 20 sessions, one experienced and one naive subject participated in 10 sessions and the remaining four participated in only three sessions. The results from the first session for one subject who participated in 20 sessions were removed from the data analysis because they varied significantly and differed significantly from the rest of his sessions. Subjects participated in one session per day, every day or with a less than 5-day interval. All subjects signed an informed consent approved by Vilnius Region Ethics Committee of Biomedical Research (approval No. 158200-13-578-173).

Stimuli and apparatus

The stimulus was the standard Necker cube, drawn in black lines on a white (85 cd/m2—measured with PR680) background. The stimulus size was 1.7 × 1.7 degrees of visual angle. The transparent slide with the Necker cube was mounted on the specially designed tachistoscope with a 20 mm aperture. It had a chin or headrest, stabilizing the subject’s head. A white PC-controlled LED illuminated the slide; a specially written program controlled an electric circuit to form the LED luminous flux and the data was transmitted to a PC through an LPT port. The structural diagram of the experimental apparatus is presented in Fig. 1A. The stimulus was switched on and off, i.e., flashed rhythmically at selected frequencies. The flash duration had an accuracy of about 5 µs. Subjects watched the stimulus monocularly with the right eye and this flashing image was seen for a fixed period. Subjects responded by pressing a key on a response box connected to the LPT port of the PC.

Procedure

The experiments were carried out in a dark and partly soundproofed room. Before each session, the subject adapted to darkness for 10 min. The Necker cube was rhythmically turned on and off within a block lasting 180 s (Fig. 1B). On and off periods were equal and the frequency (and flash duration) of presentation in one block was constant. Eighteen blocks, each with a different flash duration (which we refer to as “stimulus duration”) and with a 60 s pause in between the blocks, were randomly presented during each session. The minimum flash duration was 4 ms, the maximum 20 ms, i.e., flash duration varied in 1 ms steps among the different blocks. The non-flashing Necker cube was presented in one block. The position of the Necker cube was called the “up position” (abbreviated UP) if its front wall was perceived higher than the rear, and the alternative position was called the “down position” (abbreviated DOWN). The task was to press and keep the key pressed when the position of the Necker cube DOWN was perceived and to release and keep the key released when the position of the Necker cube UP was perceived. Knowing the moments of perceptual changes, it was possible to determine the duration of perception of each of the Necker cube positions. We named this duration of perception an absolute perception time (abbreviated PT).

Data analysis

The analysis of the obtained data was carried out with the same analysis methods as described in the paper of Geissler et al. (2012). Firstly, as the perception time (PT) of UP and DOWN orientations of the Necker cube varied between subjects and sessions, instead of PT, we analyzed the deviations of PT (abbreviated dPT) from mean PT (i.e., absolute differences between each value of PT and the mean PT in an experimental session): i.e., $\Delta {\tau }_{\mathrm{UP}}\left(k,i\right)={\bar{\tau }}_{\mathrm{UP}}\left(i\right)-{\tau }_{\mathrm{UP}}\left(k,i\right)$ and $\Delta {\tau }_{\mathrm{DOWN}}\left(k,i\right)={\bar{\tau }}_{\mathrm{DOWN}}\left(i\right)-{\tau }_{\mathrm{DOWN}}\left(k,i\right)$. Here i = the number of session, k = the block number (k = 1, …, 18), ${\bar{\tau }}_{\mathrm{UP}}\left(i\right)$ and ${\bar{\tau }}_{\mathrm{DOWN}}\left(i\right)$ is the mean PT of respectively UP and DOWN for all chosen blocks k over whole ith session, and τ_UP(k, i) and τ_DOWN(k, i) is the mean dPT of UP and DOWN for block k of the ith session. Next, we calculated the means of dPT for the k-th blocks over all n sessions separately for UP and DOWN, i.e., $\Delta {\tau }_{\mathrm{UP},\mathrm{DOWN}}\left(k\right)={\sum }_{i=1}^n\Delta {\tau }_{\mathrm{UP},\mathrm{DOWN}}\left(k,i\right)∕n$, and joint averaged UP and DOWN function: $\Delta \tau \left(k\right)=M\left(\Delta {\tau }_{\mathrm{UP}}\left(k\right)+\Delta {\tau }_{\mathrm{DOWN}}\left(k\right)\right).$

Secondly, in order to check whether the dominant time significantly depends on the frequency of the flashing stimuli, one factor ANOVA was run for each subject separately.

Next, the PCA (principal component analysis) was run on the set of data (18 means of blocks and n sessions). The main purpose of the PCA was to find how many factors influence the perception of ambiguous figures. In a similar investigation on binocular rivalry (Geissler et al., 2012; Blake & Lee, 2005), it was shown that the duration of the dominant time of the perceived stimuli depends on many factors. As different observers could produce different function of perception times on the frequency of stimulus, it is more informative to run the PCA separately on the data of different observers, however, the data of only three subjects (RB, AS, and MK) were sufficient for the PCA. Additionally, the data of AV, IS, GS, MR and AS2 subjects (abbreviated Rm5) was aggregated. Such a choice let us to compare the averaged function for five subjects with the function for separate subjects.

As not all extracted factors may be significant (some may be related to random changes/fluctuations), we need to identify non-random factors. One of the most commonly used methods is the Kaiser’s criterion (Fabrigar et al., 1999), which retains factors with eigenvalues greater than 1. It is assumed that these factors characterize the assessed process reliably, although it should be noted that, according to other researchers (Hayton & Allen, 2004), such a liberal method of factor extraction does not guarantee that the selected factors will not be random. It is therefore suggested to perform parallel factor analysis on a randomly formed data array with the same data structure as the experimental data (Fabrigar et al., 1999; Hayton & Allen, 2004). Random factors are extracted with parallel factor analysis. When eigenvalues of these random factors are higher or approximately equal to eigenvalues extracted with PCA, the latter values should be rejected as related to random influences. In order to identify non-random factors, we also used parallel factor analysis. In our case the number of non-random factors was four or five, and they explained about 67–75% of the experimental data dispersion.

Next, the analysis of extrema distribution was performed. Such an analysis allows us to reduce the fluctuation of the amplitude of dPT dependence which could mask its periodicity. Analysis of extrema distribution can also reveal whether the periodicity of a function is stable across sessions. We calculated how many times the changes of the perception of dominant stimulus occurs under each frequency of flashing. Therefore, we calculated the numbers of local extrema (maxima) of Δ τ(k,i) (the function of perception time deviation) as a function of the duration of the flashed stimulus: ${\displaystyle \Delta {\tau }^1\left(k,i\right)=\left\{\begin{array}{c}1,if\underset{}{\Delta \tau \left(k-1,i\right)<\Delta \tau \left(k,i\right)}>\Delta \tau \left(k+1,i\right)\hfill \\ 0,\text{in other case}\hfill \end{array}\right.}$ i.e., $\Delta {\tau }^1\left(k,i\right)$ will equal 1, if at point k a local maximum of function $\Delta \tau \left(k,i\right)$ is observed, otherwise it will equal 0. Next, we summed the number of local extrema over all sessions: $\Delta {\tau }^1\left(k\right)={\sum }_i\Delta {\tau }^1\left(k,i\right)$. The value of function $\Delta {\tau }^1\left(k\right)$ at point k is an integer number and defines how many times a local maximum at point k (duration of displayed stimulus) was observed through all sessions. Furthermore, we calculated the mean value M (Δ τ¹(k)) of function $\Delta {\tau }^1\left(k\right)$. We also calculated how many maxima at point k of function $\Delta {\tau }^1\left(k\right)$ were above and below the value M. We assigned “1” for the all values that exceeded the value M, and “0” for the all values that were below the value M. Thus, we produced a sequence of 1’s and 0’s. The total number of 1’s is named “number of case A”, and the total number of 0’s is named “number of case B”. Thus, we had separate intervals at the k-axis filled with 1’s and 0’s. The number of such intervals is called “number of runs”. We used “runs test for randomness” to check whether the distribution of 1’s and 0’s along the k-axis was random or non-random (Bradley, 1968).

In a similar way the function Δτ⁰(k) describes how the other extrema (minima) points of the function Δτ (k,i) are distributed along the k axis. Because the correlations between functions Δτ¹(k) and Δτ⁰(k) were high and equal −0.8 ÷−0.9, we analyzed only the functions Δτ¹(k).

In order to check whether the obtained functions (factor loadings and function $\Delta {\tau }^1\left(k\right)$) were periodic, we performed periodic function fitting: ${\displaystyle y\left(k\right)=a_0+Asin\left(\pi \left(k-{\phi }_0\right)∕w\right),}$ in regard to which square deviation of functions was minimal.

Hypothetical mechanism of interaction between internal rhythm and sequence of external stimulus presentation

Considering the influence of a rhythmically flickering stimulus on the alternation rate of a dominant image, it should be noted that the period of flicker is about 2 ×4 ms = 8 ms. In other words, we assume that there is some internal rhythm, which specifies the discrete shortest time moments, when the sensory system input is the most sensitive. If the frequency of the stimulus presentation is a multiple of the frequency of this internal oscillator, then the efficiency of the stimuli should recur and be maximum every 8 ms. Thus, according to these results, the frequency of an internal oscillator should be approximately equal to 10³/(2 × 4.0) = 125 cycles/s which is within the high-gamma frequency brain rhythms (80–200 Hz, see Crone, Sinai & Korzeniewska, 2006). We cannot speculate what exactly the nature of this internal rhythm is, but we suggest that it should be related to a high-gamma brain rhythm (neural oscillations) that are investigated by various scientists in electrophysiological and neurophysiological studies. There are many brain rhythms of different frequencies that are related to different perceptual, memory related, or other cognitive functions. High-gamma rhythms were observed during visual perception tasks (Lachaux et al., 2005), attention tasks (Ray et al., 2008), language (Korzeniewska et al., 2011), and other cognitive processes. Correlation of brain rhythms with perception suppose the idea that perception (and other cognitive processes) is a discrete process (VanRullen & Koch, 2003).

If a sequence of input stimuli coincides with a sequence of electrical activity of some internal oscillator, the time span of a stimulus presentation completely overlaps the time span when the system is maximally susceptible. In this case, we can speak about synchronization of a sequence of external stimulus with a rhythm generated by an internal generator. This agrees with the experimental data of other authors (Vanagas et al., 1976; Geissler, 1987; Vanagas, 2001; Hasenstaub et al., 2005; Geissler et al., 2012; Fesi & Mendola, 2015).

While the duration of flashing stimulus and flashing frequency were entangled in our experimental paradigm, with the duration of stimulus as half of total period, we suppose that the frequency could be a determinant factor for periodicity of the dependence of perception time on flashing stimulus duration. For example, lengthening the optimal duration of stimulus by 1, 2 and 3 ms, its efficiency initially reduces and recovers only after lengthening it by 4 ms. After this its efficiency reduces again, until it is lengthened again by another 4 ms, and so on. Thus, the duration of displaying stimulus alone does not determine the observed effect—the efficiency of stimulus varies every 4 ms, i.e., it is also related to the moment of time when the stimulus is switched on. Thus, it can be related to the accurate coincidence in time of two streams (external and internal) of neuron impulses (Huber et al., 2008; Stanley et al., 2012). That means that the precise timing of the switching on of the stimulus and action of the internal impulses is important in order to produce the optimal influence on the alternation rate of perceived stimulus.

The question is whether such an information processing method, when the static signal is differentiated with respect to time, can occur under natural conditions, when there is no flashing signal. An investigation of neuronal processes in the retina (Roska, Molnar & Werblin, 2006; Hsueh, Molnar & Werblin, 2008) confirmed that the differentiation of signals with respect to time could be initiated at the low level of the visual system. It is shown that ganglion cells receive excitation signals from bipolar cells and inhibition delayed signals from amacrine cells. Due to this interaction, ganglion cells get differentiated signals with respect to time. Thus, at the outputs of ganglion cells, a high-frequency sequence of discrete signals can be formed (Vaitkevicius et al., 1983). Moreover, it is well known that the eye is constantly moving, hence the image of an object is shifted in time from one place to another on the retina. Amplitudes of the small movements (or ocular tremor) are about 20–40 arcsec with a frequency of ∼90 Hz (Martinez-Conde, Macknik & Hubel, 2004), but in extreme case it can go up to 150 Hz (Spauschus et al., 1999; Carpenter, 1988). There are also experimental findings confirming that the micro movements of the eyes could be involved in this low-level coding process of sensory information (differencing of signals with respect to time and space) (Kulikowski, 1971; Leopold & Logothetis, 1998; Roska, Molnar & Werblin, 2006).

An alternative explanation of our findings, which does not related to the process of synchronization of two streams, could be based on a perceived brightness of stimulus. It is well known that perceived brightness of flashing stimulus depends on the frequency of flashing and stimulus duration (Talbot-Plateau law). In other words, the perceived brightness depends on stimulus power (which in our case is constant). The law holds when the frequency of flashing stimulus is higher than the critical flicker fusion (Hecht & Wolf, 1932; Bartley, 1938; Bartley, 1939); otherwise, the influence of rhythmic stimulus on perception is more complex. In any case, the dependence of stimulus brightness on stimulus duration and flash frequencies used in our study should be more monotonic and cannot explain the periodicity observed in our experiments.

A common mechanism for binocular rivalry and perception of ambiguous figures

It is also important to note that according to our data, the influence of the frequency of stimulus flicker on the alternation rate of the dominant image perception is similar in both phenomena of bistable perceptions: binocular rivalry and monocular perception of bistable images. Binocular rivalry originates from the different images presented to the retinas of each eye: it is impossible for the human to perceive two different stimuli at the same point in space. At any given moment of time only one object (the dominant image) is perceived, and another object (the image on the retina of the other eye) is not perceived—it is suppressed. The situation is different in the case of the Necker cube: the image of a cube is displayed in the retina of one eye. In other words, two different Necker cubes can create exactly the same perceived image. Since it is impossible to perceive two different objects at the same time and in the same point in space, the subject perceives only one of two possible images (the dominant image) at different moments in time, and any other possible perceptual option is suppressed. The loadings on the factors (F3) as a function of stimulus duration are similar both in the case of binocular rivalry and in the case of the Necker cube (see Fig. 4). Thus, we can assume that these factor loadings are the result of similar processes involved both in monocular and binocular perception. Comparing perception of ambiguous figures and binocular rivalry, O’Shea et al. (2009) previously drew the same conclusion. On the other hand, (Cao et al., 2018) argue that experimental data suggest partially independent processes for bistable perception of different types of stimuli.