In Experiment 1, 20 healthy students (25.4 ± 4.2 years, 10 females) from the University of Oldenburg participated. All subjects gave written informed consent before their participation. The experimental protocol was approved by the ethics committee of the University of Oldenburg and was conducted in accordance with the Declaration of Helsinki. Three subjects' data sets had to be discarded. For two of them the 50% threshold in the behavioral target detection task was outside of the examined range of light intensities (one above and one below). The third subject showed a sudden impedance drift during the EEG recording. In Experiment 2, 20 healthy students (23.2 ± 2.4 years, 12 females) from the University of Oldenburg participated; none of them participated in the first experiment. The datasets of six subjects had to be excluded, because the 50% threshold of the detection task was above the examined range. The number of excluded subjects exceeds that of Experiment 1 probably due to the higher luminance in Experiment 2. Increased luminance causes pupil downsizing (Spring and Stiles, 1948; Watson and Yellott, 2012), which in turn is accompanied by decreased light sensitivity (Troland, 1917).

Participants in the remaining samples had normal or corrected to normal vision and reported no psychiatric disorders, epilepsy in family history or febrile convolutions during childhood. According to the Edinburgh handedness inventory (Oldfield, 1971), all subjects were right-handed.

The procedure was exactly the same for both experiments. The only difference was the light intensity of the visual flicker (Experiment 1: 118 cd/m², Experiment 2: 262 cd/m²). The target light intensity, frequency of the flicker, as well as any other parameter (see below) was identical in both experiments.

Subjects were seated in a dark sound-attenuated EEG chamber, 60 cm from a 24″ monitor (Samsung SyncMaster P2470) with a refresh rate of 100 Hz. The flicker was generated by a flashing annulus, located in the center of the screen at a visual angle of 2° (outer margin and 1° inner margin, see Figure 2) with a light intensity of 118 cd/m² (262 cd/m² in Experiment 2). To produce a 10 Hz rhythm in the rhythmic conditions, the annulus was presented for 50 ms followed by a 50 ms black screen (Figure 2). The experiments were structured in a 2 × 2 design with factors rhythmicity [rhythmic (R), arrhythmic (A)] and target position [90 (1)/270° (2), see Figure 2]. For the arrhythmic condition, the duration of the black screen was jittered between 10 and 90 ms (mean = 50 ms), while the flicker-on phases were kept at 50 ms to maintain constant luminous energy in both conditions (rhythmic/arrhythmic, see Figure 3 for stimulation details).

The same jitter duration never appeared twice in a row to preclude potential short-term entrainment, except for the target presentation period: before and after target presentation a black screen was always presented for 50 ms to keep light conditions constant around the target and preclude differences in target perception due to backward or forward masking (Eriksen, 1966) between the rhythmic and the arrhythmic target presentation. Targets were presented in the center of the flicker annulus at a visual angle of 1° (outer margin) for a duration of 10 ms either during presentation of an annulus or between two annuli (see Study design, Figure 2) and could appear at eight different light intensities between 0 and 262 cd/m² in logarithmic steps. Each target presentation was repeated 20 times, resulting in 160 target presentations per condition, 640 targets in total. The experiment was written in MATLAB R2012b (The MathWorks Inc., Natick, MA, USA) using the Psychophysics Toolbox extensions (Brainard, 1997; Kleiner et al., 2007).

The experiments were structured in a 2 × 2 block design with the factors flicker regularity (rhythmic/arrhythmic) and target position [peak (90°, 1)/trough (270°, 2) of stimulation phase] to modulate detection rates. Each of these four conditions was presented in a separate block with continuous flicker presentation and targets appearing every 4 ± 0.58 s (within the range of 3–5 s). The block order was randomized between subjects. No effect was found for the order [one-way ANOVA F_{(1, 3)} = 1.08, p = 0.36]. Each condition was repeated two times, resulting in 8 × 5 min blocks. After four blocks, the experiment was paused for at least 3 min, 1 min after each block. In the beginning and after the 3 min pause in the middle of the experiment, a short 1 min adaptation block was presented. Subjects were advised to press a button whenever a target (in the center of the flicker annulus) was detected. The ongoing flicker was unaffected by the button press. Before the actual experiment, 2 min resting state with eyes closed was recorded. Subsequently, a feedback block was presented for the subjects to learn the task. In contrast to the actual experiment, here subjects received feedback after each target, depending on whether the target was detected (green happy smiley), missed (1500 ms after target presentation; red sad smiley) or when subjects pressed a button when no target was shown during the preceding 1500 ms. The feedback loop was repeated until at least 80% of the test-targets (light intensities from 60 to 262 cd/m²) were detected.

Electroencephalogram (EEG) was recorded during the whole experiment at 32 Ag–AgCl electrodes, mounted in an elastic cap (Easycap, Falk Minow, Munich, Germany) with an extended 10–20 system layout, referenced to the nose. FPz was used as ground electrode. As Pz has been described to capture the peak of alpha power in the parieto-occipital region, we chose this electrode for further analysis (Ergenoglu et al., 2004). Impedances were kept below 10 kΩ. EEG was recorded using a 16-bit Brain Amp DC amplifier and Brain Vision Recorder software (Brain Products GmbH, Gilching, Germany) with an online band pass filter of 0.016–250 Hz and a sampling rate of 1000 Hz. EEG was amplified in the range of ±16.384 μV at a resolution of 0.5 μV/bit. We recorded stimulus markers and responses were together with the EEG using Brain Vision recorder and stored data for further offline analysis.

Via photo diode we monitored the temporal accuracy of the flicker during stimulation. No inaccuracies were detected during measurements.

The modulation depth was the behavioral outcome combining the four conditions (of the factors flicker regularity and target position) and reflects the modulation of phase-dependent perception due to differences in flicker regularity (see Methods Section and supporting information (Figure S1) for derivation of the formula for the modulation depth).

In the first step, amplitude spectra of the stimulated periods and the resting state data were calculated and averaged over subjects. The averaged resting state spectra reveal slightly enhanced amplitudes (normalized amplitudes in the figure reveal 1/f corrected amplitudes) compared to the induced stimulated sequence (Figures 5A,B). This is because resting state was measured with eyes closed, which generally results in higher amplitudes as compared to eyes open. As expected, rhythmic stimulation resulted in a peak at 10 Hz, whereas arrhythmic stimulation shows a rather unspecific elevated spectrum in the area of 10 Hz (Figure 5B, induced spectrum). In the evoked spectrum (Figure 5C), where EEG sequences were first averaged, the 10 Hz peak cancels out in the arrhythmic conditions (A1/A2) but shows a clear peak in the rhythmic conditions (R1/R2).

In the second step we validated this measure. We predicted that with stronger entrainment during rhythmic stimulation, modulation depth should increase. The ratio of the 50% detection threshold during A1 (arrhythmic stimulation, target position at 90°) and the 50% detection threshold during A2 (arrhythmic stimulation, target position at 270°) varied strongly between subjects (between 0.75 and 1.63) and served as a control on a single-subject level. The stronger the deviation of the ratio R1/R2 from A1/A2 (target position 90°/270°) on a single subject level, the greater the modulation depth.

If indeed entrainment was the causal reason for alternations of the detection threshold, then an electrophysiological measure of entrainment, such as the inter-trial coherence (ITC) during rhythmic stimulation should correlate with the modulation depth. Figure 6 depicts the relationship between these two factors, ITC and behavioral modulation depth (R² = 0.25, p = 0.04). Subjects with low ITC, thus less entrainment, show a modulation depth close to zero. Subjects with high ITC, on the other hand, reveal a stronger modulation depth, thus show differences in the detection threshold during rhythmic compared to arrhythmic stimulation. This correlation could not be found for ITC during arrhythmic stimulation (R² = 0.03, p = 0.49). The relationship of ITC during rhythmic stimulation and the modulation depth is, however, although significant, comparably small (R² = 0.25) and further variance can be explained by the subjects individual EEG phase shift (Henry and Obleser, 2012). Therefore, the subjects' mean phase angle at target onset (R1) was determined.

We then hypothesized, that an individual alpha phase angle at target onset of ½ π or 3/2 π was optimal for the modulation depth (Figure 4), because these two phases reflect the peak (or trough, respectively) of a sine and lead to maximal modulation depth (see Figure 1). An alpha phase angle of 0 as well as π at target onset, on the other hand, is considered as least optimal, because in that instance both targets would be presented during zero crossing of the EEG oscillation (Figure 4A). Based on this assumption, we fitted a sine with two peaks per period to the modulation depth of the 17 subjects as a function of the individual phase at target onset (R1) with a fixed phase shift of ½ π (as described above). The model was found to significantly describe the relationship between phase at target onset [Figure 7A, F_{(1, 15)} = 5.28, p = 0.036, R² = 0.26, compare also prediction in Figure 4B]. The following estimates resulted from the fitted function: b₀ = 0.16 ± 0.02 and b₁ = 0.07 ± 0.03, resulting in the following model function y = 0.16 + 0.07 *sin (2 * Φ -12π)

In Figure 7B, 17 panels additionally show the alpha phase during both target presentations R1 and R2 as well as the amplitude as a relative measure of the ITC. On a subject level, it is shown that ITC as well as individual phase angle at target onset influence the modulation depth.

In the second experiment, nothing but the visual flicker intensity in all four conditions was altered. Instead of a flicker at 118 cd/m², we presented the flickering stimulus with 262 cd/m². Most probably due to an altered pupil size (Troland, 1917; Spring and Stiles, 1948; Watson and Yellott, 2012), we found increased detection thresholds for all four conditions (see Table 1 for details).

Based on the concept of the Arnold tongue, an increased light intensity is expected to lead to stronger phase locking. Indeed we found an increased inter-trial coherence using a one-sided t-test for unequal variance [Figure 8, right panel; t₍₂₀₎ = 1.83, p = 0.041, d = 0.68]. As a consequence, the modulation depth was expected to increase. Our results show that modulation depth is increased during stimulation at increased light intensity [mean modulation depth and standard error at medium intensity: 0.14 ± 0.02 vs. high intensity: 0.24 ± 0.05; t_(19.5) = 1.9, p = 0.037, d = 0.71].

In order to investigate whether the resting state oscillation frequency relates to the strength of entrainment, we determined the peak frequency in the alpha range for every subject prior to the experiment. The overall mean frequency was 10.09 ± 1.46 Hz. The mean individual distance from 10 Hz was 0.91 ± 1.12 Hz. After median split of the minimum ITC of conditions R1 and R2 per subject, for the resulting two groups the mean individual alpha frequency distances from 10 Hz were determined. No significant differences were found using a signed rank test [z = 0, p = 1].

The occipito-parietal alpha phase has been shown to modulate visual detection (Klimesch et al., 2007). Based on these findings, we here designed a behavioral paradigm to investigate the underlying mechanism of SSVEPs. We therefore introduced a new measure of modulation depth that includes arrhythmic and rhythmic stimulation at two opposing phase angles. Due to a number of confounds that necessarily appear in visual detection tasks during visual stimulation (target contrast, temporal attention shifts, pupil size; see below), the absolute detection thresholds of the four conditions (factors flicker regularity and target position) are not suitable for a direct comparison (see also Data sheet S1).

Our results show that the modulation depth increased with increasing inter-trial coherence (ITC) as a measure of entrainment in the rhythmic condition. The ITC in the arrhythmic condition appears not to be linked to the modulation depth. In other words, subjects that showed stronger entrainment also had a higher modulation depth of their behavioral performance, whereas subjects that could not be entrained by the external flicker (low ITC) revealed a behavioral modulation depth close to zero (Figure 4). A modulation depth close to zero reveals either the fact that arrhythmic and rhythmic stimulation did not induce different effects on relative target detection or that the individual EEG phase angles did not differ at the two target onsets of R1 and R2 (see below). This result is in line with previous studies that reported phase dependent behavioral performance as a consequence of visual entrainment (Mathewson et al., 2011; de Graaf et al., 2013; Spaak et al., 2014), which evaluates our measure of behavioral modulation depth.

Additionally, we determined the alpha phase angle at 10 Hz during target onset. Brain responses of the parietal cortex show an individual shift between EEG and stimulation phase as it has previously been described for the auditory system (Henry and Obleser, 2012). We found this individual shift in our data to predict the modulation depth: if the two target presentations (90° and 270°) coincided with local maxima and minima of the alpha oscillation, perception was modified maximally (high modulation depth). Target presentations near or at the zero crossing of the alpha oscillation (0, π, 2π) led to rather similar detection thresholds at the two target positions (see schematic explanation in Figures 1, 5 and the sinusoidal fit in Figure 7).

Furthermore, for subjects with low entrainment (small ITC) the determined phase angle is rather coincidental and not a valid predictor for the modulation depth. In conclusion, both factors, inter-trial coherence and phase angle at target onset play a crucial role in the behavioral modulation depth. Altogether, the ITC and the alpha phase angle at target onset validate the, to our knowledge, newly introduced measure of the modulation depth.

Likewise, the different contrast levels at which targets were presented in conditions R1 and R2 did not bias our results, as the relative measure (R1/R2) was corrected by subtracting the equivalent ratio of the arrhythmic stimulation (A1/A2). Thus, this confound was eliminated from our behavioral measure as well.

Based on these findings we further conclude that phase dependent detection modulation during rhythmic stimulation is not based on phase reset produced by an ERP (Hanslmayr et al., 2007b; Capilla et al., 2011). During arrhythmic stimulation the flicker stimuli around the target presentation were kept constant and identical to the rhythmic condition (gray boxes in Figure 2). A potential ERP-elicited phase-reset would thus be the same for both flicker regularities. As a conclusion, an ERP-elicited alpha synchronization cannot bias our results, because if occurring at all it would be present in both types of stimulation and thus result in a modulation depth at around zero.

As a conclusion, it seems likely that SSVEPs reflect an entrained alpha rhythm. Neural populations oscillate between states of high and low excitability in resting state and have been shown to predict the likelihood of a visual stimulus to be perceived (Hanslmayr et al., 2007a). These neural populations show more or less phase and frequency synchronized activity, with higher synchronization during decreased attention and less synchrony when attention is focused on perception (Cooper et al., 2003). The flicker is suggested to entrain this ongoing oscillator or enhance the amplitude by forcing neural populations to oscillate at the external frequency. This induces a predictable detection of targets, presented at specific phases of this entrained alpha rhythm.

However, Mathewson et al. (2012) found that the effect of phase dependent detection can also be gained via arrhythmic stimulation. As our measure only describes a difference of the relative detection modulation during arrhythmic and rhythmic stimulation, we cannot exclude that detection is modulated during arrhythmic stimulation as well, but to a lower extent, which is why Experiment 2 was performed.

Temporal attention describes a mechanism that prepares the brain for upcoming events after an expected time window (Barnes and Jones, 2000; Nobre et al., 2007) and entrainment is often described as a mechanism that creates temporal attention (Lakatos et al., 2008; de Graaf et al., 2013). Likewise, Mathewson et al. (2012) described temporal attention as the underlying mechanism of entrainment. In their study, targets were presented after a rhythmic or an arrhythmic flicker sequence. The (average) frequency of the flicker sequence enhanced perception of targets presented at an inter-trial interval that equals that of the previous flicker (or the average of the inter-trial interval, respectively). In order to find out if indeed arrhythmic stimulation may cause entrainment but to a weaker extent, we here intended to investigate whether, beyond temporal attention, the two types of stimulation elicit different fundamental mechanisms in the brain. Compared to Mathewson et al. (2012), who presented targets subsequent to a fixed stimulation period of 576 ms with a jittered interval of 36–177 ms, in our study temporal attention was strongly reduced due to the continuous block paradigm. Targets were presented every 3–5 s during a 5 min flicker block.

On the millisecond scale, temporal attention may arise from flicker regularity (Barnes et al., 2005; Lakatos et al., 2008; Stefanics et al., 2010). This confounding factor was eliminated by the ratios of the 50% thresholds within the factor flicker regularity (R1 divided by R2 and A1 divided by A2).

The phase dependent performance modulation reported by Mathewson et al. (2012), however, reflects amplitude differences of their behavioral measure between rhythmic and arrhythmic stimulation as well and we cannot exclude that temporal attention, even though reduced to a minimum, may have biased our results (Lasley and Cohn, 1981). Interestingly, Schnuerch et al. (2013) showed, that temporal attention and stimulus intensity do not interact, thus stronger stimulation intensity is not expected to result in stronger temporal attention.

Thus, we performed a second experiment with the exact same parameters but with increased light intensity for the flicker in both the rhythmic and the arrhythmic condition. Based on the findings reported by Schnuerch et al., 2013), a difference in behavioral performance cannot be explained by temporal attention. Furthermore, if both rhythmic and arrhythmic stimulation revealed a superposition of ERPs, changes in the perceptual threshold would change equally for all four conditions and result in a similar behavioral modulation depth, independently of the flicker intensity.

In line with the concept of the Arnold tongue (Pikovsky et al., 2003) we here found a significant increase of the modulation depth when the stimulation intensity was increased. As a function of stimulation frequency and intensity, the Arnold tongue predicts the brain responses of the parietal cortex during external stimulation in case entrainment is the underlying mechanism (Notbohm et al., 2016).

Thus, our finding of increased entrainment (determined via ITC) and an increased behavioral modulation depth in Experiment 2 is interpreted as evidence for both stimulation types causing different mechanisms in the brain. As possible explanation, we suggest that during rhythmic stimulation the intrinsic alpha oscillator is entrained to the external stimulation in a way that cannot be explained purely by temporal attention but may include a bottom-up component that entrains alpha oscillations in addition to attentional modulation (Thut et al., 2006), that has also been shown to interact with the SSVEP (Müller et al., 2003). While arrhythmic stimulation may induce temporal attention effects, we suggest that this bottom-up component of entrainment is not induced via arrhythmic stimulation.

Here, we stimulated all subjects at 10 Hz, independently of their individual alpha frequency. This was mainly due to technical reasons: adjusting the paradigm to the individual alpha frequency would mean that either the flicker on- and off-times would have to differ between subjects (at a refresh rate of 100 Hz, 9 Hz (ca. 111 ms per cycle) can only be produced by e.g., 50 ms (five screens) flicker on and 60 ms (six screens) flicker off (= 9.09 Hz) or the refresh rate would have to alter between subjects, which would then result in different durations of target presentation. We decided to avoid this confound at a cost of differing distances to the individual alpha frequency, which was found to be rather low. Assuming these limitations were not existent, stronger entrainment would be expected altogether, especially for those subjects with greater deviance of the IAF from 10 Hz.

Based on the comparison of the modulation depth between Experiment 1 and 2, we found that rhythmic and arrhythmic stimulations produce fundamentally different responses in the brain. While rhythmic stimulation produces an SSVEP, which is suggested to be based on entrainment, arrhythmic stimulation was not found to substantially interact with the ongoing alpha oscillation. The newly introduced behavioral measure (the modulation depth) allowed us to compare perception at different stimulation intensities. The different stimulus intensities used in Experiment 2 resulted in different degrees of modulation depth which cannot be explained by temporal attention.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.