University of Dundee No changes in parieto-occipital alpha during neural phase locking to visual quasi-periodic theta-, alpha-, and beta-band stimulation

Recent studies have probed the role of the parieto-occipital alpha rhythm (8–12 Hz) in human visual perception through attempts to drive its neural generators. To that end, paradigms have used high-intensity strictly-periodic visual stimulation that created strong predictions about future stimulus occurrences and repeatedly demonstrated perceptual consequences in line with an entrainment of parieto-occipital alpha. Our study, in turn, examined the case of alpha entrainment by non-predictive low-intensity quasi-periodic visual stimulation within theta(4–7 Hz), alpha(8–13 Hz), and beta (14–20 Hz) frequency bands, i.e., a class of stimuli that resemble the temporal characteristics of naturally occurring visual input more closely. We have previously reported substantial neural phase-locking in EEG recording during all three stimulation conditions. Here, we studied to what extent this phase-locking reflected an entrainment of intrinsic alpha rhythms in the same dataset. Specifically, we tested whether quasi-periodic visual stimulation affected several properties of parieto-occipital alpha generators. Speaking against an entrainment of intrinsic alpha rhythms by non-predictive low-intensity quasi-periodic visual stimulation, we found none of these properties to show differences between stimulation frequency bands. In particular, alpha band generators did not show increased sensitivity to alpha band stimulation and Bayesian inference corroborated evidence against an influence of stimulation frequency. Our results set boundary conditions for when and how to expect effects of entrainment of alpha generators and suggest that the parieto-occipital alpha rhythm may be more inert to external influences than previously

In parallel, a functional role has been ascribed to alpha phase: Cortical excitability waxes and wanes periodically within each alpha cycle (VanRullen et al., 2014;VanRullen, 2016). Stimuli delivered during a specific phase of the cycle may thus experience cortical facilitation (or less inhibition), increasing their likelihood of being detected, relative to stimuli presented during the opposite phase (Mathewson et al., 2009). This process can be adaptive: Transient alpha frequency changes produce phase shifts that serve to accommodate expected upcoming stimulation during optimal alpha phase, i.e. periods of relatively high cortical excitability .
Based on the notion that alpha phase indexes fluctuations in cortical excitability and, consequentially, perceptual outcome, attempts have been made to interact with pre-stimulus alpha activity to influence visual target processing. Recent findings from electrophysiology suggest that alpha phase can synchronize to continuous, rhythmic visual stimulation (Spaak et al., 2014;Gulbinaite et al., 2017);(but see Capilla et al., 2011;Keitel et al., 2014). In terms of behavioural consequences, this has been associated with a greater chance of transient targets being detected when they occur in-phase with the ongoing (Sokoliuk & VanRullen, 2016) or just-ceased alpha-rhythmic visual stimulation (Mathewson et al., 2012;de Graaf et al., 2013;Spaak et al., 2014).
Put differently, targets were detected more often when they occurred at a time at which a stimulus presentation could be expected.
The above findings on alpha phase synchronisation agree with model predictions of how a population of self-sustained neuronal oscillators could entrain to a rhythmic external drive (Thut et al., 2011; also see Herrmann et al., 2016a). For these effects to be explained in an entrainment framework, the following requirements (amongst others) need to be met: (1) Neuronal oscillators must be in place to be able to follow the (periodic) temporal structure of the visual input, eventually leading to a phase synchronisation. Regarding alpha-rhythmic visual stimulation (in the ~10 Hz range), this requirement is easily met because alpha rhythms dominate visual cortex activity (Keitel & Gross, 2016) and the visual cortex response to transcranial magnetic stimulation resonates particularly strongly at its natural eigenfrequencies (Rosanova et al., 2009;Herring et al., 2015).
(2) The external drive needs to be periodic -a feature that has recently been supported experimentally by comparing strictly periodic to irregular stimulation .
The model further identifies influential factors, one of which is the strength of the external drive (Pikovsky et al., 2003). For visual stimulation a strong drive can be quantified as a high peak-to-peak change in luminance or contrast. Another factor, recently suggested to play a central role especially in visual perception, is the task-relevance of the entraining stimulation (Zoefel & VanRullen, 2017).
To date, most studies into the entrainment of endogenous alpha have indeed employed highintensity, strictly periodic stimulation that was task-relevant, i.e. the stimulus phase generated predictions about the occurrence of the target (Mathewson et al., 2012;de Graaf et al., 2013;Spaak et al., 2014;. However, the limiting factors under which entrainment of endogenous alpha occurs or ceases have yet to be examined. This will be necessary in order to comprehensively characterise it as a fundamental neural process that may contribute to visual perception. To date, it remains an open question whether alpha entrainment occurs automatically in natural vision because continuous, ecologically valid stimulation is quasi-periodic at best, does not need to be of high contrast and does not necessarily fall within the alpha frequency range (Kayser et al., 2003;Blake & Lee, 2005), e.g. lip movements during speech (Chandrasekaran et al., 2009;Park et al., 2016).
In the present report, we thus tested whether quasi-periodic contrast modulations of low-intensity visual input produce effects consistent with an entrainment of endogenous alpha rhythms. Data from a recent EEG study allowed us to evaluate the influence of quasi-periodic stimulation within three distinct frequency bands -theta (4-7 Hz), alpha (8-13 Hz) and beta (14-20 Hz) -on properties of the intrinsic alpha rhythm and its functional characteristics (Keitel et al., 2017c). Note that our stimulation was not immediately task-relevant in the sense that stimulus phase had no predictive value for target detection: Participants viewed two stimuli (see Figure 1), one in each visual hemifield, that underwent concurrent quasi-periodic contrast modulations. They were cued to attend to the location of one of the two stimuli, positioned in lower left and right hemifields, and performed a visual detection task.
Our previous EEG analysis revealed that brain responses elicited by these low-intensity stimuli followed their temporal evolution (Figure 1b), thereby suggesting a neural phase synchronisation 1 (Keitel et al., 2017c). Quantifying this synchronisation required calculating a measure of phase locking between the frequency-varying stimulation and the EEG Peelle et al., 2013). A spectral representation of EEG-stimulus locking showed clear peaks within the stimulated frequency ranges. While analysing these data, we noticed that EEG power spectra were virtually unaffected by the stimulation but instead were dominated by the typical alpha peak (see Figure 1d). This suggested the absence of an influence of rhythmic visual input on the generation of intrinsic alpha rhythms in any stimulation condition (theta, alpha, & beta). This observation prompted the present, detailed investigation of the functional and systemic characteristics of the intrinsic alpha rhythm under the different stimulation conditions. More specifically, we re-examined these data for indicators of visual entrainment of endogenous alpha. We focussed on the typical retinotopic alpha lateralisation effect by attention (Kelly et al., 2006;Thut et al., 2006), as enabled by our spatial attention manipulation, and tested whether it depended on the frequency of the stimulation. We further tested whether intrinsic alpha resonates during alpha-band stimulation (Fedotchev et al., 1990;Schwab et al., 2006;Spiegler et al., 2011), i.e. shows relatively greater power increase than theta power during theta-band stimulation and beta power during beta-band stimulation. Lastly we probed individual alpha peak frequency for shifts towards the stimulation's centre frequency as would be expected during alpha entrainment. and right stimuli on a given trial. (c) Left stimulus traversing one CMF peak-to-peak cycle. (d) Spectral profiles of band-limited stimuli within theta (orange), alpha (blue) and beta frequency ranges (purple) and corresponding grand average (N = 17) EEG power spectra during stimulation (grey). Note that a constant was added to stimulus power spectra to match the scale of EEG power spectra for illustrative purposes. Right-most plot: Overlay of EEG power (logarithmic scale) during theta-, alpha-and beta band visual stimulation. Spectra were pooled across electrodes indicated on the inset scalp map. Shaded areas around EEG power spectra depict standard error of the mean.

Participants
For the present report, we re-analysed EEG data and behavioural performance of 17 volunteers recorded in an earlier study (Keitel et al., 2017c) 2 . Participants (13 women; median age = 22 yrs, range = 19 -32 yrs) declared normal or corrected-to-normal vision and no history of neurological diseases or injury. All procedures were approved by the ethics committee of the College of Science & Engineering at the University of Glasgow (application no. 300140020). Volunteers received monetary compensation. They gave informed written consent before participating in the experiment.

Stimulation
Participants viewed experimental stimuli on a computer screen (refresh rate = 100 frames per sec) at a distance of 0.8 m and displaying a grey background (luminance = 6.5 cd/m 2 ). Small concentric circles in the centre of the screen served as a fixation point (Figure 1a). At an eccentricity of 4.4° from central fixation, two blurry checkerboard patches (horizontal/vertical diameter = 6°/4.4° of visual angle) were positioned, one each in the lower left and lower right visual quadrants. Both patches changed contrast dynamically during trials: Stimulus contrast against the background was modulated by varying patch peak luminance between 7.5 cd/m 2 (minimum) and 29.1 cd/m 2 (maximum). On each screen refresh peak luminance changed incrementally to approach temporally smooth contrast modulations (Figure 1b and c) as opposed to a simple on-off flicker (Andersen & Muller, 2015).
Further details of the stimulation can be found in Keitel et al. (2017c).
Contrast modulations were generated for each experimental trial and both patch stimuli independently and obeyed one of three different spectral profiles (Figure 1d). In trials of the thetarhythmic condition, contrast modulation rates varied between 4 -7 Hz, in the alpha-rhythmic condition between 8 -13 Hz and in the beta-rhythmic condition between 14 -20 Hz. Frequencies were limited to maximally change by one bandwidth per second (e.g. ~3 Hz/sec for theta-rhythmic stimulation). Frequency modulations were controlled to be maximally uncorrelated between concurrently presented stimuli (Pearson correlation coefficient r < 0.05). Note that the experiment further featured a condition in which stimulus contrast was modulated at constant rates of 10 and 12 Hz. Corresponding data are reported in the original study and will not be considered in the primary analyses -for an exemplary investigation of alpha functional modulation during strictly rhythmic stimulation see Kelly et al. (2006). This exclusion is based on the fact that the constant-frequency stimulation differs in more than one aspect (strictly rhythmic, consistently distinct frequencies left and right) from the frequency-varying conditions. Therefore, statistical differences arising between conditions cannot be unambiguously attributed to either manipulation. This caveat notwithstanding, the Supplementary Material contains a section Analyses including the strictly-rhythmic stimulation condition that retraces all analysis steps described below including the constant-frequency stimulation conditions for future reference.

Procedure and Task
Participants performed the experiment in an acoustically dampened and electromagnetically shielded chamber. In total, they were presented with 576 experimental trials, subdivided into 8 blocks with durations of ~5 min each. Between blocks participants took self-paced breaks. Prior to the experiment, participants practiced the behavioural task (see below) for at least one block. After each block they received feedback regarding their accuracy and response speed. The experiment was Single trials began with cueing participants to attend to the left or right stimulus (Figure 1a) for 0.5 sec, followed by presentation of the dynamically contrast-modulating patches for 3.5 sec. After patch offset, an idle period of 0.7 sec allowed participants to blink before the next trial started.
To control whether participants maintained a focus of spatial attention they were instructed to respond to occasional brief "flashes" (0.3 sec) of the cued stimulus (= targets) while ignoring similar events in the other stimulus (= distracters). Targets and distracters occurred in one third of all trials and up to 2 times in one trial with a minimum interval of 0.8 sec between subsequent onsets.
Detection was reported as speeded responses to flashes (recorded as space bar presses on a standard key board).

Behavioural data recording and analyses
Flash detections were considered a 'hit' when a response occurred from 0.2 to 1 sec after target onset. Delays between target onsets and responses were considered reaction times (RT). Statistical comparisons of mean accuracies (proportion of correct responses to the total number of targets and distracters) and median RTs between experimental conditions were conducted and reported in Keitel et al. (2017c). In the present study, we further tested how individual alpha power influenced task performance based on these data as described below.

Electrophysiological data recording
EEG was recorded from 128 scalp electrodes and digitally sampled at a rate of 512 Hz using a BioSemi ActiveTwo system (BioSemi, Amsterdam, Netherlands). Scalp electrodes were mounted in an elastic cap and positioned according to an extended 10-20-system (Oostenveld & Praamstra, 2001). Lateral eye movements were monitored with a bipolar outer canthus montage (horizontal electrooculogram). Vertical eye movements and blinks were monitored with a bipolar montage of electrodes positioned below and above the right eye (vertical electro-oculogram).

Electrophysiological data during stimulation
From continuous data, we extracted epochs of 5 s starting 1 s before patch onset (= cue offset) using the MATLAB toolbox EEGLAB (Delorme & Makeig, 2004). In further pre-processing, we excluded epochs that corresponded to trials containing transient targets and distracters (24 per condition) as well as epochs with horizontal and vertical eye movements exceeding 20 μV (~ 2° of visual angle) or containing blinks. For treating additional artefacts, such as single noisy electrodes, we applied the 'fully automated statistical thresholding for EEG artefact rejection' (FASTER, Nolan et al., 2010). This procedure corrected or discarded epochs with residual artefacts based on statistical parameters of the data. Artefact correction employed a spherical-spline-based channel interpolation. Epochs with more than 12 artefact-contaminated electrodes were further excluded from analysis.
From 48 available epochs per condition, we discarded a median of 12 epochs (25 %) per participant with a between-subject range of 5 to 20.5 epochs (10 -43%). Because within-participant variation of numbers of epochs per condition remained small (with a median maximum difference of 8 trials between conditions) trial numbers were not artificially matched.
Subsequent analyses were carried out in Fieldtrip (Oostenveld et al., 2011) in combination with custom-written routines. We extracted segments of 3 s starting 0.5 s after patch onset from preprocessed artefact-free epochs (5 s). Data prior to stimulation onset (1 s), only serving to identify eye movements shortly before and during cue presentation, were omitted. To attenuate the influence of stimulus-onset evoked activity on EEG spectral decomposition, the initial 0.5 s of stimulation were excluded. Lastly, because stimulation ceased after 3.5 s, we also discarded the final 0.5 s of original epochs. The remaining data were further segmented into epochs of 1 s with an overlap of 0.5 s.

Electrophysiological data peri-stimulation
In addition to data allowing EEG analyses during stimulation, we extracted epochs of 6 sec immediately before experimental blocks started and after blocks ended to obtain a measure of the participants' alpha rhythm shortly before and after ('peri-') stimulation using Fieldtrip (Oostenveld et al., 2011). Participants were instructed to remain still during these periods. Before blocks they viewed a 6-sec countdown preparing them for the upcoming stimulation and after blocks they were prompted to patiently expect the processing of their behavioural track record for a similar duration.
Data from the resulting 16 segments was concatenated and cut into epochs of 1 sec with an overlap of 0.5 sec. Artefact-contaminated epochs and channels were rejected by visual inspection (fieldtrip function ft_rejectvisual, method 'summary'). For each participant, we retained more than 100 epochs (range: 102 -171, median = 134) and excluded up to 4 channels (median = 2). After re-referencing the data to average reference, an independent component analysis using the logistic infomax algorithm (Bell & Sejnowski, 1995) served to minimize contamination by blinks and eye movements: Per participant, between 1 and 3 independent components were removed. Globally contaminated channels, removed during visual inspection, were spherical-spline interpolated after component removal.
Note that an ICA for eye artefact removals was not applied on EEG data recorded during stimulation.
Instead trials containing eye artefacts were simply discarded because blinks interrupted the continuous visual input and eye movements may have changed retinotopic projections to visual cortex, greatly influencing the stimulus-driven brain response (Walter et al., 2012).

Figure 2
Analysis flow. Each participants EEG recording was preprocessed differently depending on whether they received visual stimulation or not (i.e. shortly before and after experimental blocks = 'peri'-stimulation).
Preprocessed data entered three main analyses paths (numbered yellow backdrops 1, 2 and 3). Path 1 and 2 extracted individual alpha power and peak frequencies. Path 1 investigated retinotopic alpha power lateralisation during focused spatial attention, allowed a comparison of alpha power between stimulation conditions and provided input for Path 3. Alpha power and peak frequencies extracted along Path 2 were used to regress similar parameters extracted along Path 1. Detailed methods and results regarding Path 3 are documented in the Supplementary Material. * EEG-stimulus locking analyses are described in detail in Keitel et al. (2017c).

Electrophysiological data analyses
EEG data analyses were aimed at identifying modulations of the intrinsic alpha rhythm as a function of stimulation frequency. Different analysis paths are illustrated in Figure 2 and laid out in detail below. In brief, we focussed on the following aspects of the data: First we sought to replicate the typical pattern of hemispheric alpha power lateralisation observed during endogenous shifts of spatial attention to the left or right hemifield positions (Kelly et al., 2006;Thut et al., 2006) and compared attentional modulations between conditions. This step further served to define clusters of EEG sensors on which to conduct subsequent analyses.
Secondly, we correlated alpha power and individual alpha peak frequency (IAF) during stimulation with the same measures peri-stimulation. Data obtained in this step also served to establish links between individual alpha power during stimulation and behavioural performance.
In an additional analysis, we explored single-trial variations in alpha power lateralisation at individual peak frequencies and their influence on neural phase-locking to the visual stimulation All EEG analyses were conducted on frequency-domain data obtained as described in the following.

Spectral decomposition
Epochs of 1 s length, derived from EEG data during-as well as peri-stimulation, were converted to scalp current densities (SCDs), a reference-free measure of brain electrical activity (Ferree, 2006;Kayser & Tenke, 2015), by means of the spherical spline method (Perrin et al., 1987) as implemented in Fieldtrip (function ft_scalpcurrentdensity, method 'spline', lambda = 10 -4 ). Detrended (i.e. mean and linear trend removed) SCD time series were then Hanning-tapered and subjected to Fourier transforms while employing zero-padding in order to achieve a frequency-resolution of 0.5 Hz. We calculated power spectra as the squared absolute values of complex Fourier spectra. IAF was determined based on raw power spectra (see section Alpha power and peak frequency during vs peristimulation below). For further analyses, power spectra were normalised by converting them to decibel scale, i.e. taking the decadic logarithm, then multiplying by 10 (hereafter termed log-power spectra).

Alpha power attentional modulation and lateralisation
We identified two sets of parieto-occipital electrodes, one above each hemisphere, which showed systematic variation in alpha power by attentional allocation as follows: Mean log-power across the range of 8 -12 Hz was pooled over conditions in which participants either attended to the right or left stimulus positions separately yielding two alpha power topographies for each participant. These were compared by means of cluster-based permutation statistics  using N = 1000 random permutations. We clustered data across channel neighbourhoods with an average size of 7.9 channels that were determined by proximity in a planar projection of 3D electrode locations (function ft_prepare_neighbours, method 'triangulation'). The resulting probabilities (Pvalues) were corrected for two-sided testing.
We expected to find a right-hemispheric positive and a left-hemispheric negative cluster of electrodes because we subtracted right-lateralized (Attend-Right conditions) from left-lateralized (Attend-Left) alpha power topographies. This approach yielded two functionally defined left and right parieto-occipital clusters (see Figure 3) that were used in all subsequent analyses.
As for average alpha power within the 8-12 Hz band, we conducted further statistical analyses. A three-way repeated-measures analysis of variances (ANOVA) probed differences in alpha power between hemispheres (left vs right electrode clusters), attended stimulus positions (contra-vs ipsilateral hemifield, with respect to hemisphere) and stimulation frequency (theta, alpha or beta).
In all repeated measures ANOVAs conducted in this study that featured factors with more than two levels, the Greenhouse-Geisser (GG) adjustment of degrees of freedom was applied to control for violations of sphericity (Greenhouse & Geisser, 1959). Original degrees of freedom, corrected pvalues (P GG ) and the correction coefficient epsilon (ε GG ) are reported for significant effects. Effect sizes are documented as ω p 2 (Keren & Lewis, 1979). Further specific contrasts of alpha power modulations (attended minus unattended) against zero employed two-tailed t-tests. The resulting P-Values were Holm-Bonferroni-corrected (reported as P HB ) for multiple comparisons (Holm, 1979).
In addition to the classical frequentist approach described above, we also applied Bayesian inference.
Participants were considered as a random factor.
Crucially, this Bayesian equivalent to an ANOVA allowed us to quantify the evidence that our experimental factors (hemisphere, attended position and stimulus frequency), as well as their interactions, explained variance in the data beyond the random between-subject fluctuations. In other words, we tested whether we have more evidence in favour of a factor having no systematic influence (null hypothesis, H 0 ) on alpha power vs having an influence (alternative hypothesis, H 1 ). For each test, the corresponding Bayes factor (called BF 10 ) shows evidence for H 1 (compared to H 0 ) if it exceeds a value of 3, and no evidence for H 1 if BF 10 < 1, with the intervening range 1 -3 termed 'anecdotal evidence' by convention (Wagenmakers et al., 2011). Inversing BF 10 , to yield a quantity termed BF 01 , serves to quantify evidence in favour of H 0 on the same scale. For BF 10 and BF 01 values < 1 are taken as inconclusive evidence for either hypothesis.

Alpha power and peak frequency during vs peri-stimulation
To test for stimulation-specific effects on alpha-rhythmic activity, we compared two characteristics, individual alpha peak frequency (IAF) and alpha power between EEG data recorded during stimulation and data recorded shortly before and after stimulation.
First, we determined IAF based on raw power spectra for peri-stimulation data, as well as for the three stimulation conditions separately. To this end, we took the second order gradient of power spectra averaged across the two electrode clusters (as extracted in stage 1). Sign-flipped (i.e. multiplied by -1) gradient spectra were then smoothed by means of an 11-point, third-order polynomial Savitzky-Golay filter (Savitzky & Golay, 1964). This procedure was implemented to accentuate peaks in participants with indistinct maxima in raw spectra while providing virtually identical results for participants with clear alpha peaks (see Figure S1). A similar step has been implemented in a recent algorithmic approach of IAF determination (Corcoran et al., 2017).
Individual alpha power (IAP) was extracted as the average spectral power within the band IAF ± 1 Hz from log-power spectra averaged across electrodes. Using IAFs, we further derived a measure of individual alpha lateralisation, for which we subtracted IAP collapsed across sensors of the cluster ipsilateral to the attended position from IAP collapsed across contralateral sensors in each condition.
First, we tested whether peri-stimulation IAF/IAP predicted measurements during stimulation by means of regressions using robust linear fits (Matlab function robustfit) for all three stimulation conditions separately. Linear fits are determined by two coefficients, their intercept (β 0 ) and their slope (β 1 ). The intercept did not have a meaningful interpretation for IAF. We thus standardized (zscored) IAF across participants prior to regression to focus on the slope as a possible indicator of entrainment of endogenous alpha. In the case of individual alpha power, the intercept (β 0 ) could have been an indicator of a general power increase (or decrease) during stimulation. We thus ran regression analyses on non-standardized log-power values.
Statistical significance of regression coefficients was assessed by bootstrapping (N = 1000) two-tailed 95% confidence intervals (CIs) involving the bias-corrected and accelerated percentile method (Efron, 1987) to control for deviations from normality of the underlying bootstrapped distribution. The null hypothesis (H 0 ) was rejected when the bootstrapped CI excluded zero.
Subsequently, when testing for systematic differences between slopes (i.e. between conditions), H 0 was rejected when the CI based on the bootstrapped distribution of slope differences excluded zero.
Due to the post-hoc nature of these tests, CIs were evaluated on a Bonferroni-adjusted significance level of 1-0.05/n (hereafter termed CI BF ) with n = 3, i.e. the maximum number of pairwise comparisons within each family of regressions.
Employing a similar approach, we explored the relationship between individual alpha power during stimulation and behavioural performance in the visual detection task. To this end, we transformed the performance measure (proportion of correct responses (in %)) using a logit-link function as a means of normalisation and removing bounds. Then we tested whether standardized (z-scored) IAP, as well as alpha lateralisation during theta, alpha and beta-band stimulation predicted respective standardised performance measures using robust linear regression. In case of yielding conditionspecific significant regression slopes, these were subjected to pairwise comparisons between conditions as described above.

Attention modulates alpha power retinotopically
Attention modulated alpha power as expected (Figure 3a). In line with previous findings, cluster- Grand average log-power spectra in Figure 3a illustrate alpha suppression effects when participants attended contralateral hemifields (collapsed across left and right electrode clusters) in all three stimulation conditions. Testing these differences (Attended minus Unattended) against zero separately for left and right clusters yielded substantial modulations of alpha power for each stimulation frequency (all six comparisons: P HB < .05, see Figure 3c).

No evidence for an influence of visual stimulation frequency on alpha power
A repeated-measures ANOVA based on the data pooled within each cluster confirmed a general decrease in alpha power when the contralateral stimulus position was attended (main effect Bayesian inference also showed strong evidence for an influence of attended position on alpha power (BF 10 = 4,195,405.000 ± 0.55%). Also, we found strong evidence for an imbalance in overall alpha power between hemispheres (BF 10 = 171.166 ± 0.69%) that the frequentist ANOVA did not capture. In fact, alpha power measured over the right hemisphere (M = -2.807 dB, SEM = ± 1.022) was greater than alpha power measured over the left hemisphere (M = -3.340 dB, SEM = ± 1.029).
However, and in line with the above results, the factor stimulus frequency showed substantial evidence in favour of H 0 , i.e. no effect of stimulation frequency on alpha power (1/BF 10 = BF 01 = 5.962 ± 0.26%). The remaining factors and interactions failed to provide conclusive evidence for H 1 or H 0 (all BF 10 < 0.22).
Note that the absence of an effect of alpha-band stimulation on alpha power precluded further dedicated analyses of an alpha resonance effect, i.e. a greater increase in alpha power during alpha band stimulation than in theta power during theta-band or beta-power during beta-band stimulation. Although our stimulation may have produced increased theta power (see Figure 1d, right-most panel), we did not find a similar effect in the alpha band to compare this increase to.

No evidence for interaction of frequency of visual stimulation with power and peak frequency of intrinsic alpha oscillations
We hypothesised that intrinsic alpha rhythms should be most effectively entrained during alphaband stimulation. One first indicator of pronounced entrainment could have been a resonance phenomenon, expressed as a greater increase in alpha power during alpha-band stimulation than during theta-or beta-band stimulation compared with alpha power when no stimulation was presented (Fedotchev et al., 1990;Schwab et al., 2006;Herrmann et al., 2016a).
Secondly, assuming that alpha generators were indeed contributing to the neural response to the ongoing stimulation, we expected individual alpha frequencies, measured in the absence of stimulation, to be pulled towards the centre frequency of the alpha band stimuli during stimulation (Thut et al., 2011;Herrmann et al., 2016b). This effect of entraining endogenous alpha has recently been demonstrated with transcranial alternating current stimulation (Cecere et al., 2015). Note however that our study was not specifically designed for the purpose of these analyses. Our results should thus be considered exploratory.
In our data, EEG power spectra during stimulation versus immediately before and after stimulation (peri -stimulation) showed comparable properties, characterised by a prominent alpha peak at around 10 Hz in all cases (Figure 4a-d). Topographical representations (averaged across attention conditions for data during stimulation) indicated that the alpha power distribution was highly similar and electrode clusters derived from alpha lateralisation analyses covered bilateral maxima. For further analyses, we determined individual alpha frequency (IAF) and power (IAP) from log-power spectra averaged across electrode clusters. We then tested whether peri-stimulation measures predicted online measures and whether predictions differed between stimulation conditions.

Behavioural performance not coupled to individual alpha power
In the original analysis of the behavioural data, reported in Keitel et al. (2017c), we found overall differences in performance between stimulation frequencies. Put briefly, participants detected target stimuli less accurately during beta-band stimulation and reaction times were found to be increased during theta-band stimulation.
Here Neither alpha power nor lateralisation predicted response speed (median reaction times) in any of the stimulation conditions.

Figure 6
Linear regression: Individual performance in the behavioural task (z-scored, y-axis) during theta-band (a), alpha-band (b) and beta-band (c) stimulation as a function of total alpha power (z-scored, x-axis). Grey dots represent participants. Coloured lines depict a straight line fit and its confidence interval (dashed lines).
Goodness-of-fit of the linear model provided as R 2 along with corresponding P-Value. (d-f) Same as in (a) to (c) but for performance as a function of alpha power lateralisation (z-scored).

DISCUSSION
The present re-analysis of previously published data (Keitel et al., 2017c) examined the influence of quasi-rhythmic ongoing visual stimulation with frequencies in theta-(4 -7Hz), alpha-(8 -13Hz), and beta-bands (14 -20Hz) on the EEG-recorded parieto-occipital alpha rhythm. We found that alpha power showed the typical effects of hemispheric lateralisation when participants attended to left or right stimuli irrespective of visual stimulation frequencies. Also, we compared individual alpha frequency and power measured immediately before and after stimulation (peri-stimulation) with alpha frequency and power during stimulation and failed to reveal effects consistent with a stimulus-driven entrainment of the intrinsic alpha rhythm (Thut et al., 2011;Herrmann et al., 2016a). Below we discuss the implications of our findings as well as possible reasons for why intrinsic alpha remained largely unaffected by our visual stimulation.

Typical functional characteristics of alpha prevail during stimulation
Following the presentation of the cue on each trial, alpha power was modulated in a well-known fashion: A relative decrease in alpha power over parieto-occipital cortices contralateral to the cued location and an ipsilateral increase indicated corresponding covert shifts of spatial attention (Worden et al., 2000;Rihs et al., 2007;Capilla et al., 2012) the quasi-rhythmic stimulation notwithstanding.
Alpha power thus reflected the anticipatory attentional biasing of location-specific neural populations in early visual cortices (Kelly et al., 2006;Thut et al., 2006;Snyder & Foxe, 2010;Gould et al., 2011). Higher alpha power ipsilateral to the attended position likely indicated suppression in visual cortices that received task-irrelevant input. Lower contra-lateral alpha power indexed a relative facilitation of visual input. In the present study, alpha thus retained its known functional characteristics during quasi-periodic visual stimulation irrespective of its spectral content.
Further, we found an imbalance in total alpha power between hemispheres. Higher right-than lefthemispheric alpha power has been consistently observed before (Slagter et al., 2016;Benwell et al., 2017a;Newman et al., 2017) and has been linked to resource depletion within the right-hemispheric dorsal fronto-parietal attention network (the DAN; Sturm & Willmes, 2001;Corbetta & Shulman, 2011). Greater DAN activity relates inversely to alpha power (Sadaghiani et al., 2012;Chang et al., 2013;Zumer et al., 2014). A depletion of DAN resources over the course of the experiment within the right hemisphere may have produced the here observed alpha power imbalance between hemispheres. Although an interesting effect, it was not in the focus of the current study and was thus not further investigated.
Previous studies have also demonstrated linear relationships between behavioural performance and alpha power, i.e. higher power coincides with lower hit rates (Hanslmayr et al., 2005;van Dijk et al., 2008), or its retinotopic lateralisation, i.e. greater lateralisation accompanies higher hit rates (Thut et al., 2006), in target detection tasks. These dependencies were largely absent in our data, possibly due to the specific analysis approach employed here and our measure of behavioural performance.
First, alpha power and lateralisation were evaluated on trials without target presentations making them only an indirect indicator of cortical processing at the time of target onset. Secondly, we measured behavioural performance as the proportion of correct responses, which is a measure of individual accuracy. However, alpha power variability, as an index of baseline cortical excitability (Romei et al., 2008;Haegens et al., 2014), may rather influence the response/perceptual bias, i.e. whether participants report detection or not regardless of the veracity of the percept (Limbach & Corballis, 2016;Benwell et al., 2017a;Iemi et al., 2017;Samaha et al., 2017). Our analysis may thus have been insensitive to other alpha power and performance dependencies.

No evidence for entrainment of the intrinsic visual alpha rhythm by quasi-periodic stimuli
We expected to observe two phenomena, alpha phase locking and alpha resonance if our stimuli were to entrain intrinsic (visual) alpha rhythms. Stimulation in the alpha frequency band indeed produced significant phase locking -but similarly so did theta and beta stimulation frequencies (see Keitel et al., 2017c). Also, theta stimulation produced stronger phase-locking than alpha stimulation.
This precise reflection of stimulus spectral content in the EEG, with a monotonous gradient of decreasing phase-locking from lower to higher frequency bands, speaks against a special proneness of alpha generators in visual cortex (Rosanova et al., 2009;Herring et al., 2015;Keitel & Gross, 2016) to entrain to visual quasi-periodic alpha band stimulation.
Alpha resonance, in turn, should have expressed as a greater increase in alpha power during stimulation within the IAF range (Fedotchev et al., 1990;Schwab et al., 2006) than theta and beta power during theta-and beta-band stimulation, respectively. Entrainment models explain such nonlinear response gains through a population-wide phase alignment, whereby neuronal oscillators with a preferred frequency in the alpha band synchronize with the external drive. This mass synchronization would then shape a rhythmic neural response that can be measured macroscopically (Thut et al., 2006). Evidently, our stimulation failed to produce a detectable alpha resonance. Alpha power was not significantly increased during alpha-band stimulation as compared with theta-or beta-band stimulation. This null-effect further translated into comparable alpha power lateralisation during sustained attention. Additionally, "baseline" alpha power in the absence of stimulation predicted individual alpha power during stimulation similarly in all three quasi-rhythmic conditions.
Bayesian inference confirmed that an effect of stimulation frequency on alpha power was implausible. Note however that demonstrating entrainment effects on power statistically requires higher signal-to-noise ratios than other spectral measures, such as inter-trial phase consistency .
The absence of alpha resonance effects may have been a direct consequence of a lack of phase locking of intrinsic alpha generators: If intrinsic alpha (as opposed to stimulus-related neural activity) entrained to the external drive, this should have led to a synchronization of intrinsic alpha to stimulation. Entrainment should therefore entail an overall shift in individual alpha frequencies (IAFs) when these do not match the spectral profile of the stimulation. However, alpha band stimulation did not pull IAFs towards the stimulation centre frequency (10.5 Hz) in our case. Instead, IAF measured in the absence of stimulation predicted IAF during stimulation comparably well, irrespective of stimulation frequency.
Note however that these effects on frequency may be small and escape the here achieved spectral resolution (0.5 Hz). They may also depend non-linearly on the difference between IAF and stimulation centre frequency, such that participants with IAFs further removed from the centre frequency (10.5 Hz) may be less prone to experience a pull effect. Further, considering that our stimulation was only quasi-rhythmic, i.e. occurred within a band around but not at the centre frequency may have weakened a pull effect additionally. Lastly, work on the role of intrinsic rhythms in tactile perception has led to the argument that focussing on individual peak frequencies only may neglect effects on rhythmic activity beyond the peak (Baumgarten et al., 2017). Also note that the EEG is likely dominated by a strong parieto-occipital alpha generator. However recent research suggests more than one concurrent alpha rhythmic 'mode' involved in visual processing (Keitel & Gross, 2016;Barzegaran et al., 2017). It is therefore possible that our stimulation failed to influence the dominant rhythm but affected a less prominent alpha component that is more difficult to observe given the sparse spatial resolution of EEG recordings. Dedicated source reconstructions in future MEG experiments may shed further light on this issue.

Current results suggest boundary conditions for the entrainment of endogenous alpha generators in the visual system
Taken together, we did not find that intrinsic alpha rhythms entrained to our low intensity quasirhythmic visual stimuli at alpha frequency. It is not clear whether this was a direct consequence of the quasi-rhythmicity of our stimulation. If so, our results would be consistent with a recent claim that only strictly periodic stimulation can produce alpha entrainment .
Alternatively, stimulation intensity could have been too low to force cortical alpha generators to follow the entrainment regime (Pikovsky et al., 2003;Thut et al., 2011;Herrmann et al., 2016a). In line with this assumption, a recent study delivered separate rhythmic trains at rates around (and including) individual alpha frequencies with an orthogonal luminance manipulation and demonstrated the positive influence of stimulus intensity on entrainment .
Note that in , for stimulus intensities greater than 300 cd/m 2 entrainment occurred within a range of stimulus frequencies of IAF ± 2 Hz approximating the dynamic bandwidth of our alpha-band stimulation (8-13 Hz). The intensity however exceeded the maximum luminance of the stimulation employed here (~30 cd/m 2 ) by one order of magnitude. Put differently, our stimulation intensity would have had to be increased ten-fold to expect entrainment effects to emerge while assuming that variations in frequency do not influence the process of entraining endogenous alpha.
Studies reporting neural phenomena consistent with alpha entrainment typically used stimulation parameters that feature one or more of the following properties: Stimulation was of high intensity and employed strictly rhythmic on-off flicker. Also, entraining stimuli were typically presented centrally and therefore close to the fovea ; but see Sokoliuk & VanRullen, 2016) and in isolation (Mathewson et al., 2012; but see Gulbinaite et al., 2017), i.e. in the absence of potentially competing stimuli (Keitel et al., 2013). In contrast, our stimulation consisted of two para-foveal stimuli presented laterally at low intensity. Although luminance was modulated locally, it was the global stimulus contrast that varied (quasi-) sinusoidally over time. In an attempt to formulate boundary conditions, we thus suggest that low-intensity, non-foveal and frequencyvarying stimulation, as employed here, may be insufficient to produce purely stimulus-driven entrainment of endogenous alpha rhythms in the visual system.
Physical stimulus properties aside, previous research has also argued for a top-down aspect in entrainment: rhythmic stimulus presentations may not only entrain brain oscillations directly (bottom-up) but generate predictions about future stimulus occurrences (Nobre, 2001;Thut et al., 2011;Wiener & Kanai, 2016;Breska & Deouell, 2017). In that case, entrainment may be realised through recurring feedback loops that connect higher-order with early visual cortices . A candidate network providing this feedback might be the dorsal fronto-parietal attention system (Corbetta & Shulman, 2011). The quasi-rhythmic nature of our stimulation may have therefore prevented strong and precise temporal predictions about the temporal evolution of the stimulus. Also, the randomness in stimulus frequency fluctuations likely impeded memory-based predictions (Breska & Deouell, 2017; also see Obleser et al., 2017). Moreover, the waxing and waning of stimulus contrast in our design was of little relevance for performing in the behavioural task.
Stimulation phase had no predictive value for target presentation, and target duration (0.3 sec) exceeded the length of a 4-Hz cycle (.25 sec, i.e. the lower boundary of the lowest stimulation frequency used in this study), further precluding potential entrainment effects.
These collective arguments for the absence of intrinsic alpha entrainment effects in our study notwithstanding, we emphasise that we found substantial EEG phase-locking to the stimulation. This neural response was highly specific to the spectral composition of each stimulus (Keitel et al., 2017c) and demonstrated that stimulation was generally strong enough to elicit neural responses. Weighing the absence of alpha entrainment effects against the substantial EEG-stimulus locking in our study, we suggest that the presence of a frequency-following response to a stimulus alone is not sufficient to conclude that intrinsic rhythms, specifically alpha, have been entrained by the stimulation (Keitel et al., 2014).

Boundary conditions challenge role of stimulus-driven visual alpha entrainment in sensory sampling
The current concept of the role of entrained intrinsic rhythms in perception largely borrows from research into auditory perception. Rhythmic, and thus deterministic, auditory stimuli afford efficient neural encoding (Large & Jones, 1999;Schroeder et al., 2010;. For these type of stimuli, entrainment enables precise predictions of future stimulus occurrences through lowfrequency brain-stimulus synchronisation (Henry & Obleser, 2012;. Similar effects of rhythmic stimulation have since been reported for visual perception (Cravo et al., 2013;Calderone et al., 2014;Spaak et al., 2014;Sokoliuk & VanRullen, 2016).
Most important in the present context: speech is naturally quasi-rhythmic. This vital property allows it to convey information. Apart from speech, quasi-rhythms typically compose natural dynamic visual scenes (Kayser et al., 2003;Butts et al., 2007;Mazzoni et al., 2011) and it has been argued that they benefit visual perception more than strictly rhythmic input (Buracas et al., 1998;Blake & Lee, 2005).
Therefore, in an entrainment framework of visual perception it would seem sensible to assume that the cortical generators underlying intrinsic rhythms should resonate with a range of stimulus frequencies even under low-intensity conditions. Consequently, this would allow them to accommodate dynamic changes in quasi-rhythmic input within their preferred frequency range, at least to some extent. It is thus disputable whether visual alpha entrainment can fulfil a role similar to low-frequency entrainment in speech perception, when it can only be produced by strictly periodic stimulation under certain conditions (high intensity, foveal presentation) in an experimental setting.
We point out that drawing immediate parallels between how auditory and visual systems exhibit entrainment entails the implicit assumption that both respond similarly to rhythmicity in sensory input. Challenging this notion, Zoefel and VanRullen (2017) have recently argued that vision and audition may rely on distinct internal sampling strategies that exploit stimulus rhythmicity differently. In contrast to the auditory system, phase-locking to a dynamic stimulus may not be an integral part of the attentional selection process in vision. Instead, the visual system could maintain an autonomous visual sampling strategy that is independent of the stimulus and whose neural signature is the parieto-occipital alpha rhythm. Our paradigm likely promotes such a strategy because the stimulus dynamics are behaviourally irrelevant. Also, we found a tendency of EEG phaselocking to theta-band stimulation to be reduced on trials in which alpha power was high (see Supplementary Material) further suggesting an interplay in cortical visual processing that may rely on the autonomy of stimulus-driven and intrinsic rhythms. In line with this autonomy assumption, van Wassenhove (2016) has recently proposed that the ability of intrinsic rhythms to decouple from (periodicities in) external stimulation may be a vital prerequisite for a stimulus-independent monitoring of the passage of time.
In summary, our findings do not support an entrainment of the intrinsic parieto-occipital alpha rhythm driven by quasi-periodic visual stimulation in the alpha band. We have discussed a number of mitigating factors (quasi-periodicity, low-intensity, task irrelevance of the stimulation) that may have contributed to the absence of effects. We suggest that future studies into visual entrainment may need to take into account that phase synchronisation of neural activity with visual stimulation per se is a necessary but insufficient condition to infer entrainment of intrinsic brain rhythms.

Supporting Information
Additional supporting information can be found in the online version of this article.

Competing interests
The authors declare no competing interests.

Author contributions
CK designed research, performed research, analysed data and wrote the article. JG designed research analysed data and wrote the article. CSYB and GT designed research and wrote the article.

Data accessibility
EEG data are available on the Open Science Framework (OSF) under the URL osf.io/apsyf (Keitel et al., 2017b)