Evan Lewis-Healey Student Number: 11676760
Supervisor: Dr. Ruben Laukkonen (Vrije Universiteit Amsterdam) Co-assessor: Dr. Aidan Lyon (Universiteit van Amsterdam)
A Thesis
Submitted to the Institute of Interdisciplinary Studies University of Amsterdam
In Partial Fulfillment of the Requirements for the Degree of Master in
Brain and Cognitive Sciences July 2020
Abstract
The reliance on self-report paradigms has been touted as an issue within the study of consciousness, as the act of reporting can influence both perception and neural activation. Researchers have therefore sought to identify and validate electrophysiological signatures of perception that may be used as no-report paradigms, highlighting this as the next requite step in the study of consciousness. In the present study, we aimed to develop a no-report method in conjunction with binocular rivalry, a perceptual phenomenon that occurs when two distinct images are presented dichoptically. Neural activity was recorded with EEG, and the two distinct stimuli used in the task were frequency-tagged with distinct flicker frequencies. This elicited steady-state visual evoked potentials (SSVEPs) at the response frequencies in the EEG signal, which were expected to match the phenomenological percept within binocular rivalry trials. We developed a novel statistical technique drawing on the temporal dynamics of the SSVEP to predict the perceptual switch rate in binocular rivalry trials. We were able to track what the participant saw with extremely high consistency when trials were pooled together (r=.95,
p<.001). We discuss the implications of these findings and propose that this novel method can be
used in future studies to investigate the neuroplastic effects of meditation on the dynamics of binocular rivalry.
Keywords: Binocular rivalry, no-report paradigms, steady-state visual evoked potential,
Introduction
One of the primary goals of consciousness research is to explain and track the neural correlates of phenomenal experience (Tsuchiya et al., 2015). However, previous research has continuously relied on participants to communicate to researchers what they are perceiving using self-report methods. As a result, when attempting to identify the elusive neural correlates of consciousness, a prevailing point is being increasingly cited in contemporary neuroscience: it is important to distill these correlates to the fundamental mechanisms that underpin them (Aru et al., 2012). When asking participants to track their phenomenal experience via self-report, fronto-parietal network activation is associated with metacognition and introspection (Koch et al., 2016) rather than the minimal neural mechanisms necessary for conscious experience to emerge. This evidence therefore demonstrates that the explicit act of reporting can become a confound when attempting to disentangle the neural mechanisms purely associated with conscious awareness. To overcome this issue associated with active reports, researchers have called for more studies that utilise “no-report” paradigms, where (electro)physiological signals are used as reliable
corollaries of perceptual status of specific stimuli.
One popular visual perceptual phenomenon that has been frequently used to study conscious awareness is binocular rivalry (BR; Wheatstone, 1838). BR is a visual perceptual phenomenon that occurs due to the dichoptic presentation of two distinct images. Presenting these distinct images to each eye separately will lead to the two stimuli alternately reaching conscious awareness, as well as the potential fusion of both stimuli for short periods of time during the transition period (also known as ‘mixed percepts’). The popularity of BR in studies of consciousness is due to the fact that it provides a direct measure of what enters individual's conscious awareness, without modulating the stimuli (Frith et al., 1999). BR paradigms have
therefore been used over the past several decades in order to identify necessary factors that permit consciousness (for a review, see Tong et al., 2006). Additionally, BR paradigms have also been used to investigate the effects of phenomena such as subjective value (Balcetis, et al., 2012; Wilbertz et al., 2014) and emotional processing (Alpers & Pauli, 2006; Alpers & Gerdes, 2007; Yoon et al., 2009), on early visual processing. However, much like other studies of
consciousness, BR paradigms have relied on self-report methods to elucidate the phenomenal experience of participants. As stated above, this has become an issue when identifying the neural correlates of consciousness, as medial frontal network activation has been associated with actively reporting the stimulus, rather than conscious awareness of the stimulus in BR trials (Frässle et al., 2014; Frässle et al., 2013).
Binocular Rivalry and Meditation
Another issue with the use of self-report methods is found in a seminal study by Carter et al. (2005). The researchers used BR to investigate how long-term meditation may influence low-level perceptual processing. In their study, experienced Tibetan meditators were recruited to investigate the effects of distinct meditation practices on the dynamics of BR. Practitioners were asked to conduct one of two meditations. One of which was a ‘compassion’ meditation, defined as “a non-referential contemplation of suffering within the world combined with the emanation of loving kindness” (cited from Carter et al., p.1). The other of which was ‘focused-attention’ meditation (FA), defined as the maintenance of selective attention on an object of choice such as the breath (Lutz et al., 2008). After completing one of the meditations, the practitioners then underwent a BR trial. It was found that, after periods of FA meditation, 50% of the practitioners reported extreme increase of perceptual dominance durations (the length of time one stimuli
spends in conscious awareness), in comparison to a control condition without meditation. In addition to this, a greater number of practitioners reported extreme increases of perceptual dominance durations if they conducted FA meditation during a BR trial, with three reporting complete perceptual stability during the whole 5-minute trial. These findings are contradictory to prior results that suggest that selective attention can not facilitate sustained rivalry (Meng & Tong, 2004; Paffen & Alais, 2011), thereby gleaning a fascinating insight into the neuroplastic effects of meditation. However, Carter et al. (2005) required the use of post-hoc verbal reports for BR trials conducted with meditation, as actively reporting the percept via button presses disrupted the practitioners meditative state. Therefore, the reliance on these retrospective reports may undermine the validity of the study, concretely exemplifying the necessity of no-report paradigms in BR research.
Hypotheses from the Predictive Processing Framework
Despite the methodological limitations of the aforementioned study, the findings are supported by theoretical research contextualised in the framework of predictive processing (Friston, 2003; Huang & Rao, 2011). Simply put, predictive processing proposes that the brain is an inference machine, whereby the difference between priors (predictions) and sensory
information form prediction errors, which influences posteriors (expectations). In addition to this, the brain is organised into a predictive processing ‘hierarchy’, where higher layers (such as prefrontal cortical regions) encode increasingly abstract and temporally thick statistical concepts (Corcoran et al., 2020). Hohwy et al. (2008) utilised the predictive processing framework to explain the occurrence of BR. The researchers argued that, due to the existence of a hyperprior in the processing hierarchy, only one stimulus reaches conscious awareness in BR. This hyperprior
encodes the belief that only a single object may exist at one spatiotemporal location. This hyperprior is depicted as a stubborn prediction (Yon et al., 2019), as it is not heavily influenced by the generation of prediction error. Further to this, Hohwy et al. (2008) also argue that the two stimuli alternate in reaching conscious awareness due to the continuous generation of prediction errors from the unperceived stimulus, while the prediction errors from the perceived stimulus are “explained away” through top down expectations.
The neuroplastic effects of meditation on BR, found in Carter et al.’s (2005), study may also be explained within the context of predictive processing. In a predictive processing
framework, directing attention towards an object corresponds with increasing the precision (confidence) of the percept (Feldman & Friston, 2010). This ‘precision-weighting’ mechanism as a function of FA has recently been highlighted in predictive processing accounts of meditation (Lutz et al., 2019; Pagnoni, 2019). As explained above, Hohwy et al. (2008) attribute the perceptual dynamics in BR to the prediction errors of the conscious percept being explained away by top-down influences. Therefore, by directing attention towards the stimulus that is being perceived (through the practice of meditation), prediction errors generated from the conscious percept are upweighted. As a result of this, the alternation rate will greatly reduce as a function of FA meditation, as the prediction errors generated from the stimulus will no longer be
“explained away” due to top down expectations. This is in line with the findings of Carter et al. (2005).
No-Report Paradigms in Binocular Rivalry
In sum, contemporary cognitive neuroscientists have emphasised that the integration of no-report paradigms are crucial within the study of consciousness (Aru et al., 2012; Koch et al.,
2016; Tsuchiya et al., 2015). In a concrete example, the use of a no-report paradigm in BR in conjunction with the study of meditation validates the findings of Carter et al. (2005). Therefore, it will now briefly be explored how previous research has attempted to capture switches in conscious awareness using no-report paradigms that rely primarily on (electro)physiological signatures of perception.
Previously, studies have utilised multivariate pattern analysis (MVPA) within fMRI (Wilbertz et al., 2018; Wilbertz et al., 2017) and EEG/MEG (Baker, 2017; Sandberg et al., 2013) to decode the perceptual state of participants. Within these studies, a classifier is provided with a training set of data, which is used to decode which stimulus the participant is perceiving at a specific time in a test set of data. The issue with this approach, however, is that MVPA studies often require a large data set to train the classifier. For example, Wilbertz et al. (2017) required up to six baseline 180s BR trials for classification training.
Other studies have used eye tracking techniques such as optokinetic nystagmus (OKN; Frässle et al., 2014; Fujiwara et al., 2017; Marx & Einhäuser, 2015) and pupil dilation (Naber et al., 2011). In studies using OKN, the differing dichoptic stimuli move in contrasting directions. When the participant is perceiving one stimulus, eye movements will match the direction of the perceived stimulus, allowing the researcher to track the perceptual status within a BR paradigm. Similarly, if the two different stimuli presented are distinct in luminosity, tracking the dilation of the pupil is also a suitable way to probe the perceptual contents within BR. Despite the
remarkably high accuracy of OKN as a no-report paradigm (e.g. ~88% accuracy; Frässle et al., 2014), the method may not be suitable when used to investigate altered states of consciousness, such as meditation. This is because deep meditative states are cultivated through directing
sustained attention on a specific object of focus (in FA), and the distracting nature of the stimuli used in OKN may disrupt the meditative state, thereby undermining the validity of the results.
Finally, there has been a variety of studies that have used the steady-state visual evoked potential (SSVEP; Alpers et al., 2005; Brown & Norcia, 1997; Jamison et al., 2015; Zhang et al., 2011; Zhang, et al., 2006) to circumvent active reports in BR. The principle of the SSVEP is as follows: when an individual is presented with a stimulus that is flickering at a particular
frequency, neural oscillations will match that specific frequency. Dubbed the response frequency, these neural oscillations are time-locked to when the stimulus reaches conscious awareness. The SSVEP can be applied to BR paradigms, as a flicker frequency can be applied to one (or both) stimuli, allowing the researcher to track the perceptual status of each stimuli in conscious awareness. Typically, these SSVEP extraction processes utilise the “best-electrode approach”, whereby a power spectrum analysis reveals the electrode that yields the highest power for the response frequency. The time series from this specific electrode is then used in subsequent analyses. For the sake of brevity, two of the most recent applications of SSVEPs using EEG in BR are outlined below.
Brown & Norcia (1997) used SSVEPs in a group of eight participants. Within the experiment, cosine gratings were dichoptically presented to participants. One grating was flickering at a frequency of 5.5Hz, whilst the other was flickering at 6.6Hz. The researchers found that the amplitudes of the SSVEPs followed an anticorrelation pattern when perceptual rivalry occurred. They were able to corroborate this by correlating the amplitude of the right eye stimulus with the left eye stimulus during periods of rivalry binned at 0.9s, finding that the amplitude of the two SSVEPs were significantly anticorrelated under conditions of rivalry.
Zhang et al. (2011) also used SSVEPs to investigate whether the phenomenon of rivalry occurs when visual attention is not present. The researchers presented checkerboard stimuli to each eye, both flickering at different frequencies (6.6Hz for the left eye, 7.5Hz for the right eye). The participants observed the stimuli under two conditions: attended and unattended. In the attended condition, the participants simply attended to the two different stimuli, whilst reporting their perceptual status with button presses. In the unattended condition, the participants had to complete a demanding colour-shape conjunction detection task located at the central fixation point, whilst ignoring the checkerboard stimuli. They found counterphase modulation in the two SSVEP time series in the attended condition, but failed to find this counterphase modulation in the unattended condition (figure 1). Moreover, the researchers corroborated this finding by binning the time courses and correlating the amplitudes of the SSVEPs in every bin for all trials. They found a strong negative correlation between the amplitudes of the SSVEPs in the attended rivalry condition, but not the unattended rivalry condition, indicating that attention is required for rivalry to occur. Additionally, the researchers also intuitively used intermodulation frequencies as a corollary of the perception of mixed percepts during rivalry. Mixed percepts are defined as the experience of both stimuli overlapping into conscious awareness, creating a fusion of both stimuli. The intermodulation frequencies are the sum of the two response frequencies, and have demonstrated to have heightened power when two frequency-tagged stimuli are simultaneously perceived (Fuchs et al., 2008; Gundlach & Müller, 2013). Zhang et al. (2011) found that the intermodulation frequencies of the two response frequencies were higher during transition periods of rivalry, where mixed percepts are most often perceived.
Figure 1 (taken from Zhang et al., 2011): A & B) A schematic of the experimental procedure. Rivalry conditions involved dichoptic presentation, and replay conditions involved the presentation of stimuli on a mutually exclusive basis. C & D) A plot of the timeseries in the attended rivalry and replay conditions (respectively). E & F) A plot of the SSVEP timeseries in the
unattended rivalry and replay timeseries (respectively). The researchers showed that, when participants attended to the stimuli, the timeseries moved in counterphase modulation, which closely matched the reported perceptual status of the two stimuli in the rivalry condition. This counterphase modulation was, however, not found when participants did not attend to the stimuli.
Zhang et al.’s study demonstrates how SSVEPs are particularly useful in circumventing the issue of self-report paradigms; by using SSVEPs, the researchers were able to elucidate how binocular rivalry operates without visual attention. This question, however, would not be
answerable through self-report, as actively reporting the phenomenological experience requires visual attention. In addition to this, the application of SSVEPs in BR are a suitable way to probe
the contents of perception in altered states of consciousness, such as during meditation, as, unlike OKN, the stimuli are not distracting to participants.
However, there remains some limitations when using SSVEPs within BR paradigms. First, Brown & Norcia (1997) have highlighted that low signal-to-noise ratio (SNR) is an issue when using SSVEPs within BR, especially over longer time windows. This issue of low SNR is usually negated by averaging trials together. However, this is not possible as the phenomenology of separate BR trials undergo different time courses and would thus cancel out the ‘waxing and waning’ of the SSVEP signatures. Therefore, to provide researchers with more valuable trials, novel methods need to be explored that maximise SNR when using SSVEPs in BR studies. Second, although counterphase modulation of the SSVEP signatures have been demonstrably linked to the conscious awareness of stimuli in rivalry trials (e.g. Wang, Gao & Gao, 2004; Lansing, 1964), previous research has merely presented single and representative trials. Moreover, there has not been a quantifiable way to establish the perceptual switch rate over many trials. We therefore want to contribute to the literature by applying a novel SSVEP
extraction method (Cohen & Gulbinaite, 2017) to a BR paradigm, to investigate the effectiveness of this method in a no-report paradigm.
The novel method, dubbed rhythmic entrainment source separation (RESS), has several advantages over traditional SSVEP extraction processes. First, it maximises the potential signal-to-noise ratio (SNR) of specific frequencies through the application of a spatial filter to the raw time series. This therefore allows more trials to be included in the analysis. Second, it bypasses the issue of finding an electrode/cluster of electrodes, as in the “best-electrode approach”, by using a weighted combination of the electrodes to form a single time series (the RESS
traditional approaches (from now on referred to as the “best-electrode approach”; BEA), the RESS method has never, to the author’s knowledge, been used in a BR paradigm.
Research Questions and Aim of the Present Study
In sum, this thesis primarily aims to contribute to the existing literature by using the novel RESS method in a BR paradigm. Moreover, this study aims to corroborate previous findings that the RESS method is better at extracting SSVEPs than the BEA (Cohen & Gulbinaite, 2017). Therefore, the present study will ultimately contribute by demonstrating RESS as an effective SSVEP extraction method in BR, thereby proving useful in no-report paradigms, which have been highlighted as the next requisite step in the study of consciousness (Tsuchiya et al., 2015; Koch et al., 2016). As this is an exploratory analysis, there are several hypotheses to be tested. First, it is hypothesised that the SNR will be greater using the RESS method in comparison to the BEA. Second, it is expected that the two SSVEPs will move in a counter phase modulation, as displayed in the previous studies. Finally, it is expected that the SSVEPs will provide a useful physiological signal that provides an insight into the contents of conscious awareness during BR trials.
The methods section is divided into two different experiments. Data from experiment one was collected by a previous researcher. Data from experiment two was collected by the author, and several other researchers. The stimuli are the same as in experiment one, but each trial was conducted for exploratory purposes. It is noteworthy that the previous purpose of this research project, and the reason why meditation has been frequently mentioned, was to investigate the effects of different styles of meditation on the dynamics of binocular rivalry. As explored above, the phenomenology of different styles of meditation has influenced the dynamics of BR in expert
meditators (Carter et al., 2005). However, the reliance on post-hoc verbal reports somewhat undermines the findings of this study. Therefore, the eventual goal of this research was to recruit expert meditation practitioners to replicate the previous findings of Carter et al. (2005) using an accurate no-report paradigm. Data collection for experiment two, however, ceased early due to the COVID-19 pandemic. Therefore, the resulting goal of the present study was to validate and develop a no-report paradigm based on data from both experiments, which can subsequently be used in future research. Experiment one and experiment two will first be summarised. Data from both analyses will subsequently be compiled together to present a cohesive set of findings.
Method Experiment One
Experiment one was conducted to explore whether SSVEPs could be used to track the perceptual status in binocular rivalry trials, specifically under conditions of different meditative practices in novices.
Participants
Participants were recruited through Vrije Universiteit Amsterdam. Data was collected from ten participants (four male, mean age of 21.7 years). The following inclusion criteria was applied: under 10 hours of meditation experience, fluency in Dutch, between 18-30 years of age, and no epilepsy or relatives with epilepsy, migraine, vision problems, glasses, colour blindness, amblyopia, or diagnosis of a psychiatric/neurological conditions. The study was approved by the ethics committee of the Vrije Universiteit Amsterdam.
Materials and Procedure
Stimuli were presented to the participants on a 22-inch Samsung SyncMaster2233 monitor in Psychopy 2 (Peirce et al., 2019) on a black and white background. A red and cyan checkerboard stimulus was presented to the left eye and flickering at 12Hz, while a green and magenta checkerboard stimulus was presented to the right eye and flickering at 15Hz (see figure 2 for stimuli). A mirror stereoscope (Geoscope Standard, Stereo Aids) was used to present the stimuli to each individual eye.
The study used a within participants design. There were four separate six-minute BR trials that each participant underwent. The trials were: a control block, a replay block, a focused attention (FA) block, and an open monitoring (OM) block (figure 3). The latter two blocks were preceded by a guided meditation of approximately 17 minutes (in Dutch) pertaining to the specific meditative styles. The manipulation of the instructions, and the guided meditations, served as the dependent variables. The control block was a button press trial, where participants were presented both stimuli simultaneously (figure 2A) and had to report via button press on a keyboard which stimulus they were perceiving. Reporting ‘1’ represented the perception of the left checkerboard, ‘2’ represented a mixed percept, and ‘3’ represented the perception of the right checkerboard. The control block was preceded by a practice block of 60, 120 or 180 seconds.
The replay block (figure 2B) followed the control block. In the replay block, the stimuli were presented individually as a reflection of the button presses in the control block. That is, if ‘1’ was pressed at a latency of 10 seconds into the control block, then the red and cyan
checkerboard stimulus would be presented to the left eye at 10 seconds in the replay block. If a mixed percept was perceived, the participant was presented with both stimuli simultaneously, at
Figure 2: Stimuli used in BR trials for both experiments. A) In rivalry trials, stimuli are presented simultaneously, with the perception modulating from one to the other as a function of time. B) In the replay trials, stimuli are presented individually to each eye, with the perception modulating from one to the other as a function of stimulus presentation.
the corresponding time that the participant perceived it in the control block. The FA block and the OM block followed the replay block and were counterbalanced for each participant. In these blocks, the participants were presented with both stimuli simultaneously, and simply had to observe the stimuli without reporting perceptual status.
Experiment Two
As explained above, data from experiment two are pilot data, with collection being cut short due to COVID-19 restrictions. The data were collected to establish the effectiveness of the RESS method in a BR paradigm. Further to this, the data were collected to determine optimal SSVEP frequencies to present to participants in a future study on meditation practices and visual consciousness. It was deemed necessary to do so, as there is a discrepancy within the literature. Previous empirical research using SSVEP in BR has presented stimuli flickering in low
Figure 3: A schematic of the procedure of experiment one. The control condition was a rivalry trial with button presses. The replay condition was a replay condition with no button presses. FA and OM signified no-report rivalry trials with instructions pertaining to the specific meditation styles. Prior to FA and OM rivalry trials, the participants undertook a guided meditation.
frequency bands (i.e. 6-12Hz; Zhang et al., 2011; Brown & Norcia, 1997). However, Wang, Gao & Gao (2005) demonstrated that, based on SNR and successful SSVEP classification in a BR paradigm, the optimal flicker frequencies for individual participants were above 30Hz. To solve this discrepancy, this pilot data was collected among a broad range of flicker frequencies to determine the optimal SNR.
Participants
Seven participants were included in this analysis. Three participants were recruited through Vrije Universiteit Amsterdam, and the same exclusion criteria as experiment 1 applied (excluding Dutch fluency). Three participants were members of the Slagter lab at Vrije
Materials and Procedure
As the data was collected for exploratory purposes, the participants did not undergo identical experimental conditions. The stimuli were flickering at different frequencies for each trial to determine the combination of flicker frequencies that generated the highest SNR. In addition to this, the length of trials also varied. A summary of these experimental conditions for each participant can be found in appendix A. The materials used in the trials were identical to experiment one.
Participants would undergo two different types of trials. One of which is a rivalry trial, where both stimuli are presented simultaneously (figure 2A), but dichoptically (as explained in experiment one). The participant would either report the stimuli’s perceptual status via button press (i.e. active report) or view the stimuli without reporting perceptual status (i.e. no-report). Button press data was collected from four participants. However, one participants’ button press data was excluded from the analysis. This was due to the participant reporting perceptual switches seven times in a 180s trial, which was deemed an anomalously low number of perceptual switches of a BR trial of this length. When asked to report perceptual status, participants were asked to use only buttons ‘1’ and ‘3’. That is, the experimenters did not ask participants to report mixed percepts. This was justified as reporting all of these experiences within rivalry trials is notoriously demanding to do so accurately, due to the rapidly changing dynamics of BR.
The other trial type was a replay condition. The replay condition was the same as in experiment one (see figure 2B); stimuli were presented individually, rather than simultaneously. However, in these replay conditions the experimenters modulated the stimuli so that their
for a duration of five seconds, excluding 1 participant, who also underwent trials that presented stimuli for a duration of two seconds. This replay condition was necessary to establish that the RESS method could successfully extract the stimulus at the temporal location in which it was perceived.
As the experimental procedures of both experiments have been summarised, the rest of the thesis will now use data from both experiments. If a portion of data analyses only uses trials from one specific experiment, this will be explicitly mentioned, and the choice to do so will be justified.
EEG Data Acquisition and Preprocessing
During both experiments, EEG data was collected for all blocks. EEG data was collected via 64 electrodes, placed on the scalp using the 10/20 BioSemi ActiveTwo system, with a sampling rate of 512Hz. EEGlab (Delorme & Makeig, 2004) was used within MATLAB to preprocess the data. The data was re-referenced by the average of two electrodes placed on the participants earlobes. The data was high-pass filtered at 0.1Hz. Excessively noisy channels (Kurtosis Z-score threshold of 8) were rejected and interpolated using the spherical method. No other preprocessing was applied to remove artifacts such as blinks, as the RESS method
suppresses said artifacts (Cohen & Gulbinaite, 2017).
Rhythmic Entrainment Source Separation (RESS)
The rhythmic entrainment source separation (RESS; Cohen & Gulbinaite, 2017) method was used to extract the SSVEP signal from the EEG data. A MATLAB script from the authors (see mikecohen.com/data) was adapted and modified for the purposes of this paper. The RESS
method is applied through the construction of linear spatial filters that are used to multiply the time series data collected in the trials, which then creates a separate RESS component time series. This RESS component time series is a weighted combination of all electrodes and is a suitable alternative to the best electrode approach (BEA), which simply uses the electrode that possesses the highest power for the frequency of interest. The main advantages of the RESS method are two-fold. First, it maximises the signal at the frequency of interest (i.e. the response frequency), whilst suppressing the noise. Second, it uses a weighted combination of all
electrodes, which allows the RESS component to contain more signal at the designated response frequency, thereby proving advantageous over the BEA.
The data analysis procedure was as follows. The EEG data were temporally filtered at the response frequency, and two reference frequencies (above and below the response frequency). This was done by applying a Fourier transform to the EEG-signal and multiplying this by a Gaussian distribution. The dimensions of the Gaussian distribution can be modified. However, we consistently used a distribution with a full width at half maximum (FWHM) of 0.5 for the response frequency, as this produced the maximum SNR for the response frequencies compared to other FWHMs. The neighbouring frequencies (i.e. reference frequencies) were +/- 2Hz away from the response frequency, with a FWHM of 2. An inverse Fourier transform was then applied to the temporally filtered data, allowing analysis in the time-domain. Covariance matrices were then calculated with the response frequency and the neighbouring frequencies. These covariance matrices are used to compute generalised eigendecomposition. Generalised eigendecomposition is used to find the eigenvector with the largest eigenvalue that maximally differentiates the response frequency and the reference frequencies.
In the original paper (Cohen & Gulbinaite, 2017), the eigenvalues are used as spatial filters by multiplying the electrode time series with the eigenvalues to create the RESS
component. In addition to this, we multiplied the eigenvalues to the temporally filtered data at the response frequency, and applied this whole process to each stimulus frequency, resulting in multiple RESS time series. A justification for this process is as follows. Binocular rivalry trials using SSVEPs contain information about each response frequency (i.e. in a trial with a stimulus flickering at 12Hz, and another flickering at 15Hz, the time series would contain the signal for both response frequencies). Therefore, although the RESS time series suppresses noise, and maximises the signal at the response frequency, signal for the opposing stimulus frequency would still be contained in the original RESS time series. To gain information about the power of the response frequencies in the time-domain, the Hilbert method was used. The Filter-Hilbert method requires the time series data to be bandpass filtered. Therefore, the bandpass filtered data (i.e. of the response frequency point-wise multiplied by a Gaussian distribution of FWHM = 0.5) were multiplied by the eigenvalues. Here we applied a Hilbert transform to the bandpass-filtered time series data and computed the squared absolute values of this Hilbert transform. The subsequent generated time series (from now on referred to as the RESS power time series), was computed for both flicker frequencies found in each trial.
The signal-to-noise ratio (SNR) spectrum and topographical plots were also computed for each RESS component. SNR plots were generated to compare the BEA to the RESS method, and quantitatively investigate whether the latter SSVEP extraction method was advantageous over the former. The generation of topographical plots were necessary to ensure that the highest power was concentrated specifically in occipital electrodes.
Traditional SSVEP Analysis using the “Best-Electrode Approach”
In prior SSVEP research, it is commonplace to simply identify the electrode that maximally responds to the frequency/ies of interest (e.g. Fuchs et al., 2008). To compare the RESS method to the BEA, a Fourier transform was applied to the raw data. The two electrodes within a cluster of 10 electrodes that exhibited the highest power for the frequencies of interest were identified. The 10 electrodes were the occipital electrodes (‘PO7’, ‘PO3’, ‘POZ’, ‘PO4’, ‘PO8’, ‘O1’, ‘O2’, ‘OZ’), electrode ‘IZ’, and electrode ‘PZ’. The narrowband filtered data at the two response frequencies were then used for plotting the time series data, and for subsequent comparative analyses.
Tracking Self-Reported Percepts with Neural SSVEP Signatures
To further validate the RESS method in a no-report BR paradigm, the relationship between turning points in the RESS power time series and the perceptual switches were
investigated. To identify the turning points of the SSVEPs, the moving slope function (D’errico, 2020) was used to calculate the difference between the gradients of each time series over a five data point window. The moving slope function was used with this five-point window as it is more robust to noisier data sequences. Furthermore, points of inflection within the time series are less likely to be included. This created two vectors of gradients (one for each RESS power time series). It was then calculated how many successive data points in these vectors went from positive to negative or vice-versa, signifying a turning point in the time series, creating four variables for each trial. The mean of these four variables was then computed for each trial.
As the turning points of the time series were expected to represent a change in perceptual status of the stimuli, a correlation coefficient was computed between the turning points of the SSVEPs and the perceptual switches experienced in a replay trial. This served to validate the use of the turning points as a corollary of perceptual switches. For further validation of the
relationship between turning points and perceptual switches in rivalry trials, a correlation coefficient was computed between the reported button presses in active report rivalry trials and the turning points in the SSVEP time series. Further to this, as dominance durations have demonstrable inter-trial consistency within participants (Patel et al., 2015), it was expected that perceptual switch rate would be similar in no-report and active report trials within this study. Therefore, another correlational analysis was conducted between the frequency of button presses and the turning points of a separate rivalry trial with no-report. If a correlation was found, this would further strengthen the utility of using turning points as a no-report technique in no-report rivalry trials. In addition to the above correlational analyses, one final analysis was conducted where the turning points and perceptual switches were pooled together for every participant. Within this analysis, the mean number of turning points was computed for every participant, as well as the mean number of perceptual switches. The perceptual switches were quantified via self-report (i.e. active report rivalry trials), or via replay conditions (as illustrated above). Collating all the data together provides a relatively conclusive validation of the strength of association between the turning points of the SSVEPs and the dynamics of BR, ultimately shedding light on the accuracy of our method. All of the above correlations were also calculated using the BEA as an SSVEP extraction method.
Bayesian Analysis
Statistical analyses in this paper will be conducted using JASP (JASP Team, 2020). JASP permits the application of Bayesian statistical analyses, which can have several advantages over conventional null hypothesis significance testing (NHST; Marsman & Wagenmakers, 2017; van Doorn et al., 2019; Wagenmakers et al., 2016; Wagenmakers, 2007). First, Bayesian hypotheses use prior distributions and likelihoods to ascertain the presence or absence of an effect. The presence or absence of an effect is determined through the Bayes factor, which allows
researchers to illustrate in a quantitative manner how likely the data is under the null hypothesis or the alternate hypothesis (van Doorn et al., 2019). Second, if the data is more likely to occur under the alternate hypothesis, posterior distributions and/or confidence intervals may be used to determine the size of the effect. As there is a small sample size due to the interruption of this project, it was further advantageous to use Bayesian statistical analyses to promote accuracy of statistical analyses and to capture the probability that effects are reliable. However, NHST p-values will also be provided alongside Bayesian analyses. This allows researchers that may not be familiar with the reporting of Bayesian statistics to similarly follow the results. For a
comprehensive overview in the reporting of Bayesian analyses, see van Doorn et al. (2019).
Results
Successful SSVEP Extraction and Counterphase Modulation in Replay Conditions
To illustrate the effectiveness of using the RESS method in a BR paradigm, the RESS power time series and the best-electrode time series for the response frequencies in a sample replay trial for a representative participant are plotted in figure 4. In the first two panels of column A, the time series, topographical plots and SNR spectrum are shown for the RESS
(power) components. In the first two panels of column B, the same is plotted for the BEA. The RESS power time series clearly matches the stimulus presentation; the SSVEPs rise and fall with the corresponding stimulus presentation. However, the SSVEPs extracted via the BEA fail to match the stimulus presentation as effectively as the RESS method. Further to this, the SNR for the response frequencies were higher using the RESS method in comparison to the BEA for the sample trial.
To validate the premise that the SSVEPs move in counterphase modulation during the replay conditions, we sought to quantify the correlation coefficients between the average amplitude of the two SSVEPs in 0.5s time bins, as previously conducted by Zhang et al. (2011) and Brown and Norcia (1997). Data from each replay condition (n=7 participants) in experiment two were included in the analysis (n = 42 trials). Replay conditions from experiment one were not included. This was justified as ‘mixed percepts’ were included in the replay conditions, and the presentation of stimuli were not presented at consistent intervals, which may therefore affect the counterphase modulation/correlation coefficients. Each participant had a varying number of trials. Therefore, to prevent violation of independence of assumptions, the correlation coefficient between the amplitudes was calculated for each participant, and the mean correlation coefficient was then computed. However, for transparency, and to compare the correlation coefficients, the statistical analyses will also be presented for the participants data collated together. The time series for the two response frequencies (using the RESS method and the BEA) for each trial were normalised within a range of [-1, 1], and standardised by subtracting the mean of the RESS power time series from each data point. The data were then divided into 0.5s time bins, and the mean was calculated for the two time series for every time bin. A Pearson’s r correlation
Figure 4: A) The two panels of column A are the time series and topographical plots using the RESS method. The time series clearly matches the stimulus presentation within the replay trial. B) The two panels in column B are the time series and topographical plots using the BEA. The time series has periods when the two SSVEPs overlap (e.g. 0-5 seconds), demonstrating less counterphase modulation.
(r= -.39, p<.001) for the RESS power time series in all replay trials in experiment two. The plotting of a prior and posterior distribution was not possible in JASP due to an anomalously high posterior peak. A Pearson’s r analysis revealed that there was no significant correlation between the two response frequencies (r=.02, p=.99) when plotting the power time series
Figure 5: Two regression plots for the normalised and standardised average amplitudes of the two SSVEPs for replay conditions in experiment two. A) A moderate negative corellation was found between the average amplitudes of the left and right stimulus when extracting the SSVEPs using the RESS method (r=-.39). The mean correlation coefficient for all participants was slightly higher (r=-.29) B) No correlation was found when extracting the SSVEPs using the BEA (r=.02). The mean correlation coefficient when calculating separately for all participants was slightly higher (r=.05).
using the BEA. The collated plots can be found in figure 5. However, when calculating the correlation coefficients separately, and computing the mean coefficient, a slightly weaker negative correlation (r=-.29) was found between the average amplitudes of the SSVEPs when extracted via the RESS method. For the BEA, there was no correlation found (r=.05) when the mean correlation coefficient was computed between all participants. This correlation roughly corroborates the findings above, and indicate that the SSVEPs in the RESS power time series moved in counterphase modulation (in relation to the stimulus presentation), whereas the SSVEPS in the BEA failed to do so. The implication of this finding will be further contextualised in the discussion.
Comparison of SNR using RESS and BEA
A paired samples t-test was used to compare the average SNR of all trials pooled together in experiment one and experiment two. After computing the mean of the two response
frequencies for both the RESS method and the BEA, a significant difference was found between the RESS and BEA SNR (t(75)=6.77, p<.001), however the Shapiro-Wilk test of normality reached significance (W=.63, df=75, p<.001), indicating that the data were not normally distributed. Therefore, the natural log transformation was taken for each data point. The log values did not violate assumption of normality (W=.98, df=75, p=.46), and a paired t-test reached significance (t(75)=12.50, p<.001, g=1.15).
A Bayesian paired t-test was performed on the log transformation of the SNR. The prior default prior distribution was selected (a Cauchy distribution with spread r set to 1/√ 2). As a one-sided alternative hypothesis was specified (a prediction that the RESS method yielded a higher SNR than the BEA), the prior distribution was truncated at zero. A Bayesian paired t-test revealed that the log transformation of the data were 1.98e^17 more likely to occur under the alternative hypothesis (that the SNR of the two frequencies are significantly higher using the RESS method than the BEA) than the null hypothesis (that there is no significant difference between the SNR of the RESS method and the BEA). This provides extreme evidence for the alternative hypothesis. The median value of the posterior distribution is 1.41, with 95% credible intervals at 1.09 and 1.73, indicating a large effect size (see appendix B for figures of Bayesian analyses). This demonstrates that the RESS method successfully extracted the SSVEPs with a higher SNR than the BEA.
SSVEPs Partly Match the Percept: A Representative Rivalry Trial
Figure 6 displays the time series for an active report rivalry trial, with SSVEPs extracted using the RESS method and the BEA. Panel A is the timeseries of the SSVEPs when extracted using the RESS method, and demonstrates the ‘waxing and waning’ of the two SSVEPs, which
sometimes match the reported stimulus perception. For example, from around 10-20 seconds the peaks and troughs of the two SSVEPs are in line with the reported stimulus perception (i.e. the peaks of the 14Hz SSVEP align with the 14Hz stimulus perception, and vice-versa). However, there are also periods where the peaks and troughs do not match the percept experienced. Due to the visual inspection of rivalry time series also like this, we sought to forego the use of SSVEPs as a temporally accurate no-report method, and investigate the association between the turning points of the SSVEPs and the perceptual switch rate.
Validating the Turning Point Method for Replay Conditions
A correlational analysis was conducted to ascertain the relationship between turning points in the SSVEPs of the response frequencies and the number of stimulus switches that occurred in the replay conditions. A total of 41 trials were compiled for this correlational analysis (one trial was removed due to an anomalous amount of turning points in the data). The turning points were calculated for the two time series as above, and the perceptual switches for each trial were computed. In an example trial, the trial length was 180s, and the stimuli switched every five seconds. Therefore, the number of perceptual switches experienced was 36 (180/5). To ensure that the independence of observations assumption was not violated, the trials for every participant were collapsed into one data point (total number of participants = 7).
Figure 6: A) The time series of the SSVEPs from an active report rivalry trial from a representative participant using the RESS method. B) The time series of the SSVEPS from the same trial yet extracted through the BEA. In both A & B, there are periods where the SSVEPs match the reported percept (e.g. 10-20 seconds for the RESS power time series). However, the time series do not always accurately reflect the reported phenomenological percept.
A Shapiro-Wilk test revealed that the data were normally distributed (W=.81, df=6,
p=.051). Therefore, a Pearson’s r correlational analysis was conducted. It was revealed that there
was a significant correlation between the stimulus switches and the turning points of the RESS power time series (r=.85, p =.007). Using a Bayesian approach, the alternative hypothesis postulated that there was a significant positive correlation between the number of perceptual switches experienced and the turning points of the SSVEPs. Therefore, the prior distribution was a default stretched beta prior with a width of 1, which was truncated at zero so that only positive correlations were possible. This prior distribution was used in all subsequent Bayesian
correlational analyses. A Bayesian analysis revealed that the data were around 10 times more likely to occur under the alternative hypothesis rather than the null hypothesis. The median of the posterior distribution was 0.71, with the 95% credible intervals falling between 0.17 and 0.97. The correlation plot and posterior distribution are presented in figure 7.
As above, another analysis was conducted between the turning points of the SSVEPs extracted using the BEA and the perceptual switches experienced. The data was collapsed together as above so that the independence of observations assumption was not violated. Again, a Shapiro-Wilk test revealed that the data were normally distributed (W=.92, df=6, p=.49). A Pearson’s r correlation revealed a significant correlation between the BEA response frequencies and the stimulus switches (r=.80, p=.02). A Bayesian analysis also revealed that the data were 6 times more likely to occur under the alternative hypothesis than the null hypothesis. The median of the subsequent posterior distribution was .65, with the 95% credible intervals falling between 0.11 and 0.95 (see appendix C). The analyses above demonstrated that the turning points of the RESS power time series were more strongly associated with the perceptual switches experienced in replay conditions, in comparison to the BEA approach.
Figure 7: A) Scatterplot depicting the relationship between the RESS power time series turning points and perceptual switches experienced. B) Grey dots indicate the prior and posterior density at the test value. The dotted line represents the prior
distribution, and the solid line represents the posterior distribution. The median and the 95% confidence intervals are presented in the top right corner. This wide posterior distribution indicates uncertainty about the ‘true’ correlational value between the variables.
Validating the Turning Point Method in Rivalry Conditions
As it was demonstrated that the turning points were a useful indicator of how many perceptual switches were experienced within the replay trials, the method was also applied to rivalry trials with button presses. Data was used from all active report rivalry trials in experiment one, as well as five active report rivalry trials in experiment two. As above, to ensure that the independence of observations assumption was not violated, multiple rivalry trials from one participant were collapsed into a single data point. Within this analysis, perceptual switches were quantified by taking the sum of the button press data for the left stimulus or the right stimulus. A button press signifying a mixed percept was excluded from this total.
A Shapiro-Wilk test revealed that the data were normally distributed (W=.96, df=8,
p=.81). A Pearson’s r correlation was conducted between the turning points of the RESS power
time series for the two response frequencies, and the number of button presses (indicating the dominance of one stimulus in conscious awareness) reported in rivalry conditions. There was a strong correlation found (figure 8A) between the turning points of the RESS power time series, and the number of button presses during the active report rivalry trials (r=.87, p=.001). A
Bayesian analysis revealed that the data were 43 times more likely to occur under the alternative hypothesis, in comparison to the null hypothesis, providing very strong evidence that there is a significant correlation between turning points in the time series and the frequency of button presses. The median of the posterior distribution (figure 8B) was 0.78, with 95% credible
intervals in the range of 0.34 to 0.97, Therefore, we can be 95% certain that the true correlational value lies within this range.
The same procedure was conducted for the BEA. A Shapiro-Wilk test revealed that the data were normally distributed (W=.95, df=8, p=.73). A Pearson’s r correlation was therefore used. A significant correlation was revealed between the button presses and the number of turning points in the SSVEPs using the BEA (r=.76, p=.009). A Bayesian correlational analysis supported this result. The Bayes factor revealed that the data were 9 times more likely to occur under the alternative hypothesis (that there is a significant correlation between the turning points of the SSVEPs extracted via the BEA and the button presses), than the null hypothesis. The median of the posterior distribution was 0.64, with 95% credible intervals in the range of .15 to . 93 (see appendix C). Comparing the two posterior distributions demonstrates that there is more likely a stronger association between the RESS power time series turning points and the reported button presses, compared to the BEA.
Figure 8: A) A scatterplot denoting a strong relationship between the turning points of the RESS power time series and the perceptual switches reported in active report rivalry trials. B) A relatively wide and skewed posterior distribution of the Bayesian correlational analyses indicates that the true value of the correlation may be weaker than reported.
Validating the Turning Point Method for Trials in No-report BR Trials
To further corroborate this method, it was investigated whether there was a significant correlation between the number of perceptual switches experienced in separate rivalry trials, and the turning points of the SSVEPs in rivalry trials where no button press data was collected. Therefore, within this data set, the button presses for each participant were taken from active report rivalry trials, whereas the turning points were taken from no-report rivalry trials. Data from both experiments were used. Any trials that the participants conducted multiple times were collapsed into a single data point for each participant (n=7).
A Shapiro-Wilk test revealed that the data were normally distributed (W=.95, df=6,
p=.70), therefore a Pearson’s correlational analysis was conducted. A significant correlation was
found (r=.83, p=.011) between the button presses (in separate active report trials) and turning points in the RESS power time series of no-report rivalry trials (figure 9A). Further to this, a
Figure 9: A) A scatterplot denoting the relationship between the inferred perceptual switch rate of participants and the turning points of the RESS power time series in a no-report rivalry trial. B) The Bayes Factor, posterior distribution, and confidence intervals for the Bayesian correlational analysis. The very wide posterior distribution indicates that uncertainty about the ‘true’ correlation between the two variables.
Bayesian analysis was conducted, revealing that the data were 8 times more likely to occur under the alternative hypothesis (that there is a correlation between active report button presses and turning points in the RESS power time series of no-report rivalry trials) than the null hypothesis. This data, therefore, provides moderate evidence for the alternative hypothesis. The median of the posterior distribution was 0.68, with the 95% credible intervals located at 0.14 and 0.96 (figure 9).
A correlational analysis was also conducted for the turning points of the time series using the BEA and the button presses. A Shapiro-Wilk test revealed that the data were not normally distributed (W=.71, df=6, p=.004). A non-parametric correlation test was therefore calculated. A Kendall correlation measure was chosen, as it has demonstrated to be more robust and efficient than Spearman’s rho (Croux & Dehon, 2010). A nonsignificant relationship was found between the two variables (τ=.52, p=.07). A Bayesian Kendall correlation analysis revealed that the data
were around 3 times more likely to occur under the alternative hypothesis, indicating anecdotal evidence of a significant relationship between the two variables. The posterior distribution had a median of .36, with 95% credible intervals falling at .04 and .76 (see appendix C). Again, in comparison to the BEA, statistical analyses demonstrably displayed a stronger association between the turning points of the RESS time series and inter-trial perceptual switch rate in no-report rivalry trials.
Collapsing Trials to Increase Correlation Coefficient
Finally, to determine the strength of the association between the turning points and the perceptual switch rate, and considering there were a small number of participants that could be included in the analysis, all trials were pooled together for a correlational analysis between the turning points and reported or inferred perceptual switches. All trials were collapsed into a single data point for each participant. A total of 13 participants were included for the analysis. A Shapiro-Wilk analysis revealed that the data were normally distributed (W=.95, df=12, p=.56). A Pearson’s correlation was performed, which revealed a very strong positive correlation (figure 10A) between the average button presses and the average perceptual switches (r=.95, p<.001). A Bayesian analysis revealed that the data were 48,639 times more likely to occur under the alternative hypothesis than the null hypothesis, providing extreme evidence for the alternative hypothesis. The median of the posterior distribution is located at .93, with the 95% credible intervals falling at .78 and .99 (figure 10B).
Figure 10: A) A scatterplot denoting an extremely strong correlation between the (average) turning points for participants and perceptual switches experienced across all trial types. B) The Bayes factor, posterior distribution, and credible intervals for the correlational analysis. An extremely high Bayes factor indicates a strong certainty that there is a correlation present, and a narrow posterior distribution conveys certainty that the ‘true’ correlation is extremely strong.
Correlation coefficients were also computed for turning points of the SSVEPs in the best-electrode and the average perceptual switches experienced per participant. A Shapiro-Wilk analysis revealed that the data were normally distributed (W=.88, df=12, p=.07). A Pearson’s analysis revealed that there was also strong positive correlation between the two variables (r=.79, p<.001). A Bayesian analysis revealed that the data were 68 times more likely to occur under the alternative hypothesis than the null hypothesis, providing strong evidence for the alternative hypothesis. The median of the posterior distribution is located at .71, with the 95% credible intervals falling at .78 and .99 (see appendix C). In sum the turning points of the RESS power time series were much more closely related to the perceptual switches, with an extremely strong correlation when collating trials together. Further to this, the correlations between the turning points of the SSVEPs and the perceptual switches were stronger in every trial type when the SSVEPs were extracted via the RESS method (in comparison to the BEA).
Discussion
The present study aimed to compare the RESS method and the “best-electrode approach” (BEA) as SSVEP extraction methods in BR trials, as well as to develop a no-report paradigm for use in future studies investigating the effect of meditation on the perceptual dynamics of BR. It was found that the use of the RESS method, a novel linear spatial filter that utilises a weighted sum of a combination of electrodes, yielded a significantly higher SNR than the electrode with the highest power at the response frequency. The fact that the RESS method was able to
successfully extract SSVEPs with a higher SNR than the electrode that yields the highest power at the response frequencies is consistent with the original findings (Cohen & Gulbinaite, 2017). However, the previous researchers also compare the RESS method to other linear spatial filters that have previously been used in SSVEP research. Within our research, these linear spatial filters were not applied due to the limited amount of time for the research project. What is novel within this research, however, is the finding that the RESS method can be applied to BR trials.
We specifically found that, within replay trials, the SSVEPs extracted through the RESS method moved in counterphase modulation (as reflected through a negative correlation between the average amplitudes of the two response frequencies). However, a negative correlation was not found for the BEA. The RESS method may be superior due to the use of its linear spatial filter; the RESS method is used to maximise the response frequency and minimise the surrounding noise, whereas the BEA does not use any sort of spatial filter. Also, within the replay conditions of this study, many trials presented stimuli flickering within the alpha range (~8-12Hz). This frequency band has previously been avoided in SSVEP research, as it likely contains spontaneous EEG activity, which may interfere with the validity of the signal (Labecki et al., 2016; Wang et al., 2006). However, the RESS method serves to suppress surrounding
noise, whereas the BEA does not. Therefore, endogenous noise within these response frequencies may be more likely to affect the timeseries in the BEA, which may cause the SSVEPs to move in synchrony, rather than in counterphase modulation.
In addition to this, a representative rivalry trial was also presented. It was found that the SSVEPs partially matched the phenomenology of the BR trial. However, the time series were not fully representative of what the exemplary participant reportedly perceived. This may be
explained due to the complex dynamics of BR. Within this representative trial, the participant was asked to only report the dominance of either stimuli, rather than the experience of mixed percepst. Therefore, the dynamics of the phenomenology of BR was not accurately captured. Some researchers have overcome this issue by using a joystick as an analog continuous measure of the perception of stimuli within rivalry trials, rather than a binary button press measure (e.g. (Fahle et al., 2011). This may therefore be interesting to explore in future research, to investigate the association between SSVEPs and the gradual changes in perceptual dominance.
Turning Points as a Highly Accurate Corollary of Perceptual Switch Rate
The current study also aimed to explore techniques that could be used to quantify the perceptual switch rate in both rivalry and replay trials. Within this study, correlation coefficients were computed between the turning points of the SSVEPs and a) button presses in rivalry trials, b) the frequency of perceptual switches in replay trials, and c) expected perceptual switch rate in a no-report rivalry trial. Furthermore, to validate the method, when the data was pooled together for all participants there was extreme evidence for a very strong correlation (r=.95) between the turning points of the SSVEPs and the perceptual switch rate in all types of trials.
The predictive accuracy of the SSVEP turning points as a corollary of perceptual switch rate in BR trials is particularly promising, and advantageous over other no-report paradigms for a number of reasons. For example, as mentioned in the introduction, previous research using MVPA in BR require numerous baseline trials to train the classifier, which still yields a
relatively low classification accuracy - one study could only successfully classify the conscious percept 62% of the time at maximum performance (Baker, 2017). The method highlighted in this study, however, still yields a strong correlation between the turning points of the perceptual switches even when only a single trial is used. Therefore, our turning point method is
demonstrably more effective if only a single trial is to be conducted. Moreover, the use of the RESS method optimises the SNR, thereby allowing more trials to be used within the analyses.
Another reason why the method is advantageous is that it permits the pooling and averaging of trials together, which has not been possible to do in other BR studies using SSVEPs. Again, as mentioned in the introduction, previous SSVEP studies have found that the ‘waxing and waning’ of the SSVEPs match closely with the phenomenal percept of rivalry (e.g. Zhang et al., 2011; Brown & Norcia, 1997), but averaging trials together would mean the counterphase modulation would no longer be temporally accurate when identifying which stimuli was perceived. By using our method, however, many trials can be collapsed together to provide an extremely accurate corollary of the perceptual switch rate; the magnitude of the correlation is reflected in the highly skewed Bayesian posterior distribution (figure 9B).
A Discrete Measurement for Perceptual Switch Rate in No-report Trials
As previous research has demonstrated stability over the course of one session in rates of intra-individual perceptual rivalry (Carter & Pettigrew, 2003; Patel et al., 2015; van Ee, 2005), it
was therefore deemed intuitive to investigate the relationship between the turning points of the SSVEPs and the reported perceptual switch rates in separate trials. Figure 8 provides additional evidence validating this method, as a strong correlation was found. Again, the results support the use of the RESS method over the BEA, as computing a correlation between the turning points of the SSVEPs and the perceptual switches using the BEA yielded an insignificant result. This finding is also important, as previous research has demonstrated that actively reporting the perceptual status of the stimuli can change the dynamics of rivalry (Frassle et al., 2014; Naber et al., 2011). Therefore, finding a strong correlation between inferred perceptual switches and turning points of the SSVEPs provides additional validity when extrapolating the method to a genuine no-report rivalry trial. Additionally, to the author’s knowledge, much of the research that has used no-report paradigms in BR have only been validated their techniques on active report rivalry trials. Therefore, our findings go beyond the previous literature and demonstrate that our technique may be effective in successfully decoding the perceptual switch rate in no-report rivalry trials.
Limitations of the Present Study
The results highlighted above are particularly promising for a pilot study. However, there are some limitations worth mentioning. First, data collection was ceased early due to the
COVID-19 pandemic. Therefore, we were not able to collect the desired number of participants. Psychological science and medicine continues to face a replication crisis (Open Science
Collaboration, 2012; 2015), which has been underscored by low sample sizes (Button et al., 2013; Francis, 2012; Maxwell et al., 2015). Although this statement seems like a tired platitude, it is nevertheless important to mention that the above results should be interpreted with caution. Regardless of the low sample size, however, incorporating Bayesian analyses within studies
enables researchers to somewhat circumvent these issues, and has been encouraged by the scientific community in recent years (Dienes, 2016; Etz & Vandekerckhove, 2016; Shrout & Rodgers, 2018; Verhagen & Wagenmakers, 2014). As explained previously, a Bayesian approach provides a method that allows the quantification of the strength of the evidence for both the alternative and the null hypothesis. Additionally, unlike their frequentist counterparts, Bayesian approaches produce posterior distributions that provide a useful visualisation to convey where the ‘true’ effect may lie. Contextualising this within the present study, we can be most certain that there is a relationship between the turning points and button presses within rivalry trials when the SSVEPs are extracted through the RESS method (figure 7). However, the
posterior distribution is fairly wide, indicating that future research is required to shed light on the true correlational value. However, when pooling together the data, the data provide very extreme evidence for the existence of a correlation between the turning points of the SSVEPs and the perceptual switch rate, with a relatively narrow posterior distribution, indicating that the ‘true’ correlation is very strong.
Despite the overwhelming evidence for the existence of a correlation when pooling the data together, this leads on to a second crucial limitation of the study. Pooling all trials together for each participant required the analysis of a mixture of rivalry and replay trials. This is an issue as we may not conclude that the perceptual switch rate can be inferred through the turning points purely in rivalry trials. Although the correlation between turning points in the rivalry trials and the button presses is demonstrably strong, the posterior distribution is relatively wide, suggesting that a higher sample size would improve our chances of determining a ‘true’ correlation.
Third, and finally, our method is not temporally accurate. While the mean number of SSVEP turning points within a trial provides a discrete variable that demonstrably correlates
strongly with perceptual switches, this may not be used to determine which percept occurs at a specific timepoint. Other no-report BR paradigms, such as OKN and decoding studies, are used as continuous measures of perceptual status in rivalry trials. OKN studies have been highly accurate in predicting the phenomenal percept (~82% of timepoints are accurate in rivalry trials for OKN; Frassle et al., 2014), and may therefore be deemed advantageous over our particular method if researchers aim to use a continuous no-report measure. However, despite this high accuracy in BR studies using OKN, we may briefly touch upon some advantages of using
frequency-tagged stimuli over OKN stimuli. First, OKN stimuli are sinusoidal gratings that move in opposing directions, characterising them as stimuli with solely low-level features. Therefore, due to these low-level features, it may not be possible to use OKN in studies that investigate top-down effects, such as emotional processing, on early visual processing. Contrary to this,
although the stimuli used within the present study are composed of low-level visual features, SSVEPs have recently been used to predict the phenomenal experience of complex visual stimuli (de Heering et al., 2019), thereby demonstrating a wider stimulus catalogue that can be used with the SSVEP technique in BR. Second, as explored in the introduction, the stimuli used within OKN are particularly distracting. This issue is particularly pertinent when seeking to investigate how altered states of consciousness, such as meditation, may affect perceptual switch rate within BR. This is due to the consistent movement of the stimuli becoming a distraction, thereby potentially confounding the effect of the meditation or other altered states of consciousness. This demonstrates that the use of SSVEPs as a no-report paradigm is more suitable to study the effects of altered states of consciousness on the dynamic of BR.
