Abstract
Gamma range activity in human visual cortex is believed to play a major role in cognitive functions, such as selective attention. Although recent studies have revealed substantial variability in gamma activity, its origins are still unclear.
We investigated whether variability in stimulus-induced gamma activity is related to the spontaneous dynamics of resting-state networks using Hidden Markov Modelling. The magnetoencephalogram (MEG) of 15 healthy participants was recorded at rest and while they were performing a task involving a visual stimulus inducing strong, narrow-band gamma activity. Brain states were inferred from the task’s baseline periods and from resting-state recordings, respectively.
Our results show how network states are related to the amplitude of stimulus-induced gamma responses. Across trials, we found an association between the amplitude of gamma responses and the brain state occurring immediately prior to stimulus presentation. Strong gamma responses followed a state characterized by prominent delta/theta oscillations in parieto-occipital regions and comparably weak alpha activity. Across subjects, the overall probability of visiting this state in the baseline period, i.e. the individual preference for this state, correlated positively with the amplitude of the trial-averaged gamma response. Remarkably, this relationship persisted when states were inferred from resting-state recordings rather than the task’s baseline.
In summary, both within- and across-subject variability in stimulus-induced gamma activity can in part be explained by the ongoing dynamics of whole-brain network states. Fast, pre-stimulus modulations of brain states account for differences between trials while stable, individual state preferences account for differences between subjects.
Introduction
Narrow-band gamma activity has been observed in numerous species and brain areas with various recording techniques (1), including M/EEG recordings in humans (2). It has been proposed to play a role in a variety of cognitive processes, including attention (3, 4), feature binding (5, 6), memory encoding (7, 8), memory retrieval (9, 10), decision-making (11, 12), and reward processing (13, 14).
Like any physiological response, stimulus-induced gamma activity varies within and between subjects. Within-subject variability of stimulus-induced gamma responses is substantial. Invasive recordings in monkeys (15) and humans (16) revealed that gamma responses vary markedly from trial to trial. Overall, single-trial gamma responses have been described as transient events of varying amplitude, duration and frequency, suggesting that the trial average, which resembles a continuous oscillation, does not capture the actual physiological processes engaged in single trials (17, 18). Although potentially misleading about the nature of gamma responses, averaging across trials results in a remarkably reproducible pattern within individuals, as shown by MEG studies measuring trial-average gamma responses in human visual cortex repeatedly in the same subjects (19, 20). Between subjects, in contrast, the trial-average response differs markedly with respect to amplitude, frequency and bandwidth (20) and this between-subject variability has been shown to have a relatively strong genetic basis (21).
The most common approach to studying gamma-band activity in humans is to compare trial-or subject-averages across experimental conditions (e.g. 22, 23). In this framework, within- and between-subject variability is usually not a parameter of interest. The present study, in contrast, focuses on the variability of gamma responses and how it may be related to ongoing network activity immediately prior to stimulus onset and in the resting-state (before/after task performance). We aimed at answering two major research questions. The first question, relating to variability across trials, is whether the strength of the gamma response depends on the network state immediately preceding stimulus onset. In other words, could gamma responses differ across trials because the pre-stimulus brain state varies from trial to trial? Previous M/EEG studies have already revealed an influence of pre-stimulus oscillations (typically, ≤ 1s before stimulus onset) on behavioural performance in perception tasks (24–26), suggesting that a similar influence might be exerted on stimulus-induced brain responses. The second question, relating to variability across subjects, is whether the amplitude of the trial-average gamma response is related to individual phenotypes of network dynamics. In other words, do individuals differ in their gamma response because some subjects spend more time in certain network states than others? Unlike the first question, the latter does not address the immediate, pre-stimulus period, but temporally stable features of whole-brain network activity. Similar stable features of network activity have been found to predict stimulus-induced brain responses in functional magnetic resonance (fMRI) studies (27, 28).Here, we sought to find neurophysiological correlates at higher temporal resolution using MEG imaging.
In contrast to previous M/EEG studies, we did not restrict our analysis to a specific brain area or frequency band; instead, we studied network activity in a wide frequency range (1-35 Hz) with Hidden Markov Models (HMMs). HMMs are probabilistic sequence models that specialise in finding recurring patterns in multivariate data (29). Unlike sliding-window approaches, they can reveal fast state changes present in multichannel, electrophysiological recordings (30–33). HMMs describe the dynamics of brain activity as a sequence of transient events, each of which corresponds to a visit to a particular brain state. For each state, the HMM infers a time-course that describes the probability of that state being active. Furthermore, each state is characterized by a unique spatio-spectral profile.
In summary, HMM brain states can be considered a compact description of multi-faceted, recurring patterns in dynamic network activity. HMMs have been widely used in a variety of applications, such as the decoding of speech (34), the comparison of nucleotide sequences (35) or the detection of pathological brain signals (36).
The paradigm and rationale of the present study are illustrated in Fig. 1. In short, MEG data were acquired from 15 healthy participants while they performed a reaction time task. Subjects were presented with an inward-moving, circular sine wave grating, known to induce strong gamma activity in visual cortex (19). They were instructed to press a button as soon as they detected an increase in grating speed. In addition, two resting-state MEG measurements were obtained: one before and one after the task. Whole-brain network states were derived from 1-35 Hz ongoing activity in 1) the prestimulus task baseline and 2) the resting-state recordings. The restriction to spontaneous sub-gamma activity was made to prevent the detection of trivial relationships between pre- and post-stimulus gamma activity (see Materials and Methods).
Results
State properties
We assessed the spectral and temporal profile of four states derived from the baseline periods of the task. Whereas it is possible to describe the data using more states, four were adequate for our purposes (justified in Materials and Methods). Fig. 2A shows the power and coherence spectra associated with each state. Although all state spectra were dominated by parieto-occipital alpha peaks, baseline states differed with respect to multiple spectral features.
We investigated the temporal properties of these baseline states. The smallest number of visits for any state-subject combination was 338, i.e. all subjects visited all states repeatedly in the baseline period. On average, a state visit lasted 106 ms. This average lifetime defined the pre-stimulus time window of interest (-106 to 0 ms), which was designed to capture the state last visited before the appearance of the moving grating. Fig. S1 describes additional, time-average state properties.
We next investigated how the state probabilities estimated by the HMM evolved in the baseline period of the task. To this end, we averaged the state probabilities, time-locked to the beginning of the baseline period (fixation-cross onset), across trials. The resulting average, referred to as fractional occupancy (FO), quantifies how often a given state occurred at each point in the baseline period (30). Although HMM inference was performed without providing explicit information about the timing of the experiment, FO changed systematically as stimulus presentation approached, suggesting an effect of stimulus anticipation (Fig. 2B). State 1 was found to be predominant early in the baseline, but its FO decreased over time (mean slope = -0.065, p < 0.001; t-test). State 2’s FO increased over time (mean slope = 0.086, p < 0.001; t-test). The FO of state 3 showed a weak negative dependency on time (mean slope = -0.020, p = 0.02; t-test) and state 4’s FO did not change significantly (mean slope = -0.001, p = 0.87; t-test). We verified that FO was independent of heartbeat and eye blinks (Fig. S2).
Gamma responses and pre-stimulus network state
Next, we investigated whether the spontaneous occurrence of whole-brain network states immediately before grating onset can account for within-subject, trial-to-trial variability of induced gamma responses. As depicted in Fig. 1, the HMM provided a probability for each state at each time point in the baseline period. We averaged these probabilities across the pre-stimulus time window of interest (-106 to 0 ms) and used the average probabilities as weights for the computation of state-specific, weighted trial-averages. This procedure can be considered a soft-assigned, within-subject grouping of trials by pre-stimulus state. Subsequently, we tested whether the resulting state-specific trial averages differed with respect to post-stimulus gamma amplitude. Note that such differences may only occur if there is quantitative relationship between pre-stimulus state and post-stimulus gamma amplitude, since trials were grouped by the former.
As depicted in Fig. 2C, the amplitude of stimulus-induced gamma activity differed across pre-stimulus states (p = 0.013; Friedman test). Post-hoc comparisons revealed that baseline state 2 was associated with stronger stimulus-induced gamma activity than baseline state 4 (p = 0.004; Wilcoxon rank-sum test). This pattern was seen in most individual subjects (Fig. S3) and was not biased by the trial-weighting procedure (Supplementary Material). These results demonstrate that state switching in the baseline period can explain part of the within-subject variability in stimulus-induced gamma responses.
Gamma responses and individual state preferences
To investigate the contribution of baseline states to inter-subject variability, we correlated the power of the trial-averaged, stimulus-induced gamma response with the mean state probability in the entire baseline period of the trial (from 1 to max. 3 s relative to fixation-cross onset; Fig 1). We found that the probability of being in baseline state 2 (the state that elicited strong oscillatory responses within subjects) was positively correlated with trial-averaged gamma power (r = 0.690, p = 0.004), i.e. subjects spending more time in baseline state 2 tended to exhibit stronger stimulus-induced gamma activity on average. The other states showed a weaker, negative correlation (state 1: r = -0.57, state 3: r = -0.32, state 4: r = -0.41). These results demonstrate that state preferences in the baseline period can explain between-subject variability in stimulus-induced gamma activity.
To investigate the link between the amplitude of stimulus-induced gamma activity and resting-state activity, we re-ran the HMM inference on the resting-state recordings preceding and following the task, respectively. The three recordings (rest-pre, task, and rest-post) were recorded in direct succession in most subjects (see Materials and Methods). For both resting-state recordings, we identified a state reminiscent of baseline state 2, characterized by strong power between 1 and 5 Hz and the lack of an alpha peak in the region-average power spectrum (Fig. 3A). Topographically, the 15 Hz peak mapped to bilateral parietal and sensorimotor cortices (Fig. 3B). Similar to the baseline periods (r = 0.690), the probability of being in the high delta/low alpha state at rest was positively correlated with trial-averaged, stimulus-induced gamma power (rest-pre: r = 0.700, p = 0.005; rest-post: r = 0.538, p = 0.046), i.e. subjects spending more time in this state at rest tended to show stronger gamma activity in the task (Fig. 3C). This persisting correlation demonstrates that time-average state probabilities reflect individual state preferences which are stable across several hours and across experimental conditions (cf. Fig. S4).
The gamma-enhancing network state
Our observations suggest the existence of a whole-brain state with an enhancing effect on gamma responses occurring both at rest and in the baseline period of a task. To further characterize this state, we maximized the amount of available information by concatenating the data and the state probabilities from the baseline periods and the two resting state recordings, and we computed the topography of power and coherence in this state (Fig. 4). The gamma-enhancing network state exhibited strong delta/theta power in central parieto-occipital regions and sensorimotor cortex, as well as weak alpha power in all areas posterior to the central sulcus and in the temporal lobes. The spatial distribution of power was remarkably symmetric with respect to the interhemispheric fissure. The topography of coherence was similar to the topography of power in the alpha and beta band, but deviated at lower frequencies. Delta coherence, in particular, was high in left primary somatosensory cortex.
Low posterior alpha power does not explain strong gamma responses
We considered the possibility that the gamma-enhancing network state owes its gamma-enhancing properties solely to low pre-stimulus alpha power in parieto-occipital cortex. To explore this possibility, we split the trials into two groups based on alpha power observed in the cuneus over the last 106 ms before stimulus onset (lower 50% vs. higher 50%). Stimulus-induced gamma power did not differ between these groups within subjects (p = 0.43; Friedman test) and pre-stimulus alpha power did not correlate with stimulus-induced gamma power across subjects (r = 0.008, p = 0.974). Similar results were obtained when comparing three levels of alpha power and when considering all parieto-occipital brain areas instead of only the cuneus (data not shown). These results suggest that low parieto-occipital alpha power does not fully explain the enhancement the gamma response, highlighting the relevance of spontaneous network dynamics provided by the HMM.
Discussion
We have demonstrated that spontaneously occurring network states account for within- and between-subject variability in stimulus-induced gamma activity. In particular, we have provided evidence for a network state favouring strong gamma responses of visual cortex to an inward-moving grating. Stimulus-induced gamma activity was stronger when this state preceded stimulus onset on a given trial. Further, stimulus-induced gamma activity was stronger in subjects visiting this state frequently during the baseline periods of the task or during rest.
The effect of pre-stimulus oscillations on induced gamma activity
An important insight from this study is that stimulus-induced gamma activity is related to prestimulus states derived from activity between 1 and 35 Hz, suggesting that the gamma response depends on slower, pre-stimulus oscillations. These results are in agreement with a recent MEG study demonstrating that post-stimulus gamma lateralization in response to a spatial cue is correlated with pre-stimulus alpha lateralization (37). The authors further showed that the phase of alpha oscillations modulates the amplitude of gamma activity in the pre-stimulus period and that alpha activity in visual cortex is driven by the frontal eye field. Their results support a general framework for inter-area communication, in which gamma activity mediates bottom-up communication and alpha/beta oscillations are markers of top-down influences (38–40). Such frequency-specific communication is believed to enable fundamental aspects of human perception, such as spatial attention, and indeed, both alpha and gamma activity are strongly modulated by attention (41–44). Although our findings argue against alpha as an exclusive mediator of pre-stimulus effects in this paradigm (see below), it is conceivable that brain state dynamics in the baseline period reflect dynamic modulation of attention, mediated by concerted oscillations below 35 Hz.
Network vs. local activity
A crucial feature of our approach is that it allows for relating network activity, rather than local activity, to visual processing. This is achieved by the use of Hidden Markov Modelling, which models the activity of all sources simultaneously and can fully leverage the high temporal resolution of electrophysiological data. Recent MEG studies using HMMs revealed a rich repertoire of fast-changing network states characterized by distinct topographies of spectral power and coupling, many of which were reminiscent of the resting-state networks originally obtained with fMRI (30–33).
HMMs and other whole-brain models have also been applied to describe dynamic connectivity in fMRI data (45, 46).
The ability to investigate network activity allowed a more complete description of spontaneous activity in relation to stimulus processing. Given the highly-interconnected structure of the brain, it is unlikely for the local processes serving the gating of sensory information (such as the modulation of posterior alpha power) to work in isolation. In line with this assumption, we have shown that low posterior alpha power is a major feature of the gamma-enhancing network state, but is in itself not sufficient to explain the predisposition for strong gamma responses.
Spontaneous activity is correlated with stimulus-induced activity
We found an association between stimulus-induced gamma activity and network states occurring in the absence of a stimulus, implying that spontaneous activity could predict individual stimulus-induced responses. This is in agreement with a number of fMRI studies demonstrating interactions between resting-state and task-related activity (47). Resting-state and task-related networks were found to be highly similar across a wide variety of tasks (48, 49). Furthermore, stimulus-induced patterns of activation could be predicted from resting-state activity (27, 28). These studies suggest that task-related activity arises by relatively minor modulations of the basic functional connectome, which was demonstrated to be a robust, individual trait, allowing for accurate identification of individual subjects (50). Neurophysiological activity has seldom been investigated in this context; we only know of one electrocorticography study in non-human primates reporting high similarity between resting-state and stimulus-induced neuronal activity in visual cortex (51).
While fMRI studies on spontaneous activity have mostly, but not exclusively (48, 49), addressed the resting-state, electrophysiological studies in humans have related brain activity occurring immediately before stimulus onset (≤ 1s) to perception. Pre-stimulus alpha and beta oscillatory activity, for example, were found to bias the perception of briefly presented or difficu lt-to-distinguish visual (24, 54, 55) and tactile stimuli (56–59). Unlike resting-state networks, which are usually obtained by collapsing activity over time and thus emphasize stable configurations of brain activity, pre-stimulus activity is believed to reflect processes that vary on a trial-by-trial basis, such as attention and/or stimulus anticipation (43).
In this study, we have assessed the relationship of both pre-stimulus and resting-state activity with stimulus-induced gamma activity. Pre-stimulus brain states were found to affect the amplitude of gamma responses within subjects, suggesting that the dynamics of pre-stimulus brain states reflect fast-changing internal processes distinguishing between trials, such as the level of anticipation. An anticipatory effect is further supported by the fact that state probabilities underwent systematic modulations as stimulus onset approached (Fig. 2).
When considering state probabilities averaged over the entire baseline period rather than the immediate, pre-stimulus interval, we found that the overall fraction of time spent in the state preceding strong gamma responses correlated positively with the amplitude of the individual, trial-average gamma response. Thus, the same brain state, referred to as the gamma-enhancing network state, predicted strong responses within and across subjects. Note that such correspondence between trial- and subject-level is not unexpected, since spending a lot of time in a gamma-enhancing network state increases the probability of responding strongly to stimulus onset in any given trial, thus favoring a strong average response. It is, however, a good indicator that the reported subject-level correlations are not driven by outliers. While it is possible that any brain state is overrepresented in strong responders by chance, it is very unlikely that the same state enhances gamma responses within these subjects (trial-level). Conversely, differences arising by chance within subjects are not expected to translate into a relationship across subjects.
A state very similar to the gamma-enhancing network state observed at baseline was found in the resting-state recordings. Again, the individual preference for this state correlated with the individual gamma response. These observations suggest that the general preference for the gamma-enhancing network state is an individual characteristic that can be estimated from any recording containing spontaneous activity, irrespective of context and time. Provided that future studies confirm its robustness and predictive power in other settings, the probability of visiting the gamma-enhancing network state might turn out to be a highly informative and compact feature of the individual functional connectome, summarizing key aspects in a single number.
Limitations
While this work demonstrates a correlation between resting-state activity and brain responses, it does not attempt to predict brain responses form resting-state activity, as performed in previous fMRI studies (27, 28). Making detailed predictions about multiple response parameters, including frequency band and spatial distribution, in a wide variety of tasks will be an important challenge for future studies.
Another limitation of this study is that it does not relate brain states to behaviour. While the paradigm did involve the measurement of reaction time, we found the variability of reaction times to be unusually large, most likely because subjects occasionally missed the acceleration of the moving spiral and simply pressed the button after a waiting period. An investigation of this matter would require a different paradigm with a more reliable assessment of behaviour.
Furthermore, due to the use of Principal Component Analysis for dimensionality reduction, the method applied here biases the state decomposition towards slow, high-amplitude oscillations (33). Hence, faster rhythms such as beta oscillations are possibly underrepresented, whereas delta and theta oscillations dominate state inference. Future work will be necessary to find similar effects in higher bands.
Conclusions
We have shown that within- and across-subject variability in stimulus-induced gamma activity can in part be explained by brain state dynamics. Spontaneously occurring brain states reflect both fast-changing factors distinguishing between trials and temporally stable factors distinguishing between subjects.
Material and Methods
Participants
15 healthy participants were recruited for this study (21-45 years; 5 female). The study was approved by the Montreal Neurological Institute’s ethics committee (NEU 011-036) and was in accordance with the Declaration of Helsinki. All participants gave written informed consent and were compensated for their participation.
Paradigm
Subjects were presented with a modified version of the visual stimulation paradigm by Hoogenboom et al. (19): An inward-moving, circular sine wave grating with a diameter of 5° accelerated from 1.6 deg/s to 2.2 deg/s at an unpredictable moment between 3-5 seconds after stimulus onset. Subjects indicated that they detected the velocity change by pressing a button with the index finger of the dominant hand. The button press ended the trial and the stimulus was turned off. During the intertrial interval (baseline period), subjects were presented with a central fixation cross. Inter-trial intervals varied between 2 and 4s. A few trials with longer interval (17 – 19 s) were randomly interspersed in the trial sequence for all subjects but P1 (6 – 16 per subject; mean: 13). This was done to facilitate an analysis of the influence of baseline duration, but is not relevant for the analyses reported here.
Experimental Procedure
Each session started with a 5 min resting-state recording with eyes open, which was immediately followed by task practice and recording. Before the start of the reaction time task, participants completed 10 practice trials. The task was divided into 2 – 5 blocks, containing 35 – 78 trials each (mean: 62.85). After each block, participants received a feedback on the accuracy of their responses and had the possibility to take a break. Following the reaction time task, a further 5 min resting-state recording was acquired.
In two subjects (P3 and S006R), additional task data were acquired 6 days and 1 day after the first recording session, respectively. Subject P1 was not recorded in resting state.
Data acquisition
Participants were measured in a seated position with a 275-channel VSM/CTF MEG system at a sampling rate of 2400 Hz (no high-pass filter, 660 Hz anti-aliasing online low-pass filter). Electrocardiography (ECG) and vertical electrooculography (EOG) were recorded simultaneously using MEG-compatible electrodes. Magnetic shielding was provided by a magnetically-shielded room with full 3-layer passive shielding. Participant preparation consisted of affixing 3 head-positioning coils to the nasion and both pre-auricular points. The position of the coils relative to the participant’s head was measured using a 3-D digitizer system (Polhemus Isotrack, Colchester, USA).
A T1-weighted MRI of the brain (1.5 T, 240 x 240 mm field of view, 1 mm isotropic, sagittal orientation) was obtained from each participant either at least one month before or immediately after the session. In case the MRI was obtained before the MEG, a waiting period of 1 month was adhered to in order to prevent potential magnetic contamination.
Preprocessing
Data were preprocessed and analysed using the HMM-MAR (27, 28)* and Fieldtrip (60)† toolboxes for Matlab (The Mathworks). All data were screened visually. Noisy channels and noisy epochs were excluded from analysis. Data were down-sampled to 250 Hz. A 60 Hz discrete Fourier transform filter was applied to remove line noise. Cardiac and eye movement artefacts were isolated by FASTICA (61) and removed in non-automatic component selection.
Source reconstruction
Individual T1-weighted MR scans were aligned to the MEG’s coordinate system, segmented and used for the construction of a single-shell, realistic head model (62). To define a set of source coordinates, the “colin27” template MRI (63) was inflated using FreeSurfer (64) and a cortical mesh consisting of 2052 sources was constructed using MNE (65). The corresponding coordinates in individual head space were obtained by applying the inverse of the normalizing transform matching the individual to the template MR scan. The lead field (forward model) was computed based on the source coordinates and the head model. Subsequently, a Linearly Constrained Minimum Variance (LCMV) spatial filter (66) was computed based on the lead field and the sensor covariance matrix, and data were projected through this filter trial-by-trial. Note that the sign of the beamformer output is arbitrary. Because our analysis requires sign consistency across subjects, we applied a sign flipping procedure to maximize sign consistency; see (31) and (33) for details.
To reduce dimensionality, we grouped sources into parcels, defined by the Talairach Tournoux atlas (52), and carried out all subsequent analyses on the parcel level. First, each source was either assigned to one of 25 bilateral brain areas of interest or discarded from further analysis if it was more than 5 mm away from an area of interest (325 of 2052 sources). The areas of interest consisted of all cortical areas contained in the atlas, with the exception of seven areas at the base of the brain or deep within the interhemispheric fissure, which were assumed to have poor MEG signal quality (rectal gyrus, parahippocampal gyrus, subcallosal gyrus, transverse temporal gyrus, orbital gyrus, and uncus). The 25 bilateral brain areas of interest were further sub-divided into a left- and a right-hemispheric parcel, resulting in 50 cortical parcels of interest (Tab. 1 of the Supplementary Material). The first principle component was extracted from each parcel of interest and magnetic field spread between parcels was reduced by symmetric, multivariate orthogonalization (68).
Stimulus-induced gamma activity
We quantified post-stimulus gamma responses in order to relate them to brain states inferred from slower activity (≤35 Hz) occurring in the pre-stimulus baseline period or the resting-state recordings. Post-stimulus gamma responses were computed by multitaper spectral estimation using 2 Slepian tapers (69). Power was estimated for frequencies between 40 Hz and 100 Hz in a 300 ms sliding window which was moved in steps of 50 ms. We screened post-stimulus parcel activity and identified a frequency band, a time window and a location of interest. Because individual gamma peak frequencies varied markedly across subjects (between 42 and 74 Hz), frequency selection was subject-specific, i.e. we defined an individual gamma band for each subject (individual gamma peak frequency ±10 Hz). The time window of interest was set to 0.6 to 2 s relative to stimulus onset because all subjects were found to exhibit stable gamma activity in this window. The bilateral cunei were chosen as the locations of interest because this was generally the area with the strongest gamma response. For the analyses described in the following, gamma power within ±10 Hz of individual gamma peak frequency was normalized frequency-by-frequency by computing the percent change relative to mean power in the response baseline (-0.5 to -0.2 ms from grating onset) and averaged over frequency, time and locations of interest.
State inference
We selected either the baseline periods of the task, the rest recording preceding the task, or the rest recording following the task for state inference. In case the baseline period was selected, the first second of each trial was removed because it was assumed to contain activity related to the button press of the previous trial. Next, we z-scored and concatenated the data from all subjects in time, resulting in a total of 71.44 min of pre-task rest data (per subject mean: 5.10 min, STD: 1.40 min), 164.85 min of baseline data (per subject mean: 10.99 min, STD: 2.19 min) and 63.47 min of post-task rest data (per subject mean: 4.53 min, STD: 0.69 min). Importantly, we applied a spectral filter with a pass-band of 1 to 35 Hz to ensure that brain states were not based on gamma activity, which might lead to trivial relationships between brain states and gamma responses. For example, without such filtering, a baseline state might be characterized by strong gamma activity. Stimulus-induced, relative increases of gamma amplitude following this state might be low because the gamma amplitude cannot increase much further (ceiling effect).
State inference was performed by applying a Hidden Markov Model (HMM, 25), which was fitted to the data using stochastic variational inference (32). The HMM assigns one set of state probabilities (one probability for each state) to each sample of the multi-channel recording, while simultaneously estimating the parameters of each state from the data. Here, we used a variety of the HMM designed to capture transient patterns of power and phase-coupling, referred to as Time-delay Embedded HMM (TDE-HMM; 33). In this model, each state is characterized by the cross-correlations within a certain window of interest, implicitly containing spectrally-defined patterns of power and phase-coupling. Following (33), the length of the window was chosen to be 15 samples (60ms). As the resulting embedded space is very high-dimensional, Principal Component Analysis was used to reduce dimensionality to 100, i.e. twice the number of parcels.
Similar to the frequency resolution in spectral analysis, the number of states K in a HMM determines the level of detail of the solution. As this study distributed trials across states (see below), we set K=4 to guarantee a reasonable amount of trials per state. Similar results were obtained for K=3.
State properties
Following state inference, we computed the power and coherence associated with each state as detailed in (31). In short, source activity was weighted by state probability before spectral estimation was performed using a multitaper approach, resulting in Fourier coefficients for each parcel and state. These coefficients were used for the computation of power and coherence. For topographic illustrations, power and coherence were interpolated on a 3D-reconstruction of the template brain after computing the relative difference with respect to the mean over states. In case of coherence, we display the average coupling with all other parcels.
For analyses involving fractional occupancy, we first determined the current state for each point in time by selecting the state with maximum posterior probability (posterior decoding). Subsequently, we computed the fraction of time spent in each state. Linear trends in fractional occupancy were revealed for each subject by linear regression analysis and regression coefficients were tested for consistent deviations from 0 using a one-sample t-test.
Analysis of within-subject variability
We hypothesized that the strength of stimulus-induced gamma activity depends on the network state immediately before stimulus presentation (Fig. 1). To test this, we first computed for each state the average state probability in the pre-stimulus time window of interest (-106 to 0 ms), which served as state-specific trial weight. Subsequently, we computed a weighted trial average for each state using these weights. This procedure can therefore be considered a weighted (soft-assigned), within-subject grouping of trials by pre-stimulus state. Next, we tested whether the resulting trial groups consistently differed in post-stimulus gamma amplitude across subjects. This was achieved by running a Friedman test, followed by post-hoc Wilcoxon rank sum tests. Note that trials were grouped by pre-stimulus state, not post-stimulus gamma amplitude, i.e. any consistent difference in gamma amplitude must be due to a relationship between pre-stimulus state and post-stimulus gamma amplitude.
Analysis of between-subject variability
We also assessed whether the amplitude of trial-averaged, stimulus-induced gamma responses is related to state preferences in the baseline periods of the task and/or the rest recordings preceding and following the task. State probabilities were averaged across the entire baseline/rest recording and tested for a linear correlation with the amplitude of the trial-averaged gamma response using a significance test for Pearson’s correlation coefficient (Matlab function corrcoef). Note that a strong correlation with any of the states will induce a correlation of opposite sign with the remaining states, given that the states are mutually exclusive.
Acknowledgments
The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z). DV is supported by a Wellcome Trust Strategic Award (098369/Z/12/ Z). MWW is supported by the Wellcome Trust (106183/Z/14/Z) and the MRC UK MEG Partnership Grant (MR/K005464/1). SB was supported by a Discovery Grant from the Natural Science and Engineering Research Council of Canada (436355–13), the NIH (1R01EB026299-01) and a Platform Support Grant from the Brain Canada Foundation (PSG15-3755). EF is supported by the Volkswagen Foundation (Lichtenberg program 89387).