The frequency gradient of human resting-state brain oscillations follows cortical hierarchies

It is well established that the brain’s cortical areas differ in their cyto- and myeloarchitectonic structure, local and long-range anatomical connectivity, activity and, by consequence, their function (Glasser et al., 2016; Huntenburg et al., 2017). Interestingly, many structural features that distinguish individual brain areas change gradually in an orderly manner across the cortex, leading to spatial feature gradients. The most prominent and best established gradients are evident along the posterior-anterior axis (Eickhoff et al., 2018; Felleman and Van Essen, 1991; Huntenburg et al., 2018). For instance, neuron density decreases and neuronal connectivity increases from posterior to anterior brain areas. These differences have been attributed to differences in neurogenesis for posterior compared to anterior brain areas (Hill et al., 2010; Huntenburg et al., 2018). A similar posterior-anterior gradient has been observed for myelin content, cortical thickness, and gene expression (Burt et al., 2018). Next to the posterior-anterior gradient, other global spatial organization principles have been proposed to explain the variation of microstructural features across the cortex. For instance, Huntenburg et al. suggest a sensorimotor to transmodal gradient as an important intrinsic organizing dimension of human cortex (Huntenburg et al., 2018) reflecting gradual changes in structural features from functionally unimodal (dedicated sensory or motor) areas to higher order, transmodal areas.

In addition to structural gradients as an organizing principle reflecting global cortical organization, it is well acknowledged that cortical areas are structurally connected into larger networks, which often display a hierarchical organization. Cortical hierarchies are typically established based on the degree of microstructural differentiation of the connected areas, and on the classification of the anatomical connections as feedforward or feedback using histological tract-tracing. Early sensory areas with predominantly feedforward outgoing connections are placed at the bottom of the hierarchy and higher order association areas with mostly feedback outgoing connections are placed at the top of the hierarchy (Felleman and Van Essen, 1991; Markov et al., 2014). A noninvasive, but indirect index of these hierarchies is cortical thickness, a macroscopic feature of the cortex, which can be estimated from MRI scans. It has been shown that cortical thickness mirrors global hierarchical organization of the cortex as well as local hierarchies in visual, auditory and somatosensory areas (Jasmin et al., 2019; Wagstyl et al., 2015), and, therefore, could be used as a basis for understanding hierarchy-gradient relationships in the cortex.

The presence of these anatomical gradients raises the question to what extent they are reflected in features of brain activity and brain function. Indeed, it has been shown that cortical areas follow a hierarchical ordering in their timescales of intrinsic fluctuations as for example measured in the autocorrelation of spiking activity (Murray et al., 2014). Sensory areas show faster fluctuations while frontal areas show slower fluctuations. Shorter timescales in sensory areas enables them to reflect dynamic changes in the environment, whereas the longer timescales in prefrontal areas allows for integration of information. Particularly, this gradient of ‘temporal receptive windows’ has been demonstrated in visual (Himberger et al., 2018) and auditory processing (Jasmin et al., 2019) and could be related to the frequency of spontaneous brain oscillations. Oscillations are a prominent feature of brain activity, and have been suggested to play a central role in coordinating neuronal activity (Fries, 2005; Wang, 2010). Similar to many anatomical features described above, the spectral activity patterns have been shown to be characteristic for each brain area (Keitel and Gross, 2016). This is consistent with the view that the individual anatomical structure of a brain area shapes its rhythmic neuronal activity, which led us to hypothesize the existence of a posterior-anterior gradient in the frequency of spontaneous brain rhythms.

Spontaneous rhythms have been studied in the past but typically by focusing on the power in specific frequency bands (Hillebrand et al., 2016; Keitel and Gross, 2016; Mellem et al., 2017). Overall, these MEG studies revealed strongest cortical generators for the dominant alpha rhythm (7–13 Hz) in occipito-parietal brain areas. The beta band (15–30 Hz) shows strongest activity in sensorimotor areas while delta (1–3 Hz) and theta (3–7 Hz) bands are associated with activity in wide-spread areas including frontal cortex.

Here, we adopt a different approach that is based on sophisticated identification of spectral peaks in the power spectra of source-localized resting-state MEG data and included modelling of the 1/f spectral background (Haller et al., 2018). This approach offers two distinct advantages. First, focusing on spectral peaks ensures that results are indeed based on brain oscillations. This is not necessarily the case when using the power in a pre-defined frequency band or using band-pass filtered data. Second, by explicitly modeling the 1/f spectral background across the entire cortex we can dissociate contributions due to aperiodic neuronal background activity from those originating from oscillatory activity.

We used this approach to specifically test the hypothesis of a posterior-anterior gradient in the frequency of spontaneous brain rhythms. We identified the frequencies of the dominant brain rhythm across the cortex in source-localized resting-state MEG data of 187 individuals.

As we describe below, we found spatial gradients of the dominant peak frequency across the cortex following the cortical hierarchy.

This study is the first comprehensive demonstration of frequency gradients across the human cortex using a large set of resting-state MEG recordings. We found that the dominant peak frequency in a brain area decreases significantly, gradually and robustly along the posterior-anterior axis, following the global cortical hierarchy from early sensory to higher order areas. This finding establishes a frequency gradient of resting-state brain rhythms that complements previous anatomical studies reporting a posterior-anterior gradient in microscale and macroscale anatomical features of animal and human cortex (Huntenburg et al., 2018).

Several MEG/EEG studies have demonstrated that alpha activity (~10 Hz) is strongest in occipito-parietal brain areas and theta activity (~5 Hz) strongest in more frontal brain areas (Chiang et al., 2011; Voytek et al., 2010). There is also evidence that the dominant frequencies differ between brain areas (Groppe et al., 2013; Hillebrand et al., 2016; Keitel and Gross, 2016). However, we provide the first comprehensive (in frequency and space) statistical model of frequency gradients in a large resting-state brain activity.

Our results are consistent with a recent invasive study showing a systematic decrease of peak frequency from posterior to anterior brain areas in ECoG recordings of epilepsy patients (Zhang et al., 2018).

A differentiating feature of our approach was that we used a large number of healthy participants (N = 187), reconstructed cortical activity from noninvasive MEG recordings, and considered further anatomical features (i.e. cortical thickness). Notably, estimating the power spectrum in finely parcellated ROIs allowed us an accurate and robust identification of peak frequencies and characterization of their spatial gradients across the entire cortical surface. Importantly, we focus on peaks in the power spectrum that indicate the presence of rhythmicity in the neuronal activity, instead of focusing on predefined frequency bands where these rhythms might be absent. As slope and offset of frequency gradient could dramatically vary across participants, averaging across participants may not yield a reliable representation of PF gradient. Instead, we used mixed effect modelling of PF along the cortical hierarchies, where the between-participant variability was taken into account as a random effect. For example, the peak frequency in occipital brain areas and the slope of the frequency gradient varies across individuals, and thus the intercept and slope of the corresponding least square fit change. These individual differences are specifically modelled by a mixed effect model as random effects. Importantly, a mixed effect model will only show a significant gradient if it is significant across cortical areas at the individual level, and consistent across participants at the group level.

Results of our analyses showed that, just as peak frequency significantly decreased along the posterior-anterior axis, CT significantly increased in the same direction, which resulted in a significant anticorrelation between PF and CT. The observed correlation holds after removing the effect of spatial location (x,y,z). This seems to indicate that PF and CT are more closely related to each other than can be explained by spatial location alone. Since cortical hierarchies do not strictly follow a single linear trajectory in space (e.g. posterior-anterior) our results are consistent with the idea that both PF and CT, follow cortical hierarchies. Indeed, such local spatial gradients have been reported in multiple features of cortex during auditory perception (Jasmin et al., 2019) and visual processing streams (Himberger et al., 2018). From a broader view, local gradients could mirror complex organization of gradients in human cortex and support the approach of global gradient along the sensory to transmodal areas (Huntenburg et al., 2018). On the other hand, posterior-anterior gradient of PF was significant after subtracting CT scores from PF values. This suggests a partial independence of both measures. Since PF is a measure derived from brain activity the reported gradient could be modulated dynamically depending on cognitive state or task demands. Further studies are needed to investigate this in more detail.

We further addressed the question if our results can be explained by the linear superposition of activity from an occipital alpha source and a frontal theta source. Along the posterior-anterior axis, differential superposition of both sources could lead to a frequency gradient, due to imperfect unmixing of the signals. However, our analysis revealed that a significant frequency gradient is already evident within 2–3 cm of V1 where the effect of a frontal theta source (which has on average a lower power compared to occipital alpha) is negligible. Furthermore, A more comprehensive analysis showed existence of this gradient for posterio-pariatal, central, and frontal areas, separately, acknowledging the globally and continuously decreasing nature of the posterior-anterior gradient.

Additional supporting evidence can be drawn from intracranial studies, where the data is directly recorded from cortex. Zhang et al., 2018 have shown that oscillations generally propagate in a posterior-to-anterior direction because they are coordinated by an overall decrease in intrinsic oscillation frequency from posterior to anterior regions (see Figures S6 and 7 of Zhang et al., 2018). Overall, this indicates the existence of a gradual decrease of PF along the posterior-anterior axis.

What is the potential functional role of this frequency gradient? Zhang et al. demonstrated the existence of travelling waves along the frequency gradient (Zhang et al., 2018). Interestingly, they found that local frequencies along the posterior-to-anterior direction are positively correlated with waves’ propagation speed and direction consistent with a proposed model of travelling waves based on weakly coupled oscillators (WCO) (Ermentrout and Kleinfeld, 2001). Travelling waves along the posterior-anterior axis have also been reported during visual stimulation (Alamia and VanRullen, 2019; Lozano-Soldevilla and VanRullen, 2019). These travelling waves might serve to drive neural communication along the cortical hierarchy possibly through nested gamma oscillations thereby linking travelling waves to the concept of pulsed inhibition (Bahramisharif et al., 2013). In addition, travelling waves have been associated with memory consolidation and learning (Muller et al., 2018). It is of interest to note that frequency gradients have been reported previously in the entorhinal cortex (Giocomo et al., 2011; Giocomo and Hasselmo, 2009). Here, a frequency decrease and corresponding travelling waves have been observed in the dorsal-ventral direction and have been related to a representational gradient of spatial scales from coarse to fine (Muller et al., 2018). Indeed, converging evidence across recording methods, species and cortical domains suggests that representations become more ‘integrated’ with decreasing ‘dominant’ frequency of the underlying neuronal population. A prime example is the auditory cortex where response latencies and complexity of processing increase along the posterior-anterior axis (Jasmin et al., 2019). This is also mirrored by an increase in cortical thickness and increased ratio of feedback to feedforward connections along this axis. Similar observations have been made across more widely distributed cortical areas where timescales of intrinsic fluctuations in spiking activity increase from posterior to anterior brain areas (Murray et al., 2014). Not surprisingly, these time scales are largely determined by the time constants of synaptic transmission (Duarte et al., 2017). But interestingly, in a computational model of activity in macaque cortex using anatomical connectivity a gradient of time scales also emerges with short, transient responses to input in sensory areas and slower, sustained responses in higher order areas (Chaudhuri et al., 2015) (see also Kiebel et al., 2008).

Our approach additionally revealed that cortical peak frequencies decrease systematically along the inferior-superior axis. As seen in Figure 1 this seems to result from the fact that higher order frontal areas with lower PF have higher z-coordinates compared to the early sensory areas with higher PF. A similar inferior-superior gradient was also observed for cortical thickness. This finding is supported by a recent study reporting an inferior-superior gradient organization of the CT in human and macaque monkeys (Valk et al., 2020), and has been attributed to the organization patterns expected based on the theory of dual origin (Goulas et al., 2018).

Our detailed analysis was based on the cortical ROIs’ spectral peak with strongest power (PF). However, we identified all peaks in the power spectrum of each ROI. Since spectral peaks indicate the presence of brain rhythms, this data represents a comprehensive overview of these rhythms across the cortex. The histogram of spectral peaks across ROIs and participants provided a data-driven definition of frequency bands. Interestingly, the histogram delineates the classical frequency bands with histogram peaks centering at 4–7.5 (theta), 8.5–13 (alpha), 15–25 (low-beta) 27.5–34 (high-beta) (see Figure 5). This is the first MEG study to our knowledge to identify frequency bands from peak frequencies in a large data set (see Groppe et al., 2013 for a similar approach in a smaller sample of ECoG data).

We further analyzed these specific frequency bands for gradients and found significant posterior-anterior frequency changes in the theta, alpha and beta frequency band. Results in the alpha band mirrored the previous results based on the overall strongest peak frequency. Interestingly, and in contrast to the alpha band, peak frequencies increased along the posterior-anterior direction in the theta and beta frequency band. In the model used by Zhang et al. this would correspond to travelling waves from anterior to posterior brain areas (Zhang et al., 2018) that might represent frequency channels for top-down effects (Michalareas et al., 2016; Wang, 2010).

An alternative explanation for the observed posterior-to-anterior or anterior-to-posterior changes of the band-specific PFs may come from the laminar organization of the cortex, where several layers exhibit distinct frequency profiles (Bastos et al., 2018) and thickness patterns (Wagstyl et al., 2020). In particular, similar to our results for the spatial gradients of band-specific PFs, Wagstyl and colleagues (Wagstyl et al., 2020) have identified both increasing and decreasing gradients of thickness along the posterior-anterior axis for cortical layers, in the somatosensory, auditory, and motor cortex (see Figure 6 of Wagstyl et al., 2020).

In summary, our findings show that peak frequencies of cortical areas form a spatial gradient, which follows the global posterior-anterior hierarchy as well as local anatomical hierarchies. Previous research also points to spatial gradients in multiple features of the human and animal cortex. Further research might explore implications of frequency gradients in different cognitive states, disease, and aging.

We used a publicly available dataset for this study (https://data.donders.ru.nl/collections/di/dccn/DSC_3011020.09_236?0).

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Author details

1. Keyvan Mahjoory

   Institute for Biomagnetism and Biosignalanalysis (IBB), University of Muenster, Muenster, Germany

   Contribution

   Resources, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   For correspondence

   kmahjoory@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0386-1135

2. Jan-Mathijs Schoffelen

   Radboud University Nijmegen, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, Netherlands

   Contribution

   Data curation, Software, Formal analysis, Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0923-6610

3. Anne Keitel

   Psychology, University of Dundee, Scrymgeour Building, Dundee, United Kingdom

   Contribution

   Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4498-0146

4. Joachim Gross

   1. Institute for Biomagnetism and Biosignalanalysis (IBB), University of Muenster, Muenster, Germany
   2. Centre for Cognitive Neuroimaging (CCNi), University of Glasgow, Glasgow, United Kingdom
   3. Otto-Creutzfeldt-Center for Cognitive and Behavioral Neuroscience, University of Muenster, Muenster, Germany

   Contribution

   Supervision, Funding acquisition, Validation, Methodology, Writing - review and editing

   For correspondence

   joachim.gross@uni-muenster.de

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3994-1006

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