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

The human cortex is characterized by local morphological features such as cortical thickness, myelin content, and gene expression that change along the posterior-anterior axis. We investigated if some of these structural gradients are associated with a similar gradient in a prominent feature of brain activity - namely the frequency of oscillations. In resting-state MEG recordings from healthy participants (N = 187) using mixed effect models, we found that the dominant peak frequency in a brain area decreases significantly along the posterior-anterior axis following the global hierarchy from early sensory to higher order areas. This spatial gradient of peak frequency was significantly anticorrelated with that of cortical thickness, representing a proxy of the cortical hierarchical level. This result indicates that the dominant frequency changes systematically and globally along the spatial and hierarchical gradients and establishes a new structure-function relationship pertaining to brain oscillations as a core organization that may underlie hierarchical specialization in the brain.

The visual system's cortical hierarchy largely progresses along the posterior-anterior 176 direction, and starts in early visual areas in occipital cortex and progresses along the 177 dorsal and ventral streams to anterior areas. Since this progression of cortical 178 hierarchical level coincides with the observed gradient in PF, we tested the hypothesis 179 that the PF gradient is more closely related to cortical hierarchical level than to spatial 180 location. We used cortical thickness (CT) as a proxy for the quantification of the 181 hierarchical level of brain areas (Wagstyl et al., 2015). 182 We used Freesurfer to estimate CT as the shortest distance between corresponding tested for a significant relationship between CT and PF. Robust correlation (r = -0.14, p 192 < 0.001, Figure 3B) and LMEM (t = -13.8, p << 0.001) showed a significant negative 193 relationship between PF and CT. Next, we asked the question if this relationship is still 194 significant after removing from both, PF and CT, the effect of ROI coordinates (x,y,z). 195 This was done by modeling the dependencies of PF and CT respectively on ROI 196 coordinates and computing the residuals PFres and CTres. These residuals describe 197 individual spatial variations of PF and CT that cannot be explained by a linear model of 198 their spatial location. PFres and CTres are still significantly related (LMEM: t = -6.9, p << 199 0.001, Figure 3C) indicating that they are more directly related to each other than can be explained by their individual dependency on location (x,y,z). This result suggests that 201 peak frequency is related to structural features that likely represent cortical hierarchies. showing strong homology to macaques visual areas (V1, V2, V4, MT, DP, TEO, 7A) 209 using the cortical parcellation of Glasser et al. (Glasser et al., 2016). We modelled spatial 210 changes of PF along the visual hierarchy, using LMEM (see method section for details), 211 and found a significant decrease of PF (t = -10.1, p << 0.001) and a significant increase 212 of CT (t = 54.9, p << 0.001, Figure 4A).

213
Previous studies have shown that cortical regions can be contextualized in terms of eight  Ito et al., 2017) we assigned all areas to eight networks. We then averaged PF and CT 0.001; CT: F-stats = 746, p << 0.001). To test whether PF and CT variation follows the 228 sensory-association axis, we used LMEM, with networks designated to 'sensory' and 229 'association' categories (PF: t = -11.1, p << 0.001; CT: t = 14.7, p << 0.001, Figure 4C).

230
Similar to the significant difference of T1w/T2w between sensory and association 231 networks we also see significant differences in PF and CT. As expected PF is higher in 232 sensory areas compared to association areas while an opposite effect is observed for 233 CT. In the results presented so far, we defined the PF per ROI, as the most prominent band-239 limited peak in the spectrum. Multiple ROIs, however, showed more than a single spectral 240 peak. Figure 5 shows a histogram (across ROIs and participants) of all detected spectral 241 peaks. This histogram of peak frequencies clearly delineates the classical frequency 242 bands that are used in the EEG and MEG literature (4-7.5 (theta), 8.5-13 (alpha), 15-243 25 (low beta) 27.5-34 (high beta)). Defining the theta, alpha and beta frequency bands 244 based on the histogram, we determined for each ROI and participant the band-specific 245 PF (BS-PF). Next, we modelled the spatial distribution of BS-PFs across the cortex, 246 similar to the analysis shown above. Analogous to the PF analysis, we used LMEM to 247 model BS-PF as a function of the ROIs' coordinates. We found a significant decrease of This study is the first comprehensive demonstration of frequency gradients across the 259 human cortex using a large set of resting-state MEG recordings. We found that the 260 strongest peak frequency in a brain area decreases significantly, gradually and robustly 261 along the posterior-anterior axis, following the global cortical hierarchy from early sensory 262 to higher order areas. This finding establishes a frequency gradient of resting-state brain participant variability was taken into account as a random effect. Our approach additionally revealed that cortical peak frequencies decrease systematically along the 282 inferior-superior axis. As seen in Figure 1 this seems to result from the fact that higher-283 order frontal areas with lower PF have higher z-coordinates compared to the early 284 sensory areas with higher PF.

285
Results of our analyses showed that, just as peak frequency significantly decreased 286 along the posterior-anterior axis, CT significantly increased in the same direction, which 287 resulted in a significant anticorrelation between PF and CT. The observed correlation 288 holds after removing the effect of spatial location (x,y,z). This seems to indicate that PF 289 and CT are more closely related to each other than can be explained by spatial location

352
We further analyzed these specific frequency bands for gradients and found significant 353 posterior-anterior frequency changes in the theta, alpha and beta frequency band.

354
Results in the alpha band mirrored the previous results based on the overall strongest 355 peak frequency. Interestingly, and in contrast to the alpha band, peak frequencies 356 increased along the posterior-anterior direction in the theta and beta frequency band. In  predictions for a ROI located at centroid coordinates of ( ) as follows

467
To examine if the spatial distribution of PF across the cortex is independent of the spatial  The authors declare that they have no competing interests.