Fig 1.
Schematics of identifying genuine and spurious interareal CFC.
(a) Schematic illustration of PS, LF:HF (n:m) CFS, and LF:HF PAC. In PS, 2 spatially distant processes oscillating at the same frequency exhibit a (statistically) constant phase relationship. In CFS, a constant n:m-phase relationship exists between 2 processes at frequencies LF and HF, so that LF:HF = n:m. In PAC, the amplitude of the HF signal is correlated with the phase of the LF signal. These processes can either take place in the same region (local CFC) or between 2 regions (interareal CFC). (b) Observations of local CFC can be either genuine or spurious. A measured signal from a single sensor or electrode can either be the sum of 2 (statistically) sinusoidal processes oscillating at distinct frequencies or a single nonsinusoidal process, and these possibilities are difficult to dissociate from the single signal. Local CFC can be observed in both cases because of filter artifacts produced by nonsinusoidal signals. (c) Genuine interareal CFC between 2 spatially distant sinusoidal processes A and B. (d) An example of spurious observation of interareal CFC. Process A is sinusoidal, but B is nonsinusoidal and causes spurious local CFC to be observed at location B, as shown in (b). If A and B are connected by LF PS, spurious interareal CFC will also be observed between A and B. This spurious observed interareal CFC forms a “triangle motif” with PS and the spurious CFC couplings. (e) Example of spurious observation of interareal CFC in which process B is sinusoidal, but A has a nonzero mean, and spurious local CFC will be observed at location A. Again, if A and B are connected by HF PS, spurious interareal CFC will also be observed between A and B, again forming a triangle motif. (f) Constellations of observations that unambiguously indicate genuine CFC between regions A and B. In none of the cases is there a triangle motif of PS and local CFC. (g) Constellations of observations with ambiguous finding of interareal CFC between regions A and B. Although here, interareal CFC is genuine, it is part of a triangle motif formed with PS and (true or spurious) local CFC. Such constellations cannot be distinguished by our graph-theory–based method from spurious interareal CFC. (h) Constellations with spurious interareal CFC. These include the 2 constellations from (d) and (e) in the left column and other possible constellations, including those in which there is spurious local CFC at both locations (right column). In all cases, the spurious interareal CFC is part of a triangle motif. CFC, cross-frequency coupling; CFS, cross-frequency PS; HF, high frequency; LF, low frequency; PAC, phase–amplitude coupling; PS, phase synchrony.
Fig 2.
Generative modeling of joint 1:1 and 1:2 cross-frequency phase coupling.
(a) Two areas (A and B), each containing 2 populations of Kuramoto oscillators (N = 500) at LFs and HFs. The populations exhibit intermediate and intermittent internal synchronization (see time series) and are mutually coupled by population-signal–based 1:1 PS or 1:2 CFS phase coupling (see ε). (b) Increasing the 1:1 and local CFS coupling between populations led to strengthening of the corresponding phase correlations (PLV, red and blue lines for PS and purple for local CFS) and, in the regime of strong coupling, also to the emergence of spurious interareal CFS (green lines). Each data point indicates the observed phase correlation (PLV) in a single simulation with 100,000 iterations (5,000 cycles of the fast oscillation) with random initial parameters in a series of 512 simulations for coupling factors from 0 to 0.3. Shaded areas indicate the 16th to 84th PLV percentiles across simulations. The gray line and shaded area indicate the PLV threshold for nominally significant CFS at p < 0.01. (c) Phase correlation statistics: small squares indicate significant (p < 0.01) or n.s. phase correlation observations in individual simulations in the example of series of panel (b). Lines and the shaded areas indicate the fraction of significant observations as a function of the shared coupling factor c. Black frames indicate the observations of interareal CFS that were not associated with significant local CFS and 1:1 PS and would thus remain as false positives after the correction proposed in this study. CFC, cross-frequency coupling; CFS, cross-frequency PS; FPR, false positive rate; HF, high frequency; LF, low frequency; n.s., not significant; PLV, phase-locking value; PS, phase synchrony.
Fig 3.
Genuine interareal CFS and PAC at the single-subject level.
(a) Averaged broadband time series and α-band (11 Hz)–filtered LF time series time-locked to the α peaks in the left supTS for a representative MEG subject. TFR of the broadband average reveals α oscillations (highlighted by lower gray box) but an absence of β oscillations (in area of upper gray box) and thus the absence of both nonsinusoidal filter artifacts and genuine local 1:2 CFS. (b) Averaged broadband-filtered and β-band (22 Hz)–filtered HF time series for right vmCS time-locked to the α LF peaks identified in supTS. TFR of the broadband average reveals β oscillations but an absence of α oscillations. Thus, vmCS shows no filter artifacts, local CFS, or interareal α or β CFS (highlighted by gray boxes). (c) PLV time series (green line) for 1:2 α:β CFS for the LF and HF time series averaged over α-peak time-locked segments. Dotted gray line shows the PLV value above which CFS is significant at p < 0.01. (d) Averaged broadband-filtered and α-band (11 Hz)–filtered LF time series time-locked to the α troughs in an electrode contact c1 located in the mTG in a representative SEEG subject. The electrode location is marked by the red circle on the brain, and the closest white matter contact (used as reference) by the white circle next to it. TFR of the averaged broadband time series reveals α oscillations (highlighted by gray box) and an absence of higher-frequency components, suggesting the absence of systematic nonsinusoidal filter artifacts that would show up as local CFS here. (e) Averaged broadband time series in an electrode contact c2 in iTS that is time-locked to the α troughs in contact c1 reveals no clear α oscillations, showing an absence of α PS between c1 and c2. The location of electrode contact c2 is marked by the blue circle on the brain, and the closest white matter contact (reference) by the white circle next to it. (f) TFR of oscillation amplitudes in c1 time-locked to α peaks shows little modulation of γ amplitudes by α phase at frequencies above 40 Hz. (g) TFR of oscillation amplitudes in c2 show comodulation of γ amplitudes in c2 and α cycles (i.e., α phase) in c1. The frequency region at around 55 Hz, at which the HF of the 1:5 PAC should be seen, is marked with gray boxes. (h) PLV time series (green line) for 1:5 PAC between LF time series in c1 and LF-filtered amplitude envelope of 55 Hz NB in c2. Dotted gray line shows the PLV value above which PAC is significant at p < 0.01. Plot data for a–h are available online at https://datadryad.org/stash/dataset/doi:10.5061/dryad.0k86k80. CFS, cross-frequency PS; HF, high frequency; iTS, inferior temporal sulcus; LF, low frequency; MEG, magnetoencephalography; mTG, middle temporal gyrus; NB, narrowband; PAC, phase–amplitude coupling; PLV, phase-locking value; PS, phase synchrony; SEEG, stereoelectroencephalography; supTS, superior temporal sulcus; TFR, time frequency representation; vmCS, ventromedial central sulcus.
Fig 4.
Genuine observations of interareal CFS and PAC.
(a) Connection density (K), i.e., the fraction of significant connections over all possible connections, of interareal CFS in SEEG at the group level before (left) and after removing possible spurious connections (right) for LF:HF ratio 1:2 (top row) and ratios 1:3–1:7 (bottom row). The x axis shows the LF. K values are plotted with 95% confidence limits obtained from surrogate data. (b) The same data as in (a), but presented in a matrix in which each frequency-ratio combination is a matrix element. K is again presented before (left) and after removal of possibly spurious connections (right). (c–d) Interareal CFS in MEG before and after removing possibly spurious connections. Robust α:β CFS at ratio of 1:2 and α:γ CFS at ratios 1:3 characterize SEEG and MEG data before removing spurious connections. Although K is reduced by removing the putatively spurious connections, α:β at 1:2 ratio and α:γ CFS at 1:3 ratio remain significantly above zero. (e–f) Interareal PAC in SEEG data and (g–h) in MEG data before and after removing spurious connections as in (a)–(d). SEEG is characterized by robust PAC of θ–α oscillations to HFs in α–γ bands at ratios 1:2–1:7, indicating that α–γ band amplitudes are modulated by phases of θ–α oscillations. In MEG, PAC is observed between α phase and β–γ band amplitudes at ratios 1:2–1:4, as well as between γ and Hγ oscillations at all ratios. The connection densities are reduced by removing putatively spurious connections but remain significantly above the zero. Plot data and underlying connectome data are available online at https://datadryad.org/stash/dataset/doi:10.5061/dryad.0k86k80. CFS, cross-frequency PS; HF, high frequency; LF, low frequency; MEG, magnetoencephalography; PAC, phase–amplitude coupling; PS, phase synchrony; SEEG, stereoelectroencephalography.
Fig 5.
Interareal CFS and PAC decrease as a function of distance.
(a) Connection density (K) for uncorrected (left) and corrected (right) interareal CFS estimated separately in 3 distance bins containing equal numbers of connections for 1:2 (top row) and 1:3 (bottom row) interareal CFS in SEEG data. All values are plotted, with 95% confidence limits indicated by shades. The colored bars and stars indicate LFs where K values between distance bins were significantly different (Wilcoxon test, p < 0.05, corrected) between distance bins (purple: short versus medium; turquoise: short versus long; orange: medium versus long). (b) Same as (a) for CFS in MEG. (c) Same as (a) for interareal PAC in SEEG and (d) in MEG. Connection density of CFC was larger for the shortest than for the longest distance bin for CFS at ratio 1:2 and for PAC at ratios 1:2 and 1:3 in both SEEG and in MEG data across most of the frequency spectrum. Plot data and underlying connectome data are available online at https://datadryad.org/stash/dataset/doi:10.5061/dryad.0k86k80. CFC, cross-frequency coupling; CFS, cross-frequency PS; LF, low frequency; MEG, magnetoencephalography; PAC, phase–amplitude coupling; PS, phase synchrony; SEEG, stereoelectroencephalography.
Fig 6.
CFS and PAC in different laminar depths in SEEG data.
(a) Connection density K for uncorrected (left) and corrected (right) interareal CFS at ratio 1:2 (top row) and 1:3 (bottom row) in SEEG among electrode pairs that were either both in more superficial (s) layers (red) or both in deeper (d) layers (blue), when the LF electrode was in a more superficial layer and the HF electrode in a deeper layer (green), and vice versa (purple). The colored bars and stars indicate LFs at which K values were significantly different between laminar depth combinations (Wilcoxon test, p < 0.05, corrected) (purple: s–s versus d–d; beige: s–s versus s–d; pink: s–s versus d–s; turquoise: d–d versus s–d; dark blue: d–d versus d–s; gray: s–d versus d–s). (b) Same for interareal PAC in SEEG data. In both CFS and PAC, for the uncorrected data, the connection densities were highest for connections in which both electrodes were localized within superficial layers and lowest for both localized within deeper layers. In corrected PAC, K was highest when LF electrodes were localized to deeper and HF to superficial layers and lowest when vice versa. Plot data and underlying connectome data are available online at https://datadryad.org/stash/dataset/doi:10.5061/dryad.0k86k80. CFS, cross-frequency PS; HF, high frequency; LF, low frequency; PAC, phase–amplitude coupling; PS, phase synchrony; SEEG, stereoelectroencephalography.
Fig 7.
CFC networks have an asymmetric LF and HF hub architecture.
The functional organization of CFC networks as measured with localization of LF and HF hubs. Hubness was measured as relative LF and HF degree of each brain region (parcel). Relative degree values indicate whether a parcel is primarily a LF hub (blue) or HF hub (red) in interareal CFC. Top row: brain anatomy of LF and HF hubs for CFS and PAC at ratio 1:2 connecting θ:α and α:β frequencies. Bottom row: brain anatomy of LF and HF hubs for CFS and PAC networks at ratio 1:3 connecting δ:α and α:γ frequencies. CFS and PAC networks show saliently opposing anatomical structures connecting anterior and posterior brain regions. Plot data and underlying connectome data are available online at https://datadryad.org/stash/dataset/doi:10.5061/dryad.0k86k80. CFC, cross-frequency coupling; CFS, cross-frequency PS; HF, high frequency; LF, low frequency; MEG, magnetoencephalography; PAC, phase–amplitude coupling; PS, phase synchrony; SEEG, stereoelectroencephalography.
Table 1.
Parcel values are correlated between SEEG and MEG data.
Table 2.
Parcel values are anticorrelated between CFS and PAC.
Fig 8.
Correlation of CFS with neuropsychological test scores.
The correlation of CFS GS in MEG data with scores from neuropsychological assessments for all ratios and frequency pairs (Spearman rank correlation test, p < 0.05). The assessments include TMTs A and B and Zoo Map Plan and Time Tests, as well as Forward Digits, Backward Digits, and Digit Symbol Tests, and the Letter-Number Sequencing from Wechsler Adult Intelligence Scale–III. Red color indicates a positive correlation, so that stronger CFS is associated with better performance, while blue indicates a negative correlation between CFS and performance. Correlations with p > 0.05 are masked (low saturation colors). The asterisks indicate the observations that remain significant after correction for multiple comparisons (see Methods, Neuropsychological assessment and correlation of CFC with neuropsychological test results) across the 8 neuropsychological tests and CFC frequency pairs. Plot data and underlying connectome data and neuropsychological data are available online at https://datadryad.org/stash/dataset/doi:10.5061/dryad.0k86k80. CFC, cross-frequency coupling; CFS, cross-frequency phase synchrony; GS, graph strength; MEG, magnetoencephalography; TMT, Trail-Making Test.