Phase Synchrony among Neuronal Oscillations in the Human Cortex

Cross-frequency phase synchrony among cortical oscillations

Superimposed α-frequency (8-14 Hz) and β-/γ-frequency (14-50 Hz) band oscillations were readily observed in filtered gradiometer data (Fig. 1A) recorded during R (see Materials and Methods). We first addressed the presence of CF phase synchrony, which thus far has remained undiscovered in cortical activity. We obtained the continuous phase (Fig. 1B, red and blue traces) of the α and β/γ oscillations using the Hilbert transform, evaluated their phase difference (Fig. 1B, purple trace), and computed 1:m phase-locking factors in narrow sliding time windows (Fig. 1C,D) (PLF_1:m; see Materials and Methods). We found that intermittent periods of 1:3 and 1:4 γ-α (Fig. 1A-D) as well as 1:2 β-α (data not shown) phase synchronies were strikingly prominent in the spontaneous activity of posterior brain areas.

To obtain the continuous phases of 3-80 Hz activities over whole recording sessions and within all MEG gradiometers, we then mapped the occurrence of CF phase synchrony by using Morlet wavelets and estimated the corresponding PLF_1:m with m = 2-6. Figure 1E shows the percentage of gradiometers detecting statistically significant (p < 0.01) synchrony between oscillations at frequencies f_x and f_y (color scale) averaged over subjects (N = 17). The frequency of the faster oscillation (f_x) is plotted on the y-axis, and the m factor that gives the frequency of the slower oscillation (f_y) (f_y = f_x/m) is on the x-axis. Because the gradiometers are the most sensitive to neuronal sources directly underneath them (Hämäläinen et al., 1993), such within-channel CF phase synchrony reflects mainly local interactions in cortical networks. During rest, we found significant 1:2 or 1:3 phase synchronies between all analyzed frequency bands (Fig. 1E). Phase synchronies (1:2) were dominated by the locking of β-(∼20 Hz) and α-band (∼10 Hz) oscillations widely over the cortex but predominantly over occipitoparietal and central/somatomotor regions (Fig. 1F, left). However, 1:3 phase synchrony was found mainly between γ-band (∼30 Hz) and α-band oscillations and mostly over the occipitoparietal and somatomotor regions (Fig. 1F, right).

Mental arithmetic tasks enhance local CF phase synchrony

Next, we asked whether these patterns of CF phase synchrony would be affected by mental arithmetic tasks T1 and T2 (Fig. 2A) (see Materials and Methods). Both tasks strongly enhanced local 1:2 γ-β, 1:2 β-α, and 1:3 γ-α synchronies (Fig. 2B) compared with R. These effects were most pronounced over right-hemispheric parietal and temporal/prefrontal areas but were also highly significant over corresponding left-hemispheric areas (Fig. 2B). The differences in local CF phase synchrony between T1 and T2 were much more subtle and exhibited greater intersubject variability. Interestingly, however, T2 was associated with significantly stronger 1:3 γ-α synchrony than T1 over right-hemispheric parietal areas (average over nine parietal gradiometer locations: right hemisphere, 17%, p < 0.01; left hemisphere, 1.6%, p > 0.8; also see below, the T2 vs T1 data on interareal phase synchrony).

The contribution of artifactual harmonics to CF phase synchrony

The frequency content of oscillations with nonsinusoidal (spiky, for instance) waveforms is not limited to the band corresponding to the fundamental frequency of the oscillation. Such nonsinusoidal signals produce harmonic peaks in power spectra and CF phase synchrony that is artifactual in the sense that it does not reflect an interaction between two oscillations at distinct frequencies. Nonsinusoidal waveforms, in contrast, also arise when two interacting oscillations at different frequencies are actually present in the data. We addressed whether the present observations of CF synchrony can be accounted for by artifactual harmonics.

First, visual inspection of the data revealed that, during periods of prominent CF phase synchrony, the faster oscillation was also detectable in broadband-filtered data, indicating that it did not arise as a filter artifact from the slower oscillation (Fig. 1A). Second, we estimated CF phase synchrony over recording sessions using the Hilbert transform and temporally very narrow, broad-pass-band filters (Fig. 3A,B) (see Materials and Methods). The results were comparable with those obtained with Morlet wavelets, whereas CF phase synchrony caused by filter artifacts should have been dramatically weaker (compare Figs. 1E, 3A and Figs. 2B, 3B). Third, we estimated the strength and form of CF amplitude correlations within gradiometers with cross-amplitude histograms (Fig. 3C) and Spearman's rank-order coefficients (data not shown). The CF amplitude correlations were, in general, extremely weak, albeit positive (Fig. 3C). If the detection of faster oscillations was strongly biased by nonsinusoidal properties of the slower oscillations, the amplitudes of faster oscillations should have been tightly linked to the amplitude of the slower oscillations. Moreover, in contrast to the band-specific enhancements of CF phase synchrony (Fig. 2B), T1 and T2 robustly weakened the amplitude correlations between all frequency pairs below the γ band compared with R (Fig. 3D). This indicates that the enhancement of CF phase synchronies during T1 and T2 was not attributable to changes in α waveform.

Together, several lines of evidence indicate that CF phase synchronies reported in this study do indeed reflect the interactions of networks oscillating in distinct frequency bands.

Interareal phase synchrony

The data above (Figs. 1, 2, 3) showed that CF phase synchrony is present among cortical oscillations and that it is modulated by differences in cognitive operations. To obtain a more complete picture of its characteristics, we then addressed phase synchrony between anatomically distinct areas. We quantified 1:2 and 1:3 phase synchronies of 10, 20, and 30 Hz oscillations for all pairs of the MEG gradiometers as well as the “classical” 1:1 synchronization within these frequency bands. In rest, 1:1 phase synchrony was extremely robust for all frequency bands analyzed and highly significant for essentially every gradiometer pair (Fig. 4A). In contrast, 1:2 and especially 1:3 phase synchronies were weaker and more local (Fig. 4B). Furthermore, although 1:1 phase synchronies were rather homogeneously distributed over the cortex, 1:2 and 1:3 phase synchronies were concentrated over posterior cortical areas (Fig. 4, matrices). Such qualitative differences in the distributions of 1:1 and 1:2/1:3 phase synchronies suggest that the mechanisms and functions of CF and 1:1 phase synchronies are indeed distinct.

It should be noted that the magnetic field gradients produced by a focal cortical source are detected by several neighboring gradiometers that are located side by side above the source (Hämäläinen et al., 1993). Therefore, such signal spreading may contribute to observations of cross-channel synchrony between adjacent or very nearby gradiometers.

Task effects on interareal phase synchrony

The execution of T1 and T2, compared with R, enhanced interareal 1:1 phase synchronies in all frequency bands (Fig. 5A), although the strengthening of 10 Hz phase synchrony was clearly most pronounced and widespread (Fig. 6A,B). The 10 Hz phase synchrony was enhanced predominantly among posterior and anterior regions (Fig. 6A,B) and showed the strongest task effects at long distances [i.e., far from the matrix diagonal (Fig. 6A,B)]. We also plotted, as a function of gradiometer separation, the mean phase synchrony within (solid colors) and between (two-colored lines) the gradiometers in four quadrants of the MEG helmet (Fig. 7). These graphs corroborate the findings above and further highlight the central role of right-hemispheric posterior regions in large-scale 10 Hz synchrony (Fig. 7A, red lines in the 10-10 Hz row). A conspicuous feature of T1/T2-related 10 Hz phase synchrony was the marginality of task effects on synchrony within and between left-hemispheric posterior and anterior regions, despite the fact that these regions were massively synchronized with the right hemisphere (Figs. 6A, lower-left quadrant of the 10 Hz matrix, 7A, yellow and green lines). Phase synchronies (20 and 30 Hz), on the other hand, were predominantly found within posterior and between posterior and anterior brain regions (Fig. 5A) but much less so within anterior regions (Figs. 6A,B, matrix corners, 7A, blue and green lines) and with much less prominent right-hemispheric dominance than that observed for the 10 Hz phase synchrony (Fig. 6A).

Interareal 1:2 β-α and 1:3 γ-α synchronies were also considerably stronger during T1 and T2 than during R (Fig. 5B). Surprisingly, the interareal CF phase synchronies, 1:2 β-α in particular, were enhanced even more than the 1:1 phase synchronies (Fig. 6, compare A, B with C, D; note the different range for β-α synchrony). Moreover, in stark contrast to the 1:1 phase synchronies, the CF phase synchronies were most strongly enhanced on short distances (Fig. 7B) and over the right hemispheric posterior regions (Fig. 6C,D), providing additional evidence for the fundamentally distinct characters of 1:1 and CF phase synchronies. The strongest long-range CF phase synchronies were found between right posterior and anterior regions as well as between right and left posterior regions (Fig. 7B, blue-red and red-yellow lines, respectively).

The differences in interareal 1:1 (Fig. 5C) and CF (Fig. 5D) synchronies between T1 and T2 were much weaker than between T1/T2 and R (Fig. 5, compare A, B). However, although the differences were relatively small, 1:3 γ-α phase synchrony was clearly stronger during T2 than during T1 (Fig. 6G,H), mainly over right parietal regions (Figs. 6G,H, 8B, red line). In contrast, the massive 1:2 β-α synchrony showed only a small difference between T1 and T2, suggesting that the functional roles of these 1:2 and 1:3 phase synchronies are distinct. In addition, 1:1 phase synchronies were significantly stronger in T2 than in T1 (Fig. 6E,F) but were enhanced less than the 1:3 γ-α synchrony (Fig. 8, compare A, B). Interestingly, 10 Hz 1:1 phase synchrony was enhanced within the left hemisphere and bilaterally within the anterior regions, apparently linking and recruiting specifically those areas that were the least involved in the task execution in T1. Because T1 and T2 differed essentially only in the number of simultaneously memorized object representations, these data strongly suggest that 1:3 γ-α phase synchrony has a role in the neuronal mechanisms of working memory maintenance.

Task effects on oscillation amplitudes

To relate the data obtained with the present tasks to previous studies using working memory paradigms, we evaluated the oscillation amplitudes with Morlet wavelets for all frequency bands in Figures 1, 2, 3. The results showed that amplitudes of α (Bastiaansen et al., 2002; Halgren et al., 2002; Jensen et al., 2002) and β/γ (Tallon-Baudry et al., 1998; Pesaran et al., 2002; Howard et al., 2003) bands were slightly but significantly increased in T1 and T2 compared with R (Fig. 9). The amplitude enhancements were mainly observed over occipitoparietal and temporal/prefrontal areas. Interestingly, the amplitudes of θ-band (3-8 Hz) oscillations were enhanced over prefrontal regions (Gevins et al., 1997; Howard et al., 2003) but were suppressed widely over the posterior regions (cf. Bastiaansen et al., 2002).

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Figure 9.

Mental arithmetic tasks enhance frontal 5-8 Hz and posterior 8-40 Hz oscillations and attenuate the posterior 3-8 Hz oscillations. A, The traces show the wavelet amplitudes (for frequencies in Figs. 1 and 2) averaged within recording sessions and across the gradiometers and subjects (R, blue; T1, green; T2, red). B, C, Topographies of the oscillation amplitudes in R (B) and the topographies and significance levels of task effects (C) averaged over the frequency bands that are indicated by the black horizontal bars. NS, Not significant.

The enhancement of CF phase synchrony by cognitive processes

CF phase synchrony was robust and present during each task among all frequency bands analyzed. However, mental calculation and working memory demands of T1 and T2 enhanced specifically the 1:2-1:4 phase synchronies among α, β, and γ oscillations. The enhancements of the 1:1 phase synchrony, the oscillation amplitudes, and the distinct spatial patterns of 1:1 synchrony of these oscillations, imply, in good agreement with other evidence (Singer, 1999; Tallon-Baudry and Bertrand, 1999; von Stein et al., 2000; Varela et al., 2001; Howard et al., 2003), that α, β, and γ oscillations are all involved in the performance of T1 and T2 but with distinct functional roles. Thus, CF phase synchrony among these oscillations is well posed to mediate the integration of this spectrally distributed processing into the cognitive operations required by mental calculations and working memory.

The role of 1:3 γ-α phase synchrony in working memory

The mental arithmetic tasks in this study affected the amplitude, 1:1 phase synchrony, and hemispheric lateralization of ongoing neuronal activity in a manner very similar to that observed previously in working memory tasks, which is well in line with the notion that the principal task load during easy mental calculation is on the working memory system (Houdé and Tzourio-Mazoyer, 2003). Nevertheless, the comparison of task T1/T2 and rest does not allow the dissection of working memory-related activities from those involved in, for example, the mental calculation, but reveals the overall differences between minimal and near-maximal cognitive load. However, the comparison of tasks T1 and T2 reveals specifically the components sensitive to working memory load. It is therefore intriguing to find that 1:3 γ-α phase synchrony was moderately but highly significantly stronger during T2 than during T1. This result suggests that 1:3 synchronized γ and α oscillations may play a role in the neuronal mechanisms of working memory. Taking the proposed “representational” (Singer, 1999; Tallon-Baudry and Bertrand, 1999) and attentional (von Stein et al., 2000; VanRullen and Koch, 2003) roles of β/γ and α oscillations, the results suggest that such 1:3 synchronization of these oscillations may mediate the contents-to-context binding of neuronal object representations into working memory and/or the multiplexing of these object representations, which is required when multiple representations must be kept active simultaneously.

Parietal focus of CF phase synchrony

β-α and γ-α phase synchronies were strongest over the right hemispheric parietal regions, as were their task-related enhancements. At the same time, the corresponding 1:1 synchronies were widely distributed over the cortex. In addition to the fact that these results support the differential origin of CF phase and within-frequency synchronies, they also support the notion that CF phase synchronies are related to attentional and working memory functions. The right-hemispheric parietal regions have been shown to play a critical role in attention and working memory by imaging studies (Corbetta et al., 1998; Kastner and Ungerleider, 2000; Awh and Jonides, 2001; Linden et al., 2003) and by the diversity of attentional deficits caused by parietal damage (Friedman-Hill et al., 1995; Driver and Vuilleumier, 2001). In addition, the brain areas specifically responsible for multiplexing functions (Friedman-Hill et al., 1995) are located, at least partly, in the parietal regions, as suggested again both by imaging studies localizing cortical activity correlated with working memory capacity (Linden et al., 2003) and by findings that damage in parietal regions can result in an inability to perceive multiple objects simultaneously (simultagnosia) (Friedman-Hill et al., 1995).

Putative cellular-level mechanisms involved in CF phase synchrony

The concept of “dynamic binding” posits that the postsynaptic impact of “bound” presynaptic inputs is greater than the impact of “unbound” ones (Singer, 1999). Although excitatory inputs synchronized in a 1:1 manner have better chances of evoking action potentials in downstream target neurons than asynchronous inputs (Konig et al., 1996; Singer, 1999), little is known about the functional significance of 1:m (m > 1) synchronization in neuronal signaling.

Interestingly, a type of neocortical layer 5 (L5) pyramidal cell with dendrites spanning all cortical layers has characteristics that are relevant in this context. The main excitatory connections to proximal and basal dendrites of these cells originate from specific thalamic nuclei (Jones, 2002), from local layer 4 spiny stellate cells, and, overall, from cortical areas at the same level or lower in hierarchy (Felleman and Van Essen, 1991). In contrast, inputs to distal apical dendrites primarily arise from diverse nonspecific thalamic regions (Jones, 2002) and from cortical areas higher in hierarchy (Felleman and Van Essen, 1991; Cauller et al., 1998). L5 pyramidal cells thus receive bottom-up and top-down signals in distinct integrative compartments, and both proximal (bottom-up) and distal (top-down) inputs alone, if sufficiently strong, can evoke action potentials or burst firing (Helmchen et al., 1999; Larkum et al., 1999; Williams and Stuart, 1999; Larkum and Zhu, 2002). However, burst firing is facilitated if the proximal and distal inputs are temporally correlated with a precision of ∼5 ms (Larkum et al., 1999). Because bursts have a much stronger impact on postsynaptic neurons than single action potentials (Lisman, 1997; Williams and Stuart, 1999), L5 pyramidal cells can effectively signal the coincidence of bottom-up and top-down signals and thus are able to mediate cross-hierarchical integration.

Although the feedforward/bottom-up inputs to L5 pyramidal cells often involve γ-band rhythmicity (Steriade et al., 1996; Castelo-Branco et al., 1998; Singer, 1999; von Stein et al., 2000), the feedback/top-down signals are more likely to have periodicities in the α band (von Stein et al., 2000; Mima et al., 2001; Halgren et al., 2002; Yamagishi et al., 2003). L5 pyramidal cells can also entrain each other (Silva et al., 1991) as well as their subcortical targets in the brainstem (Nicolelis et al., 1995) and superior colliculus (Brecht et al., 1998) into ∼10 Hz oscillations. Moreover, the regenerative Ca²⁺ action potentials underlying distal dendritic excitation (Helmchen et al., 1999; Larkum et al., 1999; Larkum and Zhu, 2002) cannot occur at frequencies more than ∼10 Hz (Larkum and Zhu, 2002). The narrowness of the correlation window (Larkum et al., 1999) indicates that oscillatory proximal and distal inputs in 20-40 and <10 Hz bands, respectively, can readily induce burst firing only when they are phase synchronized in a 1:m manner. This implies that the L5 pyramidal neurons can function as “read-out devices” for 1:m phase synchrony. Moreover, this kind of mechanism would also enable an unambiguous and rapid attentional selection of target representations from among other intermittent assemblies. Therefore, it is of interest to note that many of the subcortical targets of L5 pyramidal cells, such as the pulvinar and superior colliculus, have a critical role in attention and visual orienting (Karnath et al., 2002).

Another type of neuron that deserves attention in this context is fast rhythmic-bursting (FRB) cells. In a manner akin to L5 pyramidal neurons, they can switch from single-spiking to burst-firing mode, in which they show very fast (300-600 Hz) bursts at γ (30-40 Hz) frequencies (Steriade et al., 1998, 2004). Notably, FRB cells, located in all cortical layers from 2 to 6, are key elements in the reciprocal thalamocortical loops that are involved in the generation of β-/γ-frequency band oscillations (Steriade et al., 1996, 1998).

Conclusion

We propose that cross-frequency phase synchrony mediates cross-hierarchical and cross-functional integration essential for unified cognitive operations by enabling the integration of spectrally distributed neuronal processing.