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. 2013;9(3):e1002985.
doi: 10.1371/journal.pcbi.1002985. Epub 2013 Mar 21.

Neuronal avalanches differ from wakefulness to deep sleep--evidence from intracranial depth recordings in humans

Viola Priesemann  1 , Mario Valderrama, Michael Wibral, Michel Le Van Quyen
Affiliations

Neuronal avalanches differ from wakefulness to deep sleep--evidence from intracranial depth recordings in humans

Viola Priesemann et al. PLoS Comput Biol. 2013.

Abstract

Neuronal activity differs between wakefulness and sleep states. In contrast, an attractor state, called self-organized critical (SOC), was proposed to govern brain dynamics because it allows for optimal information coding. But is the human brain SOC for each vigilance state despite the variations in neuronal dynamics? We characterized neuronal avalanches--spatiotemporal waves of enhanced activity--from dense intracranial depth recordings in humans. We showed that avalanche distributions closely follow a power law--the hallmark feature of SOC--for each vigilance state. However, avalanches clearly differ with vigilance states: slow wave sleep (SWS) shows large avalanches, wakefulness intermediate, and rapid eye movement (REM) sleep small ones. Our SOC model, together with the data, suggested first that the differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate at criticality proper but close to SOC. Independent of criticality, the analysis confirms that SWS shows increased correlations between cortical areas, and reveals that REM sleep shows more fragmented cortical dynamics.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. The global correlation structure between units is reflected in the avalanche distribution.
A. Each of the four raster plots depicts events from a different stochastic process with 44 units each. Each process had the same event rate (¼Hz) but different correlations structures between its 44 units: independent Poisson processes (green), stochastic input to two different subsets of the units (pink), and high correlation between units (orange). The black dots represent events recorded from the human brain (44 electrodes, ¼Hz event rate). The horizontal gray line depicts the bin size applied to get the p(s) in (B). B. Each of the avalanche size distributions p(s) corresponds to one of the processes in (A). p(s) reflects the correlation structure of the data. High correlations resulted in more large avalanches (orange, pink), while the Poisson processes show f(s) close to an exponential (green). However, here only p(s) from the human data (black) showed a power law.
Figure 2
Figure 2. Definition of neuronal avalanches.
Black traces show LFP from 44 parallel intracranial depth recording sites in one patient. For each recording site the area under the deflection lobe between two zero crossings was calculated (see green box – blue indicates the area under the deflection lobe). A binary event (red dot) was counted by selecting the biggest area values such, that each recording site during each phase of constant sleep stage had an event rate of exactly ¼ Hz (in this example). The binary events across recording sites occurred in clusters (yellow background). These clusters are called neuronal avalanches. The avalanches were separated by pauses of no activity (white background). The avalanche size s is defined as the total number of binary events in one cluster. As examples, the sizes s of three avalanches were indicated above the raw traces.
Figure 3
Figure 3. The neuronal avalanche size distribution f(s) for humans approximated a power law.
A. The colored line shows f(s) for all avalanches across all 10 nights, evaluated at different event rates and at bs = 1·formula image. The gray lines show f(s) at r = ¼Hz separately for each of the nights to indicate the variability between recording nights and patients. For better visibility, the gray distributions have some offset, while the colored distributions all are in absolute counts. f(s) approximated a power law (τ = 1.5 was indicated by the dotted line). The cut off around s = 50 is known to coincide with the number of recording electrodes, 51 on average. B. The slope of f(s) changed with the temporal scale or bin sizes (bs). The bs was between 1/32 formula image and 4 formula image, while here r was fixed at r = ¼ Hz. With larger bs, the slope of f(s) became flatter, but the distributions always resembled a power law. C. The slope τ of f(s) depended on the bin size (bs), but little on the rate (colored lines). The full lines show τ from fitting a power law, while the dashed lines show τ and α for a power law with cutoff (see inset for α). τ and α for small bs at high rates are not defined, because the bs there became smaller than the time resolution from sampling (2.5 ms). Estimation errors for τ and α scale with n −½ where n is the number of samples . Here, n≈106, and thus the error is of the order 10−3, and thus error bars are close to line thickness. For details on the fitting parameters and quality, see also Supplementary Table S1 and Figure S1. D. The branching parameter σ was plotted over the bs. σ changed with the bs, but was similar across event rates (colored lines). The (+) depicts [σ = 1, bs = 1] for visual guidance.
Figure 4
Figure 4. Avalanche distributions differed with vigilance states and synaptic strength dE.
A. The avalanche size distribution f(s) for the neuronal avalanches was evaluated for each vigilance state separately. f(s) was similar for all vigilance states, however, it showed fewer large avalanches for REM sleep than for SWS (s2 and s3/s4). All f(s) were normalized such that f(s = 1): = 1. B Here, we showed the same results as in A, however, f(s) was plotted separately for each of the 10 recording nights to show that the differences in f(s) with vigilance states were present in each night. (Logarithmic binning to smooth the curves; the offset between the sets is two orders of magnitude.) C. The avalanche distribution for the subsampled SOC model was close to a power law for the critical state (black line). To deviate from the critical state, the synaptic strength dE was varied systematically by up to 0.6% (colored lines). Technically, for dE<1 the model is subcritcal and for dE>1 it is supercritical. With larger dE, f(s) showed an increased number of large avalanches. For the supercritical state (dE>1) a significant amount of avalanches was larger than 64, the number of sampling sites. D. The results for the fully sampled model look similar to the subsampled model, except that the cutoff is, as expected, at larger s.
Figure 5
Figure 5. Avalanches from virtual LFP signals of the “spiking” SOC model showed a power law.
A. We sampled virtual LFPs from the SOC model with 4×4×4 = 64 virtual electrodes. Each virtual electrode sampled from a 3D sphere centred on the electrode tip. The sampling weights for a slice with 4×4 electrodes are indicated here in colour. B. The avalanche size distributions p(s) on the 64 virtual electrodes showed a power law for a wide range of thresholds (coloured traces). For the virtual LFP, avalanches were calculated the same way as for the real LFP: Whenever the area under a deflection lobe exceeded a certain threshold, a binary event was attributed. p(s) was more noisy for higher thresholds since less events contributed to the distribution.
Figure 6
Figure 6. The avalanche measures all were larger with SWS in humans.
A–C The avalanche measures (formula image, đ, and σ) were plotted over the bin size separately for each vigilance state (colours) and each night (traces). (+) indicate the mean measure across nights for each vigilance state. For SWS (s3/s4 and s2), neuronal avalanches were larger, longer and showed a larger branching parameter. The results here were shown for r = ¼Hz, however, the same results held for other rates (Supplementary Figure S6). D–F The same avalanche measures were plotted for the subsampled model. The model was varied from critical (black traces) to various degrees of subcriticality (dE<1). Subcritical models (dE<1) that were closer to the critical state (dE = 1) showed larger and longer avalanches, and larger branching parameter.
Figure 7
Figure 7. The avalanche measures differed between vigilance states.
Each of the three measures (formula image, đ, and σ) was larger for SWS (s3/s4, s2) and smaller for REM sleep and wakefulness. For illustration purpose, we here combined the values of each measure across all patients, temporal bin sizes, and rates, although the statistical test distinguished between these parameters. Boxes indicate the median, and error bars indicate the 25th and 75th percentiles. The error bars are relatively wide, since the parameters (bs and r) influenced the avalanche measures. All three avalanche measures showed similar test results in the statistical test, therefore test results were indicated only once (* p<0.05, ** p<0.001, after sequential Bonferoni correction; s indicates “significant for formula image only”, and s,d “significant for formula image and đ, but not for σ”).
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