Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws

Abstract

Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form long-range temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit power-law size and lifetime distributions. However, it remains unknown whether these neuronal scaling laws are correlated with those characterizing behavioral performance or whether neuronal LRTCs and avalanches are related. Here, we show that the neuronal scaling laws are strongly correlated both with each other and with behavioral scaling laws. We used source reconstructed magneto- and electroencephalographic recordings to characterize the dynamics of ongoing cortical activity. We found robust power-law scaling in neuronal LRTCs and avalanches in resting-state data and during the performance of audiovisual threshold stimulus detection tasks. The LRTC scaling exponents of the behavioral performance fluctuations were correlated with those of concurrent neuronal avalanches and LRTCs in anatomically identified brain systems. The behavioral exponents also were correlated with neuronal scaling laws derived from a resting-state condition and with a similar anatomical topography. Finally, despite the difference in time scales, the scaling exponents of neuronal LRTCs and avalanches were strongly correlated during both rest and task performance. Thus, long and short time-scale neuronal dynamics are related and functionally significant at the behavioral level. These data suggest that the temporal structures of human cognitive fluctuations and behavioral variability stem from the scaling laws of individual and intrinsic brain dynamics.

Fig. 1.

Paradigm for mapping individual behavioral and neuronal scaling laws with TSDTs and source-reconstructed M/EEG recordings. (A) Examples of noise-embedded visual and auditory stimuli whose SNRs are tuned before the experiment to yield an ∼50% hit rate and then kept constant (Fig. S1). (B) Behavioral performance time series of detected (upward ticks) and undetected (downward ticks) display rich dynamics in a bimodal audiovisual TSDT (visual, red; auditory, blue; time series are for the first 10 min of a 30-min session of a representative subject). (C) Visual and auditory detection time series exhibit LRTCs that may be characterized for each subject by DFA exponents, β_V and β_A. (D) Amplitude fluctuations of neuronal oscillations in local cortical patches (here, 10 Hz in the inferior parietal gyrus) are fractally self-similar and (E) show robust LRTC. (F) Avalanche dynamics are salient in source-reconstructed broad-band data. The time series of cortical patches in the example avalanche (see also Fig. S3A) are color coded by the peak latency. These colors correspond to those displayed on pial and flattened cortical surfaces and show the progression of this activity cascade from posterior parietal to temporal and postcentral loci. (Bottom) The avalanche time series (black lines) show the number of cortical patches in which a peak was found, with zeros indicating interavalanche periods. (G) The sizes and lifetimes of cortical avalanches are approximately power-law distributed with exponents, α, close to those of a critical branching process (−1.5 and −2, respectively). (H) In line with this notion, the kappa index, κ, for the size distribution is close to 1. All data in this figure are from the same 30-min session of a subject representative in having β closest to population mean.

Fig. 2.

Scale-free neuronal dynamics are correlated with interindividual variability in behavioral scaling laws. (A) Mean local LRTCs in the 10-Hz band (β) both during the TSDT task performance and in a separate resting-state session are correlated with the mean behavioral scaling exponents (β_behav.). (B) This correlation was significant in frequency bands from 5 to 30 Hz, in broad-band data, and for the avalanche DFA (*P < 0.05, **P < 0.01; ***P < 0.005). (C) Scaling exponents of the size (purple) and lifetime (black) distributions of neuronal avalanches in task- and resting-state data are correlated with the behavioral scaling exponents. (D) The LRTC scaling exponents of neuronal amplitude fluctuations in the 10-Hz and (E) all other studied frequency bands are strongly correlated with the scaling exponents of neuronal avalanches. (F) Partial correlation analysis shows that neuronal LRTCs also are correlated with behavioral LRTC when the contribution of neuronal avalanches is factored out and that the correlation between avalanches (α) and behavioral LRTC (β*) is mediated through the correlation between neuronal LRTCs (β) and avalanches (see also D and E).

Fig. 3.

Neuronal correlates of behavioral scaling laws. Pearson correlation coefficients were computed between β_behav. and β in the six narrow-frequency bands for each cortical patch (Fig. 2B), and significant (P < 0.05, FDR corrected) correlations were displayed on cortical surfaces collapsed into θ/α (5, 7.5, and 10 Hz) and β/γ (15, 20, and 30 Hz) frequency ranges. For each cortical patch of the Destrieux parcellation, the color intensity indicates the fraction of significant correlations across the three bands (pale, 1/3; medium, 2/3; full, 3/3). (A) Correlation of visual behavioral scaling exponents, β_V, with the β of neuronal LRTCs during visual task performance. (B) Correlation of β_V with β in separate resting-state data. (C) Correlation of auditory behavioral scaling exponents, β_A, with the β of neuronal LRTCs during auditory task performance. (D) Correlation of β_A with β in separate resting-state data. a, Anterior; C, central; CI, cingulate; CN, cuneus; F, frontal; G, gyrus; i, inferior; LIN, lingual; m, middle; O, occipital; P, parietal; p, posterior; pr, pre; s, superior; T, temporal. Colors: red, occipital; green, parietal; blue, frontal; yellow, temporal; purple, cingulate. iPG shows the angular part.