Self-organized criticality and stochastic resonance in the human brain

The human brain spontaneously generates neuronal network oscillations at around 10 and 20 Hz with a large variability in amplitude, duration, and recurrence. Despite more than 70 years of research, the complex dynamics and functional significance of these oscillations have remained poorly understood. This Thesis concerns the dynamic character and functional significance of noninvasively recorded 10- and 20-Hz oscillations in the human brain. The hypotheses, experimental paradigms, data analyses, and interpretations of the results are inspired by recent insights from physics - most notable the theory of self-organized criticality and the phenomenon of stochastic resonance whose applicability to large-scale neuronal networks is explained. We show that amplitude fluctuations of 10- and 20-Hz oscillations during wakeful rest are correlated over thousands of oscillation cycles and that the decay of temporal correlations exhibits power-law scaling behavior. However, when these ongoing oscillations are perturbed with sensory stimuli, the amplitude attenuates quickly, reliably, and transiently, and the long-range temporal dynamics is affected as evidenced by changes in scaling exponents compared to rest. In addition to the rich temporal dynamics in local areas of the cortex, ongoing oscillations tend to synchronize their phases and exhibit correlated amplitude fluctuations across the two hemispheres, as shown for oscillations in homologous areas of the sensorimotor cortices. Finally, it is revealed that intermediate amplitude levels of ongoing oscillations provide the optimal oscillatory state of the sensorimotor cortex for reliable and quick conscious detection of weak somatosensory stimuli. We propose that the long-range temporal correlations, the power-law scaling behavior, the high susceptibility to stimulus perturbations, and the large amplitude variability of ongoing oscillations may find a unifying explanation within the theory of self-organized criticality. This theory offers a general mechanism for the ubiquitous emergence of complex dynamics with power-law decay of spatiotemporal correlations in non-linear self-organizing stochastic systems consisting of many units. The optimal ability to detect consciously and respond behaviorally to weak somatosensory stimuli at intermediate levels of ongoing sensorimotor oscillations is attributed to stochastic resonance - the intuitively paradoxical phenomenon that the signal-to-noise ratio of detecting or transmitting a signal in a non-linear system can be enhanced by noise. Based on the above results, we conjecture that a mechanism of intrinsic stochastic resonance between self-organized critical and stimulus-induced activities may be a general organizing principle of great importance for central nervous system function and account for some of the variability in the way we perceive and react to the outside world.reviewe

Long-Range Amplitude Coupling Is Optimized for Brain Networks That Function at Criticality

Brain function depends on segregation and integration of information processing in brain networks often separated by long-range anatomic connections. Neuronal oscillations orchestrate such distributed processing through transient amplitude and phase coupling, yet surprisingly, little is known about local network properties facilitating these functional connections. Here, we test whether criticality, a dynamical state characterized by scale-free oscillations, optimizes the capacity of neuronal networks to couple through amplitude or phase, and transfer information. We coupled in silico networks which exhibit oscillations in the α band (8–16 Hz), and varied excitatory and inhibitory connectivity. We found that phase coupling of oscillations emerges at criticality, and that amplitude coupling, as well as information transfer, are maximal when networks are critical. Importantly, regulating criticality through modulation of synaptic gain showed that critical dynamics, as opposed to a static ratio of excitatory and inhibitory connections, optimize network coupling and information transfer. Our data support the idea that criticality is important for local and global information processing and may help explain why brain disorders characterized by local alterations in criticality also exhibit impaired long-range synchrony, even before degeneration of axonal connections. SIGNIFICANCE STATEMENT To perform adaptively in a changing environment, our brains dynamically coordinate activity across distant areas. Empirical evidence suggests that long-range amplitude and phase coupling of oscillations are systems-level mechanisms enabling transient formation of spatially distributed functional networks on the backbone of a relatively static structural connectome. However, surprisingly little is known about the local network properties that optimize coupling and information transfer. Here, we show that criticality, a dynamical state characterized by scale-free oscillations and a hallmark of neuronal network activity, optimizes the capacity of neuronal networks to couple through amplitude or phase and transfer information

Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. A control parameter $p$ determines the probability of threshold adaptations vs. link rewiring. For any $p < 1$, we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity $\bar{K}_{evo}$ than networks without threshold adaptation ($p =1$). While $\bar{K}_{evo}$ and evolved out-degree distributions are independent from $p$ for $p <1$, in-degree distributions become broader when $p \to 1$, approaching a power-law. In this limit, time scale separation between threshold adaptions and rewiring also leads to strong correlations between thresholds and in-degree. Finally, evidence is presented that networks converge to self-organized criticality for large $N$.Comment: 4 pages revtex, 6 figure

Scaling laws of human interaction activity

Even though people in our contemporary, technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in two social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than one year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.Comment: 20+7 pages, 4+2 figure

Breakdown of long-range temporal correlations in theta oscillations in patients with major depressive disorder

Neuroimaging has revealed robust large-scale patterns of high neuronal activity in the human brain in the classical eyes-closed wakeful rest condition, pointing to the presence of a baseline of sustained endogenous processing in the absence of stimulus-driven neuronal activity. This baseline state has been shown to differ in major depressive disorder. More recently, several studies have documented that despite having a complex temporal structure, baseline oscillatory activity is characterized by persistent autocorrelations for tens of seconds that are highly replicable within and across subjects. The functional significance of these long-range temporal correlations has remained unknown. We recorded neuromagnetic activity in patients with a major depressive disorder and in healthy control subjects during eyes-closed wakeful rest and quantified the long-range temporal correlations in the amplitude fluctuations of different frequency bands. We found that temporal correlations in the theta-frequency band (3-7 Hz) were almost absent in the 5-100 s time range in the patients but prominent in the control subjects. The magnitude of temporal correlations over the left temporocentral region predicted the severity of depression in the patients. These data indicate that long-range temporal correlations in theta oscillations are a salient characteristic of the healthy human brain and may have diagnostic potential in psychiatric disorders. We propose a link between the abnormal temporal structure of theta oscillations in the depressive patients and the systems-level impairments of limbic-cortical networks that have been identified in recent anatomical and functional studies of patients with major depressive disorder. Copyright © 2005 Society for Neuroscience

Scale-free amplitude modulation of neuronal oscillations tracks comprehension of accelerated speech

Speech comprehension is preserved up to a threefold acceleration, but deteriorates rapidly at higher speeds. Current models posit that perceptual resilience to accelerated speech is limited by the brain's ability to parse speech into syllabic units using δ/θ oscillations. Here, we investigated whether the involvement of neuronal oscillations in processing accelerated speech also relates to their scale-free amplitude modulation as indexed by the strength of long-range temporal correlations (LRTC). We recorded MEG while 24 human subjects (12 females) listened to radio news uttered at different comprehensible rates, at a mostly unintelligible rate and at this same speed interleaved with silence gaps. δ, θ, and low-γ oscillations followed the nonlinear variation of comprehension, with LRTC rising only at the highest speed. In contrast, increasing the rate was associated with a monotonic increase in LRTC in high-γ activity. When intelligibility was restored with the insertion of silence gaps, LRTC in the δ, θ, and low-γ oscillations resumed the low levels observed for intelligible speech. Remarkably, the lower the individual subject scaling exponents of δ/θ oscillations, the greater the comprehension of the fastest speech rate. Moreover, the strength of LRTC of the speech envelope decreased at the maximal rate, suggesting an inverse relationship with the LRTC of brain dynamics when comprehension halts. Our findings show that scale-free amplitude modulation of cortical oscillations and speech signals are tightly coupled to speech uptake capacity.SIGNIFICANCE STATEMENT One may read this statement in 20-30 s, but reading it in less than five leaves us clueless. Our minds limit how much information we grasp in an instant. Understanding the neural constraints on our capacity for sensory uptake is a fundamental question in neuroscience. Here, MEG was used to investigate neuronal activity while subjects listened to radio news played faster and faster until becoming unintelligible. We found that speech comprehension is related to the scale-free dynamics of δ and θ bands, whereas this property in high-γ fluctuations mirrors speech rate. We propose that successful speech processing imposes constraints on the self-organization of synchronous cell assemblies and their scale-free dynamics adjusts to the temporal properties of spoken language

A power-law distribution of phase-locking intervals does not imply critical interaction

Neural synchronisation plays a critical role in information processing, storage and transmission. Characterising the pattern of synchronisation is therefore of great interest. It has recently been suggested that the brain displays broadband criticality based on two measures of synchronisation - phase locking intervals and global lability of synchronisation - showing power law statistics at the critical threshold in a classical model of synchronisation. In this paper, we provide evidence that, within the limits of the model selection approach used to ascertain the presence of power law statistics, the pooling of pairwise phase-locking intervals from a non-critically interacting system can produce a distribution that is similarly assessed as being power law. In contrast, the global lability of synchronisation measure is shown to better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits throughout. Clarified relationship between theoretical critical coupling for infinite size system and 'effective' critical coupling system for finite size system. Improved presentation and discussion of results; results unchanged. Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11 pages, 7 figure

Genetic contributions to long-range temporal correlations in ongoing oscillations

The amplitude fluctuations of ongoing oscillations in the electroencephalographic (EEG) signal of the human brain show autocorrelations that decay slowly and remain significant at time scales up to tens of seconds. We call these long-range temporal correlations (LRTC). Abnormal LRTC have been observed in several brain pathologies, but it has remained unknown whether genetic factors influence the temporal correlation structure of ongoing oscillations. We recorded the ongoing EEG during eyes-closed rest in 390 monozygotic and dizygotic twins and investigated the temporal structure of ongoing oscillations in the alpha- and beta-frequency bands using detrended fluctuation analysis (DFA). The strength of LRTC was more highly correlated in monozygotic than in dizygotic twins. Statistical analysis attributed up to ∼60% of the variance in DFA to genetic factors, indicating a high heritability for the temporal structure of amplitude fluctuations in EEG oscillations. Importantly, the DFA and EEG power were uncorrelated. LRTC in ongoing oscillations are robust, heritable, and independent of power, suggesting that LRTC and oscillation power are governed by distinct biophysical mechanisms and serve different functions in the brain. We propose that the DFA method is an important complement to classical spectral analysis in fundamental and clinical research on ongoing oscillations. Copyright © 2007 Society for Neuroscience