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Criticality in the brain: A synthesis of neurobiology, models and cognition

Luca Cocchi, Leonardo L. Gollo, Andrew Zalesky, Michael Breakspear

arXiv:1707.05952v1q-bio.NC

TL;DR

Neuroscience needs frameworks that accommodate activity across multiple biological scales rather than focusing on scale-specific phenomena. This paper synthesizes criticality in physical and neural systems, reviews evidence and computational implications, and highlights both its potential relevance to cognition and brain disorders and the need for cautious inference.

  • Problem

    Neuroscience has advanced through scale-specific research silos, but comprehensive explanations of brain activity and cognition require coordination across multiple scales.

  • Method

    The paper reviews critical phenomena in physical systems, classic and recent studies of neuronal criticality, and applications to healthy and maladaptive cognition.

  • Results

    Models indicate that neural systems have maximum adaptability near a critical point, whereas epilepsy, encephalopathy, bipolar disorder, and schizophrenia may correspond to departures from it.

  • Takeaways & Limitations

    Criticality offers a framework for understanding multiscale neural dynamics and their possible computational advantages, including broad sensitivity to input intensities.

  • Takeaways & Limitations

    Power-law scaling alone does not establish criticality because non-critical stochastic systems can produce similar statistics under some conditions.

Abstract

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Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.

1. Introduction

Neuroscience has made progress across multiple scales, but the principles linking brain function across those scales remain largely unknown. The paper presents criticality as a framework for understanding such multiscale dynamics while reviewing evidence, applications, and methodological cautions.

  • Neuroscience research has advanced from molecular and cellular processes to cortical circuits and large-scale brain networks, often within scale-specific silos.
  • Criticality describes systems poised between order and disorder, exhibiting scale-free fluctuations that span spatial and temporal scales.
  • Emerging research suggests that critical neural dynamics may support brain function, with models indicating maximum adaptability near a critical point.
  • The review examines criticality in healthy and pathological brain dynamics and considers its potential for theories of healthy and maladaptive cognition.
  • Because criticality is relatively new in neuroscience and is sometimes used metaphorically, the authors emphasize operational criteria and caution about interpretive pitfalls.

2. Criticality in physical systems

Criticality describes fluctuations near dynamic instability in systems ranging from a few interacting components to many spatially extended elements. Its signatures include scale-free fluctuations, slowing down, multistability, and, in complex systems, avalanches across scales.

  • 2. Criticality in physical systems: Criticality occurs when a dynamical system approaches loss of stability, producing erratic fluctuations and signatures including scale-free activity, slowing down, and multistability.
  • 2.1. Criticality and bifurcations: Near a supercritical bifurcation, fluctuations become high-amplitude, slow, and scale-free, whereas noise-driven multistable switching lacks power-law statistics.
  • 2.1. Criticality and bifurcations: Subcritical bifurcations create coexistence between fixed-point and oscillatory states, allowing noise-driven jumps between attractors.
  • 2.1. Criticality and bifurcations: In a supercritical bifurcation, increasing a control parameter switches the system from damped equilibrium to sustained oscillation through a critical point.
  • 2.2. Criticality and phase transitions: Phase transitions in systems with many interacting components generate avalanches whose sizes can span scales and follow power-law distributions at criticality.
  • 2.2. Criticality and phase transitions: At a continuous phase transition, increasing correlation length links local elements into coherent domains, while discontinuous transitions can produce noise-driven switching without scale-free statistics.
  • 2.2. Criticality and phase transitions: Branching processes model criticality without requiring spatial structure, with criticality arising when activation and decay rates are equal.
  • 2.3. The conceptual appeal of criticality: Criticality is conceptually appealing because diverse mechanisms can bring different systems near instability, yielding a shared response to stochastic perturbations.

3. Criticality in the brain

Research across neural recordings and models supports criticality as a multiscale framework for brain dynamics, linking scale-free activity to computation, network organization, and cognition. The review also identifies important trade-offs and conditions that constrain how criticality can support biological function.

  • Scale-free spatiotemporal fluctuations have been observed across neural recordings from in vitro preparations to in vivo cortical and large-scale imaging data.
  • Critical dynamics can recapitulate resting-state networks and may relate functional connectivity to the brain’s structural connectome.
  • Criticality maximizes dynamic range, enabling neuronal systems to respond to and amplify inputs across a broad spectrum of intensities.
  • Models and empirical recordings indicate that criticality supports high-fidelity information transmission and may optimize information storage and capacity.
  • Optimal perceptual performance may combine critical units with high sensitivity and non-critical units with improved reliability.
  • Critical models face a biological challenge because enhanced fluctuations can trap systems in inactive absorbing states, while inhibition can support ceaseless activity and critical avalanches.

4. Challenges and pitfalls of the criticality hypothesis

The review identifies statistical, mechanistic, and measurement pitfalls that can make neural dynamics appear critical without demonstrating criticality. It therefore emphasizes principled distributional testing, causal models, and careful disambiguation from other emergent dynamics.

  • Statistical inference: Power-law fits can be misleading because log-log regression underweights sparse distribution tails and violates independence assumptions for cumulative distributions.Clauset et al.'s approach provides a more principled alternative for testing heavy-tailed statistics.
  • Alternative mechanisms: Several neuronal phenomena are better explained by alternative long-tailed distributions, including alpha rhythms modeled as noise-driven multistability rather than classic criticality.Fluctuating alpha rhythm appears to follow a stretched exponential distribution, not a power law.
  • Null models: Non-critical stochastic systems can produce irregular time series with power-law statistics over limited ranges, so power-law observations alone do not establish criticality.Caution is especially warranted when scaling spans less than two orders of magnitude or has a steep exponent greater than 2.5.
  • Alternative mechanisms: Metastable winnerless competition can generate non-trivial sequential dynamics without invoking criticality.It arises through transitions along a sequence of unstable states and has been proposed for gait, perceptual rivalry, and sequential decision-making.
  • Measurement and modeling: Finite sensor bounds, physiological and scanner noise, and other measurement artifacts can bias power-law model selection or create false positives.The review recommends considering alternative heavy-tailed distributions, modeling causal mechanisms, and accounting for measurement constraints.
  • Disambiguating dynamics: Criticality should be distinguished from multistability and metastability because these instabilities produce different dwell-time statistics and dynamical signatures.Critical systems show scale-free fluctuations, whereas multistable and metastable systems show stretched-exponential or characteristic-time-scale dwell patterns.

5. Emerging role of criticality in cognition

Growing empirical and modeling research links near-critical neural dynamics with cognition, behavior, mental states, and adaptive processing. The evidence also indicates that criticality is context-dependent: it may support exploratory variability at rest while being suppressed during demanding tasks.

  • Emerging role of criticality: Growing empirical and modeling research supports the view that neural dynamics likely occur near critical instabilities, opening criticality to cognitive and clinical research.The review presents this as evidence beyond an initial proof-of-principle stage.
  • Brain and behaviour: Periods of inactivity show power-law statistics whose scaling differs between wakefulness, sleep, and major depression, whereas activity periods fit stretched exponentials.Context-dependent statistical shifts are presented as a tool for studying healthy and pathological brain function.
  • Brain and behaviour: Reaction times across sequential trials show long-range correlations and possible power-law structure, although the evidence and criticality explanation remain contentious.Human activity and memory also exhibit complex temporal structure across many orders of magnitude.
  • Brain-behaviour links: Critical exponents of scale-free neural dynamics correlate with individual differences in behavioral scaling laws across task-related brain regions.Reported anatomical associations include posterior parietal cortex, cuneus, inferotemporal areas, and default mode network regions.
  • Brain-behaviour links: Near-critical neural processes are strongly interdependent across resting-state and task-specific conditions and may shape perceptual and cognitive fluctuations.This connects resting-state dynamics with processes observed during task performance.
  • Suppression during task performance: Increasing attentional load shifts cortical activity farther from criticality, suggesting that demanding task execution suppresses resting-state variability.The proposed account attributes this suppression to dorsal attentional networks.
  • Consciousness: Loss of consciousness is characterized by fewer eigenmodes near instability, while recovery is accompanied by an increase in such modes.These findings are consistent with a link between near-critical dynamics and conscious cognition.
  • Mental states: Neural avalanche occurrence varies with vigilance: it is most frequent during slow-wave sleep, intermediate during wakefulness, and least frequent during REM sleep.The pattern links changes in near-critical dynamics with distinct mental states.

6. Criticality in disease

Critical dynamics appear across neurological and neuropsychiatric disorders, with evidence ranging from seizures and neonatal burst-suppression to altered stability in psychiatric conditions. These findings also suggest possible diagnostic and therapeutic applications, although neuropsychiatric interpretations remain preliminary.

  • 6.1. Bifurcations and seizures: Seizures can be understood as dynamic disorders arising from critical instabilities and bifurcation-related transitions.
  • 6.2. Crackling noise and neonatal burst-suppression: Neonatal burst-suppression exhibits long-tailed, scale-free burst properties spanning six orders of magnitude, whose exponents can pre-empt clinical outcomes.
  • 6.2. Crackling noise and neonatal burst-suppression: Figure 5 shows burst energy scaling over 3 orders of magnitude, power-law length–duration scaling, and truncated-power-law model superiority.
  • 6.3. Criticality and neuropsychiatric disorders: Measures of near-criticality in clinical burst-suppression recordings could serve as prognostic markers, while bifurcation tracking may support seizure control and early warning.
  • 6.3. Criticality and neuropsychiatric disorders: Computational models and empirical analyses link deviations from an optimal critical point to epilepsy, encephalopathy, bipolar disorder, schizophrenia, melancholia, depression, and obsessive-compulsive disorder.
  • 6.3. Criticality and neuropsychiatric disorders: Neuropsychiatric findings are preliminary, and psychiatric phenotypes may involve compensatory replacement of critical dynamics by different processes.

7. Summary

The review presents criticality as a candidate framework for linking brain dynamics across scales and considers mechanisms, adaptive advantages, pathology, and analytic standards. It concludes that criticality is promising but that its relationship to cognition and the interpretation of empirical evidence require further clarification.

  • Criticality’s computational advantages have motivated broad scientific interest, including benefits across multiple systems and measurable quantities.
  • Potential mechanisms for brain criticality include synaptic plasticity, homeostatic regulation, slow energy accumulation, and fast energy release, likely operating together.
  • Pathological failures of adaptive criticality may arise from disturbed supporting mechanisms, including imbalanced inhibition or interoceptive and metabolic disruptions.
  • The relationship between cognition and criticality remains unresolved, and increasingly sophisticated models must be tempered by emerging empirical caveats.
  • Unifying criticality models can organize associations between cognitive functions and neural dynamics, while recent studies implicate transitions from critical to super-critical regimes.
  • Scale-free statistics should be assessed with formal likelihood tests and comparisons against other heavy-tailed processes, rather than invoked metaphorically.

Box 1: Ten-Point Summary

Criticality is associated with dynamic instability and scale-free fluctuations, providing a framework for understanding multiscale brain activity.

  • Criticality arises near dynamic instability and is reflected by scale-free temporal and spatial fluctuations.

2. Critical temporal fluctuations (crackling noise) occur in simple systems close to a bifurcation

Critical temporal fluctuations, or crackling-noise avalanches, occur in simple systems near bifurcations and have been observed across neuronal recordings. Models associate criticality with several adaptive computational benefits.

  • Critical spatiotemporal fluctuations known as avalanches occur in complex systems close to a phase transition.
  • Crackling noise and avalanches have been observed in neuronal recordings across scales, species, health, and disease.
  • Computational models associate criticality with maximum dynamic range, optimal information capacity, storage and transmission, and selective enhancement of weak inputs.

6. Resting-state EEG and fMRI data show evidence of critical dynamics

Criticality describes neural dynamics near instability, where fluctuations can span multiple temporal and spatial scales. The review connects these dynamics to cognition, pathological brain states, and methodological caution.

  • 6. Resting-state EEG and fMRI data show evidence of critical dynamics: The review proposes that a cognitive function may arise through stabilization of a particular subcritical state under sustained attention.
  • 6. Resting-state EEG and fMRI data show evidence of critical dynamics: Mounting evidence and models suggest that epilepsies and neonatal encephalopathy may involve bifurcations or phase transitions into pathological states.
  • 6. Resting-state EEG and fMRI data show evidence of critical dynamics: Criticality-based tools may offer insights into schizophrenia and melancholia, but this application remains somewhat speculative.
  • 6. Resting-state EEG and fMRI data show evidence of critical dynamics: Criticality in neuroscience requires appropriate methods, consideration of alternative complex processes, and computational models combined with data analysis.
  • 6. Resting-state EEG and fMRI data show evidence of critical dynamics: Criticality occurs near dynamic instability, producing fluctuations across temporal and spatial scales rather than at one privileged scale.These fluctuations include power-law temporal activity and spatiotemporal avalanches, with scaling laws linking behavior across scales.
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