The Brain Criticality Hypothesis

An interactive demo is available here:
Brain Criticality Demo and Brief Explanation.

The Brain Criticality Hypothesis proposes that healthy brain activity operates near a critical point: a dynamic boundary between overly weak signal propagation and excessive, unstable excitation. This idea comes from statistical physics, where criticality describes systems poised near phase transitions, such as the transition between liquid and gas or between ordered and disordered magnetic states.

In neuroscience, the hypothesis suggests that the brain may use this near-critical regime to balance two competing demands:

• information storage, which requires stable and differentiated activity patterns;
• information transmission, which requires activity to propagate efficiently across neural circuits.

A brain that is too subcritical may fail to transmit signals effectively. A brain that is too supercritical may over-amplify signals, producing unstable or pathological activity. Criticality is therefore proposed as a functional operating regime for neural systems rather than simply a metaphor from physics.

Neurodegenerative Disease and Early Detection

Neurodegenerative diseases are a heterogeneous group of disorders characterized by progressive synaptic dysfunction, neuronal damage, and neuronal loss. Examples include Alzheimer’s disease, Parkinson’s disease, amyotrophic lateral sclerosis, Huntington’s disease, and chronic traumatic encephalopathy.

A major difficulty in neurodegenerative disease is that clinical symptoms often appear only after substantial biological damage has already occurred. Once neurons are lost, current therapies generally cannot restore them. Existing treatments are therefore often limited to symptom management or slowing progression rather than reversing established damage.

This makes early detection important. If abnormal brain dynamics can be detected before severe symptoms or structural damage appear, there may be a larger window for monitoring, prevention, or early intervention.

Criticality in Physical Systems

Criticality originally comes from physics. A familiar example is the critical point of matter. Carbon dioxide, for example, becomes a supercritical fluid only when both pressure and temperature exceed specific threshold values. Below that point, liquid and gas phases may remain distinguishable. Above the critical point, the system becomes a homogeneous supercritical phase without a clear boundary between phases.

This physical example is useful because it shows that criticality is not simply an intermediate state. It is a special regime where the macroscopic behavior of a system changes qualitatively.

Magnetic Criticality and the Ising Model

The Ising model provides another useful analogy. In a magnetic system, individual spins may become highly aligned at low temperature and disordered at high temperature. Near the critical temperature, the system lies between rigid order and randomness.

At this critical point, local interactions can propagate over long distances. The system becomes highly sensitive: small perturbations can influence large-scale organization. This combination of local variability and global coordination is one reason criticality is relevant to neuroscience.

The brain is not an Ising magnet, but the analogy is useful. Neural systems also consist of many locally interacting units. The criticality hypothesis asks whether neural activity may similarly operate near a boundary where local events can propagate efficiently without becoming unstable.

What Is Brain Criticality?

The brain contains many interacting neurons and neural populations. Each neuron can influence other neurons through synaptic connections, and large-scale activity emerges from these local interactions.

In a subcritical state, neural activity tends to die out. A firing neuron triggers, on average, fewer than one additional neuron. Signals are stable but poorly propagated.

In a supercritical state, neural activity expands too strongly. A firing neuron triggers, on average, more than one additional neuron. Signals propagate easily but may become unstable or excessive.

At criticality, the system lies between these regimes. Activity can propagate across the network without either vanishing immediately or exploding uncontrollably.

Branching Ratio

The branching ratio, usually denoted by \( \sigma \), estimates the average number of future active units caused by each currently active unit.

• \( \sigma < 1 \): subcritical activity
• \( \sigma = 1 \): critical activity
• \( \sigma > 1 \): supercritical activity

If \( x \) neurons are initially active, then after \( t \) steps the approximate number of active neurons is:

When \( \sigma < 1 \), activity decays toward zero. When \( \sigma > 1 \), activity can grow rapidly. When \( \sigma = 1 \), activity is approximately maintained across time.

This is the method used for criticality estimation in the Live Demo.

However, the branching ratio is difficult to estimate reliably in real brains. It requires assumptions about time bins, observed units, causal propagation, and sampling completeness. Because real recordings observe only a small part of the brain, the branching ratio is useful but not sufficient on its own.

Neuronal Avalanches

A common empirical approach to brain criticality analyzes neuronal avalanches. A neuronal avalanche is a cascade of neural activity that begins when activity exceeds a threshold and ends when activity returns below that threshold.

Avalanches can be characterized by:

• size, often measured by the number of active units or events;
• duration, measured by how long the cascade lasts;
• frequency, measured by how often avalanches of a given size or duration occur.

At criticality, avalanche size and duration distributions are often expected to follow approximate power laws. This means that small events are common, large events are rare, and the relationship appears approximately linear on a log-log plot.

Deviation From Criticality Coefficient

The Deviation from Criticality Coefficient, or DCC, measures how closely avalanche statistics conform to the scaling relationships expected near criticality.

One commonly used procedure is:

1. Plot avalanche duration against avalanche frequency on a log-log scale. Let the fitted slope be \( \alpha \).
2. Plot avalanche size against avalanche frequency on a log-log scale. Let the fitted slope be \( \tau \).
3. Calculate the predicted scaling relation:

1. Plot avalanche size against avalanche duration on a log-log scale. Let the fitted slope be \( \beta_f \).
2. Compute:

A smaller DCC indicates that the observed avalanche statistics are closer to the scaling relationship expected at criticality.

This method was proposed by Ma et al. in 2019 and has been used to evaluate altered brain states, including disease states, sleep states, and other changes in neural dynamics.

Scale Invariance

Critical systems often exhibit scale invariance, meaning that certain statistical properties remain similar across different spatial or temporal scales. In the brain, scale invariance would imply that neural activity has related structure across short and long timescales or across local and distributed activity patterns.

One way to study scale-dependent structure is through autocorrelation, which measures how activity at one time point relates to activity at later time points. If neural activity decays too quickly, the system may be overly subcritical. If activity remains excessively persistent or synchronized, the system may be overly supercritical.

There are also newer methods, such as \( d_{\beta} \)-based analyses, that attempt to quantify critical scaling with fewer data points than DCC. These approaches may be computationally efficient, but they are less established and remain under active debate.

My adaptation of the \( d_{\beta} \) analysis code, with multithreading support, vectorization, and Python translation, is available here .

Criticality and Neurodegenerative Disease

The scientific motivation for applying criticality to neurodegenerative disease is that brain disease may alter large-scale neural dynamics before gross structural damage becomes visible.

If neurodegeneration disrupts synaptic function, neuronal excitability, or circuit connectivity, it may shift neural activity away from the critical regime. These deviations may be detectable through electrophysiological recordings or other neural activity measurements.

Some deviations may also be region-specific. For example, Alzheimer’s disease may affect hippocampal regions such as CA1 more strongly than primary visual cortex regions such as V1. If criticality metrics are computed regionally, they may help characterize where neural dynamics are most disrupted.

Brain criticality is therefore not a replacement for existing diagnostic tools. Rather, it may become a complementary screening or monitoring layer: a way to detect abnormal network dynamics before symptoms, structural atrophy, or irreversible damage become obvious.

EEG-Based Applications

Electroencephalography, or EEG, is especially relevant because it is non-invasive, relatively inexpensive, and directly measures brain activity. In principle, EEG recordings can be used to estimate avalanche-like dynamics and compute criticality-related metrics such as DCC.

This gives EEG-based criticality analysis several possible advantages:

• it may be relatively low-cost;
• it is non-invasive;
• it may reflect functional network dynamics rather than only structural damage;
• it may be applicable across multiple diseases rather than being tied to one disease-specific marker.

However, EEG criticality analysis remains a research tool, not a validated clinical diagnostic standard. It requires careful preprocessing, sufficient recording duration, artifact control, and rigorous validation against clinical outcomes.