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The Brain Criticality Hypothesis

This hypothesis originates not from biology but from physics.

The theory of Self-Organized Criticality was introduced in the 1980s to explain how complex systems, such as avalanches or earthquakes, can spontaneously organize themselves into a critical state without external influence (just like the building up of a pile of sand that when it got too steep, it collapse on its own without any external influences). In neuroscience, it was adapted as the "Brain Criticality Hypothesis."

What is criticality?

The brain must balance two essential functions: storing and transmitting information.

In a sub-critical state, the brain can store large amounts of information but struggles to transmit it. In a super-critical state, it transmits information efficiently but sacrifices storage capacity.

Also, when the brain is the sub-critical state, when a neuron fires, it triggers, on average, less than one neuron to fire (\(\sigma<1\)), while in a super-critical state, it triggers more than one neuron to fire (\(\sigma>1\)).

Note \(\sigma\) is the branching ratio, which is the average number of neurons that fire in response to a single neuron firing.

Thus, the brain operates at a critical state—a balance between sub-critical and super-critical states.

Why is it important?

Deviations from the critical state impair brain function. Minor deviations are linked to reduced cognitive ability, while major deviations are associated with neurodegenerative diseases like Alzheimer's, Parkinson's, and Huntington's.

These deviations are cortex-specific. For example, Alzheimer's patients show significant deviations in the CA1 region of the hippocampus, while the V1 region of the visual cortex remains relatively unaffected.

This understanding could lead to methods for measuring or predicting neurodegenerative diseases, making it a promising research area.

How to measure criticality?

Deviation from Criticality

The brain is a complex system, and measuring its criticality is challenging. One approach involves analyzing the power-law distribution of brain activity. The Deviation from Criticality Coefficient (DCC) quantifies how close the brain is to criticality, with values closer to zero indicating proximity to the critical state.

When a neuron fires, it triggers a cascade of activity involving multiple neurons. These cascades, characterized by their size and duration, follow power-law distributions.

  1. Plot the duration vs. the number of avalanches on a log-log scale. Let the slope of the line be \( \alpha \).
  2. Plot the size of avalanches vs. the number of avalanches on a log-log scale. Let the slope of this line be \( \tau \).
  3. Calculate \( \beta_{p} = \frac{\alpha - 1}{\tau - 1} \).
  4. Plot the size of avalanches vs. their duration on a log-log scale. Let the slope of this line be \( \beta_{f} \).

Finally, the DCC is defined as: \( |\beta_{p} - \beta_{f}| \)

This method was proposed by Zhengyu Ma et al. in 2019.

Invariance

Critical systems, such as the brain, exhibit invariance(1), meaning certain features remain unchanged when the scale of time or space is altered. Learn more about invariance and criticality.

  1. Scale invariance refers to a property of a system that remains consistent across different scales.

One way to measure invariance is through autocorrelation, which quantifies how the system behaves under scale transformations.

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

This method requires fewer data points than calculating the DCC and is easier to compute. However, it is less established and not as widely used as the DCC.

Conclusion

The Brain Criticality Hypothesis is a relatively new concept with ongoing debates. This introduction highlights its significance and some methods for measuring criticality, offering a foundation for further exploration.