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3D reconstruction of selected neurons in a small region of the human cortex dataset. Image credit: Harvard University/Google

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3D reconstruction of selected neurons in a small region of the human cortex dataset. Image credit: Harvard University/Google

When a magnet is heated, it reaches a critical point where it loses its magnetization. This point of high complexity, known as “criticality,” is reached when a physical object smoothly transitions from one phase to the next.

Now, a new study from Northwestern University has found that the structural features of the brain lie near a similar critical point—either at or near a structural phase transition. Surprisingly, these results are consistent in the brains of humans, mice, and fruit flies, suggesting that the discovery may be universal.

Although the researchers do not know which phases the brain’s structure moves between, they believe this new information could enable new designs for computer models of the brain’s complexity and emergent phenomena.

The study was published today in News physics.

“The human brain is one of the most complex systems known and many details of its structure are not yet understood,” said István Kovács of Northwestern University, the study’s lead author.

“Several other researchers have studied brain criticality in terms of neuron dynamics. But we are looking at criticality at a structural level to ultimately understand how it underpins the complexity of brain dynamics. This was a missing piece of the puzzle in our understanding of brain complexity. Unlike a computer, where any software can run on the same hardware, in the brain the dynamics and the hardware are tightly coupled.”


Examples of single neuron reconstruction from fruit fly, mouse, and human datasets. (Not to scale). Image credit: Northwestern University

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Examples of single neuron reconstruction from fruit fly, mouse, and human datasets. (Not to scale). Image credit: Northwestern University

“The structure of the brain at the cellular level appears to be near a phase transition,” said Helen Ansell of Northwestern University, the study’s lead author. “An everyday example of this is when ice melts into water. They are still water molecules, but they are going through a transition from solid to liquid. We are certainly not saying that the brain is about to melt. In fact, we have no way of knowing which two phases the brain might switch between. Because if it were on either side of the critical point, it wouldn’t be a brain.”

Kovács is an assistant professor of physics and astronomy in the Weinberg College of Arts and Sciences at Northwestern University. At the time of the research, Ansell was a postdoctoral fellow in his lab; she is now a Tarbutton Fellow at Emory University.

While researchers have long studied brain dynamics using functional magnetic resonance imaging (fMRI) and electroencephalograms (EEG), only recently have advances in neuroscience provided extensive data sets on the brain’s cellular structure. These data opened the door for Kovács and his team to apply statistical physics techniques to measure the physical structure of neurons.

For the new study, Kovács and Ansell analyzed publicly available data from 3D brain reconstructions of humans, fruit flies and mice. By examining the brains at nano-resolution, the researchers found that the samples exhibited features of physical properties associated with criticality.

One such property is the well-known fractal-like structure of neurons. This nontrivial fractal dimension is an example of a set of observables called “critical exponents” that appear when a system approaches a phase transition.


Snapshot of selected neurons from the human cortex dataset, viewed using the online platform Neuroglancer. Image credit: Harvard University/Google

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Snapshot of selected neurons from the human cortex dataset, viewed using the online platform Neuroglancer. Image credit: Harvard University/Google

Brain cells are arranged in a fractal-like statistical pattern at different scales. When zoomed in, the fractal shapes are “self-similar,” meaning that smaller parts of the sample resemble the entire sample. The sizes of the different neuron segments observed are also different, providing another clue. According to Kovács, self-similarity, long-range correlations, and broad size distributions are all signs of a critical state where features are neither too organized nor too random. These observations lead to a set of critical exponents that characterize these structural features.

“These are things we observe in all critical systems in physics,” said Kovács. “It seems as if the brain is in a delicate balance between two phases.”

Kovács and Ansell were amazed to find that all the brain samples they examined – from humans, mice and fruit flies – showed consistent critical exponents across all organisms, that is, they shared the same quantitative characteristics of criticality. The underlying, compatible structures between organisms suggest that a universal guiding principle may be at play. Their new findings could potentially help explain why the brains of different creatures share some of the same basic principles.

“At first, these structures look very different – an entire fly brain is about the size of a small human neuron,” said Ansell. “But then we discovered surprisingly similar properties.”

“For the many features that vary greatly from organism to organism, we relied on suggestions from statistical physics to test which measures might be universal, such as critical exponents. In fact, these are uniform across all organisms,” said Kovács.


3D reconstruction of selected neurons in a small region of the human cortex dataset. Image credit: Harvard University/Google

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3D reconstruction of selected neurons in a small region of the human cortex dataset. Image credit: Harvard University/Google

“An even deeper sign of criticality is that the critical exponents obtained are not independent – from any three we can calculate the rest, as statistical physics dictates. This insight opens the possibility of formulating simple physical models to capture statistical patterns of brain structure. Such models are useful inputs for dynamic brain models and can serve as inspiration for the architecture of artificial neural networks.”

Next, the researchers plan to apply their techniques to new data sets, including larger brain regions and more organisms, to see if universality still holds.

More information:
Helen S. Ansell et al, Unveiling universal aspects of the cellular anatomy of the brain, News physics (2024). DOI: 10.1038/s42005-024-01665-y

Information about the magazine:
News physics

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