New study reveals fractal structure of the brain akin to phase transition, a finding that may be universal to all species

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

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

Although the researchers don't know between which phases the brain's structure evolves, they say this new information could enable new designs of computational models of the brain's complexity and emergent phenomena.

The research was published today in Physics of communications.

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

“Several other researchers have studied the criticality of the brain in terms of neuron dynamics. But we are looking at criticality at the structural level in order to ultimately understand how it underlies the complexity of brain dynamics. It's a missing piece in the way we to think about the complexity of the brain Unlike a computer where any software can run on the same hardware, in the brain, dynamics and hardware are closely linked.

“The structure of the brain at the cellular level appears to be close to a phase transition,” said Helen Ansell of Northwestern, first author of the paper. “An everyday example of this is when ice melts in water. They are still water molecules, but they are undergoing a transition from solid to liquid. We are certainly not saying that the brain is about to melt. In fact, we don't have a hypothesis for a way of knowing which two phases the brain could go through. 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 at Northwestern's Weinberg College of Arts and Sciences. At the time of the research, Ansell was a postdoctoral researcher in his laboratory; 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), advances in neuroscience have only recently provided massive data sets on the structure brain cells. These data opened up the possibility 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 on 3D brain reconstructions of humans, fruit flies and mice. By examining the brain at nanometer resolution, the researchers found that the samples exhibited physical property characteristics associated with criticality.

One of these properties is the well-known fractal-like structure of neurons. This non-trivial fractal dimension is an example of a set of observables, called “critical exponents”, that emerge when a system is close to a phase transition.

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 neuronal segments observed are also diverse, which provides another clue. According to Kovács, self-similarity, long-range correlations, and broad size distributions are all signatures 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 see in all critical systems in physics,” Kovács said. “It appears that the brain is in a delicate balance between two phases.”

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

“Initially, these structures appear very different: an entire fly brain is about the size of a small human neuron,” Ansell said. “But then we discovered surprisingly similar emergent properties.”

“Among the many characteristics that differ greatly across organisms, we relied on suggestions from statistical physics to check which metrics are potentially universal, like critical exponents. Indeed, these are consistent across organisms,” said Kovacs.

” An even deeper sign of criticality, the critical exponents obtained are not independent: from any three, we can calculate the remainder, as statistical physics dictates. This discovery paves the way for the formulation of simple physical models to capture statistical patterns of the brain Such models are useful inputs for dynamic brain models and can be a source of inspiration for artificial neural network architectures.

Next, the researchers plan to apply their techniques to new and emerging data sets, including larger sections of the brain and more organisms. They aim to determine whether universality will still apply.