Scientists have employed a traditional field of mathematics in an entirely novel approach to investigate the anatomy of human brains. They revealed that the brain is filled of multidimensional geometrical structures that operate in up to 11 dimensions.

We're used to seeing the world in three dimensions, so this may sound difficult, but the findings of this new study could be the next important step in understanding the fabric of the human brain - the most intricate structure we've discovered.

The Blue Brain Project, a Swiss scientific endeavour dedicated to developing a supercomputer-powered recreation of the human brain, created its latest brain model.

The team used algebraic topology, a branch of mathematics used to describe the properties of objects and spaces regardless of how they change shape. They found that groups of neurons connect into '**cliques**', and that the number of neurons in a clique would lead to its size as a high-dimensional geometric object.

"We found a world that we had never imagined. There are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to 11 dimensions." says lead researcher, neuroscientist Henry Markram from the EPFL institute in Switzerland.

Human brains are estimated to have a staggering 86 billion neurons, with multiple connections from each cell webbing in every possible direction, forming the vast cellular network that somehow makes us capable of thought and consciousness. With such a huge number of connections to work with, it's no wonder we still don't have a thorough understanding of how the brain's neural network operates. But the new mathematical framework built by the team takes us one step closer to one day having a digital brain model.

To perform the mathematical tests, the team used a detailed model of the neocortex the Blue Brain Project team published back in 2015. The neocortex is thought to be the most recently evolved part of our brains, and the one involved in some of our higher-order functions like cognition and sensory perception.

After developing their mathematical framework and testing it on some virtual stimuli, the team also confirmed their results on real brain tissue in rats. According to the researchers, algebraic topology provides mathematical tools for discerning details of the neural network both in a close-up view at the level of individual neurons, and a grander scale of the brain structure as a whole.

By connecting these two levels, the researchers could discern high-dimensional geometric structures in the brain, formed by collections of tightly connected neurons (cliques) and the empty spaces (cavities) between them.

"We found a remarkably high number and variety of high-dimensional directed cliques and cavities, which had not been seen before in neural networks, either biological or artificial," the team writes in the study.

"Algebraic topology is like a telescope and microscope at the same time. It can zoom into networks to find hidden structures, the trees in the forest, and see the empty spaces, the clearings, all at the same time." says one of the team, mathematician Kathryn Hess from EPFL.

Those clearings or cavities seem to be critically important for brain function. When researchers gave their virtual brain tissue a stimulus, they saw that neurons were reacting to it in a highly organized manner.

"It is as if the brain reacts to a stimulus by building [and] then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates." says one of the team, mathematician Ran Levi from Aberdeen University in Scotland.

These findings provide a tantalising new picture of how the brain processes information, but the researchers emphasise that it is not yet clear what causes the cliques and cavities to form in such specific ways, and that more research will be required to determine how the complexity of these multidimensional geometric shapes formed by our neurons correlates with the complexity of various cognitive tasks.

But this is far from the last we'll hear about algebraic topology's insights into the most enigmatic of human organs - the brain.

The study was published in **Frontiers of Computational Neuroscience**.

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