Neuroscientists
have used a classic branch of maths in a totally new way to peer into the
structure of our brains. What they've discovered is that the brain is full of
multi-dimensional geometrical structures operating in as many as 11 dimensions.
We're used to thinking of the world from a 3-D perspective.

This
may sound a bit tricky, but the results of this new study could be the next
major step in understanding the fabric of the human brain - the most complex
structure we know of. This latest brain model was produced by a team of
researchers from the
Blue Brain Project, a Swiss research initiative devoted to building a
supercomputer-powered reconstruction of the human brain.

Diagram representing groups of neurons and connections between them that, topologically speaking, make up multi-dimensional ‘cliques’.

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. 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.

“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.

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.

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.

“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.

These
findings provide a tantalizing new picture of how the brain processes
information, but the researchers point out that it's not yet clear what makes
the cliques and cavities form in their highly specific ways and more work will
be needed to determine how the complexity of these multi-dimensional geometric
shapes formed by our neurons correlates with the complexity of various
cognitive tasks.

But
this is definitely not the last we'll be hearing of insights that algebraic
topology can give us on this most mysterious of human organs - the brain.

“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.

The
study was published in

*Frontiers of Computational Neuroscience*
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