Neuroscientists have discovered previously unknown geometric structures inside the brain that could explain how we remember things and perform intricate tasks.
A team of researchers, including Professor Ran Levi from the University of Aberdeen's Institute of Mathematics, has discovered a "universe" of multidimensional geometric structures within brain networks using the algebraic topology, a branch of mathematics that uses the tools of abstract algebra to study geometric objects.
Using this sophisticated technique in a way never before used in neuroscience, they made an important discovery that could have significant implications for our understanding of the brain.
Professor Levi explained: "For a topologist, the brain is like a gigantic network with points (neurons) and paths (connections between them).
"From this it is natural to infer the existence of geometric structures that arise when a group of neurons forms a clique, with each neuron connecting to every other neuron in the group to generate a precise geometric object: three neurons form a triangle, four a tetrahedron, and so on.
"We have discovered tens of millions of such structures in brain networks, which in some cases have up to seven dimensions, that is, a network of eight neurons connected to each other in a very organized way. Our research suggests that there may be structures that can have up to eleven dimensions or more."
The research was conducted by the Blue Brain Project, a research institute based at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland that aims to build detailed digital reconstructions and simulations of the brain.
Numerous tests were performed on virtual brain tissue to demonstrate that the discovered multidimensional brain structures could not have been produced by chance. Experiments were then performed on real brain tissue in the Blue Brain laboratory in Lausanne, which confirmed that the previous findings in virtual tissue are biologically relevant.
The findings also suggest that the brain is constantly re-creating itself during activity to build a network with as many high-dimensional structures as possible, which the team described as a brain that is continually creating and then destroying “sand castles.”
Professor Levi said: "When stimulated, the cliques of progressively larger dimensions momentarily assemble to enclose high-dimensional holes or 'cavities'.
"The appearance of these cavities when the brain is processing information means that the neurons in the network are responding to stimuli in a highly organized way. This is an exciting insight that begins to reveal the deepest architectural secrets of the brain."
Professor Levi worked with Blue Brain Project founder Professor Henry Markram and EPFL mathematician Professor Kathryn Hess. Their work was published in Frontiers in Computational Neuroscience.
Professor Markram said: "The big question we are now asking is whether the complexity of the tasks we can perform depends on the complexity of the multidimensional 'sandcastles' that the brain can build."
"Neuroscientists have also struggled to find where the brain stores its memories. They may be 'hidden' in these high-dimensional cavities."