Neuroscientists have discovered previously unknown geometric structures within the brain that could potentially explain how we remember things and perform intricate tasks.
A team of researchers, including Professor Ran Levi from the Institute of Mathematics at the University of Aberdeen, has uncovered a ‘universe’ of multi-dimensional geometric structures within brain networks by using algebraic topology - a branch of mathematics that uses tools from abstract algebra to study geometric objects.
By using this sophisticated technique in a way never before used in neuroscience, they have made an important breakthrough that could have significant implications for our understanding of the brain.
Professor Levi explained: “To a topologist the brain is like a gigantic network with dots (neurons) and pathways (connections among them).
“From this it is natural to infer the existence of geometric structures which 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 that in some cases have up to seven dimensions - that is, a network of up to eight neurons all connected to each other in a very organised manner. Our research suggests that there may be some structures that could have anything up to eleven dimensions or more.”
The research has been carried out 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.
Multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance. Experiments were then performed on real brain tissue in the Blue Brain’s wet lab in Lausanne, which confirmed that the earlier discoveries in the virtual tissue are biologically relevant.
The results also suggest that the brain constantly rewires during activity to build a network with as many high-dimensional structures as possible, which the team have described as akin to the brain continually creating and then disintegrating ‘sandcastles’.
Professor Levi said: “When stimulated, cliques of progressively higher dimensions assemble momentarily 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 react to stimuli in an extremely organized manner. This is an exciting insight that is beginning to reveal the brain’s deepest architectural secrets.”
Professor Levi worked alongside Blue Brain Project founder Professor Henry Markram and Professor Kathryn Hess, a mathematician from EPFL. Their work has been published in Frontiers in Computational Neuroscience.
Professor Markram said: “The big question we are asking now is whether the intricacy of tasks we can perform depends on the complexity of the multi-dimensional ‘sandcastles’ the brain can build.
“Neuroscience has also been struggling to find where the brain stores its memories. They could be ‘hiding’ in these high-dimensional cavities.”