Computational Neuroscience
Henry Markram's controversial Blue Brain Project has announced that our brains may not just be operating in three dimensions. According to the team's new mathematical models, they have demonstrated that the brain operates on up to potentially eleven dimensions.
By using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain. According to the researchers, the discovery brings us closer to understanding the fundamental mysteries of neuroscience: the link between the structure of the brain and how it processes information.
The research, published recently in Frontiers in Computational Neuroscience, shows that these structures arise when a group of neurons forms what they call a clique.
In a clique, each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object.
"We found a world that we had never imagined," says neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland, "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 eleven dimensions."
"We found a world that we had never imagined."
According to Markram, this work may explain why it has been so hard for us to understand the brain. "The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly."
The research team, including mathematicians Kathryn Hess from EPFL and Ran Levi from Aberdeen University used a branch of mathematics called algebraic topology to explain these processes. Algebraic topology
uses tools from abstract algebra to study topological spaces.If 4D worlds stretch our imagination, worlds with 5, 6 or more dimensions are nearly impossible for most of us to comprehend. Algebraic topology can describe systems with any number of dimensions.
"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," explains Hess.
In 2015, Blue Brain published the first digital copy of a piece of the neocortex - the most evolved part of the brain and the seat of our sensations, actions, and consciousness. In this latest research, using algebraic topology, 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 confirming that the earlier discoveries in the virtual tissue are biologically relevant and also suggesting that the brain constantly rewires during development to build a network with as many high-dimensional structures as possible.
"We verified the existence of high-dimensional directed simplices in actual neocortical tissue. We further found similar structures in a nervous system as phylogenetically different as that of the worm C. elegans, suggesting that the presence of high-dimensional topological structures is a general phenomenon across nervous systems," the researchers conclude. C. elegans is an ideal model to test such computational neuroscience work with, as it has a fully mapped connectome.
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When the researchers presented the virtual brain tissue with a stimulus, cliques of progressively higher dimensions assembled momentarily to enclose high-dimensional holes, that the researchers refer to as cavities. "The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner," says Levi."It is as if the brain reacts to a stimulus by building 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."
The big question these researchers 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 may be 'hiding' in high-dimensional cavities," Markram speculates.
“In future work we intend to study the role of plasticity—the strengthening and weakening of connections in response to stimuli—with the tools of algebraic topology. Plasticity is fundamental to the mysterious process of learning, and we hope that we will be able to provide new insight into this phenomenon,” Hess told Newsweek.
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