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The Multi-Dimensional Universe Inside Your Brain

Jennifer McDowall explores how new research methods are revealing the complex processes behind our decision-making

Photo by Amanda Dalbjorn


The brain is one of the most complex organs in the body and, despite huge amounts of research, a concrete link between its structure and function has remained elusive. However, a research initiative situated at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland is changing that.


Founded by Professor Henry Markram, the project’s current director, the Blue Brain Project is breaking new ground in the study of the brain by combining biological and theoretical data with computer models.


In 2016, Markram stated, “Our mission is to build a detailed, realistic computer model of the human brain.” The Blue Brain Project, which aims to construct a digital simulation of the mouse brain, is one of the steps towards achieving this goal.


In a paper published in Frontiers in Computational Neuroscience, the authors describe the presence of complex structures within the brain, found with the help of a simulation of the neocortex. These structures consist of groups of neurons called cliques, where each neuron is connected to every other neuron in the group. The more neurons present, the higher the ‘dimension’ of the structure.


“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” Henry Markram.

The “Multi-Dimensional Sandcastle”


In addition to these multi-dimensional structures, the researchers reported the presence of cavities, which are formed when neurons from different cliques link together. These cavities can increase in size, as the dimension of the linked cliques increases.


Following a stimulus, the complexity of cliques and cavities increase dramatically and then disappear, suggesting a direct correlation between brain activity and these multi-dimensional structures. The authors suggest that the formation of multi-dimensional cliques and cavities is how the brain processes stimuli.


Ran Levi, Chair in Mathematics at the University of Aberdeen, and collaborating author on the paper, explains:


"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 organised manner... 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 materialises out of the sand and then disintegrates."

This finding was backed up by observing the phenomenon in biological tissue samples of the neocortex, and also in other organisms. This suggests that Markram and his co-authors have uncovered a universal property of the nervous system.


Observing the Decision-Making Process

The researchers were able to discern these structures using a technique called algebraic topology. In very simple terms, this involves using maths to analyse spaces and it allows both the local and global properties of a neural network to be quantified.


This process allowed researchers to observe patterns in the neuronal firing of their simulated neural network, which is almost impossible to detect without it. Kathryn Hess Bellwald, a researcher for the Laboratory for Topology and Neuroscience at EPFL, believes that this method allows researchers to visualise “the brain’s own code”.


“When you look at this pattern of firing through the filter of algebraic topology, different structures emerge, in terms of which families of neurons are firing in which order... When we looked at the evolution of such a pattern through time, it gives us a mathematical signature that describes this pattern that was hidden in the seemingly chaotic firing of the network.” – Kathryn Hess Bellwald

Algebraic topology enables the researchers to describe the encoding process, and maybe even visualise the moment a decision is made. "That’s what we’re detecting", says Hess, "we’re detecting the information processing and decision-making processes of the brain.”


Although this finding is ground-breaking, there remains a lot about the brain we still don’t understand. However, research continues, and the Human Brain Project is now underway at the EPFL, with 135 institutions from all over the world collaborating. More revelations about our incredible brains will undoubtedly soon be revealed.


Similar: Anxiety and Depression: The Common Concerns of Modern Society

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