Brain’s Neurons Arrangement has a Math Pattern

Human Brain Project (HBP) researchers from Forschungszentrum Jülich and the University of Cologne (Germany) have discovered how neuron densities in the mammalian brain are distributed across and within cortical areas. The universal lognormal distribution of neuron density has been revealed as a key organizational element of cortical cytoarchitecture. The number of neurons and their spatial arrangement are critical in shaping the structure and function of the brain. Despite the abundance of cytoarchitectonic data available, the statistical distributions of neuron densities remain mostly unknown. The latest HBP study, published in Cerebral Cortex, adds to our understanding of mammalian brain architecture.

The researchers relied on nine publicly accessible datasets from seven different species: mouse, marmoset, macaque, galago, owl monkey, baboon, and human. They discovered that neuron concentrations within each cortical area follow a consistent pattern—a lognormal distribution—after evaluating the cortical areas of each. This shows that the densities of neurons in the mammalian brain are governed by a basic organizing principle.

A lognormal distribution is a statistical distribution with a skewed bell curve. It occurs, for example, when calculating the exponential of a regularly distributed variable. In various aspects, it differs from a normal distribution. Most notably, the normal distribution curve is symmetric, but the lognormal distribution curve is asymmetric with a large tail.

These findings are important for appropriately simulating the brain.

“Not least because the distribution of neuron densities influences the network connectivity,”  explains Sacha van Albada, senior author of the article and leader of the Theoretical Neuroanatomy group at Forschungszentrum Jülich. “For instance, if the density of synapses is constant, regions with lower neuron density will receive more synapses per neuron,” she explains. Such considerations are also important in the development of brain-inspired technology, such as neuromorphic hardware.

“Furthermore, as cortical areas are often distinguished on the basis of cytoarchitecture, knowing the distribution of neuron densities can be relevant for statistically assessing differences between areas and the locations of the borders between areas,” Van Albada also added.

These findings support the fact that a surprising number of brain features have a lognormal distribution. “One reason why it may be very common in nature is because it emerges when taking the product of many independent variables,” mentioned Alexander van Meegen, the study’s co-first author. In other words, the lognormal distribution emerges naturally from multiplicative processes, much as the normal distribution does when numerous independent variables are added together.

Van Meegen mentioned  “Using a simple model, we were able to show how the multiplicative proliferation of neurons during development may lead to the observed neuron density distributions”.

According to the study, in theory, cortical organizational structures could be by-products of growth or evolution without any computational purpose; however, the fact that the same organizational structures can be seen across most cortical areas and across many species suggests that the lognormal distribution has some use.

According to study first author Aitor Morales-Gregorio, “We cannot be sure how the lognormal distribution of neuron densities will influence brain function, but it will likely be associated with high network heterogeneity, which may be computationally beneficial,” Previous studies have suggested that heterogeneity in the connectivity of the brain may promote effective information transmission. Additionally, heterogeneous networks promote strong learning and increase the capacity of neural circuits’ memories.

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