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The mathematical rule behind the distribution of neurons in our brains has been discovered

The mathematical rule behind the distribution of neurons in our brains has been discovered

Neuronal densities in cortical regions of the mammalian brain follow a consistent distribution pattern. This discovery has profound implications for brain modeling and the development of brain-inspired technologies. Credit: Morales Gregorio

Human Brain Project researchers from Forschungszentrum Jülich and the University of Cologne (Germany) have discovered how neuron densities are distributed across and within cortical regions in the mammalian brain. They revealed a fundamental organizing principle of cortical cytoarchitecture: the ubiquitous lognormal distribution of neuronal densities.

Neuron numbers and their spatial arrangement play a critical role in shaping brain structure and function. However, despite the wealth of cytoarchitecture data available, the statistical distributions of neuronal densities remain largely uncharacterised. The new study of the Human Brain Project (HBP), published in the journal cerebral cortexenhances our understanding of the organization of mammalian brains.

Analysis of data sets and lognormal distribution

Nine of the seven publicly available datasets classify (mouse, monkey, macaque, galago, owl monkey, baboon, and human) provided the basis for the research team’s investigations. After analyzing the cortical regions of each, they found that the neuron densities within these regions followed a consistent pattern — a lognormal distribution. This points to a fundamental organizing principle that underlies neuronal densities in the mammalian brain.

A lognormal distribution is a statistical distribution characterized by a skewed, bell-shaped curve. It arises, for example, when taking the exponent of a normally distributed variable. It differs from a normal distribution in several ways. More importantly, the normal distribution curve is symmetric, while the lognormal curve is asymmetric and has a heavy tail.

The implications and significance of the results

These insights are central to accurate brain modeling. “Not least because the distribution of neuronal densities influences network connectivity,” says Sascha van Alpada, Group Leader of Theoretical Neuroanatomy at Forschungszentrum Jülich and senior author of the paper. “For example, if the density of synapses is constant, then regions with lower neuron density will receive more synapses per neuron,” she explains. These aspects are also relevant to the design of brain-inspired technology such as neuromodulators.

“Moreover, since cortical regions are often distinguished on the basis of cytoarchitecture, knowledge of the distribution of neuronal densities can be relevant to the statistical assessment of differences between regions and the locations of boundaries between regions,” Van Alpada adds.

Understanding the lognormal distribution in brain properties

The results are consistent with previous observations that many brain properties follow a normal rational distribution. “One of the reasons they are so common in nature is that they appear when the product of many independent variables is taken into account,” says Alexander van Meijn, co-first author of the study. In other words, a lognormal distribution arises naturally as a result of multiplication operations, similar to how a normal distribution appears when many independent variables are added.

“Using a simple model, we were able to show how the doubling of neurons during development might lead to the observed neuronal density distributions,” van Meijn explains.

According to the study, in principle, organizational structures at the level of the cerebral cortex may be by-products of development or development and do not serve any computational function; But the fact that the same organizational structures can be observed for many species and across most cortical regions suggests that the log-normal distribution serves a purpose.

“We cannot be sure how the lognormal distribution of neuron densities affects brain function, but it is likely related to the high network heterogeneity, which could be computationally advantageous,” says Aitor Morales Gregorio, first author of the study, citing previous work. which suggest that heterogeneity in brain connectivity may promote efficient information transmission. In addition, heterogeneous networks support robust learning and enhance the memory capacity of neural circuits.

Reference: “Ubiquitinated log-normal distribution of neuron density in the mammalian cerebral cortex” By Aitor Morales-Gregorio, Alexander van Meijen, and Sasha G. van Albada, 6 July 2023, Available here. cerebral cortex.
doi: 10.1093/sircor/bhad160

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