Mind-Blowing: A Mathematical Rule Discovered Behind the Distribution of Neurons in Our Brain

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

The number of neurons and their spatial arrangement play a crucial role in shaping brain structure and function. However, despite the wealth of cytoarchitectonic data available, the statistical distributions of neuronal densities remain largely unknown. The new Human Brain Project (HBP) study, published in the journal Cerebral cortexadvances our understanding of mammalian brain organization.

Analysis of datasets and lognormal distribution

Nine out of seven publicly available datasets

” data-gt-translate-attributes=”[{“attribute”:”data-cmtooltip”, “format”:”html”}]”>species (mouse, marmoset, macaque, galago, owl monkey, baboon and human) formed the basis of the research team’s investigations. After analyzing the cortical areas of each, they found that the neuronal densities within those areas follow a consistent pattern – a lognormal distribution. This suggests a fundamental organizing principle underlying neural densities in the mammalian brain.

A lognormal distribution is a statistical distribution characterized by an asymmetrical bell-shaped curve. This happens, for example, when taking the exponential of a normally distributed variable. It differs from a normal distribution in several ways. More importantly, the curve of a normal distribution is symmetrical, while the lognormal one is asymmetrical with a heavy tail.

Implications and relevance of the results

This information is essential for accurate brain modeling. “Particularly because the distribution of neuronal densities influences the connectivity of the network,” explains Sacha van Albada, head of the theoretical neuroanatomy group at Forschungszentrum Jülich and lead author of the article. “For example, if synapse density is constant, regions with lower neuronal density will receive more synapses per neuron,” she explains. These aspects are also relevant for the design of brain-inspired technologies, such as neuromorphic hardware.

“Furthermore, since cortical areas are often distinguished on the basis of cytoarchitecture, knowing the distribution of neuronal densities may be relevant to statistically assess the differences between areas and the location of boundaries between areas,” adds van Albada.

Understanding the lognormal distribution of brain characteristics

The results agree with previous observations that surprisingly many brain features follow a lognormal distribution. “One of the reasons why this can be very common in nature is that it arises by taking the product of many independent variables,” says Alexander van Meegen, co-first author of the study. In other words, the lognormal distribution arises naturally as a result of multiplicative processes, similar to how the normal distribution arises when many independent variables are added together.

“Using a simple model, we were able to show how the multiplicative proliferation of neurons during development can lead to the observed neuronal density distributions,” says van Meegen.

According to the study, in principle, cortex-wide organizational structures could be developmental or evolutionary byproducts that serve no computational function; but the fact that the same organizational structures can be observed for several species and in most cortical areas suggests that the lognormal distribution serves a purpose.

“We cannot be sure how the lognormal distribution of neuronal densities will influence brain function, but it will likely be associated with high network heterogeneity, which could be computationally beneficial,” says Aitor Morales-Gregorio , first author of the study, citing previous work. which suggest that heterogeneity in brain connectivity may promote efficient transmission of information. Moreover, heterogeneous networks promote robust learning and improve the memory capacity of neural circuits.

Reference: “Pervasive lognormal distribution of neuronal densities in mammalian cerebral cortex” by Aitor Morales-Gregorio, Alexander van Meegen and Sacha J van Albada, July 6, 2023, Cerebral cortex.
DOI: 10.1093/cercor/bhad160