Summary: New research delves into how the statistical distributions of neuron densities shape mammalian brains.
The study analyzed seven species, discovering that neuron densities follow a lognormal distribution – a fundamental organizational principle. This distribution is distinct due to its asymmetric curve and is significant for understanding brain connectivity and the design of brain-inspired technology.
As many attributes of the brain align with this distribution, it hints at its potential computational benefits.
Neuron densities in the brains of seven studied mammalian species, including humans, follow a consistent lognormal distribution pattern.
A lognormal distribution emerges as a result of multiplicative processes and influences network connectivity within the brain.
Heterogeneity in brain connectivity, potentially linked to the lognormal distribution, can enhance information transmission, learning, and memory capacities of neural circuits.
Source: Human Brain Project
Numbers of neurons and their spatial arrangement play a crucial role in shaping the brain’s structure and function. Yet, despite the wealth of available cytoarchitectonic data, the statistical distributions of neuron densities remain largely undescribed.
The new HBP study, published in Cerebral Cortex, advances our understanding of the organisation of mammalian brains.
The team based their investigations on nine publicly available datasets of seven species: mouse, marmoset, macaque, galago, owl monkey, baboon and human. After analysing the cortical areas of each, they found that neuron densities within these areas follow a consistent pattern – a lognormal distribution.
This suggests a fundamental organisational principle underlying the densities of neurons in the mammalian brain.
A lognormal distribution is a statistical distribution characterised by a skewed bell-shaped curve. It arises, for instance, when taking the exponential of a normally distributed variable. It differs from a normal distribution in several ways. Most importantly, the curve of a normal distribution is symmetric, while the lognormal one is asymmetric with a heavy tail.
These findings are relevant for modelling the brain accurately.
“Not least because the distribution of neuron densities influences the network connectivity,” says Sacha van Albada, leader of the Theoretical Neuroanatomy group at Forschungszentrum Jülich and senior author of the paper.
“For instance, if the density of synapses is constant, regions with lower neuron density will receive more synapses per neuron,” she explains. Such aspects are also relevant for the design 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 adds.
These results are in agreement with the observation that surprisingly many characteristics of the brain follow 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,” says Alexander van Meegen, joint first author of the study.
In other words, the lognormal distribution arises naturally as a result of multiplicative processes, similarly to how the normal distribution emerges when many independent variables are summed.
“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” explains van Meegen.
According to the study, in principle, cortex-wide organisational structures might be by-products of development or evolution that serve no computational function; but the fact that the same organisational structures can be observed for several species and across most cortical areas suggests that the lognormal distribution serves some purpose.
“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,” says Aitor Morales-Gregorio, first author of the study, citing previous works that suggest that heterogeneity in the brain’s connectivity may promote efficient information transmission.
In addition, heterogeneous networks support robust learning and enhance the memory capacity of neural circuits.
Ubiquitous lognormal distribution of neuron densities in mammalian cerebral cortex
Numbers of neurons and their spatial variation are fundamental organizational features of the brain. Despite the large corpus of cytoarchitectonic data available in the literature, the statistical distributions of neuron densities within and across brain areas remain largely uncharacterized.
Here, we show that neuron densities are compatible with a lognormal distribution across cortical areas in several mammalian species, and find that this also holds true within cortical areas.
A minimal model of noisy cell division, in combination with distributed proliferation times, can account for the coexistence of lognormal distributions within and across cortical areas.
Our findings uncover a new organizational principle of cortical cytoarchitecture: the ubiquitous lognormal distribution of neuron densities, which adds to a long list of lognormal variables in the brain.