The exponential distance rule (EDR) describes a consistent relationship between distances and connection strength. When studying the global architecture of the cortical networks in rodents (with small brains) and comparing that to primates (with large brains), researchers have found that both sized brains are organized by common principles. The cerebral cortex is responsible for motor, sensory and cognitive functions in mammals, including humans. To provide insights into the computations the neuronal networks in the cortex carry out, the organization of these networks needs to be understood.
New research shows that primate brains have weaker long-distance connections than mammals with smaller brains, in spite of the overall network similarities. Zoltán Toroczkai, from the University of Notre-Dame, USA; Mária Ercsey-Ravasz, from Babes-Bolyai University, Romania; and Henry Kennedy, from the University of Lyon, France, speculate that this might be why larger brains are more susceptible to mental illnesses such as Alzheimer disease and Schizophrenia.
When combining network theory with tracing studies visualizing connections in the brain, the researchers have shown that the cortical network structure in macaques (a type of monkey with a larger brain) is governed by the exponential distance rule (EDR). Axons are nerve fibers that serve as the transmission lines of the nervous system, and the EDR predicts that there are fewer long-range axons in the brain than there are short ones. In areas of the cortex such as the auditory and the visual cortex areas, the closer two areas are to each other, the more connections exist between them. This prediction was found to be consistent with the tracing results obtained by the team and the number of connections between areas can now be quantified by a mathematical equation.
The researchers used detailed tracing data to quantify connections between functional areas in a mouse, with a much smaller cortex, and a macaque — a mammal with a large cortex. Although the study found differences in cortex organization and the cortex size between the species is substantially different, the fundamental statistical features of all the neural networks followed the EDR. Further experiments using high-resolution tracer equipment were done on a mouse lemur (a primate with a very small brain) and in small brain areas from a macaque and a mouse.
Toroczkai and his team now theorize that the EDR describes an operational design principle that stays constant during the evolution of mammalian brains, no matter what the size. In addition to the experimental data obtained, they present mathematical opinions that support the theory that EDR, as a governing principle of cortical connectivity, is universally applicable. It then follows that larger-brained animals have optimized the layout of the inter-areal cortical network through evolution in order to maintain increased neuron numbers combined with communication efficiencies. This optimization follows the EDR.
EDR predicts that neuronal connections weaken exponentially with distance, and the tracing data obtained seems to confirm this. If the assumptions regarding the application of EDR to all mammalian brains is correct, it follows that long-distance connections in the human cortex are quite weak, as the human brain is approximately five times larger than that of the macaque.
Alzheimer disease and schizophrenia are known as disconnection syndromes, and the research concludes that a contributing factor to these illnesses may well be the low weight of human long-range connections.