Léo RamosThe mathematical relationship between the cortex and folded paper: the thinner the paper, the more folds it has under pressureLéo Ramos
A piece of paper folded up into a ball can explain how the brain of a mammal folds onto itself to form the ridges and grooves that give it the wrinkled appearance of a walnut. The formation of these folds, with their gyri and sulci, is a function of a universal physical mechanism that is driven by variations in the thickness and length of the cerebral cortex as the brain develops, suggests a study by neuroscientist Suzana Herculano-Houzel and physicist Bruno Mota, both of whom work at the Federal University of Rio de Janeiro (UFRJ), published in the July 2, 2015 edition of the journal Science.
For a long time, people believed that the degree of foldedness in the cerebral cortex, which is the brain’s surface layer, was related to its capacity to hold more neurons. According to this view, the folds would be the result of the increase in the number of neurons distributed across the region over the course of mammalian evolution. So, a brain that has more ridges and grooves would have more neurons than one with a smoother cerebral cortex. This is the case, for example, when one compares large brains, like those of humans, which have more folds, to those of smaller creatures, like mice. According to this logic, the cortices of animals like whales and elephants, because they are larger and have more folds than the human brain, would have more neurons and hence a more complex cognitive capacity. The opposite is actually true however: the human brain has three times as many neurons as the brains of pachyderms or cetaceans.
To shed light on this paradox, the researchers analyzed data on the cortices of 74 different species. They analyzed the degree of foldedness, the thickness, and the volume and quantity of neurons contained therein. They confirmed that all of the brains had folds that conformed to an existing mathematical relationship between the entire surface area of the cerebral cortex and its thickness. “The brains of humans and other mammals begin to fold during embryo development,” says Herculano-Houzel. “In this process, the cortex takes on a more stable shape as its top layer is folding in response to the forces to which it is subjected during development, such as pressure generated by the cerebro-spinal fluid, which pushes it outwards, and nerve fibers, which push it inwards.”
The same mathematical relationship would explain the degree of foldedness in a crumpled paper ball. One 8 x 11 sheet of paper, if balled up, will have more folds than four or five sheets balled up together. The thinner the top layer — and the larger its area —the more it will fold under pressure. “This is true for the cerebral cortex as well as for crumpled-up pieces of paper,” says Herculano-Houzel. She believes this physical mechanism explains the degree of foldedness of all cortical layers, smooth and wrinkled, including the human cortex and that of other mammal species, like the manatee, which has a large cortex with few folds, and cetaceans, whose cortex is large and has more folds than does the human brain. “The degree of foldedness in the cortex has nothing to do with the number of neurons or how they are distributed in this brain region; it conforms to a physical equation,” she concludes.
Folds in formation
The advantage of having a cortex with more folds, according to Herculano-Houzel, is more efficient communication between neurons. “Thicker cortices, which are smoother as a result, would mean that there is more space between the neurons. This could compromise the exchange of information between them,” she says.
The cerebral cortex is the part of the brain mainly responsible for cognitive functions like attention, memory and language. Although the folds are one of its main features, they have never been adequately explained. Many studies have attempted to understand the mechanisms related to the formation of these ridges and grooves, which has given rise to several theories in recent years to explain their existence. In an article published in 2014 in the Proceedings of the National Academy of Sciences (PNAS), a group of researchers from a variety of institutions in Europe and the United States explained how they were able to reproduce the brain development process and the formation of cortical folds in a laboratory. In the study, they confirmed that the folds resulted from the interaction between the brain’s white and gray matter. According to this interpretation, the gray matter grows more quickly than white matter, leading to the formation of the cortical folds.
In another study, published in 2013 in the journal Physical Biology, researchers in England and the United States proposed a mathematical model in which the degree of cortical foldedness is related to its tangential expansion, while the deeper layers develop in response to stress caused by this process. They believe that if the cortex expands more rapidly, the length of the cerebral convolutions, known as gyri, would be shorter and have more folds. In contrast, if the process were slower, the length of these convolutions would be greater and its surface area would be smoother.
Gaining a better understanding of brain development is key to grasping brain function and nature’s strategies to construct an organ that is so complex that, in the case of humans, it led to the emergence of consciousness. The physical mechanism proposed by the team at UFRJ offers a possible explanation for lissencephaly, a rare brain formation disorder characterized by the absence of folds in the cerebral cortex. Even if the brain is normal size, the lack of folds can cause a loss of cerebral function. Lissencephaly in humans is associated with genetic mutations that disturb the migration of neurons during brain development. As a result, the cortex becomes smoother, which, according to Herculano-Houzel, would be enough to cause fewer folds.
Martín Cammarota, a neuroscientist at the Brain Institute of the Federal University of Rio Grande do Norte (UFRN), believes the UFRJ study could provide a new perspective on research in this field. “The study is interesting, but more experiments need to be conducted.” This is the next step for the Rio team. “We plan to test the hypothesis by analyzing the formation of folds in the brains of different species during the development process,” says Herculano-Houzel. “Based on these studies, we hope to understand better how neurons are distributed in the cortex and which factors play a bigger role in determining the gain or loss of density and volume.”
Scientific articles
HERCULANO-HOUZEL, S. e MOTA, B. Cortical folding scales universally with surface area and thickness, not number of neurons. Science. V. 349, N. 6243, p. 74-7. July 2015.
TALLINEN, T. et al. Gyrification from constrained cortical expansion. PNAS. V. 111, N. 35, p. 12667–72. April 2014.
BAYLY, P. V. et al. A cortical folding model incorporating stress-dependent growth explains gyral wavelengths and stress patterns in the developing brain. Physical Biology. V. 10, N. 1. Feb. 2013.
