This 3D gel model of a smooth fetal brain is coated with a thin layer of elastomer gel and immersed in solvent. The gel absorbs the solvent, causing it to swell relative to the deeper regions. Within minutes, the resulting compression leads to the formation of folds similar in size and shape to real brains. (credit: Mahadevan Lab/Harvard SEAS)

Folded brains likely evolved to fit a large cortex into a small volume, with the added benefit of reducing neuronal wiring length and improving cognitive function. But how does the brain fold?

A simple mechanical instability associated with buckling, researchers at the Harvard John A. Paulson School of Engineering and Applied Sciences, collaborating with scientists in Finland and France, have discovered in research published in Nature Physics.

Expanded gray matter

“We found that we could mimic cortical folding using a very simple physical principle and get results qualitatively similar to what we see in real fetal brains,” said L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics.

The number, size, shape, and position of neuronal cells present during brain growth all lead to the expansion of the gray matter (cortex) relative to the underlying white matter. This puts the cortex under compression, leading in turn to a mechanical instability that causes it to crease locally.

“This simple evolutionary innovation, with iterations and variations, allows for a large cortex to be packed into a small volume, and is likely the dominant cause behind brain folding, known as gyrification,” said Mahadevan, who is also a core faculty member of the Wyss Institute for Biologically Inspired Engineering and a member of the Kavli Institute for Bionano Science and Technology, both at Harvard University.

Mahadevan’s previous research found that the growth differential between the brain’s outer cortex and the soft tissue underneath explains the variations in the folding patterns across organisms in terms of just two parameters: the relative size of the brain and the relative expansion of the cortex.

Testing a 3D gel model

Left: All notable gyri as identified on a real fetal brain. Right: Analogous regions shown in a simulated brain driven by relative constrained growth. In both cases, the coloring is based on visual identification of the major gyri. (credit: adapted from P. D. Griffiths et al./Atlas of fetal and neonatal brain MR imaging, with permission from Elsevier; and Tuomas Tallinen et al./Nature Physics)

Building on this, the team collaborated with neuroanatomists and radiologists in France and directly tested this theory using data from human fetuses. The team made a 3D gel model of a smooth fetal brain based on MRI images. The model’s surface was coated with a thin layer of elastomer gel, as an analog of the cortex. To mimic cortical expansion, the gel brain was immersed in a solvent that is absorbed by the outer layer, causing it to swell relative to the deeper regions. Within minutes of being immersed in liquid solvent, the resulting compression led to the formation of folds similar in size and shape to real brains.

The extent of the similarities surprised even the researchers. “When I put the model into the solvent, I knew there should be folding but I never expected that kind of close pattern compared to human brain,” said Jun Young Chung, a postdoctoral fellow and co-first author of the paper. “It looks like a real brain.”

The key to those similarities lies in the unique shape of the human brain. “The geometry of the brain is really important because it serves to orient the folds in certain directions,” said Chung. “Our model, which has the same large-scale geometry and curvature as a human brain, leads to the formation of folds that matches those seen in real fetal brains quite well.

“Brains are not exactly the same from one human to another, but we should all have the same major folds in order to be healthy,” said Chung. “Our research shows that if a part of the brain does not grow properly, or if the global geometry is disrupted, we may not have the major folds in the right place, which may cause dysfunction in the brain.”

The distinctive folds of the human brain are not present in most animals — only in a handful of species, including some primates, dolphins, elephants, and pigs. In humans, folding begins in fetal brains around the 20th week of gestation and is completed only when the child is about 18 months old.

Scientists at Jyvaskyla University in Finland, the Institut Mines-Télécom in France, and the University of Aix-Marseille, France were also involved in the research, which was supported by the Academy of Finland, the Wyss Institute for Biologically Inspired Engineering, and fellowships from the MacArthur Foundation and the Radcliffe Institute.

Abstract of On the growth and form of cortical convolutions

The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure^. Recent studies have focused on the genetic and cellular regulation of cortical growth, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain. To study this, we use magnetic resonance images to build a 3D-printed layered gel mimic of the developing smooth fetal brain; when immersed in a solvent, the outer layer swells relative to the core, mimicking cortical growth. This relative growth puts the outer layer into mechanical compression and leads to sulci and gyri similar to those in fetal brains. Starting with the same initial geometry, we also build numerical simulations of the brain modelled as a soft tissue with a growing cortex, and show that this also produces the characteristic patterns of convolutions over a realistic developmental course. All together, our results show that although many molecular determinants control the tangential expansion of the cortex, the size, shape, placement and orientation of the folds arise through iterations and variations of an elementary mechanical instability modulated by early fetal brain geometry.