Brain Folding

Computation shows that the skull guides the wrinkling

In the four months before birth, a fetus’s brain grows from a smooth tube of neurons into a highly crinkled, convolved mass of tissue. Because the cerebral cortex has a surface area nearly three times as big as that of its skull cavity, scientists have proposed that this real-estate-space squeeze is what drives the brain’s folding process. Now results from a computational three-dimensional geometric model agree that the skull does help guide the wrinkling—but they also suggest that a growing brain folds up regardless of its container.


Growth of the cortex under different assumptions. From left to right, the images show simulated development of the cortex over time. The cortex grows (a) within a skull of fixed size, (b) without a skull, or (c) within a skull that also grows at the same time (which corresponds to a fetus' developing skull). Major cortical folds developed much earlier and faster during simulations with skull constraints. But the cortex increases its surface area and convolutes itself to reduce the fast-growing internal tension, with or without skull constraint.“Mechanical constraints imposed by the skull are important regulators,” says Tianming Liu, PhD, assistant professor of computer science at University of Georgia and lead author on the study, which was published in May 2010 in the Journal of Theoretical Biology. “But our simulations indicate that skull constraint is not necessarily the dominant mechanism.”


The computational model underneath the simulations had two main features: geometric constraints of the skull, and partial differential equations that model biological processes driving the growth of neurons. To start off the simulation, researchers used MRI data from the brains of two human fetuses; then solutions to the differential equations guided the changing surface geometry of the cortex.


The team simulated how the cortex grows under various conditions: without a skull, with a skull of fixed size, and with a skull that grows at the same time as the brain does. As expected, brains grown in a skull were more convoluted than those allowed to develop unfettered. But even without a skull to confine it, a cortex will still fold in on itself, results showed. This happens as a natural response in a fast-growing cortex, as the tissue attempts to reduce the increasing mechanical tension among axons, dendrites, and neuroglia, Liu says.


Tweaking other parameters in the model revealed how cellular growth affects these folding patterns. When neurons themselves grow rapidly—during synapse development and neuron dendritic projection, for example—the cortical folding increases dramatically too. And when certain areas of the cortex grow more quickly than others, this imbalance subtly shapes what kinds of folds become most prominent.


Computational models can help explain normal brain development as well as what happens when things go wrong, says Bernard S. Chang, MD, assistant professor of neurology at Harvard Medical School.  For example, in some forms of microcephaly, the brain surface is almost completely smooth with no folds; in others, the folding is normal. “A model that predicts how folding is affected by the skull’s physical constraints might help us to understand why some patients have one form and not another,” he says. Since animal models don’t capture the complexity of the human brain, and doing repeated MRIs of developing fetuses for research isn’t feasible, Chang says, “we need to rely on these theoretical models as tools to help us understand what we’re observing clinically.”

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