The exterior of the mammalian brain—the cerebral cortex—has
a conserved layered structure whose thickness varies little across
species. However, selection pressures over evolutionary time scales
have led to cortices that have a large surface area to volume ratio in
some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can
arise as a nonlinear consequence of a simple mechanical instability
driven by tangential expansion of the gray matter constrained by
the white matter. A physical mimic of the process using a layered
swelling gel captures the essence of the mechanism, and numerical
simulations of the brain treated as a soft solid lead to the formation
of cusped sulci and smooth gyri similar to those in the brain. The
resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are
consistent with observations of a wide range of brains, ranging
from smooth to highly convoluted. Furthermore, this dependence
on two simple geometric parameters that characterize the brain
also allows us to qualitatively explain how variations in these
parameters lead to anatomical anomalies in such situations as polymicrogyria, pachygyria, and lissencephalia