  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.
