Size and curvature regulate pattern selection in the mammalian brain

Mammalian brains display a wide variety of shapes and surface morphologies. Their characteristically folded surface is closely correlated to neuronal activity and serves as a clinical indicator for physiological and pathological conditions. Yet, the regulators of pattern formation in evolution and development remain poorly understood. Here we show how brain size and curvature affect the folding pattern in the developing mammalian brain. We model cortical folding as the instability problem of a bilayered system subjected to growth-induced compression. Using analytical estimates and continuum models for finite growth, we systematically explore the effects of geometric factors on the evolution of surface shape. We demonstrate that extrinsic geometric features–including brain size, cortical thickness, and cortical curvature–tightly regulate pattern selection: The mammalian brain is extremely soft and even small environmental changes can create extremely large alterations in its surface morphology. Our simulations explain why gyrification increases with brain size and why longer brains tend to fold more longitudinally than radially. Our results suggest that brain folding is driven, at least in part, by extreme mechanics, rather than by phylogeny alone.