  We consider the mechanisms by which folds, or sulci (troughs) and gyri
(crests), develop in the brain. This feature, common to many gyrencephalic
species including humans, has attracted recent attention from soft matter
physicists. It occurs due to inhomogeneous, and predominantly tangential,
growth of the cortex, which causes circumferential compression, leading to a
bifurcation of the solution path to a folded configuration. The problem can be
framed as one of buckling in the regime of linearized elasticity. However, the
brain is a very soft solid, which is subject to large strains due to
inhomogeneous growth. As a consequence, the morphomechanics of the developing
brain demonstrates an extensive post-bifurcation regime. Nonlinear elasticity
studies of growth-driven brain folding have established the conditions
necessary for the onset of folding, and for its progression to configurations
broadly resembling gyrencephalic brains. The reference, unfolded,
configurations in these treatments have a high degree of symmetry--typically,
ellipsoidal. Depending on the boundary conditions, the folded configurations
have symmetric or anti-symmetric patterns. However, these configurations do not
approximate the actual morphology of, e.g., human brains, which display
unsymmetric folding. More importantly, from a neurodevelopmental standpoint,
many of the unsymmetric sulci and gyri are notably robust in their locations.
Here, we initiate studies on the physical mechanisms and geometry that control
the development of primary sulci and gyri. In this preliminary communication we
carry out computations with idealized geometries, boundary conditions and
parameters, seeking a pattern resembling one of the first folds to form: the
Central Sulcus.
