Optimizing information transmission rates drives brain gyrification

We investigate the functional optimality of the cerebral cortex of an adult human brain geometry. Unlike most competing models, we postulate that the cerebral cortex formation is driven by the objective of maximizing the total information transmission rate. Starting from a random path model, we show that this optimization problem is related to the Steklov eigenvalue problem. Combining realistic brain geometries with the finite-element method, we calculate the underlying Steklov eigenvalues and eigenfunctions. By comparison to a convex hull approximation, we show that the adult human brain geometry indeed reduces the Steklov eigenvalue spectrum and thus increases the rate at which information is exchanged between points on the cerebral cortex. With a view to possible clinical applications, the leading Steklov eigenfunctions and the resulting induced magnetic fields are computed and reported.