Instability of bilayered systems under surface pressure: The effect of cerebrospinal fluid on cortical folding

Buckling instability is a common phenomenon in many biological and engineering layered structures. Once the compressive strain in a layered material reaches a critical value, the system becomes unstable, and it forms different patterns, such as wrinkles, folds, and creases. However, instability analysis is primarily conducted for zero-stress boundary conditions and in the absence of surface pressure. Here, we focused on the brain as a bilayer and aimed to study the influence of cerebrospinal fluid (CSF) pressure on its gyrification process. We present a nonlinear finite element solution for instability of a 3D bilayer under surface pressure, which consists of two inhomogeneous, incompressible layers (gray and white matter). We analyzed the effect of surface pressure on the critical strain and buckling criteria over a range of stiffness ratios, from 1.5 to 4, and normalized pressures, from 0.2 to 3. We also investigated thickness variations between gyral hills and sulcal valleys in relation to the CSF pressure. Our results suggested that adding pressure decreases the system's stability, especially in low stiffness contrasts with softer films.