A Numerical Study on the Influence of Cerebrospinal Fluid Pressure on Brain Folding

Abstract

Over the past decades, the buckling instability of layered materials has been the subject of analytical, experimental, and numerical research. These systems have traditionally been considered with stress-free surfaces, and the influence of surface pressure is understudied. In this study, we developed a finite element model of a bilayer experiencing compression, and found that it behaves differently under surface pressure. We investigated the onset of buckling, the initial wavelength, and the post-buckling behavior of a bilayer system under two modes of compression (externally applied and internally generated by growth). Across a wide range of stiffness ratios, 1 < μf/μs < 100, we observed decreased stability in the presence of surface pressure, especially in the low-stiffness-contrast regime, μf/μs < 10. Our results suggest the importance of pressure boundary conditions for the stability analysis of bilayered systems, especially in soft and living matter physics, such as folding of the cerebral cortex under cerebrospinal fluid pressure, where pressure may affect morphogenesis and buckling patterns.