Investigation of the Buckling Instabilities in Multilayer Systems under Constraints, Focusing on the Mechanics of Brain Folding

The process of gyrification, by which the brain develops the intricate pattern of gyral hills and sulcal valleys, results from biological and mechanical interactions during brain development. Yet, despite decades of research, many outstanding questions remain — How is the folding pattern determined? How does it vary between individuals and species? What causes abnormal folding in neurological and neurodegenerative disorders such as Autism Spectrum Disorder, schizophrenia, and epilepsy? In addition to innovative experimental studies to answer these questions, researchers have developed various mathematical models to research aspects of brain development. This dissertation studies the mechanics of a developing brain, focusing on analytical and computational investigations on the instability of multilayered systems under of external boundary conditions. Analytical predictions provide preliminary insight into the critical growth ratio for instability and crease formation of the developing brain, followed by computational modeling to offer clues for the brain’s post-buckling morphology. This manuscript also presents a new perspective on recent advances in biomechanical models of the brain development process and suggests new opportunities for further investigation and challenges ahead.