Mathematical Model of Cerebral Cortical Folding Development Based on a Biomechanical Hypothesis

The cerebral cortex is a thin folded sheet of neural tissue forming the outmost layer of the cerebrum (brain). Several biological hypotheses have suggested dierent mechanisms involved the development of its folding pattern into sulci (inward valleys) and gyri (outward hills). One hypothesis suggests that mechanical tension along cortico-cortical connections is the principal driving force for cortical folding development. We propose a new mathematical model based on the tension-based hypothesis surrounding the 26th week of gestational age when the human brain cortex noticeably begins to fold. In our model, the deformation of a two-dimensional semi-circular domain is analyzed through the theory of elasticity. The governing coupled partial differential equations are implemented computationally using a finite element formulation. Plausible brain tissue elasticity parameters with reasonable brain domain size parameters were used in our simulation. Gyrication index which is a measure of cortical foldings is employed to compare the degree of folding between the simulation results. The proposed model provides an approach for studying the connections between two different biological hypotheses by determining the magnitude of the applied tension force from the previous mathematical models of cortical folding which are based on a biochemical hypothesis. It allows our model to explain the mechanisms behind disorders occurring in all stages of development. In addition, the ability to freely set the directions and magnitudes of the applied forces allows to analysis of various abnormal cortical foldings by comparing MR imaging features of human brain cortical disorders. Our simulation results show that the unveiled mechanisms underlying the abnormal cortical folding development are well captured by our proposed model.