A Turing Reaction-Diffusion Model for Human Cortical Folding Patterns and Cortical Pattern Malformations

Modeling and understanding cortical folding pattern formation is important for quantifying cortical development. We present a biomathematical model for cortical folding pattern formation in the human brain and apply this model to study diseases involving cortical pattern malformations associated with neural migration disorders. Polymicrogyria is a cortical malformation disease resulting in an excessive number of small gyri. Our mathematical model uses a Turing reaction-diffusion system to model cortical folding. The lateral ventricle (LV) and ventricular zone (VZ) of the brain are critical components in the formation of cortical patterning. In early cortical development the shape of the LV can be modeled with a prolate spheroid and the VZ with a prolate spheroid surface. We use our model to study how global cortex characteristics, such as size and shape of the LV, affect cortical pattern formation. We demonstrate increasing domain scale can increase the number of gyri and sulci formed. Changes in LV shape can account for sulcus directionality. By incorporating LV size and shape, our model is able to elucidate which parameters can lead to excessive cortical folding.