Approaches to Embryonic Neurodevelopment: From Neural Cell to Neural Tube Formation through Mathematical Models

Abstract

Abstract The human central nervous system (CNS) undergoes development from early embryonic stages to well beyond birth, with various neurological and neuropsychiatric diseases originating from prenatal events. Mathematical models offer a direct avenue for understanding these neurodevelopmental processes, particularly during the embryonic period. However, approaching and initiating such modeling presents challenges, including the formulation of appropriate equations that capture the dynamics of neurodevelopment.Therefore, this study aimed to comprehensively address the mathematical challenges by exploring different approaches. The approaches were divided into three embryonical categories: cell division, neural tube growth and neural plate growth. We concluded that the neural plate growth approach provides a suitable platform for simulation of brain formation/neurodevelopment compared to cell division and neural tube growth. We devised a novel equation and designed algorithms that include geometrical and topological algorithms that could fit most of the essential elements of the neurodevelopmental process during the embryonic period.