A mechanical model for axon pathfinding in a folding brain

Understanding axonal growth and pathfinding during cortical folding is crucial to unravel the mechanisms underlying brain disorders that disturb connectivity during human brain development. However, this topic remains incompletely understood. Here, we propose and evaluate a diffusion-based continuum model to understand how axons grow and navigate in the folding brain. To do so, a bilayer growth model simulating the brain was devised with a thin gray matter (GM) overlying a thick white matter (WM). The stochastic model of axonal growth was linked with the stress and deformation fields of the folding bilayer system. Results showed that the modulus ratio of the GM to the WM and the axonal growth rate are two critical parameters that influence axon pathfinding in the folding brain. The model demonstrated strong predictive capability in identifying axonal termination points and offered a potential explanation for why axons settle more in gyri (ridges) than sulci (valleys). Importantly, the findings suggest that alterations in the mechanical properties of the folding system impact underlying connectivity patterns. This mechanical insight enhances our understanding of brain connectivity development during the fetal stage and provides new perspectives on brain disorders associated with cortical folding abnormalities and disrupted connectivity.