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Abstract Understanding the processes of axonal growth and pathfinding during cortical folding in the brain is crucial to unravel the mechanisms underlying brain disorders that disturb connectivity throughout human brain development. However, this topic remains incompletely understood, highlighting the need for further investigation. Here, we propose and evaluate a diffusion based-mechanistic model to understand how axons grow and navigate in the folding brain. To do so, a bilayer growth model simulating the brain was devised involving a thin gray matter overlying a thick white matter. Innovatively, the stochastic model of axonal growth was linked with the stress and deformation fields of the folding bilayer system. The results showed that the modulus ratio of the gray matter to the white matter and the axonal growth rate are two potentially critical parameters that significantly influence axon pathfinding in the folding brain. The model demonstrated robust predictability in identifying axonal termination points and offered a potential mechanism explaining why axons settle more in gyri (ridges) than sulci (valleys) of the brain. Importantly, the results explain how alterations in the mechanical properties of the folding system can impact the underlying connectivity patterning. This mechanistic insight not only enhances our understanding of brain connectivity development during the fetal stage but also sheds light on brain disorders characterized by linked abnormalities in cortical folds and disruptions in connectivity. 

Abstract The important mechanical parameters and their hierarchy in the growth and folding of the human brain have not been thoroughly understood. In this study, we developed a multiscale mechanical model to investigate how the interplay between initial geometrical undulations, differential tangential growth in the cortical plate, and axonal connectivity form and regulate the folding patterns of the human brain in a hierarchical order. To do so, different growth scenarios with bilayer spherical models that features initial undulations on the cortex and uniform or heterogeneous distribution of axonal fibers in the white matter were developed, statistically analyzed, and validated by the imaging observations. The results showed that the differential tangential growth is the inducer of cortical folding, and in a hierarchal order, high-amplitude initial undulations on the surface and axonal fibers in the substrate regulate the folding patterns and determine the location of gyri and sulci. The locations with dense axonal fibers after folding settle in gyri rather than sulci. The statistical results also indicated that there is a strong correlation between the location of positive (outward) and negative (inward) initial undulations and the locations of gyri and sulci after folding, respectively. In addition, the locations of 3-hinge gyral folds are strongly correlated with the initial positive undulations and locations of dense axonal fibers. As another finding, it was revealed that there is a correlation between the density of axonal fibers and local gyrification index, which has been observed in imaging studies but not yet fundamentally explained. This study is the first step in understanding the linkage between abnormal gyrification (surface morphology) and disruption in connectivity that has been observed in some brain disorders such as Autism Spectrum Disorder. Moreover, the findings of the study directly contribute to the concept of the regularity and variability of folding patterns in individual human brains.