Astrocytes in white matter respond to tensile cues during cortical folding: a numerical study

Our understanding of the process of formation of gyri (ridges) and sulci (furrows) in the cerebrum during development is moving beyond the role of neurons. Glial cells such as astrocytes, which are the most common cell type in the brain, are especially prominent under the gyri and have been shown to be essential for gyrification in ferrets. Their dysfunction has been linked to a host of neurodevelopmental diseases and disorders in humans, leading to abnormal folding patterns, hence, it is crucial to understand their role in the mechanics of folding. In this work, we propose two hypotheses of how astrocytes affect cortical folding. Our previous study demonstrated that astrocytes proliferate in the white matter (subcortex), and that inhibiting this process impairs gyrification. This leads to the 'pushing' hypothesis, where astrocytes push up the cortex outwards, leading to formation of folds. On the other hand, ex vivo studies demonstrate areas of the cortex and subcortex that experience tension, due to the differential growth between materials in the brain tissue. This leads to the 'pulling' hypothesis, where astrocytes experience tension from the surrounding tissue, leading to their proliferation, distribution of tensile stresses, and initiation of growth in those regions. Using the theory of finite growth, we implement these hypotheses via morphogenetic growth (pushing) and stress-driven (pulling) growth criteria. We find that morphological trends during development between the pushing and pulling effects are not dissimilar, with a comparable gyrification index. The stress distributions from both models also show common features, but the pulling effect shows tension in the subcortex, which matches trends observed in experiments. Therefore, it is more likely that the astrocytes affect gyrification by proliferating as a response to tensile cues and decrease the tension they experience, leading to deeper folds, rather than astrocytes independently proliferating under a gyri and then pushing the cortex up.