Hierarchical “buckling without bending” and brain shape*

While studies of brain shape development have focused on the cerebrum, the cerebellum, otherwise known as the little brain, typically houses more neurons than the cerebrum and has a distinct morphology with 8-10 primary lobes that subsequently branch into smaller lobes. A recent “buckling without bending” model quantifies the onset of shape change in the developing cerebellum. It consists of an inner incompressible core of cells and an outer fluid-like cortical layer of dividing cells encased by a basement membrane. Additionally, there are two types of fibrous cells---ones spanning the cerebellum and ones spanning the cortical layer. The onset of shape change is a consequence of mechanical constraints on the outer fluid-like cortical layer as it proliferates. This model is now generalized beyond the onset of shape change to predict shape development at later stages. In particular, a hierarchical version of the model is implemented to predict subsequent branching of the smaller lobes. Predictions are compared with various mammalian cerebella exhibiting varied counts of branching generations. We also explore how some aspects of “buckling without bending” may lead to a new level of detail for characterizing shape change in the developing cerebrum.