Hierarchical “buckling without bending” and cerebellar 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. Mammalian cerebella have 8-10 primary lobes which subsequently branch into smaller lobes. Recently, a “buckling without bending” model has been introduced to quantify the onset of shape change in the developing cerebellum and other brain organs/organoids. It consists of an inner incompressible core of cells and an outer fluid-like cortical layer of dividing cells encased by a pia 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. Predictions of the model have been recently supported by experimental studies of the developing mouse cerebellum. Here, we generalize the model beyond the onset of shape change to predict shape development at later stages. We implement a hierarchical version of the above model to predict subsequent branching of the smaller lobes. Predictions are compared with various mammalian cerebella exhibiting varied counts of branching generations.