A model for maxilloturbinate morphogenesis in seals

The nasal cavities of mammals contain the maxilloturbinate bones, which are involved in reducing heat and water losses. The maxilloturbinates of Arctic seals develop into particularly elaborate labyrinthine patterns, which are well adapted to retain heat and moisture from exhaled gas. These structures develop prenatally and continue to grow postnatally. The developmental mechanism of labyrinthine patterning is unknown. Here we report a model of maxilloturbinate pattern formation in prenatal and juvenile seals based on a simple algorithmic description and three key parameters: target turbinate porosity, characteristic ossification time scale, and typical gestation time scale. Under a small set of geometrical and physical rules, our model reproduces key features of the patterns observed in the turbinate structure of three seal species. To validate our model, we measure complexity, hydraulic diameter, backbone fractal dimension, and Horton-Strahler statistics for a rigorous quantitative comparison with actual tomograms of grey and harp seal skull specimens. Our model closely replicates the structural development of seal turbinates in these respects. Labyrinthine maxilloturbinate development may depend on the ability for neighbouring bone branches to detect and avoid each other, potentially through the mechanosensing of shear stresses from amniotic fluid and air flow.