Learning About Teeth: Data-driven Continuum Models of Amelogenesis

Amelogenesis, the process by which the enamel layer of a tooth is formed, features the robust coordination of the collective motion of epithelial cells over a multi-year time-span and a length-scale vastly exceeding individual ameloblast size. Based on a minimal set of assumptions about the behavior of individual cells, we develop a coarse-grained continuum model of epithelial front motion and enamel deposition, which we solve using recently developed deep learning techniques for inverse problems. We validate our simulations by replicating several empirical features using histological sections of six clinically extracted upper premolars from the United Kingdom. Our modeling approach allows us to quantitatively evaluate competing theories on the regulatory mechanisms required for reliable tooth formation. Finally, we discuss how investigating internal and incremental connections between ameloblast movement, perikymata distributions, enamel thickness, and overall enamel crown shape allows us to significantly improve our ability to interpret developmental variables in fossil hominin teeth.