Strain fields and solitary strain waves as determining factors for the cross-sectional geometry of mouse incisor enamel

Dental enamel in the mouse incisor is the subject of one of the most detailed histological records of cell motion and action during the formation and shaping of any organ in any species. We use the rich data to test the hypothesis that the shape of the enamel body on a perpendicular cross-section of the long, sabre-like incisor can be predicted by assuming that the formative ameloblast cells respond to strain and strain-rate cues that inform individual cells of position and time. The strain field is generated when growth of the forming enamel stretches the ameloblast population. Simultaneously, the strain is relaxed by coherent wavy cell movements. We hypothesize that wave motion arises when cells maintain homeostasis in their area density, with the rate of their recovery from a density perturbation assumed proportional to the magnitude of the perturbation. Density homeostasis gives rise to a nonlinear wave equation, which results in solitary waves propagating within computed strain fields. We predict the final thickness of the enamel by assuming ameloblasts stop generating enamel after they experience a critical strain condition. The thickness profile vs position is correctly determined to within a constant factor, which is the unknown rate constant in the wave equation. When the rate constant is calibrated by the peak amplitude of the thickness profile, the commencement of enamel formation (the onset of ameloblast secretion) vs position is then also correctly predicted by the passage of solitary waves, implying that the strain jump within the solitary wave may be the trigger for the onset of secretion.