Hannukainen, A. | Search bioRxiv

bioRxiv2019

Modeling tissue growth with the Stokes equation

We present a cell-free continuum model for simulating generalized bulk tissue growth in 3D. We assume that the tissue behaves mechanically as viscous fluid so that its behavior can be described with the Stokes equation with mass sources. The growth is directed by a diffusing morphogen produced by specialized signaling centers, whose positions are established through a reaction-diffusion system coupled with differentiation. We further assume that the tissue interface may be stiff (modeled as surface tension), and that tissue adhesion can vary (modeled as variable viscosity). The numerical validity of the implementation is investigated using test cases with known solutions, and the model dynamics are demonstrated in simulations of idealized tissue growth. The combination of Stokes equation and diffusing morphogens allow the integration of patterning and growth as in real organs systems such as limbs and teeth. We propose that the presented techniques could be useful for simulating and exploring mechanistic principles of tissue growth in various developing organs.

biophysics↗

bioRxiv2019

Modeling enamel matrix secretion in mammalian teeth

The most mineralized tissue of the mammalian body is tooth enamel. Especially in species with thick enamel, three-dimensional (3D) tomography data has shown that the distribution of enamel varies across the occlusal surface of the tooth crown. Differences in enamel thickness among species and within the tooth crown have been used to examine taxonomic affiliations, life history, and functional properties of teeth. Before becoming fully mineralized, enamel matrix is secreted on the top of a dentine template, and it remains to be explored how matrix thickness is spatially regulated. To provide a predictive framework to examine enamel distribution, we introduce a computational model of enamel matrix secretion that maps the dentine topography to the enamel surface topography. Starting from empirical enamel-dentine junctions, enamel matrix deposition is modeled as a diffusion-limited free boundary problem. Using laboratory microCT and synchrotron tomographic data of pig molars that have markedly different dentine and enamel surface topographies, we show how diffusion-limited matrix deposition accounts for both the process of matrix secretion and the final enamel distribution. Simulations reveal how concave and convex dentine features have distinct effects on enamel surface, thereby explaining why the enamel surface is not a straightforward extrapolation of the dentine template. Human molar simulations show that even subtle variation in dentine topography can be mapped to the enamel surface features. Mechanistic models of extracellular matrix deposition can be used to predict occlusal morphologies of teeth.

biophysics↗