An intramembranous ossification model for the in silico analysis of bone tissue formation in tooth extraction sites

The accurate modeling of biological processes allows us to predict the spatiotemporal behavior of living tissues by computer-aided (in silico) testing, a useful tool for the development of medical strategies, avoiding the expenses and potential ethical implications of in vivo experimentation. A model for bone healing in mouth would be useful for selecting proper surgical techniques in dental procedures. In this paper, the formulation and implementation of a model for Intramembranous Ossification is presented aiming to describe the complex process of bone tissue formation in tooth extraction sites. The model consists in a mathematical description of the mechanisms in which different types of cells interact, synthesize and degrade extracellular matrices under the influence of biochemical factors. Special attention is given to angiogenesis, oxygen-dependent effects and growth factor-induced apoptosis of fibroblasts. Furthermore, considering the depth-dependent vascularization of mandibular bone and its influence on bone healing, a functional description of the cell distribution on the severed periodontal ligament (PDL) is proposed. The developed model was implemented using the finite element method (FEM) and successfully validated by simulating an animal in vivo experiment on dogs reported in the literature. A good fit between model outcome and experimental data was obtained with a mean absolute error of 3.04%. The mathematical framework presented here may represent an important tool for the design of future in vitro and in vivo tests, as well as a precedent for future in silico studies on osseointegration and mechanobiology.