Surface remodeling of trabecular bone using a tissue level model.

Abstract

We propose a two-dimensional mathematical model of trabecular bone remodeling that simulates the surface-based addition and removal of material in the actual physiological process. The model is based on a finite element representation of individual trabecular struts in which the material properties of the subtrabecular elements are constant. The remodeling stimulus is strain energy density, sensed and communicated through the osteocytic network as proposed by Mullender et al. We propose a modified osteocyte communication scheme that incorporates bone-lining cells and examines the implications of set point locations in one or the other of these two cell types. This model produces trabecular struts that align with its general loading direction. Placing the set point in the bone-lining cells rather than in the osteocytes makes the model more sensitive to changes in the other biological parameters. Introduction of a dead zone causes the model to reach a less oscillatory equilibrium in fewer iterations and produces better in-filling of trabecular strut intersections. The model gravitates to equilibrium states in which the average strain energy density is inversely proportional to the bone volume fraction to the 3.2 power.