A Novel Mathematical Model Identifies Potential Factors Regulating Bone Apposition

The development of pharmaceutical treatments for bone disease can be enhanced by mathematical models that predict their effects on matrix apposition during cancellous bone remodelling. Therefore, a mathematical model was constructed to simulate the rate of focal bone formation from the number of osteoid-forming osteoblasts at one microsite and their rate of activity. The number of mature osteoid-forming cells was simulated from a relationship describing the proliferation of preosteoblasts. Osteoblast activity was described by Michaelis-Menten enzyme kinetic equations adapted to describe cellular activity. The model incorporates the negative feedback effects on the rates of bone apposition due to the reduction in size of mature osteoblasts with continuing differentiation and the reduction in number of osteoid-forming cells with apoptosis and osteocyte formation. In addition, the rate of mineralisation is limited according to osteoid substrate availability. Results of sensitivity analysis revealed the amount of bone formed at one microsite to be more sensitive to changes in factors that controlled cell growth during proliferation and the number of mature osteoid-forming osteoblasts than to those that determined cellular activity. Matrix and osteocyte signalling were shown to have potentially important roles in controlling rates of osteoid apposition in normal, healthy bone. This simple model supports the critical role of controlled mitotic growth in normal bone apposition. It can also help to explain how the homeostatic processes of bone resorption and apposition during remodelling can be disrupted by growth factors that affect the mitotic fraction and division time of proliferative preosteoblast cells.