Mathematical modeling of the effects of Wnt-10b on bone metabolism

Bone health is determined by many factors including bone metabolism or remodeling. Wnt-10b has been shown to alter osteoblastogenesis through pre-osteoblast proliferation and differentiation as well as the osteoblast apoptosis rate, which collectively lead to the increase of bone density. To model this change, we adapted a previously published model of bone remodeling. The resulting model is a single compartment system that includes ordinary differential equations for active osteoclasts, pre-osteoblasts, osteoblasts, and osteocytes and a differential equation that tracks the amount of bone present at the remodeling site. Our alterations to the original model consist of extending it past a single remodeling cycle and implementing a direct relationship to Wnt-10b. Four new parameters were estimated and validated using normalized data from mice. The model connects Wnt-10b to bone metabolism and predicts the change in bone volume caused by a change in Wnt-10b. We find that this model predicts the expected increase in pre-osteoblasts and osteoblasts while also pointing to a decrease in osteoclasts when Wnt-10b is increased.