A semi-mechanistic model of bone mineral density and bone turnover based on a circular model of bone remodeling

Development of novel therapies for bone diseases can benefit from mathematical models that predict drug effect on bone remodeling biomarkers. Therefore, a bone cycle model (BCM) was developed that takes into consideration the concept of the basic multicellular unit and the dynamic equilibrium of bone remodeling. The model is a closed form cyclical model with four compartments representing resorption, formation, primary mineralization, and secondary mineralization. Equations describing the time course of bone turnover biomarkers were developed using the flow rate of bone cycle units (BCU) between the compartments or the amount of BCU in each compartment. A disease progression model representing bone loss in osteoporosis, a vitamin D and calcium supplementation (placebo) model, and a drug model for antiresorptive treatments were added to the model. Initial model parameter values were derived from published bone turnover data. The BCM accurately described biomarker-time profiles in postmenopausal women receiving either placebo or bisphosphonate treatment. The slow continual increase in bone mineral density (BMD) observed after 1 year of treatment was accurately described when changes in bone turnover were combined with increases in mineralization. For this purpose, the secondary mineralization compartment was replaced by three catenary chain compartments representing increasing mineral content. The refined BCM satisfactorily predicted biomarker profiles after long-term (10-year) bisphosphonate treatment. Furthermore, the model successfully described individual bone turnover markers and BMD results following treatment with denosumab in postmenopausal women. Analyses with this model could be used to optimize dosing regimens and to predict effects of novel osteoporotic treatments.