Predicting Nonlinear Changes in BMD Over Time using a Physiologically-Based Mathematical Model

Purpose: Develo pa mathematical model component to extend an existing physiologically-based model of calcium and bone homeostasis and enable prediction of nonlinear changes in bone mineral density (BMD) observed during, and following discontinuation of, anti-osteoporosis treatments. Methods: The underlying physiologically-based model has been published and is described fully in Bone 46 (2010) 49-63 (1). Data for denosumab, a receptor activator of NF-kapp aB ligand inhibitor being developed for the treatment of osteoporosis, was used fortting the BMD component. Mean serum C-telopeptide (sCTX), bone-specic alkaline phosphatase (BSAP), and lumbar spine BMD were digitized and extracted fromgures contained within a clinical publication describing the on- and o�-treatment eects of denosumab over 48 months (2). Dierential equations were constructed to link the prior de- scription of bone resorption and formation markers, scaled appropriately, to provide a prediction of BMD values following treatment with denosumab. Alternate model constructs were then evaluated to ensure the most predictive structure was chosen. Results: An indirect feedback dierential equation model linked the bone markers to BMD. Changes in BMD were described by a zero-order input andrst-order elimination, scaled by percentage changes in formation and resorption markers, re- spectively. The composite model was able to reasonably predict the percentage accumulation oumbar spine BMD for the subcutaneously (SC) administered 30 mg every 3 months (q3M) and 210 mg q6M regimens from start of treatment to 24 months, the decline in BMD following discontinuation of these treatments at 24 months, and the return in BMD upon reinstitution of treatment a ta SC dose of 60 mg q6M. The observed data demonstrated approximately 7-8% increases in lumbar spine BMD at 24 months, followed by declines to 1-2% at 36 months (12 months after discontinuation). Upon reinstitution of treatment of the 30 mg group at 60 mg q6M, BMD gains returned to approximately 8% within 12 months. Conclusions: A mathematical model has been developed that is able to reasonably predict nonlinear changes in mean BMD both during, and following discontinuation of, denosumab treatment, and provides a structure to be further generalized to accommodate other osteoporosis treatments.