Optimizing Bone Remodeling: A Control-Theoretic Approach to Model the Combination Therapy of Parathyroid Hormone and Denosumab

Osteoporosis treatment options can be classified into two main groups: anabolic agents and antiresorptive agents. The initial anabolic agent to receive approval is Teriparatide, a 1-34 amino-terminal segment of parathyroid hormone(PTH). In contrast, denosumab, a fully monoclonal antibody, demonstrates strong binding affinity to RANKL, impeding RANKL-RANK interactions, and is recognized as a potent antiresorptive agent. The current model addresses monotherapy limitations by combining denosumab and PTH. Additionally, a proposed mathematical framework explores the temporal effects of plasma PTH and external PTH dosages. This dual-mechanism approach integrates biochemical and biomechanical signals, incorporating key bone remodeling pathways such as RANK-RANKL-OPG and Wnt-Scl-LRP5/6, along with the role of osteocytes in sensing mechanical stimuli. The primary objective of this study is to predict osteogenic responses with precision by employing mathematical modeling techniques, numerical simulations, stability analysis, sensitivity analysis and control theory approach. This involves evaluating the therapeutic effects of PTH and denosumab, as well as considering various elements within bone signaling pathways that serve as integrating factors in osteoblast-osteoclast interactions. The assessment encompasses the impact of PTH on the glands, denosumab's ability to inhibit RANKL on osteoclasts, and the regulatory functions of Runx_2, pCREB, and Bcl_2 in osteoblast apoptosis and bone volume alterations. The present study conducts numerical evaluation for both pre- and post-menopausal scenarios, considering two cases: prior to and subsequent to preosteoblast saturation. Observation of cell dynamics behavior with and without control, using various weight functions is also conducted. By combining pharmacological and biomechanical insights, this research aims to enhance the clinical significance of osteoporosis treatment, offering a deeper understanding of how combination therapy influences bone remodeling and ultimately improving therapeutic strategies for osteoporosis management.