Reverse engineering Frost's mechanostat model in mouse tibia: Insights from combined PTH and mechanical loading

Osteoporosis is a widespread skeletal disease impacting billions, with treatments aimed at enhancing bone mass or preventing bone loss essential for reducing fracture risk and related health complications. Clinical evidence shows that intermittent parathyroid hormone (PTH) treatment increases cortical width at certain skeletal sites, with effects further amplified when combined with mechanical loading (ML), making this pharmacological and exercise approach promising for dual osteoporosis therapy. However, the mechanisms through which PTH enhances osteogenic response are not fully understood. This study uses $\mu$ CT endpoint imaging data from the mouse tibia loading model together with mechanical assessment of strain patterns in cortical bone to quantitatively compute parameters in Frost's mechanostat model. Particularly, we investigate the effects of PTH alone and in combination with ML on bone formation threshold and rate. Our analysis shows that PTH alone promotes periosteal bone formation independently of strain patterns induced by habitual loading in a dose-dependent manner. PTH lowers the bone formation modeling threshold (${\mathrm{MES}}_m$) in bones undergoing ML in a dose-dependent and site-specific manner. The highest sensitivity is observed around 37 % of tibial height, where ${\mathrm{MES}}_m$ decreases from $1060.6\mu \epsilon$ in untreated bones to $212.1\mu \epsilon$ at an $80\mu$g/kg/day g PTH dose. This region also exhibits the highest adaptation response, with a maximum modeling velocity (MaxFL) of approximately $7\mu \epsilon$/day at $80\mu$g/kg/day PTH. Although the formation velocity modulus (FVM) increases in PTH-treated bones compared to untreated ones across all regions, this change is not dose-dependent.