The interrelationship between calcium-phosphorus homeostasis and bone remodelling. Impact of dietary changes on bone in patients with primary hyperparathyroidism and chronic kidney disease.

Introduction: Calcium-phosphorus homeostasis is closely linked to bone remodelling, and disturbances in either system contribute to bone loss in conditions such as chronic kidney disease and hyperparathyroidism. Existing physiological models, such as the Peterson and Riggs formulation, incorporate systemic Ca/P regulation but often rely on simplified representations of bone turnover. Consequently, current frameworks generally lack the detailed coupling between systemic mineral balance and the cellular mechanisms of bone remodelling required to evaluate how endocrine imbalance, renal dysfunction, or dietary changes jointly affect bone metabolism. Methods: In this work, we develop an integrated mathematical framework that overhauls the bone compartment of the Peterson and Riggs model by coupling it with a mechanistic cell-population model, while also introducing refined descriptions of systemic mineral fluxes. The model incorporates dynamic PTH regulation, mineral exchange between plasma, bone marrow, and bone matrix, and a revised mineralisation algorithm that links systemic mineral availability to local bone properties. Results: After calibration against clinical data for vitamin D deficiency, chronic kidney disease, and primary hyperparathyroidism, we use the model to explore how changes in dietary calcium, phosphate, and vitamin D intake influence Ca/P homeostasis and bone density under healthy and pathological conditions. Discussion: This integrated approach captures multiscale interactions between systemic mineral regulation and cellular bone remodelling, enabling quantitative analysis of disease mechanisms and the impact of dietary interventions on skeletal health.