Mathematical Modeling of Bone Formation and Resorption: Effects of Parathyroid Hormone and Vitamin D

摘要

A mathematical model is proposed here in order to investigate the effects of parathyroid hormone and vitamin D on bone formation and resorption processes. Singular perturbation technique is then applied to analyze the model. The conditions on the system parameters for which a limit cycle exists are then derived. Numerical investigation is also carried out to support our theoretical prediction. The result shows that the model can exhibits a periodic solution corresponding to the pulsatile secretion of parathyroid hormone observed in the clinical evidence.