A mathematical model of bone remodeling process: Effects of parathyroid hormone and vitamin D

Parathyroid hormone and vitamin D play an important role in calcium homeostasis as well as in bone remodeling process. We propose here a system of nonlinear differential equations to describe bone remodeling process accounted for the concentrations of parathyroid hormone and vitamin D, the number of active osteoclasts and the number of active osteoblasts. We then utilize the singular perturbation technique to analyze our model in order to obtain the delineating conditions on the system parameters for which the different kinds of dynamic behavior can be occurred. The model is then investigated numerically. The theoretical and numerical results show that a periodic behavior which corresponds to the pulsatile pattern observed clinically in the levels of parathyroid hormone and vitamin D can be expected from our model.