A Mathematical Model of Calcium Homeostasis: Effects of Parathyroid Hormone and Vitamin D

摘要

In human, adequate amounts of calcium ion in the extracellular fluid are necessary for normal function of all cells. There are many factors involve in the maintenance of calcium homeostasis such as parathyroid hormone, vitamin D and calcitonin. A system of nonlinear differential equations is developed here in order to investigate the effects of parathyroid hormone and vitamin D on calcium homeostasis. Singular perturbation technique is then utilized to derive the conditions on the system parameters for which a periodic behaviour can be assured. Numerical investigation is also carried out to support our theoretical prediction. Both theoretical and numerical results indicate that the developed model can exhibit a periodic behaviour conforming to the pulsatile behaviour observed clinically by many researchers in the serum levels of parathyroid hormone and vitamin D.