A mathematical/physiological model of parathyroid hormone secretion in response to blood-ionized calcium lowering in vivo.

The aim of the present study was to test a mathematical model of the biochemical processes in the parathyroid glands responsible for the secretion of parathyroid hormone resulting from extracellular calcium reduction. A double exponential curve described the parathyroid hormone secretion induced by rapid lowering of blood-ionized calcium in humans with normal as well as abnormal parathyroid tissue. Our data show that it was possible to establish a simple mathematical model of the parathyroid hormone response to blood-ionized calcium lowering, sufficient to fit experimental data obtained from patients with abnormal and normal parathyroid tissue. The fitted parameters showed no significant differences between patients with insulin-dependent diabetes mellitus and controls. In primary hyperparathyroidism, the parathyroid hormone production and steady-state transport across the cell membrane were increased, probably due to the larger amount of parathyroid tissue in these patients. These observations reveal a striking functional similarity between abnormal and normal parathyroid tissue. Furthermore, an apparently linear relationship between the rate of parathyroid hormone elimination from the blood plasma and the rate of cellular production/secretion was observed. This could be interpreted as an adaptation of the parathyroid gland's ability to produce parathyroid hormone depending on the average demand from the body.