Mechanism-based pharmacokinetic/pharmacodynamic model of parathyroid hormone-calcium homeostasis in rats and humans.

The purpose of this study was to develop a mechanism-based pharmacokinetic/pharmacodynamic model that describes the regulation of the parathyroid hormone (PTH)-Ca(2+) system in rats and humans. Temporal concentration data for endogenous PTH and Ca(2+) were extracted from literature for rats (normal adult males) and humans. In addition, exogenous PTH was administered subcutaneously to male Sprague-Dawley rats with jugular vein catheters, and plasma concentrations were measured over time. A mathematical model was developed and fitted simultaneously to endogenous PTH, Ca(2+), and exogenous PTH concentrations in rats. Ca(2+) concentrations were described using a turnover model, with its depletion being induced by a chelating agent, and PTH concentrations were characterized using a precursor-dependent indirect response model. The same structural model was used for fitting data obtained in humans. PTH stimulation was driven by occupancy of the Ca(2+) sensing receptor, and lowering of physiological Ca(2+) concentrations increased PTH secretion, with PTH profiles being adequately described by the model. PTH stimulatory capacity was baseline-dependent in rats [S(max_rats) = 34.8 x PTH(0)] and humans [S(max_humans) = 392/PTH(0)]. Modeling results suggest that normal rats are twice as sensitive to Ca(2+)-induced PTH stimulation compared with humans. In conclusion, the developed model adequately characterizes the PTH-Ca(2+) regulation across species and may be useful in the development of therapeutic drugs targeting this system.