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)-Ca²⁺ system in rats and humans. Temporal concentration data for endogenous PTH and Ca²⁺ 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. Ca²⁺ 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 Ca²⁺ 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 × PTH₀] and humans [S_max-humans = 392/PTH₀]. Modeling results suggest that normal rats are twice as sensitive to Ca²⁺-induced PTH stimulation compared with humans. In conclusion, the developed model adequately characterizes the PTH-Ca²⁺ regulation across species and may be useful in the development of therapeutic drugs targeting this system.