A mathematical model of calcium and phosphorus metabolism in two forms of hyperparathyroidism

Abstract

Parathyroid hormone (PTH) plays a critical role in calcium and phosphorus metabolism. Interestingly, in two forms of hyperparathyroidism (excessive amount of PTH in the serum), the metabolic disturbances in patients with chronic kidney disease (CKD) significantly differ from those with primary hyperparathyroidism (PHP). Since an intuitive understanding of these PTH-linked regulatory mechanisms are hardly possible, we developed a mathematical model using clinical data (1586 CKD and 40 PHP patients). The model was composed of a set of ordinary differential equations, in which the regulatory mechanism of PTH together with other key factors such as 1,25-Dihydroxyvitamin D (1,25(OH) 2 D) and calcium was described in the tissues including bone, the kidney, the serum, and the parathyroid glands. In this model, an increase in PTH was induced by its autonomous production in PHP, while PTH in CKD was elevated by a decrease in feedback inhibition of 1,25(OH) 2 D in the serum, as well as an increase in stimulation by phosphorus in the serum. The model-based analysis revealed characteristic differences in the outcomes of hyperparathyroidism in CKD and PHP. The calcium exchange in bone, for instance, was predicted significantly higher in PHP than CKD. Furthermore, we evaluated the observed and predicted responses to the administration of calcimimetics, a recently developed synthetic drug that modulated efficacy of calcium-sensing receptors. The results herein support the notion that the described model would enable us to pose testable hypotheses about the actions of PTH, providing a quantitative analytical tool for evaluating treatment strategies of PHP and CKD.

Use of a Systems Pharmacology Model Based Approach Toward Dose Optimization of Parathyroid Hormone Therapy in Hypoparathyroidism

“…Mechanistic effects of PTH have been incorporated in a number of calcium homeostasis models available in the literature, including a comprehensive minimal mathematical model of calcium homeostasis by Raposo et al 10 and other similar models. [11][12][13] One such comprehensive model of calcium homeostasis was published by Peterson and Riggs. 6 The base version of this model (implemented in R with code available in public domain) was adapted to achieve our objective.…”

“…Mechanistic effects of PTH have been incorporated in a number of calcium homeostasis models available in the literature, including a comprehensive minimal mathematical model of calcium homeostasis by Raposo et al . and other similar models …”

A Multi-Compartment Model Capturing the Pharmacokinetics of the Calcimimetic Cinacalce

“…The mechanisms leading to CKD-MBD are many and highly complex. Thus, a multitude of mathematical models were established in order to gain a better understanding of the multidimensional factors controlling the PTH household [27][28][29] or PTH and bone remodeling [30]. For clinical application any proposed model should be able to predict the state of individual patients and ideally indicate an optimal treatment strategy.…”

Coupling between phosphate and calcium homeostasis: a mathematical model

“…to develop a mathematical model of calcium and phosphate homeostasis in the rat so as to gain a better understanding of this complex regulatory network. There have been a few published models of Ca and PO 4 regulation in humans [61,65,66]; however they do not incorporate the binding of Ca 2+ and PO 4 to each other and to other ions in plasma, the presence of complexation inhibitors such as fetuin-A, and the multiple effects of FGF23 on calcium and phosphate fluxes.…”