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A Minimal Mathematical Model of Calcium Homeostasis

Endocrinology Department of the Portuguese Cancer Institute (J.F.R., L.G.S.), 1099-023 Lisboa, Portugal; Abel Salazar’s Institute of Biomedical Sciences, University of Oporto (H.G.F.), 4099-003 Oporto, Portugal; and Department of Chemistry (H.G.F.), Faculty of Science and Technology, New University of Lisbon, 2829-516 Caparica, Portugal

Address all correspondence and requests for reprints to: Dr. J. F. Raposo, Endocrinology Department, Portuguese Cancer Institute, R. Prof. Lima Basto, 1099-023 Lisboa, Portugal. E-mail: . filipe.raposo{at}mail.telepac.pt

Abstract

A mathematical model of calcium homeostasis is presented in which the controlling factors are the plasma concentrations of calcium, PTH, and calcitriol, and the effector organs are the parathyroids, bone, kidney, and intestine. Other factors can be added as the need arises. The model is aimed at simulating what happens in a single individual, but its parameters and variables were adjusted to the corresponding published average values.

Simulations of published observations in humans undergoing the infusion of calcium or its chelators are presented. With a single exception, these simulations provided a good fit to the data. The response of the system to extrinsic perturbations was characterized by simulating chronic infusions of calcium, PTH, and calcitriol. Finally, the steady state response to perturbations in some of its parameters (the secretory mass of the parathyroids and the affinity and/or sensitivity of the calcium, PTH, and calcitriol receptors) and to renal failure were also investigated in an attempt to analyze the pathogenesis of clinical hypo- or hypercalcemias.

In its present form the model cannot be used to base clinical decisions in individual cases. However, it requires modest computational resources, and clinicians with a modest mathematical background can manipulate it. It is a useful tool for the analysis of general mechanisms of the diseases of calcium metabolism and for the design of clinical experiments aimed at characterizing these diseases. The model can also be the core of future autoadaptive extensions to be used in individual patients.

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