A mathematical model of calcium and phosphate homeostasis and early chronic kidney disease

Abstract

A complex network of hormones, buffers, and signaling mechanisms must work together to maintain proper calcium and phosphate levels in the human body. Quantification of this network is necessary to gain understanding about how various pathophysiologies develop, and how they can be treated. In particular, calcium and phosphate homeostasis are intertwined through the interactions of parathyroid hormone (PTH), fibroblast growth factor 23 (FGF23), and 1α,25(OH)2D3 (Calcitriol). In vitro and in vivo studies were used to parameterize a model of hormone production and secretion for PTH, FGF23, and calcitriol including anabolic and catabolic pathways. In addition, it contains a three‐stage kinetic model of Vitamin D with the metabolic shunt path of 24 hydroxylation. The homeostatic mechanism includes various buffering mechanisms within the extracellular fluid compartment, hormonal influence on renal clearance mechanisms, and servo‐control of the calcium‐phosphorus product by a solubility model proposed by Talmage, Bronner, and Stein. The model responds properly to disturbances in the clearance of FGF23 characteristic in autosomal dominant hypophosphatemic rickets, and simulates low calcium or high phosphate diets properly. As an application of the model, we demonstrate the mechanism believed to describe the onset of metabolic bone disease as a complication of chronic kidney disease. In particular, renal damage reduces the ability of the kidney to create calcitriol resulting in increased PTH leading to increased FGF. When renal damage is minimal, compensation is possible, but as kidney damage becomes more intense, compensation is lost and FGF23 rises, the first general clinical indicator of skeletal involvement of CKD. This model does not include a specific bone cell axis, and is thus unable to demonstrate the effects of subsequent decompensation. This project is supported by NIH 1T32HL105324‐01 and EPSCoR 0903787.