A simulation model of calcium metabolism

A mathematical model is proposed for human calcium metabolism. The bodily calcium content is divided into one homogeneous compartment containing plasma calcium, three homogeneous compartments exchanging with it and representing a part of the tissue and bone calcium, a series of homogeneous compartments representing calcium in the gastro-intestinal tract, and an un-mixed compartment representing the remainder of body calcium. Expressions are given to represent the following: (a) The movement of ingested calcium through the gastrointestinal tract. (b) The dependence of the rate of intestinal calcium absorption on position in the intestine, the calcium concentration in the lumen and the plasma concentrations of parathormone and 25-hydroxycholecalciferol. (c) The dependence of the rate of urinary calcium excretion on the plasma concentrations of calcium, parathormone and calcitonin. (d) The dependence of the rate of calcium flow from bone to plasma on the plasma concentrations of parathormone and calcitonin. (e) The dependence of the plasma concentrations of parathormone and calcitonin on the calcaemia. The model describes events with durations of between about 5 minutes and 3 weeks. Numerical values for many of the parameters of the model have been collected from the literature, but little quantitative data could be found for the actions of parathormone; calcitonin, and 25-hydroxycholecalciferol. A digital computer programme, (CAMET), based on the mathematical model, has been written to simulate calcium metabolism. CAMET is used to successfully simulate the absorption of ingested calcium and tracer calcium, and the resulting plasma concentrations and excretion rates. Conclusions are drawn as to what new experimental work is required in order to further test and extend the model. Also described is some experimental work carried out on a method of directly comparing calcium concentrations by alternating the sample feed to an atomic absorption spectrometer