Modelling of magnesium metabolism in dairy cattle

Abstract

A model of magnesium metabolism in dairy cattle has been developed by adapting and improving an earlier model of magnesium metabolism in sheep. The model in cattle has been developed for the purpose of estimating the proportion of animals within a dairy herd at risk of developing hypomagnesaemic tetany, which occurs when magnesium concentrations in cerebrospinal fluid (CSF) fall below 0.57-0.62 mmol.l⁻¹ (Pauli and Allsop, 1974; Allsop and Pauli, 1985). CSF magnesium concentrations are related to plasma magnesium concentration, which is determined by the balance between the absorption and secretion of magnesium along the gastrointestinal tract and the excretion of magnesium in milk, urine and faeces.

In an initial revision the sheep model was scaled to represent a dairy cattle sized animal, but in a simulation of magnesium deficiency over time, simulated plasma magnesium concentrations fell much faster than the experimental data. The equations for absorption and secretion of magnesium in the hindgut compartment of the model were revised to provide better representation of the processes of magnesium secretion into the small intestine and absorption further down the gastrointestinal tract, providing an additional mechanism for magnesium homeostasis in the model. The modified model predicts a reduction of faecal endogenous Mg loss related to the decline in plasma Mg concentration during magnesium deficiency, rather than a constant rate of endogenous loss. Evidence of this effect is provided by re-analysis of published experimental data. Further validation of the revised model is that the rate of change in plasma Mg concentration during severe magnesium deficiency is more realistic.

In the final stage of model development, a term to represent the effect of electrical driving forces on passive Mg absorption from the hindgut compartment was included. With this modification, the model was able to simulate the changes of plasma Mg concentration during induced severe hypomagnesaemia in close agreement with experimental data over a 14 day period. This modification has provided new insights into the mechanisms of Mg homeostasis, and provides the basis for the development of a conceptual model of intestinal magnesium absorption and secretion based on passive electrochemical driving forces.

During the onset of Mg deficiency, initially only a small proportion of animals within a dairy herd are at risk of developing hypomagnesaemic tetany, with the number of animals likely to be affected increasing as the deficiency becomes more severe. To estimate tetany risk, the biological variation between animals is modelled by implementing model parameters as distributions. Using the Monte-Carlo method the model is run repeatedly using (scalar) parameters sampled from the parameter-distributions to represent individuals within the herd. Tetany risk is then taken to be the proportion of animals that have CSF magnesium concentrations below the critical level. Having adopted this approach the task of establishing the correct parameter-distributions presents a substantial problem. In many cases parameter distributions are available from experimental observation with high accuracy, in other cases measurements may be available but with poor accuracy. Establishing the variance components requires special considerations, since the phenotypic variation within a particular herd is likely to be less than the variation over the full population. Since the variation of parameters and model inputs determines the variation in model output and therefore the estimation of tetany risk, it is necessary to establish the parameter-distributions to the best accuracy possible. A generalised algorithm for refining parameter-distributions of non-linear model systems is developed to estimate parameter-distributions in the dairy cow magnesium model. The biological range of each parameter to be refined is used to establish the a priori distribution estimate. Adjustments of the parameter-distributions during refinement are weighted by the a priori distribution's error range and the sensitivity of the model output to changes in each parameter's distribution. Operation of the refinement algorithm is verified by estimating parameter-distributions of the daily urinary magnesium excretion flux, chosen as a non-linear test case for which experimental data sets exhibit a large variable component.

The completed dairy cow magnesium model was evaluated by simulating a study of experimentally induced hypomagnesaemic tetany in dairy cattle. The estimate of tetany risk from the model was found to be consistent with experimental observation. The principles of performing an on-farm calibration of the model using information obtained from urine samples, and then using the calibrated model to estimate the proportion of cows in the herd at risk of developing tetany were demonstrated using artificial data.