Calibration of dynamic responses in a physiological model

Abstract

Dynamic physiological models are often constructed to gain insight into the operation of a complex biological function. In applications such as the study of disease risk, different individuals may vary in susceptibility to disease or response to treatment. An example of this type of application is the dairy cow magnesium model (Bell et al. 2008) used to asses the proportion of animals in a herd at risk of developing hypomagnesaemic tetany. The onset of tetany occurs when the concentration of Mg in cerebrospinal fluid (CSF) falls below a critical level of ~0.54 mmol.l-1 (Allsop & Pauli, 1985). The CSF magnesium concentration is determined by the exchange of Mg between plasma and CSF (Robson et al. 2004). Bell (2006) used the experiment of McCoy et al. (2001) to demonstrate simulation of dynamic changes of plasma and cerebrospinal fluid (CSF) magnesium concentration in dairy cattle that occur in response to feeding a magnesium deficient diet over a period of 15 days. Biological variation between animals was modelled by implementing selected parameters of the dynamic model as distributions, and then a Monte-Carlo method was used to generate a distribution of a selected model response variable (response distribution). A problem with this approach is that the accuracy of the response distribution depends on the accuracy of the parameter distributions used in the model simulations. The refinement algorithm described by Bell et al. (2006) provides a method to obtain parameter distributions that minimise the error between a simulated response distribution and a corresponding experimentally observed response distribution (such as Mg excreted in urine). The adjustments to parameter distributions are constrained within their feasible biological range (a priori range), and are made by combining information for each parameter about both the sensitivity of the response to change in the parameter, and the constraint to the a priori range.The refinement procedure is currently limited to using a single response distribution when calculating updated parameter distributions. An important issue is the calibration of model parameters specific to the dairy herd in which the risk of tetany is estimated. In the model Mg intake is determined by feed intake and pasture characteristics, which may change from day to day due to changes in feed management practice on the farm. Measuring feed and Mg intake directly is not practical for a commercial dairy herd. A possible method of calibrating the model to a specific herd is to take measurements of Mg in samples of urine on successive days, then estimate parameters for feed and Mg intake that minimise the error between the simulated and measured urinary Mg excretion. This paper describes an extension of the refinement procedure to include time-series dynamic response data into the selection of updated parameter distributions, which allows improved calibration of dynamic responses in the model.