Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations

M. Berglund, M. Sunnåker, M. Adiels, M. Jirstrand, and B. Wennberg. Mathematical Medicine and Biology, 30 July 2011.

Abstract

Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.

Authors and Affiliations

  • M. Berglund, Department of Mathematical Sciences, University of Gothenburg, and Department of Mathematical Sciences, Chalmers University of Technology
  • M. SunnÃ¥ker, Fraunhofer-Chalmers Research Centre for Industrial Mathematics
  • M. Adiels, Department of Mathematical Sciences, University of Gothenburg; Department of Mathematical Sciences, Chalmers University of Technology, and Wallenberg Laboratory for Cardiovascular Research, University of Gothenburg
  • M. Jirstrand, Fraunhofer-Chalmers Research Centre for Industrial Mathematics
  • B. Wennberg, Department of Mathematical Sciences, University of Gothenburg, and Department of Mathematical Sciences, Chalmers University of Technology



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