Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations.
Journal article, 2012

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.

compartmental models

leucine kinetics

tracer experiments

non-linear mixed effects models

stochastic differential equations

ordinary differential equations

Ornstein-Uhlenbeck process

two stage approach


Martin Berglund

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Mikael Sunnåker

Swiss Federal Institute of Technology in Zürich (ETH)

Fraunhofer-Chalmers Centre

Competence Center for Systems Physiology and Metabolic Diseases

Martin Adiels

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Mats Jirstrand

Fraunhofer-Chalmers Centre

Bernt Wennberg

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Mathematical medicine and biology : a journal of the IMA

1477-8602 (eISSN)

Vol. 29 4 361-384

Subject Categories

Computational Mathematics






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