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

Journal article
Authors Martin Berglund
Mikael Sunnåker
Martin Adiels
Mats Jirstrand
Bernt Wennberg
Published in Mathematical medicine and biology : a journal of the IMA
Volume 29
Issue 4
Pages 361-384
ISSN 1477-8602
Publication year 2012
Published at Department of Mathematical Sciences
Institute of Medicine, Department of Molecular and Clinical Medicine
Department of Mathematical Sciences, Mathematics
Pages 361-384
Language en
Keywords non-linear mixed effects models; two stage approach; compartmental models; tracer experiments; leucine kinetics; ordinary differential equations; stochastic differential equations; Ornstein-Uhlenbeck process
Subject categories Applied mathematics, Medical and Health Sciences


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.

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