Journal Article

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

Martin Berglund, Mikael Sunnåker, Martin Adiels, Mats Jirstrand and Bernt Wennberg

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 4, pages 361-384
Published in print December 2012 | ISSN: 1477-8599
Published online September 2011 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqr021
Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations

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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.

Keywords: non-linear mixed effects models; two stage approach; compartmental models; tracer experiments; leucine kinetics; ordinary differential equations; stochastic differential equations; Ornstein–Uhlenbeck process

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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