A Matlab Toolbox for Nonlinear Mixed Effects Modeling – Illustrated with a Model for Lipoprotein Kinetics

M. Sunnåker, M. Berglund, B. Wennberg, M. Adiels, and M. Jirstrand, The 9th Int. Conf. on Systems Biology, Gothenburg, Sweden, August 2008.

Objective: Mathematical models constitute an important step towards an increased understanding of the processes underlying biological systems. Such systems are often complex, which puts high demands on the modeling techniques used. A crucial part of any modeling effort is to estimate the model parameters, which are often uncertain and may even vary between subjects. These issues can be handled by applying a statistical framework known as nonlinear mixed effects (NLME) modeling, in combination with stochastic differential equations (SDEs).

Results: We present a Matlab toolbox that can be used for model specification, simulation, and parameter estimation of NLME models with SDEs. The toolbox, which is called NLMEtools, is based on the Systems Biology Toolbox for Matlab which has previously been developed at the Fraunhofer-Chalmers Centre. The toolbox constitutes a natural platform for the analysis of biological data from several individuals. A user-friendly graphical user interface is provided to support the system identification workflow from specification of the model structure to estimating parameters as well as generation of synthetic data and comparison with real estimation data.

Conclusions: The parameters of a previously published compartmental model for lipoprotein kinetics in the blood plasma are analyzed, as an illustrative example of the usage of the toolbox. To monitor the kinetics of the lipoproteins an isotope-labeled tracer, leucine, is used in the experimental setup. The kinetic parameters of the model are estimated for artificially generated data and the statistical properties of the estimates are discussed.




  • Mikael Sunnåker, Fraunhofer-Chalmers Centre
  • Mats Jirstrand, Fraunhofer-Chalmers Centre
  • Martin Berglund, Mathematical Sciences, Chalmers University of Technology
  • Bernt Wennberg, Mathematical Sciences, Chalmers University of Technology
  • Martin Adiels, Wallenberg Laboratory for Cardiovascular Research, Gothenburg University


Photo credits: Nic McPhee