Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 67, Issue 3, Pages 547-561Publisher
SPRINGER
DOI: 10.1016/j.bulm.2004.09.005
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Deterministic and stochastic differential equations models of the uptake of dodecanedioic acid (Cl2) are fitted to experimental data obtained on nine isolated, perfused rat livers. 11500 mu g of Cl 2 were injected as a bolus into the perfusing liver solution. The concentrations of Cl2 in perfusate samples taken over 2 h from the beginning of the experiments were analyzed by High Performance Liquid Chromatography (HPLC). A two-compartment deterministic model is studied. To include spontaneous erratic variations in the metabolic processes the parameter for the uptake rate is randomized to obtain a stochastic differential equations model. Parameters are estimated in a two-step procedure: first, parameters in the drift part are estimated by least squares; then, the diffusion parameter is estimated using Monte-Carlo simulations to approximate the unknown likelihood function. Parameter estimation is carried out over a wide range of reasonable measurement error variances to check robustness of estimates. It is concluded that the kinetics of dodecanedioic acid, in the experimental conditions discussed, is well approximated by a model including spontaneous erratic variations in the liver uptake rate. (c) 2004 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.
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