Improved Estimation of Human Lipoprotein Kinetics with Mixed Effects Models - PubMed (original) (raw)

Improved Estimation of Human Lipoprotein Kinetics with Mixed Effects Models

Martin Berglund et al. PLoS One. 2015.

Abstract

Context: Mathematical models may help the analysis of biological systems by providing estimates of otherwise un-measurable quantities such as concentrations and fluxes. The variability in such systems makes it difficult to translate individual characteristics to group behavior. Mixed effects models offer a tool to simultaneously assess individual and population behavior from experimental data. Lipoproteins and plasma lipids are key mediators for cardiovascular disease in metabolic disorders such as diabetes mellitus type 2. By the use of mathematical models and tracer experiments fluxes and production rates of lipoproteins may be estimated.

Results: We developed a mixed effects model to study lipoprotein kinetics in a data set of 15 healthy individuals and 15 patients with type 2 diabetes. We compare the traditional and the mixed effects approach in terms of group estimates at various sample and data set sizes.

Conclusion: We conclude that the mixed effects approach provided better estimates using the full data set as well as with both sparse and truncated data sets. Sample size estimates showed that to compare lipoprotein secretion the mixed effects approach needed almost half the sample size as the traditional method.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Fig 1

Fig 1. Model structure of compartmental model.

The same structural model was used for all individuals and in both the mixed effects and the STS model. Model constraints, k 2,1 = k 1,2, k 3,4 = 0.1 k 4,3, k 9,8 = k 7,5 and k 0,9 = k 0,7 were used. Compartment 1 represents the free leucine in the plasma, compartments 3 and 4 represents leucine recycling in non-hepatic tissue and compartment 2 is the intrahepatic leucine that feeds the apoB synthesis compartment represented as a delay (D1-D7). Newly synthesized apoB enters the plasma as VLDL1 (large particles, compartment 5) or VLDL2 (small particles, compartment 8). VLDL2 may also be produced through conversion of VLDL1 via compartment 6. Particles may leave the system through compartments 6, 7, 9 or 10.

Fig 2

Fig 2. Residual plots of enrichment data using all data.

The residuals (model fit minus measurement data) for the three enrichment data sets (A and B, plasma leucine; C and D, VLDL1; E and F VLDL2) were plotted for the two methods (STS and NLME) and the two groups (A, C and E, Control; B, D and F, type 2 diabetes mellitus (DM2)). Both methods produced good fits to the data. The NLME approach used a sequential procedure; the plasma leucine were fitted first and the VLDL1 and VLDL2 curves were fitted using the leucine results. This may explain the worse fit for the plasma leucine in the STS approach. Lines, mean of mixed effects approach (red) and STS approach (black); Areas, mean ± SD for mixed effects approach (red) and STS approach (black).

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