Bayesian inference and model selection for physiologically-based pharmacokinetic modeling of superparamagnetic iron oxide nanoparticles

The growing use of superparamagnetic iron oxide nanoparticles (SPIONs) in early cancer detection technologies has created a demand for physiologically-based pharmacokinetic (PBPK) models that accurately model and predict the biodistribution of SPIONs in the mouse and human model. The objective of this work is to use a Bayesian approach built upon nested-sampling to select a model based on qualitative criteria of the fit of the model and the likelihood function landscape, as well as quantitative criteria of the evidence and maximum likelihood values. Four first-order PBPK compartmental models of ranging complexity are considered. Compartments included in the models comprise of a combination of the plasma, liver, spleen, tumor, and "other" (the remaining body tissue), with parameters including the volume, blood flow rate, and plasma:tissue distribution ratios. The model parameters for each model are evaluated using Bayesian inference, in addition to the respective evidence integrals, maximum log-likelihoods, and Bayes factors. The model containing all compartments and the model containing the plasma, liver, tumor and "other" had the highest log-likelihood and evidence values, indicating both a high goodness-of-fit and a high likelihood of the model given the data. This is similarly reflected in a faithful quality-of-fit and non-flat log-likelihood landscapes. Overall, these findings illustrate the strength of the Bayesian model selection framework in ranking different models to determine the best model that accurately represents the experimental data.