Bayesian evaluation of a physiologically-based pharmacokinetic (PBPK) model of long-term kinetics of metal nanoparticles in rats

- Biologically-based modeling of nanoparticle kinetics is needed to estimate internal tissue dose.
- Bayesian MCMC analyses improves estimation of parameter variability and uncertainty.
- Bayesian MCMC analyses also aids in evaluation of the utility of specific data sets.
- Additional data are needed to reduce uncertainty in predictions of metal nanoparticle kinetics.

Biomathematical modeling quantitatively describes the disposition of metal nanoparticles in lungs and other organs of rats. In a preliminary model, adjustable parameters were calibrated to each of three data sets using a deterministic approach, with optimal values varying among the different data sets. In the current effort, Bayesian population analysis using Markov chain Monte Carlo (MCMC) simulation was used to recalibrate the model while improving assessments of parameter variability and uncertainty. The previously-developed model structure and some physiological parameter values were modified to improve physiological realism. The data from one of the three previously-identified studies and from two other studies were used for model calibration. The data from the one study that adequately characterized mass balance were used to generate parameter distributions. When data from a second study of the same nanomaterial (iridium) were added, the level of agreement was still acceptable. Addition of another data set (for silver nanoparticles) led to substantially lower precision in parameter estimates and large discrepancies between the model predictions and experimental data for silver nanoparticles. Additional toxicokinetic data are needed to further evaluate the model structure and performance and to reduce uncertainty in the kinetic processes governing in vivo disposition of metal nanoparticles.