Parameter grouping and co-estimation in physiologically based kinetic models using genetic algorithms

Physiologically based kinetic (PBK) models are widely used in pharmacology and toxicology for predicting the internal disposition of substances upon exposure, voluntarily or not. Due to their complexity, a large number of model parameters need to be estimated, either through in silico tools, in vitro experiments, or by fitting the model to in vivo data. In the latter case, fitting complex structural models on in vivo data can result in overparameterization and produce unrealistic parameter estimates. To address these issues, we propose a novel parameter grouping approach, which reduces the parametric space by co-estimating groups of parameters across compartments. Grouping of parameters is performed using genetic algorithms and is fully automated, based on a novel goodness-of-fit metric. To illustrate the practical application of the proposed methodology, two case studies were conducted. The first case study demonstrates the development of a new PBK model, while the second focuses on model refinement. In the first case study, a PBK model was developed to elucidate the biodistribution of titanium dioxide (TiO2) nanoparticles in rats following intravenous injection. A variety of parameter estimation schemes were employed. Comparative analysis based on goodness-of-fit metrics demonstrated that the proposed methodology yields models that outperform standard estimation approaches, while utilizing a reduced number of parameters. In the second case study, an existing PBK model for perfluorooctanoic acid (PFOA) in rats was extended to incorporate additional tissues, providing a more comprehensive portrayal of PFOA biodistribution. Both models were validated through independent in vivo studies to ensure their reliability.