Comparison of biokinetic models for non-dissolvable engineered nanomaterials in freshwater aquatic organisms

Abstract

Understanding the uptake and elimination kinetics of engineered nanomaterials (ENMs) in aquatic organisms is essential for their environmental risk assessment. This study offers a comparative mathematical analysis of biokinetic models for non-dissolvable ENMs in freshwater organisms. Five models were applied to 34 datasets covering the following ENMs: titanium dioxide (TiO₂), silica (SiO₂), fullerene, graphene, gold (Au), carbon nanotubes (CNTs), and graphene oxide. Four of these models are the first-order one-compartment model and its variants considering the storage fraction and growth dilution. The fifth model is the Michaelis–Menten kinetics. The quality of models was evaluated regarding the adjusted R squared and the bias-corrected Akaike information criterion. The results suggest that no general model is able to predict all the experimental data properly. First-order one-compartment models with storage fraction seem to show more flexibility to describe various bioaccumulation patterns, especially when depuration is clearly incomplete. These models can make valid predictions for more than 85% of the experimental data. The uptake rate constants estimated for D. magna (12 000 L kg⁻¹ h⁻¹) are significantly higher than the rate constants for zebrafish (7 L kg⁻¹ h⁻¹). A significant difference in the elimination rate constants between D. magna (0.5 1/h) and zebrafish (0.06 1/h) is only observed in the model with a storage fraction. To better understand the biokinetics of ENMs and reduce the uncertainty in modelling, we suggest to use an appropriate length for the exposure and elimination periods in future experimental designs. Additionally, more information related to particle characterization in the exposure medium should be reported.