Tools and rules for modelling uptake and bioaccumulation of nanomaterials in invertebrate organisms

Quantification of the uptake and elimination of nanomaterials (NMs) by organisms is key in assessing the environmental risks of NMs. For this, uptake models for conventional solutes may be used, although no consensus exists on their applicability for NMs. In this critical review therefore, conventional modelling approaches are scrutinised for their applicability for NMs. Statically derived accumulation factors, like BCF or BAF based on measured concentrations, are considered to be flawed because NMs are thermodynamically not stable, an important assumption for this approach. Dynamically derived accumulation factors, based on kinetic exposure experiments, may be applicable because no equilibrium between the organism and exposure medium is needed. Currently there is no full understanding of the passive uptake of NMs, which hampers assessment of the applicability of biotic ligand models. Passive uptake, however, is generally considered to be very limited, which would imply a limited applicability of BLMs for NMs. Physiologically based pharmacokinetic (PBPK) models, or biodynamic models, have successfully been applied in uptake studies with NMs. Their underlying assumptions can be met in experiments addressing NMs and case studies presented in this review demonstrate their applicability to model NM-form specific kinetics, integrated with environmental fate models, including relevant physiological processes. Their application requires the a priori definition of the major mechanisms driving the uptake kinetics and the quantification of the associated kinetic rate constants. This limits their application to those mechanisms for which the kinetic rate constants can actually be quantified. Within these limitations, PBPK models have been shown to be applicable and provide a promising general approach to improve modelling of NM-accumulation in organisms.