How to describe the time-dependent dissolution of engineered nanomaterials?

Numerous processes such as solubility, agglomeration/aggregation, or protein corona formation may change over time and significantly affect engineered nanomaterial (ENM) structure, property, and availability, resulting in their reduced or increased toxicological activity. Therefore, understanding the dynamics of these processes is essential for assessing and managing the risks of ENMs during their lifecycle, ensuring safety by design. Of these processes, the importance of solubility (i.e., the ability to release ions from the surface) is undeniable. Thus, we propose a practical approach, the Kalapus equation (KEq), to determine ENMs' dissolution over time. As a proof-of-concept, the KEq was applied to determine the solubility of six commercially used metal and metal oxide nanoparticles over time. The KEq exhibited a higher coefficient of determination (R2=0.995-0.999) than the logarithmic equation (R2=0.835-0.986), and the pseudo-first-order equation (R2=0.915-0.994) over a range of experimental data. The newly introduced Kalapus equation outperformed the logarithmic and pseudo-first-order equations when extrapolating beyond the time range in which solubility was experimentally determined. The mean absolute error in solubility prediction for the KEq was 3.29% and 4.28% for the first and second data points, respectively, significantly lower than the 13.46% and 18.05% observed for the pseudo-first-order/first-order equation. The proposed equation can be used as a part of New Generation Risk Assessment (NGRA) methodology, especially new Integrated Approaches to Testing and Assessments (IATAs).