Risk-relevant indices for the characterization of persistence of chemicals in a multimedia environment

The present research study proposes a new set of appropriately defined indices for the characterization of persistence of chemicals in a multimedia environment that prominently figures as a key exposure-based indicator within contemporary frameworks of chemical hazard and risk assessment, as well as recent international regulatory initiatives. Effectively overcoming some of the limitations associated with traditional approaches that could lead to a potential misclassification of chemical substances, the proposed set of persistence indices retain also a conceptually insightful and computational appeal. Conceptually inspired by certain measures/indices for the characteristic time found in classic dynamic systems theory, and technically relying on notions and methods from the theory of matrices, the new performance indices can be easily calculated on the basis of a dynamic multimedia environmental model and the aid of a software package such as MATLAB. In particular, an extension of the notion of equivalence width as a quantitative proxy of overall persistence is introduced, that captures the dynamic history of the chemical's environmental behavior, while remaining independent of the particular release pattern and discharge conditions (thus overcoming the standardization difficulties encountered when a large number of chemicals need to be first screened and classified in a tiered hazard assessment methodology). Furthermore, a second persistence index is introduced whose value can be analytically calculated through the solution of a simple Lyapunov matrix equation bearing some resemblance to certain measures of system resilience used in theoretical biology and ecology, yet inspired by system-theoretic notions associated with the Lyapunov framework of analysis in systems science. Furthermore, for both persistence measures a comparison is made with the slowest time-constant associated with the specific chemical dynamics in a multimedia environment, and upper and lower bounds are established. Finally, the proposed persistence indices are calculated on the basis of a standard dynamic multimedia environmental model for various representative cases involving chemicals of particular interest.