1. Development of guidance for evaluating and calculating degradation kinetics in environmental media. W.P. Eckel 1, D.S. Spatz 1, R.D. Jones 1, D. Young 1, M. Shamim 1, K. White 1, S. Mendelsohn 1, L. Avon 2, I. Kennedy 2, A. McCoy 2, S. Kirby 2, G. Malis 2, R. Matthew 2. (1) Office of Pesticide Programs, U.S. EPA, (2) Environmental Assessment Directorate, PMRA, Health Canada. Figure 1. Example biotransformation dataset with poor SFO fit (green). For modeling, the SFO curve is calculated as the exponential curve with the same DT 90 as the best-fit model (either FOMC/IORE or DFOP). The DT 50 of this curve is calculated as the best-fit-model DT 90 /3.32 (i.e. log 10/log 2). The resulting SFO conservatively represents the concentration decline until 90% has degraded. Table 1. Choice of models used for evaluating kinetics ModelIntegrated Equation 1. Single First Order (SFO) C t = C 0 e -kt C t = Total amount of chemical present at time t C 0 = Total amount of chemical present at time t=0 k = Rate constant 2. Double First Order in Parallel (DFOP) C t = C 1 e - k 1 t + C 2 e -k 2 t or C = C 0 (ge -k 1 t + (1-g)e -k 2 t ) C = Total amount of chemical present at time t C 1 = Amount of chemical applied to compartment 1 at time t=0 C 2 = Amount of chemical applied to compartment 2 at time t=0 C 0 = C 1 + C 2 = Total amount of chemical applied at time t=0 g = fraction of C 0 applied to compartment 1 k 1 = Rate constant in compartment 1 k 2 = Rate constant in compartment 2 3a. Indeterminate Order Rate Equation (IORE) (1/n-1)*(1/C t n-1 – 1/C 0 n-1 ) = kt C t = Total amount of chemical present at time t C 0 = Total amount of chemical present at time t=0 k = Rate constant n = Reaction order 3b. Gustafson & Holden - First- Order Multi- Compartment (FOMC) C t = C 0 /(t/β + 1) α C t = Total amount of chemical present at time t C 0 = Total amount of chemical applied at time t=0 α = Shape parameter determined by coefficient of variation of k values β = Location parameter A case study was initiated at the US EPA to compare FOMC and IORE with regard to the ease of use, accuracy, and the descriptive abilities of each to provide an understanding of the degradation kinetics of pesticides. For comparison, SFO and second-order fits were also examined; however DFOP was not evaluated within this case study. IORE, like DFOP, is based on a generalization of the SFO equation. IORE utilizes fairly intuitive parameters (C0; k, a rate constant; and n, a reaction order) and is relatively straightforward, while FOMC, although algebraically equivalent, has somewhat unintuitive parameters (C0, α, and β). For datasets which are close to first order, in IORE, n is near 1 but in FOMC α=1/n-1 starts to approach infinity, making fitting FOMC difficult. Based on the preliminary experience of EPA evaluators, the FOMC method, using Excel solver, had difficulty converging on a reasonable solution while IORE fit such datasets quickly using TableCurve 2D. This could be due to the way FOMC initial parameters were selected, but since a different software tool was used for each respective method, there is uncertainty in these preliminary conclusions. Further study will be necessary to fully address this issue. Introduction. The Environmental Fate and Effects Division (EFED) of the US EPA and the Environmental Assessment Directorate (EAD) of Health Canada’s PMRA are responsible for the environmental risk assessment of pesticides. A part of the assessment process is characterizing the environmental fate of pesticides, and for providing estimates of environmental exposure to pesticides. This entails the review and evaluation of environmental fate studies, including laboratory studies of abiotic (hydrolysis and photolysis) and biotic transformation (metabolism) processes. The calculation of degradation kinetics parameters is an important part of the environmental exposure assessment. The EPA and PMRA initiated a project to harmonize methods for describing pesticide degradation kinetics. The primary goal of this project is to develop recommended procedures for characterizing and quantifying pesticide persistence in environmental media. Simulation models used to predict environmental exposure usually employ first-order kinetics to describe degradation, while the results of laboratory experiments, especially metabolism studies, often do not follow first-order decay. When this is the case, the application of first- order kinetic equations to such experiments gives a poor fit to the data. Traditional methods such as linear regression of log- transformed data often overestimate the time for 50% decay (DT 50 ), while non-linear regression of untransformed data (SFO) underestimates concentrations later in the experiment (e.g., the 90% decay time or DT 90 ). For these cases, alternate kinetic models are being explored. Materials and Methods. The NAFTA workgroup considered recent work on kinetics from the European Union (FOCUS, 2006) as well as the traditional chemical kinetics literature (Moore & Pearson, 1981). Recommended equations were tested with data sets from actual laboratory metabolism experiments and with idealized first-order and non-first-order data sets. The available approaches were narrowed down to four equations: single first order (SFO), double first order in parallel (DFOP), first order multi-compartment (FOMC), and indeterminate order rate equation (IORE). To deal with the problem of non-first order metabolism data, it was decided to split the methodology into two tracks, “descriptive” and “model input,” which is consistent with the approach outlined in FOCUS (2006). The descriptive track attempts to provide as accurate a description of the decay curve as possible, using the simplest kinetic equation. When the SFO does not fit the data, the models identified above are evaluated. The model input track uses first-order kinetics to define a half-life for input to computer models that assume first-order kinetics. The data quality objective for the model input parameter was that it should not underestimate concentrations late in the experiment (defined as the 90% degradation time or DT 90 ), and that it should minimize overestimation of concentrations before DT 90. To determine an acceptable exponential approximation, it is suggested to look at experimental data in one of three ways, depending on whether the data follow first-order kinetics and whether the measured concentrations reach 10% of the initial concentration by study end. The three steps are: 1. If the SFO model fits, use it. 2. If SFO does not fit and the data decline to below 10% of the starting concentration, then use an alternative kinetic model to fit the data around the DT 90. Calculate the half-life input parameter as the 90% decay time (DT 90 ) divided by 3.32, which is the ratio of the DT 90 to the DT 50 in first-order kinetics (ln 10/ln 2). 3. If the SFO does not fit, and measured concentrations are still above 10% of initial concentrations by the end of the study, then find the degradation rate at the end of the study by using such alternative models as DFOP, FOMC, and IORE. Results. The workgroup agreed to the use of the equations shown in the Table 1. These methods include non-linear first order (SFO), double first order in parallel (DFOP), and non-first-order equations (FOMC and IORE). The non-first-order equations were needed to accomplish the descriptive track objective of the most accurate description of the actual decay. Discussion. Issues with the extrapolation of non-first-order data sets to DT 90 for back- calculation of the model input parameter, and with the statistical description of “goodness” or “lack” of fit are still under discussion. Methods for the selection of initial values of alpha and beta for FOMC are needed, however this may be avoided by solving IORE first, and calculating alpha and beta from the IORE order (n) and rate constant (k). References. FOCUS (2006) “Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, EC Document Reference Sanco/10058/2005 version 2.0, 431 pp. Jacquez, John A., 1985. Compartmental Analysis in Biology and Medicine. The University of Michigan Press, Ann Arbor Moore, J.W. and R.G. Pearson, Kinetics and Mechanism, 3rd Ed., Wiley Interscience, New York, 1981. Figure 1 is an example of a biotransformation study dataset. Application of the SFO (green line) demonstrates the poor fit that is frequently seen when first-order methods are applied to non-first order data. In this case, as described in step 2 above in the Materials and Method, the “best curve” data (dark red line), either described by DFOP or by IORE/FOMC, does pass through the DT 90, The resulting SFO conservatively represents the concentration decline until 90% has degraded and allows for a conservative input for descriptive or modeling purposes.