KABAM Version 1.0 User's Guide and Technical Documentation  Appendix H  Methods for Estimating Metabolism Rate Constant
Metabolism Rate Constant (k_{M})
(K_{ow} (based) Aquatic BioAccumulation Model)
Appendix H. Methods for Estimating Metabolism Rate Constant (k_{M})
Generally, chemicalspecific data are not available to determine the metabolism rate constant (k_{M}) for aquatic organisms. However, this parameter can be estimated using data from available bioconcentration factor (BCF) studies, in combination with estimated rate constants. Two separate approaches can be employed to estimate k_{M}. The first utilizes Equation A1 from Arnot and Gobas 2004. The second utilizes a method described by Arnot et al. 2008. These approaches are described below.

H.1 Use of Equation A1
In this approach, Equation A1 (see Table A1 of Appendix A) is rearranged to solve for k_{M} (Equation H1). In a BCF study, fish are fed uncontaminated food; therefore, uptake through the dietary pathway is assumed to be negligible. As a result, it is assumed that k_{D} = 0. BCF studies with fish involve wateronly exposures, so fish do not respire pore water. As a result, m_{O} = 1 and m_{P} = 0. To calculate k_{M}, the model user should use the measured concentration of pesticide in the test water. In this case, it is assumed that this value represents the freely dissolved pesticide in the water, and therefore, Φ = 1. Based on these assumptions, Equation H1 can be restated as Equation H2.
Equation A1
C_{B} = [k_{1} * (m_{0} * Φ * C_{WTO} + m_{P} * C_{WDP}) + k_{D} *Σ (P_{i} * C_{Di})] / (k_{2} + k_{E} + k_{G} + k_{M}) (From Appendix A)
Equation H1
k_{M} = {[k_{1} * (m_{0} * Φ * C_{WTO} + m_{P} * C_{WDP}) + k_{D} * ∑(P_{i} * C_{Di})] / (C_{B})}  (k_{2} + k_{E} + K_{G})
Equation H2
k_{M} = {[k_{1} * (C_{WTO})] / C_{B}}  k_{2}  k_{E}  k_{G}
Equation H2 can be used to estimate k_{M} from available data from a BCF study.

Empirical estimates of k_{1} (L/kg*d), total pesticide concentration in fish tissues (C_{B}; g/kgww) and C_{WTO} (g/L) from the BCF study should be entered into this equation.

k_{2} (d^{1}) is calculated as k_{1(empirical)}/K_{BW} (see Table A6 of Appendix A). To calculate K_{BW}, it is necessary to have estimates of
% lipid, % nonlipid organic matter (NLOM), and % water of the test fish (V_{LB}, V_{NB} and V_{WB}, respectively).
If % lipid data are not available for the test fish, this approach should not be used and it should be assumed that k_{M} = 0.

If % lipid data are available, but % NLOM and % water are not available, it can be assumed that the fish are 73% water and that % NLOM is equal to 10073% lipid.


k_{E} (d^{1}) can be estimated using the KABAM tool. The model user should use the large fish of KABAM to calculate k_{E}.

Body weight of the fish and water temperature should be set to mean reported values from the study. If body weight data are not available for the test fish, this approach should not be used and it should be assumed that k_{M} = 0.

This constant is influenced by the % lipid, % NLOM, and % water of the diet (V_{LD}, V_{ND} and V_{WD}, respectively). Calculation of this constant requires input of diet of the large fish to be 100% medium fish (Table 6 of KABAM tool). If data are available from the BCF study report to define the % lipid, % NLOM, and % water of the feed of the test fish, the data should be entered in the appropriate columns of Table 5 of the KABAM tool for the medium fish. Otherwise, if these data are not available, the % lipid, % NLOM, and % water of the medium fish can be set to the default values of 4, 23, and 73%, respectively.


k_{G} (d^{1}) can be estimated from empirical data on body weight over the study period. If k_{G} cannot be estimated, the model user can use k_{G} from the large fish.


H.2 Use of Arnot et. al. 2008
In this approach, it is assumed that the elimination rate constant measured during the BCF study (k_{T}) is the sum of elimination through respiration, fecal elimination and metabolism of the pesticide by the fish as well as growth dilution (Equation H3, Arnot et al. 2008). Equation H3 can be rearranged into Equation H4, to solve for k_{M}.
Equation H3
k_{T} = k_{2} + k_{E} + k_{G} + k_{M}
Equation H4
k_{M} = k_{T}  k_{2}  k_{E}  k_{G}
Equation H4 can be used to estimate k_{M} from available data from a BCF study.

k_{T} (d^{1}) is the total elimination rate constant estimated from the depuration period of the BCF study.

As with the first approach, k_{2} (d^{1}) can be calculated as k_{1(empirical)}/K_{BW} (see table A6 of Appendix A).

k_{E} (d^{1}) can be estimated using the KABAM tool. See discussion above on how to derive this constant value.

k_{G} (d^{1}) can be estimated from empirical data on body weight over the study period. If k_{G} cannot be estimated, the model user can use k_{G} from the large fish.


H.3 Assumptions and Uncertainties
If k_{M} is calculated as a negative value, it should be assumed that no biotransformation of the chemical occurs and k_{M} should be set to 0 in Table 2 of the KABAM tool. Since a negative biotransformation rate would indicate that the organism is creating the pesticide, it is assumed that this is not possible for a pesticide.
There is some uncertainty in using the model estimated k_{G} value (using Equation A7), as it may differ from the growth rate of the test species of the BCF study.
The first approach involves use of total pesticide concentration in fish tissues (C_{B}; g/kgww) and C_{WTO} (g/L). It would be appropriate to enter mean values for these parameters into equation H2. However, variability in these parameters can influence predictions of k_{M}. Therefore, the model user should explore variability associated with these values by considering standard deviation, as well as minimum and maximum values for these parameters. This will result in a range of relevant k_{M} values.
Both approaches involve use of fish body composition data (V_{LB}, V_{NB}, and V_{WB}). It would be appropriate to use mean values to calculate K_{BW} (and ultimately k_{2}). However, variability in these parameters can influence predictions of k_{M}. Therefore, the model user should explore variability associated with these values by considering standard deviation, as well as minimum and maximum values for these parameters. This approach will result in a range of relevant k_{M} values.
Both approaches involve using the KABAM tool to calculate k_{E}. This involves the use of diet composition data (V_{LD}, V_{ND}, and V_{WD}). In the case that data are not available from the study report to define the % lipid, % NLOM, and % water of the diet of the test fish, there is uncertainty in using default values for these parameters, as they may differ from the diet of the test species of the BCF study.