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)

• H.1 Use of Equation A1
• H.2 Use of Arnot et. al. 2008
• H.3 Assumptions and Uncertainties

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Appendix H. Methods for Estimating Metabolism Rate Constant (k_M)

Generally, chemical-specific 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 water-only 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 = [k₁ * (m₀ * Φ * C_WTO + m_P * C_WDP) + k_D *Σ (P_i * C_Di)] / (k₂ + k_E + k_G + k_M)      (From Appendix A)

  Equation H1

  k_M = {[k₁ * (m₀ * Φ * C_WTO + m_P * C_WDP) + k_D * ∑(P_i * C_Di)] / (C_B)} - (k₂ + k_E + K_G)

  Equation H2

  k_M = {[k₁ * (C_WTO)] / C_B} - k₂ - k_E - k_G

  Equation H2 can be used to estimate k_M from available data from a BCF study.

  • Empirical estimates of k₁ (L/kg*d), total pesticide concentration in fish tissues (C_B; g/kg-ww) and C_WTO (g/L) from the BCF study should be entered into this equation.

  • k₂ (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, % non-lipid 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 100-73-% 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.

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• 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 = k₂ + k_E + k_G + k_M

  Equation H4

  k_M = k_T - k₂ - 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, k₂ (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.

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• 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/kg-ww) 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 k₂). 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.