Calculation of time weighted average concentrations with mkin • mkin

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Since version 0.9.45.1 of the ‘mkin’ package, a function for -calculating time weighted average concentrations for decline kinetics -(i.e. only for the compound applied in the experiment) is -included. Strictly speaking, they are maximum moving window time -weighted average concentrations, i.e. the maximum time weighted -average concentration that can be found when moving a time window of a -specified width over the decline curve.

Time weighted average concentrations for the SFO, FOMC and the DFOP -model are calculated using the formulas given in the FOCUS kinetics -guidance (FOCUS Work Group on Degradation -Kinetics 2014, 251):

SFO:

\[c_\textrm{twa} = c_0 \frac{\left( 1 - -e^{- k t} \right)}{ k t} \]

FOMC:

\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - -\alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} -- 1 \right) \]

DFOP:

\[c_\textrm{twa} = \frac{c_0}{t} \left( - \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]

HS for \(t > t_b\):

\[c_\textrm{twa} = \frac{c_0}{t} \left( - \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} -\right) \right) \]

Often, the ratio between the time weighted average concentration -\(c_\textrm{twa}\) and the initial -concentration \(c_0\)

\[f_\textrm{twa} = -\frac{c_\textrm{twa}}{c_0}\]

is needed. This can be calculated from the fitted initial -concentration \(c_0\) and the time -weighted average concentration \(c_\textrm{twa}\), or directly from the -model parameters using the following formulas:

SFO:

\[f_\textrm{twa} = \frac{\left( 1 - e^{- k -t} \right)}{k t} \]

FOMC:

\[f_\textrm{twa} = \frac{\beta}{t (1 - -\alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} -- 1 \right) \]

DFOP:

\[f_\textrm{twa} = \frac{1}{t} \left( - \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]

HS for \(t > t_b\):

\[f_\textrm{twa} = \frac{1}{t} \left( - \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} -\right) \right) \]

Note that a method for calculating maximum moving window time -weighted average concentrations for a model fitted by ‘mkinfit’ or from -parent decline model parameters is included in the -max_twa_parent() function. If the same is needed for -metabolites, the function pfm::max_twa() from the ‘pfm’ -package can be used.

-FOCUS Work Group on Degradation Kinetics. 2014. Generic Guidance for -Estimating Persistence and Degradation Kinetics from Environmental Fate -Studies on Pesticides in EU Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics. -

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Calculation of time weighted average -concentrations with mkin

Johannes -Ranke

Last change 18 September 2019 -(rebuilt 2023-04-16)