From 5f6faef514c603c04b5824b80bbaf3bfb5cd2eb7 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Tue, 28 Mar 2017 10:47:46 +0200 Subject: Add the vignette to the docs directory --- docs/articles/twa.html | 185 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 185 insertions(+) create mode 100644 docs/articles/twa.html diff --git a/docs/articles/twa.html b/docs/articles/twa.html new file mode 100644 index 00000000..6861d9fc --- /dev/null +++ b/docs/articles/twa.html @@ -0,0 +1,185 @@ + + + + + + + + + + + + + + + +Calculation of time weighted average concentrations with 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.

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

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SFO:

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

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FOMC:

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

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DFOP:

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

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

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

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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:

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SFO:

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

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FOMC:

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

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DFOP:

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

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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://focus.jrc.ec.europa.eu/dk.

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