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author | Johannes Ranke <jranke@uni-bremen.de> | 2017-03-28 10:44:50 +0200 |
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committer | Johannes Ranke <jranke@uni-bremen.de> | 2017-03-28 10:44:50 +0200 |
commit | 063ae84c199e1223a620fe512ab8713371119f5f (patch) | |
tree | d862da26840ff15704f9aff5cbc4ea8860369493 /vignettes/twa.Rmd | |
parent | 4a80cdabfb080a0b1082e02c5af9adfb5e3c99b0 (diff) |
Change vignette format for twa vignette, update docs
Diffstat (limited to 'vignettes/twa.Rmd')
-rw-r--r-- | vignettes/twa.Rmd | 57 |
1 files changed, 57 insertions, 0 deletions
diff --git a/vignettes/twa.Rmd b/vignettes/twa.Rmd new file mode 100644 index 00000000..60188223 --- /dev/null +++ b/vignettes/twa.Rmd @@ -0,0 +1,57 @@ +--- +title: Calculation of time weighted average concentrations with mkin +author: Johannes Ranke +date: "`r Sys.Date()`" +bibliography: references.bib +vignette: > + %\VignetteEngine{knitr::rmarkdown} + %\VignetteIndexEntry{Calculation of time weighted average concentrations with mkin} + %\VignetteEncoding{UTF-8} +--- + +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. + +Time weighted average concentrations for the DFOP model are calculated using +the formulas given in the FOCUS kinetics guidance [@FOCUSkinetics2014, p. 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: + +$$c_\textrm{twa} = \frac{c_0}{t} \left( + \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) $$ + +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: + +$$f_\textrm{twa} = \frac{1}{t} \left( + \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) $$ + |