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author | Johannes Ranke <jranke@uni-bremen.de> | 2017-03-04 09:58:00 +0100 |
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committer | Johannes Ranke <jranke@uni-bremen.de> | 2017-03-04 09:58:00 +0100 |
commit | 3010c9dcbc7f90f15b55c14919f6688d61d14414 (patch) | |
tree | 781d9678bd25b451bce0c7b6d47e396be9c6ca1c /vignettes | |
parent | b847fec686bc1db59079412eb18063d3514ecf75 (diff) |
Mention pkgdown.jrwb.de/mkin in README
Add very small twa vignette, update pkgdown docs
Diffstat (limited to 'vignettes')
-rw-r--r-- | vignettes/twa.pdf | bin | 0 -> 147283 bytes | |||
-rw-r--r-- | vignettes/twa.rmd | 57 |
2 files changed, 57 insertions, 0 deletions
diff --git a/vignettes/twa.pdf b/vignettes/twa.pdf Binary files differnew file mode 100644 index 00000000..f39c64a7 --- /dev/null +++ b/vignettes/twa.pdf diff --git a/vignettes/twa.rmd b/vignettes/twa.rmd new file mode 100644 index 00000000..5c3f0ca3 --- /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: + +$$c_\textrm{twa} = c_0 \left( 1 - e^{- k t} \right) $$ + +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: + +$$f_\textrm{twa} = \left( 1 - e^{- k t} \right) $$ + +FOMC: + +$$f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) $$ + +DFOP: + +$$f_\textrm{twa} = \frac{1}{t} \left( + \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) $$ + |