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diff --git a/vignettes/twa.Rmd b/vignettes/twa.Rmd deleted file mode 100644 index 6f283eb2..00000000 --- a/vignettes/twa.Rmd +++ /dev/null @@ -1,79 +0,0 @@ ---- -title: Calculation of time weighted average concentrations with mkin -author: Johannes Ranke -date: "`r Sys.Date()`" -bibliography: references.bib -output: rmarkdown::html_vignette -vignette: > - %\VignetteIndexEntry{Calculation of time weighted average concentrations with mkin} - %\VignetteEngine{knitr::rmarkdown} - %\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. 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 -[@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: - -$$c_\textrm{twa} = \frac{c_0}{t} \left( - \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) $$ - -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. |