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Diffstat (limited to 'vignettes/twa.Rmd')
| -rw-r--r-- | vignettes/twa.Rmd | 21 |
1 files changed, 15 insertions, 6 deletions
diff --git a/vignettes/twa.Rmd b/vignettes/twa.Rmd index 60188223..c4fe861f 100644 --- a/vignettes/twa.Rmd +++ b/vignettes/twa.Rmd @@ -11,10 +11,14 @@ vignette: > 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. +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 DFOP model are calculated using -the formulas given in the FOCUS kinetics guidance [@FOCUSkinetics2014, p. 251]: +Time weighted average concentrations for the SFO, FOMC and the DFOMP model are +calculated using the formulas given in the FOCUS kinetics guidance +[@FOCUSkinetics2014, p. 251]: SFO: @@ -22,7 +26,7 @@ $$c_\textrm{twa} = c_0 \frac{\left( 1 - e^{- k t} \right)}{ k t} $$ FOMC: -$$c_\textrm{twa} = c_0 \frac{\beta}{t (1 - \alpha)} +$$c_\textrm{twa} = c_0 \frac{\beta}{t (1 - \alpha)} \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) $$ DFOP: @@ -32,7 +36,7 @@ $$c_\textrm{twa} = \frac{c_0}{t} \left( \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) $$ Often, the ratio between the time weighted average concentration $c_\textrm{twa}$ -and the initial concentration $c_0$ +and the initial concentration $c_0$ $$f_\textrm{twa} = \frac{c_\textrm{twa}}{c_0}$$ @@ -46,7 +50,7 @@ $$f_\textrm{twa} = \frac{\left( 1 - e^{- k t} \right)}{k t} $$ FOMC: -$$f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} +$$f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) $$ DFOP: @@ -55,3 +59,8 @@ $$f_\textrm{twa} = \frac{1}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) $$ +Note that a method for calculating maximum moving window time weighted average +concentrations for any model fitted by 'mkinfit', and also for metabolites in +such models, can be found in the 'pfm' package, which is currently not published on +CRAN, but available from [github](https://github.com/jranke/pfm) and +[documented](https://pkgdown.jrwb.de/pfm) at my website. |