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-rw-r--r--vignettes/twa.Rmd21
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.

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