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Diffstat (limited to 'vignettes/twa.html')
| -rw-r--r-- | vignettes/twa.html | 108 |
1 files changed, 73 insertions, 35 deletions
diff --git a/vignettes/twa.html b/vignettes/twa.html index fd0fe2d6..0b079516 100644 --- a/vignettes/twa.html +++ b/vignettes/twa.html @@ -28,22 +28,6 @@ document.addEventListener('DOMContentLoaded', function(e) { } }); </script> -<script>// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> -// v0.0.1 -// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. - -document.addEventListener('DOMContentLoaded', function() { - const codeList = document.getElementsByClassName("sourceCode"); - for (var i = 0; i < codeList.length; i++) { - var linkList = codeList[i].getElementsByTagName('a'); - for (var j = 0; j < linkList.length; j++) { - if (linkList[j].innerHTML === "") { - linkList[j].setAttribute('aria-hidden', 'true'); - } - } - } -}); -</script> <style type="text/css"> code{white-space: pre-wrap;} @@ -59,6 +43,29 @@ document.addEventListener('DOMContentLoaded', function() { +<style type="text/css"> +/* for pandoc --citeproc since 2.11 */ +div.csl-bib-body { } +div.csl-entry { + clear: both; +} +.hanging div.csl-entry { + margin-left:2em; + text-indent:-2em; +} +div.csl-left-margin { + min-width:2em; + float:left; +} +div.csl-right-inline { + margin-left:2em; + padding-left:1em; +} +div.csl-indent { + margin-left: 2em; +} +</style> + <style type="text/css">body { background-color: #fff; margin: 1em auto; @@ -251,19 +258,32 @@ code > span.er { color: #a61717; background-color: #e3d2d2; } -<h1 class="title toc-ignore">Calculation of time weighted average concentrations with mkin</h1> +<h1 class="title toc-ignore">Calculation of time weighted average +concentrations with mkin</h1> <h4 class="author">Johannes Ranke</h4> -<h4 class="date">Last change 18 September 2019 (rebuilt 2022-03-02)</h4> +<h4 class="date">Last change 18 September 2019 (rebuilt 2023-01-05)</h4> -<p>Since version 0.9.45.1 of the ‘mkin’ package, a function for calculating time weighted average concentrations for decline kinetics (<em>i.e.</em> only for the compound applied in the experiment) is included. Strictly speaking, they are maximum moving window time weighted average concentrations, <em>i.e.</em> the maximum time weighted average concentration that can be found when moving a time window of a specified width over the decline curve.</p> -<p>Time weighted average concentrations for the SFO, FOMC and the DFOP model are calculated using the formulas given in the FOCUS kinetics guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, 251)</span>:</p> +<p>Since version 0.9.45.1 of the ‘mkin’ package, a function for +calculating time weighted average concentrations for decline kinetics +(<em>i.e.</em> only for the compound applied in the experiment) is +included. Strictly speaking, they are maximum moving window time +weighted average concentrations, <em>i.e.</em> the maximum time weighted +average concentration that can be found when moving a time window of a +specified width over the decline curve.</p> +<p>Time weighted average concentrations for the SFO, FOMC and the DFOP +model are calculated using the formulas given in the FOCUS kinetics +guidance <span class="citation">(FOCUS Work Group on Degradation +Kinetics 2014, 251)</span>:</p> <p>SFO:</p> -<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\left( 1 - e^{- k t} \right)}{ k t} \]</span></p> +<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\left( 1 - +e^{- k t} \right)}{ k t} \]</span></p> <p>FOMC:</p> -<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - \alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) \]</span></p> +<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - +\alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} +- 1 \right) \]</span></p> <p>DFOP:</p> <p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + @@ -271,15 +291,25 @@ code > span.er { color: #a61717; background-color: #e3d2d2; } <p>HS for <span class="math inline">\(t > t_b\)</span>:</p> <p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]</span></p> -<p>Often, the ratio between the time weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span> and the initial concentration <span class="math inline">\(c_0\)</span></p> -<p><span class="math display">\[f_\textrm{twa} = \frac{c_\textrm{twa}}{c_0}\]</span></p> -<p>is needed. This can be calculated from the fitted initial concentration <span class="math inline">\(c_0\)</span> and the time weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span>, or directly from the model parameters using the following formulas:</p> + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} +\right) \right) \]</span></p> +<p>Often, the ratio between the time weighted average concentration +<span class="math inline">\(c_\textrm{twa}\)</span> and the initial +concentration <span class="math inline">\(c_0\)</span></p> +<p><span class="math display">\[f_\textrm{twa} = +\frac{c_\textrm{twa}}{c_0}\]</span></p> +<p>is needed. This can be calculated from the fitted initial +concentration <span class="math inline">\(c_0\)</span> and the time +weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span>, or directly from the +model parameters using the following formulas:</p> <p>SFO:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{\left( 1 - e^{- k t} \right)}{k t} \]</span></p> +<p><span class="math display">\[f_\textrm{twa} = \frac{\left( 1 - e^{- k +t} \right)}{k t} \]</span></p> <p>FOMC:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) \]</span></p> +<p><span class="math display">\[f_\textrm{twa} = \frac{\beta}{t (1 - +\alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} +- 1 \right) \]</span></p> <p>DFOP:</p> <p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + @@ -287,11 +317,19 @@ code > span.er { color: #a61717; background-color: #e3d2d2; } <p>HS for <span class="math inline">\(t > t_b\)</span>:</p> <p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]</span></p> -<p>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 <code>max_twa_parent()</code> function. If the same is needed for metabolites, the function <code>pfm::max_twa()</code> from the ‘pfm’ package can be used.</p> -<div id="refs" class="references hanging-indent"> -<div id="ref-FOCUSkinetics2014"> -<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p> + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} +\right) \right) \]</span></p> +<p>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 +<code>max_twa_parent()</code> function. If the same is needed for +metabolites, the function <code>pfm::max_twa()</code> from the ‘pfm’ +package can be used.</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-FOCUSkinetics2014" class="csl-entry"> +FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for +Estimating Persistence and Degradation Kinetics from Environmental Fate +Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. </div> </div> |