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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>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>DFOP:</p> <p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]</span></p> <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> <p>SFO:</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>DFOP:</p> <p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]</span></p> <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> </div> </div> <!-- code folding --> <!-- dynamically load mathjax for compatibility with self-contained --> <script> (function () { var script = document.createElement("script"); script.type = "text/javascript"; script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; document.getElementsByTagName("head")[0].appendChild(script); })(); </script> </body> </html>