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<!DOCTYPE html>
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<meta name="description" content="Fast simulation from ordinary differential equation (ODE) based models typically employed in quantitative pharmacology and systems biology.">
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<div class="page-header"><h1 id="mrgsolve-">mrgsolve <img align="right" src="reference/figures/MRG-Solve-Hex.png" width="135px"><a class="anchor" aria-label="anchor" href="#mrgsolve-"></a>
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<p><a href="https://github.com/metrumresearchgroup/mrgsolve/actions/workflows/main.yaml" class="external-link"><img src="https://github.com/metrumresearchgroup/mrgsolve/actions/workflows/main.yaml/badge.svg" alt="Build Status"></a> <a href="https://cran.r-project.org/package=mrgsolve" class="external-link"><img src="http://www.r-pkg.org/badges/version/mrgsolve" alt="CRAN"></a> <a href="http://www.gnu.org/licenses/gpl-2.0.html" class="external-link"><img src="http://img.shields.io/badge/license-GPL%20%28%3E=%202%29-brightgreen.svg?style=flat" alt="License"></a> <a href="https://github.com/metrumresearchgroup/mrgsolve/issues" class="external-link"><img src="https://img.shields.io/badge/ask_for-Help-brightgreen.svg" alt="questions"></a> <a href="http://metrumrg.com" class="external-link"><img src="https://img.shields.io/badge/contact-MetrumRG-brightgreen.svg" alt="MetrumRG"></a></p>
<p>mrgsolve is an R package for simulation from hierarchical, ordinary differential equation (ODE) based models typically employed in drug development. mrgsolve is free and open-source software.</p>
<div class="section level2">
<h2 id="resources">Resources<a class="anchor" aria-label="anchor" href="#resources"></a>
</h2>
<p>Please see <a href="https://mrgsolve.github.io" class="external-link">mrgsolve.github.io</a> for additional resources, including:</p>
<ul>
<li><a href="https://mrgsolve.github.io/user_guide" class="external-link">User Guide</a></li>
<li><a href="https://mrgsolve.github.io/docs" class="external-link">R Documentation</a></li>
<li><a href="https://mrgsolve.github.io/vignettes" class="external-link">Vignettes</a></li>
<li><a href="https://github.com/mrgsolve/gallery" class="external-link">Gallery</a></li>
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<div class="section level2">
<h2 id="installation">Installation<a class="anchor" aria-label="anchor" href="#installation"></a>
</h2>
<p>Install the latest release on CRAN</p>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html" class="external-link">install.packages</a></span><span class="op">(</span><span class="st">"mrgsolve"</span><span class="op">)</span></span></code></pre></div>
<p><strong>Please</strong> be sure to see important install-related information <a href="https://github.com/metrumresearchgroup/mrgsolve/wiki/mrgsolve-Installation" class="external-link">here</a>.</p>
<p>Install the current development version</p>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu">remotes</span><span class="fu">::</span><span class="fu"><a href="https://remotes.r-lib.org/reference/install_github.html" class="external-link">install_github</a></span><span class="op">(</span><span class="st">"metrumresearchgroup/mrgsolve"</span><span class="op">)</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="interaction">Interaction<a class="anchor" aria-label="anchor" href="#interaction"></a>
</h2>
<p>We welcome <strong>questions</strong> about anything mrgsolve: installation, getting your model to work, understanding better how mrgsolve works. We also welcome <strong>suggestions</strong> for how to make mrgsolve more useful to you and to the pharmacometrics community.</p>
<p>Please interact with us at the <a href="https://github.com/metrumresearchgroup/mrgsolve/issues" class="external-link">Issue Tracker</a>. This requires a GitHub account.</p>
</div>
<div class="section level2">
<h2 id="some-examples">Some examples<a class="anchor" aria-label="anchor" href="#some-examples"></a>
</h2>
<div class="section level3">
<h3 id="a-simple-simulation">A simple simulation<a class="anchor" aria-label="anchor" href="#a-simple-simulation"></a>
</h3>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://mrgsolve.org/docs/">mrgsolve</a></span><span class="op">)</span></span></code></pre></div>
<p>Load a model from the internal library</p>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><-</span> <span class="fu"><a href="reference/mread.html">mread</a></span><span class="op">(</span><span class="st">"pk1"</span>, <span class="fu"><a href="reference/modlib.html">modlib</a></span><span class="op">(</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<p>Simulate a simple regimen</p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="reference/ev.html">ev</a></span><span class="op">(</span>amt <span class="op">=</span> <span class="fl">100</span>, ii <span class="op">=</span> <span class="fl">24</span>, addl <span class="op">=</span> <span class="fl">9</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span></span>
<span> <span class="fu"><a href="reference/mrgsim.html">mrgsim</a></span><span class="op">(</span>end <span class="op">=</span> <span class="fl">300</span>, delta <span class="op">=</span> <span class="fl">0.1</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">CP</span><span class="op">~</span><span class="va">time</span><span class="op">)</span></span></code></pre></div>
<p><img src="reference/figures/README-pk-figure-1.png"><!-- --></p>
<p>A more complicated regimen: 100 mg infusions over 2 hours every 24 hours for one week, followed by 50 mg boluses every 12 hours for 10 days:</p>
<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="reference/ev_rx.html">ev_rx</a></span><span class="op">(</span><span class="st">"100 over 2h q 24 x 7 then 50 q 12 x 20"</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span></span>
<span> <span class="fu"><a href="reference/mrgsim.html">mrgsim</a></span><span class="op">(</span>end <span class="op">=</span> <span class="fl">600</span>, delta <span class="op">=</span> <span class="fl">0.1</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">CP</span><span class="op">~</span><span class="va">time</span><span class="op">)</span></span></code></pre></div>
<p><img src="reference/figures/README-regimen-figure-1.png"><!-- --></p>
</div>
<div class="section level3">
<h3 id="population-simulation">Population simulation<a class="anchor" aria-label="anchor" href="#population-simulation"></a>
</h3>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><-</span> <span class="fu"><a href="reference/mread.html">mread</a></span><span class="op">(</span><span class="st">"popex"</span>, <span class="fu"><a href="reference/modlib.html">modlib</a></span><span class="op">(</span><span class="op">)</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> <span class="fu"><a href="reference/zero_re.html">zero_re</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<p>A data set looking at different patient weights and doses</p>
<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://dplyr.tidyverse.org" class="external-link">dplyr</a></span><span class="op">)</span></span>
<span></span>
<span><span class="va">data</span> <span class="op"><-</span> <span class="fu"><a href="reference/expand.idata.html">expand.ev</a></span><span class="op">(</span>amt <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">100</span>,<span class="fl">150</span><span class="op">)</span>, WT <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="fl">40</span>,<span class="fl">140</span>,<span class="fl">20</span><span class="op">)</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> <span class="fu"><a href="https://dplyr.tidyverse.org/reference/mutate.html" class="external-link">mutate</a></span><span class="op">(</span>dose <span class="op">=</span> <span class="va">amt</span><span class="op">)</span></span>
<span></span>
<span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">data</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb9"><pre class="sourceCode R"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a>. ID time amt cmt evid WT dose</span>
<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>. <span class="dv">1</span> <span class="dv">1</span> <span class="dv">0</span> <span class="dv">100</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">40</span> <span class="dv">100</span></span>
<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>. <span class="dv">2</span> <span class="dv">2</span> <span class="dv">0</span> <span class="dv">150</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">40</span> <span class="dv">150</span></span>
<span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a>. <span class="dv">3</span> <span class="dv">3</span> <span class="dv">0</span> <span class="dv">100</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">60</span> <span class="dv">100</span></span>
<span id="cb9-5"><a href="#cb9-5" tabindex="-1"></a>. <span class="dv">4</span> <span class="dv">4</span> <span class="dv">0</span> <span class="dv">150</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">60</span> <span class="dv">150</span></span>
<span id="cb9-6"><a href="#cb9-6" tabindex="-1"></a>. <span class="dv">5</span> <span class="dv">5</span> <span class="dv">0</span> <span class="dv">100</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">80</span> <span class="dv">100</span></span>
<span id="cb9-7"><a href="#cb9-7" tabindex="-1"></a>. <span class="dv">6</span> <span class="dv">6</span> <span class="dv">0</span> <span class="dv">150</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">80</span> <span class="dv">150</span></span></code></pre></div>
<p>Simulate</p>
<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="reference/data_set.html">data_set</a></span><span class="op">(</span><span class="va">data</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="reference/carry_out.html">carry_out</a></span><span class="op">(</span><span class="va">dose</span>,<span class="va">WT</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span></span>
<span> <span class="fu"><a href="reference/mrgsim.html">mrgsim</a></span><span class="op">(</span>delta <span class="op">=</span> <span class="fl">0.1</span>, end <span class="op">=</span> <span class="fl">72</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">IPRED</span><span class="op">~</span><span class="va">time</span><span class="op">|</span><span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">dose</span><span class="op">)</span>,scales <span class="op">=</span> <span class="st">"same"</span><span class="op">)</span></span></code></pre></div>
<p><img src="reference/figures/README-population-figure-1.png"><!-- --></p>
</div>
<div class="section level3">
<h3 id="sensitivity-analysis-with-pbpk-model">Sensitivity analysis with PBPK model<a class="anchor" aria-label="anchor" href="#sensitivity-analysis-with-pbpk-model"></a>
</h3>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><-</span> <span class="fu"><a href="reference/modlib.html">modlib</a></span><span class="op">(</span><span class="st">"pbpk"</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb12"><pre class="sourceCode R"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a>. Building pbpk ... done.</span></code></pre></div>
<p>Reference</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode R"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a> Model file<span class="sc">:</span> pbpk.cpp </span>
<span id="cb13-2"><a href="#cb13-2" tabindex="-1"></a> </span>
<span id="cb13-3"><a href="#cb13-3" tabindex="-1"></a> <span class="sc">$</span>PROB</span>
<span id="cb13-4"><a href="#cb13-4" tabindex="-1"></a> <span class="co"># HUMAN PBPK MODEL</span></span>
<span id="cb13-5"><a href="#cb13-5" tabindex="-1"></a> <span class="dv">1</span><span class="sc">:</span> Jones H, Rowland<span class="sc">-</span>Yeo K. Basic concepts <span class="cf">in</span> physiologically based</span>
<span id="cb13-6"><a href="#cb13-6" tabindex="-1"></a> pharmacokinetic modeling <span class="cf">in</span> drug discovery and development. CPT Pharmacometrics</span>
<span id="cb13-7"><a href="#cb13-7" tabindex="-1"></a> Syst Pharmacol. <span class="dv">2013</span> Aug <span class="dv">14</span>;<span class="dv">2</span><span class="sc">:</span>e63. doi<span class="sc">:</span> <span class="fl">10.1038</span><span class="sc">/</span>psp.<span class="dv">2013</span>.<span class="fl">41.</span> PubMed PMID<span class="sc">:</span></span>
<span id="cb13-8"><a href="#cb13-8" tabindex="-1"></a> <span class="dv">23945604</span>; PubMed Central PMCID<span class="sc">:</span> PMC3828005.</span></code></pre></div>
<p>Model parameters</p>
<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="reference/param.html">param</a></span><span class="op">(</span><span class="va">mod</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb15"><pre class="sourceCode R"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a>. </span>
<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>. Model <span class="fu">parameters</span> (<span class="at">N=</span><span class="dv">52</span>)<span class="sc">:</span></span>
<span id="cb15-3"><a href="#cb15-3" tabindex="-1"></a>. name value . name value . name value </span>
<span id="cb15-4"><a href="#cb15-4" tabindex="-1"></a>. BP <span class="fl">0.98</span> <span class="sc">|</span> fumic <span class="dv">1</span> <span class="sc">|</span> FVve <span class="fl">0.0514</span></span>
<span id="cb15-5"><a href="#cb15-5" tabindex="-1"></a>. BW <span class="dv">70</span> <span class="sc">|</span> fup <span class="fl">0.681</span> <span class="sc">|</span> HLM_CLint <span class="dv">8</span> </span>
<span id="cb15-6"><a href="#cb15-6" tabindex="-1"></a>. CLrenal <span class="dv">0</span> <span class="sc">|</span> FVad <span class="fl">0.213</span> <span class="sc">|</span> Ka <span class="fl">2.18</span> </span>
<span id="cb15-7"><a href="#cb15-7" tabindex="-1"></a>. CO <span class="dv">108</span> <span class="sc">|</span> FVar <span class="fl">0.0257</span> <span class="sc">|</span> Kpad <span class="fl">0.191</span> </span>
<span id="cb15-8"><a href="#cb15-8" tabindex="-1"></a>. F <span class="dv">1</span> <span class="sc">|</span> FVbo <span class="fl">0.0856</span> <span class="sc">|</span> Kpbo <span class="fl">0.374</span> </span>
<span id="cb15-9"><a href="#cb15-9" tabindex="-1"></a>. FQad <span class="fl">0.05</span> <span class="sc">|</span> FVbr <span class="fl">0.02</span> <span class="sc">|</span> Kpbr <span class="fl">0.606</span> </span>
<span id="cb15-10"><a href="#cb15-10" tabindex="-1"></a>. FQbo <span class="fl">0.05</span> <span class="sc">|</span> FVgu <span class="fl">0.0171</span> <span class="sc">|</span> Kpgu <span class="fl">0.578</span> </span>
<span id="cb15-11"><a href="#cb15-11" tabindex="-1"></a>. FQbr <span class="fl">0.12</span> <span class="sc">|</span> FVhe <span class="fl">0.0047</span> <span class="sc">|</span> Kphe <span class="fl">0.583</span> </span>
<span id="cb15-12"><a href="#cb15-12" tabindex="-1"></a>. FQgu <span class="fl">0.146</span> <span class="sc">|</span> FVki <span class="fl">0.0044</span> <span class="sc">|</span> Kpki <span class="fl">0.597</span> </span>
<span id="cb15-13"><a href="#cb15-13" tabindex="-1"></a>. FQh <span class="fl">0.215</span> <span class="sc">|</span> FVli <span class="fl">0.021</span> <span class="sc">|</span> Kpli <span class="fl">0.57</span> </span>
<span id="cb15-14"><a href="#cb15-14" tabindex="-1"></a>. FQhe <span class="fl">0.04</span> <span class="sc">|</span> FVlu <span class="fl">0.0076</span> <span class="sc">|</span> Kplu <span class="fl">0.62</span> </span>
<span id="cb15-15"><a href="#cb15-15" tabindex="-1"></a>. FQki <span class="fl">0.19</span> <span class="sc">|</span> FVmu <span class="fl">0.4</span> <span class="sc">|</span> Kpmu <span class="fl">0.622</span> </span>
<span id="cb15-16"><a href="#cb15-16" tabindex="-1"></a>. FQlu <span class="dv">1</span> <span class="sc">|</span> FVpl <span class="fl">0.0424</span> <span class="sc">|</span> Kpre <span class="fl">0.6</span> </span>
<span id="cb15-17"><a href="#cb15-17" tabindex="-1"></a>. FQmu <span class="fl">0.17</span> <span class="sc">|</span> FVrb <span class="fl">0.0347</span> <span class="sc">|</span> Kpsk <span class="fl">0.6</span> </span>
<span id="cb15-18"><a href="#cb15-18" tabindex="-1"></a>. FQre <span class="fl">0.104</span> <span class="sc">|</span> FVre <span class="fl">0.0998</span> <span class="sc">|</span> Kpsp <span class="fl">0.591</span> </span>
<span id="cb15-19"><a href="#cb15-19" tabindex="-1"></a>. FQsk <span class="fl">0.05</span> <span class="sc">|</span> FVsk <span class="fl">0.0371</span> <span class="sc">|</span> Kpte <span class="fl">0.6</span> </span>
<span id="cb15-20"><a href="#cb15-20" tabindex="-1"></a>. FQsp <span class="fl">0.0172</span> <span class="sc">|</span> FVsp <span class="fl">0.0026</span> <span class="sc">|</span> . . </span>
<span id="cb15-21"><a href="#cb15-21" tabindex="-1"></a>. FQte <span class="fl">0.0108</span> <span class="sc">|</span> FVte <span class="fl">0.01</span> <span class="sc">|</span> . .</span></code></pre></div>
<p>Set up a batch to simulate</p>
<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">idata</span> <span class="op"><-</span> <span class="fu"><a href="reference/expand.idata.html">expand.idata</a></span><span class="op">(</span>Kpli <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">20</span>,<span class="fl">2</span><span class="op">)</span><span class="op">)</span></span>
<span></span>
<span><span class="va">idata</span></span></code></pre></div>
<div class="sourceCode" id="cb17"><pre class="sourceCode R"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a>. ID Kpli</span>
<span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a>. <span class="dv">1</span> <span class="dv">1</span> <span class="dv">4</span></span>
<span id="cb17-3"><a href="#cb17-3" tabindex="-1"></a>. <span class="dv">2</span> <span class="dv">2</span> <span class="dv">6</span></span>
<span id="cb17-4"><a href="#cb17-4" tabindex="-1"></a>. <span class="dv">3</span> <span class="dv">3</span> <span class="dv">8</span></span>
<span id="cb17-5"><a href="#cb17-5" tabindex="-1"></a>. <span class="dv">4</span> <span class="dv">4</span> <span class="dv">10</span></span>
<span id="cb17-6"><a href="#cb17-6" tabindex="-1"></a>. <span class="dv">5</span> <span class="dv">5</span> <span class="dv">12</span></span>
<span id="cb17-7"><a href="#cb17-7" tabindex="-1"></a>. <span class="dv">6</span> <span class="dv">6</span> <span class="dv">14</span></span>
<span id="cb17-8"><a href="#cb17-8" tabindex="-1"></a>. <span class="dv">7</span> <span class="dv">7</span> <span class="dv">16</span></span>
<span id="cb17-9"><a href="#cb17-9" tabindex="-1"></a>. <span class="dv">8</span> <span class="dv">8</span> <span class="dv">18</span></span>
<span id="cb17-10"><a href="#cb17-10" tabindex="-1"></a>. <span class="dv">9</span> <span class="dv">9</span> <span class="dv">20</span></span></code></pre></div>
<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">mod</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="reference/ev.html">ev</a></span><span class="op">(</span>amt <span class="op">=</span> <span class="fl">150</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span> </span>
<span> <span class="fu"><a href="reference/idata_set.html">idata_set</a></span><span class="op">(</span><span class="va">idata</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span></span>
<span> <span class="fu"><a href="reference/mrgsim.html">mrgsim</a></span><span class="op">(</span>end <span class="op">=</span> <span class="fl">6</span>, delta <span class="op">=</span> <span class="fl">0.1</span><span class="op">)</span> <span class="op"><a href="reference/zchain.html">%>%</a></span></span>
<span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">Cp</span><span class="op">~</span><span class="va">time</span><span class="op">)</span></span></code></pre></div>
<p><img src="reference/figures/README-pbpk-figure-1.png"><!-- --></p>
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