Commit 97a82f19 authored by Vesa Oikonen's avatar Vesa Oikonen
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---
title: MTGA
author: Vesa Oikonen
updated_at: 2019-03-24
updated_at: 2021-04-21
created_at: 2008-04-02
tags:
- Logan plot
......@@ -258,7 +258,8 @@ calculated from the ratio of distribution volumes for the region of interest and
</div>
<p>where linearity is achieved after the intercept (<em>Int</em>) is effectively constant
(Logan, <a href="https://doi.org/10.1016/S0969-8051(00)00137-2">2000</a> and
(Logan et al., <a href="https://doi.org/10.1038/jcbfm.1990.127">1990</a>,
<a href="https://doi.org/10.1016/S0969-8051(00)00137-2">2000</a> and
<a href="https://doi.org/10.1016/S0969-8051(03)00114-8">2003</a>).</p>
<p><a href="https://doi.org/10.1016/j.nucmedbio.2009.06.007">Tantawy et al. (2009)</a> introduced
......@@ -284,12 +285,14 @@ formulation (as "new plot"), because it avoids the noise-induced negative biases
<em>V<sub>T</sub></em> and <em>BP<sub>ND</sub></em> estimates of the traditional Logan plot
formulation.</p>
<h3><a name="logan_ref" title="logan_ref"></a>Logan plot without plasma sampling</h3>
<p>When <a href="./model_reference_tissue.html">reference region</a> is available, then
<em>V<sub>T</sub></em> ratio (distribution volume ratio, <a name="DVR"></a>DVR) can be calculated
directly without blood sampling by using reference region in place of the arterial plasma integral:
</p>
directly without blood sampling by using reference region in place of the arterial plasma integral
(<a href="https://doi.org/10.1097/00004647-199609000-00008">Logan et al., 1996</a>):</p>
<div class="eqs">
<script type="math/tex; mode=display">
......@@ -303,10 +306,23 @@ directly without blood sampling by using reference region in place of the arteri
compartment model or <em>k<sub>2</sub>/(1+k<sub>5</sub>/k<sub>6</sub>)</em> of two-tissue compartment
model) must be determined from studies with plasma sampling. Fortunately, in many cases the term
containing the population average of apparent <em>k'<sub>2</sub></em> can be omitted
(<a href="https://doi.org/10.1016/S0969-8051(03)00114-8">Logan, 2003</a>).</p>
(<a href="https://doi.org/10.1097/00004647-199609000-00008">Logan et al., 1996</a>;
<a href="https://doi.org/10.1016/S0969-8051(03)00114-8">Logan, 2003</a>). Reformulation of
the equation above to</p>
<div class="eqs">
<script type="math/tex; mode=display">
\frac{\int_0^T C_{ROI}(t)dt}{C_{ROI}(T)} =
\frac{V_T}{V_T^{ref}} \times \frac{\int_0^T C_{ref}(t)dt}{C_{ROI}(T)} +
\frac{V_T}{V_T^{ref} \times \bar{k_2^{,}}} \times \frac{C_{ref}(T)}{C_{ROI}(T)} + Int^{'}
</script>
</div>
<p>shows that when ratio <em>C<sub>ref</sub>/C<sub>ROI</sub></em> becomes reasonably constant the
<em>k'<sub>2</sub></em> effectively becomes part of the plot intercept.
<p>The negative of the intercept in the Logan plot with reference tissue input is the <em>relative
residence time</em> (<em>RRT</em>), which can be used to measure the clearance of
<p>The negative of the intercept, -Int', in the Logan plot with reference tissue input is the
<em>relative residence time</em> (<em>RRT</em>), which can be used to measure the clearance of
PET radiopharmaceutical from region-of-interest relative to reference region
(<a href="https://doi.org/10.1097/00019442-200201000-00004">Shoghi-Jadid et al, 2002</a>).</p>
......@@ -315,6 +331,24 @@ time, because Logan plot method requires both tissue and input integrals startin
However, in some cases the analysis may be possible from late-scan data
(<a href="https://doi.org/10.1016/j.nucmedbio.2009.06.007">Tantawy et al., 2009</a>).</p>
<h4><a name="alternative_logan_ref" title="alternative_logan_ref">Alternative graphical analysis
with reference tissue input</a></h4>
<p>Based on the <a href="#alternative_logan">alternative Logan plot</a> with plasma input,
with its relatively bold assumptions,
<a href="https://doi.org/10.1016/j.neuroimage.2008.09.021">Zhou et al (2009)</a> introduced
"new plot" in form</p>
<div class="eqs">
<script type="math/tex; mode=display">
\frac{\int_0^T C_{ROI}(t)dt}{C_{ref}(T)} =
\frac{V_T}{V_T^{ref}} \times \frac{\int_0^T C_{ref}(t)dt}{C_{ref}(T)} + Int^{''}
</script>
</div>
<br>
<p>For each radiopharmaceutical, the reference input methods have to be validated against plasma
input methods. See for example
<a href="https://doi.org/10.1016/j.nucmedbio.2007.12.004">Anteror-Dorsey et al. (2008)</a>.</p>
......
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