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Commit 1bcc4be1 authored by Vesa Oikonen's avatar Vesa Oikonen
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simulation on cavity contamination

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---
title: MPI with chemical microspheres
author: Vesa Oikonen
updated_at: 2023-03-16
updated_at: 2023-03-18
created_at: 2023-02-27
tags:
- Perfusion
......@@ -500,8 +500,71 @@ images.
<h3><a name="contamination">The effect of spillover on LV cavity</a></h3>
<p>Script and data used to make these simulations are available in
<p>In the present model and previous simulations the assumption is that true arterial blood curve
can be extracted from a small ROI drawn in the middle of the LV cavity.
In practise, the blood curve may be contaminated by myocardial muscle curve because of spillover
and partial volume effects.
In this simulation, the cavity curves were simulated with &beta; values 100%, 95%, 90%, and 85%,
meaning contamination of 0%, 5%, 10%, and 15% from myocardium, respectively.
Since the level of tissue curve is dependent on perfusion, the simulation is
performed with three different K<sub>1</sub> values, 0.5, 1.0, and 2.0.
The simulated data were then fitted using <a href="./tpcclib/doc/fitmtrap.html">fitmtrap</a>
according to <a href="#eq_9">Eq 9</a>. The model fitted the simulated curves perfectly (not shown).
The simulated cavity curves and myocardial curve, and the bias induced to the estimated model
parameters, are shown in <a href="#fig_10">Fig 10</a>.
The simulations suggest that tissue-contaminated blood curve leads to overestimation of all model
parameters. The bias in both K<sub>1</sub> and V<sub>B</sub> is similar to the contamination-% of
the cavity curve. While the higher perfusion leads to higher overestimation of cavity curve,
this does not influence the bias in estimated K<sub>1</sub> values, which seems to be overestimated
by about the same percentage in all perfusion levels.
Most of the bias seems to be absorbed by the parameter k<sub>2</sub>.</p>
<p><a name="fig_10"></a></p>
<figure style="border: 1px solid #000; width: 98%;">
<a href="./pic/mtrap_f05_bcon.svg"><img src="./pic/mtrap_f05_bcon.svg"
style="margin: 1em; width: 45%;"
alt="Effect of spillover and partial volume effect on LV cavity curve when K1=0.5"></a>
<a href="./pic/mtrap_f05_cavbias.svg"><img src="./pic/mtrap_f05_cavbias.svg"
style="margin: 1em; width: 45%;"
alt="Effect on estimated model parameters when K1=0.5"></a>
<a href="./pic/mtrap_f10_bcon.svg"><img src="./pic/mtrap_f10_bcon.svg"
style="margin: 1em; width: 45%;"
alt="Effect of spillover and partial volume effect on LV cavity curve when K1=1.0"></a>
<a href="./pic/mtrap_f10_cavbias.svg"><img src="./pic/mtrap_f10_cavbias.svg"
style="margin: 1em; width: 45%;"
alt="Effect on estimated model parameters when K1=1.0"></a>
<a href="./pic/mtrap_f20_bcon.svg"><img src="./pic/mtrap_f20_bcon.svg"
style="margin: 1em; width: 45%;"
alt="Effect of spillover and partial volume effect on LV cavity curve when K1=2.0"></a>
<a href="./pic/mtrap_f20_cavbias.svg"><img src="./pic/mtrap_f20_cavbias.svg"
style="margin: 1em; width: 45%;"
alt="Effect on estimated model parameters when K1=2.0"></a>
<figcaption style="margin: 1em;"><b>Figure 10.</b>
The effect of spillover and partial volume effects on the blood curves extracted from the LV cavity
(left side), and the induced bias on estimated model parameter (right side), with three different
perfusion levels (K<sub>1</sub> 0.5, 1.0, and 2.0).
In this simulation the V<sub>B</sub> in myocardial regions is 0.25 and k<sub>2</sub>=0.24.
The biases in K<sub>1</sub> and V<sub>B</sub> estimates are similar, causing the curves to overlap.
</figcaption>
</figure>
<p>Overall, the results of this simulation suggest that the possible contamination of LV cavity
curve by myocardial muscle causes overestimation of K<sub>1</sub>, the bias remains at acceptable
level. On the other hand, the nuisance parameter k<sub>2</sub> is severely biased, suggesting that
k<sub>2</sub> should not be constrained if contamination of LV cavity curve is suspected.</p>
<p><br><br>Script and data used to make these simulations are available in
<a href="https://gitlab.utu.fi/vesoik/simulations/">https://gitlab.utu.fi/vesoik/simulations/</a>.
</p>
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