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J.E. Garay Labra 1 year ago
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      presentation/pres03.tex

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presentation/pres03.tex

@ -80,7 +80,9 @@
\setbeamerfont{page number in head/foot}{size=\large}
\setbeamertemplate{footline}[frame number]
%\setbeamertemplate{footline}[frame number] number in footer
\setbeamertemplate{footline}{}
\title[A new mathematical model for verifying the Navier-Stokes compatibility of 4D flow MRI data]{ A new mathematical model for verifying the Navier-Stokes compatibility of 4D flow MRI data}
@ -113,14 +115,21 @@ University of Groningen\\[0.5cm]
\end{frame}
\section{4D flow MRI}
\section[4D flow MRI]{4D flow MRI}
\begin{frame}
\frametitle{4D flow MRI}
\begin{columns}[c]
\column{.55\textwidth} % Left column and width
\footnotesize
4D flow MRI has been shown potential in the assesment of blood flow dynamics in heart and large arteries, allowing wide variety of options for visualization and quantification.
4D flow MRI has been shown potential in the assesment of blood flow dynamics in the heart and also large arteries, allowing wide variety of options for visualization and quantification.
Some advantages respect others techniques:
\begin{itemize}
\item Full 3D coverage of the region of interest
\item Retrospective plane positioning
\item Rich post-proccesing: derived parameters
\end{itemize}
\column{.5\textwidth} % Right column and width
@ -145,7 +154,7 @@ We want to introduce a novel measure for quantify the quality of the 4D flow mea
\end{frame}
\section{The corrector field}
\section[]{The corrector field}
\begin{frame}
\frametitle{The corrector field}
@ -157,22 +166,24 @@ We assume a perfect physical velocity field $\vec{u}$
\end{eqnarray*}
And a corrector field $\vec{w}$ which satisfies:
\begin{align}
\vec{u} & \approx \vec{u}_{meas} + \vec{w} \quad \text{in} \quad \Omega \label{eq:corrector} \\
\nabla \cdot \vec w & = 0 \quad \text{in} \quad \Omega \label{eq:correctorDiv} \\
\vec w & = \vec 0 \quad \text{on} \quad \partial \Omega \label{eq:correctorBC}
\end{align}
$\vec{w}$ measures the level of agreedment of the 4D flow measures respect to the Navier-Stokes equations.
The corrector field $\vec{w}$ measures the level of agreedment of the 4D flow measures respect to the Navier-Stokes equations.
\end{frame}
\section[Synthetic data]{Experiments using synthetic data }
\begin{frame}
\frametitle{Numerical tests}
\begin{columns}[c]
\column{.6\textwidth} % Left column and width
\footnotesize
We tested the corrector using CFD simulations as a measurements, in the following testcases:
@ -180,67 +191,133 @@ We tested the corrector using CFD simulations as a measurements, in the followin
\item Womersley flow in a cilinder
\item Navier-Stokes simulations in an aortic mesh
\end{itemize}
Also perturbations were added into the measurements:
\begin{itemize}
\item velocity aliasing
\item additive noise
\item simulated k-space undersampling
\item velocity aliasing (varying the $venc$ parameter)
\item additive noise (setting SNR in decibels)
\item simulated k-space undersampling (compressed sensing for the reconstruction)
\end{itemize}
All simulations were done using a stabilized finite element method implemented in FEniCS. Afterwards, all numerical simulations were interpolated into a voxel-type structured mesh
\end{frame}
\begin{frame}
\frametitle{Numerical tests: details}
\begin{columns}[c]
\column{.6\textwidth} % Left column and width
\footnotesize
\textbf{Channel:}
\begin{itemize}
\item Convective term was neglected
\item Non-slip condition at walls
\item Oscilatory pressure at $\Gamma_{inlet}$
\end{itemize}
\column{.5\textwidth} % Right column and width
\footnotesize
\begin{figure}[!hbtp]
\begin{center}
\includegraphics[height=\textwidth]{images/aorta_blender.png}
\caption{Aortic mesh }
\includegraphics[height=0.3\textwidth]{images/cilinder_2.png}
\end{center}
\end{figure}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Experiments}
\begin{columns}[c]
\column{.6\textwidth} % Left column and width
\footnotesize
\textbf{Aorta}
\begin{itemize}
\item We performed 4D flow measurements in a silicon aortic phantom
\item 4 healthy volunteers were scanned using a clinical standard 4D flow protocol.
\item a mild coartation was added in the descending aorta
\item $u_{inlet}$ simulates a cardiac cycle
\item 3-element Windkessel for the outlets
\item Non-slip condition at walls
\end{itemize}
\end{frame}
\column{.5\textwidth} % Right column and width
\footnotesize
\begin{figure}[!hbtp]
\begin{center}
\includegraphics[height=0.7\textwidth]{images/aorta_blender.png}
\caption{\tiny{Channel mesh}}
\end{center}
\end{figure}
\end{columns}
\end{frame}
\section{Results}
\begin{frame}
\frametitle{Results}
\frametitle{Results: aliasing and noise}
\footnotesize
results for the synthetic data. Comparison againts the perfect correction field: du.
For comparison we defined a perfect corrector field as: $\delta \vec u = \vec u_{ref} - \vec u_{meas}$
\begin{figure}[!hbtp]
\begin{center}
\includegraphics[height=0.5\textwidth]{images/perturbation_pres.png}
\caption{Different perturbation scenarios}
\end{center}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{Results}
\frametitle{Results: undersampling}
\footnotesize
results for experimental phantom
\begin{figure}[!hbtp]
\begin{center}
\includegraphics[height=0.6\textwidth]{images/undersampling_final.png}
\caption{Different perturbation scenarios}
\end{center}
\end{figure}
\end{frame}
\section[4D flow data]{Experiments using real 4D flow data }
\begin{frame}
\frametitle{Experiments}
\footnotesize
\begin{itemize}
\item We performed 4D flow measurements in a silicon aortic phantom
\item 4 healthy volunteers were scanned using a clinical standard 4D flow protocol.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Results}
\footnotesize
results in healthy volunteers
results for experimental phantom
\end{frame}
\section{Conclusions}

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