J.E. Garay Labra 2 years ago
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  1. 79
      presentation/pres03.tex

79
presentation/pres03.tex

@ -102,7 +102,7 @@ University of Groningen\\[0.5cm] @@ -102,7 +102,7 @@ University of Groningen\\[0.5cm]
\frame{\titlepage}
% \onslide<1->
@ -131,50 +131,65 @@ University of Groningen\\[0.5cm] @@ -131,50 +131,65 @@ University of Groningen\\[0.5cm]
\begin{frame}
\frametitle{4D flow MRI}
\footnotesize
Main limitation for its clinical applicability is the long scan times involved. Therefore, multiple strategies emerged in order to make acquisition faster>
Main limitation for its clinical applicability is the long scan times involved. Therefore, multiple strategies emerged in order to make acquisition faster, such as:
\begin{itemize}
\item Navigator gating
\item modest spatial resolutions $2.5 \times 2.5 \times 2.5 \ mm3$
\item modest spatial resolutions $ \sim (2.5 \times 2.5 \times 2.5 \ mm^3)$
\item partial data coverage
\end{itemize}
Typical quality estimators are> SNR, VNR, peak flows/velocities, mass conservation (zero divergence
Typical quality estimators: SNR, VNR, peak flows/velocities, mass conservation (zero divergence)
We want to introduce a novel measure for quantify the quality of the 4D flow measurements, using the conservation of momentum of the flow.
We want to introduce a novel measure for quantify the quality of the 4D flow measurements, using the conservation of momentum of the flow (Navier-Stokes compatibility).
\end{frame}
\section{The corrector field}
\begin{frame}
\frametitle{The corrector field}
\begin{columns}[c]
\column{.6\textwidth} % Left column and width
\footnotesize
\onslide<1-> We assume a perfect velocity \begin{eqnarray*}
We assume a perfect physical velocity field $\vec{u}$
\begin{eqnarray*}
\rho \frac{\partial \vec{u}}{\partial t} + \rho \big ( \vec{u} \cdot \nabla \big) \vec{u} - \mu \Delta \vec{u} + \nabla p = 0 \quad \text{in} \quad \Omega \label{eq:NSmom}
\end{eqnarray*}
\onslide<2-> And a corrector field which
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}
\onslide<3-> asd
\begin{itemize}
$\vec{w}$ measures the level of agreedment of the 4D flow measures respect to the Navier-Stokes equations.
\end{frame}
\begin{frame}
\frametitle{Numerical tests}
\begin{columns}[c]
\column{.6\textwidth} % Left column and width
\footnotesize
\item[]<4-> $u = u_{in} \quad \text{in} \quad \Gamma_{inlet}$
We tested the corrector using CFD simulations as a measurements, in the following testcases:
\begin{itemize}
\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
\end{itemize}
\column{.5\textwidth} % Right column and width
\footnotesize
\begin{figure}[!hbtp]
\onslide<1->
\begin{center}
\includegraphics[height=\textwidth]{images/aorta_blender.png}
\caption{Aortic mesh }
@ -184,38 +199,25 @@ We want to introduce a novel measure for quantify the quality of the 4D flow mea @@ -184,38 +199,25 @@ We want to introduce a novel measure for quantify the quality of the 4D flow mea
\end{frame}
\begin{frame}
\frametitle{The corrector field}
\footnotesize
To study the corrector in several scenarios> synthetic data, experimental phantom and healthy volunteers.
\end{frame}
\begin{frame}
\frametitle{The corrector field}
\frametitle{Experiments}
\footnotesize
different data treatments> aliasing and noise. Undersampling
\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}
\section{Results}
\begin{frame}
\frametitle{Results}
\footnotesize
results for the synthetic data. Comparison againts a perfect correction case with du.
results for the synthetic data. Comparison againts the perfect correction field: du.
\end{frame}
@ -243,10 +245,15 @@ results in healthy volunteers @@ -243,10 +245,15 @@ results in healthy volunteers
\begin{frame}
\frametitle{Results}
\frametitle{Conclusions and future}
\footnotesize
potential of the new quality parameter> analize real data. use the specificity for label zones with strong disagreedment. Use the field for create new inverse problems which can be used for further accelerations
potential of the new quality parameter:
\begin{itemize}
\item analize real data
\item use the specificity for label zones with strong disagreedment
\item Use the field for create new inverse problems which can be used for further accelerations
\end{itemize}
\end{frame}

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