v2

presentation/pres03.tex

@@ -102,7 +102,7 @@ University of Groningen\\[0.5cm]
 \frame{\titlepage}
 
 
-
+% \onslide<1->
 
 
 
@@ -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
 \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
 
 
 \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}