advanced

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}