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\documentclass[xcolor=dvipsnames]{beamer}
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%\documentclass{beamer}
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\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}
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%\author[Jeremías Garay Labra]
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%{Jeremías Garay Labra}
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\institute[University of Groningen]
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{
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Bernoulli Institute\\
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Faculty of Sciences and Engineering\\
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University of Groningen\\[0.5cm]
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%\includegraphics[height=1.5cm]{Imagenes/escudoU2014.pdf}
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% \includegraphics[height=1cm]{Imagenes/fcfm.png} \\[0.5cm]
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\texttt{Jeremías Garay Labra \\ \ j.e.garay.labra@rug.nl}
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}
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\date{\today}
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\begin{document}
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\frame{\titlepage}
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\begin{frame}
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\frametitle{Index}
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\tableofcontents
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\end{frame}
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\section{4D flow MRI}
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\begin{frame}
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\frametitle{4D flow MRI}
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\begin{columns}[c]
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\column{.55\textwidth} % Left column and width
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\footnotesize
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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.
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\column{.5\textwidth} % Right column and width
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\end{columns}
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\end{frame}
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\begin{frame}
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\frametitle{4D flow MRI}
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\footnotesize
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Main limitation for its clinical applicability is the long scan times involved. Therefore, multiple strategies emerged in order to make acquisition faster>
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\begin{itemize}
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\item Navigator gating
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\item modest spatial resolutions $2.5 \times 2.5 \times 2.5 \ mm3$
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\item partial data coverage
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\end{itemize}
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Typical quality estimators are> SNR, VNR, peak flows/velocities, mass conservation (zero divergence
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We want to introduce a novel measure for quantify the quality of the 4D flow measurements, using the conservation of momentum of the flow.
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\end{frame}
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\section{The corrector field}
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\begin{frame}
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\frametitle{The corrector field}
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\begin{columns}[c]
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\column{.6\textwidth} % Left column and width
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\footnotesize
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\onslide<1-> We assume a perfect velocity \begin{eqnarray*}
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\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}
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\end{eqnarray*}
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\onslide<2-> And a corrector field which
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\begin{align}
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\vec{u} & \approx \vec{u}_{meas} + \vec{w} \quad \text{in} \quad \Omega \label{eq:corrector} \\
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\nabla \cdot \vec w & = 0 \quad \text{in} \quad \Omega \label{eq:correctorDiv} \\
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\vec w & = \vec 0 \quad \text{on} \quad \partial \Omega \label{eq:correctorBC}
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\end{align}
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\onslide<3-> asd
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\begin{itemize}
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\footnotesize
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\item[]<4-> $u = u_{in} \quad \text{in} \quad \Gamma_{inlet}$
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\end{itemize}
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\column{.5\textwidth} % Right column and width
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\begin{figure}[!hbtp]
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\onslide<1->
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\begin{center}
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\includegraphics[height=\textwidth]{images/aorta_blender.png}
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\caption{Aortic mesh }
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\end{center}
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\end{figure}
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\end{columns}
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\end{frame}
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\begin{frame}
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\frametitle{The corrector field}
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\footnotesize
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To study the corrector in several scenarios> synthetic data, experimental phantom and healthy volunteers.
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\end{frame}
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\begin{frame}
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\frametitle{The corrector field}
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\footnotesize
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different data treatments> aliasing and noise. Undersampling
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\end{frame}
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\section{Results}
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\begin{frame}
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\frametitle{Results}
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\footnotesize
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results for the synthetic data. Comparison againts a perfect correction case with du.
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\end{frame}
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\begin{frame}
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\frametitle{Results}
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\footnotesize
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results for experimental phantom
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\end{frame}
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\begin{frame}
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\frametitle{Results}
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\footnotesize
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results in healthy volunteers
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\end{frame}
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\section{Conclusions}
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\begin{frame}
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\frametitle{Results}
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\footnotesize
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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
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\end{frame}
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\begin{frame}
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\begin{center}
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\huge{Thank you for your time!}
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\end{center}
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\end{frame}
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%\includegraphics<1>[height=4.5cm]{images/pat1.png}
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%\includegraphics<2>[height=4.5cm]{images/pat2.png}
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\end{document}
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