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+\usepackage{graphicx} +\usepackage{multimedia} +\usepackage{media9} + +%\usetheme{default} +%\usetheme{AnnArbor} +%\usetheme{Antibes} +%\usetheme{Bergen} +%\usetheme{Berkeley} +%\usetheme{Berlin} +%\usetheme{Boadilla} +%\usetheme{CambridgeUS} +%\usetheme{Copenhagen} +%\usetheme{Darmstadt} +%\usetheme{Dresden} +%\usetheme{Frankfurt} +%\usetheme{Goettingen} +%\usetheme{Hannover} +%\usetheme{Ilmenau} +%\usetheme{JuanLesPins} +%\usetheme{Luebeck} +%\usetheme{Madrid} +%\usetheme{Malmoe} +%\usetheme{Marburg} +%\usetheme{Montpellier} +%\usetheme{PaloAlto} +%\usetheme{Pittsburgh} +%\usetheme{Rochester} +%\usetheme{Singapore} +%\usetheme{Szeged} +\usetheme{Warsaw} + +%\usecolortheme{albatross} +%\usecolortheme{beaver} +%\usecolortheme{beetle} +\usecolortheme{crane} +%\usecolortheme{dolphin} +%\usecolortheme{dove} +%\usecolortheme{fly} +%\usecolortheme{lily} +%\usecolortheme{orchid} +%\usecolortheme{rose} +%\usecolortheme{seagull} +%\usecolortheme{seahorse} +%\usecolortheme{whale} +%\usecolortheme{wolverine} + +%\useoutertheme{infolines} +%\useoutertheme{miniframes} +%\useoutertheme{sidebar} +\useoutertheme{smoothbars} +%\useoutertheme{shadow} +%\useoutertheme{smoothtree} +%\useoutertheme{split} +%\useoutertheme{tree} + + +\usepackage{amssymb,mathrsfs,amsmath,latexsym,amsthm,amsfonts} +\useinnertheme{rectangles} + + +\setbeamertemplate{navigation symbols}{} % quitar simbolitos + + +\setbeamerfont{page number in head/foot}{size=\large} +\setbeamertemplate{footline}[frame number] + + +\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} +%\author[Jeremías Garay Labra] +%{Jeremías Garay Labra} +\institute[University of Groningen] +{ +Bernoulli Institute\\ +Faculty of Sciences and Engineering\\ +University of Groningen\\[0.5cm] + %\includegraphics[height=1.5cm]{Imagenes/escudoU2014.pdf} + % \includegraphics[height=1cm]{Imagenes/fcfm.png} \\[0.5cm] + \texttt{Jeremías Garay Labra \\ \ j.e.garay.labra@rug.nl} +} +\date{\today} + + +\begin{document} +\frame{\titlepage} + + + + + + + +\begin{frame} + \frametitle{Index} + \tableofcontents +\end{frame} + + +\section{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. + +\column{.5\textwidth} % Right column and width + +\end{columns} +\end{frame} + + +\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> +\begin{itemize} +\item Navigator gating +\item modest spatial resolutions $2.5 \times 2.5 \times 2.5 \ mm3$ +\item partial data coverage +\end{itemize} + +Typical quality estimators are> 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. + +\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*} +\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 +\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} +\footnotesize +\item[]<4-> $u = u_{in} \quad \text{in} \quad \Gamma_{inlet}$ +\end{itemize} + +\column{.5\textwidth} % Right column and width +\begin{figure}[!hbtp] +\onslide<1-> + \begin{center} + \includegraphics[height=\textwidth]{images/aorta_blender.png} +\caption{Aortic mesh } + \end{center} + \end{figure} +\end{columns} +\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} +\footnotesize + +different data treatments> aliasing and noise. Undersampling + + +\end{frame} + + + + + + +\section{Results} + +\begin{frame} + \frametitle{Results} +\footnotesize + +results for the synthetic data. Comparison againts a perfect correction case with du. + +\end{frame} + +\begin{frame} + \frametitle{Results} +\footnotesize + +results for experimental phantom + +\end{frame} + + +\begin{frame} + \frametitle{Results} +\footnotesize + +results in healthy volunteers + +\end{frame} + + + + +\section{Conclusions} + + +\begin{frame} + \frametitle{Results} +\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 + +\end{frame} + + + + + +\begin{frame} +\begin{center} +\huge{Thank you for your time!} +\end{center} +\end{frame} + + + + + + + +%\includegraphics<1>[height=4.5cm]{images/pat1.png} +%\includegraphics<2>[height=4.5cm]{images/pat2.png} + + + +\end{document} +