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@ -1,4 +1,5 @@
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\documentclass[xcolor=dvipsnames]{beamer}
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\documentclass[xcolor=dvipsnames,notheorem,mathserifs]{beamer}
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\usepackage{amsmath}
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%\documentclass{beamer}
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%\documentclass{beamer}
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\usepackage[english]{babel}
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\usepackage[english]{babel}
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%\usepackage[latin1]{inputenc}
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%\usepackage[latin1]{inputenc}
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@ -13,11 +14,20 @@
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%\usepackage{graphicx}
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%\usepackage{graphicx}
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%\usepackage{movie15}
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%\usepackage{movie15}
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%\usepackage{media9}[2013/11/04]
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%\usepackage{media9}[2013/11/04]
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\usepackage{xcolor}
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\usepackage{graphicx}
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\usepackage{graphicx}
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\usepackage{multimedia}
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\usepackage{multimedia}
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\usepackage{media9}
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\usepackage{media9}
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\usepackage{listings,xcolor,caption, mathtools, wrapfig}
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\usepackage{amsfonts}
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\usepackage{amssymb,graphicx,enumerate}
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\usepackage{hyperref}
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\usepackage[normalem]{ulem} % for strike out command \sout
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@ -97,7 +107,7 @@ Faculty of Sciences and Engineering\\
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University of Groningen\\[0.5cm]
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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=1.5cm]{Imagenes/escudoU2014.pdf}
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% \includegraphics[height=1cm]{Imagenes/fcfm.png} \\[0.5cm]
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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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\texttt{Jeremías Garay Labra join with Hernan Mella, Julio Sotelo, Sergio Uribe, Cristobal Bertoglio and Joaquin Mura.}
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}
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}
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\date{\today}
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\date{\today}
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@ -124,13 +134,12 @@ University of Groningen\\[0.5cm]
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\column{.55\textwidth} % Left column and width
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\column{.55\textwidth} % Left column and width
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\footnotesize
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\footnotesize
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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.
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\onslide<1-> 4D flow MRI has been shown potential in the assesment of blood flow dynamics in the heart and also large arteries.\\[0.2cm]
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\onslide<2-> Some advantages:
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Some advantages respect others techniques:
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\begin{itemize}
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\begin{itemize}
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\item Full 3D coverage of the region of interest
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\item<3-> Full 3D coverage of the region of interest
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\item Retrospective plane positioning
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\item<4-> Retrospective plane positioning
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\item Rich post-proccesing: derived parameters
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\item<5-> Rich post-proccesing: derived parameters
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\end{itemize}
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\end{itemize}
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\column{.5\textwidth} % Right column and width
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\column{.5\textwidth} % Right column and width
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@ -142,16 +151,22 @@ Some advantages respect others techniques:
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\begin{frame}
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\begin{frame}
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\frametitle{4D flow MRI}
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\frametitle{4D flow MRI}
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\footnotesize
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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, such as:
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\onslide<1-> Main limitation $\longrightarrow$ long scan times involved.\\
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\vspace{0.2cm}
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\onslide<2-> In order to mitigate:
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\begin{itemize}
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\begin{itemize}
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\item Navigator gating
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\item<3-> Navigator gating
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\item modest spatial resolutions $ \sim (2.5 \times 2.5 \times 2.5 \ mm^3)$
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\item<4-> modest spatial resolutions $ \sim (2.5 \times 2.5 \times 2.5 \ mm^3)$
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\item partial data coverage
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\item<5-> partial data coverage
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\end{itemize}
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\end{itemize}
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Typical quality estimators: SNR, VNR, peak flows/velocities, mass conservation (zero divergence)
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\vspace{0.5cm}
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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 (Navier-Stokes compatibility).
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\onslide<6-> Typical quality estimators: SNR, VNR, peak flows/velocities, mass conservation (zero divergence)
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\vspace{0.5cm}
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\onslide<7-> This work $\longrightarrow$ conservation of linear momentum (Navier-Stokes compatibility).
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\end{frame}
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\end{frame}
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@ -162,19 +177,19 @@ We want to introduce a novel measure for quantify the quality of the 4D flow mea
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\frametitle{The corrector field}
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\frametitle{The corrector field}
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\footnotesize
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\footnotesize
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We assume a perfect physical velocity field $\vec{u}$
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\onslide<1-> We assume a perfect physical velocity field $\vec{u}$
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\begin{eqnarray*}
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\onslide<2-> \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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\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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\end{eqnarray*}
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And a corrector field $\vec{w}$ which satisfies:
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\onslide<3-> And a corrector field $\vec{w}$ which satisfies:
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\begin{align}
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\onslide<4-> \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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\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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\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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\vec w & = \vec 0 \quad \text{on} \quad \partial \Omega \label{eq:correctorBC}
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\end{align}
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\end{align}
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The corrector field $\vec{w}$ measures the level of agreedment of the 4D flow measures respect to the Navier-Stokes equations.
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\onslide<5-> The corrector field $\vec{w}$ measures the level of agreedment of the 4D flow measures respect to the Navier-Stokes equations.
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\end{frame}
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\end{frame}
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@ -183,16 +198,18 @@ The corrector field $\vec{w}$ measures the level of agreedment of the 4D flow me
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\frametitle{The corrector field: Continuum problem}
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\frametitle{The corrector field: Continuum problem}
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\footnotesize
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\footnotesize
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Applying the decomposition $\vec{u} \approx \vec{u}_{meas} + \vec{w}$ into the original equation and writing a variational problem for $\vec w$ we have the following: Find $(\vec w(t) ,p(t)) \in H^1_0(\Omega)\times L^2(\Omega)$ such that
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\onslide<1-> Applying the decomposition $\vec{u} \approx \vec{u}_{meas} + \vec{w}$ into the original equation and writing a variational problem for $\vec w$ we have the following: Find $(\vec w(t) ,p(t)) \in H^1_0(\Omega)\times L^2(\Omega)$ such that
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\begin{equation*}
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\onslide<2-> \begin{equation*}
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\int_{\Omega} \rho \frac{\partial \vec{w}}{\partial t} \cdot \vec{v} + \rho \big ( ( \vec{u}_{meas} + \vec w) \cdot \nabla \big) \vec{w} \cdot \vec{v} + \rho \big ( \vec{w} \cdot \nabla \big) \vec{u}_{meas} \cdot \vec{v} + \mu \nabla \vec{w} : \nabla \vec{v} - p \nabla \cdot \vec{v} + q \nabla \cdot \vec{w} \notag
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\int_{\Omega} \rho \frac{\partial \vec{w}}{\partial t} \cdot \vec{v} + \rho \big ( ( \vec{u}_{meas} + \vec w) \cdot \nabla \big) \vec{w} \cdot \vec{v} + \rho \big ( \vec{w} \cdot \nabla \big) \vec{u}_{meas} \cdot \vec{v} + \mu \nabla \vec{w} : \nabla \vec{v} - p \nabla \cdot \vec{v} + q \nabla \cdot \vec{w} \notag
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\end{equation*}
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\end{equation*}
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\begin{equation*}
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\begin{equation*}
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= - \int_{\Omega} \rho \frac{\partial \vec{u}_{meas}}{\partial t} \cdot \vec{v} + \rho \big ( \vec{u}_{meas} \cdot \nabla \big) \vec{u}_{meas} \cdot \vec{v} + \mu \nabla \vec{u}_{meas} : \nabla \vec{v} + q \nabla \cdot \vec{u}_{meas}
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= - \int_{\Omega} \rho \frac{\partial \vec{u}_{meas}}{\partial t} \cdot \vec{v} + \rho \big ( \vec{u}_{meas} \cdot \nabla \big) \vec{u}_{meas} \cdot \vec{v} + \mu \nabla \vec{u}_{meas} : \nabla \vec{v} + q \nabla \cdot \vec{u}_{meas}
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\end{equation*}
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\end{equation*}
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or in simple terms:
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\vspace{0.2cm}
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\begin{equation*}
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\onslide<3-> or in simple terms:
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\onslide<4-> \begin{equation*}
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A(\vec w,p;\vec v ,q ) = \mathcal{L} (\vec v)
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A(\vec w,p;\vec v ,q ) = \mathcal{L} (\vec v)
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\end{equation*}
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\end{equation*}
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@ -207,27 +224,26 @@ for all $(\vec v,q) \in H^1_0(\Omega) \times L^2(\Omega)$.
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\frametitle{The corrector field: Discrete problem}
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\frametitle{The corrector field: Discrete problem}
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\footnotesize
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\footnotesize
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In the Discrete, we can write the problem as follows:
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\onslide<1-> In the Discrete, we can write the problem as follows:
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\begin{equation}
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\onslide<2-> \begin{equation}
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A_{k}(\vec w,p;\vec v ,q ) + S^{conv}_{k}(\vec w;\vec v) + S^{press}_{k}(\vec w,p;\vec v ,q) = \mathcal{L}_j (\vec v)
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A_{k}(\vec w,p;\vec v ,q ) + \color{red}{S^{conv}_{k}(\vec w;\vec v)} + \color{blue}{S^{press}_{k}(\vec w,p;\vec v ,q)} \color{black}{ = \mathcal{L}_j (\vec v)}
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\label{eq:Corrector_discrete}
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\end{equation}
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\end{equation}
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With $ S^{conv}_{k}(\vec w;\vec v)$ and $ S^{press}_{k}(\vec w,p;\vec v ,q)$ terms for the stabilization of the convection and pressure respectively.
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\begin{itemize}
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\begin{itemize}
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\small
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\small
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\item $
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\item<3-> $
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A_{k}(\vec w,p;\vec v ,q ) := \int_{\Omega} \frac{\rho}{\tau} \vec{w} \cdot \vec{v} + \rho \big ( ( \vec{u}_{meas}^k + \vec{w}^{k-1} ) \cdot \nabla \big) \vec{w} \cdot \vec{v} + \rho \big ( \vec{w} \cdot \nabla \big) \vec{u}_{meas}^k \cdot \vec{v} + \mu \nabla \vec{w} : \nabla \vec{v} - p \nabla \cdot \vec{v} + q \nabla \cdot \vec{w}
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A_{k}(\vec w,p;\vec v ,q ) := \int_{\Omega} \frac{\rho}{\tau} \vec{w} \cdot \vec{v} + \rho \big ( ( \vec{u}_{meas}^k + \vec{w}^{k-1} ) \cdot \nabla \big) \vec{w} \cdot \vec{v} + \rho \big ( \vec{w} \cdot \nabla \big) \vec{u}_{meas}^k \cdot \vec{v} + \mu \nabla \vec{w} : \nabla \vec{v} - p \nabla \cdot \vec{v} + q \nabla \cdot \vec{w}
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$ \vspace{0.2cm}
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$ \vspace{0.2cm}
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\item $
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\item<3-> $ \mathcal{L}_j (\vec v) := \int_{\Omega} \frac{\rho}{\tau} \vec{w}^{k-1} \cdot \vec{v} + \mathcal{\ell}_j (\vec v,q) $
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\vspace{0.2cm}
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\item<4-> \color{red}$
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S^{conv}_{k}(\vec w;\vec v) := \int_{\Omega} \frac{\rho}{2} \ \big( \nabla \cdot (\vec u^k_{meas} + \vec w^{k-1}) \big) \ \vec{w} \cdot \vec{v}
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S^{conv}_{k}(\vec w;\vec v) := \int_{\Omega} \frac{\rho}{2} \ \big( \nabla \cdot (\vec u^k_{meas} + \vec w^{k-1}) \big) \ \vec{w} \cdot \vec{v}
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$ \vspace{0.2cm}
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$ \vspace{0.2cm}
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\item $
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\item<5-> \color{blue}$
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S^{press}_{k}(\vec w,p;\vec v ,q) := \delta \sum_{K \in \Omega}\int_{K} \frac{h_j^2}{\mu} \bigg ( \rho \big ( (\vec u^k_{meas} + \vec w^{k-1}) \cdot \nabla \big) \vec{w} + \rho \big ( \vec{w} \cdot \nabla \big) \vec{u}_{meas}^k + \nabla p \bigg) \cdot \notag \bigg ( \rho \big ( (\vec u^k_{meas} + \vec w^{k-1}) \cdot \nabla \big) \vec{v} + \rho \big ( \vec{v} \cdot \nabla \big) \vec{u}_{meas}^k + \nabla q \bigg )
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S^{press}_{k}(\vec w,p;\vec v ,q) := \delta \sum_{K \in \Omega}\int_{K} \frac{h_j^2}{\mu} \bigg ( \rho \big ( (\vec u^k_{meas} + \vec w^{k-1}) \cdot \nabla \big) \vec{w} + \rho \big ( \vec{w} \cdot \nabla \big) \vec{u}_{meas}^k + \nabla p \bigg) \cdot \notag \bigg ( \rho \big ( (\vec u^k_{meas} + \vec w^{k-1}) \cdot \nabla \big) \vec{v} + \rho \big ( \vec{v} \cdot \nabla \big) \vec{u}_{meas}^k + \nabla q \bigg )
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$ \vspace{0.2cm}
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$
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\item $ \mathcal{L}_j (\vec v) := \int_{\Omega} \frac{\rho}{\tau} \vec{w}^{k-1} \cdot \vec{v} + \mathcal{\ell}_j (\vec v,q) $
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\end{itemize}
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\end{itemize}
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\end{frame}
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\end{frame}
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@ -235,6 +251,37 @@ $ \vspace{0.2cm}
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\begin{frame}
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\frametitle{The corrector field: Well-posedness}
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\footnotesize
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\onslide<1->
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\begin{theorem}
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There exists a unique solution of Problem \ref{eq:Corrector_discrete} under condition: $$\rho/\tau + C_\Omega^{-2} \mu/2 - \rho 3 \| \nabla\vec u_{meas}^k\|_\infty > 0$$ for all $k>0$.
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\end{theorem}
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\onslide<2->
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We can furthermore prove the following energy balance:
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\onslide<3->
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\begin{theorem} For $(\vec w^k ,p^k)$ solution of Problem \ref{eq:Corrector_discrete}, with $\ell_j(\vec v,q)=0$ it holds
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\begin{equation*}\label{eq:energy}
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\| \vec w^k \|^2_{L_2(\Omega)} \leq \| \vec w^{k-1} \|^2_{L_2(\Omega)}
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\end{equation*}
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under the condition
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\begin{equation*}\label{eq:condstab}
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\mu \geq C_\Omega^2 \rho \| \nabla \vec u_{meas}^k\|_\infty
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\end{equation*}
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\end{theorem}
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\end{frame}
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\section[Synthetic data]{Experiments using synthetic data }
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\section[Synthetic data]{Experiments using synthetic data }
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\begin{frame}
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\begin{frame}
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@ -253,27 +300,29 @@ Experiments using synthetic data
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\frametitle{Numerical tests}
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\frametitle{Numerical tests}
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\footnotesize
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\footnotesize
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We tested the corrector using CFD simulations as a measurements, in the following testcases:
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\onslide<1-> We tested the corrector using CFD simulations as a measurements, in the following testcases:
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\onslide<2->
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\begin{itemize}
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\begin{itemize}
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\item Womersley flow in a cilinder
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\item Womersley flow in a cilinder
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\item Navier-Stokes simulations in an aortic mesh
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\item Navier-Stokes simulations in an aortic mesh
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\end{itemize}
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\end{itemize}
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\onslide<3->
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Also perturbations were added into the measurements:
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Also perturbations were added into the measurements:
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\begin{itemize}
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\begin{itemize}
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\item velocity aliasing (varying the $venc$ parameter)
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\item<4-> velocity aliasing (varying the $venc$ parameter)
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\item additive noise (setting SNR in decibels)
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\item<5-> additive noise (setting SNR in decibels)
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\item simulated k-space undersampling (compressed sensing for the reconstruction)
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\item<6-> simulated k-space undersampling (compressed sensing for the reconstruction)
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\end{itemize}
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\end{itemize}
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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
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%\onslide<7-> 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
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\end{frame}
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\end{frame}
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\begin{frame}
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\begin{frame}
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\frametitle{Numerical tests: details}
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\frametitle{Numerical tests: channel}
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\begin{columns}[c]
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\begin{columns}[c]
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\column{.6\textwidth} % Left column and width
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\column{.6\textwidth} % Left column and width
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\footnotesize
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\footnotesize
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@ -284,16 +333,75 @@ All simulations were done using a stabilized finite element method implemented i
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\item Oscilatory pressure at $\Gamma_{inlet}$
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\item Oscilatory pressure at $\Gamma_{inlet}$
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\end{itemize}
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\end{itemize}
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\column{.5\textwidth} % Right column and width
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\column{.5\textwidth} % Right column and width
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\footnotesize
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\footnotesize
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\begin{figure}[!hbtp]
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\begin{figure}[!hbtp]
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\begin{center}
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\begin{center}
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\includegraphics[height=0.3\textwidth]{images/cilinder_2.png}
|
\includegraphics[height=1.0\textwidth]{images/cilinder.png}
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|
\caption{3D channel mesh}
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||||||
\end{center}
|
\end{center}
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||||||
\end{figure}
|
\end{figure}
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\end{columns}
|
\end{columns}
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||||||
|
\end{frame}
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\begin{frame}
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|
\frametitle{Results for channel: aliasing and noise}
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|
\footnotesize
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|
\onslide<1-> For comparison we defined a perfect corrector field as: $\delta \vec u = \vec u_{ref} - \vec u_{meas}$
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|
\onslide<2->
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|
\begin{figure}[!hbtp]
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|
\begin{center}
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|
\includegraphics[height=0.5\textwidth]{images/perturbation_pres.png}
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|
\caption{Different perturbation scenarios}
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|
\end{center}
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|
\end{figure}
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|
\end{frame}
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|
\begin{frame}
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|
\frametitle{Results for channel: undersampling}
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|
\footnotesize
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|
\begin{figure}[!hbtp]
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|
\begin{center}
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||||||
|
\includegraphics[height=0.6\textwidth]{images/histo_channel.png}
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|
\caption{ \footnotesize Histograms of different undersampling rates for the channel}
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|
\end{center}
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|
\end{figure}
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||||||
|
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||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{Results for channel: undersampling}
|
||||||
|
\footnotesize
|
||||||
|
|
||||||
|
\begin{figure}[!hbtp]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[height=0.6\textwidth]{images/undersampling_press.png}
|
||||||
|
\caption{ \footnotesize Different undersampling rates for the channel}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{Numerical tests: aorta}
|
||||||
|
|
||||||
\begin{columns}[c]
|
\begin{columns}[c]
|
||||||
\column{.6\textwidth} % Left column and width
|
\column{.6\textwidth} % Left column and width
|
||||||
@ -311,8 +419,8 @@ All simulations were done using a stabilized finite element method implemented i
|
|||||||
\footnotesize
|
\footnotesize
|
||||||
\begin{figure}[!hbtp]
|
\begin{figure}[!hbtp]
|
||||||
\begin{center}
|
\begin{center}
|
||||||
\includegraphics[height=0.7\textwidth]{images/aorta_blender.png}
|
\includegraphics[height=1.0\textwidth]{images/aorta_blender.png}
|
||||||
\caption{\tiny{Channel mesh}}
|
\caption{Aortic mesh}
|
||||||
\end{center}
|
\end{center}
|
||||||
\end{figure}
|
\end{figure}
|
||||||
\end{columns}
|
\end{columns}
|
||||||
@ -321,43 +429,10 @@ All simulations were done using a stabilized finite element method implemented i
|
|||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
\begin{frame}
|
|
||||||
\frametitle{Results for channel: aliasing and noise}
|
|
||||||
\footnotesize
|
|
||||||
|
|
||||||
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 for channel: undersampling}
|
|
||||||
\footnotesize
|
|
||||||
|
|
||||||
\begin{columns}[c]
|
|
||||||
\column{.6\textwidth} % Left column and width
|
|
||||||
|
|
||||||
other results concerning undersampling....
|
|
||||||
|
|
||||||
\column{.5\textwidth} % Right column and width
|
|
||||||
\begin{figure}[!hbtp]
|
|
||||||
\begin{center}
|
|
||||||
\includegraphics[height=1.2\textwidth]{images/undersampling_final.png}
|
|
||||||
\caption{ \footnotesize Different undersampling rates for the channel}
|
|
||||||
\end{center}
|
|
||||||
\end{figure}
|
|
||||||
|
|
||||||
\end{columns}
|
|
||||||
\end{frame}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\begin{frame}
|
\begin{frame}
|
||||||
@ -374,6 +449,23 @@ other results concerning undersampling....
|
|||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{frame}
|
||||||
|
\frametitle{Results for aorta: undersampling}
|
||||||
|
\footnotesize
|
||||||
|
|
||||||
|
\begin{figure}[!hbtp]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[height=0.6\textwidth]{images/histo_blender.png}
|
||||||
|
\caption{ \footnotesize Histograms of different undersampling rates for the aortic mesh}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\begin{frame}
|
\begin{frame}
|
||||||
\frametitle{Results for aorta: undersampling}
|
\frametitle{Results for aorta: undersampling}
|
||||||
\footnotesize
|
\footnotesize
|
||||||
@ -413,10 +505,10 @@ Experiments using real 4D flow data
|
|||||||
\column{.6\textwidth} % Left column and width
|
\column{.6\textwidth} % Left column and width
|
||||||
|
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
\item 4D flow measurements were taken from a silicon thoracic aortic phantom made of silicon.
|
\item<1-> 4D flow measurements were taken from a silicon thoracic aortic phantom made of silicon.
|
||||||
\item A controled pump injects to the system a blood mimicking fluid and allows the control of: heart rate, peak flow, stroke volume and flow waveform
|
\item<2-> A controled pump injects to the system a blood mimicking fluid and allows the control of: heart rate, peak flow, stroke volume and flow waveform
|
||||||
\item A stenosis of $11 \ mm$ of diameter was added in the descending aorta
|
\item<3-> A stenosis of $11 \ mm$ of diameter was added in the descending aorta
|
||||||
\item The phantom was scanned using a clinical $1.5 \ T$ MR scanner (Philips Achieva, Best, The Netherlands)
|
\item<4-> The phantom was scanned using a clinical $1.5 \ T$ MR scanner (Philips Achieva, Best, The Netherlands)
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
|
|
||||||
|
|
||||||
@ -426,7 +518,7 @@ Experiments using real 4D flow data
|
|||||||
\begin{center}
|
\begin{center}
|
||||||
\footnotesize
|
\footnotesize
|
||||||
\includegraphics[height=\textwidth]{images/phantom.jpg}
|
\includegraphics[height=\textwidth]{images/phantom.jpg}
|
||||||
\caption{\footnotesize Experiment done at the Centre of Biomedical Images (CIB) of the Catholic Unversity of Chili (PUC)}
|
\caption{\footnotesize{Experiment done at the Centre of Biomedical Images (CIB) of the Catholic Unversity of Chili (PUC)}}
|
||||||
\end{center}
|
\end{center}
|
||||||
\end{figure}
|
\end{figure}
|
||||||
|
|
||||||
@ -467,14 +559,15 @@ Experiments using real 4D flow data
|
|||||||
|
|
||||||
|
|
||||||
\begin{frame}
|
\begin{frame}
|
||||||
\frametitle{Conclusions and future}
|
\frametitle{Conclusions and future work}
|
||||||
\footnotesize
|
\footnotesize
|
||||||
|
|
||||||
potential of the new quality parameter:
|
\onslide<1-> Potential of the new quality parameter:
|
||||||
|
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
\item analize real data
|
\item<2-> The detect zones with strong disagreedment
|
||||||
\item use the specificity for label zones with strong disagreedment
|
\item<3-> To better recognize common acquisition artifacts
|
||||||
\item Use the field for create new inverse problems which can be used for further accelerations
|
\item<4-> The use of the field for create new inverse problems which can be used for further accelerations
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
|
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
Loading…
Reference in New Issue
Block a user