Assessment of turbulent blood flow and wall shear stress in aortic coarctation using image-based simulations

Figures

• 

  Fig. 1. Comparison of measured (4D-flow MRI) and simulated (CFD) normalized velocity magnitude (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v/v_0$$\end{document}v/v0, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_0$$\end{document}v0 is the mean inlet velocity) and turbulent kinetic energy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k/v_0^2$$\end{document}k/v02 profiles at characteristic locations along the bend tube (A–F) (profiles extracted in the middle). The lines indicate various turbulence models: standard \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

• 

  Fig. 2. The contours of the velocity magnitude (|v|) in the central horizontal plane for CFD (original resolution), DCFD (downsized resolution), and MRI (original resolution), where the last contour indicates the absolute difference between DCFD and MRI

• 

  Fig. 3. The contours of the out-of-plane vorticity component at selected cross-sections (A–F)—comparison of CFD (original spatial resolution), DCFD (downsized spatial resolution) and MRI

• 

  Fig. 4. a The contours of the WSS at the phantom surface: CFD (original), DCFD (downsized) and MRI results; b the two-dimensional representation of the WSS at the phantom surface; c the two-dimensional map of the normalized WSS (WSS/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSS}_{\mathrm{mean}}$$\end{document}WSSmean), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSS}_{\mathrm{mean}}$$\end{document}WSSmean is a spatially averaged mean WSS calculated for each modality

• 

  Fig. 5. Profiles of the non-dimensional circumferentially averaged wall shear stress (WSS/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSS}_{\mathrm{mean}}$$\end{document}WSSmean) obtained from original and downsized CFD results and MRI

• 

  Fig. 6. The patient-specific CoA case: the stream-traces colored by the velocity magnitude at the peak systole for CFD and 4D flow MRI (a); the contours of the non-dimensional WSS (WSS/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSS}_{\mathrm{mean}}$$\end{document}WSSmean) at the aorta wall (b); the 2D map of WSS distribution for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CFD}_{{\mathrm{sm}}}$$\end{document}CFDsm (c) and 4D-flow MRI (d); the scatter plots (symbols) and circumferentially averaged profiles (lines) of the non-dimensional WSS for 4D-flow MRI and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox…

• 

  Fig. 7. a Phantom experimental setup (-left) with: variable power source (a), flow indicator (b), submersible pump (c), flow phantom in the MRI scanner (d), and the phantom geometry (-right) represented with the main diameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_0$$\end{document}d0, stenotic diameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_S$$\end{document}dS, and total length of L; b the mass flow rate at the inlet of the patient-specific aorta with coarctation (CoA) from MRI and the fitted spline; c the patient-specific CoA with a highlighted position of narrowing (in red), inlet, and the branching arteries: brachiocephalic trunk (BT), left common carotid artery (LCCA), Left subclavian artery (LSA), celiac trunk (CT), left renal artery (LRA), right renal artery (RRA), and the rest of abdominal aorta (AbAo)