Super-resolution 4D flow MRI to quantify aortic regurgitation using computational fluid dynamics and deep learning

Fig. 1. Sketches of the basic (top), angled (middle), and offset (bottom) constricted sections, respectively

Fig. 2. Relative error across all 200 epochs during training for each network. Networks trained with five geometries were not included as the general trend seen was the same

Fig. 3. Predictions on an LR patch from the synthetic 4D flow MRI phase image for different networks with and without aliasing error, focused on the constricted section at two different views along the width (top) and length (bottom) of the geometry. A 2D slice, along the length of the geometry, of the velocity magnitude is shown from the 3D patch for visualisation purposes. Scale is in m s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1

Fig. 4. Regression and Bland–Altman plots for prediction on non-aliased (left) and aliased (right) data with 4DFlowNet-CSP-A (top) and 4DFlowNet-CSP (bottom). These plots are for each of the velocity components and magnitude (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_x$$\end{document}vx, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_y$$\end{document}vy, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_z$$\end{document}vz, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

Fig. 5. Regression and Bland–Altman plots for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert v\Vert$$\end{document}‖v‖ prediction within the constricted section, comparing the baseline 4DFlowNet (left) against the adapted 4DFlowNet-CSP (right)

Fig. 6. Predicted SR images on actual 4D flow MRI data. Two sets of 4D flow MRI data were used (top and bottom), with the original LR images on the left and the SR images in the other three columns, titled by the network used for prediction. These are 2D slices of the 3D image, showing the velocity magnitude taken at peak flow. Scale is in m s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1

Fig. 7. Original 4D flow MRI image against the SR image produced by 4DFlowNet-CSP at systole and diastole, visualised in ParaView. The regurgitant jet can be clearly seen during diastole in the SR image produced. Scale is in m s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1

Fig. 8. Comparison of networks for different metrics and results, varied by the data set size and whether aliasing was used. Values were normalised to be within 0 and 1, representing the worst and best values, respectively, for a specific metric relative to other networks