Estimation of myocardial deformation using correlation image velocimetry

Figures

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  Fig. 1. a 128 × 128 phantom image, b pre-processed phantom image, c 112 × 112 patient image, d pre-processed patient image. The images shown in 1a & b contain square grids of size around 6 pixels, and the corresponding bounding lines are approximately 2 pixels thick

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  Fig. 2. Workflow Pipeline

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  Fig. 3. a 512 × 512 synthetic grid image with grids of dimensions 23 ×23 pixels, bounded by 8 pixels thick white lines. The red horizontal line represents the cross-sectional cut used to estimate the errors shown in Fig. 4 a and b. Imposed displacement field: b d u(x,y), the x component and c d v(x,y), the y component, as described by Eqs. (5) and (6). The minimum and maximum values of |d u| are 0 & 11 pixels, respectively; the corresponding values for |d v| are 0 & 9 pixels

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  Fig. 4. Errors corresponding to the estimated displacement fields obtained from a CIV analysis of the synthetic grid images with an imposed analytical velocity field. a Error in slope (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$e^{u}_{s}$\end{document}esu, defined in Eq. 7) plotted as a function of C B and S B. b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$e^{v}_{s}$\end{document}esv plotted as a function of C B and S B. c Error in the horizontal displacement field (e u, defined in Eq. 8) plotted at every pixel location (x,y) for (C B,S B)=(25,55). d Error in the vertical displacement field (e v) plotted at every pixel location (x,y) for (C B,S B)=(25,55). The white lines in (c) and (d) correspond to |d u|=3 pixels and |d v|=3 pixels, respectively. The colorbars in (c) and (d) are saturated at an error of 0.2 to bring out…

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  Fig. 5. The estimated displacement fields using (C B,S B)=(25,55) pixels: a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d_{c}^{u}$\end{document}dcu, b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d_{c}^{v}$\end{document}dcv as a function of x and y on the 512 × 512 pixels phantom image. The imposed displacement fields are shown in 3 b–c. c Error e u in the horizontal displacement field plotted at every pixel location (x,y) for (C B,S B)=(25,55). d Error in the vertical displacement field (e v) plotted at every pixel location (x,y) for (C B,S B)=(25,55). The white lines in c) and d) correspond to |d u|=3 pixels and |d v|=3 pixels, respectively. The boundaries of the myocardium, i.e. the grid-like region in the 512 × 512 pixels phantom image are marked approximately by the black circles. The colorbars in c) and d) are saturated…

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  Fig. 6. Dense displacement fields through a full cardiac cycle in patient-1 of the Challenge dataset. The images in (a)–(f) correspond to six different phases of the cardiac cycle, with (a)–(c) being systole. The white boxes in each of the images bound the myocardium, and only the displacement field within these boxes are shown. The arrows indicate the direction of the net displacement at the corresponding pixel location, and the arrow length is proportional to the magnitude of displacement

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  Fig. 7. Tracking landmark positions (shown as white dots in the first column of images) at each heart level (a) Apex b) Mid c) Base over a full cardiac cycle. The red and green lines represent ground truth and calculated positions, respectively. The x and y coordinates of the landmark position, indicated using the subscript p, are plotted in the second and third columns, respectively. Comparing ground truth (red) and calculated (green) landmark instantaneous displacements at each heart level over a full cardiac cycle. Ground truth includes data from two separate observers to show inter-observer variability. Both x (fourth column) and y (fifth column) components are plotted, with the error bars being based on inter-observer variability. The time t=0 corresponds to end diastole in all the plots

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  Fig. 8. Comparison between CIV (shown in red) and HARP (shown in blue) for estimated mean (across 15 healthy individuals) circumferential strain in various segments of the heart. The x-axis of every plot signifies one cardiac cycle, with x=0 corresponding to end diastole. The error bars are based on the standard deviation across the 15 individuals

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  Fig. 9. Comparison between CIV (shown in red) and HARP (shown in blue) for estimated mean (across 15 healthy individuals) radial strain in various segments of the heart. The x-axis of every plot signifies one cardiac cycle, with x=0 corresponding to end diastole. The error bars are based on the standard deviation across the 15 individuals