A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Figures

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  Fig. 1. Basic 3D example of the aortic valve geometry we want to obtain for our simulations in open (1a) and closed (1b) position. Here, inter- and intra-leaflet symmetry are enforced

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  Fig. 2. The outer circle’s radius, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{ro}$$\end{document}lro, represents the size of the aorta and the inner circle’s radius, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{ri}$$\end{document}lri, determines the valve’s state (the bigger the measurement, the more open the valve). The leaflet angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_a$$\end{document}la determines the half leaflet region of interest highlighted in the last picture

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  Fig. 3. The sinus curve (dark grey) is a Bézier curve defined by the shown control points (black bullets)

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  Fig. 4. The symmetry curve (dark grey) is a cubic Bézier curve defined by the shown control points (black bullets)

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  Fig. 5. Curves enclosing the top (black) and the bottom (grey) part of the half leaflet

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  Fig. 6. The valve models of the first 5 patients are shown here, one in each row: a qualitative comparison between the obtained geometry and the CT images (left column), the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}γ, suitably thresholded to show only the nonzero values (central column), and the theoretical 3D valve structure (right column)

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  Fig. 7. The valve models of the last 5 patients are shown here, one in each row: a qualitative comparison between the obtained geometry and the CT images (left column), the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}γ, suitably thresholded to show only the nonzero values (central column), and the theoretical 3D valve structure (right column)

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  Fig. 8. The relation between pressure gradient and maximum velocity is reported in this picture. The red curve represents the second-order polynomial fitting of our data (blue bullets). The yellow curve represents the theoretical relation obtained using the simplified Bernoulli equation

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  Fig. 9. Velocity results of the blood flow simulations through the aortic valve for the first 6 patients at peak systole: for each patient, we show the velocity contours on a slice of the domain (on the left) and a 3D representation of the flow through the valve (on the the right)

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  Fig. 10. Velocity results of the blood flow simulations through the aortic valve for the last 4 patients at peak systole: for each patient, we show the velocity contours on a slice of the domain (on the left) and a 3D representation of the flow through the valve (on the the right)

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  Fig. 11. Pressure results of the blood flow simulations through the aortic valve at peak systole for all the 10 patients in the dataset

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  Fig. 12. Aligned visualization panels in TeraRecon: xy-plane (a), yz-plane (b) and xz-plane (c)