An Image-Based Computational Fluid Dynamics Study of Mitral Regurgitation in Presence of Prolapse

Figures

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  Fig. 1. Steps to complete the geometry and its displacement. (A) Union of the atrium with the ventricular endocardium and addition of an aortic flow extension. (B) Inclusion of a template of the aortic valve (as an example, here we reported the open configuration). (C) Harmonic extension of the ventricular endocardial displacement for the atrium and for the aorta. (D) Geometries of the six current configurations together with the corresponding magnitude of the displacement field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {d}}_{{\text {h}},{\text {MRI}}}^{i}({\mathbf {x}})$$\end{document}dh,MRIi(x) with respect to the ES instant

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  Fig. 2. Flow chart to reconstruct the mitral valves and to define the virtual scenarios. (A) Cine-MRI images of the mitral valve. (B) Tracing of the leaflets profile on each of the 18 longitudinal planes. (C) 3D point cloud of the mitral valve obtained by tracing the leaflets profiles in all the planes. (D) Fitting and resampling procedure of the rings (the case of the annulus is reported here as an example). (E) The 3D point cloud as a result of the fitting and resampling procedure performed for all the rings. (F) Creation of a surface mesh of the mitral valve. (G) Generation of scenarios H and R1 (to obtain scenario R2, we dilated the geometry and the displacement field of R1 by a factor 1.25)

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  Fig. 3. Section of the mitral valve with prolapse of the posterior leaflet. In red the anterior leaflet and in blue the posterior one. The dashed curve represents a possible position of the posterior leaflet in the healthy configuration. The prolapse of the P2 segment moves the posterior leaflet from configuration A to B towards the atrium

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  Fig. 4. Left: computational domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega (t)$$\end{document}Ω(t) with its boundaries: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma _{\text {w}}(t)$$\end{document}Σw(t) represents the ventricular endocardium and the physical wall of the atrium and aortic root; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma _{1}(t)$$\end{document}Σ1(t) is the atrium outlet and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

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  Fig. 5. For each of the two views A and B comparison between the original end diastolic reconstructed surface and the one obtained after the registration procedure (left) and the corresponding relative error (right)

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  Fig. 6. Panel A, top: trend in time of the ventricle and aortic pressures (computed in the blue and orange slices reported in panel B, left); \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {o}}$$\end{document}to is the time instant where the aortic valve opens; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {c}}$$\end{document}tc is the time instant where the aortic valve closes. Panel A, middle: plot over the time of the flow rate at the level of the LVOT (computed in the black slice reported in panel B, middle); \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{{\text {v}}1}$$\end{document}tv1 and \documentclass[12pt]{minimal}…

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  Fig. 7. Pressure field at three representative time instants, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1}$$\end{document}t1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{2}$$\end{document}t2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{3}$$\end{document}t3 (see the text for their definition), in the three scenarios

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  Fig. 8. Velocity magnitude at three time instants in the three scenarios. In yellow we reported a slice of the two valves. For the instants refer to Fig. 6A. For H we used the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta taken from R2

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  Fig. 9. Top: ratio between the turbulent viscosity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _{\text {sgs}}$$\end{document}μsgs and the physical viscosity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ in the three scenarios at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta. For H we used the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta taken from R2. Bottom: trend…

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  Fig. 10. Top: streamlines of the velocity magnitude through the mitral and aortic orifices and magnitude of the WSS on the mitral valve. Instant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta; three different views; R1 and R2 configurations. Bottom, left: in red the selected region with the points used to compute the histogram and the plot reported on the right. Bottom, middle: distribution of the WSS magnitude acting on the red region at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta. Bottom, right: trend in time of the average (in space) of the WSS magnitude acting on the red region

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  Fig. 11. Top: for each of the columns A and B: volume rendering of the velocity magnitude (left) and spatial distribution of the WSS magnitude (right). Time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta. Bottom, left: in red the selected regions with the points used to compute the histogram and the plot on the right. Bottom, middle: distribution of the WSS magnitude acting on the red regions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{\text {a}}$$\end{document}ta. Bottom, right: trend in time of the average (in space) of the WSS magnitude acting on the red regions