Turbulent blood dynamics in the left heart in the presence of mitral regurgitation: a computational study based on multi-series cine-MRI

Figures

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  Fig. 1. Flowchart to reconstruct the geometries of LH and valves and their displacements. Continuous lines refer to the steps followed to reconstruct the LH walls and the dashed lines to the reconstruction of the valves. A: Geometric reconstruction of the LV endocardium for all the 30 frames by adopting the strategy described in Fumagalli et al. (2022) (here we reported the geometries at two representative frames as an example). B: Geometric reconstruction of AR and LA for all the 30 frames by adopting the strategy proposed in Renzi et al. (2022) (two representative frames reported as an example). C: Creation of a connection to merge LV with AR and LA to obtain the final LH geometry. D: Registration 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}$$\textbf{d}^i_{LH}(\textbf{x})$$\end{document}dLHi(x) with respect to the end systolic configuration (magnitude of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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  Fig. 2. A: Location of the points where ECD measures were acquired. B: Computational domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega$$\end{document}Ω with its boundaries. In green, we reported the aortic and mitral valves \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma _{AV}$$\end{document}ΓAV and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma _{MV}$$\end{document}ΓMV. The computational mesh of patient R is also displayed. C: Trend in time of the pressures imposed at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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  Fig. 3. For each scenario: A: trend in time of the mean ensemble ventricle (LV), aortic (AR) and atrial (LA) pressures in the blue, red and magenta spheres, respectively; B: trend in time of the ensemble flow rates through AV (blue section) and MV (red section). \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$AV_{closure}$$\end{document}AVclosure: closure of aortic valve; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$MV_{closure}$$\end{document}MVclosure: closure of mitral valve

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  Fig. 4. Magnitude of the ensemble velocity at three representative time instants (peak systole \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{PS}$$\end{document}tPS, peak E-wave \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{EW}$$\end{document}tEW, peak A-wave \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{AW}$$\end{document}tAW) over a slice along the 3CH axis in the two scenarios. At \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{PS}$$\end{document}tPS, we…

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  Fig. 5. For each scenario in two different views: A: volume rendering of the ensemble velocity magnitude at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{PS}$$\end{document}tPS; B: spatial distribution of TAWSS, reported in the end systolic configuration; C: spatial distribution of RRT, reported in the end systolic configuration

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  Fig. 6. A: trend in time of GTKE evaluated in LV and LA. Notice the different scale used for H (left) and R (right). In the right figure, also the H LV case has been reported for a direct comparison; B: slices along the 2CH (left) and 3CH (right) axis with the velocity SD at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{GTKE}$$\end{document}tGTKE and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{EW}$$\end{document}tEW

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  Fig. 7. Top: volume rendering at two different 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 and \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 of the maximum tangential stress \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{max}$$\end{document}τmax quantifying the possible damage caused to blood cells in the regurgitant scenario; Bottom, left: Percentage \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. 8. Comparison of the ensemble velocity pattern with Cine-MRI at three representative frames in the regurgitant scenario. The arrows highlight the good agreement between computations and measures