Investigating the Shortcomings of the Flow Convergence Method for Quantification of Mitral Regurgitation in a Pulsatile In-Vitro Environment and with Computational Fluid Dynamics

Figures

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  Fig. 1. a Principle of flow convergence: The flow approaching the aperture is described as an idealized sink flow in which increasing flow velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{4}<v_{3}<v_{2}<v_{1}$$\end{document}v4<v3<v2<v1 is found on concentric hemispheric shells with decreasing surface area. In the shown example \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{3}$$\end{document}v3 is chosen as the aliasing velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{\text{a}}$$\end{document}Va. It is multiplied with the area of the corresponding hemispheric shell located at distance r from the aperture to obtain the…

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  Fig. 2. Different mitral regurgitation orifice phantoms (MROP) shapes: circle, slit (pointed oval), and drop; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h=$$\end{document}h= height (corresponds to the diameter for circle), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w=$$\end{document}w= width

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  Fig. 3. a Schematic of the test rig. Please note, that the ultrasound probe and the PIV set-up (camera and light sheet optics) were not used simultaneously. b Photograph of PIV set-up with field of view (FOV) and notation of the axes

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  Fig. 4. Flow convergence method to determine the regurgitation volume by a physician. a In color-Doppler mode the aliasing velocity is adjusted and the PISA radius is measured. Subsequently the US machine calculates the flow rate. b In CW-Doppler mode the VTI area has to be marked, which translates in combination with the maximal velocity into the EROa and RVol. (MR Radius: PISA radius r; MR Alias Geschw: aliasing velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{\text{a}}$$\end{document}Va; MR Flussrate: RFlow; MR ERO: EROa; MR Volumen: RVol)

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  Fig. 5. Instantaneous flow field of the regurgitation jet at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=245$$\end{document}t=245 ms with underlying vortex Q criterion [20] to indicate vortical structures for circle-L. Every third/fifth vector in y/x-direction is shown for clarity. In the background the raw data image with the PVC film and the orifice is visible

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  Fig. 6. a Temporal evolution of velocity profiles for the regurgitation jet close to the orifice at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x/h=0.2.$$\end{document}x/h=0.2. b Temporal evolution of maximum velocity during one cardiac cycle; both for circle-L. Dashed lines show points in time during diastole, which should not be compared to a realistic cardiac cycle

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  Fig. 7. Maximum captured velocity for PIV and US. The ultrasound measurements are displayed individually (symbols) and as mean values (bars), while the PIV measurements show the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2 \sigma$$\end{document}2σ-confidence interval superimposed to the mean values (see “PIV Uncertainty Estimation” in Appendix 1 for more details)

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  Fig. 8. a The regurgitation volume of each MROP measured by ultrasound (US) with the flow convergence method and particle image velocimetry (PIV). The ultrasound measurements are displayed individually (symbols) and as mean values (bars), while the PIV measurements show the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2 \sigma$$\end{document}2σ-confidence interval (see “PIV Uncertainty Estimation” in Appendix 1 for more details). b The mean regurgitation volume over orifice area for each MROP, where a systematic underestimation of US for larger areas becomes visible

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  Fig. 9. a Streamlines with isolines extracted from \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 at different aliasing velocities \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{\text{a}}$$\end{document}Va overlayed with the PISA estimation for the circular large orifice (circle-L) at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{\text{a}}=20$$\end{document}Va=20 cm/s. Right panel: deviation introduced by the choice of aliasing velocity threshold into the PISA estimation at the constant flow rate of RFlow \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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  Fig. 10. For each of the 42 phase positions within the cardiac cycle, 100 double-images were recorded and averaged for the cardiac-phase resolved evaluation, while only one image was used for an instantaneous flow field evaluation. For the regurgitation volume extraction another 1000 images were recorded along the entire cycle

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  Fig. 11. Schematic of the extracted PIV data for the calculation of RVol for drop-M MROP: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u(x_0,y,z,t)$$\end{document}u(x0,y,z,t) during systole is used for further processing

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  Fig. 12. Instantaneous flow field for drop-M as colored vector plot overlayed with the raw data image. The integration limits and the x-position of the RVolextraction are indicated with yellow lines