Feasibility of large-scale in silico transcatheter aortic valve implantation trials using a fast-to-evaluate model

Fig. 1. Schematic representation of a self-expandable TAVI valve, deployed in the native valve (adapted from Fornell (2014)). Frame and skirt heights are indicated. Paravalvular leakage is depicted with the yellow arrow

Fig. 2. Flowchart summarising the steps to perform in silico trials. The PVL output metric is regurgitant fraction (RF). Corresponding sections are indicated

Fig. 3. Side view (a) and top view (b) of the NURBS aortic valve template, showing the control net and control points in black. In (a), the aorta, sinus, LVOT, and middle (diamond-shaped) patches are colored orange, blue, light blue, and grey, respectively. In (b), leaflet patches are shown in red and sinus patches in blue. The opening parameter ΔΔ is indicated in light blue

Fig. 4. Schematic representation of the TAVI deployment model at two stages: a initial configuration and b intermediate configuration. Relevant model parameters are indicated, with spring constants k and cylinder expansion rates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{r}$$\end{document}r˙

Fig. 5. Visualisation of the leakage gap at three different slices throughout the aortic valve geometry, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_i$$\end{document}ri and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_o$$\end{document}ro the radial distances from the guide wire to the cylinder and the aortic wall, respectively. The aortic valve geometry is in white, and the cylinder in orange. The gap heights are indicated with the grey arrows

Fig. 6. Schematic 0D lumped parameter leakage model with skirt, valve (AV), frame and paravalvular (para) segments, and L, R, B, C, p, and Q representing inductances, resistors, Bernoulli resistors, capacitors, pressures and flows, respectively. Note that the aorta is depicted on the right, in contrast to previous figures

Fig. 7. a Prescribed left ventricular \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{\text {LV}}$$\end{document}pLV and aortic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{\text {Ao}}$$\end{document}pAo pressure waveforms. b Total output flow (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_{\text {tot}}$$\end{document}Qtot), comprising transvalvular flow (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_{\text {AV}}$$\end{document}QAV) and paravalvular flow…

Fig. 8. Regurgitant fraction (RF) as a function of the six varied model parameters, for the case whose median RF was closest to the overall median. Spearman correlation coefficients are depicted in the upper right corner

Fig. 9. Boxplots of Spearman correlation coefficients between each of the six model parameters and regurgitant fraction

Fig. 10. Median regurgitant fraction (RF) per patient as a function of age, and shape features. Spearman correlations coefficients are depicted in the upper right corner

Fig. 11. Boxplots of age and five shape features for non-significant (below grade II) and significant aortic regurgitation (grade II or higher) groups. P-values for the Wilcoxon rank sum test are indicated at the top

Fig. 12. Boxplots of the LVOT-to-ascending aorta angle (left), and the ratio of LVOT to annulus area (right) for three different groups based on Spearman correlation (ρρ) between implantation depth and RF