Subject-specific multiscale modeling of aortic valve biomechanics

Figures

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  Fig. 1. AR Biomechanics is simulated over two cardiac cycles; a leaflet subregion (black square evidenced by a red circle) is considered and the time dependent nodal displacement (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overrightarrow{{u}^{{org}}}$$\end{document}uorg→ ) at the boundary of the subregion are extracted. Tissue length scale. The leaflet subregion is considered, and the layered structure of the tissue is accounted for (green = fibrosa, white = spongiosa, orange = ventricularis). The displacement boundary conditions (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overrightarrow{u}^{{org}}_{Rad}$$\end{document}u→Radorg, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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  Fig. 2. a cMRI planes (6 out of 18 planes are depicted). b AR substructures manually traced on a cMRI plane. c Reconstructed 3D geometry of the AR. d Detail of an AV leaflet

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  Fig. 3. Fitting of experimental data for the intact leaflet (top), fibrosa layer (middle) and ventricularis layer (bottom)

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  Fig. 4. From the left to the right: the organ scale model, the selected patch with the original mesh and the remeshed patch with the layer-specific material definition

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  Fig. 5. Top (a), side (b) and isometric (c) view of the cell length-scale patch

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  Fig. 6. Aortic view of the circumferential (right column) and radial (left column) strain computed on AV leaflets surface at peak diastolic transvalvular pressure for each simulated AV model

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  Fig. 7. Circumferential (left column) and radial (right column) stretch ratios in the center of the belly region of the left-coronary (LC), non-coronary (NC) and right-coronary (RC) leaflets over the systolic and diastolic phases of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${2^{\mathrm{nd}}}$$\end{document}2nd simulated cardiac cycle for the three subjects. The time-course of the transvalvular pressure is reported in the bottom row of each column

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  Fig. 8. Linear regression between the peak diastolic value of circumferential stress (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{circ}$$\end{document}σcirc) and radial stress (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{rad}$$\end{document}σrad) (top row) vs. leaflet surface area, and between the peak diastolic circumferential strain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon _{circ}$$\end{document}ϵcirc) and radial strain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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  Fig. 9. Section of the LC leaflet patch of subject 1; the three different layer are represented on the top, and the max principal stress through the thickness is plotted on the bottom

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  Fig. 10. Circumferential (left column) and radial (right column) stress in the fibrosa layer of the patch for the LC, NC and RC leaflets over the diastolic phase of the 2nd cardiac cycle for the three subjects. The time-course of the transvalvular pressure is reported in the bottom row of each column

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  Fig. 11. Correlation of circumferential stress (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{circ}$$\end{document}σcirc) and radial stress (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{rad}$$\end{document}σrad) with the leaflet surface area. For each stress and strain component, the data represents the maximum value reported in the plots of Fig. 10. Dots = data computed by the models of subject 1 (blue), subject 2 (yellow) and subject 3 (green); dashed red line = regression line. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document}R2 is reported

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  Fig. 12. Max principal stress on the cell length-scale model. The sections on the circumferential and radial plane are plotted on the top and left of the patch, respectively.