A modelling study of right ventricular growth with valvular regurgitation

Figures

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  Fig. 1. Schematic illustration of the human biventricle model coupled to systemic circulation and pulmonary circulation (a), in which R represents the resistance between cavities, C represents the compliance of a cavity, and the diode controls the unidirectional flow. MV: mitral valve, AV: aortic valve, RA: right atrium, TV: tricuspid valve, PV: pulmonary valve, LA: left atrium, Ao: aorta, Sys: systemic circulation, Pul: pulmonary circulation, PR: PV regurgitation, TR: TV regurgitation. The bi-ventricle model is further divided into three parts (b): the left ventricular free wall (LVFW) in blue, the right ventricular free wall (RVFW) in red, and the septum in yellow. (c) The rule-based myofibre structure where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{f}_0,\,\textbf{s}_0,\,\textbf{n}_0$$\end{document}f0,s0,n0 are the unit myofibre, sheet, and sheet-normal directions in the reference configuration

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  Fig. 2. Schematic illustration of myocardial growth and remodelling in the updated reference configuration with non-zero residual stress. The current configuration of the biventricular model, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {B}_1$$\end{document}B1, can be reverted to a fictitious incompatible state, labelled as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {B}}_{0}$$\end{document}B0 through the application of the residual elastic deformation tensor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{F}_\text {r}$$\end{document}Fr. By applying \documentclass[12pt]{minimal} \usepackage{amsmath}…

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  Algorithm 1. Residual deformation in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {B}_2$$\end{document}B2 after growth from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {B}_1$$\end{document}B1.

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  Fig. 3. Instantaneous pressure-volume loops of the LV a and the RV b from the baseline case, with PR, TR and both PR and TR. Note, G&R has not started

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  Fig. 4. Distribution of myofibre stress (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _\text {ff}$$\end{document}σff) at end diastole (ED) and end systole (ES) before any G&R with deformed biventricle geometries

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  Fig. 5. G&R results of the PR, TR and P&TR eccentric growth cases, specifically the mean accumulative growth ratio in the RVFW (a) and the septum (b), with corresponding the mean incremental growth ratios (c) and (d). The distribution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta }$$\end{document}θ in the grown heart (e) from different views in the top panel, and the comparison of geometry before (blue) and after (grey) growth in the bottom panel

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  Fig. 6. Comparison of the instantaneous pressure-volume loops in the baseline, the regurgitation state before and after growth in the RV for PR (a), TR (b) and P&TR (c) cases, and corresponding LV loops in (d–f)

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  Fig. 7. Hybrid G&R in the RV. The increased mean accumulative growth ratio in the RVFW and the septum (a), along with the distributions of the eccentric growth ratio (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ^\text {f}$$\end{document}θf) and the concentric growth ratio (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ^\text {c}$$\end{document}θc) at the end of the growth cycle (b)

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  Fig. 8. Comparison of RV G&R with concentric growth (grey) and without (blue) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ^\text {c}$$\end{document}θc (a), along with the cut views from positions (red dotted lines), and instantaneous pressure-volume loops in the RV (b) and the LV (c)

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  Fig. 9. Comparison of hybrid G&R with and without LV G&R: (a) mean accumulative concentric ratio (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ^\text {c}$$\end{document}θc) and eccentric growth ratio (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ^\text {f}$$\end{document}θf) in the LVFW, RVFW and septum; b the final grown geometry with (grey) and without (blue) LV G&R, along with distributions of growth ratios with LV G&R after 7 G&R cycles; instantaneous pressure-volume loops for the RV (c) and the LV (d)

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  Fig. 10. Comparison of simulated growth trajectories with clinical data from Caravita et al. (2025) and Greutmann et al. (2022). (a) RVEDV ranges for different TR severity groups (no/mild, moderate, and severe) reported by Caravita et al. (2025), with mean values indicated by solid lines, and the horizontal axis represents the extracted regurgitant volume for each group, mild: ≤ 23≤23 ml, moderate: 23–45 ml, severe: ≥≥45 ml. Clinical data from Greutmann et al. (2022) are also included (light grey region), with mean values shown as dashed lines; (b) trajectories of RVEDV for the TR-Ecc (black) and P&TR-Ecc (green) cases, plotted within the severe group. Each arrow represents one growth cycle