Stimulus–effect relations for left ventricular growth obtained with a simple multi-scale model: the influence of hemodynamic feedback

Fig. 1. Lumped parameter model of the circulation. With mitral valve (MV), aortic valve (AV), venous and arterial resistance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\rm {V}}$$\end{document}RV and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\rm {A}}$$\end{document}RA), compliance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{\rm {V}}$$\end{document}CV and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{\rm {A}}$$\end{document}CA) and inertance…

Fig. 2. Aortic stenosis (AS) case for the acute state (Acute), the growth only cases (G) and the cases with growth and hemodynamic feedback (GH). Results are grouped by a strain stimulus only, a stress stimulus only, and a mixed stimulus of both stress and strain. For ease of notation, on the horizontal axis the four stimuli are denoted by: (1) sarcomere strain amplitude \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\epsilon }^\mathrm{{amp}}$$\end{document}Sϵamp, (2) maximum strain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\epsilon }^\mathrm{{max}}$$\end{document}Sϵmax, (3) average sarcomere stress \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

Fig. 3. Aortic stenosis (AS) case for the acute state (Acute), the growth only cases (G) and the cases with growth and hemodynamic feedback (GH). Results are grouped by a strain stimulus only, a stress stimulus only, and a mixed stimulus of both stress and strain. For ease of notation, on the horizontal axis the four stimuli are denoted by: (1) sarcomere strain amplitude \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\epsilon }^\mathrm{{amp}}$$\end{document}Sϵamp, (2) maximum strain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\epsilon }^\mathrm{{max}}$$\end{document}Sϵmax, (3) average sarcomere stress \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

Fig. 4. Results for the aortic regurgitation (AR) case, presented according to the format in Fig. 2. Cases 1-2 and 4-3 are unstable for both G and GH simulations

Fig. 5. Results for the aortic regurgitation (AR) case, presented according to the format in Fig. 3. On the three panels, patient data are identified as mean with standard deviation, with data collected from Wisenbaugh et al. 1984 for end diastolic volume EDVI and mass index MI while Seldrum et al. (2018) is used for relative wall thickness RWT. On the right side, patient data are represented as clinical occurrence in percentage (Barbieri et al. 2019b)

Fig. 6. Results for the mitral regurgitation (MR) case, presented according to the format in Fig. 2. Cases 1-2 and 4-3 are unstable for both G and GH simulations

Fig. 7. Results for the mitral regurgitation (MR) case, presented according to the format in Fig. 3. On the three panels, patient data are identified as mean with standard deviation, with data collected from Wisenbaugh et al. 1984 for end diastolic volume EDVI and mass index MI, while Seldrum et al. 2018 is used for relative wall thickness RWT. On the right side, patient data are represented as clinical occurrence in percentage (Barbieri et al. 2019a, b)