A comprehensive mathematical model for cardiac perfusion

Figures

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  Figure 1. The perfusion is the result of complex interactions among different models.

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  Figure 2. Description of the general layout of the computational model. On the top, computational domains: the left heart solid domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{\Omega }^{\textrm{s}}$$\end{document}Ω^s in green, the left heart fluid domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega ^{\textrm{f}}$$\end{document}Ωf in blue, and the biventricular geometry \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega ^{\textrm{p}}$$\end{document}Ωp in yellow. On the bottom, coupling of different models: the 3D-0D electromechanics model (in green, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

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  Figure 3. (a) The three computational meshes for the multiphysics problem. (b) Aortic and mitral valves in the open and closed configuration. (c) Perfusion regions in the biventricular geometry.

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  Figure 4. Results from a physiological simulation. (a) electromechanics of the left heart: calcium concentration during ventricular depolarization and displacement magnitude during ventricular contraction. (b) left heart hemodynamics: on the top, volume rendering of velocity magnitude and pressure during filling and ejection phases; on the bottom, focus on the epicardial coronary arteries. (c) myocardial perfusion: Darcy pressure in three different compartments during filling. Test I.

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  Figure 5. Results from physiological 3D electromechanical - 0D circulation simulation: (a) left ventricular pressure-volume loop; (b) left ventricular volume versus time. Test I.

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  Figure 6. Results from physiological 3D Navier–Stokes–3D Darcy simulation in a representative heartbeat: (a) flow rates in pulmonary veins and aortic outlet section; (b) flow rates in epicardial coronary arteries; (c) average pressure in aortic outlet sections and coronary outlets; (d) pressure in the three Darcy’s compartments. Test I.

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  Figure 7. Simulation of aortic r egurgitation (AR): (a) aortic valve in ventricular diastole modeled with the RIIS method, comparison between physiological (PH) and AR cases; (b) volume rendering of velocity magnitude during ventricular filling; (c) aortic pressure prescribed on the ascending aorta outlet section in the PH and AR cases; (d) coronary flowrates over time, comparison between PH and AR cases; (e) velocity during diastole in the coronary tree, comparison between PH and AR cases; (f) Mean Blood Flow at diastolic peak in PH and AR cases. Test II and comparisons with PH case.