Characterizing variability in passive myocardial stiffness in healthy human left ventricles using personalized MRI and finite element modeling

Fig. 1. Representative cine bSSFP, tagged MRI, and cDTI (b=0) images from one subject showing both short and long-axis views at end-systole and end-diastole.

Fig. 2. Cine bSSFP image slice alignment. Slice misalignment due to breath-hold differences and subject motion was corrected using a contour-based approach.

Fig. 3. LV surface geometry generation from cine bSSFP images. A surface model was fit to guide points placed on the (a) short and (b) long-axis images. (c) Intersection of the LV surface geometry with all the images. (d) Final diastasis and end-systolic surface geometries for all subjects. All are scaled uniformly by the same amount and a scale bar is included. The endocardial surface is colored green and the epicardial surface is colored blue.

Fig. 4. cDTI geometric distortion is corrected by combining the (a) blip-up and (b) blip-down images using TOPUP and the FSL package. (c) The geometrically corrected images correspond better to the (d) cine bSSFP images. Manually contoured epicardial (blue) and endocardial (green) outlines are overlayed on the images. (e) the myocardial diffusion tensors are calculated on each slice of the geometrically corrected images. (f) The primary eigenvectors of the diffusion tensors for a representative slice colored by the fiber angle (helix angle) are shown.

Fig. 5. Different fiber orientations tested for each subject. Myofiber orientations were personalized using in vivo cDTI and alternatively described using the rule-based LDRB algorithm34. \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} is the helix angle.

Fig. 6. Pipeline for integrating geometry (cine bSSFP), microstructure (cDTI), and kinematics (tagged MRI) data into a finite element mechanics model for estimating passive myocardial stiffness. The material parameter estimation procedure using the forward FE mechanics model and the kinematic data is also summarized.

Fig. 7. Displacement error (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\Delta u_{sim-exp}|$$\end{document}) between experimentally determined nodal positions and simulated nodal positions using one optimal c and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} combination. In all subjects, the experimentally measured and simulated end-diastolic nodal positions matched well. All surface geometries are scaled uniformly by the same amount and a scale bar is included.

Fig. 8. Optimal c-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} coupling curves for each subject (a-g). A direct comparison of all subjects and a comparison of literature values for passive myocardium parameters in healthy humans appears in (h). Solid colored lines are for models with personalized (cDTI) fibers and the uncertain region around this line (colored range bars) represents the upper and lower bounds of the behavior due to a ±20% variation in LV end-diastolic pressure.

Fig. 9. Comparison of each subject’s myocardial stiffness parameter estimation under controlled deformation (a-g). A direct comparison of all subjects appears in (h). Simulations show Cauchy stress vs. stretch from idealized uniaxial tension along the fiber direction for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} = 32

Fig. 10. Comparison of material parameter estimates (c at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}=32) between models with personalized cDTI fibers (triangle) vs rule-based fibers (circle). The solid and dotted error bars represent the variation due to end-diastolic pressure (within the expected beat-to-beat range) and rule-based descriptions of fiber orientation, respectively. Generally, the variation in passive myocardial stiffness due to end-diastolic pressure exceeds that which is due to fiber variability

Fig. 11. Fiber Cauchy stress and stretch distribution in the LV myocardium at end-diastole. Wall fraction is the proportion of the myocardial wall experiencing a given fiber stress or stretch relative to the total wall volume

Fig. 12. Comparison of estimated material parameters for all subjects with results from (a) Nasopoulou et al.13, (a) Wang et al.46 and (c) Xi et al.39 who each performed passive material parameter estimation in healthy humans. Cauchy stress vs. stretch from idealized uniaxial tension along the fiber direction is shown using the corresponding c for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} from the previous studies