A preoperative planning procedure of septal myectomy for hypertrophic obstructive cardiomyopathy using image-based computational fluid dynamics simulations and shape optimization

Figure 1. Reconstructed 3D models based on CTA images for selected patients with HOCM.

Figure 2. Initial 3D model of patient 1, and the modified model prepared for steady CFD simulation. The red planes in the LVOT are used to quantify the pressure gradient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta P_{LVOT}$$\end{document} along the LVOT.

Figure 3. Geometric modification of the septal wall for the shape optimization step. The initial model is used to calibrate the inlet mass flow rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{m}}_{in}$$\end{document} and the modified model is used for preoperative planning.

Figure 4. Illustration of boundary conditions for the transient simulation of LVOT. (a) Computaional domain at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0.3\,\hbox {s}$$\end{document}, the wall motion was imposed through dynamic mesh method, the anterior leaflet of mitral valve was colored in blue. (b) Mesh deformation at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0.1\,\hbox {s}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0.3\,\hbox {s}$$\end{document}. (c) Volume change of the computational domain during the cardiac cycle. (d) Pressure profile imposed at the outlet boundary.

Figure 5. The anterior mitral leaflet in the three-chambers view and the corresponding valve region (where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta _{\Gamma , \varepsilon }(\varphi ) > 0$$\end{document}) used by the RIIS valve model at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t = 0.0\,\hbox {s}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t = 0.3\,\hbox {s}$$\end{document}.

Figure 6. Computational mesh topology with a zoom of local refinement around the obstruction region. (a) Mesh generated for steady and transient simulations of patient 0 with RIIS valve model. (b) Mesh generated for steady simulations of patient 1 with exclusion of the aortic and mitral valves from the computational domain.

Figure 7. Distributions of relative pressure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P^\prime$$\end{document} (left) and shape sensitivity (middle) for patient 1. The resection extent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _{SM}$$\end{document} (right) is selected around the region of significant sensitivity (colored in red).

Figure 8. Comparison of the parametric septal wall designed after virtual resection for patient 1 with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{cut}$$\end{document} varies from 4 to 20 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1.25$$\end{document}. The transparent light blue surface corresponds to the initial septal wall.

Figure 9. Comparison of the parametric designed septal wall deformation with n varies from 0.5 to 1.5 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{cut}=20$$\end{document} for patient 1.

Figure 10. Transferring optimal resection (blue) from systole (left) to diastole (right) based on the RBF method using nodes of the interventricular septum (red) as control points.

Figure 11. Workflow of the septal myectomy planning procedure.

Figure 12. Flow fields within the extruded part of inlet and outlet of the steady simulation of LVOT for Patient 0. (a) Velocity distribution at five parallel slices in the extruded part of inlet. (b) Axial velocity profil along the local axis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^\prime$$\end{document} in the extruded part of inlet. (c) Velocity distribution at a slice in the extruded part of outlet.