Computational construction and design optimization of a novel tri-tube heart valve

Fig. 1. a Experimental construction of the tri-tube tissue-engineered heart valve (TEHV) by suturing three biologically-engineered tubes together. b Comparison between an experimental TEHV and a TEHV constructed and simulated in silico. Figure from (Syedain et al. 2021) reproduced with permission

Fig. 2. Tri-tube valve definition, in silico construction, and simulation conditions. a The top and bottom edges of the conduit are fixed while the material in between is free to move from applied pressure. Portions of the tubes colored red that become the three leaflets in the valve are seen in the expanded view. b Dimension of a single tube with diameter D and height of 50 mm. L is the amount of material needed to be removed to define the leaflet height H given the fixed position of the leaflet base (19 mm above the bottom edge). The red shaded area is the resulting leaflet. The valve geometry resulting from construction is determined entirely by H and D and the constitutive model. c Top view of two-step valve construction. Step 1: each tube is pushed toward a construction plane oriented as shown, then the tubes are flattened by a prescribed pressure simulating the effect of gravity observed during suturing on the lab bench. Step 2: the three planes are progressively bent to form a closed ring of the tubes with the target valve diameter (see Supplementary material 1 for animation). d Pressure profile applied uniformly to the outflow surfaces of the leaflets and outflow segment of the…

Fig. 3. Tube stress–strain behavior and constitutive model fits: a AHYPER model in axial and circumferential directions by fitting high strain rate tension data from planar equi-biaixal testing and low strain rate unconfined compression data using Mclibration. Inset: example of a test sample with speckles placed on the cruciform for strain tracking. The gauge area is demarcated by the black square. b HYPERFORM model used for improved fitting of unconfined compression data and used in valve construction simulation. Two fitted curves shown: the purple fit focused on compression data and the orange fit included averaged tension data. Inset: zoomed fit in compression

Fig. 4. a Simulation snapshot of a closed valve under 7.5 mmHg. The dashed line represents the plane defined to measure coaptation length. b The plane view illustrates the measurement of coaptation length, which is defined as the red line. c Simulation snapshot of a closed valve under 16 mmHg. d Pulse duplicator snapshot of the closed valve

Fig. 5. Design space of leaflet area. Solid circles mark 26 design points. Green markers represent two examples (Cases I and II) discussed subsequently. Blue markers show three design points selected (Cases A-C) for FSI simulation

Fig. 6. Comparison of two design points for dynamics from 1 -1.5 s during valve closure simulation. Case I (D = 16.5 mm, H = 12 mm, A = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$311 m{m}^{2}$$\end{document}311mm2) and Case II (D = 15.625 mm, H = 8.25 mm, A = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$202 m{m}^{2}$$\end{document}202mm2). a Top view of leaflet shape evolution. Measured metrics during t = 1–1.5 s: b coaptation area, c regurgitation area, d pinwheel index, and e prolapse area. See animation in Supplementary material 3 for the evolution of these two cases

Fig. 7. Response surfaces of metrics: a coaptation area, b regurgitation area, c pinwheel index, and d prolapse area. The star labels the optimal design resulting from optimization

Fig. 8. Evolution of the free edge (top view) and velocity contour slice (side view) for three selected designs of approximately the same leaflet area and GOA. The dotted line at t = 0s indicates the location of the slice view. a Case A: D = 15 mm, H = 12 mm. b Case B: D = 16.25 mm, H = 10.75 mm. c Case C: D = 16.875 mm, H = 10 mm. See animation in Supplementary material 4 for the evolution of these three cases

Fig. 9. Particle tracking snapshots for three selected designs. a Case A: D = 15 mm, H = 12 mm. b Case B: D = 16.25 mm, H = 10.75 mm. c Case C: D = 16.875 mm, H = 10 mm. d Evolution of particles “trapped” (retained) in the simulation domain. See animation in Supplementary material 5 for the evolution of these three cases