Fluid–Structure Interaction Models of Bioprosthetic Heart Valve Dynamics in an Experimental Pulse Duplicator

Figure 1. (a) A customized pulse duplicator based on the commercial ViVitro pulse-duplicator system adapted with prototype electro-optical subsystem for measuring aortic valve projected dynamic valve area (PDVA), or alternate configuration for measuring mitral valve PDVA. (b) A schematic diagram of the custom pulse duplicator based on the commercial ViVitro pulse-duplicator system adapted with prototype electro-optical subsystem for measuring aortic valve PDVA or alternate configuration for measuring mitral valve PDVA. The commercial ViVitro system is similar but lacks the back light and the photo sensor for acquiring PDVA.

Figure 2. (a) Model porcine bioprosthetic valve geometry and fiber architecture. The idealized geometry of the Labcor TLBP A Supra porcine aortic valve is reconstructed based on literature values.20 The model fiber structure is generated using Poisson interpolation.69 (b) Model bovine pericardial bioprosthetic valve geometry and fiber architecture. This valve geometry is obtained from micro-CT imaging of a Carpentier–Edwards PERIMOUNT RSR Model 2800 surgical aortic heart valve. The model fiber structure is generated based on the small angle light scattering (SALS) data of Sun et al.66 The SALS data show that the mean fiber orientation of a bovine pericardial valve leaflet is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$45^{\circ }$$\end{document}45∘.

Figure 3. Three-dimensional aortic test section models for the porcine (a) and bovine pericardial (b) BHV simulations along with the reduced-order models that provide driving and loading conditions. Three-element Windkessel models are used at the downstream (outlet) for both cases. (a) A three-element Windkessel model is used at the upstream (inlet) for the porcine aortic valve simulations. The pump pressure is derived from pressure and flow data from the ventricular outflow tract of the pulse duplicator. (b) Because the pump flow waveform and atrial pressure are available for the bovine pericardial valve experiments, a more detailed pump model is used upstream for the bovine pericardial valve simulations.

Figure 4. Comparisons between simulated and experimental pressure and flow rate waveforms for the porcine aortic valve (a, b) and bovine pericardial valve (c, d). The experimental waveforms shown are the average waveforms over 10 consecutive cycles of data, with shaded regions showing where 95% of the data fall. The experimental and computational stroke volumes for the porcine aortic valve are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$69.4 \pm 0.4$$\end{document}69.4±0.4 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$72.7\,{\text {mL}},$$\end{document}72.7mL, respectively, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$71.6 \pm…

Figure 5. Comparisons between simulated and experimental projected dynamic valve area (PDVA) for the porcine aortic (a) and bovine pericardial (b) valves. (a) The experimental data (acquired using the custom apparatus depicted in Fig. 1b) are manually aligned with the beginning of the valve opening with the simulation data. The experimental PDVA measurement shown is the average PDVA over 10 consecutive cycles of data with shaded region showing where 95% of the data fall. (b) The experimental data are acquired using a high-speed videographic method, from which we reconstruct PDVA data using automatic image analysis using DataTank. Videographic data are available for only a single cycle for the pericardial BHV.

Figure 6. Detailed comparison of the bovine pericardial valve leaflet kinematics during closure in the simulation (top) and experiment (bottom). The simulation captures the behavior of each of the leaflets closing one at a time (order: bottom \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}→ right \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}→ left leaflet) as observed in the experiment. The time increment between frames for simulation is 9.6 ms.

Figure 7. Cross-section view of simulated flow patterns using the porcine aortic (a) and bovine pericardial (b) valve models. The color shows the axial velocity through the aortic test section at the center plane, with red indicating forward flow and blue indicating reverse flow. (a) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re_{{\text {peak}}} = \text{20,576}.$$\end{document}Repeak=20,576. (b) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re_{{\text {peak}}} = \text{19,330}.$$\end{document}Repeak=19,330. The time increment between frames is 57.6 ms.

Figure 8. Leaflet kinematics of the porcine aortic (a) and bovine pericardial (b) valves during opening. (a) The time increment between frames is 1.92 ms. (b) The time increment between frames is 3.84 ms.

Figure 9. Leaflet kinematics of the porcine aortic (a) and bovine pericardial (b) valves during closure. (a) The time increment between frames is 9.6 ms. (b) The time increment between frames is 19.2 ms.

Figure 10. von Mises stress (kPa) on the porcine aortic (a, c) and bovine pericardial (b, d) valves during diastole (a, b) and systole (c, d). The time increment between frames in panels (a, b) is 30.72 ms, and the time increment between frames in panels (c, d) is 11.52 ms.