Bioprosthetic aortic valve diameter and thickness are directly related to leaflet fluttering: Results from a combined experimental and computational modeling study

Figures

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  Experimental and computational models quantify influences of device geometry on valve dynamics.

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  Figure 1. Experimental and computational pulse duplicators. A, Customized pulse duplicator with electro-optical subsystem for measuring aortic valve projected dynamic valve area. B, Computer model of the aortic valve test section in the pulse duplicator with pericardial bioprosthetic heart valve (BHV) and reduced-order models of the upstream and downstream system components. C, Three-dimensional rendering of the model BHV leaflets. Leaflet kinematics are detailed on the highlighted cross-sections in Figures E5 and E6.

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  Figure 2. Analysis of experimental and computational leaflet kinematics. Experimental measurements show variations over 10 consecutive cycles, with shaded regions showing where 95% of the data fall. For each available valve diameter, the computer model matches the experimental operating conditions, which are different for each valve. Panels A through C compare simulated results to the experimental data for projected dynamic valve area (PDVA), and insets show the simulated displacement of the leaflet tip from the center of the valve. Panels D through F show frequency analyses. Dominant fluttering frequencies from experimental and simulated PDVA signals and simulated tip displacement signals are, respectively, D, 70.97 ± 2.11 Hz, 59.63 Hz, 59.26 Hz; E, 32.74 ± 3.14 Hz, 38.62 Hz, 32.88 Hz; and F, 26.03 ± 1.04 Hz, 21.05 Hz, 26.32 Hz. Smaller valves clearly show markedly higher fluttering frequencies.

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  Figure 3. Comparison of linear regressions of fluttering frequency versus valve diameter between simulations and experiments. Blue circles represent dominant fluttering frequency data from simulations that match the different experimental operating conditions of each device. Red triangles represent dominant fluttering frequency data with respect to valve diameters obtained from experimental projected dynamic valve area measurements. Linear regressions demonstrate that both simulation and experiment show negative relations between frequency response and valve diameter, with proportionality coefficients –5.65 Hz/mm and –7.79 Hz/mm, respectively, for simulation (blue solid) and experiment (red dashed).

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  Figure 4. Linear regressions of fluttering frequency versus valve diameter and leaflet thickness under consistent operating conditions. Blue circles represent dominant fluttering frequency data from simulations with respect to (A) valve diameter and (B) leaflet thickness under consistent operating conditions. Linear regressions demonstrate that simulations show (A) negative relations between frequency response and valve diameter, with proportionality coefficient –5.65 Hz/mm, and (B) positive relations between frequency response and leaflet thickness, with proportionality coefficient 41.1 Hz/mm.

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  Figure 5. Comparison of leaflet fluttering frequency versus scaling model for different bioprosthetic heart valve (BHV) diameters and leaflet thicknesses. Panel A compares fluttering frequencies obtained for different BHV diameters to frequencies determined from the scaling law. Panel B compares fluttering frequencies obtained for different BHV leaflet thicknesses to frequencies determined from the scaling law. The results are consistent in both cases.

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  Figure 6. Linear regression of fluttering frequency versus valve diameter at physiological Reynolds numbers with consistent operating and flow conditions. Blue circles represent dominant fluttering frequency data with respect to valve diameters obtained for a fixed operating condition but varying flow conditions (quantified by Reynolds number). Red triangles represent dominant fluttering frequency data with respect to valve diameters in which the driving condition is modified to match Reynolds number. Linear regressions show negative relations between frequency response and valve diameter, with proportionality coefficients –5.83 Hz/mm (blue solid) and –4.10 Hz/mm (red dashed) for consistent operating conditions and flow conditions, respectively.

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  Figure 7. Graphical abstract that summarizes methodology, main results, and clinical implications. We leverage both (A) experimental and (B) computational platforms (C) to analyze the dominant leaflet flutter frequency. Our main results suggest that as valve diameter decreases and leaflet thickness increases the flutter frequency increases independent of flow and operating conditions. Our proposed scaling model rationalizes these results. This study may help us better understand geometrical and mechanical factors to optimize bioprosthetic heart valve (BHV) design.

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  Figure E1. Reduced-order models that provide driving and loading conditions. Three-element Windkessel (R-C-R) models are used at the downstream (outlet) for both cases. A, A three-element Windkessel model is used at the upstream (inlet) for simulations that use saline as test fluid. B, A more detailed upstream model is used at the upstream for simulations that use glycerin-based blood analog as test fluid. Because pump flow rate data are available for the experiments that used a glycerin-based blood analog, we are able to modify the pump flow rate to impose consistent flow conditions necessary for the study reported in Figure 7.

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  Figure E2. Reduced-order model fits of the experimental pressure data for the saline and glycerin-based analog cases. Panels A through D show the fits of the experimental downstream pressure data for both saline and glycerin-based blood analog cases. These fits are obtained using the nonlinear optimization routine fmincon in MATLAB by comparing experimental values of downstream pressure to the computed downstream pressure from the reduced-order model with experimental values of downstream flow rate as inputs to the model. Panel E shows the experimental upstream pressure data for glycerin-based blood analog case. The fit is obtained by comparing experimental values of upstream pressure to the computed upstream pressure from the reduced-order model with experimental values of left atrial pressure and pump flow rate as inputs to the model.

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  Figure E3. Parameter fitting for the valve material models. A, Schematic of the biaxial tensile tests of Kim and colleagues20 for bovine pericardium tissue specimens to study their material response. X1 is the preferred mean fiber direction, also shown by gray lines, X2 is the cross-preferred fiber direction, and X′1 and X′2 are the directions in which forces were applied. B, Parameter fitting for the bovine pericardial valve using the equibiaxial data from Kim and colleagues20 compared with the plot using parameters determined by Kim and colleagues, who used a finite element model of the biaxial test.

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  Figure E4. Analysis of experimental and computational pressure and volumetric flow rates. Experimental measurements show variations over 10 consecutive cycles, with shaded regions showing where 95% of the data fall. For each available valve diameter, the computer model matches the experimental operating conditions, which are different for each valve. We compare simulated (A through C) pressure waveforms and (D through F) flow rates to the experimental data. The simulated pressure and flow rates are in excellent agreement with the experimental data.