Abstract

Current heart valve replacements lack durability and prolonged performance, especially in pediatric patients. In part, these problems may be attributed to the materials chosen for these constructs, but another important contributing factor is the design of the valve, as this dictates hemodynamic performance and impacts leaflet stresses which may accelerate structural valve deterioration. Most current era bioprosthetic valves adhere to a fundamental design where flat leaflets are supported by commissural posts, secured to a sewing ring. This overall design strategy is effective, but functionality and durability can be improved by incorporating features of the native valve geometry. This paper presents a novel workflow for developing and analyzing bio-inspired valve designs computationally. The leaflet curvature was defined using a mathematical equation whose parameters were derived from the three-dimensional model of a native sheep pulmonary valve obtained via microcomputed tomography. Finite element analysis was used to screen the various valve designs proposed in this study by assessing the effect of leaflet thickness, Young's modulus, and height/curvature on snap-through (where leaflets bend against their original curvature), geometric orifice area (GOA) and the stress in the leaflets. This workflow demonstrated benefits for valve designs with leaflet thicknesses between 0.1 and 0.3 mm, Young's moduli less than 50 MPa, and elongated leaflets with higher curvatures. The proposed workflow brings substantial efficiency gains at the design stage, minimizing manufacturing and animal testing during iterative improvements, and offers a bridge between in vitro and more complex in silico studies in the future.

Introduction

Valvular heart disease has become one of the greatest burdens known to man, with the main contributors including calcific aortic stenosis and rheumatic heart disease, affecting almost 1% of the total global population [1]. While repair of the patient's valve is almost always preferred, replacement of the diseased valve is often required [2]. There are approximately 300,000 heart valve replacements performed each year globally and this number is expected to increase to almost 1 × 106 in the next 30 years [2]. The current standard for treatment is a mechanical valve, a bioprosthetic valve, or a human allograft (homograft). Unlike bioprostheses and homografts, mechanical valves have superior durability but require lifelong anticoagulation. Bioprostheses and homografts are susceptible to immune responses and structural valve deterioration [3]. Unfortunately, these poor outcomes tend to manifest earlier for younger patients, forcing them to undergo multiple operations throughout their lifetime [46].

Tissue engineered heart valves have been extensively studied and are appealing in concept, but the presence of host cells in the new valve has not translated into superior outcomes. In vivo testing, including in human studies, reveal instances of leaflet shortening and calcification leading to regurgitation, presumably because of an inability to control cellular behavior in various hosts [7,8]. More promising are polymeric heart valves. Although they have not lived up to the initial expectations since they were first trialed in the 1950s [9,10], technical developments in material science and design have generated renewed interest [11]. Polymeric heart valves have the potential to address the durability issues of mechanical and bioprosthetic valves while offering good mechanical, biological, and hemodynamic properties. Throughout these years, researchers have mainly steered their focus toward the different types of elastomeric polymers that have shown ideal characteristics as a biomaterial on top of their diverse processability. While significant attention has been paid to the material properties of existing valve substitutes, such as development of anticalcification treatments of bovine pericardium, innovation in valve design has been slow. For bioprostheses and most new generation polymeric valves, where flat leaflets are engineered to fit into a mount, a negative consequence is the substantial transvalvular pressure gradients, particularly in small size bioprostheses, that add significant afterload for the ventricle. Several groups proposed valve designs with mathematically derived leaflet shapes based on bioprostheses, but because of the non-native valve geometry, their performance may not necessarily be a direct representation of the real valve [1218].

In this paper, we present a streamlined workflow for producing a biomimetic valve design that is inspired by the native heart valve (Fig. 1). The novel methodology consists of microcomputed tomography (micro-CT) imaging to obtain a three-dimensional (3D) model of a sheep pulmonary valve. This model is taken into computer-aided design (cad) software, where it is used to produce a representative heart valve geometry whose curvature is based on a mathematical equation extracted from the micro-CT images. To ensure the proposed valve design was functional, one of the key aspects to investigate was whether the leaflets could fully open during loading. This was assessed computationally through a phenomenon called snap-through, where the valve cusps bend against their original curvature under pressure. Valves that achieved snap-through were considered fully open. Preliminary studies employing finite element analysis (fea) software were used as a screening technique to investigate the impact of leaflet thickness and Young's modulus on snap-through and geometric orifice area, the stress distribution in the valve, as well as to compare performance between valves with different leaflet curvatures and lengths. These computational studies are a steppingstone toward more complex fluid structure interaction (FSI) analysis that can account for the flow interaction with the valve. Further, they may help to bridge in silico and in vitro studies of valve design.

Fig. 1
Process flow diagram of workflow from first stages of micro-CT scanning to computational analysis. The leaflet that is chosen to extract the geometry is highlighted by an arrow. A curve extraction tool (spaceclaim) was used to extract the geometry of the curve which is traveling along the length of the selected leaflet.
Fig. 1
Process flow diagram of workflow from first stages of micro-CT scanning to computational analysis. The leaflet that is chosen to extract the geometry is highlighted by an arrow. A curve extraction tool (spaceclaim) was used to extract the geometry of the curve which is traveling along the length of the selected leaflet.
Close modal

Methods

Microcomputed Tomography Imaging.

The three leaflets of pulmonary heart valves naturally bend in a way where the fibrosa (outflow layer) is in compression and the ventricularis (inflow layer) is under tension. Both the natural curvature and tri-layered microstructure of leaflets are complex yet important design aspects that are crucial to the valve's mobility and load-bearing ability [1922]. They are what allow for proper coaptation during diastole and large enough orifice openings during systole, enabling superior function and durability. Cusp shape evidently plays a central role in valve physiology, and therefore emulating this feature could result in improved performance.

Microcomputed tomography was used to derive the leaflet curvature of freshly dissected sheep pulmonary heart valves. Each valve was rinsed in sterile phosphate-buffered saline before being fixed into a small clear container. The leaflets were placed in a semiclosed position to best represent native unloaded curvature. Specimen cusps were either stitched or superglued to help keep them in the unloaded position. No fixing or staining agents were used as both chemicals can lead to wrinkling and stiffening of biological tissues. Upon closing the lid of the container to prevent dehydration from occurring, the valve was mounted into the micro-CT scanner (SkyScan 1272, Bruker). The following scanning parameters were established after numerous trials and optimization: 21.53 μm pixel size, 100 kV voltage, 100 μA current, 2100 s exposure time, 1224 × 820 pixel resolution, 0.4 deg rotation, 360 deg scanning, and an aluminum (Al) 0.5 + copper (Cu) 0.038 filter. Scans were typically run for 45 min to 1 h and the obtained two-dimensional slices were exported as resized portable network graphic files.

In subsequent steps, image reconstruction (NRecon, Bruker) was carried out to create a clean 3D representation of the valve geometry by going through several iterations of smoothing, ring artifact removal, and fixed misalignment. The reconstructed model underwent segmentation (amira, Thermo Fisher Scientific) by means of either thresholding or water shedding for more complex geometries. The resulting valve construct was saved as a stereolithography binary little endian file. This workflow was repeated for all valve samples studied.

Bio-Inspired Geometry Development.

To create a bio-inspired valve geometry on computer-aided design (cad) software (spaceclaim, ansys), one curve of an appropriately shaped leaflet from the micro-CT scanned 3D valve body was obtained using a curvature extraction tool. The extracted curve was plotted using a two-dimensional Cartesian system and then printed out. Then, using a digital caliper, numerous (x, y) coordinate points were measured along the plotted curve (similar to plots in Fig. 5(a)). Note that more sophisticated methods could be used to avoid the manual measurement of coordinates. For instance, image processing tools could be used to extract the required coordinate data directly from the digital image of the curve that was obtained from the middle of the leaflet. The measured coordinates of the points were then used to fit the cubic polynomial function
y=a3x3+a2x2
(1)

The analytical curve obtained from Eq. (1) is in fact the mathematical approximation of the curve that was extracted from the 3D scanned image of the leaflet. There is no constant term in Eq. (1) as this simply shifts the curve in space along the y-axis (pointing “upward” with respect to the curve). Initially, a small linear term was retained but it was found that a1 (the coefficient of the x term) was negative. While the term was small, it introduced a negative slope near the valve base. Although this change of slope near the valve base, from negative to positive, had a minimal effect on the valve shape, overall, it was later shown to be detrimental to meshing for the finite element analysis (FEA) model so the term was removed.

Using another cad software (Creo Parametric, PTC), the equation was plotted on the default coordinate system in its parametric form. The resulting curve was rotated around the y-axis two times (three in total) with a 60 deg angle between each adjacent curve. The curves were lofted together to form a smooth surface which was defined as a single leaflet of the eventual tri-leaflet valve. A single leaflet was constructed such that the x-axis represented the distance from the leaflet belly to the free edge and the y-axis was the leaflet height. An axis parallel to the y-axis was created facing the inner side of the leaflet, at the middle of the cusp as illustrated in Fig. 2(c). The leaflet was rotated 120 deg about the axis, such that three equidistant and symmetrical leaflets were formed. Datum points were sketched at the commissures and lowermost belly region for each leaflet. Smooth lines were used to connect the commissures between adjacent cusps and curves were chosen for joining neighboring points at the belly using the spline tool. Each set of commissural lines, belly splines, and adjoining sides of leaflets defined one of three interleaflet regions of the resulting valve. Once all interleaflet regions were created, all surfaces were merged to form a single body. The final geometry was taken into a FEA modeling software (ansysmechanical) for screening.

Fig. 2
Detailed step-by-step development of tri-leaflet valve design from scan-derived mathematical equation: (a) three copies of curved defined by scan-derived mathematical equation rotated around the y-axis (side view), (b) leaflet geometry produced from lofting together the three curves (side view), (c)leaflet geometry patterned around central axis to produce three symmetrical leaflets (side view), (d) formation of interleaflet region between adjacent leaflets (side view), (e) formation of all three interleaflet regions (top view), and (f) full tri-leaflet valve (side view)
Fig. 2
Detailed step-by-step development of tri-leaflet valve design from scan-derived mathematical equation: (a) three copies of curved defined by scan-derived mathematical equation rotated around the y-axis (side view), (b) leaflet geometry produced from lofting together the three curves (side view), (c)leaflet geometry patterned around central axis to produce three symmetrical leaflets (side view), (d) formation of interleaflet region between adjacent leaflets (side view), (e) formation of all three interleaflet regions (top view), and (f) full tri-leaflet valve (side view)
Close modal

Setting Up Computational Modeling.

Computational modeling using ansysmechanical 2022R1 was utilized as a screening technique to help validate the established workflow and the resulting bio-inspired valve geometries before in vitro fabrication and testing. This setup allows for a more efficient translation from CAD models to real polymeric heart valves manufactured in the laboratory.

The equation of motion for an elastic solid is given by
ρs2ut2=·σ
(2)

where ρs is the instantaneous material density and u is the displacement vector.

Using conservation of mass
ρs=ρ0det(F)
(3)
where ρ0 is the undeformed density and F is the deformation gradient, defined by
F=uX
(4)

where X is the location of the undeformed model.

The strain, e, is related to the displacement via
e=12(u+(u)T)
(5)
Assuming a linear elastic solid, the stress tensor, σ, is given by
σ=νE(1+υ)(12υ)tr(e)I+E(1+υ)e
(6)

where E and ν are the Young's modulus and Poisson's ratio, respectively. tr denotes the trace of the tensor and I is the unit tensor.

The leaflet thickness varied over the range of 0.1–0.7 mm in this study. Shells are the best choice of element as they can represent the thickness effect well and have rotational and translational degrees-of-freedom. A quadratic basis function was applied and five integration points through the element thickness were used to ensure the snap through behavior was captured properly. A mesh sizing of 0.5 mm was applied to all surfaces (Fig. 3) which gave mesh independent results. To ensure the solution was not influenced by the mesh size, simulations were run for mesh element sizes of 0.4 mm, 0.5 mm, and 0.6 mm for the base case conditions described below. The differences between displacement values varied by less than 1%, showing mesh independence. The 0.5 mm mesh was chosen for all future simulations.

Fig. 3
Meshed valve geometry with a 0.5 mm face sizing (a) top view and (b) side view
Fig. 3
Meshed valve geometry with a 0.5 mm face sizing (a) top view and (b) side view
Close modal

The material properties used for this model were those of a promising grade of polyurethane elastomer (polysiloxane urethane urea). The valve material properties used were Young's modulus of 15 MPa [23], a Poisson's ratio of 0.45 [24,25], and a density of 1000 kg m−3. A final pressure of 600 Pa, which was applied using temporal ramping over 0.8 s and then held constant for another 0.2 s was used as the loading. The ramping makes the implicit solution easier (see Supplemental Fig. S1 available in the Supplemental Materials on the ASME Digital Collection). The maximum pressure is inside the range of typical values, and this loading resulted in fully opened leaflets for most valve models. Higher pressures did not change the geometric orifice area (GOA) or opening behavior for given conditions. The model was constrained using a fixed support applied to the three base edges of the valve.

The transient implicit numerical method using the sparse (symmetric) solver was used to solve the resulting equations. An initial time-step of 1 ms was set and it was allowed to vary between 0.1 ms and 10 ms, ensuring convergence at each step. Once solved, the total deformation, equivalent stress, and equivalent strain were evaluated for analysis. A typical simulation took 1500 CPU seconds using an Intel® Xeon® Bronze 3204 1.90 GHz processor using six cores. Table 1 summarizes the material parameters and boundary conditions which were used for the computational modeling.

Table 1

List of material parameters and boundary conditions used in the computational modeling

Density (kg m−3)E (MPa)Poisson's ratioThickness (mm)Height (mm)Pressure (Pa)Pressure profileFixed boundary
10005–5000.450.1–0.77.73–24.09600Linear ramp from 0 s (0 Pa) to 0.4 s (600 Pa), then held at 600 Pa from 0.4 s to 0.6 s.Valve bottom edge
Density (kg m−3)E (MPa)Poisson's ratioThickness (mm)Height (mm)Pressure (Pa)Pressure profileFixed boundary
10005–5000.450.1–0.77.73–24.09600Linear ramp from 0 s (0 Pa) to 0.4 s (600 Pa), then held at 600 Pa from 0.4 s to 0.6 s.Valve bottom edge

Method for Measuring Geometric Orifice Area.

The GOA is defined as the anatomical cross-sectional area formed by the leaflet free edges [26]. The fully open valve geometry was exported as an stereolithography file and read into the cad software. A plane parallel to the valve base was created and dragged to an appropriate position along the y-axis that could be used to determine the area formed by the free edges (Fig. 4(a)). This plane was placed at the highest point of the valve where the free edges and commissural regions would form a closed-loop. The closed-loop opening which was formed by the intersection of this plane with the valve was used to create a surface body and its area was read using a measuring tool in the software. The resulting surface area was characterized as the GOA in millimeters squared.

Fig. 4
(a) Schematic diagram illustrating the planes where GOA and base area were measured; (b) GOA/base ratio versus simulation number; horizontal line indicates a GOA/Base ratio of 0.84, the threshold for snap-through; (c and d) diagrams of valve designs that snapped through and (e and f) did not snap-through, from top and side views. Valves are approximately 30 mm in diameter.
Fig. 4
(a) Schematic diagram illustrating the planes where GOA and base area were measured; (b) GOA/base ratio versus simulation number; horizontal line indicates a GOA/Base ratio of 0.84, the threshold for snap-through; (c and d) diagrams of valve designs that snapped through and (e and f) did not snap-through, from top and side views. Valves are approximately 30 mm in diameter.
Close modal

Development of Various Valve Models.

From the derived valve leaflet curvature equation, several geometries with varying curvatures were developed by modifying the initial equation. A list of all models in order of descending leaflet height (from longest to shortest) is shown in Supplemental Table S1 available in the Supplemental Materials on the ASME Digital Collection. For each geometry, the x3 and x2 term coefficients, a brief description, leaflet height, midleaflet curvature, and end curvature were tabulated. The mid- and end curvatures were calculated from the second derivative at x=7.3mm and x=14.5mm, respectively (Fig. 5(a)). These points were chosen as they intersected all curves at the middle and end.

Fig. 5
Demonstration of how the scan-derived mathematical equation is implemented in the valve design: (a) graph showing curves with modified equations used to define leaflet curvature for seven valve models from longest to shortest leaflets; the x-axis represents the radius of the valve base and x values range from 0 to 14.5 mm; the y-axis represents the height of the leaflets in millimeters; the first vertical dashed line represents an x value of 7.27 mm where the midcurvature was calculated and the second vertical dashed line represents an x value of 14.5 mm where the end curvature was measured; the data points are the measured values directly obtained from the scanned images; (b) side profile of a leaflet where the highlighted curve represents its curvature given by the mathematical equation; (c) side view of whole tri-leaflet valve where a single leaflet is highlighted and the same curve based on an equation illustrated in (b) is shown
Fig. 5
Demonstration of how the scan-derived mathematical equation is implemented in the valve design: (a) graph showing curves with modified equations used to define leaflet curvature for seven valve models from longest to shortest leaflets; the x-axis represents the radius of the valve base and x values range from 0 to 14.5 mm; the y-axis represents the height of the leaflets in millimeters; the first vertical dashed line represents an x value of 7.27 mm where the midcurvature was calculated and the second vertical dashed line represents an x value of 14.5 mm where the end curvature was measured; the data points are the measured values directly obtained from the scanned images; (b) side profile of a leaflet where the highlighted curve represents its curvature given by the mathematical equation; (c) side view of whole tri-leaflet valve where a single leaflet is highlighted and the same curve based on an equation illustrated in (b) is shown
Close modal

Note that designs with different curvatures and equations resulted in leaflets of different lengths because the diameter of the valve geometries was kept constant at 30 mm. This was achieved geometrically by fixing the range of x values for each curve as seen in Fig. 5(a). Here, the x-axis represents the radius/diameter/base of the valve and ranges from 0 to 14.5 mm, and the y-axis shows the valve height (mm). Therefore, the distance from the leaflet belly (attached edge) to the leaflet free edge was fixed. Due to having different equations, each curve yielded different heights (i.e., different y values).

Generally, longer valves had higher curvatures than those with shorter leaflets and thus a descending trend was observed (see Supplementary Table S1 available in the Supplemental Materials on the ASME Digital Collection). This was true for all but valves 3 and 5, which showed increases in both the mid- and end-curvatures compared with the models with longer leaflets. The main difference between these constructs and others was that their equation was modified by changing the coefficient of the quadratic term rather than the cubic term. The trends relating to changes in curvature were independent of where the second derivative was calculated due to the form of the equation.

Base Case.

Detailed studies investigating the effect of leaflet thickness, Young's modulus, and curvature/leaflet height on GOA and stress were performed on this valve design. As previously discussed, GOA is an essential parameter that can be used to characterize the opening behavior of a valve. Stress magnitude and location are also important factors to consider in the development of a durable and functional heart valve replacement. It has been previously shown that local stress patterns influence mechanical and physical durability (tearing) [2729], as well as biological characteristics such as calcification at regions of concentrated stress on the leaflets [12,30,31]. Localized concentration of stress leads to creation of microcracks and tears, causing rapid deterioration of valves. Using computational modeling to simulate the stress pattern experienced by the valve is an efficient way to better understand the localized concentration of stress for different valve designs.

After several iterations and preliminary simulations, valve 2 with long leaflets was chosen as the base case due to its ability to snap through for the various conditions, i.e., with changes to the leaflet thickness and the elastic modulus. The base area of this valve was approximately 718 mm2. The following were used as reference values based on real pulmonary valve properties: 0.2 mm leaflet thickness [32] and 15 MPa Young's modulus [23]. With the given conditions and setup, a 600 Pa pressure was enough to allow for complete valve opening for most models.

Results and Discussion

Using the developed workflow, in silico studies were performed to evaluate the effect of different parameters on the opening performance of the valve. This assisted in determination of the best models for FSI studies and in vitro analysis. As the method of analysis chosen did not involve any fluid dynamics, the GOA was used instead of the effective orifice area as a measure of valve opening for comparative studies. Table S2 available in the Supplemental Materials on the ASME Digital Collection lists the values for GOA and peak stress which were obtained computationally for the seven valve models.

Importance of Snap-Through.

As mentioned earlier, snap-through is the term given to any valve model that could bend against the natural leaflet curvature once in the fully opened position, analogous to the movement of native leaflets (Figs. 4(c)4(f)). This would inevitably result in a larger and more circular orifice area, which would allow for a more biomimetic hemodynamic performance due to decreased resistance to blood flow (see Supplement Material on the ASME Digital Collection for movies showing dynamic behavior). After multiple simulations, a quantitative method for defining snap-through was established using the GOA to Base area ratio. The Base area of each construct was found on the plane coinciding with the base of the valve (as the name suggests) and is indicated in Fig. 4(a). The surface area of the base was calculated using the same protocol as the GOA using cad software. The GOA to Base ratio is simply defined as the GOA divided by the base area. It was observed that regardless of input parameters (i.e., leaflet thickness, modulus, curvature, length) a GOA to Base ratio greater than 0.84 would result if snap-through occurred (Fig. 4(b)). This is, to the best of our knowledge, a novel finding that has not been reported previously.

Effect of Leaflet Thickness on Geometric Orifice Area and Stress.

The thickness of leaflets has previously been shown to greatly impact the flow performance of polymeric valves [33]. From the results, it is evident that leaflet thickness has a significant impact on both the GOA and stress. In general, increasing the leaflet thickness caused a decrease in GOA for the same elastic modulus (15 MPa) and applied pressure (600 Pa) (Fig. 6(a)). A gradual decrease in orifice area followed by a nearly linear trend for thicknesses between 0.4 and 0.7 mm was observed. Snap-through and large circular orifices (697–621 mm2) were demonstrated only for the thinner valves. Valves with thicknesses greater than 0.4 mm were not able to bend against their natural curvature and due to the restricted leaflet mobility, only produced small triangular openings. It is apparent that even slight changes in leaflet thickness can significantly influence their opening behavior. For the chosen setup, the leaflet thickness should be limited to 0.3 mm. As native valve leaflets are immensely thin and flexible, it is promising to see that thinner leaflets exhibited snap-through and large GOAs.

Fig. 6
Graphs demonstrating effect of different parameters on GOA and GOA/base ratio: (a)GOA versus leaflet thickness ranging from 0.1 to 0.7 mm for base case valve model; (b) GOA versus leaflet Young's modulus ranging from 5 to 300 MPa for the base case valve model; (c) GOA versus end curvature for seven different valve designs where valves were produced from equations with changes to their a3 parameter or a2 parameter; (d) GOA/Base ratio versus end curvature for seven different valve designs where valves were produced from equations with changes to their a3 parameter or a2 parameter; (e) versus leaflet height for seven different valve designs
Fig. 6
Graphs demonstrating effect of different parameters on GOA and GOA/base ratio: (a)GOA versus leaflet thickness ranging from 0.1 to 0.7 mm for base case valve model; (b) GOA versus leaflet Young's modulus ranging from 5 to 300 MPa for the base case valve model; (c) GOA versus end curvature for seven different valve designs where valves were produced from equations with changes to their a3 parameter or a2 parameter; (d) GOA/Base ratio versus end curvature for seven different valve designs where valves were produced from equations with changes to their a3 parameter or a2 parameter; (e) versus leaflet height for seven different valve designs
Close modal

For the range of thicknesses that were investigated (0.1–0.7 mm), the maximum von-Mises stress and the stress distribution were also compared in Fig. 7. The models that snapped through showed a maximum stress of 1–1.2 MPa which is comparable with other studies [34,35]. Areas of high stress were seen on the leaflet belly and interleaflet components at the regions of snap-through. Moderate values of stress were observed in the commissures due to their role in supporting the fully opened leaflets. Relatively low stresses were exerted on most parts of the leaflet faces and interleaflet regions closer to the base of the valve. The stress was spread evenly around the valve showing symmetrical opening of the leaflets. The 0.3 mm thick valve exhibited more areas with stress concentration and lower peak stress in comparison with the 0.1 mm and 0.2 mm models. For thicknesses greater than 0.3 mm, valves did not snap-through as previously mentioned. The highest stress was seen around the commissural regions for these constructs and moderate stress values were observed at the base of the valve. The valve with 0.4 mm thickness demonstrated the highest maximum stress of 1.3 MPa. This value decreased for thicker leaflets, with the 0.7 mm valve showing a 0.6 MPa maximum stress. Although thicker leaflets generally resulted in lower maximum stresses, their poor opening behavior rules out their use. These findings propose focusing on thinner valve designs which result in larger GOAs and have maximum von-Mises stresses within an acceptable range.

Fig. 7
Stress distribution from side and top views for valves with different leaflet thicknesses: (a) 0.1 mm, (b) 0.2 mm, (c)0.3 mm, (d) 0.4 mm, (e) 0.5 mm, (f) 0.6 mm, and (g) 0.7 mm. Scale is in MPa.
Fig. 7
Stress distribution from side and top views for valves with different leaflet thicknesses: (a) 0.1 mm, (b) 0.2 mm, (c)0.3 mm, (d) 0.4 mm, (e) 0.5 mm, (f) 0.6 mm, and (g) 0.7 mm. Scale is in MPa.
Close modal

Effect of Leaflet Young's Modulus on Geometric Orifice Area and Stress.

Other than the physical properties of the leaflets and the loads they experience, their intrinsic material characteristics, such as the elastic modulus, also affect the opening performance. As shown in Fig. 6(b) having stiffer leaflets resulted in a decreased opening orifice area for the same thickness (0.2 mm) and applied pressure (600 Pa). As expected, Young's modulus has a significant impact on the GOA. Over a relatively wide range of moduli tested, from 5 to 300 MPa, models demonstrated snap-through when the modulus was less than 25 MPa. The constructs with an elastic modulus of 50 MPa and greater did not snap through. These data demonstrate that a functioning valve construct could be created over a spectrum of stiffnesses, which implies a plethora of materials that could be considered for heart valve implant fabrication.

Young's modulus of the leaflets not only affects the GOA but also has an impact on the stress a valve experiences. The results in Fig. 8 show that the stress distribution was similar for the models that snapped through, i.e., with elastic moduli ranging from 5 to 25 MPa. The highest stress was observed in the belly and interleaflet region at the position where snap through occurred. Moderate stress values were observed in the commissures, with relatively lower stresses elsewhere. Increasing Young's modulus resulted in a much higher maximum stress. Since fully opened valves exhibited similar 3D shapes after opening, all had similar strains. Therefore, those valves with higher Young's modulus resulted in higher stresses in their structure. The maximum stress ranged from 0.5 MPa to 5.8 MPa amongst the different constructs studied. The data in Fig. 9 confirmed that snap-through was not achieved for materials with Young's modulus of 50 MPa or above. For leaflets with a modulus of 50 MPa and above, the stress distribution was visibly different for these models. The regions with the highest stress were shown to be at the commissures, upper interleaflet regions, and valve base. All models presented symmetrical stress distributions. The results clearly demonstrate that for the same leaflet thickness and pressure applied, materials with Young's moduli less than 50 MPa should be considered to avoid excessive stresses and limited valve opening.

Fig. 8
Stress distribution from side and top views for valves that snapped through with different Young's moduli: (a) 5 MPa, (b) 10 MPa, (c) 20 MPa, and (d) 25 MPa. Scale is in MPa.
Fig. 8
Stress distribution from side and top views for valves that snapped through with different Young's moduli: (a) 5 MPa, (b) 10 MPa, (c) 20 MPa, and (d) 25 MPa. Scale is in MPa.
Close modal
Fig. 9
Stress distribution from side and top views for valves that did not snap through with different Young's moduli: (a)50 MPa, (b) 100 MPa, (c) 200 MPa, and (d) 300 MPa. Scale is in MPa.
Fig. 9
Stress distribution from side and top views for valves that did not snap through with different Young's moduli: (a)50 MPa, (b) 100 MPa, (c) 200 MPa, and (d) 300 MPa. Scale is in MPa.
Close modal

Effect of Leaflet Curvature and Height on Geometric Orifice Area and Stress.

For this study, the impacts of a3 and a2 (the coefficients of the x3 and x2 terms, respectively) on GOA and stress were assessed and compared. For the same leaflet thickness (0.2 mm), Young's modulus (15 MPa), and applied pressure (600 Pa), the GOA and GOA to Base ratio were plotted against both the leaflet height and end curvature for each valve design. In general, as shown in Figs. 6(c)6(e), valve models with steeper curvatures and elongated leaflets exhibited better opening performance, i.e., larger GOAs. Almost all models snapped through except for valve 7, and this is further illustrated by a GOA to base ratio that is less than 0.84 (the established threshold). In Fig. 6(c), complex interplay was exhibited by changes in the a3 and a2 coefficients (with respect to the original equation).

For changes in the a3 parameter, there is a definitive pattern where increasing curvature also increases the orifice area. On the other hand, increasing the a2 parameter led to increasing curvature and negligible effect on the GOA. The findings suggest that higher x2 term coefficients could yield larger curvatures and therefore GOAs for valves with shorter leaflets. This is highlighted by valve 5, which has leaflets shorter than those of valves 3 and 4 but has a similar/larger opening area. The general relationship between leaflet height, curvature, and GOA underlines that larger curvatures and longer leaflets will most likely result in better flow performance. For elastomeric polymer valves, this may be beneficial as it may allow for adaptation to valve expansion in younger patients, who suffer from somatic growth and consequent multiple re-operations with current treatments such as bioprosthetic valves [36]. Thus, longer leaflets with steeper curvatures are favored as they may provide both a larger GOA and prolonged coaptation [37]. However, it is pivotal to consider a balance as excessively long leaflets may result in unfavorable wrinkling behavior which can impede blood flow [38].

The seven valve models shown in Fig. 10 generally demonstrated symmetrical stress distributions with the highest von-Mises stress occurring at the regions of snap-through and at the commissures. Interestingly, based on computational simulation results the valves with the longest and shortest leaflets showed the highest maximum stress of more than 1.5 MPa. All other valves in between had a maximum stress of approximately 1.1 MPa. Shorter leaflets also resulted in higher stresses even for models that snapped through, such as valve 6. Of note, experimental data obtained from mechanical testing suggest that for thermoplastic constructs that undergo cyclic movements fatigue strength is approximately 0.5–0.8 of the ultimate strength [39]. In this study, a more conservative stress threshold was selected to prevent fatigue. Under this selected criterion, the maximum stress in the construct must remain below 10% of the ultimate stress of the material. The ultimate stress of most polyurethanes used for fabrication of polymeric heart valves is in the range of 25–50 MPa. Under this assumption, the stress generated in the polymeric heart valves modeled in this study remains below the fatigue threshold. Nevertheless, at the given conditions if the valve is not excessively tall, longer leaflets with higher curvatures most likely have better performance in terms of minimum stresses with even loading and optimal opening behavior.

Fig. 10
Stress distribution from side and top views for valves with different curvatures: (a) valve 1, (b) valve 2, (c) valve 3, (d)valve 4, (e) valve 5, (f) valve 6, and (g) valve 7. Scale is in MPa.
Fig. 10
Stress distribution from side and top views for valves with different curvatures: (a) valve 1, (b) valve 2, (c) valve 3, (d)valve 4, (e) valve 5, (f) valve 6, and (g) valve 7. Scale is in MPa.
Close modal

Limitations

The biomimetic geometry here assumes taking micro-CT scans of real valves in the semiclosed position gives the best representation of natural leaflet curvature. It is very difficult to keep valve leaflets in their natural state without them being inside their native environment. The natural curvature bends in the same direction as fully closed leaflets and as a result, the semiclosed position was chosen to best represent the leaflet curvature.

The valve geometry consists of three completely symmetrical leaflets, which is not necessarily the case for real heart valves. Implementing this symmetry simplifies the design and modeling process but may not necessarily be the best representation of a real heart valve. Nonetheless, the main aim is to be able to produce a synthetic valve that can withstand the dynamic environment in which it is implanted. That is a valve that is both competent and able to fully snap-through/open. For this reason, we believe it is not crucial to mimic the asymmetry of native leaflets but rather, to develop a design that results in a well-functioning valve regardless of the symmetry in its geometry.

We acknowledge that there are limitations in extracting leaflet curvature using the current method. At this stage, only one geometry-defining curve was used to generate the model. A more comprehensive approach to implement biomimicry has been developed based on this work and will be presented as soon as provisional patent protection is granted. This paper presents a methodology through which the micro-CT scanned image of a heart valve is translated to mathematical models rather than an exhaustive design optimization. A much wider range of geometries will be considered in future work.

The material chosen for simulation is isotropic when in reality heart valve tissue is quite complex, heterogeneous, and known to have anisotropic mechanical properties. The material properties used in this study are those of a promising grade of polyurethane (polysiloxane urethane urea) which is currently being considered in one of two polymeric heart valves in clinical trials. Anisotropic fiber orientations for the leaflets will be considered in upcoming studies to more closely mimic native valves. This may be done by introducing patterns on the leaflet design that are analogous to the tri-layered microstructure of valve leaflets. We suspect the behavior of the leaflets would more closely follow that of native valves once this design feature is implemented.

The simulations assume a constant pressure applied to the leaflet face. In a real situation, there will be a pressure drop through the valve. Thus, in a dynamic setup that implements these changes in pressure, the performance of the valve may not necessarily be the same. However, this method is still one of the quickest and simplest ways to predict the opening of different valve geometries before going into more complex in silico analyses. If we can identify valve designs that do not work well in this setup, it is likely they would not work well in a more sophisticated one.

This study only focuses on the opening behavior of the valve. Ultimately, the closing performance of the valve should also be assessed and will be done in future work. We are working on developing a computational setup that runs through both systolic and diastolic behavior in a single cycle to mimic the movement of the leaflets for one real heartbeat.

The model does not include the flexible conduit to which the valve is normally attached but this is not expected to change the trends. It would allow the valve base area to increase slightly but this would affect all valves and therefore, comparison between valve designs would likely not change.

No fluid is introduced in this system for simplicity, and it is assumed that the valve would have similar opening behavior when fluid passes through it. The proposed workflow will be tested and compared with full FSI studies in future work. As previously stated, despite the simplicity of this method of computational analysis, it is still a good measure of valve opening performance and can most definitely be used as a screening tool to decipher what parameters lead to good valve designs.

Conclusion and Future Work

This study reports upon a novel procedure to parameterize a real physical valve, develop a bio-inspired computational valve model, and produce a workflow to evaluate the performance of the suggested valve design rapidly and easily. The proposed system is most useful when implemented as a scoping tool to filter out suboptimal valve geometries and to select designs for further analysis and development. With the suggested workflow, we have managed to achieve realistic outcomes and patterns that are consistent with our expectations. For example, increases in leaflet thickness and Young's modulus resulted in smaller geometric orifice areas and higher stresses. With the solved computational models, interpretation of the outcomes and their implications for the best valve design was determined. From the findings, valves with a leaflet thickness between 0.1 and 0.3 mm, Young's modulus less than 50 MPa, and longer leaflets with higher curvatures are the most favorable.

The aim of this study was to develop a screening technique to aid in the later stages of valve development where improved designs can be tested using the same methods described in this paper. Whilst the current system does not introduce FSI and is limited to simulating the opening behavior of the valves, it is a necessary step that can lead into avenues for more complex future work. Future studies will involve introducing nonlinear, anisotropic, hyperelastic materials, and multimaterial models with improved cusp shapes and valved conduit designs. We plan to perform FSI simulations using several different approaches and validation of these results with in vitro hydrodynamic assessments using pulse duplicator technology. Hydrodynamic testing is currently underway where the preliminary results with the initial valve prototypes are promising.

Acknowledgment

The authors acknowledge the facilities, and the scientific and technical assistance of the Micro-Imaging Facility at the Innovation Centre, Victor Chang Cardiac Research Institute, and Mr Taju Joseph's support from LEAP Australia for his assistance in using Creo Parametric.

Funding Data

  • Medical Research Future Fund (Grant No. MRFF-ARGCHD000015).

  • Australian Research Council (Grant No. ARC DP200102164; Funder ID: 10.13039/501100000923).

References

1.
Coffey
,
S.
,
Roberts-Thomson
,
R.
,
Brown
,
A.
,
Carapetis
,
J.
,
Chen
,
M.
,
Enriquez-Sarano
,
M.
,
Zühlke
,
L.
, and
Prendergast
,
B. D.
,
2021
, “
Global Epidemiology of Valvular Heart Disease
,”
Nat. Rev. Cardiol.
,
18
(
12
), pp.
853
864
.10.1038/s41569-021-00570-z
2.
Yacoub
,
M. H.
, and
Takkenberg
,
J. J.
,
2005
, “
Will Heart Valve Tissue Engineering Change the World?
,”
Nat. Clin. Pract. Cardiovasc. Med.
,
2
(
2
), pp.
60
61
.10.1038/ncpcardio0112
3.
Harris
,
C.
,
Croce
,
B.
, and
Cao
,
C.
,
2015
, “
Tissue and Mechanical Heart Valves
,”
Ann. Cardiothorac. Surg.
,
4
(
4
), p.
399
.10.3978/j.issn.2225-319X.2015.07.01
4.
Baird
,
C. W.
,
Chavez
,
M.
,
Sleeper
,
L. A.
,
Borisuk
,
M. J.
,
Bacha
,
E. A.
,
Burchill
,
L.
,
Guleserian
,
K.
,
Ilbawi
,
M.
,
Nguyen
,
K.
,
Razzouk
,
A.
,
Shinkawa
,
T.
,
Lu
,
M.
, and
Fuller
,
S. M.
,
2021
, “
Reintervention Rates After Bioprosthetic Pulmonary Valve Replacement in Patients Younger Than 30 Years of Age: A Multicenter Analysis
,”
J. Thorac. Cardiovasc. Surg.
,
161
(
2
), pp.
345
362
.10.1016/j.jtcvs.2020.06.157
5.
Hofferberth
,
S. C.
,
Saeed
,
M. Y.
,
Tomholt
,
L.
,
Fernandes
,
M. C.
,
Payne
,
C. J.
,
Price
,
K.
,
Marx
,
G. R.
,
Esch
,
J. J.
,
Brown
,
D. W.
,
Brown
,
J.
,
Hammer
,
P. E.
,
Bianco
,
R. W.
,
Weaver
,
J. C.
,
Edelman
,
E. R.
, and
Del Nido
,
P. J.
,
2020
, “
A Geometrically Adaptable Heart Valve Replacement
,”
Sci. Transl. Med.
,
12
(
531
), p. eaay4006. 10.1126/scitranslmed.aay4006
6.
Saxena
,
A.
,
Salve
,
G. G.
,
Betts
,
K.
,
Arora
,
N.
,
Cole
,
A. D.
,
Sholler
,
G. F.
,
Orr
,
Y.
,
Ayer
,
J. G.
, and
Winlaw
,
D. S.
,
2021
, “
Outcomes Following Heterotopic Placement of Right Ventricle to Pulmonary Artery Conduits
,”
World J. Pediat. Congenital Heart Surg.
,
12
(
2
), pp.
220
229
.10.1177/2150135120975769
7.
Bennink
,
G.
,
Torii
,
S.
,
Brugmans
,
M.
,
Cox
,
M.
,
Svanidze
,
O.
,
Ladich
,
E.
,
Carrel
,
T.
, and
Virmani
,
R.
,
2018
, “
A Novel Restorative Pulmonary Valved Conduit in a Chronic Sheep Model: Mid-Term Hemodynamic Function and Histologic Assessment
,”
J. Thorac. Cardiovasc. Surg.
,
155
(
6
), pp.
2591
2601
.10.1016/j.jtcvs.2017.12.046
8.
Uiterwijk
,
M.
,
Smits
,
A. I.
,
van Geemen
,
D.
,
van Klarenbosch
,
B.
,
Dekker
,
S.
,
Cramer
,
M. J.
,
van Rijswijk
,
J. W.
,
Lurier
,
E. B.
,
Di Luca
,
A.
,
Brugmans
,
M. C.
,
Mes
,
T.
,
Bosman
,
A. W.
,
Aikawa
,
E.
,
Gründeman
,
P. F.
,
Bouten
,
C. V.
, and
Kluin
,
J.
,
2020
, “
In Situ Remodeling Overrules Bioinspired Scaffold Architecture of Supramolecular Elastomeric Tissue-Engineered Heart Valves
,”
JACC Basic Transl. Sci.
,
5
(
12
), pp.
1187
1206
.10.1016/j.jacbts.2020.09.011
9.
Braunwald
,
N. S.
,
Cooper
,
T.
, and
Morrow
,
A. G.
,
1960
, “
Complete Replacement of the Mitral Valve: Successful Clinical Application of a Flexible Polyurethane Prosthesis
,”
J. Thorac. Cardiovasc. Surg.
,
40
(
1
), pp.
1
11
.10.1016/S0022-5223(19)32638-8
10.
Roe
,
B. B.
, and
Moore
,
D.
,
1958
, “
Design and Fabrication of Prosthetic Valves
,”
Exp. Med. Surg.
, 16(2–3), pp.
177
182
.https://pubmed.ncbi.nlm.nih.gov/13586325/
11.
Oveissi
,
F.
,
Naficy
,
S.
,
Lee
,
A.
,
Winlaw
,
D. S.
, and
Dehghani
,
F.
,
2020
, “
Materials and Manufacturing Perspectives in Engineering Heart Valves: A Review
,”
Mater. Today Bio
,
5
, p.
100038
.10.1016/j.mtbio.2019.100038
12.
Gharaie
,
S. H.
, and
Morsi
,
Y.
,
2015
, “
A Novel Design of a Polymeric Aortic Valve
,”
Int. J. Artif. Organs
,
38
(
5
), pp.
259
270
.10.5301/ijao.5000413
13.
Hamid
,
M. S.
,
Sabbah
,
H. N.
, and
Stein
,
P. D.
,
1986
, “
Influence of Stent Height Upon Stresses on the Cusps of Closed Bioprosthetic Valves
,”
J. Biomech.
,
19
(
9
), pp.
759
769
.10.1016/0021-9290(86)90199-5
14.
Jiang
,
H.
,
Campbell
,
G.
,
Boughner
,
D.
,
Wan
,
W. K.
, and
Quantz
,
M.
,
2004
, “
Design and Manufacture of a Polyvinyl Alcohol (PVA) Cryogel Tri-Leaflet Heart Valve Prosthesis
,”
Med. Eng. Phys.
,
26
(
4
), pp.
269
277
.10.1016/j.medengphy.2003.10.007
15.
Jiang
,
H.
,
Campbell
,
G.
, and
Canas
,
R.
,
2005
, “
Leaflet Geometry Extraction and Parametric Representation of a Pericardial Artificial Heart Valve
,”
Proc. Inst. Mech. Eng., Part H J. Eng. Med.
,
219
(
2
), pp.
143
152
.10.1243/095441105X9183
16.
Leat
,
M. E.
, and
Fisher
,
J.
,
1994
, “
A Synthetic Leaflet Heart Valve With Improved Opening Characteristics
,”
Med. Eng. Phys.
,
16
(
6
), pp.
470
476
.10.1016/1350-4533(94)90071-X
17.
Loerakker
,
S.
,
Argento
,
G.
,
Oomens
,
C. W.
, and
Baaijens
,
F. P.
,
2013
, “
Effects of Valve Geometry and Tissue Anisotropy on the Radial Stretch and Coaptation Area of Tissue-Engineered Heart Valves
,”
J. Biomech.
,
46
(
11
), pp.
1792
1800
.10.1016/j.jbiomech.2013.05.015
18.
Mohammadi
,
H.
,
Boughner
,
D.
,
Millon
,
L. E.
, and
Wan
,
W. K.
,
2009
, “
Design and Simulation of a Poly(Vinyl Alcohol)-Bacterial Cellulose Nanocomposite Mechanical Aortic Heart Valve Prosthesis
,”
Proc. Inst. Mech. Eng. Part H J. Eng. Med.
,
223
(
6
), pp.
697
711
.10.1243/09544119JEIM493
19.
Hinton
,
R. B.
, and
Yutzey
,
K. E.
,
2011
, “
Heart Valve Structure and Function in Development and Disease
,”
Annu. Rev. Physiol.
,
73
(
1
), pp.
29
46
.10.1146/annurev-physiol-012110-142145
20.
Lim
,
K. H.
,
Candra
,
J.
,
Yeo
,
J. H.
, and
Duran
,
C. M.
,
2004
, “
Flat or Curved Pericardial Aortic Valve Cusps: A Finite Element Study
,”
J. Heart Valve Dis.
,
13
(
5
), pp.
792
797
.https://pubmed.ncbi.nlm.nih.gov/15473482/
21.
Merryman
,
W. D.
,
Engelmayr
,
G. C.
,
Liao
,
J.
, and
Sacks
,
M. S.
,
2006
, “
Defining Biomechanical Endpoints for Tissue Engineered Heart Valve Leaflets From Native Leaflet Properties
,”
Prog. Pediat. Cardiol.
,
21
(
2
), pp.
153
160
.10.1016/j.ppedcard.2005.11.001
22.
Sugimoto
,
H.
, and
Sacks
,
M. S.
,
2013
, “
Effects of Leaflet Stiffness on In Vitro Dynamic Bioprosthetic Heart Valve Leaflet Shape
,”
Cardiovasc. Eng. Technol.
,
4
(
1
), pp.
2
15
.10.1007/s13239-013-0117-y
23.
Desai
,
A.
,
Vafaee
,
T.
,
Rooney
,
P.
,
Kearney
,
J. N.
,
Berry
,
H. E.
,
Ingham
,
E.
,
Fisher
,
J.
, and
Jennings
,
L. M.
,
2018
, “
In Vitro Biomechanical and Hydrodynamic Characterisation of Decellularised Human Pulmonary and Aortic Roots
,”
J. Mech. Behav. Biomed. Mater.
,
79
, pp.
53
63
.10.1016/j.jmbbm.2017.09.019
24.
Kerr
,
M. M.
, and
Gourlay
,
T.
,
2021
, “
Design and Numerical Simulation for the Development of an Expandable Paediatric Heart Valve
,”
Int. J. Artif. Organs
,
44
(
7
), pp.
518
524
.10.1177/0391398820977509
25.
Rozeik
,
M. M.
,
Wheatley
,
D. J.
, and
Gourlay
,
T.
,
2017
, “
Investigating the Suitability of Carbon Nanotube Reinforced Polymer in Transcatheter Valve Applications
,”
Cardiovasc. Eng. Technol.
,
8
(
3
), pp.
357
367
.10.1007/s13239-017-0313-2
26.
Garcia
,
D.
, and
Kadem
,
L.
,
2006
, “
What Do You Mean by Aortic Valve Area: Geometric Orifice Area, Effective Orifice Area, or Gorlin Area?
,”
J. Heart Valve Dis.
,
15
(
5
), pp.
601
608
.https://pubmed.ncbi.nlm.nih.gov/17044363/
27.
Claiborne
,
T. E.
,
Slepian
,
M. J.
,
Hossainy
,
S.
, and
Bluestein
,
D.
,
2012
, “
Polymeric Trileaflet Prosthetic Heart Valves: Evolution and Path to Clinical Reality
,”
Expert Rev. Med. Devices
,
9
(
6
), pp.
577
594
.10.1586/erd.12.51
28.
Hyde
,
J. A.
,
Chinn
,
J. A.
, and
Phillips
,
R. E.
, Jr.
,
1999
, “
Polymer Heart Valves
,”
J. Heart Valve Dis.
,
8
(
3
), pp.
331
339
.https://pubmed.ncbi.nlm.nih.gov/10399670/
29.
Yoganathan
,
A. P.
,
Chandran
,
K. B.
, and
Sotiropoulos
,
F.
,
2005
, “
Flow in Prosthetic Heart Valves: State-of-the-Art and Future Directions
,”
Ann. Biomed. Eng.
,
33
(
12
), pp.
1689
1694
.10.1007/s10439-005-8759-z
30.
Levy
,
R. J.
,
Schoen
,
F. J.
,
Anderson
,
H. C.
,
Harasaki
,
H.
,
Koch
,
T. H.
,
Brown
,
W.
,
Lian
,
J. B.
,
Cumming
,
R.
, and
Gavin
,
J. B.
,
1991
, “
Cardiovascular Implant Calcification: A Survey and Update
,”
Biomaterials
,
12
(
8
), pp.
707
714
.10.1016/0142-9612(91)90017-5
31.
Vyavahare
,
N. R.
,
Chen
,
W.
,
Joshi
,
R. R.
,
Lee
,
C. H.
,
Hirsch
,
D.
,
Levy
,
J.
,
Schoen
,
F. J.
, and
Levy
,
R. J.
,
1997
, “
Current Progress in Anticalcification for Bioprosthetic and Polymeric Heart Valves
,”
Cardiovasc. Pathol.
,
6
(
4
), pp.
219
229
.10.1016/S1054-8807(97)00017-3
32.
Stradins
,
P.
,
Lacis
,
R.
,
Ozolanta
,
I.
,
Purina
,
B.
,
Ose
,
V.
,
Feldmane
,
L.
, and
Kasyanov
,
V.
,
2004
, “
Comparison of Biomechanical and Structural Properties Between Human Aortic and Pulmonary Valve
,”
Eur. J. Cardio-Thorac. Surg.
,
26
(
3
), pp.
634
639
.10.1016/j.ejcts.2004.05.043
33.
Bernacca
,
G. M.
,
O'Connor
,
B.
,
Williams
,
D. F.
, and
Wheatley
,
D. J.
,
2002
, “
Hydrodynamic Function of Polyurethane Prosthetic Heart Valves: Influences of Young's Modulus and Leaflet Thickness
,”
Biomaterials
,
23
(
1
), pp.
45
50
.10.1016/S0142-9612(01)00077-1
34.
Gaetano
,
F.
,
Bagnoli
,
P.
,
Zaffora
,
A.
,
Pandolfi
,
A.
,
Serrani
,
M.
,
Brubert
,
J.
,
Stasiak
,
J.
,
Moggridge
,
G. D.
, and
Costantino
,
M. L.
,
2015
, “
A Newly Developed Tri-Leaflet Polymeric Heart Valve Prosthesis
,”
J. Mech. Med. Biol.
,
15
(
02
), p.
1540009
.10.1142/S0219519415400096
35.
Gulbulak
,
U.
,
Ertas
,
A.
,
Baturalp
,
T. B.
, and
Pavelka
,
T.
,
2020
, “
The Effect of Fundamental Curves on Geometric Orifice and Coaptation Areas of Polymeric Heart Valves
,”
J. Mech. Behav. Biomed. Mater.
,
112
, p.
104039
.10.1016/j.jmbbm.2020.104039
36.
David
,
T. E.
,
2016
, “
Aortic Valve Replacement in Children and Young Adults
,”
J. Am. Coll. Cardiol.
,
67
(
24
), pp.
2871
2873
.10.1016/j.jacc.2016.04.023
37.
Miller
,
J. R.
,
Henn
,
M. C.
,
Lancaster
,
T. S.
,
Lawrance
,
C. P.
,
Schuessler
,
R. B.
,
Shepard
,
M.
,
Anderson
,
M.
,
Kovacs
,
A.
,
Matheny
,
R. G.
,
Eghtesady
,
P.
,
Damiano
,
R. J.
, and
Boston
,
U. S.
,
2016
, “
Pulmonary Valve Replacement With Small Intestine Submucosa-Extracellular Matrix in a Porcine Model
,”
World J. Pediat. Congenital Heart Surg.
,
7
(
4
), pp.
475
483
.10.1177/2150135116651113
38.
Burriesci
,
G.
,
Marincola
,
F. C.
, and
Zervides
,
C.
,
2010
, “
Design of a Novel Polymeric Heart Valve
,”
J. Med. Eng. Technol.
,
34
(
1
), pp.
7
22
.10.3109/03091900903261241
39.
Mellot
,
S. R.
, and
Fatemi
,
A.
,
2014
, “
Fatigue Behavior and Modeling of Thermoplastics Including Temperature and Mean Stress Effects
,”
Polym. Eng. Sci.
,
54
(
3
), pp.
725
738
.10.1002/pen.23591

Supplementary data