A Parametric Computational Study of the Impact of Non-circular Configurations on Bioprosthetic Heart Valve Leaflet Deformations and Stresses: Possible Implications for Transcatheter Heart Valves

Abstract

Although generally manufactured as circular devices with symmetric leaflets, transcatheter heart valves can become non-circular post-implantation, the impact of which on the long-term durability of the device is unclear. We investigated the effects of five non-circular (EllipMajor, EllipMinor, D-Shape, TriVertex, TriSides) annular configurations on valve leaflet stresses and valve leaflet deformations through finite element analysis. The highest in-plane principal stresses and strains were observed under an elliptical configuration with an aspect ratio of 1.25 where one of the commissures was on the minor axis of the ellipse. In this elliptical configuration (EllipMinor), the maximum principal stress increased 218% and the maximum principal strain increased 80% as compared with those in the circular configuration, and occurred along the free edge of the leaflet whose commissures were not on the minor axis (i.e., the “stretched” leaflet). The D-Shape configuration was similar to this elliptical configuration, with the degree to which the leaflets were stretched or sagging being less than the EllipMinor configuration. The TriVertex and TriSides configurations had similar leaflet deformation patterns in all three leaflets and similar to the Circular configuration. In the D-Shape, TriVertex, and TriSides configurations, the maximum principal stress was located near the commissures similar to the Circular configuration. In the EllipMinor and EllipMajor configurations, the maximum principal stress occurred near the center of the free edge of the “stretched” leaflets. These results further affirm recommendations by the International Standards Organization (ISO) that pre-clinical testing should consider non-circular configurations for transcatheter valve durability testing.

INTRODUCTION

Transcatheter aortic valve replacement (TAVR) has emerged as an innovative technology for treatment of aortic stenosis in patients at high risk for surgical aortic valve replacement (SAVR), with over 50,000 TAVR procedures performed every year world-wide.^7,18 As opposed to traditional SAVR, transcatheter heart valves (THVs) are held in place via the interaction between the valve frame and the surrounding calcified native leaflets and aortic annulus. Non-circular configurations of THV frames post-implantation have been observed clinically.^1,15,22,23 Zegdi et al. visually assessed the geometry of a self-expandable stent acutely implanted in the annulus in 35 patients and observed that more than half of the valves experienced non-circular deformations after deployment.²³ The flexible frame of the stent was visibly elliptical, triangular, or D-shaped. Schultz et al. evaluated the self-expanding Medtronic CoreValve THV in 30 patients with multislice computed tomography (MSCT) and found that all valves exhibited some degree of non-circular or non-uniform deformations.¹⁵ Based on the data presented in the paper, an elliptical aspect ratio (major axis divided by minor axis) was calculated to be 1.18 on average (ranging from 1.05 to 1.41). Caudron et al. measured the geometry of the balloon-expandable Edwards SAPIEN THV with MSCT in 34 patients.¹ At the inflow end of the valve frame, 26% were found to be generally elliptical. Based on the data presented in the paper, the elliptical aspect ratio was calculated to be 1.05 on average (ranging from 1.02 to 1.10).

Experience with surgical tissue valves has demonstrated the importance of proper leaflet coaptation, the absence of which can lead to valve dysfunction and/or reduced durability.¹⁹ The non-circular configurations of the deployed THV frames may change the coaptation pattern and the kinematics of the leaflets and potentially affect THV hydrodynamic performance and leaflet durability.^13,21 Therefore, ISO 5840–3 recommends that heart valve testing such as accelerated durability testing be conducted under both round and out-of-round configurations.⁵ Sun et al. found that a generic THV deformed into an elliptical configuration had increased central backflow leakage of 0.6–0.8 L/min and a 143% increase in peak principal stress in the leaflet when compared to the nominal circular geometry.¹⁷ Gunning et al. also found that a THV deployed in a real calcified patient anatomy had less ideal leaflet coaptation in addition to increased stresses.⁴ Such regions of increased leaflet stresses could accelerate structural valve deterioration and potentially decrease leaflet durability. These previous studies provided insights into some irregular geometries in THV. Depending on the patient’s native anatomy, the implantation technique, and the design of the THV frame, the same THV can result in several post-implant geometries different from a circular configuration. This could impact the valve leaflets which are the main functional components of the THV. THV therapy is being expanded to patient populations of lower risk profiles who are likely to have longer life expectancy, however long term leaflet durability is still unknown.¹⁸ It is therefore important to better understand the impact of non-circular valve configurations on valve durability. To achieve this ultimate objective, it is necessary to first investigate how different non-circular valve configurations impact the valve leaflet stresses and deformations. The stress–strain distributions can then eventually be correlated with leaflet wear patterns observed in accelerated wear testing. In this study, we took the first step and extended the studies by Sun et al. and Gunning et al.^4,17 to include two additional triangular configurations of a valve with different commissure orientations. Specifically, we used finite element analysis (FEA) to evaluate several non-circular configurations that were determined from a careful study of the available literature to incorporate a number of clinically relevant THV configurations.^1,15,22,23 Supplemental bench testing was performed to provide qualitative validation of our computational model.

MATERIALS AND METHODS

Valve Leaflet Geometry

The three-dimensional representative valve geometry was constructed from a previously published trileaflet model of a 26 mm diameter aortic valve.⁸ Ansys’s DesignModeler (v12) was used to smooth the existing leaflet surface prior to import into Simulia’s Abaqus (6.10 & 6.11, see Fig. 1). The leaflet was assumed to have a uniform thickness of 0.5 mm, which is comparable to the average thickness of bovine pericardial tissue commonly found in bioprosthetic valves^6,16 and measurements taken optically (0.478 ± 0.072 mm) of a Model 2800 Edwards Lifesciences 25 mm diameter surgical aortic valve. For the purposes of this study, the pericardial tissue leaflet design of a surgical bioprosthetic valve is assumed to be similar to that of a THV. A simulated adapter ring of the same diameter as the representative valve was included in the model to help deform the valve into the different non-circular annular configurations (described below).

FIGURE 1.

The model valve geometry with its simulated adapter ring after meshing. The original leaflet geometry was obtained from Labrosse et al.⁸

Non-circular Annular Configurations

Six annular configurations were selected for the study; they were based on clinical evidence of non-circularity after THV post-implantation covering a complete set of possible post-implant configurations.^1,15,22,23 They are as shown in Fig. 2: (1) Circular; (2) elliptically deformed with a commissure on the major axis—EllipMajor; (3) elliptically deformed with a commissure on the minor axis—EllipMinor;(4) D-Shape; (5) triangular with commissures on the vertices—TriVertex; and (6) triangular with commissures centered on the sides of the triangle—TriSides. To characterize the non-circular annular configurations, the following geometric parameters were defined (as illustrated in Fig. 3): Elliptical Aspect Ratio (AR—ratio of major to minor diameter), D-Ratio (ratio of major to minor radii defined within the minor diameter), and Tri-ratios for TriVertex or TriSides (ratio of commissural chord length to the shorter perpendicular distance from the chord center to the ring). All Tri-ratios were obtained by averaging three values corresponding to each pair of commissures of a TriVertex or TriSides valve. For example, a circular configuration will have an elliptical AR of 1.0, D-Ratio of 1.0, and Tri-ratio of 3.33. The average geometric parameters were first determined experimentally from images taken of three 25 mm sized surgical aortic valves (Model 2800 from Edwards Lifesciences) deformed in vitro into one of the non-circular configurations described above using customized aluminum adapter rings. The surgical valves were sutured onto these adapter rings using 0.23 mm diameter fishing line suture (STREN Original). All configurations were developed experimentally keeping the orifice area along the plane of the adapter ring the same (~1.125 ± 0.02 inch²). These geometric parameters were later reproduced in the FEA, as shown in Fig. 2 and Table 1.

FIGURE 2.

Surgical tissue valve shown in six different configurations without diastolic pressure loading.

FIGURE 3.

Representative images showing calculations for aspect ratio (AR), D-ratio and Tri-ratio for the EllipMajor, D-Shape and TriSides configurations.

TABLE 1.

Geometric parameters describing the degree of non-circular deformation.

Geometric parameters from respective non-circular annular configurations	Aspect ratio (AR) as measured on the bench	Aspect ratio (AR) as measured from FEA
AR (from EllipMajor or EllipMinor)	1.30	1.25
D-Ratio (from D-Shape)	1.16	1.16
TriVertex Ratio (from TriVertex)	4.01	4.00
TriSides Ratio (from TriSides)	2.30	2.54

Material and Mesh Properties

For our representative valve leaflets, an isotropic nonlinear hyperelastic Marlow’s strain-energy potential was used to fit the stiffest of the nonlinear stress–strain behavior of gluteraldehyde-treated bovine pericardial tissue published previously; experimental data was obtained from Kim et al.^6,16 Poisson’s ratio and the density of the leaflets were chosen to be 0.3 and 1100 kg/m³, respectively.^16,17 The leaflets were modeled using the S4 quadrilateral large-strain fully integrated shell elements in Abaqus. The simulated adapter ring around the valve was modeled using the S4R quadrilateral large-strain reduced integration shell elements and had the same material properties as the leaflets. Sensitivity analysis on the static coefficient of friction between leaflets in the Circular and the EllipMinor configurations showed the maximum von Mises and maximum principal stresses in each configuration were similar. The similarity between these two different stress measures indicated that the stress dominated in only one direction in our simulations with the use of Abaqus’s S4 quadrilateral large-strain fully integrated shell elements and isotropic leaflet material model. The stress and strain measures were highest for the EllipMinor configuration with a frictional coefficient value of 0.2. Hence, the static coefficient of friction at the contact interface between the leaflets was set to 0.2 for all subsequent simulations, based on our results as well as previous frictional studies of explanted porcine and re-engineered cartilage tissue.^3,11 Mesh refinement was performed with the Circular configuration to obtain a single refined mesh based on the convergence of the errors (within 10%) in maximum von Mises stress and maximum principal logarithmic strain from successive simulations. A logarithmic plot of the errors in Fig. 4 showed a decreasing trend for the Circular mesh in the order of 10⁻². The location of the maximum von Mises stress and maximum principal logarithmic strain did not change as the mesh density was increased. A final mesh size of ~15,200 elements was employed for all subsequent analyses, with the exception of the TriSides configuration where the mesh size had to be reduced to 8656 elements because of convergence issues. All quasi-static simulations were carried out using the dynamic explicit solver with a step time of ~2.954E–6 s, on a Dell Precision T7500 standalone computer with 2 quad-core processors.

FIGURE 4.

Mesh refinement studies performed showing a logarithmic decrease in maximum von Mises stress and maximum principal Logarithmic (LE) strain in the Circular configuration. The total number of leaflet elements was varied from ~4000 to ~15,200. The pattern of convergence of the error in maximum stress and strain between successive simulations was similar. The maximum stress and strain occurred near the leaflet commissures in the Circular configuration.

Boundary Conditions and Applied Loads

The interaction between any two leaflets was modeled with ‘general contact’ in Abaqus, which automatically defined an all-inclusive surface and interactions between bodies in that surface. The non-free edges of the three leaflets were bound to the simulated adapter ring using the TIE constraints (i.e., the ring as master and the leaflet periphery as slave surfaces). The quasi-static simulation was modeled as a two-step process:

Step 1: Deform the simulated adapter ring to obtain the desired non-circular annular configuration.

Step 2: Apply a quasi-static uniform pressure of 15 kPa (~110 mmHg) on the aortic side of the leaflets simulating the diastolic phase of the cardiac cycle.

In Step 1, the ring was radially deformed by applying forces on different sections of the ring as necessary to form the appropriate non-circular annular configuration. Displacement along the longitudinal axis as well as all rotational degrees of freedom of the ring were restricted.

Because it has been shown previously that diastolic loading on the leaflets causes the maximum increase in leaflet stresses, we modeled only the diastolic phase of the cardiac cycle in Step 2.^4,9,17 A hypertensive pressure of 110 mmHg was chosen for our model. Displacement and rotational degrees of freedom of the nodes at the leaflet edges where they attach to the simulated adapter ring were restricted along all axes in Step 2. This restriction was applied to simulate the expected rigidity of a THV frame at the level of the commissure and other leaflet attachment points. In contrast to surgical valves that have flexible commissure posts that deform radially during the cardiac cycle and help reduce leaflet stresses, the THV frame at the level of the commissure attachments is expected to be less flexible and therefore subjected to lesser radial deformation during the cardiac cycle.

With the explicit solver, the amount of artificial strain energy (ASE) generated has to be low compared to the total internal energy (IE) of the system for reliable results to prevent unduly high deformation and distortion of elements. This ratio, ASE/IE, was only compared for Circular and EllipMinor configurations initially and was found to be <1.06%. The outputs of all simulations were later analyzed in terms of von Mises and in-plane principal stresses, and logarithmic (LE) strains at integration points.

Validation of FEA Model

We qualitatively compared valve leaflet deformations in all non-circular annular configurations without diastolic leaflet loading (i.e., after Step 1) with images of surgical valves that were deformed in vitro (using customized aluminum adapter rings mentioned above under ‘Non-circular Annular Configurations’) without diastolic leaflet loading. The valves deformed in vitro were imaged using a high resolution optical microscope. Additionally, valve leaflet deformations in all non-circular annular configurations with diastolic leaflet loading (i.e., after Step 2) were qualitatively compared with images of the surgical valves deformed in vitro, obtained from hydrodynamic testing at cardiac output of 5 liters per minute, pulse rate of 70 beats per minute, and mean aortic pressures of 140 mmHg (i.e., slightly elevated diastolic pressure of ~120 mmHg) as relevant physiological outputs. The hydrodynamic testing was performed using 0.9% saline solution in the commercially available Left Heart Simulator (Vivitro Systems), which simulates function of the heart by generating pulsatile flow through prosthetic heart valves. The surgical valves deformed in vitro were placed in the aortic position as test valves. A St. Jude Medical’s 27 mm bileaflet mechanical valve was used in the mitral position. The Left Heart Simulator’s pump was driven using a predefined input waveform set to 35% systolic duration per beat. The above physiological outputs were obtained by varying the peripheral resistance and compliance of the system. Imaging during hydrodynamic testing was performed at 100 frames per second using a high speed Motion Pro IDT camera (Model Y4-S1, maximum resolution of 1024 × 1024 pixels). Images depicting closed leaflet behavior during the diastolic phase of cycling were selected for qualitative validation with the computational models.

RESULTS

The deformed valve leaflets after Step 1 and Step 2 are shown in Figs. 5 and 6, respectively. These figures demonstrate that in the non-circular annular configurations, the three leaflets in the computational model do not coapt uniformly as in the Circular configuration. It can also be seen that the leaflet coaptation in the computational results appeared similar to the experimental results, as shown in Figs. 5(i) vs. 5(ii), 5(iii) vs. 5(iv), and 6(iii) vs. 6(iv). Minor dissimilarities were present in Fig. 5, such as excess gap between two leaflets as noted in the computational results for the D-Shape and TriSides configurations. However, these dissimilarities disappeared after the pressure loading was applied, as shown in Fig. 6. Differences in stress distributions among the different configurations at the belly region of the leaflets are also seen in Fig. 6. Elliptically-oriented and D-Shape configurations have two types of individual leaflet deformations in our study, referred to as “stretched” leaflet and “sagging” leaflet. We define a “stretched” leaflet as a leaflet whose commissures are separated further than those of the circular configuration and therefore the free edge of the leaflet appears stretched. The free edge of the “stretched” leaflet tends to lie above the free edge of other leaflets. We define a “sagging” leaflet as a leaflet whose commissures come closer than those of the circular configuration and the free edge of the leaflet appears to be sagging. The free edge of a “sagging” leaflet tends to lie below the free edge of the “stretched” leaflet. A representative example of “stretched” and “sagging” leaflets using EllipMajor configuration is shown in Fig. 7.

FIGURE 5.

Maximum in-plane principal stresses in all six configurations after Step 1 (i.e., without diastolic loading) are shown (top view in (i) and inclined view in (iii)). Columns (ii) and (iv) contain pictures of surgical valves corresponding to the FEA images shown in columns (i) and (iii), respectively. The arrows indicate matching features in leaflet deformations between the model and the bench.

FIGURE 6.

Inhomogeneous distribution of in-plane principal stresses in the leaflet after Step 2 (with diastolic loading) in all configurations are shown. Columns (i) and (ii) show the view of stress distribution from the top and side of the valve. Column (iii) shows a close-up view of the leaflet coaptation regions depicting lower in-plane principal stresses with the Circular, D-Shape, TriVertex, and TriSides configurations as well as higher in-plane principal stresses at leaflet free edges with the EllipMajor and EllipMinor configurations. Column (iv) shows images of valves under diastolic pressure loading taken during hydrodynamic testing. Leaflet deformation at the coaptation center was noted to be different from the Circular configuration, as depicted by arrows in EllipMajor and EllipMinor ((iii) and (iv)).

FIGURE 7.

The “stretched” and “sagging” leaflets as indicated by black and white arrows, respectively, as seen in the EllipMajor configuration are shown. A close-up of the leaflet coaptation center is shown on the right.

Regional variations in maximum principal stress and strain in leaflets indicate differences in leaflet deformations between configurations, as seen in Fig. 8. Each leaflet was subdivided into three regions associated with high stress: the free edge (region having ~17 elements), commissures (region having ~185 elements), and belly (region having ~760 elements). Maximum in-plane principal stresses and principal LE strains were obtained after Step 2 from the three regions of each leaflet. The average elemental stress and strain in each region was calculated by summing all the maximum in-plane principal stresses and strains for each element in the region (irrespective of principal directions) and dividing by the number of elements in that region. For each annular configuration, the three leaflets were arbitrarily named ‘Leaflet 1’, ‘Leaflet 2’, and ‘Leaflet 3’. In the Circular configuration (Fig. 8a), the average stress/strain values at the free edge region (0.13–0.17 MPa for stress, 8.3–9% for strain) are lower than those in the commissure and belly regions (1.12–1.66 MPa for stress, 13.7–14.1% for strain) of all threeleaflets. The “stretched” leaflets in the EllipMajor (Leaflet 2 and 3 in Fig. 8b) configuration had higher stresses (1.32–1.44 MPa) and strains (12.6–13.2%) at the free edge compared to the third leaflet (Leaflet 1; 0.11 MPa, 7.7%) and compared to all three leaflets in the Circular configuration; these two “stretched” leaflets also had lower commissural stresses (0.97–1.18 MPa) and strains (12.6–13.1%) than the commissural stress and strain (2.27 MPa and 15.3%, respectively) in the third leaflet. The “stretched” leaflet in the EllipMinor configuration (Leaflet 1 in Fig. 8c) had much higher stress (4.21 MPa) and strain (18.6%) at the free edge compared to the other two leaflets (Leaflet 2 and 3; 0.1–0.46 MPa, 7.5–10.2%) and compared to all three leaflets in the Circular configuration; this “stretched” leaflet also had lower commissural stress (1.03 MPa) and strain (12.8%) than the commissural stresses and strains (2.25 MPa and 15.3%, respectively) in the other two leaflets. One “stretched” leaflet in the D-Shape configuration (Leaflet 1 in Fig. 8d) had marginally higher stress and strain at the free edge (0.49 MPa, 11.2%) compared to the other two leaflets (Leaflet 2 and 3 in Fig. 8d, 0.03–0.13 MPa, 5.0–6.1%); the stress and strain at the commissure for this “stretched” leaflet (1.38 MPa, 13.5%) was slightly lower compared to the other two leaflets (1.78–1.8 MPa, 14.3–14.4%).

FIGURE 8.

Maximum in-plane principal stresses and principal LE strains averaged over three sections of interest (free edge, commissure, and belly regions) on each of the leaflets from all configurations. Average stresses were similar between Circular (a) and TriVertex (e) configurations. TriSides (f) had slightly lower stress and strain values at the free edge region than the Circular (a) configuration. Both EllipMajor and EllipMinor configurations had “stretched” leaflets with highest stress at the free edge compared to the commissures.

The “sagging” leaflets in the EllipMajor (Leaflet 1 from Fig. 8b) and EllipMinor configurations (Leaflet 2 and 3 from Fig. 8c), however, had higher stresses and strains at the commissural region (2.25–2.27 MPa, 15.3%) compared to the other leaflets of the same configuration (0.97–1.18 MPa, 12.6–13.1%) and compared to the Circular configuration leaflets. These “sagging” leaflets in the EllipMajor and EllipMinor configurations also had much lower free edge stresses and strains (0.1–0.46 MPa, 7.5–10.2%) compared to the other leaflets of the same configuration but were similar to the Circular configuration leaflets. Non-circular configurations except TriSides configuration did not show large changes in average stress and strain in the belly region (1.07–1.75 MPa, 12.8–14.2%) compared to the Circular configuration (1.46–1.49 MPa, 13.7–13.8%). The average stress/strain values were much lower for the TriSides configuration at the free edge region of all three leaflets (see Fig. 8f; −0.04 to 0.08 MPa, 1.6–5.8%) compared to Circular (range noted above) or TriVertex (Fig. 8e; 0.24–0.4 MPa, 9.7–10.7%) configuration.

The non-circular annular configuration with the highest maximum in-plane principal stress (12.8 MPa) and LE strain (32%) occurred in the EllipMinor configuration as can be seen in Fig. 9. The maximum in-plane principal stress and LE strain for the Circular configuration was 4 MPa and 18% respectively. In the Circular configuration, slight differences in average maximum principal stress and strain (from Fig. 8a) observed between each pair of leaflets fell within 25 and 9%, respectively. Therefore, differences greater than 25% in stress and 9% in strain between non-circular annular configurations and circular configuration were considered substantially different in our simulations. In Fig. 9, the EllipMajor configuration had slightly larger stress/strain values (6.09 MPa, 22%) compared to the Circular configuration. The D-Shape, TriVertex, and TriSides configurations had maximum in-plane principal stress (3.37–4.73 MPa) and strain (19.3–19.5%) similar to the Circular configuration. The D-Shape and TriSides configurations had maximum in-plane principal stresses and strains slightly higher than the Circular configuration (4–18% increase in stress and 7.3–8.3% increase in strain) but these differences were not considered substantially different. The TriVertex configuration, on the other hand, had 16% lower maximum in-plane principal stress compared to the Circular configuration; this finding, however, was not deemed noteworthy since stresses at the commissures and the belly region were similar to those of the Circular configuration. The commissure region average stress and strain was similar in most configurations, with the exception of elliptically-oriented configurations (as seen in Fig. 8 and described above).

FIGURE 9.

Maximum in-plane principal stresses and LE strains in the six configurations after Step 2 (diastolic loading of 110 mmHg). EllipMinor configuration had the most stressed leaflet location at the free edge of the leaflet that is somewhat parallel to the major axis of the ellipse, followed by EllipMajor and D-Shape configurations.

DISCUSSION

The non-circular valve geometric configurations were primarily based upon two major factors: (1) clinical evidence of non-circularity after THV implantation,^1,15,22,23 and (2) feasibility of using these geometries in our current hydrodynamic and accelerated wear testers in future studies. Circular, EllipMajor, and EllipMinor configurations were based on clinical evidence of non-circularity from currently available THVs.^1,15,22 Although they have not been explicitly reported to date with currently available THVs, the D-Shape, TriVertex, and TriSides configurations are possible post-implant configurations that are clinically relevant as shown by Zegdi et al.²³ A particular THV can take any non-circular configuration depending on the patient’s native anatomy, implantation technique, and design of the THV frame; this has been demonstrated previously by Gunning et al’s computational study.⁴ The geometric configurations studied herein encompass those reported in the clinical literature thus far, although further additions using the geometric parameters defined in this study could be made if clinical evidence is presented or if scientific reasoning is warranted.

The Circular configuration was our control in which the leaflets come together and support each other to form a nominal central coaptation pattern (as seen in Fig. 6). Two types of leaflet deformation patterns were seen with the non-circular annular configurations, i.e., “stretched” leaflet and “sagging” leaflet; the Circular configuration does not have “stretched” or “sagging” leaflets. In Figs. 6(ii) and 6(iii), the EllipMajor configuration had two “stretched” leaflets and one “sagging” leaflet, and the EllipMinor configuration had two “sagging” leaflets and one “stretched” leaflet. The D-Shape configuration was similar to the EllipMinor configuration with two “sagging” leaflets and one “stretched” leaflet; however the degree to which the leaflets were stretched or sagging appears less than the EllipMinor configuration. The TriVertex and TriSides configurations had similar leaflet deformation patterns as the Circular configuration; however there may be minor changes in leaflet deformation patterns due to differences in these two configurations compared to Circular configuration (as indicated also by the Tri-ratios: 4.01 for TriVertex, 2.3 for TriSides, and 3.33 for Circular); some of these minor changes include slight “stretching” of the leaflets in the TriVertex configuration and slight “sagging” of the leaflets in the TriSides configuration, although leaflets appear to support one another in these configurations. These differences in leaflet deformation patterns have been seen previously, including in patient specific modeling of THVs.^4,17 Martin et al. showed that coaptation and heterogeneity of the leaflet properties may accelerate leaflet fatigue.¹⁰ Historically, the three leaflets in a pericardial valve support each other to help reduce the peak tensile stresses on the outermost fibers near the free edge.²⁰ The clinical experience with stented surgical pericardial valves is limited to circular configurations and therefore has not shown such coaptation patterns (i.e., “sagging” leaflet or “stretched” leaflet). However, to what extent pericardial tissue failure modes and the valve durability is affected by these varying coaptation patterns more common in THVs is yet to be completely understood.

In the Circular and TriVertex configurations (as shown in Figs. 8a and 8e), the average maximum principal stress and strain were tensile in the leaflet free edge region. In contrast, all leaflets in the TriSides configuration experienced compressive stresses in several areas across the free edge region (Fig. 8f), exhibiting an effect similar to an over-constrained valve post-implantation. Compressive stresses also were present in the “sagging” leaflets in other configurations to a lesser extent. Gunning et al. observed a similar phenomenon associated with the orientation of the THV with respect to the native leaflet commissures in a patient specific anatomy.⁴ To what extent such “sagging” leaflets may affect leaflet failure modes and fatigue life is still unclear, however, it is interesting that Martin et al found differences in fatigue behavior at the commissures and suture attachments between nominal and “sagging” leaflets.¹⁰

Locations of maximum principal stress are generally considered to be associated with pericardial tissue leaflet tear or failure.^4,10,17,20 In the Circular, D-Shape, TriVertex, and TriSides configurations, the maximum principal stress was located near the commissures. In the EllipMinor and EllipMajor configurations, the maximum principal stress was located near the center of the free edge of “stretched” leaflets. Overall, the largest in-plane principal stress and strain occurred in the EllipMinor configuration and were 12.8 MPa and 32%, respectively (Fig. 9). Compared to the Circular configuration, the maximum stress in the EllipMinor configuration was 218% larger (4 and 12.8 MPa, respectively). A previous study that examined circular and elliptical configurations also reported the largest increase in the maximum principal stress in an elliptical configuration similar to our EllipMinor configuration as compared to the circular case.¹⁷ Similarly, another study of a THV implanted in a patient specific aortic root resulted in a configuration similar to our EllipMinor configuration, which also caused increases in maximum principal stress compared to the circular case.⁴ The maximum principal stress magnitude of 12.8 MPa noted in the EllipMinor configuration tends to be larger than the mean UTS (ultimate tensile strength) of gluteraldehyde treated pericardial tissue reported previously as 10.44 ± 0.96 MPa,² indicating that the center of the free edge of “stretched” leaflets may be more likely to tear causing structural deterioration. The stress magnitudes noted in the stretched leaflet of EllipMinor configuration (12.8 MPa) were higher than those noted in the stretched leaflets of EllipMajor configuration (6.09 MPa), indicating that a THV taking a EllipMinor configuration may be more likely to deteriorate early and have reduced valve durability. These results further suggest that the EllipMinor configuration may represent a non-circular configuration that should be investigated further for durability testing on THVs. Other non-circular configurations such as EllipMajor, D-Shape, or TriSides may also warrant further investigation on durability testing due to their distinct leaflet coaptation patterns. As reported previously, structural deterioration is multi-factorial resulting from abnormal valve leaflet motion, inhibition of structural rearrangements, loss of cell-mediated remodeling, and damage due to chemical pretreatments; calcific degeneration present in patients further adds complexity to clinical bioprosthetic valve failure rates.¹⁴ The degree to which the locations of maximum stress magnitudes in the leaflets and/or distinct coaptation patterns in the configurations identified in our study influence the above mentioned factors for valve durability remains unclear, and needs further investigation some of which is ongoing in our laboratory.

Study Limitations

In our simulations, we employed a representative valve geometry and assumed that the results would be generally applicable to THVs. While it is reasonable to expect some differences in results depending on individual manufacturers’ THV leaflet geometries, we expect the overall trends in stress/strain measures and coaptation patterns for different non-circular annular configurations to hold for different THV designs. In addition, although pericardial tissue is represented often with an anisotropic model, we considered an isotropic Marlow’s material model. When comparing previously published material models, similarities in leaflet deformations between completely closed and completely open valve positions in the circular valve configurations were observed; therefore, isotropic models appear adequate for studying the effects of different non-circular annular configurations on predicting regions of maximum stresses and strains and coaptation patterns during diastole, relative to the Circular configuration in our study.^4,12 We used a 26 mm diameter trileaflet model for the simulations and validated qualitatively to a 25 mm diameter surgical aortic valve using hydrodynamic data at a diastolic pressure of ~120 mmHg (in Fig. 6). We believe that this level of model validation is sufficient for understanding the differences between non-circular geometries as we do not expect these small differences in valve diameter or diastolic pressure to greatly affect qualitative observations presented in this study. Our future computational studies will consider more complex material models, valve geometries, and dynamic boundary conditions to better understand the influence of those modeling parameters on predicting differential leaflet stresses and kinematics between non-circular annular configurations. Given the variability in THV designs, it is difficult to truly find a single representative model that will reflect stress and strain differences among all designs. Individual valve characteristics need to be considered when applying the results found here to a particular THV design.

CONCLUSION

In our study, we performed a parametric analysis on the potential impact of several clinically relevant non-circular THV annular configurations on the maximum principal stress and strain in the leaflets. The EllipMinor configuration had the largest increase in maximum principal stress and strain as compared to the circular configuration. In the Circular, D-Shape, TriVertex, and TriSides configurations, the maximum principal stress was located near the commissures. In the EllipMinor and EllipMajor configurations, the maximum principal stress was located near the center of the free edge of “stretched” leaflets. In addition, non-circular configurations exhibited distinct coaptation patterns with “sagging” and “stretched” leaflets. Our results further confirm that the stress and strain in the leaflets and coaptation patterns could vary greatly between non-circular annular configurations. However, how those differences could impact the long-term durability of the valve remains unclear. It is therefore, necessary to perform long-term valve durability testing under different non-circular configurations to better understand how these configurations impact the durability of the leaflets.