Numerical and in-vitro experimental assessment of the performance of a novel designed expanded-polytetrafluoroethylene stentless bi-leaflet valve for aortic valve replacement

The expanded polytetrafluoroethylene (ePTFE) heart valve can serve as a viable option for prosthetic aortic valve. In this study, an ePTFE bi-leaflet valve design for aortic valve replacement (AVR) is presented, and the performance of the proposed valve was assessed numerically and experimentally. The valve was designed using CAE software. The dynamic behavior of the newly designed bi-leaflet valve under time-varying physiological pressure loading was first investigated by using commercial finite element code. Then, in-vitro tests were performed to validate the simulation and to assess the hemodynamic performance of the proposed design. A tri-leaflet ePTFE valve was tested in-vitro under the same conditions as a reference. The maximum leaflet coaptation area of the bi-leaflet valve during diastole was 216.3 mm2. When fully closed, no leakage gap was observed and the free edges of the molded valve formed S-shaped lines. The maximum Von Mises stress during a full cardiac cycle was 4.20 MPa. The dynamic performance of the bi-leaflet valve was validated by the in-vitro test under physiological aortic pressure pulse. The effective orifice area (EOA), mean pressure gradient, regurgitant volume, leakage volume and energy loss of the proposed valve were 3.14 cm2, 8.74 mmHg, 5.93 ml/beat, 1.55 ml/beat and 98.99 mJ, respectively. This study reports a novel bi-leaflet valve design for AVR. The performance of the proposed valve was numerically and experimentally assessed. Compared with the reference valve, the proposed design exhibited better structural and hemodynamic performances, which improved valve competency. Moreover, the performance of the bi-leaflet design is comparable to commercialized valves available on the market. The results of the present study provide a viable option for the future clinical applications.

Introduction years) and the free of reoperation rate at 10 years was above 92%. In another clinical trial, Miyazaki et al. implanted ePTFE valves (monocuspid, bi-leaflet and tri-leaflet) for RVOT in 157 patients (aged 16 days to 45.4 years, median 2 years) [14], and no mortality, morbidity or reoperation were reported during the follow-up period (5.6 to 63.7 months, mean 20.8 months). Moreover, the good biocompatibility of ePTFE artificial heart valves has been verified by several clinical studies [14,25,26]. In recent literature, the ePTFE membrane was also selected as the material for aortic valve extension [27].
However, the performances of the bi-leaflet ePTFE valve prostheses in the aortic site are yet to be studied. In this study, numerical simulation and in-vitro experiments were conducted to investigate the dynamic and hemodynamic performances of a novel designed bi-leaflet ePTFE valve prostheses under aortic loading. A fully sutured tri-leaflet valve [28,29] was tested under the same conditions as a reference.

Valve design
The native aortic valve has a complex geometry and structure, and thus, it is difficult to completely mimic the native valve in a prosthetic heart valve(PHV) design. Important design parameters for PHVs include effective orifice area (EOA), jet velocity, pressure gradient, regurgitation and thrombogenic potential, leaflet coaptation height and geometries of the leaflets [30].
At the beginning of this study, the range of several parameters, including the diameter (25 mm) and valve height (25-30 mm), were pre-defined by the surgeon in the team. Besides the quantitative parameters, an S-shaped free edge at the closed configuration that implies a surplus coaptation was expected [29]. The extra coaptation would play an important role to maintain the functionality of the valve when the aorta become bigger due to growth. In addition, the following design principles were obeyed in the design strategy [31]: • Easy and steady valve preparation; • Consistent preparation procedure; • Minimum trans-valvular pressure drop; • Minimum regurgitation; • Easy to implant; • Available in a wide range of sizes; To achieve the goal of the design, the leaflet's commissure edge was incorporated with the aortic root. The length of the leaflet's free edge was carefully selected, which is important to guarantee the full coaptation and to prevent unwanted leaflet twisting. The initial position of the leaflets was set to a fully open configuration.
A series of different leaflet designs based on the parameters and principles mentioned above were created in CAE software (Solidworks, Dassault Systems S.A., Paris, France). The leaflet designs were then converted to fully nonlinear finite element code ABAQUS (ABAQUS, Inc., Pawtucket, RI) to verify their function. The criterion of a successful design include: 1)the valve could properly open and close under static pressure loading applied on the leaflet surface; 2) An S-shape free edge can be observed in after the valve closed. Based on the above-listed parameters and requirements, the parametric design method was utilized in this study. Totally 5 models were generated by the engineer in our team. The one presented in Fig 1 is the only design that fully meets the above-mention requirements.

FEM simulation
The dynamic behaviors of the molded bi-leaflet valve, including dynamic deformation, leaflet coaptation area, and stress distribution were investigated dynamically by using ABAQUS/ Explicit modulus.
The ePTFE membranes were assumed to be isotropic and homogenous. An elastic modulus of 34 MPa and a density of 1100 kg/m 3 were assigned to the ePTFE leaflet. The aortic root was modeled as a flexible hollow cylinder. The elastic modulus and density of the aortic root were set to 2 MPa and 2000 kg/m 3 , respectively [29]. Poisson's ratio was set to 0.45 for all materials to account for the incompressible behavior of the membrane and tissues. The valve and aortic root were meshed using 4-node, doubly curved quadrilateral shell elements with reduced integration. A uniform thickness of 0.1 mm was assigned to the valve, while the thickness of the aortic root was defined to 0.4 mm.
The model was assumed to be stress-free in the fully open configuration. The radial displacement of the aortic root ends was constrained. Commissures of the leaflets were connected to the aortic root by using the tie boundary condition to simulate suturing in clinical applications. Contacts between the leaflets, and between the leaflets and conduit were considered. Fig 2 shows the FEM model.
To obtain a converged solution, an aorto-ventricular pressure gradient at diastolic (71.6 mmHg) were gradually applied to the valve leaflets in 0.1s. At the end of this step, the leaflets were at a closed, diastolic, stressed configuration. Then time-varying and spatially uniform physiological aorto-ventricular pressure gradient loadings over a full cardiac cycle of 0.83 s were applied on the valve leaflets (Fig 3). In the contact model, the friction coefficient of 0.5 was set.

In-vitro experiment
To assess the hemodynamic performance of the proposed design and to validate the FEM simulation, in-vitro experiments were carried out. According to FDA regulations, a full range of pre-clinical in-vitro test composed of 12 parts, which include bio-compatibility of the material, durability testing, hemodynamic performance, structural performance and fatigue assessments, etc. [32], is required. However, as the current study represents only the initial stage of valve design, only hemodynamic performance and dynamic performance were investigated in the in-vitro experiment.
Preparation of physical models. As described in the introduction, the preparation of the valve leaflet should be easy, steady and consistent. Thus, a set of resin molds was fabricated by using 3D printing technology (Fig 4(a)). The molds shared the same geometry of the model used in the FEM simulation. ePTFE membrane (Gore-Tex, Preclude Pericardial Membrane, W.L. Gore & Assoc., Flagstaff, AZ, USA) of 0.1 mm thickness were selected as the leaflet material. The valve leaflets were prepared by placing the ePTFE membrane in the mold and cutting along the edge. The aortic root was constructed by using a silicon polymer (VTV, MCP-HEK Tooling GmbH, Kaarst, Germany). The commissures of the leaflets were sutured to the aortic root with one running 4-0 polypropylene suture following the suture mark in the conduit (Fig  4(b)). As a reference, a fully sutured tri-leaflet valve that composed of ePTFE was also created and tested under the same in-vitro conditions in the experiment section (Fig 4(c)). The diameters of both valves at the base and at the commissures are 25 mm, and the overall leaflet heights of the bi-leaflet valve and tri-leaflet valve are 25 mm and 21.6 mm, respectively.
Experimental set-up and flow conditions. The Vivitro pulse duplicator (Vivitro Systems Inc., Victoria, BC, Canada) (Fig 5(a)) was used to generate physiological pressure and flow in the left ventricle and aorta. Two Millar MIKRO-TIP Pressure transducers (SPC 330A, Millar Instruments, Inc., Houston, TX, USA) were placed in the left ventricle and ascending aorta 10 mm above the commissural level to monitor the trans-valvular pressure gradient. The dynamic behaviors of the valve leaflet were captured by using a high-speed camera (FASTCAM-PCI R2 model 500, Photron USA, Inc., San Diego, CA, USA). The frame rate was set to 250 fps. The flow through the aortic site was measured by an electromagnetic blood flow meter (501D, Carolina Medical Electronics, East Bend, NC, USA). The experimental setup is illustrated in Fig 5(b).
The ventricular and aortic pressures were measured at the exit of the left ventricle and the exit of the aorta model. The pressures were controlled by adjusting the resistor and piston movement magnitude. The systolic and diastolic pressures in the aorta are 120 mmHg and 80 mmHg, respectively.
Flow profiles were measured by the flow probe placed at the exit of the left ventricle and were used to calculate the flow speed, cardiac output and regurgitation. All tests were conducted at a stroke volume of 75 ml (5.4 L/min) and a heart rate of 72 beats/min. Working fluid. An aqueous solution of glycerol (42% by weight) was used as the working fluid to mimic blood. The dynamic viscosity and density of the working fluid were 3.52 mPa�s and 1038 kg/m 3 , respectively.
Data acquisition. TTL signals generated by the amplifier of a Vivitro system were used as trigger signals. The flow meter, pressure transducer and high-speed camera were synced by the trigger signal. Before data collection, the system was allowed to run until all readings were stable to avoid measurement errors.

FEM simulation
Dynamic behaviors. The dynamic behaviors of the leaflets were analyzed in the FEM simulation. During a full cardiac cycle, the closing phase of the bi-leaflet valve is 0.055 s, and the fully closed state is maintained for 0.41 s. The leaflets require 0.04 s to reach the fully opened position, and the fully open state lasts 0.325 s. Fig 6 shows the dynamic displacement of the leaflets in a full cardiac cycle.
Coaptation parameters. The contact pressure normal to the leaflet was used to indicate the state of contact. A negative contact pressure indicated that the leaflet was in contact with the conduit, and a positive contact pressure implied that the leaflets were in contact with each other. Fig 7 shows the distribution of the contact pressure on the leaflets in the fully closed position. It is clear that the entire free edges of the leaflets are in the contact state at this position, and no leakage area was found. The coaptation area of a single leaflet over a cardiac cycle is plotted in Fig 8. The maximum coaptation area of the proposed design is 216.3 mm 2 .
The maximum coaptation height of the proposed valve leaflet is 13.37 mm (Fig 9). Leaflet stress distribution.

In-vitro performances
The in-vitro performance of the proposed bi-leaflet valve and reference tri-leaflet valve were assessed under the same experimental conditions. Fig 11 shows the left ventricular pressures, aortic pressures and trans-valvular pressures of the two valves.
Dynamic behaviors. To analyze the structural dynamics, key frames from the film recorded by the high-speed camera were extracted (Fig 12).
The starting point of the recording was defined as t = 0. The opening of the leaflets begins at t = 0.024 s for both valves tested. The opening stage, fully opened stage, and closing stage of the bi-leaflet valve and the reference valve are 0.056±0.00 s and 0.1±0.00 s, 0.152±0.00 s and 0.12±0.00 s, 0.132±0.00 s and 0.136±0.00 s, respectively. The leaflets of the proposed bi-leaflet and the reference valve closed fully at 0.364 s and 0.38 s, respectively (Table 1).
Hemodynamic performance. The mean trans-valvular pressure of the proposed bi-leaflet valve during the systolic phase is 8.74 mmHg, which is approximately 7.6% lower than that of the reference valve. The trans-valvular pressure and the aortic flow of the valves are shown in Fig 13.
The regurgitant volume (V R ) and leakage volume (V L ) were 5.93 ml and 1.55 ml per cycle for the proposed bi-leaflet valve and 7.09 ml and 2.81 ml for the reference valve, respectively. Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR Thus, the regurgitant fraction (RF) can be calculated by using Eq (1): where V R is the regurgitant volume, V L is the leakage volume and V F is the forward volume. The equation from ISO: 5840:2005 [33] was applied to evaluate the maximum EOA Eq (2): ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi DP=r where EOA is the effective orifice area of the valve (cm 2 ), ΔP is the mean systolic trans-valvular pressure gradient (TPG) in mmHg, ρ is the working fluid density (g/cm 3 ), and Q RMS is the Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR root mean square volumetric flow rate (ml/s) (Eq (3)).
Performance index (PI), which represent the normalized resistance of the valve [34], was evaluated by using Eq (4): Derived from the Bernoulli equation, the energy loss of the left ventricle that is associated with the valve prosthesis was calculated by integrating the aorto-ventricular pressure times the flow rate with respect to time [31,32,35] (Eq (5)): where E L is the energy loss (mJ), t 0 to t 1 is the range of a cardiac cycle, Δp is the aorto-ventricular Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR pressure difference (mmHg) and Q(t) (ml/s) is the volume flow. The calculated parameters are listed in Table 2.

Discussion
The goal of the current study was to develop a reliable bi-leaflet valve for patients who need AVR. A novel design of the bi-leaflet valve was proposed in the current study. The dynamic

Verification of the bi-leaflet valve design
Before further discussion, it is necessary to verify that the performance of the current design complies with the technical standard. As the well-accepted industry standard, ISO 5480:2055 provides a full set of criteria for evaluating a valve design [33]. The criteria that related to the current study are listed in Table 3.
The EOA and RF values of the valves tested in this study all satisfy the criteria of the standard, which provided the basis for further discussion.

Validation of the FEM simulation
The dynamic behavior of the leaflets is a key characteristic for assessing the performance of an aortic valve design [29]. Thus, the dynamic behavior of the valve was selected as the validation criterion. Dynamic deformation of the FEM model and the in-vitro model was compared in this section. Fig 14 shows a morphological comparison between the two models. Fig 15 shows the dynamic processes of the models. After fully closing, S-shaped free edges were observed in the FEM model and the in-vitro model. Table 4 lists the specific times required for different phases of the FEM and in-vitro models. During the in-vitro experiment and the FEM simulation, the same boundary conditions were used to ensure a proper comparison. The morphological characters and the dynamic behaviors of the in-vitro and FEM models matched well. Thus, the proposed FEM simulation has been validated to some extent.

Coaptation and stress
The coaptation height, coaptation area and stress distribution obtained from the FEM simulation were compared with the corresponding parameters reported by our group in the FEM investigation of a fully sutured tri-leaflet valve [28,29]. Table 5 lists these data. Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR As a critical parameter for assessing the competence of the valve, the maximum coaptation height of the bi-leaflet valve is nearly three times greater than that of the tri-leaflet valve, which suggests the former may be more competent. However, the A c of the bi-leaflet model is 27.81% smaller than that of the tri-leaflet model, which could be due to the different contact patterns of the designs. In the bi-leaflet design, most of the leaflet is in contact with another leaflet, and the remaining part of the leaflet is in contact with the conduit. In the tri-leaflet valve, the entire  leaflet is in contact with two other leaflets, thus increasing the contact area. The impact of the reduced A c is discussed further in a later section. Mechanical stress has long been related to calcification and structural failure of aortic valve prostheses [36,37]. Thubrikar et al. reported in an in vivo study [37] that, high compressive stress is closely correlated with the calcification of aortic valve prostheses leaflets. In addition to the compressive stress, the tensile stress and shear stress that act on leaflets may lead to the failure of the valve structure [36]. The multiple stress components can be represented by the Von Mises stress. Our current results show that the highest compressive stress occurs at the site of the leaflet that is most bent. The same pattern was also observed in the FEM model of the tri-leaflet valve. However, the maximum compressive stress of the bi-leaflet valve is 10.8% smaller than that of the tri-leaflet valve. The highest Von Mises stress value in the bi-leaflet valve is slightly higher (by 7.1%) than that in the tri-leaflet valve. The maximum Von Mises stress occurs at the commissures ends in both valves.
As mentioned in the validation section, S-shaped free edges were observed when the bi-leaflet valve was fully closed. This observation ensured good coaptation of the leaflets and provided more safety for the closure [29].

Dynamics and hemodynamic performance
As the FEM simulation only considered structural behaviors, evaluation of the dynamics and hemodynamic performance of the bi-leaflet design was performed by comparing the in-vitro results. The bi-leaflet valve and reference tri-leaflet valve were compared.
The results show that while both valves are capable of normal function, the dynamic performance of the proposed bi-leaflet valve is superior to that of the reference tri-leaflet valve. The bi-leaflet design required for less time than the tri-leaflet valve in the opening and closing phase. The opening of the bi-leaflet valve is 44% faster than the reference valve. During the close phase, the time cost of the bi-leaflet design is 2.9% less than the reference valve. This observation suggested that the leaflet mobility of the proposed bi-leaflet design is better than the reference valve. The fully opened state of the proposed valve lasts 26.7% longer than that of the reference valve, corresponding to 0.152 s and 0.12 s, respectively.
In addition, the novel designed bi-leaflet valve also exhibited favorable hemodynamic performance in all aspects studied compared with the reference valve. The trans-valvular pressure measurements indicated that the pressure drop of the bi-leaflet valve is 11.63% lower than that of the reference tri-leaflet valve, which in turn implies a lower flow impedance. The RF, regurgitant volume and leakage volume of the bi-leaflet valve are 4.11%, 16.36% and 44.84% lower than those of the reference valve, respectively. Based on the directly measured parameters, the calculated EOA and energy loss of the bi-leaflet valve are 9.7% larger and 23.28% smaller than those of the reference tri-leaflet valve, respectively. The larger EOA of the proposed valve design lowers the risk of post-operative trans-valvular pressure, thus reducing the resistance to Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR forward flow and energy loss. In addition to the results of the structural dynamic investigation, the simpler geometrically structure of the bi-leaflet valve guarantees faster coaptation, thus leads to a smaller regurgitant volume than the reference valve.
To further validate the function of the design proposed, a more extensive comparison of the hemodynamic performance was performed between the bi-leaflet valve proposed in the current study and aortic valve prostheses reported in the literature (Table 6).
Two critical parameters, EOA and mean pressure gradient, were selected from the table and compared visually in Figs 16 and 17. All selected valves are sized 25 mm on the label.
As illustrated in Fig 16, the EOA of the proposed bi-leaflet valve is ranked 2 nd among all 13 types of valves compared. The differences in the mean pressure gradients among different valve types are not obvious, and the proposed bi-leaflet valve exhibited comparable hemodynamic performance to currently available valve designs.
In addition to EOA and mean pressure gradient, the regurgitant and leakage volumes of the proposed valve were reasonable compared with available data (Fig 18).

Impact of the bi-leaflet design on coronary flow
Coronary arteries that connect to the left and right sinuses of aortic root are responsible for supplying blood to the heart. Unlike its tri-leaflet counterparts, the impact of the unique structural characteristics of the proposed bi-leaflet prosthetic aortic valve on the coronary flow is still unclear due to the very limited data.
To clarify the impact of the proposed bi-leaflet valve on the coronary flow, CFD simulations were conducted to investigate the coronary perfusion at t = 0.4 s of Fig 13, of which is the beginning of the diastolic of the left ventricle, and the maximum coronary flow can be expected around this point under physiological conditions.
In the simulations, the coronary arteries were added to the conduits of the bi-leaflet model and the tri-leaflet model, respectively (Fig 19).
The deformed bi-leaflet valve and tri-leaflet valve at t = 0.4 s were extracted from the FEM simulation results and incorporated into the their own conduits, respectively (Fig 20).
The in-vitro measured flow rate (-6.2 ml/s) was assigned to the distal ends aorta as inlet boundary conditions. Lump parameter resistance Rc 1 and R 2 were assigned to the end of left and right coronary arteries, respectively (Fig 21). The Rc 1 is 34625 dyne�s/cm 5 and the Rc 2 is 40338 dyne�s/cm 5 . Due to the current CFD simulations were performed under steady-state conditions, the authors did not consider the distal vascular compliance in the lumped parameter models.
In the CFD simulation, rigid wall assumption was assumed. The fluid was model as a Newtonian fluid with a dynamic viscosity of 3.5 mPa�s and a density of 1040 kg/m 3 .
The flow rates at the ends of coronary arteries were monitored on both models and listed in (Table 7).
Based on the CFD simulation, the differences in coronary flow between the bi-leaflet model and tri-leaflet model are small than 2%. The bi-leaflet valve shows no noticeable impact on the coronary flow compared with its tri-leaflet counterpart.

Impact of the bi-leaflet design on the flow in aorta
The flow in ascending aorta is highly affected by the aortic valve. Abnormal flow characteristics, such as eccentric jet and stress distribution, play important roles in the development of ascending aorta dilation [58][59][60].
Despite the proposed bi-leaflet valve prosthesis is well-designed for AVR that open and close in a symmetrical manner, particle image velocimetry (PIV) measurements were conducted on the bi-leaflet and reference tri-leaflet prosthesis to further verify the downstream flow characteristics. During the measurement, the PIV was triggered at the systolic peak and 60 pairs of PIV images were captured in the central of ascending aorta. The images were carefully calibrated and post-processed in the DaVis software (LaVision, Germany). The adaptive correlation method calculates velocity vectors within an initial interrogation area (IA) of 32 x 32 pixels with 50% overlapping. Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR  Fig 22(a) illustrated the velocity field downstream of the bi-leaflet valve at the systolic peak. Similar to its tri-leaflet counterpart (Fig 22(b)), no eccentric jet was observed.
Based on the velocity fields, the shear stress distribution downstream the bi-leaflet valve and the reference tri-leaflet valve was calculated, respectively (Fig 23). Similar shear stress levels were observed in the ascending aortas.

Limitations
The investigation on the feasibility of bi-leaflet ePTFE aortic valve prosthesis is still in the very early stage. Despite the bi-leaflet concept has been used as PVR prosthesis in the RVOT reconstructions successfully, some important investigations are yet to be carried out before the Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR Numerical and in vitro experimental assessment of a novel designed ePTFE bi-leaflet valve for AVR clinical application of the proposed prosthesis in AVR operations due to the pathological and hemodynamics environment in aorta differ from that in the pulmonary artery. Firstly, the long-term durability of the ePTFE prosthetic valve under aortic loading is yet to be explored by high cycle fatigue tests. Additionally, systemically in-vitro investigations of the impact of the sinuses of Valsava (height, depth, etc.,) on the local hemodynamics and the dynamic performance of the bi-leaflet valves would be necessary for the next stage of the study. Thirdly, the impact of the bi-leaflet aortic substitute on coronary perfusion and downstream flow is largely unknown, and detailed investigations should be conducted in the next stage. Last but not least, animal trials would be required previous to any clinical applications.

Conclusion
In conclusion, this study presents a novel ePTFE bi-leaflet valve prosthesis for AVR, and the dynamic and hemodynamic performance of the proposed bi-leaflet valve under physiological aortic loading were evaluated by using numerical and in-vitro experimental methods. The preliminary results showed that the bi-leaflet valve design is not only capable of serving as an aortic valve substitute under aortic physiological loadings in terms of structural dynamic behaviors, but also shows encouraging outcomes in certain critical hemodynamic parameters, including EOA, TPG, and RF when comparing with its commercialized counterparts. These novel findings could have implications for the further studies on the use of the ePTFE bi-leaflet valve in the pediatric patients who need AVR.