Comparative analysis of ovine and human aortic valve tissue for bioprosthetic valve development using relaxation tests and numerical simulation

Abstract

As the demand for aortic valve prostheses grows, optimizing their mechanical performance and durability is essential. While mechanical valves offer longevity, their need for lifelong anticoagulation limits their use, making bioprosthetic valves a preferred alternative. However, bioprosthetic valves made from bovine pericardium face durability challenges due to structural degradation. Given that valve functionality is heavily influenced by the collagen architecture and mechanical properties of the tissue, selecting an optimal replacement is essential. This study evaluates treated ovine aortic valves as an alternative material, comparing their mechanical behavior to native human valves. Tensile tests showed an elastic modulus of 20.17 MPa for treated ovine leaflets, while human leaflets ranged from 6.15 MPa to 28.10 MPa. Stress relaxation tests indicated a 41% stress reduction in treated ovine valves compared to 21% in human valves after 300 s, suggesting greater viscoelasticity. Finite element analysis revealed lower peak systolic stress in treated ovine valves (0.36 MPa vs. 0.72 MPa in human valves), with stress distributions aligning with clinically observed degradation sites. These findings highlight ovine tissue’s potential for improved durability and flexibility, making it a strong candidate for next-generation bioprosthetic heart valves.

Introduction

The aortic valve is a crucial unidirectional valve that prevents retrograde blood flow from the aorta into the left ventricle. It endures approximately 30 to 40 million cycles annually, amounting to around 3 billion cycles over an individual’s lifetime. Various pathologies can compromise this functionality, with aortic stenosis, often caused by fatty material deposition, being the most prevalent condition affecting the valve¹.

The standard treatment for aortic valves involves replacement with either mechanical or biological prosthetic valves. Porcine valves are preferred due to their favorable hemodynamic characteristics, which eliminate the need for anticoagulants post-surgery¹. However, xenograft valves are prone to calcification, reducing longevity. Mechanical valves, while longer lasting, require continuous anticoagulation, increasing the risk of thromboembolic events and bleeding². Additionally, they pose a higher risk of infection and inflammation post-implantation. Similar to other xenogeneic tissues, ovine heart valves have the potential to trigger immune responses and calcification. However, advanced processing techniques—such as decellularization, glutaraldehyde fixation, and anti-calcification treatments—can substantially mitigate these concerns^3,4. Therefore, understanding the mechanical properties of xenografts, including the ovine aortic valve, is crucial for improving treatment outcomes⁵.

The mechanical properties of aortic valve tissue stem from its trilayered composition, providing flexibility for continuous opening and closing while withstanding high-pressure blood flow. The valve’s strength is mainly due to the collagen fiber network, which serves as the primary load-bearing structure⁶. These fibers are organized circumferentially, carrying most of the mechanical load. As a result, the tissue’s viscoelastic properties are largely attributed to collagen⁷. Studies show the tissue exhibits non-linear, anisotropic elasticity, with stronger mechanical characteristics in the circumferential direction, consistent with the collagen fiber orientation^8,9.

Extensive studies on the mechanical properties of aortic valve leaflet tissue have used biaxial testing methods under conditions mimicking human physiology. Stress relaxation experiments showed that relaxation behavior depends on the loading direction, though creep was not observed. The tissue exhibited viscoelastic behavior within a specific strain rate range, but at physiological strain rates, it predominantly behaved as pseudo-elastic due to the prolonged operation of the organ¹⁰.

The conventional method for obtaining coefficients involves applying an initial step strain to the sample, from which coefficients are derived by matching the instantaneous elastic response to the stress-strain curve from the loading phase of the stress relaxation test. The reduced stress relaxation function is then matched to the normalized stress versus time data from the relaxation phase. This procedure yields coefficients consistent with quasi-linear viscoelasticity theory¹¹. Doehring et al. referred to this as the conventional approach, noting its effectiveness in separating elastic and time-dependent viscoelastic behavior when the step function is applied correctly¹¹. However, accurately applying step strains has been challenging in many studies. Dohring also observed that stress relaxation can occur during the loading phase, leading to reduced relaxation during the relaxation phase and inaccurate coefficient values. This is particularly important for tissues like the aortic valve leaflet, which operates over short periods, where stress relaxation during loading is critical¹¹.

An alternative approach by Abramovich and Woo uses convolution integrals for both test phases, allowing contributions from both phases to inform coefficient calculations¹². Carew et al. tried to derive coefficients through a combination of separate pairing methods and coefficient adjustments, emphasizing the need to consider both loading and stress relaxation phases for accurate coefficient derivation¹³. Goh and colleagues addressed challenges like the difficulty in applying step strains by introducing a method for viscoelastic materials that separately models strain and time-dependent responses. This approach incorporates various strain histories and instantaneous elastic functions, successfully addressing pairing challenges and aiding in deriving coefficients for quasi-linear viscoelasticity theory¹⁴.

This study examines the mechanical behavior of ovine aortic valve leaflet tissue using a methodology consistent with previous research. To address the existing gap in the field, where the viscoelastic behavior of aortic valve leaflets has not been comprehensively characterized or integrated into design considerations for biological heart valves, this work specifically focuses on treated ovine tissue. Following stress relaxation tests, the visco-hyperelastic properties of the treated ovine aortic valve tissue were characterized and compared to reported mechanical properties of untreated natural human aortic valve leaflets. In addition, finite element modeling (FEM) was employed to evaluate stress distribution and to assess valve opening and closing under physiological loading conditions¹⁵.

Materials and methods

Sample collection and preparation

Ovine heart samples were obtained immediately from healthy male animals aged 9 to 12 months that were slaughtered for food production at a licensed abattoir. No animals were sacrificed specifically for research purposes. The collection and use of discarded tissue complied with all relevant institutional and national guidelines and regulations governing the use of animal materials for scientific research. As the heart tissue was considered waste from food processing, dedicated ethical approval was not required for this study. The hearts were transported to the laboratory in a mixture of ice and normal saline solution, maintained at 4 °C. To enhance visibility, the upper portion of each heart was carefully dissected to expose the aortic valve, as shown in Fig. 1A. The aortic valve was then isolated by removing excess surrounding tissue. Tissue fixation was performed to preserve both its mechanical and biological properties. Initially, the tissue was immersed in 0.625% glutaraldehyde for 48 h. Following this, the tissue was rinsed with Hank’s balanced salt solution and immersed in 4% formaldehyde for 72 h. After rinsing again with Hank’s solution, the tissue was stored in 0.625% glutaraldehyde until the experiment commenced. Figure 1B illustrates the specimen after fixation. All chemical reagents were purchased from MilliporeSigma (Sigma-Aldrich; St. Louis, MO, USA).

Fig. 1.

Ovine heart samples. (A) Complete ovine heart and the cut location, (B) The aortic valve after completing the fixation process.

Human aortic valve leaflets were harvested from healthy subjects with no history of cardiac disease within 8 h post-mortem. Written informed consent was obtained from the families of the deceased in accordance with the guidelines of the Legal Medicine Organization. Subsequently, the harvested specimens were cleaned and stored in a cold 0.9% saline solution¹⁵.

Once fixation was completed, the aortic valve leaflets were separated from the fibrous annulus to which they were previously attached. According to Billiar and Sacks¹, the optimal region for sample extraction from the aortic valve leaflet is the lower portion due to several factors: (1) the fiber structure in this region is uniform, (2) collagen fibers are arranged parallel in the circumferential direction, and (3) samples from this area provide a more consistent stress field compared to other regions¹. This specific region is located just below the midpoint of the leaflet. Samples were cut into a square shape with dimensions of 4 × 4 mm² from the base of the leaflet. The thickness of these samples was measured using a micrometer, with an average thickness of 0.35 millimeters recorded.

Mechanical tests

Equipment

All tests were conducted using a custom-built uniaxial testing device fabricated in the laboratory^16–18. The system measures tensile forces using a load cell (UMAA 20Kgf, Dacell Co, South Korea) with a precision of 0.0025 N. An USB digital microscope camera with 300× optical zoom, 30 Hz frame rate, and 480 × 640 pixel resolution is integrated into the system. Data from the load cell and camera are synchronized and transferred to a computer via controllers using a Python-based acquisition program at 5 Hz. The device is equipped with 4-mm-wide clamps designed to securely hold small samples without damage.

Loading procedure

The sample was subjected to uniaxial loading, with the displacement applied along a single axis. The grips of the device were positioned 6 millimeters apart. The tests were conducted in the direction of the fibers (in the circumferential direction of the leaflets). Once the sample was secured between the grips, a preloading force of 0.01 N was applied. The initial length of the sample was defined as the distance between the two grips under this preloading force. Preconditioning was conducted prior to each test to ensure consistent starting conditions. For aortic valve leaflet samples, preconditioning typically involved cyclic loading, where the sample was repeatedly loaded and unloaded at a controlled rate¹⁹. In this case, the sample underwent cyclic loading from zero strain to 15% of its rupture strain at a rate of 1 mm/s, followed by a return to its original state.

The uniaxial tests were applied due to the lack of specific data regarding the strain and stress at the fracture point. To determine these values, tensile tests were performed on six specimens. The specimens were subjected to uniaxial tension at a rate of 1 mm/s until they fractured. During the test, the load cell recorded the applied force every 0.5 s, while images of the specimen were captured simultaneously. The specimen length was measured from the images using ImageJ software, allowing for the calculation of strain at each point. The initial distance between the grips was used as the reference length for the specimens. Subsequently the first Piola–Kirchhoff stress – engineering strain curves were extracted.

Stress at each point was calculated based on the average dimensions of the specimens and the recorded forces. After determining the fracture strain, stress relaxation tests were conducted. In these tests, after the pre-loading and preconditioning stages, the specimen was extended to 30% of its fracture strain during the loading phase. It was then held at that strain level for 300 s during the relaxation phase to monitor stress decay over time. This experiment was carried out on 10 specimens. The relationship between stress and time was derived from the images taken during the loading phase and used for subsequent modeling.

Development of constitutive model

To model the viscoelastic behavior of the aortic valve leaflet tissue, the quasi-linear viscoelastic (QLV) model by Fung is employed^20,21. According to this equation, stress is determined as a function of time:

1

In which, the instantaneous elastic modulus and stress relaxation function have decreased. The stress ratio is equal to , where is the strain, and if the strain history is known as a function of time , the relationship of stress ratio over time and, consequently, the instantaneous elastic modulus as a function of time can be determined, and the integral can be simplified as follows:

2

The stress relaxation function has been considered as a 5-term Prony series:

3

In which, is the stress relaxation coefficient in the long term and stress relaxation coefficient corresponds to time constants ^22,23.

Time constants of 0.2, 2, 20, and 200 s were selected to characterize stress relaxation at various stages. The instantaneous elastic modulus reflects the material’s elastic response under a stepwise strain when stress is applied and is a function of strain. Nonlinearity is incorporated into the model through this elastic modulus function, where a nonlinear strain-dependent function is used instead of direct strain. Given the significant deformation of the material, nonlinear elasticity theory is applied, specifically tailored for hyperelastic materials²⁴.

Humphrey et al. proposed a strain energy function to model the behavior of myocardial tissue, considering fiber orientation and aligning with biaxial experimental data. However, in a study by Martins and colleagues, the Humphrey strain energy function was adapted for uniaxial testing under the assumptions of tissue isotropy and incompressibility²⁴:

4

Using the strain energy function in Eq. (4), the instantaneous elastic response function has been employed in pseudo-linear viscoelasticity theory as follows:

5

Where and must be obtained through fitting with experimental data.

By substituting Eq. (3) into Eq. (2):

6

As a result, the stress in the material consists of two parts: one is the elastic response in the long term, represented by the first term on the right side of the equation, and the other is the viscoelastic response at each moment. However, this integral is not soluble for every strain history or instantaneous elastic function. Therefore, it needs to be discretized for solving.

For the time interval , you can define a small-time step:

7

The equation for the is given by:

8

Considering the following equation:

9

can be written as:

10

This expression means that the stress resulting from can be divided into two parts: one related to the strain history and the deformation history from time zero to , and the other related to the strain change at the current moment in the time interval ( , ).

In a very small-time interval ( , ), you can express the derivative of the instantaneous elastic function with respect to time as follows:

11

As a result, the stress at moment ) is equal to:

12

For coupling Eq. (12) to experimental results, the method of minimizing the error function is used. The error function is described as follows:

13

For data fitting, Eqs. (3), (5), and (12) were formulated as mathematical models in MATLAB Simulink. A coupling function was then defined in MATLAB to use the experimental data at each step, calculating the difference between the experimental and theoretical stress values. This function minimizes errors by optimizing the fitting process. The core of this coupling lies in the optimization algorithm, which, in this study, is the Particle Swarm Optimization (PSO) algorithm. One key advantage of this method is that it does not require initial estimates for the variables. Instead, it defines a range for each variable, allowing the algorithm to explore solutions within those boundaries. This characteristic is shared with other pairing techniques that have also demonstrated strong results.

In the context of the quasi-linear viscoelastic (QLV) model, the coupling process involves setting the values of within the range of 0.001 to 0.250, according to the equation:

14

The value of is then deduced from the calculated values of . Additionally, the parameters C1 and C2, which must be positive, were assumed to lie within the range of 0 to 5. In the algorithm used for this research, it was assumed that there are 1000 particles, and the process was repeated at least 20 times to ensure convergence and robustness of the results.

Statistical analysis

To evaluate the normality of the data distribution, the skewness and kurtosis were analyzed using SPSS Statistics software. Normality checks were performed for the data related to stress, strain, ultimate strength, and modules of elasticity obtained from the tensile tests. In the stress relaxation tests, the primary parameter examined was the percentage of stress relaxation over time. This analysis ensured that the data met the assumptions necessary for further statistical analysis and modeling. The experimental results were reported as mean ± SD. ANOVA analyses were performed to obtain the differences between the tissues in terms of material parameters. The significance level was set at P < 0.05.

Numerical simulation

The simulation was conducted using Abaqus 2022 (Dassault Systemes Simulia Corp., Providence, RI, USA) software. Initially, the geometric model of the valve was created using SolidWorks software, based on the model published in the study by Gharaie²⁵ (Fig. 2). Geometrically, the height of the valve was set to 8.5 mm, the height of the commissure was 1.9 mm, and the radius of the aortic cross-section was 15 mm. The leaflet geometry in the closed position was generated by sweeping the constructive cusp curve circumferentially along the radial curve. The geometry of the circumferential curve was generated using the hyperbola equation shown below:

15

Fig. 2.

Geometry of the ovine aortic prosthetic valve.

(Here, a was set to 1.732 mm and b to 1 mm, following the Gharaie study. The radial curve was also generated following the Gharaie study²⁵. The radial curve was also generated following the Gharaie study²⁵. The thickness of the human valve leaflets was set at 0.3 mm, while for the ovine valve, it was set at 0.35 mm.

The mechanical properties assigned to the leaflets were derived from the viscoelastic properties determined in this study. The leaflets were modeled with a density of 1060 kg/m³. The stent was modeled as a rigid body with a height of 8.5 mm. It was fixed in all degrees of freedom (displacement and rotation). The boundary condition was defined as a pressure distribution applied to the leaflet surfaces, with ventricular pressure applied at the inlet side and aortic pressure at the outlet side²⁶ (Fig. 3). The valve geometry was meshed with S4 shell elements. An element size of 0.19 mm and a total of 22,000 elements were used to ensure mesh-independent results. An implicit finite element method, capable of handling large deformations, was employed, and a contact force tolerance of 0.05 was applied to the simulation. The step size was also 0.01.

Fig. 3.

Variation in pressure in the left ventricle (red) and the aorta (blue) as the inlet and outlet boundary conditions, respectively.

Results

Mechanical properties

After positioning the specimens on the uniaxial flat system, a minimal preload was applied to accurately establish the initial position of the tissue. Figure 4 presents the first Piola–Kirchhoff stress – engineering strain curves from uniaxial tensile tests for treated ovine aortic valve leaflets, compared with those from human aortic valve leaflets obtained in our previous study¹⁵. The modulus of elasticity was derived from the slope of the linear portion of the stress-strain curve (between 20 and 80% of the rupture strain). Figure 5 displays the average modulus of elasticity, average ultimate tensile strength (UTS), and their respective standard deviations.

Fig. 4.

Average stress-strain curve of untreated human aortic valve and treated ovine aortic valve under uniaxial tensile test.

Fig. 5.

Elastic modulus, ultimate tensile strength (UTS) and failure strain of human valve and ovine valve under uniaxial tensile test.

Following the uniaxial tensile tests, the failure strain for each sample was determined. Subsequently, stress relaxation tests were conducted, applying a strain of 30% based on the failure strain of the samples. The stress-time curve for the leaflet samples of the treated ovine aortic valve was generated, and the data were averaged to produce a representative curve, depicted in Fig. 6. This average stress-time curve was then compared to the average data from leaflet samples of the untreated human aortic valve, as previously reported by Rassoli and colleagues¹⁵.

Fig. 6.

Average stress-time curves of untreated human aortic valve and treated ovine aortic valve under relaxation tests.

Next, the coefficients of the visco-hyperelastic model were extracted through optimization processes. The coefficients for the quasi-linear viscoelastic model, obtained by pairing with the experimental stress relaxation data for the average samples, are summarized in Table 1. To enable comparisons across different samples, the data from each sample was normalized prior to pairing. The R-squared was calculated as a measure of good fit, providing an indication of how accurately the model represented the experimental data.

Table 1.

Calculated coefficients for the quasi-linear viscoelastic model for treated ovine and untreated human aortic valve samples.

Samples
Ovine valve	0.103	0.155	0.097	0.136	0.509	1.567	3.747	0.997
Human valve	0.024	0.124	0.064	0.046	0.749	3.578	1.335	0.980

.

Numerical simulation

von Mises stress

The distribution of von Mises stress in the models was analyzed at peak systole (0.22 s into the cardiac cycle) and early diastole (0.4 s into the cardiac cycle), as shown in Fig. 7. As previously mentioned, the simulations were conducted considering the viscoelastic properties of both the treated ovine and human valve leaflets. The models exhibited different stress distributions, indicating that material properties play a significant role in the stress distribution of the leaflets.

Fig. 7.

Distribution of Von Mises stress for the ovine valve model (A) and human valve model (B) during peak systole, and for the ovine valve model (C) and human valve model (D) during diastole.

During the systole, regions of high stress were observed at the attachment points for both valve models, with average stresses of 0.36 MPa for the treated ovine model and 0.72 MPa for the human model. Notably, the average stress at the attachment point was lower in the treated ovine valve compared to the human valve. However, in the belly region of the leaflets, the stress in the human valve was lower during opening. Additionally, at the attachment points during complete closure of the valve (diastolic phase), the average stress values were 2.4 MPa for the treated ovine valve and 1.2 MPa for the human valve. In the models, bending at the attachment point led to high stress concentrations. Furthermore, in the human valve model, bending in the belly region during diastole also resulted in elevated stress levels.

Overall, the highly stressed regions in the fully closed position shifted from the attachment points toward the belly in both models. During the systole, the stress values were relatively closer, whereas in diastole, the stress on the treated ovine valve leaflet was significantly lower compared to the human valve leaflet.

Strain on the leaflets

The distribution of strain in the models was examined during peak systole (at 0.22 s of the cardiac cycle) and early diastole (at 0.4 s of the cardiac cycle) (Fig. 8). The maximum strain observed during peak systole was approximately 0.3, while at the beginning of diastole, it increased to around 0.6. This strain level aligns with the findings of Abbasi and colleagues²³. During the systole, regions of high strain were identified at the junction for the human valve, while for the treated ovine valve, the high strain was concentrated in the belly of the leaflet. At the onset of diastole, the human valve exhibited higher strain compared to the treated ovine valve²⁷.

Fig. 8.

Strain distribution for the ovine valve model (A) and human valve model (B) during peak systole, and for the ovine valve model (C) and human valve model (D) during diastole.

Discussion

This study investigates the viscoelastic properties of aortic valve leaflet tissue, employing quasi-linear viscoelastic theory for quantification. Initially, uniaxial tensile tests were performed on the samples, stress-strain curves that illustrate the highly nonlinear elastic behavior of the aortic valve leaflet tissue. As depicted in Fig. 4, the initial phase of the tensile test (approximated the strain to be in the range of 0 to 0.05) shows a slight, nearly linear stress-strain relationship, suggesting that collagen fibers are gradually being uncoiled while elastin fibers experience tension. As the test progresses, the steepening of the stress-strain curve indicates that the collagen structures have fully engaged, transferring stress from elastin to collagen until the tissue reaches its load-bearing capacity, ultimately leading to failure (approximated the strain range from 0.05 to failure). Previous work has shown that native ovine aortic valve leaflets are more compliant and exhibit greater circumferential extensibility than human leaflets under comparable loading conditions, reflecting underlying differences in collagen architecture and leaflet thickness²⁸.

The literature reports a wide variability in numerical values for elastic moduli, UTS, and failure strain, attributed to differences in testing protocols, strain rates, and sample preparation techniques, which complicate inter-study comparisons². In our study, the elastic modulus was measured as 20.17 MPa. Comparatively, Maureilas and Misirilis reported an elastic modulus of 14.55 MPa for human aortic valve leaflets²⁹, while another study recorded a modulus of 6.15 MPa in the circumferential direction⁶. In another research, Sauren et al. found an elastic modulus of 28.10 MPa for the same tissue in the circumferential direction³⁰. Notably, our findings indicate that human aortic valve leaflets exhibit stiffer mechanical properties than treated ovine aortic valve leaflets. Moreover, treated ovine valve leaflets demonstrate greater extensibility and failure strain, which is particularly advantageous for the development of bioprosthetic valves, especially transcatheter valves, as the higher extensibility may reduce tissue damage during crimping³¹.

Following determination of ultimate tensile strength and strain, stress relaxation tests were conducted, revealing stress relaxation values of 0.43% for human aortic valve tissue and 2.12% for treated ovine aortic valve tissue. This corresponds to an average stress reduction of 21 and 41% after 300 s for human and ovine tissues, respectively. Despite the limited research on the viscoelastic properties of aortic valve leaflet tissue, especially regarding quantification, our results align well with previously published data². The experimental findings from a study on porcine aortic valve leaflet tissue indicated a stress relaxation range of approximately 25 to 30%, further validating our results despite variations in sample type and testing conditions¹¹. The experimental data from our study closely corresponds with the quasi-linear viscoelastic model, which was solved using a discretization method. This approach has yielded favorable results in characterizing viscoelastic properties in soft tissues, such as brain tissue, underscoring its applicability for deriving model parameters¹⁴. This modeling method’s significance lies in its capacity to account for stress relaxation during loading, facilitating the derivation of both instantaneous elastic and relaxation coefficients from the complete dataset, thereby incorporating elastic and viscous behaviors across all testing phases. Furthermore, while our study utilized a simple linear strain history, the model is adaptable for more complex strain histories. Our experiments corroborate findings from previous studies, indicating that a substantial portion of stress relaxation occurs early in the test, gradually reaching an equilibrium state thereafter. Lee observed that a significant amount of stress relaxation transpires rapidly, with approximately 10% occurring within the initial 10 s of the test³².

It is worth emphasizing that the QLV model parameters in this study were derived solely from stress relaxation data. This approach was chosen because stress relaxation protocols enable a clear distinction between elastic and viscoelastic contributions in anisotropic soft tissues. Nonetheless, restricting the parameter fitting to relaxation data means that some aspects of leaflet behavior, particularly under rapid loading or large deformations—may not be fully captured, and uniaxial tensile responses may not be reproduced with complete fidelity. Even so, our finite element analyses showed strong agreement with experimentally observed leaflet kinematics and stress profiles, both in our data and in prior studies²¹. Additionally, although relaxation tests provide precise information about the viscoelastic behavior of tissues; more detailed investigation of viscoelastic behavior can be achieved by performing loading and unloading tests in future work.

This study employed finite element analysis (FEA) with certain simplifications, including the assumption of uniform leaflet thickness. The simulations were conducted for two cycles. Since no difference was observed between the results of the first and second cycles, the findings are reported for the first cycle only. Valve leaflets exhibit regional variations in thickness, with the belly region being thicker than the edges³³. Additionally, natural leaflet asymmetry was not considered, as all three leaflets were modeled symmetrically. Future numerical simulations incorporating these variations could enhance the physiological accuracy of the model.

While direct fluid effects were not modeled, viscous damping was included to ensure numerical stability. However, fluid-structure interaction (FSI) simulations could provide a more comprehensive evaluation of the valve’s hemodynamic performance by capturing the dynamic interplay between fluid forces and structural deformation. Given that flow-induced stresses can alter valve mechanics and trigger biochemical responses at the cellular level, potentially leading to clinical complications, incorporating FSI modeling would be beneficial³⁴.

For more accurate predictions of artificial valve behavior, future research should integrate viscoelastic properties into FSI models. For a more accurate comparison, it is also recommended that the human valve base be modeled as elastic in future studies. Additionally, FEA incorporating stent motion and elevated blood pressure, reflecting conditions seen in aortic stenosis patients, could offer deeper insights into valve mechanics and function under realistic physiological conditions.

The finite element analysis revealed that material properties significantly influence stress distribution within the leaflets³⁵. Our simulations indicated that maximum stress occurs during diastoles, surpassing that during systoles, consistent with findings from Abbasi et al.²⁷.High-stress regions were identified at the connection sites during systoles and in both the connection and belly regions during diastoles. Clinically, it has been observed that high-stress concentrations are often located at the connection site and base of the leaflets, areas prone to tissue degradation³⁶. The stress distributions and peak von Mises stresses predicted for the treated ovine leaflets are consistent with ranges reported for native ovine aortic valves in previous biomechanical and computational studies, thereby reinforcing the suitability of the ovine model as a replacement for preclinical assessment of tissue-engineered and bioprosthetic valve constructs²⁸. This methodology facilitates the comparison of tissue degradation in treated ovine valve leaflets as potential candidates for biological valve construction. Indirect evidence suggests that leaflet degradation may accelerate calcification and fibroblast growth, potentially leading to decreased valve durability³⁷.

The maximum von Mises stress in this study for the treated ovine valve leaflet is lower than the von Mises stress reported in previous studies for bovine pericardium tissue, which is currently used in the fabrication of artificial valves¹⁵. The von Mises stress analysis during systole and diastole for the four tissue types demonstrated that treated ovine valve tissue experiences lower stress levels than human valve tissue, highlighting its suitability for bioprosthetic valve applications.

Conclusion

In this study, the viscoelastic mechanical properties of treated ovine leaflet tissue were initially characterized for comparison with human aortic valve leaflet tissue. Subsequently, finite element modeling was employed to analyze the stresses and strains occurring during the opening and closing of the valve. The stress and strain responses of the treated ovine valve leaflet closely matched those of the human samples, indicating a relatively minor difference between the two types of tissues. This suggests greater reliability for the treated ovine valve leaflet compared to other previously tested samples with shorter lifespans. One of the recommendations for future research is to conduct fluid-structure interaction modeling to gain deeper insights into the behavior of treated ovine valve leaflets. Additionally, performing finite element analysis that accounts for stent movement and elevated blood pressure, like conditions experienced by patients with aortic stenosis, could provide valuable insights. Future studies should incorporate numerical simulations that account for the asymmetry of the leaflets and variations in thickness within the geometry to deepen the understanding of the mechanical behavior of aortic valve tissues. Additionally, simulations with a greater number of cycles are recommended to enable more detailed analysis and to assess valve fatigue more accurately. Finally, biaxial tensile tests are recommended to characterize the anisotropic hyperelastic properties of treated ovine valve tissues, along with fatigue tests to assess their durability.

Author contributions

F.M: Methodology, Software, Resources, Writing—Original Draft; A.R: Conceptualization, Supervision, Writing—Review and Editing; S.C: Methodology, Writing—Original Draft. S.R: Methodology, Software, Resources; N.F: Writing—Review and Editing.

Data availability

Data available on request from the authors.

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval and consent to participate

The human aortic valve specimens were obtained from cadavers preserved at the Iranian Legal Medicine Organization. In accordance with the organization’s policy, verbal consent from the families of the deceased was required. Prior to resection, informed consent was obtained from the families. Moreover, authorization to use these samples was granted by the Iranian Legal Medicine Organization to the research team under letter no. IR.LMO.REC.1397.96, dated 03/11/2018. Therefore, the standards laid down in the Declaration of Helsinki have been adhered to.