1 Introduction

Fabricating a tissue-like structure in vitro which remodels into functional tissue in vivo is well known to be of particular importance in the composition of a three-dimensional scaffold [1, 2]. In this case, the scaffold plays the role of a physical and structural support and a template for cell adhesion and tissue development. Finding an optimal chemical and physical configuration of different biomaterials with an effective call-biomaterial interaction in order to produce a functional tissue engineered structure seems to be an issue [3, 4]. In this study, we aim at the design and fabrication of the entire root, with the aortic valve and sinuses all incorporated in one piece. The model consists of hydrogel biomaterials, such as polyvinyl alcohol (PVA) and has the same mechanical properties and geometry as those of aortic valve leaflet and the root tissue. PVA is known to be a hydrophilic hydrogel with several characteristics suitable for biomedical applications [5,6,7]. This hydrogel can be transformed into a solid hydrogel by physical crosslinking using a low-temperature thermal cycling process [8,9,10]. The proposed model may be considered for the aortic root tissue engineering application.

2 Methods

2.1 Hydrogel preparation

PVA, 99+% (Sigma-Aldrich) hydrolyzed with a molecular weight of 146,000–186,000, was applied for the solution preparation. A suspension of 0.877 wt% BC in distilled water was implemented, which is produced in shake flasks by fermentation process using the bacterium Acetobacter xylinum as shown in Fig. 1.

Fig. 1
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Preparation of PVA-BC nanocomposite for the newly designed aortic valve

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The PVA solution was added to the BC suspension to achieve a 15% PVA with 0.5% BC (by weight fraction). The PVA-BC solution was poured into three aluminum molds and placed in a heated/refrigerated circulator (15L Heating Bath Circulator Model SD15H170-A11B) in which the molds are cycled one time between 20 and −20 °C at 0.1 °C/min (cycle 1). To reach the maximum anisotropy in one of the principle directions, i.e., the circumferential direction, an initial strain of 75% was implemented for all three samples. The cycle 1 samples were moved and stretched, while one extra non-stretched sample was kept as control. The molds were cycled using the freeze–thaw procedure, and one mold was removed each time at the end of each cycle for six consecutive cycles. The above procedure was applied for the preparation of the hydrogel used in the leaflet structure. For the root, a similar procedure was followed, except there was no BC fibers in the root structure and only 10% PVA was used instead.

2.2 Tensile Testing

The results of tensile tests are measured in the form of two sets of data representative of load versus extension. These values were then converted into stress–strain values using the geometrical factors of the samples and the initial gauge length after preconditioning. Due to large deformation of the samples, the stress–strain data obtained for all of the PVA samples show a non-linear and hyperelastic behavior. An appropriate constitutive model was then implemented to fit the experimentally obtained stress–strain data [8], \(\sigma = y_{0} + A\exp (B\varepsilon )\), where \(\sigma\) is true stress, \(\varepsilon\) is true strain, and \(y_{0}\), \(A\), and \(B\) are the curve-fitting variables. For each principle direction, i.e., the circumferential and the radial direction, the module of elasticity of the samples was calculated with respect to the degree of strain. For statistical comparisons, a two-way Analysis of Variance (ANOVA) is performed as described in literature [11, 12].

The tensile properties were assessed by a servohydraulic testing machine (INSTRON 8872) using a 1 kg load cell. All measurements were carried out inside a Plexiglas tank filled with distilled water at body temperature. The tensile tests were performed at a strain rate of 40 mm/s to a maximum of 60% strain. Prior to the tensile tests, all specimens were preconditioned with 10 cycles with the amplitude of 5 cm (peak to peak of 10 cm) and the frequency of two cycles per second as suggested in [11].

2.3 Material Modeling

Both the human and porcine aortic valves demonstrate highly anisotropic nonlinear elastic material properties in the radial and circumferential directions, which results in classification of the aortic leaflet tissue as a hyperelastic material [13, 14]. Based on the finite deformation theory for a continuum, hyperelastic materials can be described using an energy density function. Different material models have been used in previous studies in order to model heart valve behaviour [11, 15, 16]. A novel fiber-reinforced PVA-BC Nanocomposite biomaterial with similar material properties to the native aortic leaflets in both radial and circumferential directions has been utilized for the aortic leaflets, as discussed in the result section.

As seen in previous studies [12, 17], a hyperelastic matrix reinforced with nonlinear fiber elements has been employed for discrete constitutive modeling in order to model the anisotropy of the leaflets, as seen in Fig. 2. In this approach, the radial material properties have been considered as the base matrix material and the circumferential material properties have been developed by fiber-reinforcing the matrix.

Fig. 2
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Constructing anisotropic elements using isotropic and discrete beam elements

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The incompressible Ogden strain energy function [18] is illustrated in Eq. (1), where \(\mu_{i}\) and \(\alpha_{i}\) are material constants and the number terms used in the series represents the order of an Ogden model. Radial stress–strain test data of the 15% PVA–0.5% BC (75% initial strain—cycle 4) was employed in a nonlinear curve fitting algorithm in a Matlab software package in order to obtain the constitutive model constants, as shown in Table 1. These are based on an absolute error penalty for the residuals, and it was observed that the 1st order Ogden model indicates the best correlation with the experimental data while demonstrating the least computational burden for numerical analyses.

Table 1 Aortic leaflets matrix and aortic root constants—1st order Ogden model and Rapid valve opening (RVOT) and closure (RVCT) timing during the systolic ejection
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$$W = \mathop \sum \limits_{i = 1}^{\infty } \frac{{\mu_{i} }}{{\alpha_{i} }}(\lambda_{1}^{{\alpha_{i} }} + \lambda_{2}^{{\alpha_{i} }} + \lambda_{3}^{{\alpha_{i} }} - 3)$$
(1)

Based on the Voigt composite model, total stress in the fiber direction is composed of two different terms, demonstrating the effects of the matrix and fibers, proportional to their volume fraction in the composite:

$$\sigma = f\sigma_{F} + (1 - f)\,\sigma_{m}$$
(2)

where f is the volume fraction of the fibers in the composite and (1 − f) is the volume fraction of the matrix. Based on circumferential properties of the PVA-BC nanocomposite and by considering the volume fraction of fibers in the hyperelastic matrix as 5%, appropriate amounts for the stiffness and stress magnitudes of fibers was obtained in order to reinforce the matrix.

As reported by Tseng et al. [19], no statistically significant anisotropy exists within the aortic root before the age of 60 and therefore, isotropic material properties have been considered for the root. 10% PVA isotropic hydrogel has been used in the same modeling approach for the leaflet’s matrix, resulting 1st order Ogden energy function constants for the aortic root, Table 1.

2.4 Numerical Setups

A three dimensional geometrical model of the valved conduit was discretized into Belytschko–Tsay shell elements with four integration points through the thickness. This was done by applying a mesh mapping algorithm consistent with the material modeling approach, using the commercial software package ANSYS V15.0 [20] as a preprocessor. In order to account for material nonlinearity, large deformation, inertial effects and dynamic behavior of the aortic root and valve, the discretized model was imported to the commercial explicit dynamic solver LS-Dyna 971 R7.0 [21] for the application of boundary conditions and finite element analysis.

A pressure ramp was applied to the model before the cardiac cycle simulation began in order to pressurize the model to 80 mmHg, as observed in normal physiological conditions. In a full cardiac cycle simulation, the transvalvular pressure (∆P = Pv − Pao) and the aortic pressure (Pao) [22], Fig. 3, were uniformly distributed on the ventricular surfaces of the valve and the inner wall of the root respectively. The valve opening and closure phases were simulated consecutively. Similar to previous studies [8] translational constraints in local directions were applied to nodes of the annulus and base of the ascending aorta. A standard soft constraint contact penalty formulation has been defined between the entire surfaces of the model, considering self-contact and also contact between different parts. In the standard penalty formulation, contact is first determined if a slave node penetrates a master surface. Contact stiffness of the coaptation regions of aortic leaflets and solution time steps was properly defined in order to achieve leaflet stability and numerical convergence. A mass-weighted nodal damping criteria has been defined in LS-Dyna using the DAMPING_GLOBAL keyword [18], in order to take into account the damping effects of blood on the immersed valve and root structure and to avoid structural oscillations. In order to implement the mentioned constitutive model, hyperelastic matrix material properties have been defined using the Ogden strain energy function (MAT_077_O_OGDEN_RUBBER) and circumferential fibers have been generated by defining discrete beam elements (MAT_071_CABLE_DISCRETE_BEAM) along circumferential matrix nodes. The discretized FE model and leaflet fiber networks are demonstrated in Fig. 4.

Fig. 3
figure 3

The aortic (Pao), Ventricular (Pv) (a) and Transvalvular pressure (∆P = Pv − Pao) (b), in a cardiac cycle [12]

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Fig. 4
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Three dimensional FE model of the valved conduit. a Valved conduit, b aortic leaflets with different thickness distribution, c leaflet fiber network

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3 Results and Discussions

3.1 Biomaterial Development

In order to express and demonstrate our data properly, the subsequent convention is adopted: (1) the direction of applied force is considered RAD for the radial direction and the direction perpendicular to RAD is considered PERP for the perpendicular direction, (2) ISO stands for isotropic samples and, (3) for the porcine heart valve data, the results for the cut samples are considered as LEAF-CIRC in the circumferential direction and as LEAF-RAD in the radial direction.

3.1.1 Effect of the Number of Thermal Cycle

In Fig. 5a, d, the effects of 75% initial strain on the anisotropic properties of the samples are studied after cycles 2 and cycle 6. For comparison, the isotropic control of the same number of cycles is also provided. As shown in results, the hydrogel developed in this study has a higher modulus of elasticity in the radial direction than in the perpendicular direction and the isotropic control result lies in between the two aforementioned directions. In both Fig. 5a, b, a statistically significant difference of stress at 60% strain (P < 0.05) is observed among all of the samples.

Fig. 5
figure 5

a The developed anisotropy after cycle 2 on 75% initially strained sample, b The developed anisotropy after cycle 6 on 75% initially strained sample, c The stress–strain curves of the longitudinal samples in cycle 2, cycle 4, and cycle 6 with 75% initial strain, and d Tensile properties of the candidate biomaterial used in this study, C4 represents cycles 4, LONG represents longitudinal, PERP represents perpendicular, LEAF RAD represents porcine aortic leaflet in the radial direction, LEAF CIRC represents porcine aortic leaflet in the circumferential direction, and the physiological domain represents the physiological loading condition of the valve, and e proximate match of the tensile stress–strain curves of aorta in both directions and the hydrogel sample developed in this study (the anisotropic PVA with 75% initial strain after cycle 3) [11]

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Figure 5b, c show the stress–strain curves (obtained from the force extension data) of the radial samples for cycle 2, cycle 4 and cycle 6. The growth in modulus of elasticity as the number of cycles is evidently observed to cycle 4. A statistically substantial difference of stress at 60% tensile strain (P < 0.05) is observed among cycle 2, cycle 4, and cycle 6. Cycle 4 and cycle 6 are found statistically similar which is why cycle 4 is adequate to offer the highest possible anisotropy in this study.

3.1.2 Properties of Anisotropic PVA-BC Developed in this Study and the Properties of the Porcine Aortic Heart Valve Leaflet Tissue

We compared the mechanical properties of the porcine aortic valve leaflet tissue in the circumferential and the radial directions with the hydrogel biomaterial developed in this study. The proposed polymer offers the highest value for the modulus of elasticity of the PVA-BC composite biomaterial made for possible leaflet tissue replacement applications. Evidence shows (Fig. 5d) that the anisotropic PVA-BC offers tensile properties closely similar to those of the aortic leaflet tissue in both the circumferential and the radial directions in physiological conditions (strain between 20 and 30%). To the best of authors’ knowledge, this is the nearest match of the stress–strain curves for a candidate biomaterial and the porcine heat valve leaflet tissue.

3.1.3 Aortic Root Properties

An evaluation of all the anisotropic PVA samples and the human aorta was achieved in order to set up a conceivable match of the mechanical properties for tissue replacement applications. Figure 5e indicates the stress–strain curves of the aorta in both directions and the anisotropic pure PVA sample after cycle 3 in which the initial strain is 75%. The results are consistent with those reported by Tseng et al. [19].

3.2 Modeling and Simulation

Stress–strain behavior as well as kinematics and dynamic response of the designed aortic valve prosthesis have been simulated in a complete cardiac cycle by the application of physiological pressure. A discrete constitutive approach has been used to implement the nonlinear anisotropic properties of the previously proposed PVA-BC Nanocomposite. Leaflet stretches were represented by Green stress distribution on the leaflet surface during opening and closing phases and effective (Von-Misses) stress represents the overall stress state of leaflets. The kinematic and dynamic response of the valve has been assessed by the opening and closing configurations, valvular timing and the motion of the nodulus Arantius and aortic sinuses. Results have been compared to In-vivo clinical data [23, 24] and previous computational studies [13, 15, 22, 25], except for the aortic root, for which no experimental data exists until this study. In this case, the corresponding results have been verified by only using the previous simulation results [15, 22]. Although the effect of blood flow has not been modeled directly, the structural model represents acceptable valvular kinematic and dynamic response while minimizing the computational burden.

3.3 Aortic Valve and Root Stresses and Strains

The maximum stress on leaflets increases while the valve opens from the unpressurized configuration and reaches its greatest magnitude during systole at the fully opened configuration at t = 90 ms, Fig. 6. During the diastolic phase, stress magnitude increases after a slight drop and the highest stress magnitude in a cardiac cycle occurs at t = 366 ms. The maximum stress on the root wall represents less difference and demonstrates consistent changes in magnitude with the aortic pressure. Stress–strain distribution pattern and the location of maximum stretches and stresses varies in time as a result of valvular dynamics. Similar to previous studies on the biological aortic valve tissue [15, 22, 25], at peak systole, the stretches are greater on the leaflet belly, the maximum stress reaches a magnitude of about 148.7 kPa and higher stress values are located near the attachment region of leaflets to the root, Fig. 7. At peak diastole, the maximum stress of 626.7 kPa is located near the commissure and leaflet stretches are maxima near the root wall and leaflet belly, as also reported by [13, 15, 22]. The maximum stress on the aortic root demonstrates a magnitude of 277.5 kPa at peak aortic pressure and is located on the aortic sinuses, which is in acceptable correlation with studies conducted in Sturla 2013 and Conti et al. 2010 [15, 22]. Stress and strain distribution of the prosthesis facilitates the optimization procedure of the valve by locating the area with higher stress or stretches to be reinforced.

Fig. 6
figure 6

Stress distribution on aortic leaflets and the aortic root in a cardiac cycle—units are in Pa

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Fig. 7
figure 7

Deformed configurations, effective (Von-Misses) stress and Green strain distribution on a aortic leaflets at peak systole, b aortic leaflets at peak diastole, c aortic root at maximum aortic pressure in a cardiac cycle—units are in Pa

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3.4 Valve and Root Kinematic

Radial displacements of the nodulus of Arantius and the aortic sinuses, the coaptation level and rapid valve opening (RVOT) and closure (RVCT) times were employed to analyses the valvular kinematics.

As illustrated in Fig. 8a, radial displacement of the nodulus of Arantius, measured from its initial position at the unpressurized condition, reaches its maximum value of 8.17 mm during the systolic phase and decreases during rapid valve closure, as also reported by Sturla and Conti et al. [15, 22]. Radial position of the aortic sinuses remains relatively constant and decreases slightly in response to the aortic pressure. It should be noted that the first 300 ms duration in Fig. 8a, b include the aortic root pressurization to physiological conditions and the cardiac cycle begins at t = 300 ms in these Figures. Using the more quantitative approach to obtain RVOT and RVCT by Sturla [15], radial velocity of the nodulus of Arantius was obtained in a cardiac cycle, Fig. 8b. The obtained RVOT and RVCT timing, defined as the duration that velocity of the nodulus of Arantius reaches local maximums from mid-cycle stationary configurations, represents an acceptable correlation with in vivo measurements [23, 24] as illustrated in Table 1. This reveals similar performance of the prosthesis to the biological aortic valve tissue. Also, geometrical configuration of the prosthesis represents almost similar behaviour with human aortic valve at different time intervals [15].

Fig. 8
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a Radial displacements of the Aortic sinuses and nodulus of Arantius in a cardiac cycle, considering the initial ramped pressurization, b Radial velocity of the nodulus of Arantius in a cardiac cycle, considering the initial ramped pressurization

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The diastolic coaptation level was defined as the maximum distance between the nodulus of Arantius and the annular plane. Simulations result in 8.01 mm coaptation level which is slightly higher than the biological reported MRI data [22]. These results demonstrate that the designed prosthesis is capable of mimicking the mechanical behavior and response of human aortic valve in a cardiac cycle, resulting in similar cardiac timing and minimizing side-effects on the human hemodynamics.

3.5 Final Design

In order to improve the surface quality, as the final refinement of the surface, Bezier curves are accustomed through a trial and error procedure by removing, relocating, or interpolating the control points. The present 3D-CAD model is then developed by using a command to be transformed to shell, e.g., command Shell of I-Deas in which a uniform thickness is required to produce a shell through the designed Bezier surface. The shell model is then converted to a solid model in order to apply non-uniform thickness to the leaflets. In this study, Mechanical Desktop V2013i CAD software is used to produce the model. The final model consists of three identical leaflets, which each leaflet being symmetrical about its own midline between the top of the free edge to the midpoint of the commissure of the leaflet all located in the aortic root. The fully closed form of the leaflets was used to find the necessary control points. This is achieved by mapping the leaflet geometry using a coordinate measuring machine (CMM) with a laser scanning system such as 3D Digital Corp, 3D scanner cyberware. Finally, a cavity mold was designed and fabricated in order to manufacture the proposed valved conduit out of the developed PVA and BC. The mold parts are demonstrated in Fig. 9.

Fig. 9
figure 9

a The cavity model and its parts designed and fabricated for the human aortic root, and b the once piece synthetic human aortic root including the valve and the sinuses all made of hydrogel biomaterials

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4 Conclusion

In this study, the aortic human root including a trileaflet polymeric aortic heart valve made of PVA-BC nanocomposite material in the aortic root (valved conduit) was developed. The key factors for the design of the proposed PVA-BC nanocomposite are: (1) a mixture of 15% PVA and 0.5% BC, (2) the solidification process, i.e. thermal cycling, and (3) an initial strain of 75%. The developed nanocomposite may be a promising candidate material for the construction of trileaflet polymeric aortic valves Gallocher et al. [26] designed a poly-olefin composite material for heart valve applications. They developed a novel poly-olefin (poly-styrene-b-isobutylene-b-styrene) for use in the aortic valve leaflet tissue and evaluated its mechanical properties based on the presence of poly-propylene (PP) fibers. They used poly-urethane (PU) for comparison. The modulus of elasticity reported for the poly-olefin, the PP fiber, and PU are, respectively, 3.9 ± 0.4, 6633 ± 492, and 18.5 ± 1 MPa. Two cases of PP reinforced poly-olefins with low and high fiber content composite were investigated and the modulus of elasticity of the low fiber content composite was reported 5 ± 3 MPa while the high fiber content composite offered a modulus of elasticity of 45 ± 3 MPa. The maximum modulus of elasticity of the PVA-BC designed in this study falls within the range of 1.7 ± 0.3 MPa in the circumferential direction and 0.5 ± 0.1 MPa in the radial direction both at a strain of 25%. If we compare these values to those of the natural tissue, the modulus of elasticity of the porcine aortic valve leaflet tissue in the circumferential direction is 3.3 ± 0.3 MPa at a strain of 25% and the corresponding value in the radial direction is 0.6 ± 0.1 MPa at the same strain. Also, both poly-olefin-PP composites with high and low fiber contents offer the ultimate tensile strength (UTS) of 3.40 ± 0.55 and 7.92 ± 0.87 MPa, respectively, which was obtained in an ultimate strain (US) 30–35%. The proposed anisotropic PVA-BC nanocomposite developed in this study offers UTS more similar to that of the porcine valve tissue but in the US of larger than 50% which further justifies its application as the material for the new trileaflet polymeric valves designed in this study. Also, the normal anisotropy of the root tissue was incorporated in a 10% PVA sample which shows a close consistency with that of shown by Azadani et al. [19]. The computational work performed in this study is highly suggestive that the proposed valved conduit model can be considered for further studies such as animal trials.