Commercially available heart valves have many limitations, such as a lack of remodeling, risk of calcification, and thromboembolic problems. Many state-of-the-art tissue-engineered heart valves (TEHV) rely on recellularization to allow remodeling and transition to mechanical behavior of native tissues. Current in vitro testing is insufficient in characterizing a soon-to-be living valve due to this change in mechanical response; thus, it is imperative to understand the performance of an in situ valve. However, due to the complex in vivo environment, this is difficult to accomplish. Finite element (FE) analysis has become a standard tool for modeling mechanical behavior of heart valves; yet, research to date has mostly focused on commercial valves. The purpose of this study has been to evaluate the mechanical behavior of a TEHV material before and after 6 months of implantation in a rat subdermis model. This model allows the recellularization and remodeling potential of the material to be assessed via a simple and inexpensive means prior to more complex ovine orthotropic studies. Biaxial testing was utilized to evaluate the mechanical properties, and subsequently, constitutive model parameters were fit to the data to allow mechanical performance to be evaluated via FE analysis of a full cardiac cycle. Maximum principal stresses and strains from the leaflets and commissures were then analyzed. The results of this study demonstrate that the explanted tissues had reduced mechanical strength compared to the implants but were similar to the native tissues. For the FE models, this trend was continued with similar mechanical behavior in explant and native tissue groups and less compliant behavior in implant tissues. Histology demonstrated recellularization and remodeling although remodeled collagen had no clear directionality. In conclusion, we observed successful recellularization and remodeling of the tissue giving confidence to our TEHV material; however, the mechanical response indicates the additional remodeling would likely occur in the aortic/pulmonary position.

## Introduction

Progressive weakening, calcification, or tearing of the aortic valve can lead to complications necessitating valve replacement. In industrialized nations, there is an overall prevalence of at least 2.5% for valvular heart disease, with at least 50,000 deaths occurring from secondary causes of valvular heart disease in the U.S. alone [1]. Current clinical strategies for aortic valve replacement involve the utilization of mechanical or bioprosthetic valves. However, these have wide limitations that prevent universal utilization. For instance, the former requires that the patient undergo persistent anticoagulant therapy that may be contraindicated in elderly populations or in patients with severe cardiovascular disease [2]. On the other hand, the latter is subject to tissue degradation over time. Both of these types of valves lack the capacity to grow and remodel and thus are not suitable for pediatric and long-term application [3]. This has necessitated the search for suitable valve replacements.

Design and construction of a tissue-engineered heart valve (TEHV) is of great current interest. This is because a TEHV can be designed to be patient-specific, can utilize xenograft tissue without antigen response, and can be invaded with autologous cells to allow for growth and remodeling in vivo. There is extensive research in the field to use xenograft valves, as this tissue can be readily harvested [4]. Yet, there have been great challenges in coming up with an appropriate decellularization process to allow for the structural and mechanical properties of the tissue to remain intact. Nonionic detergents, such as sodium dodecyl sulfate (SDS) and triton, have shown promise in decellularizing the tissue while preserving glycosaminoglycans and matrix structure relative to other treatments [49]. Nevertheless, application of SDS to valvular tissue has demonstrated reductions in mechanical properties of the native tissues to an extent that could cause in vivo failure [6,7].

The outcome from implementation of novel biomaterials is difficult to forecast; however, numerical modeling techniques can be utilized to predict the potential for aortic regurgitation or failure following valve replacement in a patient specific setting. This is done through the incorporation of individualized anatomy and mechanical properties of the valve in a simulated physiological environment [10]. Furthermore, the finite element (FE) method can be utilized to predict the details of material specific valvular performance [11]. Previously, the FE method has been employed as an addition to accelerated wear testing. Specifically, FE simulations have been developed to model the effects of cyclic loading on fixed bovine pericardium valvular leaflets and have accurately predicted fatigue with great similarity to clinical findings [12]. Numerical modeling has the potential to predict the success of the physical application of a material in a physiological setting. The combination of tested mechanical parameters can be used in tandem with detailed computational modeling to determine the performance of a material as applied to its' performance of a valve. However, previous work has not investigated the potential for increases in mechanical performance of a decellularized TEHV with a subsequent process of recellularization.

In the current study, the mechanical response of an explanted TEHV following recellularized in the rat subdermis over 6 months is evaluated and contrasted to the implanted decellularized pericardium. This method provides a simpler means to evaluate the recellularization and remodeling potential of our TEHV material prior to high-risk and expensive orthotopic ovine models. Additionally, this simplicity allows a large sample number which is difficult in such ovine models. The mechanical response of each tissue type was evaluated via biaxial testing and the data fitted to an anisotropic hyperelastic constitutive model. These data were then incorporated into a FE model of an idealized TEHV, and the performance of each tissue type was contrasted using standard metrics (i.e., principal stresses and strains).

## Methods

### Tissue Collection, Preparation and Animal Studies.

Whole porcine hearts were harvested and randomly selected from a local abattoir (Hormel Food Corporation, Austin, MN). Pericardial tissue was separated from the heart, cut into appropriate sizes, and either set aside for processing then testing or sutured onto polycaprolactone rings with inner and outer diameters of 19.2 mm and 22.7 mm, respectively (Fig. 1). Additionally, native valves were excised and set aside for mechanical testing. All pericardium from the experimental groups were decellularized over 2 days utilizing constant agitation in a cocktail of SDS, DNase, and diH2O. Pericardium was then washed in a solution of 2% DNase, Tris buffer, MgCl2, 1% peroxyacetic acid (PAA), and phosphate-buffered solution over 2 days. Prior to implantation, the decellularized pericardium was sterilized using supercritical carbon dioxide (NovaSterilis, Inc., New York). Pericardium mounted on the polycaprolactone rings was then implanted subcutaneously into nine female Sprague Dawley rats at 2 sites on the animal's back and removed after 6 months. This method was chosen as it was found that mounting the tissue on the rings resulted in improved tissue remodeling compared to suturing the tissue in place or placing the tissue unsecured in the rat subdermis. Further details on the procedure can be found in Khorramirouz et al. [13].

Fig. 1
Fig. 1
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### Histology.

Histological staining, hematoxylin and eosin (H&E), and Masson's Trichrome (MT), was performed on decellularized tissue, and tissue explanted after 6 months. Collagen fiber orientation and dispersion were evaluated using the directionality feature within fiji software [14].

### Mechanical Testing

#### Biaxial Testing.

An in-house biaxial setup, with four linear actuators controlled independently by position, was used for mechanical testing. Force measurement is conducted by four 44.5 N load cells attached to the each moving stage, two in the x1 direction and two in the x2 direction which are connected to the arms holding the testing rakes (Fig. 2; Cellscale, Waterloo, ON, Canada). Testing was performed on native porcine cusps (n = 21), the implanted decellularized porcine pericardium (n = 19), and explanted recellularized pericardium (n = 16) the same day as explant. Porcine cusps were cleaned and were mounted on the biaxial machine such that the radial direction was aligned in the x1 direction of the machine. Both the implant and explant pericardium groups were carefully cleaned of connective and fatty tissue before mounting on the biaxial system. Due to no obvious fiber direction being present, no special care was made to orient the tissue on the machine with respect to fiber axis. Five rake prongs, with tine spacing of 1.7 mm, were used to secure the tissues. Samples were moistened at regular intervals with saline solution at 37 °C via pipette to maintain in vivo temperature.

Fig. 2
Fig. 2
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#### Strain Measurement.

Cyanoacrylate and graphite were combined3 and nine small markers for tracking were placed on the center region of the sample by carefully dipping a needle tip into the mixture and manually applying small dots to the tissue (Fig. 2). Care was taken to minimize the effect of the superglue on the tissue mechanical response. The displacement of the markers was recorded using a Nikon D5600 digital camera with a Nikon near-view lens (AF–S Micro–Nikkor 105 mm f/2.8G IF–ED VR) and the markers were tracked using the TrackMate plug-in within fiji software [14,15]. The components of the deformation gradient tensor were then found using finite element shape functions described in Sommer et al. [16].

#### Stress Measurement.

Due to the low shear strains measured in testing and the limited contralateral forces transferred onto the sample by the rake system, we opted to assume shear forces were negligible in this study. Furthermore, by assuming zero stress in the x3 direction, the first Piola–Kirchoff (PK1) stress tensor was simplified to
$P=f1L2T000f2L1T0000$
(1)

where $T$ is the sample thickness, $f1$ and $f2$ are the measured forces, and, $L1$ and $L2$ are the sample length along x1 and x2, respectively.

### Constitutive Modeling.

To capture and quantify the response of the pericardium the behavior must be represented by an appropriate constitutive model. For this, we choose the Gasser–Holzapfel–Ogden (GOH) constitutive model which has been used widely for modeling of valvular tissue and is available in abaqusexplicit (v.6.14, Dassault Systèmes Simulia Corp., Providence, RI) [19,20]. The strain energy function takes the form of
$WC,Hi=Wm+∑i=1,2Wfi$
(2)
where $Wm$ is the isotropic strain energy representing the ground matrix while $Wfi$ is the anisotropic strain energy for the two families of collagen fibers. The respective components are given as
$WmC=μ2λ12+λ22+λ32 −3$
(3)
and
$WfiC,Hi=k12k2[exp(k2Ei2)−1]$
(4)
where
$Ei=Hi:C−1, Hi=κI+(1−3κ)(ai⊗ai)$
(5)

Here, $λ1, λ2$, and $λ3$ are the principal stretches with the mean collagen fiber direction $θ$ in the reference configuration characterized by unit vectors $ai$. The fiber directions are defined by $a1=[cos(θ)sin(θ) 0]$ and $a2=[−cos(θ)sin(θ) 0]$ relative to the x1 direction.

The degree of fiber dispersion was captured by a statistical parameter $κ∈0,13$ such that complete alignment of fibers was described by $κ=0$ and full dispersion, resulting in isotropy, by $κ=13$. The additional parameters are $μ$, the shear modulus, $k1$, a stress-like parameter and $k2$, a dimensionless parameter. The second-order tensors $C$ and $I$ are the right Cauchy–Green deformation tensor and second-order identity tensor, respectively. The first PK1 stress was then derived from these strain energy functions as described in the Appendix.

#### Constitutive Model Parameter Estimation.

We utilized both a standard fitting approach and the inhomogeneity from experimental setup corrected (IEC) parameter fitting described in Fehervary et al. (See Fig. 1 available in the Supplemental Materials on the ASME Digital Collection) [21]. In the latter technique, a standard fitting procedure was performed, [22,23] and these parameters are then placed into a finite element simulation of the equibiaxial loading performed in the biaxial testing. Predicted PK1 stress components from the FE model ($PiiFE)$ and the analytical solution ($Piicalc$) are then utilized to find a correction vector at each time point $t$ according to
$gi(t)=PiiFE(t)Piicalc(t)$
(6)

with $i=1,2.$

The correction vector was then combined with the original experimental stress data in a new parameter fitting round. This continued until the root-mean-square error (RMSE) between the correct vector and an all-ones vector was below a specific threshold or a specified number of fitting rounds had been performed in which case the parameters that provided the lowest RMSE were selected.

The finite element model of the biaxial experiment is composed of a 25,409 four-node hybrid formulation quadrilateral elements with plane stress formulation and the solution is mesh independent for the measured variables utilized for the fitting procedure (Fig. 3). Only one biaxial testing regime (equibiaxial tension) was modeled; yet, for the standard parameter fitting portion of the IEC all available data were utilized. This was done to simplify the procedure and to minimize the time required to obtain a solution.

Fig. 3
Fig. 3
Close modal
The matlab optimization toolbox (Matlab v.2016a, MathWorks, Natick, MA) was used to minimize the error between experimental and analytical results for a planar biaxial condition of standard parameter fitting. This can be represented as
$x=argmin x[P11eq,P22eq,P11uneq1,P22uneq1,P11uneq2,P22uneq2]$
(7)
With
$Piieq(t)=‖Piimod(t)−gi(t)Pii exp (t)‖eq$
(8)
$Piiuneq1(t)=‖Piimod(t)−gi(t)Pii exp (t)‖uneq1$
(9)
and,
$Piiuneq2(t)=‖Piimod(t)−gi(t)Pii exp (t)‖uneq2$
(10)

Here, $Piimod$ and $Pii exp$ are the diagonal components of the PK1 stress tensor for the analytical model and the mean experimental data, respectively, and $x$ is a vector of the model parameters. The average experimental data were chosen rather than averaging results to reduce the number of fittings to be performed and to improve accuracy as it has been shown that average constitutive parameters are not guaranteed to represent average behavior [24]. In addition, upper and lower bounds were applied to limit the fitted parameters to be physically plausible and fits were performed to all testing conditions simultaneously to improve the reproducibility and accuracy of the fitted parameters by minimizing the potential solutions that are below the optimization tolerance. A multistart wrapper was used for analytical fitting (Eqs. (7)(10), steps 1 and 6 in Fig. 1 available in the Supplemental Materials on the ASME Digital Collection), which reduces the optimum solution dependence on starting parameters seen when fitting hyperelastic materials [25]. The fitted parameters from each method (standard fitting or IEC) were then compared, and the most suitable were utilized in the subsequent FE analysis.

### Finite Element Analysis

#### Model Setup.

Three-dimensional models of single aortic valve leaflets were created using Solidworks (Dassault Systèmes, Waltham, MA) and imported into abaqus. The leaflet geometry was an in-house design developed by optimizing performance in accelerated wear testing and in vitro flow studies. Finite element analysis models were created using abaqus. Meshing generated 246,225 nodes and 209,220 C3D8R elements with a thickness of five elements. Three leaflets were assembled with 120 deg rotation from the original instance. We applied the material constants found in Sec. 2.4.1 to the GOH anisotropic constitutive model available in abaqus explicit. The strain energy function takes the form of
$W(C¯,Hi,Jel)=W¯m+W¯fi+1D(Jel)2−12−ln(Jel)$
(11)
with
$W¯m(C¯)=μ2(λ¯12+λ¯22+λ¯32−3)$
(12)
and
$W¯fi(C¯,Hi)=k12k2[exp(k2E¯i2)−1], E¯i=Hi:C¯−1, Hi=κI+(1−3κ)(ai⊗ai)$
(13)

Here, an overbar represents the isochoric (volume preserving) portion of the respective term with the volumetric behavior described by the last section of Eq. (11) where $Jel$ is the elastic volume ratio and $D$ is 2 divided by the bulk modulus. Table 1 shows the parameters applied from fitting in Sec. 2.4.1 and $D$ was assigned a near incompressibility value of $D=(1/25μ)$ MPa−1.

Table 1

Fitted constitutive model parameters and RMSE for native valve, explant groups, and implant groups using the standard fitting procedure

$μ$$k1$$k2$$κ$$θ$RMSE
Native valve0.0125.45439.0700.32789.5580.328
Explants0.0098.09926.2650.29738.0090.029
Implants0.00924.53337.7670.3170.0000.328
$μ$$k1$$k2$$κ$$θ$RMSE
Native valve0.0125.45439.0700.32789.5580.328
Explants0.0098.09926.2650.29738.0090.029
Implants0.00924.53337.7670.3170.0000.328

Material properties were utilized with Rayleigh damping (α = 20,000) and a density of 1 × 10−6 kg/mm−3. Leaflet interactions were modeled under general contact conditions utilizing tangential behavior with penalty friction formulation and normal behavior allowing for leaflet separation. Transvalvular pressures were applied on the aortic (top) and ventricular (bottom) sides of the leaflets based on standard physiologic pressures as described by Kim et al. [26]. Pressures were applied with a uniform distribution utilizing amplitudes corresponding to the pressure waveforms. Boundary conditions were set along the exterior edges of the leaflets, running along the belly and commissure edges, with encastre conditions, to accurately represent the valve sutured to the wall during surgical implantation. Due to convergence issues when running implicit analyses, abaqusexplicit was used to solve the model.

#### Simulation.

Maximum principal stresses and strains were collected at 12 time points (t = 0.001, 0.056, 0.11, 0.148, 0.185, 0.226, 0.296, 0.404, 0.582, 0.652, 0.724, 0.760 s), with six points evenly distributed across systolic and diastolic periods, respectively. To ensure that the data were representative of the region of the FE model rather than a single node, data were analyzed for 12 elements within the leaflet belly and at the top of the commissures. The average was then taken from this data and a multicomparison test was run to find significance between tissue groups. Models were run for 110% of a cycle and the initial 10% of the second cycle replaced the preliminary 10% of the first cycle in order to account for any effects from the initial undeformed state. Images were saved at each time point, and a cumulative video of both models across the entirety of the cardiac cycle was created.

#### Validation.

Validation was performed using a valve that was made from material from the implant tissue group with laser-cut leaflets to match the CAD geometry of the computer model. The tissue was then sutured to a custom nitinol stent along the commissures and around the lower edges of the leaflets to match the boundary conditions applied to the model. This was placed into a transparent tube and tested in a pulse duplicator. Physiologic pressures and flows were then applied to the valve. An endoscope and digital camcorder were used to capture valve performance in vitro. Displacement parameters were measured using ImageJ (National Institutes of Health, Bethesda, MD) and compared to model displacement at peak systolic and diastolic pressures (Fig. 4). As a further validation technique, an identical valve composed of material from the implant tissue group was exposed to fatigue testing on an accelerated wear tester until failure (Durapulse, TA Instruments, New Castle, DE) and sites of failure were compared to stress concentrations in the FE models.

Fig. 4
Fig. 4
Close modal

## Results

### Histology.

Hematoxylin and eosin staining demonstrated a complete lack of cellularity as well as minor matrix disruption in the implant tissues. In contrast, the explant leaflets showed recellularization throughout (Fig. 5). Analysis of collagen content, via MT, showed synthesis of collagen although quantitative analysis showed the implant tissue has similar orientation in each sample while explant had large variation between each sample (Table 2). However, the dispersion is equally high for the two groups.

Fig. 5
Fig. 5
Close modal
Table 2

Quantitative analysis of fiber orientation of the implanted decellularized porcine pericardium and the samples explanted after 6 month in a rat subdermis

DirectionDispersionAmountGoodness
Implant
Mean11.46929.9180.7250.908
Standard deviation6.3094.6870.0960.048
Explant
Mean−15.23830.0550.6560.954
Standard deviation49.5557.3530.1170.031
DirectionDispersionAmountGoodness
Implant
Mean11.46929.9180.7250.908
Standard deviation6.3094.6870.0960.048
Explant
Mean−15.23830.0550.6560.954
Standard deviation49.5557.3530.1170.031

### Mechanical Testing.

Figure 6(a) shows the mean PK1 stress versus stretch for the native valvular tissue. For loading protocol 1 (equibiaxial displacement), the circumferential (x2 direction) had higher maximum stress and lower maximum stretch than the radial (x1 direction). In protocol 2, maximum stress and stretch was in the radial (x1) direction; conversely, protocol 3 yielded the highest maximum stress and stretch in the circumferential (x2) direction.

Fig. 6
Fig. 6
Close modal

The mean PK1 stress versus stretch for the explant tissue is shown in Fig. 6(b). For loading protocol 1 (equibiaxial displacement), there was similar maximum stress for each direction and the x2 direction had the lowest maximum stretch, albeit the difference is small. As with the native valve, loading protocol 2 led to a higher maximum stress and stretch in the x1 direction and lower maximum stress and stretch in the x2 direction and vice versa for protocol 3.

Figure 6(c) shows the PK1 stress versus stretch for the implant tissue group. Loading protocol 1 (equibiaxial loading) resulted in similar loading profiles in both x1 and x2 directions. Similar to explanted tissue, in loading protocol 2 the highest maximum stress and stretch were in the x1 direction and lower maximum stress and stretch were in the x2 direction and the opposite for protocol 3.

Comparing between data for the implant group (Fig. 6(c)), the stress is approximately an order of magnitude higher than for either of the two other tissue types. Both native (Fig. 6(a)) and explant tissues (Fig. 6(b)) have similar stress magnitudes; yet, stretch is lowest for the explant tissues. The explant tissue group appears slightly less isotropic than the implant group while native tissue shows the greatest anisotropy.

### Constitutive Model Parameter Estimation.

The fitted parameters are given in Table 1 for standard fitting and See Table 1 available in the Supplemental Materials on the ASME Digital Collection for IEC fittings with the RMSE. Comparing the fitting parameters between the two methods, the most notable differences are for $k2$ in native tissues and explants, and $θ$ for the explants. For the standard fittings, $k1$ was greatest for the implants and lowest for the native tissues, $k2$ was low for the explants but had a similar magnitude for the other two groups, $κ$ was lowest for the explants and highest for native tissues although the value was high for all groups; finally, $θ$ varied greatly between groups with highest values for native tissues and lowest for the implant group. The plot of the fitted data over the experimental data is shown in Fig. 7; overall, the best fits are to the explant groups with the other two groups showing similar, lower quality fits. For the IEC fittings, the angles were approximately 90 deg and $κ$ was high for all tissues. There is a large variation in both $k1$ and $k2$ between tissue types while $μ$ is highest for native valve tissue by 2 orders of magnitude. The RMSE was low for all tissues and has a similar magnitude. As for the standard fits, the comparison of analytical, simulated FE, and experimental biaxial PK1 stresses versus stretch for each tissue type is given in Fig. 2 available in the Supplemental Materials on the ASME Digital Collection.

Fig. 7
Fig. 7
Close modal

### Finite Element Analysis Simulation.

Maximum principal stress and strain were collected at six time points (See Fig. 3 available in the Supplemental Materials on the ASME Digital Collection) across a standard cardiac cycle, six points in both systole ((Fig. 8), See Fig. 4 available in the Supplemental Materials on the ASME Digital Collection) and diastole, respectively, ((Fig. 9), See Fig. 5 available in the Supplemental Materials on the ASME Digital Collection). Overall, there is little difference in behavior between native and explant tissues but lower deformation from the implant group. This is seen with the maximum principal strain contours where the implant tissue group model has evenly distributed lower intensity contours while the other two show much higher strain. A summary of the maximum principal stresses and strains at the top of the commissures and leaflet belly during systole and diastole is given below:

Fig. 8
Fig. 8
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Fig. 9
Fig. 9
Close modal

#### 3.4.1 Maximum Principal Stress at Leaflet Belly.

The implant group was significantly different to the explant group and native tissues (p < 0.05) during systole for all time points bar the second (t = 0.056 s) with the implant groups showing both higher and lower stresses than the other two groups at different time points (Fig. 10(a), peak systole; implant: −0.004 ± 0.003 MPa; native: 0.021 ± 0.001 MPa; explant: 0.021 ± 0.001 MPa). This trend continues during diastole although the implant group shows significantly higher stress (p < 0.05) than the other two groups for all time points bar the last where the stress is marginally, though still significantly, smaller (Fig. 10(a), peak diastole; implant: 0.113 ± 0.004 MPa; Native: 0.104 ± 0.004 MPa; explant: 0.104 ± 0.004 MPa).

Fig. 10
Fig. 10
Close modal

#### Maximum Principal Stress at Top of Commissures.

During systole, there was only a significant difference between any groups at the first time point (t = 0.001 s) where the implant group was significantly different (p < 0.05) to both the native and explant groups (Fig. 10(b), peak systole; implant: −0.003 ± 0.002 MPa; native: −0.004 ± 0.003 MPa; explant: −0.004 ± 0.003 MPa). For diastole, the explant group has significantly lower stress (p < 0.05) than both the implant and native groups for all time points (Fig. 10(b), peak diastole; implant: 0.186 ± 0.007 MPa; native: 0.231 ± 0.018 MPa; explant: 0.231 ± 0.019 MPa).

#### Maximum Principal Strain at Leaflet Belly.

In systole, the implant group was significantly lower (p < 0.05) than both the native and explant groups (Fig. 10(c), peak systole; implant: 0.037 ± 0.005 MPa; native: 0.083 ± 0.002 MPa; explant: 0.083 ± 0.002 MPa). The same pattern is present during diastole with the implant group showing significantly higher (p < 0.05) stress than both implant and native groups for all time points (Fig. 10(c), peak diastole; implant: 0.137 ± 0.004 MPa; Native: 0.200 ± 0.006; explant: 0.201 ± 0.006 MPa).

#### Maximum Principal Strain at Top of Commissures.

During systole, the implant group is significantly different (p < 0.05) to both the explant and native groups for four time points (t = 0.001, 0.056, 0.148, 0.185 s) and to only the native group for the remaining time points (t = 0.110 and 0.226 s) ((Fig. 10(d), peak systole; implant: 0.001 ± 0.013 MPa; native: 0.047 ± 0.068 MPa; explant: 0.028 ± 0.015 MPa). In diastole, the implant group is significantly lower (p < 0.05) than both explant and native groups for all time points except the last (t = 0.226 s) (Fig. 10(d), peak diastole; implant: 0.176 ± 0.002 MPa; native: 0.300 ± 0.078 MPa; explant: 0.321 ± 0.014 MPa).

### Validation.

The FE implementation was validated by comparing the computer simulations to the in vitro experimental hydrodynamic and accelerated wear test data. Displacement from peak systole to peak diastole was measured and contrasted between the hydrodynamic in vitro samples and in silico models.

For the pericardial valve made from the implanted material, with matching leaflet geometry to the model, there was <7% difference in displacement observed in the model relative to that measured in vitro (Figs. 4(c) and 4(d)). These values are within our acceptable validation tolerance of 25%, which is lower than other in silico vascular models [27]. Accelerated wear testing was also performed on these valves to assess sites of damage. Confidence in the FE model was established because in both experimental valves failure occurred in the leaflet belly, the site of highest stress within the model (Fig. 11).

Fig. 11
Fig. 11
Close modal

## Discussion

We were able to successfully develop a model of a tissue-engineered transcatheter aortic valve. Decellularization was achieved with histology confirming no cellular remnants, and after explant recellularization was evident with corresponding changes in mechanical response (Fig. 6). Following this, the mechanical response was characterized using a commonly used constitutive model for use in finite element models. FEA has previously used in tandem with transesophageal echocardiography to simulate valvular mechanical stress in a simulated environment [28]. In this study, three FEA aortic valve models were run based on the experimental results above and followed an average cardiac cycle obtained from literature (See Fig. 3 available in the Supplemental Materials on the ASME Digital Collection) [26].

The explanted pericardium had a large decrease in deformation and stress for the given loading conditions, which is likely because of the recellularization and subsequent remodeling of the tissue. However, comparing the mechanical response of implant and explant tissues at the same stretch (i.e., 1.1), it can be seen that the stress magnitude is similar. Thus, it may be that the explant tissue had more tearing at the attachment sites during biaxial testing or the applied strain was not distributed from the attachment sites across the tissue. Nonetheless, the mechanical response of the explanted tissue is closer to the native valve which could indicate that subcutaneous implantation may be a suitable method to recellularize tissue prior to implantation. However, the recellularized tissue shows isotropy, due to the uniform loading in the subcutaneous position. This is also reflected in the quantification of the histology images where we can see there is high dispersion and the mean fiber orientations vary greatly between samples. In comparison, the native tissue exhibited an anisotropic mechanical response demonstrating that, similar to other TEHV, further remodeling of the tissue is required for an optimum mechanical response [18]. Comparing the mechanical response to Anssari-Benam et al. at our applied strain rate, the stress is of similar magnitude although the difference between circumferential and radial data is more pronounced in their study [29]. Compared to the recent manuscript by Emmert et al., the behavior of their explanted polyglycolic acid mesh valve lies between the native and explanted tissues in our work with limited anisotropy visible in the mechanical response and a magnitude and profile that resembles the radial native valve behavior [18]. Finally, comparing to glutaraldehyde pericardium used in bioprosthetic valves, the stress was higher than both native and explanted tissues but lower than the implant tissues in this study [30]. Glutaraldehyde stiffens tissue by causing excessive crosslinking between protein fibers; thus, it is unclear why the decellularized implant tissue in this study would be stiffer. However, uniaxial tensile testing has shown that the decellularized pericardium that has undergone super critical carbon dioxide sterilization, which was used in this study, has similar ultimate strength to glutaraldehyde fixed pericardium [31].

In this work, we fitted the constitutive model parameters using a standard procedure and the IEC parameter fitting approach. We found that generally the standard fits are most representative of the experimental data where the far stiffer implant group produced a significantly higher $k1$ and a $k2$ value similar to the native group. When compared to the IEC fits, $k2$ was significantly higher for the native tissues which is not representative of the experimental data. Additionally, when comparing the data from FE analyses the native tissue in the standard procedure shows similar maximum principal stresses and strains to the explant group throughout the cardiac cycle on both regions of the valve in contrast to the more pronounced mechanical response in Fig. 6 available in the Supplemental Materials on the ASME Digital Collection. Additionally, the stiffer implants from the standard fitting show a difference in both stress and strain at both sites; however, this is not as pronounced as the difference from the mechanical test data would infer. Thus, it may be that the IEC procedure led to an increased stiffness in the native tissues to account for the anisotropy. Or alternatively, that the anisotropy in the native tissues affected the accuracy of the IEC fitting procedure. Regardless, these results imply that further study is required of this procedure and that in this work the standard fitting produced more accurate and reliable fits to the experimental data; thus, only the subsequent data from these fits will be considered in the rest of this work. Comparing the fittings performed using the standard procedure to those performed by Anssari-Benam, Tseng, and Bucchi on native valves, it can be seen that $κ$ is higher in this work, which is likely due to the mechanical response of the circumferential and radial directions being closer than in their study. This would be indicative of increased isotropy implied by the increased $κ$ parameter. These differences may be explained by the higher sample size in our study or alternatively that in the work performed by Anssari-Benam, Tseng, and Bucchi they performed the fitting of the elastic properties at a quasi-static strain rate where their mechanical results show greater anisotropy compared to their results at strain rates similar to those applied here.

Both physiologically and in computational model results, it has been shown that the leaflet belly is a region of durability concern. In the work by Hsu et al., they developed a dynamic model of a valve and utilized the mechanical properties of glutaraldehyde fixed bovine pericardium. Similar to our study, in systole the strain was located in the region of the belly and in diastole the maximum strain was highly concentrated in the commissures. However, they noted very low strain in the belly of the leaflet during diastole which, although strain is lower in the belly region in this work, is not the case here [32]. Compared to our results for the implant tissue group, the stiffer glutaraldehyde fixed tissue would be expected to show lower strain in the leaflet belly due to more even distribution of stresses mentioned previously. Labrosse et al. created a patient-specific FE model from transesophageal echocardiography images using mechanical properties from porcine and human aortic valves and the highest stress were found at the commissures at mid to late diastole [33]. This partially agrees with our results for all tissue types where we see the highest stresses in early diastole at the commissures. Most recently, Emmert et al. created a FE model of a pulmonary TEHV that included tissue remodeling and compared the predicted valve performance and collagen orientation to the explanted valves [18]. Their model correctly predicted sufficient leaflet coaptation for all cases and captured remodeling and reorientation of collagen fibers with good accuracy. The diastolic strain in the leaflet belly had a magnitude comparable to the native and explant tissues in this work which may lend confidence to the remodeling seen in the explant tissues. However, they do not evaluate the implant scaffold mechanical response, before or after in vitro recellularization, and they do not model a full cardiac cycle as such only the diastolic information is available.

Accelerated wear testing showed that the valve failure occurred in the leaflet belly region (Fig. 11). Failure of this design occurred after 21 × 106 cycles to failure which would be approximately equivalent to 1 month in vivo. Based on the results of this study, it would be expected that a recellularized valve would perform much more favorably in vitro; however, recapitulation of the in vivo environment would be necessary to do such in vitro testing. However, we propose that constitutive in silico modeling of recellularization could be utilized in conjunction with or in replacement of in vitro fatigue testing.

The low stress seen at both leaflet belly and commissures of the explant tissues is promising for the valve performance when placed in the aortic position. Additionally, the comparable strains to native tissues also lend confidence on the remodeling capacity of the scaffold. However, it is still likely that a tissue-engineered valve recellularized subcutaneously would need to undergo further remodeling when implanted in the aortic valve position to improve the anisotropic behavior of the tissue as seen in the mechanical testing data. This was expected as there were no current means to replicate the biological and mechanical conditions of a native valve and as such valves recellularized and remodeled in a bioreactor, where the forces represent in vivo conditions, still undergo further remodeling when implanted in the aortic or pulmonary positions [18]. Finally, this demonstrates the recellularization and remodeling potential of our TEHV material and its suitability for use in future ovine models. Such studies carry a higher risk of failure, due to operating on major blood vessels, so the positive mechanical evaluation in this study, of a relatively simple rat subdermis model, gives confidence going forward. Future work will therefore involve FE analysis of the TE TAVI following implantation in the orthotopic position of an ovine model to evaluate the stress imparted on the valve in the native position and appraise the alteration of the mechanical performance following remodeling of the tissue in the native environment.

## Limitations

The constitutive model employed has a number of assumptions; first, by including both the fiber angle and the fiber dispersion in the fitting procedure; both these parameters which may be considered structural are now purely phenomenological and do not inform on the tissue fiber orientation or organization. Additionally, the aortic valve is not homogenous and has three distinct layers along its through-thickness, namely the fibrosa, spongiosa, and ventricularis from aortic to ventricular sides. The fibrosa has circumferentially organized collagen fibers, the spongiosa is randomly orientated, and the ventricularis is composed of radially orientated fibers. Therefore, the constitutive model is used to describe all three layers simultaneously as a single homogeneous structure which may alter the results for the finite element model compared to defining each layer separately. This was chosen due to the difficulty in separating and testing these thin layers accurately.

The biaxial testing in this study was employed to determine constitutive parameters for the GOH model. While biaxial tests are insufficient for fully determining an orthotropic function, in the work by Holzapfel and Ogden they note that the optimization process should be bounded to ensure convexity, which was performed in this work [34]. Furthermore, Eqs. (3)(5) can be rewritten in the form of invariants to give
$WmC=μ2I1 −3$
(14)
and
$WfiC,Hi=k12k2[exp(k2κI1+1−3κI4i−12−1], i=1,2$
(15)

Where $I1$ is the first invariant and $I4i=ai⊗ai:C$ the fourth invariant for each respective fiber family. With our assumption that $a1$ is the reflection of $a2$ along the x2 direction, the fourth invariants are related. Thus, the GOH model can be fully determined from standard biaxial tests [34]. However, as with all material fitting additional data from different mechanical tests, including shear or methods such as those recently published by Abbasi et al. would make the fitted model parameters more representative of the material in question [35]. In this work, we extensively characterized the anisotropic behavior of the tissues using three loading protocols and there is a practical limit on the testing which can be performed, as such the lack of shear data is a limitation of this study. Regardless, the good correspondence seen in our validation gives confidence that the testing performed was sufficient for the purposes of this study.

In this work, we utilized histology to evaluate the recellularization and remodeling of the implant and explant tissue groups. Previous studies have utilized imaging techniques to determine the structural parameters,$κ$ and $θ$, in Eq. (5); however, the histology in this study was performed to provide visual clarification of the changes to the explanted tissue and for approximate verification of the mechanical response and fitted constitutive model parameters [36]. Imaging of the circumferential-radial plane at multiple points across the tissue through-thickness would be required to properly evaluate $κ$ and $θ$, which is ultimately unnecessary for the goals of this study.

Validation was only performed on the tissue from the implant group and not the explant group limiting the validation to the former. This was due to the explant tissues being disk shaped and so not able to be placed into the bioreactor in that configuration. Additionally, there is not enough space to place a whole valve under the rat skin. However, the low error we observed for the implant tissues lends confidence that the FE model based on the explant tissue group is accurately reflecting the behavior of the explant tissues.

In this study, the tissue was tested at strain rates in line with the manuscript by Emmert et al. [18]. However, in a study by Anssari-Benam et al., they demonstrated that native valve tissue had pronounced viscoelastic behavior, with the testing speeds in our study around the middle of their tested range [29]. In contrast, in the study by Stella et al. they observe limited viscoelasticity for a similar testing speed range [37]. Thus, it is not clear if time-dependent behavior is present in valvular tissues or the magnitude of its effect. Similarly, the magnitude of viscoelasticity of pericardium differs between studies [38,39]. However, the lack of time-dependent information is a limitation in this work as this has not been investigated for our sterilized decellularized porcine pericardium or for the tissue explanted from the rat subdermis.

Figures 8 and 9 show that the in silico valve displacements lead to closure of the leaflets and thus it would not be expected for regurgitation to occur. However, it is impossible to properly evaluate this without additional fluid analysis. Thus, an additional approach for further work would be to perform a fluid–structure analysis, allowing valve fluid performance to be evaluated.

## Conclusion and Future Work

Tissue-engineered heart valves have great promise in their potential as a lifelong therapeutic device. Yet, a complex understanding of the recellularization capacity of current approaches is required to achieve the best performance post-implantation in the aortic or pulmonary position. In this study, we utilized subcutaneous implantation as a means of recellularization and evaluated the resulting changes in mechanical response via biaxial testing and FE modeling. We found that the explant tissues had successfully recellularized and host tissues had been synthesized to replace the initial decellularized pericardium. However, the explant tissues showed reduced mechanical response compared to implant, but comparable to native tissues. Additionally, the explant tissue FE model showed the largest strains and the lowest stresses. The results imply that while the tissue had successfully recellularized, additional remodeling would had required post-implantation in the aortic/pulmonary position. Future perspectives include enhancing the recellularization capability of the tissue and expanding to an ovine orthotopic model, and expanding the constitutive framework to allow more predictive in silico modeling of recellularization, remodeling, and fatigue.

## Acknowledgment

This work is supported by the HH Sheikh Hamed bin Zayed Al Nahyan Program in Biological Valve Engineering.

### Appendix

The PK1 stress was found from Eq. (2) using
$Pa=−1λap+∂W∂λa, a=1,2,3$
(A1)

where $p$ is the intermediate Lagrange multiplier with the physical interpretation of the hydrostatic pressure. We have assumed incompressibility such that $λ1−1λ2−1=λ3$ and that collagen fibers have no component in the through-thickness so that $ai3=0$. First and fourth invariants of $C$ and $ai⊗ai$ may then be defined as $I1=λ12+λ22+λ1−1λ2−1$ and $Ii4=ai12λ12+ai22λ22$.

Using these definitions, (13) may be rewritten as $Ei=κI1+1−3κI4i−1$, which can be then expressed in terms of the principal stretches
$Ei=κ(λ12+λ22+λ1−1λ2−1)+1−3κ(ai12λ12+ai22λ22)−1$
(A2)
allowing the derivative of Eq. (A1) to be evaluated for $Wfi$ and $Wm$. In planar biaxial testing with the current assumptions, (A1) becomes
$P1=∂W(λ1,λ2, a1,a2)∂λ1 and P2=∂W(λ1,λ2, a1,a2)∂λ2$
(A3)

wherein the derivatives were evaluated using matlab symbolic toolbox.

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