Homografts and synthetic grafts are used in surgery for congenital heart disease (CHD). Determining these materials' mechanical properties will aid in understanding tissue behavior when subjected to abnormal CHD hemodynamics. Homograft tissue samples from anterior/posterior aspects, of ascending/descending aorta (AA, DA), innominate artery (IA), left subclavian artery (LScA), left common carotid artery (LCCA), main/left/right pulmonary artery (MPA, LPA, RPA), and synthetic vascular grafts, were obtained in three orientations: circumferential, diagonal (45 deg relative to circumferential direction), and longitudinal. Samples were subjected to uniaxial tensile testing (UTT). True strain-Cauchy stress curves were individually fitted for each orientation to calibrate Fung model. Then, they were used to calibrate anisotropic Holzapfel–Gasser model (R2 > 0.95). Most samples demonstrated a nonlinear hyperelastic strain–stress response to UTT. Stiffness (measured by tangent modulus at different strains) in all orientations were compared and shown as contour plots. For each vessel segment at all strain levels, stiffness was not significantly different among aspects and orientations. For synthetic grafts, stiffness was significantly different among orientations (p < 0.042). Aorta is significantly stiffer than pulmonary artery at 10% strain, comparing all orientations, aspects, and regions (p = 0.0001). Synthetic grafts are significantly stiffer than aortic and pulmonary homografts at all strain levels (p < 0.046). Aortic, pulmonary artery, and synthetic grafts exhibit hyperelastic biomechanical behavior with anisotropic effect. Differences in mechanical properties among vascular grafts may affect native tissue behavior and ventricular/arterial mechanical coupling, and increase the risk of deformation due to abnormal CHD hemodynamics.

## Introduction

Surgical cardiovascular reconstruction of congenital heart disease (CHD) is frequently accomplished by using biological or synthetic materials. Cardiovascular mechanical properties are determined by tissue structure which is integrally related to its function [1]. Adult aorta and pulmonary artery homografts, as well as grafts made of dacron (polyethylene terephthalate) or Teflon (expanded polytetra-fluoroethylene (ePTFE)), have been used clinically in cardiovascular surgeries [24]. These materials have very different structures than that of the native tissue of a neonate [5,6].

The abnormal blood flow patterns of CHD may have adverse effects on the implanted material, the native vessel, and the mechanical load on the heart [1,7,8]. These include changes in effective arterial impedance that could impair ventricular efficiency; stress changes on the adjacent native vessel; and deformation of both the native and implanted material with the risk of either luminal narrowing or aneurysm formation. Mechanical properties of homograft tissue and synthetic vascular grafts are currently not available in the literature. Determining these properties will aid in understanding tissue behavior when subjected to the abnormal hemodynamics of CHD.

We have previously reported the anisotropic stress/strain relationship of the piglet great vessels using uniaxial tension testing (UTT) [9]. The purpose of this study was to determine and compare biomechanical characteristics among adult aorta and pulmonary artery homografts, and ePTFE grafts. UTT was performed in three orientations on several vessels and graft segments, and then used to calibrate coefficients of the Holzapfel–Gasser anisotropic constitutive model. These data will be useful in future computational fluid dynamics (CFD) modeling of blood flow incorporating vessel compliance [10]. Furthermore, it will strengthen CFD use in planning surgical treatment of CHD.

## Material and Methods

### Material Preparation.

Recently expired clinical-grade homografts, two aortic from CryoLife, Inc., Kennesaw, GA (donor's age Ao1 = 17 and Ao2 = 21 yr old), and two pulmonary from LifeNet Health, Inc., Virginia Beach, VA (donor's age PA1 = 44 and PA2 = 47 yr old), and two synthetic vascular grafts, one GORE-TEX (made of ePTFE and fluorinated ethylenepropylene, SVG-GORE-TEX) from W. L. Gore & Associates, Inc., Flagstaff, AZ, and the other IMPRA (made only of ePTFE, EVG-IMPRA) from BARD Peripheral Vascular, Inc., Tempe, AZ were donated to our lab. The homografts were kept frozen at −140 °C in Dulbecco's Modified Eagle's Medium containing 10% dimethylsulfoxide and 10% fetal bovine serum and thawed to room temperature on the day of mechanical testing. Homograft segments were excised and labeled for vessel origin and orientation as ascending aorta (AA), aortic arch (Arch), innominate artery (IA), left subclavian artery (LScA), left common carotid artery (LCCA), descending aorta (DA), main pulmonary artery (MPA), left pulmonary artery (LPA), and right pulmonary artery (RPA) in circumferential (C), diagonal (D), and longitudinal (L) orientations, and anterior and posterior aspects (Fig. 1). It is mentioned that the direction of angle bisector between circumferential and longitudinal directions was considered as the diagonal direction, for some geometrically complicated regions like the Arch. Dimensions of tissue samples were acquired immediately prior to mechanical testing given in Table 1. Mechanical testing was subsequently performed within 6 h of tissue defrosting. Homograph samples were moistened until tests start by the same solution as it was stored (Dulbecco's modified Eagle's medium containing 10% dimethylsulfoxide and 10% fetal bovine serum).

The SVG-GORE-TEX graft was 40 cm long with 12 mm inner diameter, and the EVG-IMPRA graft was 10 cm long with 13 mm inner diameter. Both of them were 1.0 mm thick. The cylindrical grafts were longitudinally cut and extended into a rectangular shape, allowing us to obtain full-width samples along C, D, and L orientations (referring to Fig. 1(d)). SVG-GORE-TEX comes with a reinforced layer attached to the outer surface which was kept during mechanical testing (Fig. 1(e)).

### Mechanical Properties Testing.

The details of the testing technique have been reported elsewhere [9]. Briefly, opposite edges of samples of the homografts segments defined earlier, and synthetic grafts, were clamped with a biomedical tissue grip (G341 mechanical vice grip, Testresources, Inc., Shakopee, MN) and loaded onto a MTS Tytron 250 microforce computer-controlled high-precision tensile testing machine (MTS Systems Corporation, Eden Prairie, MN) for UTT. A 5 N load cell was used for small homograft tissue samples [11], and a 250 N load cell was utilized for the synthetic grafts samples. In all cases, UTT was conducted at a velocity of 0.1 mm/s, until tissue fracture. Strain rate effect on the tissue was ignored [12]. Tensile force data were obtained from the loading frame, and the samples' horizontal displacement during UTT was obtained by digital imaging correlation (DIC). DIC system consists of a Tokina AT-X Pro macro 100 mm-f/2.8-d 2448 × 2048 resolution lens connected to a desktop computer with VIC-2D 2009 software (Correlated Solutions, Inc., Columbia, SC). Images for DIC were obtained one per second. A figure demonstrating the entire experimental setup can be found in our previous report [9].

### Data Collection.

We collected, processed the data, and applied the constitutive model in the same manner as described in our previous report [9]. Briefly, recorded force–displacement datasets were used to calculate Cauchy stress ($σ$) and true strain ($ε$) which is the logarithm of the tissue stretch under UTT [9]. The principal true strain [13], ε, is
$ε=lnλ$
(1)
where $λ=l/l0$ is the stretch, representing the ratio of the deformed length to the original tissue length under uniaxial tension. The Cauchy stress along tensile direction is related to the original cross-sectional area of the tissue defined as the specific width of the sample multiplied by the average thickness of that sample as
$σ=FAλ=FAeε$
(2)
where F is the tensile force, and A is original cross-sectional area of the tissue defined as the specific width of the sample multiplied by the average thickness of that sample (Table 1). The tissue stiffness $E0$ (tangent value in stress–strain curve) is the first derivative of stress–strain curve at a given strain level $ε0$
$E0=dσdε|ε=ε0$
(3)

was computed and compared at $ε0$ = 10%, 20%, and 30% strain to assess fiber engagement to maintain stiffness (from elastin-dominated to partial fiber engagement), among different tissue samples [12]. A schematic of this method can be found in our previous report [9].

### Constitutive Modeling.

Arterial tissue typically exhibits anisotropic hyperelastic behavior and incompressibility [10,14]. First, a unidirectional Fung exponential stress–strain relationship [12] was utilized for data processing and to perform individual least-square curve fitting for all vessel segments individually along C, D, and L orientations (denoted by C: $θ=0 deg$, D: $θ=45 deg$, and L: $θ=90 deg$) utilizing a two-coefficient relation
$σfitting=C(eQ ε−1)$
(4)

where the C and Q fitting coefficients are obtained to describe the mechanical behavior for each orientation individually.

Subsequently, the Holzapfel–Gasser constitutive model was applied to fully capture the hyperelastic anisotropic (orientations dependent) relation for each vessel segment. This model assumes: (a) arterial tissues are treated as fiber-reinforced composite and (b) two families of collagen fibers are embedded in an isotropic ground matrix [10]. The modeled Cauchy stress–strain relationship, dependent on the sample orientation, reads
$σ(θ)=λ2[C0(1−1λ3)+2k1∑i=12Ei¯∂Ei¯∂C11ek2Ei¯2]$
where
$∂Ei¯∂C11=κ(1−1λ3)+(1−3κ)[ cos2(θ+αi)−12λ3 sin2(θ+αi)]Ei¯=κ(I1−3)+(1−3κ)(I4i−1)$
(5)

Here, $Ei¯$ is a Green strainlike quantity characterizing the strain in the collagen fiber mean direction $αi$ of the $i$ th family of fibers [10], with respect to the C tissue orientation ($θ=0 deg$). Parameter $(0≤κ≤1/3$) describes the level of dispersion in fiber directions, which directly controls degree of material anisotropy, $I1=C11+C22+C33$ is the first invariant of right Cauchy–Green strain tensor, and $I4i=C11 cos2(θ+αi)+C22 sin2(θ+αi)$ is a pseudoinvariant dependent on specimen orientation $θ$ and collagen fiber direction $αi$. $C11=λ12$, $C22=λ22$, and $C33=λ32$ are the components of the right Cauchy–Green strain tensor, respectively. $λ1=λ$ and $λ2=λ3=1/λ$ are principal stretches, respectively, based on UTT and incompressibility ($λ1λ2λ3=1$). The subscripts 11, 22, and 33 indicate direction along tension, lateral, and thickness of the UTT sample.

The modeled Cauchy stress–strain relationship is calibrated using the measured data to determine the five model parameters $C0$, $k1$, $k2$, $αi$, and $κ$ as previously described (i = 1,2 for all variables with subscript i) [9]. These parameters were obtained using a generalized reduced gradient (GRG) algorithm to correlate the Holzapfel–Gasser model with the unidirectional fitted Fung stress–strain curves in the three tested orientations [15].

The first step of Fung model least-squares curve-fitting helps to remove scatter in the original test data for each orientation. A combined fit was applied for all available experimental curves under each case. The Pearson R2-value was set as the objective function to be maximized iteratively by the GRG algorithm by adjusting the model parameters in curve-fitting first to the experimental and Fung models and then Fung and Holzapfel Gasser models.

## Statistical Analysis

To check the data normality, Kruskal–Wallis tests have been conducted for all the tissue sample stiffnesses investigated. A value of $α=0.05$ is taken as the significance level of the Kruskal–Wallis test. For all aortic and pulmonary artery homografts segments, probability distributions are the same for anterior and posterior aspects, when comparing all orientations for each region under true strain of 10%, 20%, and 30% (p > 0.11 in all regions). For all aortic and pulmonary artery homografts segments, probability distributions are the same for different orientations (C, D, and L), when comparing both aspects for each region under true strain of 10%, 20%, and 30% (p > 0.10 in all regions). For SVG-GORE-TEX, when comparing all the orientations, probability distributions are the same under true strain of 10% (p = 0.051), but not the same under true strain of 20% (p = 0.027), and 30% (p = 0.027). For EVG-IMPRA, when comparing all the orientations, probability distributions are the same under true strain of 10%, 20%, and 30% (p > 0.10).

Individual paired t-tests were applied to compare tissue stiffness of different sample orientations, aspects and vessel segments of homografts and synthetic grafts, using Microsoft Excel (version 2013). A p < 0.05 was considered statistically significant. Pearson R2 was calculated to show the strength of association between experimental and Fung models, and Holzapfel–Gasser and Fung models. Reported values are quoted as mean value ± standard deviation.

## Results

Sample length and width were measured with calipers, and the thickness was measured using DIC. Samples of IA, LScA, and LCCA were too small to be excised in more than one orientation of their anterior and posterior aspects. Therefore, these three sets of the vessel segments were obtained only in C orientation from both aspects. The general characteristics of the tissue sample are provided in Table 1.

### Constitutive Modeling.

Figures 2 and 3 illustrate raw experimental data with least-squared fitting curves (solid line) from the Fung model with associated Pearson R2 correlation values. All tested samples demonstrated nonlinear hyperelastic behavior under UTT except for SVG-GORE-TEX in C orientation and EVG-IMPRA in L orientation in the true stress–true strain curves. This prevents the application of Holzapfel–Gasser model for SVG-GORE-TEX and EVG-IMPRA. Therefore, in Fig. 3, the Fung model and raw experimental data for SVG-GORE-TEX and EVG-IMPRA are provided, but SVG-GORE-TEX in C orientation and EVG-IMPRA in L orientation only display the raw experimental data.

Figure 4 provides the GRG-calibrated Holzapfel–Gasser model parameters and displays the predicted true stress–true strain curves with fitted Fung model curves for all orientations of homograft samples. The calibrated anisotropic Holzapfel–Gasser model is capable of predicting the fitted Fung model curves with excellent correlation for all orientations (R2-values > 0.97), capturing full anisotropic mechanical behavior.

### Stiffness.

Average stiffness for all samples, orientations, and aspects obtained at the true strain levels of 10%, 20%, and 30% are exhibited in Tables 2 and 3 and Fig. 5. Figures 6 and 7 show the entire aortic and pulmonary artery homografts stiffness contours at true strain levels of 10% and 30%, respectively. A series of comparisons were made among different regions, orientations, and aspects, as follows:

1. (1)

For all aortic and pulmonary artery homografts segments, no significant differences were observed between anterior and posterior aspects, when comparing all orientations for each region under true strain of 10%, 20%, and 30% (p > 0.05 in all regions).

2. (2)

For most vessel segments, no significant differences were observed among C, D, and L orientations, when comparing both aspects for each region at three strain levels (p > 0.05 in all regions except for: DA-10% between C and L, p = 0.042; DA-30% strain between D and L, p = 0.011; and LPA-30% between D and L, p = 0.041).

3. (3)

Stiffness was significantly different among orientations for most of SVG-GORE-TEX and EVG-IMPRA samples. SVG-GORE-TEX is significantly stiffer along C than D and L, respectively, at all strain levels (p < 0.035); and D is stiffer than L at 30% strain (p = 0.002). EVG-IMPRA in L is stiffer than D orientation at all strain levels (p < 0.042); and L is stiffer than C at 20% and 30% strain (p < 0.024).

4. (4)

Stiffness was significantly different among the following regions when comparing all orientations and aspects between each two regions: Arch > AA at 20% strain (p = 0.026); Arch > DA at 10% (p = 0.040) and 20% strain (p = 0.011); AA, DA, and Arch > MPA at 10% strain (p = 0.003, 0.028, 0.004, respectively); AA > RPA at 20% strain (p = 0.043); Arch > LPA and RPA at 10% strain (p = 0.011, 0.007, respectively); Arch > RPA at 20% strain (p = 0.006); and LPA > RPA, at 30% strain (p = 0.024).

5. (5)

Stiffness is significantly greater in aortic than pulmonary artery homograft at 10% strain, when comparing all orientations, aspects, and regions (p = 0.0001). This difference in stiffness is not observed at higher strain levels of 20% (p = 0.080) and 30% strain (p = 0.588), nonetheless the aortic homograft is still slightly stiffer.

6. (6)

SVG-GORE-TEX samples along C and D orientations, and EVG-IMPRA samples along all orientations are significantly stiffer than aortic and pulmonary artery homografts at all strain levels (p < 0.046).

The limited number of samples of IA, LScA, and LCCA preclude statistical analyses of observed differences. Obtained measurements are however included for qualitative reference. The stiffnesses of IA at 10%, 20%, and 30% strain are 1078.72 ± 1197.46 kPa, 1246.70 ± 1101.51 kPa, and 1525.63 ± 1092.66 kPa, respectively. The stiffnesses of LCCA at 10%, 20%, and 30% strain are 586.52 ± 369.84 kPa, 985.84 ± 323.73 kPa, and 1100.51 ± 610.31 kPa, respectively. The stiffnesses of LScA at 10%, 20%, and 30% strain are 438.00 ± 109.47 kPa, 624.06 ± 12.58 kPa, and 980.72 ± 132.67 kPa. In contrast to stiffness at these specific points (10%, 20%, and 30% strains), the entire stress–strain behavior exhibited strong dependence among different orientations and anisotropy is captured in individual Fung and comprehensive Holzapfel–Gasser model curve fits.

## Comment and Discussion

Mechanical limitations of materials currently used by surgeons in cardiovascular operations, mainly homografts and either Dacron or polytetrafluoroethylene grafts, are sometimes evidenced by complications such as graft stenosis or dilation, noted particularly after aortic arch reconstruction [1618]. These complications could be mitigated by utilizing the graft material that best matches the mechanical properties of the native tissue being repaired. Graft stiffness and variation of its properties with orientation are important considerations. Moreover, surgical planning aids combining imaging techniques such as magnetic resonance, and computed tomography together with catheterization and CFD, will substantially benefit and become more reliable by accurately accounting for the mechanical response of graft materials in their models [1622]. This enables more sophisticated studies that may possibly predict phenomena such as local tissue strain, aneurysm formation, ventriculoarterial and arterioarterial impedance mismatch, and ventricular efficiency [23].

Our results show that stiffness of synthetic graft materials varies significantly with orientation and that all orientations of SVG-GORE-TEX and EVG-IMPRA except for L-orientation of SVG-GORE-TEX are significantly stiffer than aortic and pulmonary artery homografts. Furthermore, the L-orientation of SVG-GORE-TEX shows a good fit to the homografts in regards to stiffness at physiologic stress levels ($ε0∼10−20%$). This suggests that an implantation of the graft may provide a better mechanical match between the graft and native vasculature in the longitudinal direction.

In our previous study, we performed UTT on piglet aorta and pulmonary artery. Piglet tissue approximates the biomechanical properties of tissue from a human neonate as the anatomy of the porcine heart and vasculature is the most similar research model to that of a human [9,24].

Comparison of the aortic and pulmonary artery homografts data with that of the piglet great vessels shows that homografts from human adults are about 100 times larger in stress value when subjected to the same strain condition [9]. The increase in stress and stiffness as age increases, and tissue matures from neonatal into adult tissue, is due to the structural tissue changes occurring during growth [2527]. The age-related vascular structural changes that have been proposed to be associated with increased stiffness of the aorta include reduced collagen and elastin contents/mm2 of the aortic wall, increased fenestration of elastic laminae, and accumulation of fluorescent material in collagen and elastin [26,28]. This phenomenon results in an overall decrease in compliance as age increases. A histological study could reveal the structural difference between samples from different locations, ages, and so on. The elastic lamina and collagen bundle configuration from a histological analysis could better explain the anisotropy and mechanical variation of arteries.

A limitation of this study is that the constitutive model calibration was determined by the strain–stress response of a single loading condition (uniaxial tension, fully exhibiting the anisotropic behavior). However, hyperelastic mechanical behavior is dependent on loading conditions (uniaxial tension, biaxial tension, etc.) [8,14]. Thus, the anisotropic hyperelastic model could be better calibrated to biaxial or equibiaxial loading conditions [29]. Additionally, in order to achieve statistical power, it was necessary to pool sufficient data from the same location of the arteries.

In conclusion, aortic and pulmonary artery homografts exhibit hyperelastic mechanical characteristic with anisotropic effect. The calibrated Holzapfel–Gasser constitutive model can be applied in surgical preparation and related simulation to predict anisotropic biomechanical behavior. The synthetic vascular grafts are significantly stiffer than homografts. The mechanical properties of SVG-GORE-TEX in L orientation are comparable to those of the homografts, and this characteristic should be considered by surgeons when performing reconstructive cardiovascular surgery with this material. These differences between aortic and pulmonary artery homografts and synthetic vascular grafts may play a role in native neonatal tissue behavior, ventricular/arterial mechanical coupling, and risk of deformation due to abnormal hemodynamics of CHD.

## Acknowledgment

Professor Quanfang Chen provided access to the microloading frame. Mr. Shenghong Zhang assisted with mechanical testing. Thanks also due to partial financial support from the University of Central Florida.

## Funding Data

• Army Research Laboratory (Grant No. W911NF-15-2-0011).

## Nomenclature

### Abbreviations

Abbreviations

• AA =

ascending aorta

•
• Arch =

aortic arch

•
• C =

circumferential

•
• CHD =

congenital heart disease

•
• D =

diagonal

•
• DA =

descending aorta

•
• DIC =

digital imaging correlation

•
• ePTFE =

expanded polytetra-fluoroethylene

•
• GRG =

•
• IA =

innominate artery

•
• L =

longitudinal

•
• LCCA =

left common carotid artery

•
• LPA =

left pulmonary artery

•
• LScA =

left subclavian artery

•
• MPA =

main pulmonary artery

•
• RPA =

right pulmonary artery

•
• UTT =

uniaxial tension testing

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