## Abstract

Ascending thoracic aortic aneurysms (ATAAs) are anatomically complex in terms of architecture and geometry, and both complexities contribute to unpredictability of ATAA dissection and rupture in vivo. The goal of this work was to examine the mechanism of ATAA failure using a combination of detailed mechanical tests on human tissue and a multiscale computational model. We used (1) multiple, geometrically diverse, mechanical tests to characterize tissue properties; (2) a multiscale computational model to translate those results into a broadly usable form; and (3) a model-based computer simulation of the response of an ATAA to the stresses generated by the blood pressure. Mechanical tests were performed in uniaxial extension, biaxial extension, shear lap, and peel geometries. ATAA tissue was strongest in circumferential extension and weakest in shear, presumably because of the collagen and elastin in the arterial lamellae. A multiscale, fiber-based model using different fiber properties for collagen, elastin, and interlamellar connections was specified to match all of the experimental data with one parameter set. Finally, this model was used to simulate ATAA inflation using a realistic geometry. The predicted tissue failure occurred in regions of high stress, as expected; initial failure events involved almost entirely interlamellar connections, consistent with arterial dissection—the elastic lamellae remain intact, but the connections between them fail. The failure of the interlamellar connections, paired with the weakness of the tissue under shear loading, is suggestive that shear stress within the tissue may contribute to ATAA dissection.

## Introduction

Ascending thoracic aortic aneurysms (ATAAs) are characterized by abnormal dilation of the ascending aorta, where the vessel exceeds its normal diameter of 2–3 cm [1]. ATAA is a high-risk pathology, with aneurysm rupture or dissection likely to occur in untreated patients (21–74%) [2], and with rupture in particular having high mortality rates (94–100%) [3]. Evaluating the failure risk of ATAAs is exceptionally difficult due to the nonuniform microstructural, geometric, and mechanical changes that occur in the vessel during disease progression. Aneurysms are often affected by wall thinning, structural disorganization, loss of vascular smooth muscle cells (VSMCs), and extracellular matrix components such as elastin, collagen, and fibrillin [4]. The complex remodeling during aneurysm formation and growth undoubtedly gives rise to several underlying risk contributors, many of which may still be largely unidentified, making it difficult to determine accurately the likelihood of aneurysm failure.

Current risk assessment and patient diagnosis are based primarily on the vessel diameter. If the ATAA diameter exceeds a threshold of approximately 5–6 cm [2,5,6] or a growth rate of 0.5 cm/year [7], surgical intervention is recommended. When ATAA risk is assessed solely with measurement-based techniques, however, mechanical and structural changes, which are well known to occur in the ATAA pathology [811], cannot be considered. The inefficiency of measurement-based diagnosis was shown by Vorp et al. [10], who reported a 5-yr mortality rate of 39% for ATAAs below the 6 cm diameter threshold and 62% for those above 6 cm diameter threshold. Furthermore, Vorp et al. [10] found no correlation between aneurysm diameter and tensile strength. Clearly, failure contributors in the ATAA pathology must be better understood to help inform physicians in decision-making and improve treatment outcomes.

Morphological detail, typically obtained from computed tomography (CT), is invaluable and constantly improving as imaging science advances. The critical question, then, is how can we use our understanding of vascular mechanics to improve on the existing diameter-based guidelines? Since dissection and rupture are mechanical events, a mechanical approach is justified, which requires exploring both the strength of the tissue and the stresses generated by the blood pressure. Regarding ATAA mechanics, recent studies have quantified nonaneurysmal and aneurysmal aortic tissue's mechanical response through various loading configurations, including bulge inflation [12,13], uniaxial extension [911,1416], biaxial extension [11,1721], peel [22,23], and shear [24] testing regimes. As a general rule, those studies found significant anisotropy, with the tissue stronger in the circumferential than in the axial direction [4,11,15]. Aneurysm tissue is generally stiffer [10,25] but weaker [10,15,25] than healthy tissue, perhaps due to elastin degradation in the aneurysm pathology [26]. Regional heterogeneity has also been observed, with differences between the lesser and greater curvature wall mechanics [15,16,2729]. Although none of these trends was absolute, they provide extensive insight on aneurysm mechanics.

For stress estimation, finite element modeling has been the most popular approach [12,3033]. These models, taken collectively, describe a complex, heterogeneous stress field in the tissue. Bulk constitutive equations, such as the Holzapfel–Gasser–Ogden (HGO) model [30,34], two-fiber family model [31,35], and Demiray model [12], have become commonly used to describe the material behavior of the tissue. While these constitutive models have advantages such as reducing computational energy, they fail to incorporate fully the underlying tissue composition and structure. Such factors are essential to macroscale tissue's behavior, especially in the ATAA pathology, where microstructural changes are undoubtedly present. Furthermore, parameter values are often fit to experimental data from only one or two loading conditions (i.e., uniaxial, biaxial), which may overlook the complex mechanical behavior given by the comprehensive multidirectional response of the tissue (i.e., incorporating radial and shear directions). Without the consideration of multiple loading conditions in the parameter fitting, these models will lack the information needed to produce accurate predictive results for the complex behavior of ATAAs.

Despite much progress in understanding ATAA mechanics using both experimental testing and computational modeling, the comprehensive mechanical strength of ATAA tissue in all directions, all regions, and all loading configurations has not been well documented. Furthermore, the mechanisms of aneurysm rupture and dissection are still largely unknown. It has been proposed, however, that interlaminal strength (i.e., between wall layers) plays a significant role in the failure process [33]. Interlamellar strength has been studied in a peel [22,23] and uniaxial [24,36] geometry, with significant lower strength found than in the in-plane circumferential or axial direction. One prior study of ATAA tissue in interlamellar shear [24], like our own work on the porcine ascending thoracic aorta [37], showed a similarly low strength. The potential role of interlamellar shear is further supported by (1) the mechanical observation that a curved tube, unlike a straight tube, generates intramural shear (not to be confused with the wall shear stress from blood flow) when inflated, and (2) the clinical observation that ATAAs tend to dissect rather than outright rupture, a result consistent with shear failure in cylindrical laminates. Taken together, these observations suggest the hypothesis that interlamellar forces created by the intramural shear stress contribute to the dissection of ATAAs. To evaluate this hypothesis, we used a combination of multidirectional mechanical experiments on ATAA tissue and multiscale computational modeling.

## Methods

### Experiments.

This study was approved by the Institutional Review Board (IRB) at the University of Minnesota (Study #1312E46582). Resected human ATAA tissue was obtained from patient surgeries at the University of Minnesota Medical Center (Figs. 1(a) and 2(a)). Following surgery, tissue was stored in 1× phosphate-buffered saline solution at 4 °C. The lesser curvature region (Fig. 1(b)) was marked with a small suture stitch placed in the adventitial layer by the surgeon (Fig. 2(b)). Samples were cleaned of excess connective tissue and cut open axially along the line midway between the lesser and greater curvatures (Fig. 2(c)). Sample preparation followed the same protocol used previously for porcine ascending aortic tissue, described extensively in Ref. [37]. Uniaxial, peel, and lap samples (Fig. 3) were prepared by initially cutting a rectangular full-thickness tissue piece, approximately 10 mm × 5 mm, where the 10 mm dimension indicates either the circumferential or axial direction. Uniaxial dogbone samples were created by cutting partial semicircles out of the center of the rectangle (10 mm in length × 5 mm in width) on both sides with a biopsy punch (r = 2.5 mm), to produce a width in the neck region of 2.34 mm on average. The average thickness for uniaxial samples was 2.03 ± 0.55 mm (mean  ±  95% confidence interval (CI)). Peel samples were prepared from the rectangles (10 mm in length × 5 mm in width) by making an incision on one end, in the center of the media, parallel to the vessel wall to initiate peel propagation. The average thickness for peel samples was 2.05 ± 0.54 mm. Lap samples were cut from the same size rectangle (10 mm in length × 5 mm in width) by making an incision in the media on both ends of the rectangle and removing roughly half of the thickness on each side of the sample, leaving an overlap region of 3.69 mm on average in the center. The average thickness for peel samples was 2.04 ± 0.32 mm. Biaxial samples (Fig. 3) were cut from a square (approximately 20 mm × 20 mm) into a cruciform shape using biopsy punches (r = 12 mm) on each of the corners. The average thickness for biaxial samples was 2.21 ± 0.37 mm. Due to the size of some aortic samples, not all testing modalities could be performed for every tissue specimen. Samples were photographed prior to testing, and undeformed sample dimensions (width, length, and thickness) were measured using imagej.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

Since it has been reported [38] that temperature has only a minor effect on aorta mechanics, all tests were performed at room temperature for convenience. Uniaxial, peel, and lap samples were clamped with custom grips, placed in a 1× phosphate-buffered saline bath at room temperature, and pulled at 3 mm/min in strain-to-failure experiments on a uniaxial testing machine (MTS, Eden Prairie, MN). A static 10 N load cell recorded the forces, and the grip stretch was calculated using the actuator displacement. Results for uniaxial samples that failed near the grips instead of in the neck region were discarded (∼30% of uniaxial tests), as well as lap or peel samples that did not fail in the medial layer. Biaxial samples were tested in displacement-controlled equibiaxial experiments (Instron 8800 Microtester) to 30% grip strain while 5 N load cells recorded the forces. Because of (1) the impossibility of preconditioning the peel test, (2) the severe risk of tissue damage during any preconditioning of the lap test and, to a lesser degree, the uniaxial tests, and (3) the desire for the consistent set of conditions possible across the different loading configurations, the samples were not preconditioned.

For uniaxial, biaxial, and lap tests, an average first Piola–Kirchhoff stress (PK1) was calculated by dividing the grip force by the relevant area (i.e., the cross section for in-plane tests and the overlap region for the lap tests). The average area for uniaxial, biaxial, and lap samples was 4.90 ± 2.12 mm2, 11.09 ± 2.71 mm2, and 20.17 ± 7.05 mm2, respectively. The grip stretch was calculated by dividing the grip separation distance by the initial grip separation distance. We emphasize that the grip stretch is not the actual stretch in the tissue but serves as a boundary condition for the simulations and as a measure of how much the sample as a whole has been stretched. For the peel test, peel tension was calculated as the grip force divided by the sample width, which was 5.68 ± 1.02 mm on average. A total number of 22 aorta specimens were obtained from surgery, which were dissected into 219 total samples of various types.

### Statistical Analysis.

For the uniaxial tests, a tensile strength and a failure stretch of the vessel were reported. For lap tests, shear strength and failure stretch were reported. For peel tests, average peel tension was reported. No failure metrics were reported for biaxial tests, since only prefailure behavior was analyzed. To compare between direction (circumferential or axial) and tissue type (human ATAA or porcine) for all tests, a Tukey's multiple comparison test was performed. All statistical analysis was performed using graphpadprism 6.

## Multiscale Model

A custom multiscale model that we previously used [37] for porcine aortic tissue was implemented to simulate the ATAA tissue behavior. Specimen geometries were created and meshed as eight-node hexahedra (C3D8 elements) in abaqus based on the average dimensions of each experimental sample. Mesh sizes ranged from 600 to 1460 hexahedra elements for the geometries, with two to three elements used along the thickness direction. The multiscale model incorporates three scales: tissue (mm), network (μm), and fiber (nm) levels. The model follows an iterative loop that satisfies the global Cauchy stress balance after displacements are applied on the tissue level (Fig. 4). Once applied, tissue-level displacements are passed to the Gauss points in each finite element, where representative volume elements (RVEs) consisting of fibrous networks in parallel with a nearly incompressible Neo-Hookean component are deformed. These fibrous networks resemble the arterial media, as they consist of a planar layer of collagen and elastin fibers, surrounded on both top and bottom by interlamellar connection (I.C.) fibers representing components such as VSMCs and fibrillin, which reside between the lamellar layers. All of the network nodes are connected to a Delaunay network of fibers with infinitesimal stiffness in order to stabilize the network. The same fibrous network was used for each element in all of the different geometries. On the microscale level, each fiber is defined by a constitutive equation of the form
$F=EfAfBf(e(Bf*ϵG)−1)$
(1)
where F is the fiber force, Ef is the fiber modulus, Af is the fiber cross-sectional area, Bf is the fiber nonlinearity, and ϵG is the fiber Green strain. The fiber Green strain is given as $(λ2−1)/2$, where λ is the fiber stretch. Every fiber type had the same fiber radius (100 nm), and thus cross-sectional area (3.14 × 104 nm2). A Neo-Hookean ground matrix accounts for nonfibrous material, governed by an equation of the form
$σm¯¯=GJ(B¯¯−I¯¯)+2GνJ(1−2ν)(I¯¯*ln(J))$
(2)

where σm is the Cauchy stress of the matrix, G is the shear modulus, J is the determinant of the deformation tensor, B is the left Cauchy–Green deformation tensor, I is the identity matrix, and ν is the Poisson's ratio. After deformation is applied to the network, the internal forces are equilibrated, and the volume-averaged stress over the RVE is calculated using the forces on nodes lying on the RVE boundary (henceforth “boundary nodes”). These stresses are then passed up to the macroscale, and this process iterates until the global Cauchy stress balance is satisfied. Failure is accounted for on the microscale level, where each fiber is given a critical stretch value, above which the fiber fails and is numerically removed from the network.

Fig. 4
Fig. 4
Close modal
The direction and strength of alignment of the fibrous network were captured by an orientation tensor (described extensively in Ref. [39]). The orientation tensor is defined by
$∬ni(θ,ϕ)nj(θ,ϕ)p(θ,ϕ)dθdϕ$
(3)

where n is the unit vector defined by the angles θ and $ϕ$, and p($θ,ϕ$) is the probability distribution function for fiber directions at the point in question. The diagonal values for a given direction ($Ωzz,Ωθθ,Ωrr$) range from 0 to 1, indicating how strongly the fibers are aligned in that direction (1/3 = 3D isotropic, 0.5 = planar isotropic, 1 = fully aligned for the case of a diagonal Ω). Network composition in the ATAA model was altered from our previous healthy porcine model to incorporate physiological changes present in the aneurysm case (Fig. 4), based on histological findings in the literature [40,41]. In the new ATAA networks,

• 25% fewer elastin fibers were present to account for elastin degradation [41]

• collagen fiber arrangement was more isotropic ($Ωθθ=0.58$ in ATAA, compared to $Ωθθ=0.93$), along with I.C. fiber arrangement ($Ωθθ=0.46$ in ATAA, compared to $Ωθθ=0.59$) to represent collagen disorganization and network fragmentation [40,41].

Because a full optimization-based fit was unfeasible for our large number of model parameters and computationally demanding simulations, model parameters (Table 1) were manually adjusted from previous values [37] to produce simulations that emulated the experimental data for the uniaxial, lap, and biaxial loading conditions concurrently. For each configuration and loading condition, the model was compared to the mean of all force–displacement curves, with the same set of model parameters used for all simulations. Boundary conditions were based on the experimental setup for each loading condition. For uniaxial and lap geometries, one end was fixed in all directions, while the opposite end was displaced in the appropriate direction and fixed in the other two directions. For the biaxial geometry, each arm was displaced in the appropriate direction and fixed in the other two directions. Each simulation was run on 256 cores at the Minnesota Supercomputing Institute.

Table 1

ParametersValue
Collagen fibers
Network orientation tensor [Ωzz$Ωθθ$ Ωrr][0.42 0.58 0]
Fiber modulus [MPa (Ec)]1.76
Fiber nonlinearity (Bc)1.1
Failure stretch (λc)2.0
Elastin fibers
Network orientation tensor [Ωzz$Ωθθ$ Ωrr][0.52 0.48 0]
Fiber modulus [MPa (Ee)]1.54
Fiber nonlinearity (Be)0.9
Failure stretch (λe)2.2
Interlamellar connections
Network orientation tensor [Ωzz$Ωθθ$ Ωrr][0.3 0.46 0.24]
Fiber modulus (MPa) (EIC)3.0
Fiber nonlinearity (BIC)1.9
Failure stretch (λIC)1.7
Matrix
Poisson's ratio (ν)0.495
Shear modulus [MPa (G)]3.76 × 10−4
Proportions
Total network volume fraction, ($ϕ$ [4245])0.5
Elastin-to-collagen ratio [41,42]17:20
ParametersValue
Collagen fibers
Network orientation tensor [Ωzz$Ωθθ$ Ωrr][0.42 0.58 0]
Fiber modulus [MPa (Ec)]1.76
Fiber nonlinearity (Bc)1.1
Failure stretch (λc)2.0
Elastin fibers
Network orientation tensor [Ωzz$Ωθθ$ Ωrr][0.52 0.48 0]
Fiber modulus [MPa (Ee)]1.54
Fiber nonlinearity (Be)0.9
Failure stretch (λe)2.2
Interlamellar connections
Network orientation tensor [Ωzz$Ωθθ$ Ωrr][0.3 0.46 0.24]
Fiber modulus (MPa) (EIC)3.0
Fiber nonlinearity (BIC)1.9
Failure stretch (λIC)1.7
Matrix
Poisson's ratio (ν)0.495
Shear modulus [MPa (G)]3.76 × 10−4
Proportions
Total network volume fraction, ($ϕ$ [4245])0.5
Elastin-to-collagen ratio [41,42]17:20

Note: Initial guesses for parameters were based off of previous work with healthy porcine tissue [37].

## Multiscale Inflation

The same multiscale modeling approach was used to inflate a patient-specific ATAA geometry. A patient CT scan was obtained for one patient (see Fig. 1(a)), and the geometry was manually segmented using the Vascular Modeling Toolkit.1 The boundary of the inner lumen was clearly visible in the CT scan, but the outer boundary was not. The segmented shell of the ATAA lumen was meshed in abaqus and uniformly extruded by 2.4 mm (the average thickness from all experimental samples) in matlab. To apply an internal pressure on the ATAA mesh, nodes located on the surface of the inner lumen were identified. A force boundary condition was then applied to each of the nodes during the simulation, where nodal displacements were imposed to satisfy the pressure condition at each incremental step. The same iterative process of network equilibration, stress calculation based on network boundary nodes, and macroscale stress scaling was performed, as described previously.

Before the simulations could be run, the fiber structure at each Gauss point of each element had to be specified, which required a local radial–circumferential–axial coordinate system. To construct an appropriate local coordinate basis, an artificial solute diffusion problem was specified in FEBio. First, to define the axial direction, a diffusion problem was imposed with boundary conditions of a large concentration of solute on the proximal surface of the ATAA mesh, a zero concentration of solute on the distal surface, and no-flux conditions on the other surfaces. Steady-state Fickian diffusion was applied
$D∇2(c)=0$
(4)

where D is the diffusivity and c is the solute concentration. The problem solution formed a concentration gradient running smoothly from the proximal to the distal ATAA, and the direction of the concentration gradient was used to define the axial direction. A second problem was then constructed, with a finite solute concentration boundary condition on the inner lumen surface and a zero concentration boundary condition on the outer surface, with no-flux boundary conditions on the ends of the vessel. The solute flux in each element for the solution to this second problem was used as an initial estimate for the radial direction. Following the simulations, the cross product of the axial and radial directions was taken to define the circumferential direction for each element. Finally, in order to ensure an orthogonal coordinate system, the cross product of the circumferential and axial directions was performed to define the final radial direction used in the multiscale simulations. Networks of the same specifications used during optimization were then generated and rotated appropriately for each element, based on the calculated coordinate systems.

Fiber parameters were set as the values obtained from the optimization to the experimental data, specified previously. Since the patient CT was captured with the tissue in a loaded configuration in vivo, the unloaded length of each fiber was set to be 80% of its initial length, to simulate fiber prestretch. The nodes residing on the lumen of the proximal end of the vessel were fixed in all directions to resemble anchoring at the aortic root, while the rest of the vessel was allowed to move freely in all other directions. The ATAA geometry was inflated to a pressure of 50 mmHg, a value that was artificially reduced from that seen in vivo to account for the lack of smooth-muscle-cell contraction or adventitial support in the model. Absent those additional factors, we found that a 50 mmHg pressure load produced reasonable strains in the simulated inflated aneurysm.

## Results

### Experiments.

Strain-to-failure experiments for the uniaxial, lap, and peel loading conditions showed a few notable trends. First, ATAA tissue displayed similar nonlinear, anisotropic, prefailure behavior to healthy porcine tissue, but was weaker in most loading cases, failing at a lower stress and stretch. Second, ATAA tissue was strongest in the uniaxial loading condition, and weakest in the shear lap loading condition. There was no significant difference between tissues from the greater versus lesser curvature regions in any test (data available in the Supplemental Materials on the ASME Digital Collection), so results for the two regions were pooled in all subsequent analysis.

Ascending thoracic aortic aneurysm uniaxial samples exhibited significantly lower strength in the circumferential direction compared to porcine tissue (Figs. 5(c) and 5(e)), similar to previous studies [9,10,37]. There was, however, no difference in tensile strength between ATAA and porcine tissue in the axial direction (Figs. 5(d) and 5(e)). In both ATAA directions, the failure stretch was lower than for porcine samples (Fig. 5(f)).

Fig. 5
Fig. 5
Close modal

Lap samples were significantly stronger in the circumferential direction compared to the axial direction (Figs. 6(c)6(e)), similar to results seen by Sommer et al. [24]. ATAA samples showed significantly lower failure strength (Fig. 6(e)) compared to porcine samples. All orientations and locations exhibited a lower failure stretch compared to porcine data.

Fig. 6
Fig. 6
Close modal

Ascending thoracic aortic aneurysm peel samples exhibited a significantly higher peel tension in the axial direction compared to circumferential (Fig. 7(b)) in agreement with previous studies [22]. Both the circumferential and axial directions showed a significantly lower peel tension compared to porcine samples (Fig. 7(b)).

Fig. 7
Fig. 7
Close modal

Biaxial samples showed a slight increase in nonlinearity for both the circumferential and axial directions compared to porcine data (Figs. 8(c) and 8(d)). The similarity between ATAA and porcine aortic tissue in biaxial tests is consistent with the similar prefailure curves in Figs. 5 and 6. The biaxial samples also displayed tissue anisotropy in favor of the circumferential direction, in the same fashion as the uniaxial and lap testing.

Fig. 8
Fig. 8
Close modal

Overall, ATAA tissue showed the highest strength in uniaxial loading conditions and the lowest strength in shear for both circumferential and axial orientations. The prefailure data for uniaxial, lap, and biaxial samples were similar to porcine tissue, but the uniaxial and lap samples exhibited lower failure stresses and stretches for ATAA tissue, with ATAA tensile strength and peel tension roughly half of the corresponding values for porcine aorta. The failure stretch for uniaxial tests was also considerably lower for the ATAA samples under uniaxial and shear loading. Taking the data collectively, we conclude that the ATAA tissue shows comparable mechanics to the healthy porcine tissue at subfailure loads, but fails at significantly lower stretch/load.

### Modeling.

One set of network parameters (Table 1) was determined to fit the experimental data from the uniaxial, lap, and biaxial loading configurations. For the uniaxial case (Fig. 9, top), the model captured the anisotropic behavior prior to failure quite well, but it showed some inaccuracy in the prediction of the failure stretch. For the lap tests (Fig. 9, middle), the model showed similar good performance prior to failure and matched the failure points more closely. The model, when properly parameterized, also captured the ten-fold difference in failure stress between the uniaxial and lap experiments. Finally, for the biaxial experiments (Fig. 9, bottom), the model overpredicted the stress, but correctly described the anisotropy of the tissue. We know of no other computational model that has been applied to such a wide range of experimental data.

Fig. 9
Fig. 9
Close modal

Certain other features that are not measurable experimentally can be interrogated by the model. These include the stress field in each experiment, visualized in the middle column of Fig. 9. The regions of highest stress correspond to the locations of tissue failure, as investigated by us earlier [46] in the context of a continuum anisotropic failure model. Perhaps most important is the ability of the model to examine micromechanics, as shown in the enlarged images of individual networks, and in the pie charts in the right hand column of Fig. 9. An important difference between uniaxial and shear loading can be seen: in the uniaxial tests, between 55 and 60% of the failed fibers in the model are collagen and elastin, and only 40–45% of the failed fibers are interlamellar connections. In the shear lap case, in contrast, 49–78% of the failed fibers are interlamellar connections, suggesting that in the shear case, the lamellae may not fail at all, but rather they are allowed to slide relative to each other because of failed connections between them.

Inflation of the patient ATAA geometry yielded two major findings, (1) the sample exhibited a high amount of shear stress relative to its shear strength and (2) I.C. fibers were the primary fiber type to fail in the sample. During inflation, the sample exhibited the highest circumferential and shear strain near the greater curvature of the vessel (Figs. 10(b) and 10(c)), and a heterogeneous stress field throughout (Figs. 10(d)10(f)). The circumferential stress was higher than shear stress, with both stresses being highest in the regions of fiber failure (Figs. 10(e)10(g)). Although shear stress did not reach the same magnitude overall as stress in the circumferential direction, shear stress values were quite high, especially considering the tissue is much weaker in shear (c.f., experimental results). In certain locations, particularly near elements with high fiber failure, shear stress was even higher than circumferential stress (Fig. 10(d)). The importance of shear stress is particularly highlighted by the fact that I.C. fibers showed a much higher percentage of fiber failure compared to collagen and elastin fibers (Figs. 10(h) and 10(i)). In fact, the fraction of failed fibers that were interlamellar connections was greater in the inflation simulations (Fig. 10(i)) than in any of the simulated mechanical tests (Fig. 9). It is noted that the difference may be due to incomplete failure of the simulated vessel (i.e., the collagen and elastin would eventually fail). These results provide a comprehensive look into the mechanics and failure of ATAA tissue, and strongly suggest that shear loading plays a large role in the failure process.

Fig. 10
Fig. 10
Close modal

## Discussion

The three key results from this work are (1) that ATAA tissue shows similar prefailure behavior to porcine aorta, but has consistently lower strength, (2) that ATAA tissue is extremely weak in shear, to the point that even though shear stresses are not as large as tensile stresses in the vessel, shear failure may in fact be an important mechanism, and (3) a comprehensive approach considering multiple loading configurations must be used when assessing ATAA failure, as the vessel exhibits complex mechanical behavior.

Human ATAA tissue exhibited markedly different responses in all loading conditions and orientations compared to nonaneurysmal porcine tissue. The relative change of failure stress between ATAA and porcine samples, however, showed no dependence on location or orientation. Rather, the ATAA failure stress (or peel tension) was roughly 50% of the corresponding value for porcine tissue in all cases. These results suggest that aneurysm disease progression may not favor any specific direction, but rather that it homogeneously compromises the structural integrity of the tissue, at least on average. Lap samples showed the lowest strength out of all loading conditions, suggesting that failure could most easily occur in the shear loading condition. This finding emphasizes the importance of interlaminar shear strength in the mechanical stability of the aneurysm pathology, and implicates its consideration as a possible risk factor. Shear may also be important in terms of tissue remodeling because of the load it places on the interlamellar connections, which represent, in part, the smooth muscle cells. Unlike circumferential and axial loads, which can be borne in significant part by the collagen and elastin in the aortic wall, shear stresses must be borne by the cells and thus could be a major driver for pathological remodeling of the tissue. Furthermore, the interlamellar failure in the inflation simulation is consistent with dissection rather than outright rupture of ATAAs [2,33].

Human ATAA results for uniaxial and biaxial samples were in agreement with previous studies [10,11]. Shear failure results showed the same trend in anisotropy (circumferential > axial) compared to Ref. [24], but exhibited lower failure stresses, particularly in the axial direction. Peel samples exhibited lower average peel tension (∼65 N/m) for both the circumferential and axial directions compared to Ref. [22], but showed a similar trend in anisotropy (axial > circumferential). Here, we have presented a comprehensive resource for understanding experimental prefailure and failure behavior of ATAA tissue, particularly documenting the strength of the tissue in loading conditions previously less studied (i.e., shear).

Though useful, our multiscale model still presented a variety of limitations. Microscale networks were constructed as simplified representations of the ATAA microenvironment, and oversimplified aspects such as vascular smooth muscle cells and fibrillin by only using one fiber type to describe the interlamellar space. Only passive mechanics were studied and modeled, neglecting the clearly present role of active contractility within the vessel wall, which may significantly affect the simulated tissue behavior, and thus our conclusions. Furthermore, the medial layer of the vessel wall was the only layer modeled, even though the adventitial layer is known to contribute mechanical stability [47], and carries more than 50% of the pressure load at higher pressures [48]. The combination of modeling only passive mechanics and excluding the adventitial layer explains the large deformation observed during simulated inflation at a relatively low maximum pressure (50 mmHg). It is noted that, since some of the resected tissue samples did not form a full circumference, it was impossible to get residual stress data, and we were only able to consider tissue in the released state. Thus, we could not consider residual stress in the tissue (cf., Ref. [4952]). Rather, as a simple way to incorporate some prestress, we artificially shortened each fiber for the case of simulated inflation. A potential advantage of our multiscale approach, if sufficient data were available, would be the ability to incorporate species-dependent prestress [53,54], but since the focus of this work was the multidimensionality and structural complexity, the simpler approach was taken.

Overall, several noteworthy differences were observed between human ATAA and porcine tissue, most of which suggest that the disease remodeling and weakening may involve multiple components. Tissue composition is clearly affected in different ways, meriting further exploration of the constituents' orientation and composition. Our findings also suggest that shear plays an important role in the failure of ATAAs, and must not be overlooked. These results emphasize the importance of fully understanding the structural and mechanical changes that occur in ATAAs, especially in terms of multidirectional failure, as the tissue is constantly under complex loading conditions in vivo where risk is not fully captured by current diameter-based methods.

## Acknowledgment

The authors acknowledge the Minnesota Supercomputing Institute (MSI) and UofM hospital at the University of Minnesota for providing high-performance computing resources and tissue, respectively, that contributed to the research results reported within this paper. The authors also recognize and appreciate the technical assistance of Colleen Witzenburg, Ryan Mahutga, Celeste Blum, and Kenzie Trewartha. This work was supported by NIH grants R01 EB005813 and U01 HL139471, and by the National Science Foundation Graduate Research Fellowship Program under Grant No. 00039202 (CEK). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. CEK is a recipient of the Richard Pyle Scholar Award from the ARCS Foundation.

## Funding Data

• ARCS Foundation (Richard Pyle Scholar Award).

• National Institute of Health (R01 EB005813 and U01 HL139471; Funder ID: 10.13039/100000002).

• National Science Foundation (NSF GRFP 00039202; Funder ID: 10.13039/501100008982).

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