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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Ann Thorac Surg. Author manuscript; available in PMC 2014 May 29.
Published in final edited form as:
PMCID: PMC4037886

Peak Wall Stress Predicts Expansion Rate in Descending Thoracic Aortic Aneurysms



Aortic diseases, including aortic aneurysms, are the 12th leading cause of death in the United States. The incidence of descending thoracic aortic aneurysms is estimated at 10.4 per 100,000 patient-years. Growing evidence suggests that stress measurements derived from structural analysis of aortic geometries predict clinical outcomes better than diameter alone.


Twenty-five patients undergoing clinical and radiologic surveillance for thoracic aortic aneurysms were retrospectively identified. Custom MATLAB algorithms were employed to extract aortic wall and intraluminal thrombus geometry from computed tomography angiography scans. The resulting reconstructions were loaded with 120 mm Hg of pressure using finite element analysis. Relationships among peak wall stress, aneurysm growth, and clinical outcome were examined.


The average patient age was 71.6 ± 10.0 years, and average follow-up time was 17.5 ± 9 months (range, 6 to 43). The mean initial aneurysm diameter was 47.8 ± 8.0 mm, and the final diameter was 52.1 ± 10.0 mm. Mean aneurysm growth rate was 2.9 ± 2.4 mm per year. A stronger correlation (r = 0.894) was found between peak wall stress and aneurysm growth rate than between maximal aortic diameter and growth rate (r = 0.531). Aneurysms undergoing surgical intervention had higher peak wall stresses than aneurysms undergoing continued surveillance (300 ± 75 kPa versus 229 ± 47 kPa, p = 0.01).


Computational peak wall stress in thoracic aortic aneurysms was found to be strongly correlated with aneurysm expansion rate. Aneurysms requiring surgical intervention had significantly higher peak wall stresses. Peak wall stress may better predict clinical outcome than maximal aneurysmal diameter, and therefore may guide clinical decision-making.

Aortic disease, including aortic aneurysms, is the 12th leading cause of death in the United States [1]. While abdominal and ascending aortic aneurysms are more common, the incidence of descending thoracic aortic aneurysms (TAAs) is increasing, reaching 10.4 per 100,000 person-years [2]. The overall mortality rate of ruptured TAAs has been reported as high as 97%, with nearly 60% of patients dying in the prehospital environment [3].

The natural history of thoracic aortic aneurysms has been described as one of slow growth that ultimately culminates in catastrophic complications such as dissection or rupture. The growth rates of aortic aneurysms have been found to vary by location, with ascending aortic aneurysms growing at a rate of 0.7 mm per year, and TAAs growing at a slightly faster rate of 1.9 mm per year [4]. The rate of growth is also related to aneurysm size—larger aneurysms exhibit a higher growth rate than smaller ones. Furthermore, it has been shown that rapidly expanding aneurysms are more prone to rupture [5].

There is a growing body of literature suggesting that stress measurement in the aortic wall may aid in the identification of aneurysms that are at high risk of rupture. Ruptured abdominal aortic aneurysms (AAA) have been shown to have higher peak wall stresses than unruptured aneurysms [6]. A patient-specific study demonstrated that peak wall stress was 13% more sensitive and 12% more specific in predicting ruptured AAAs than maximum diameter alone [7]. Li and colleagues [8] correlated aneurysm shoulder stress with growth rate, showing that individual aneurysms with higher shoulder stresses were associated with increased AAA expansion. Despite the relative success of biomechanical modeling techniques in stratifying AAA rupture risk, these techniques have not commonly been applied to TAAs.

Although the use of thoracic endovascular aneurysm repair (TEVAR) is increasing, there is no prospective randomized trial data comparing TEVAR to conservative therapy. Operative intervention is still not without risk: there is a 5% 30-day mortality and a 5% incidence of spinal cord ischemia with TEVAR in some large series [9-11]. A 6.5-cm TAA has an estimated 14.1% annual risk of rupture, dissection, or death [12]. However, smaller aneurysms also rupture not infrequently: those between 5 cm and 6 cm in maximal diameter exhibit annual risks of approximately 6.5%. Therefore, improved rupture risk stratification will allow more rational implementation of TEVAR and will likely lead to improved survival of patients with TAAs.

Patients and Methods


A total of 25 patients undergoing surveillance for aneurysms of the descending thoracic aorta were retrospectively identified. Patients were identified by querying computed tomography angiography (CTA) studies from the radiology information system (Centricity RIS-IC; GE Healthcare, Waukesha, WI) utilizing PRESTO (Montage Healthcare Solutions, Philadelphia, PA). Approval was obtained from the Institutional Review Board, and the need for informed consent was waived.

All patients had at least two CTA examinations separated temporally by at least 6 months. Patients with concomitant aortic dissections, thoracoabdominal aneurysms, inflammatory or infectious aneurysms, and previous surgical procedures involving the descending thoracic aorta were excluded. All scans were initially evaluated on a three-dimensional image analysis and modeling workstation (TeraRecon, San Mateo, CA). Initial and final aortic diameters were measured as the maximum diameter orthogonal to the aortic centerline.

Image Segmentation and Aneurysm Reconstruction

Three-dimensional TAA geometries were reconstructed from individual stacks of two-dimensional CTA images. Individual CTA slices, from the apex of the aortic arch to the celiac axis, were analyzed using a series of custom MATLAB (The MathWorks, Natick, MA) algorithms. Briefly, the entire CTA image stack was converted into a matrix representation of the three-dimensional volume. Automatic windowing was applied to improve the contrast between arterial structures and surrounding tissues. Subsequently, an anisotropic diffusion filter was applied to the images to reduce noise and enhance borders [13].

Lumen boundaries were obtained automatically by employing an algorithm based upon active contours without edges originally described by Chan and Vese [14]. A luminal centerline was then calculated using a fast-marching distance transform algorithm [15], and a series of transformed image slices was generated orthogonal to the centerline.

The outer adventitial border was traced using a semi-automated method incorporating isolines constructed from smoothed pixel intensities. The algorithm automatically selected a threshold using curvature constraints and comparison to previous slices. In portions of the aortic wall where intraluminal thrombus (ILT) was present, both an entropy filter and texture analysis were used to discern the border between ILT and the inner arterial wall. Areas corresponding to thrombus were defined as being outside the luminal boundary, but inside the boundary marking the inner arterial wall. As both inner and outer boundaries of the arterial wall were separately defined, local wall thickness could be resolved. The image segmentations were subsequently reviewed for each slice and manual correction employed as necessary.

Gaussian curvature-based surface smoothing was applied to both the arterial wall and the ILT surfaces. The resulting surfaces were meshed into hexahedral and tetrahedral elements for the arterial wall and thrombus, respectively. Meshes consisted of 2.5 × 105 to 1.25 × 106 elements depending on thrombus volume. The reconstructed mesh representing the final mesh discretization of the aneurysm was then exported to Abaqus/CAE version 6.11(Simulia, Providence, RI) for finite element analysis (FEA).

Material Properties

Both ILT and the TAA wall were assumed to be hyperelastic, homogeneous and isotropic. They were modeled using the nonlinear hyperleastic formulation derived from Wang and associates [16] and Raghavan and Vorp [17], who examined the uniaxial properties of excised AAAs. The strain energy functions used to model aortic wall and ILT were:

W=C1(IB3)+C2(IB3)2for the arterial wallW=D1(IIB3)+D2(IIB3)2for ILT

In these formulations, W represents strain energy, and the constants C1, C2, and D1, D2 represent material parameters for the wall and ILT, respectively. Population mean values of C1 = 0.174 MPa, C2 = 1.881 MPa, D1 = 0.026 MPa, and D2 = 0.026 MPa were used. Calcified elements were modeled using linear elastic material properties, with Poisson’s ratio of 0.45 and Young’s modulus of 45 MPa [18].

Numerical Simulation

The FEA technique parses a structure with complex geometry into small elements where numerical simulation is more readily carried out. Solutions derived from these elements are subsequently reassembled to approximate the solution over the larger structure.

A uniform pressure of 120 mm Hg was applied to the luminal surface in Abaqus, and a nonlinear large deformation model was used. The arterial wall and intraluminal thrombus were composed of first-order hexahedral (C3D8) and tetrahedral (C3D4) elements, respectively. Contact with adjacent structures, including the spine and other adjacent organs, was not considered. Similarly, shear stress generated by blood flow was not examined, as the effects have been previously determined to be minor [19]. The aorta was translationally fixed at the proximal and distal ends, as well as by the head vessels. A “no-slip” condition was placed on the interface between the arterial wall and the ILT. The Von Mises stress, an axis-independent scalar, is frequently used as an indication of material failure and was reported for that purpose. Computations were performed on a 64-bit dual quad-core workstation with 32GB of RAM.

Statistical Analysis

Statistical analysis was performed using MATLAB. Plots were generated using SigmaPlot (Systat, San Jose, CA). Fisher’s exact test was used to compare categorical variables. Continuous variables were compared using unpaired t tests or Mann-Whitney tests. The relationships between initial maximal aortic diameter, growth rate, and wall stress were calculated using the Pearson correlation coefficient. Correlation coefficients were compared using Fisher’s r to Z transformation. All p values were two-sided, and a value of less than 0.05 was considered to be statistically significant. All results are expressed as mean ± SD, unless otherwise specified.


Twenty-five aneurysms in 25 patients were analyzed. The overall patient and aneurysm demographics are shown in Table 1. Seven aneurysms (28.0%) were located in the proximal descending thoracic aorta, 12 (48.0%) were located in the midthoracic aorta, and 6 (24.0%) were located in the distal thoracic aorta. The average patient age was 71.6 ± 10.0 years, and the average follow-up time was 17.5 ± 9 months (range, 6 to 43). The average peak wall stress across all aneurysms was 246 ± 62 kPa (range, 171 kPa to 400 kPa).

Table 1
Patient Demographics and Comorbidities

A single representative reconstructed TAA model with the stress contour distribution overlaid is shown in Figure 1. In a majority of cases (n = 24, 96.0%), the location of peak wall stress did not coincide with the plane of maximum diameter. Areas of high stress were consistently found in regions of the aorta where there were abrupt changes in aneurysm morphology corresponding to areas of high curvature, such as the aneurysm neck.

Fig 1
(A) DICOM image with segmentation into luminal surface (blue), inner arterial surface (red), and outer adventitial surface (green). (B) Three-dimensional reconstruction with stress plot overlaid. (C) Stress contour plot of entire aortic descending thoracic ...

Patients were divided into two groups by aneurysm expansion rate: 15 patients with slowly growing aneurysms (<4 mm/year) and 10 patients with rapidly growing aneurysms (>4 mm/year). Patient and aneurysm characteristics are shown in Table 2. Rapidly growing aneurysms had significantly higher peak wall stress (245 ± 64 kPa versus 213 ± 32 kPa, p = 0.003), but did not have significantly higher initial diameter (46.0 ± 6.4 mm versus 51.7 ± 8.8 mm, p = 0.08).

Table 2
Comparison Between Rapidly Expanding and Slowly Expanding Aneurysms

Six patients (24.0%) ultimately required operative intervention. Patient and aneurysm characteristics are shown in Table 3. Five patients had symptoms, consisting of chest pain (n = 4) and increasing shortness of breath resulting from bronchial compression (n = 1). The remaining patient had asymptomatic aneurysm enlargement from 62 mm to 70 mm and was repaired based on size criteria. Four patients underwent TEVAR, and 2 patients required open aneurysmectomy. Peak wall stress was elevated in patients requiring operative intervention (300 ± 75 kPa versus 229 ± 47 kPa, p = 0.01). However, aneurysms requiring intervention did not have a larger initial aortic diameter when compared with aneurysms that underwent continued observation (51.3 ± 7.7 mm versus 47.1 ± 7.9 mm, p = 0.25).

Table 3
Comparison Between Aneurysms Requiring Surgical Intervention and Aneurysms Undergoing Continued Observation

Correlation coefficients were calculated between aneurysm growth rate and peak wall stress, as well as aneurysm growth rate and initial aortic diameter. Initial aortic diameter was found to be positively correlated with aneurysm growth (r = 0.531, p = 0.006), as shown in Figure 2. Similarly, a positive correlation was found between aortic growth rate and peak wall stress (r = 0.894, p < 0.001), as shown in Figure 3. The two correlation coefficients were significantly different (Z = 2.79, p = 0.005) by Fisher’s r to Z transformation.

Fig 2
Plot showing relationship between initial maximum aortic diameter and aneurysm expansion rate.
Fig 3
Plot showing positive correlation between peak aneurysm wall stress and aneurysm expansion rate.


The goal of treating TAAs—with TEVAR or open repair—is to prevent the catastrophic outcome of aneurysm rupture, while balancing the risk of rupture with the risks of the intervention itself. The current study represents an attempt to apply structural analysis techniques to descending thoracic aortic aneurysms, and to relate the results of numerical simulation with the clinically relevant outcome of aneurysm expansion.

In the current study, by applying FEA to a series of TAAs with radiologic and clinical follow-up, a strong association was found between peak wall stress and the rate of aneurysm expansion. While a positive correlation was found between initial maximum diameter and aneurysm growth rate, that correlation was significantly weaker. Furthermore, rapidly growing aneurysms were found to have significantly higher peak wall stresses than quiescent aneurysms. Rapidly growing aneurysms were not found to have significantly higher maximum diameters, although this likely represents a type II error.

Aneurysms ultimately requiring surgical intervention also had significantly increased peak wall stress, but did not have significantly larger initial diameters. These results show that aneurysm peak wall stress is not only a strong predictor of aneurysm growth, but also suggest that it may predict clinical outcomes. Because the rupture of aneurysm under observation is rare, aneurysm growth rate is commonly used as a proxy for rupture risk [5, 8]. Therefore, the current study suggests that peak stress may predict TAA rupture risk.

The FEA results herein are based upon high-fidelity reconstructions of patient-specific geometries that include locally resolved wall thickness and use nonlinear materials models. However, there are still several important limitations to this study. Both the aortic wall and ILT were assumed to have isotropic material properties, though several studies have demonstrated anisotropy in both materials [20, 21]. Unfortunately, the degree of anisotropy has been shown to vary significantly between individual patients, and currently there exists no way of accurately estimating an individual patient’s aortic material properties in vivo.

When considering aneurysm rupture, both wall stress and wall strength must be considered. It is generally accepted that a TAA will rupture only when the local stress exceeds the local wall strength. Therefore, peak wall stress alone may be insufficient in the determination of TAA stability. In this study, the material properties assigned to the TAA wall were derived from strain testing of excised AAAs. While it has been shown that the aortic wall in ascending aorta aneurysms has twice the breaking strength of AAA specimens, material properties of the descending thoracic aorta are unavailable [22, 23]. The lack of TAA material strength data prevents the comparison of local wall strength to local wall stress.

Finally, wall stress was calculated using finite element techniques, which do not include the effect of blood flow. Traditionally, the impact of wall shear stress has been ignored, as studies in the thoracic aorta have shown it to be several orders of magnitude lower than static stresses calculated using pressure-deformation analyses [19]. Simulations using fluid-structure interactions that combine both fluid flow and solid stress have shown conflicting results in AAAs, with some studies claiming less than 5% impact on peak stress [24] and others reporting more significant increases, on the order of 20% [25]. The impact of fluid-structure interactions in TAAs represents an area of future research.

Stress analysis of TAAs requires significant expertise with biomechanical modeling, as it combines advanced image segmentation procedures with sophisticated numerical simulation techniques. As such, it is not readily accessible to individual practitioners. Therefore, prospective studies are needed to establish the role of stress modeling in patients with TAAs. Patients with smaller aneurysms with high peak wall stress might benefit from the rupture risk reduction that earlier repair would provide. Patients with significant medical comorbidities, large asymptomatic aneurysms, and low wall stresses may similarly benefit from continued surveillance. Overall, stress analysis has shown peak wall stress to be related to aneurysm growth, and this information may prove to be useful in risk-stratifying patients, and thereby guiding the management of patients with TAAs.


The funding source was the McCabe Fund, Philadelphia, Pennsylvania.


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