Association Between Aneurysm Shoulder Stress and Abdominal Aortic Aneurysm ExpansionClinical Perspective
A Longitudinal Follow-Up Study
Background—Aneurysm expansion rate is an important indicator of the potential risk of abdominal aortic aneurysm (AAA) rupture. Stress within the AAA wall is also thought to be a trigger for its rupture. However, the association between aneurysm wall stresses and expansion of AAA is unclear.
Methods and Results—Forty-four patients with AAAs were included in this longitudinal follow-up study. They were assessed by serial abdominal ultrasonography and computed tomography scans if a critical size was reached or a rapid expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up computed tomography images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline and final visit. A nonlinear large-strain finite element method was used to compute the wall-stress distribution. The relationship between wall stresses and expansion rate was investigated. Slowly and rapidly expanding aneurysms had comparable baseline maximum diameters (median, 4.35 cm [interquartile range, 4.12 to 5.0 cm] versus 4.6 cm [interquartile range, 4.2 to 5.0 cm]; P=0.32). Rapidly expanding AAAs had significantly higher shoulder stresses than slowly expanding AAAs (median, 300 kPa [interquartile range, 280 to 320 kPa] versus 225 kPa [interquartile range, 211 to 249 kPa]; P=0.0001). A good correlation between shoulder stress at baseline and expansion rate was found (r=0.71; P=0.0001).
Conclusion—A higher shoulder stress was found to have an association with a rapidly expanding AAA. Therefore, it may be useful for estimating the expansion of AAAs and improve risk stratification of patients with AAAs.
Abdominal aortic aneurysm (AAA) rupture continues to be a major source of morbidity and mortality. Rupture of the aneurysm is fatal in 70% to 90% of cases. It is the 13th leading causing of death in Western societies.1 According to the National Vital Statistics Report published in 2007, 14 000 patients had aneurysm-related deaths in 2004.2 The main clinical indicators used to assess the risk of rupture are the maximum diameter and expansion rate of the AAA. Surgery is recommended when the maximum diameter of an AAA is ≥5.5 cm. However, small aneurysms can also rupture, and the overall mortality associated with these may exceed 50%3; for example, the 12-year follow-up of the UK Small Aneurysm Trial has also shown a mortality rate of 67.3% in the surveillance group.4 Expansion rate is also considered to be an important indicator, and surgery is recommended when maximum diameter expands above 10 mm/yr for smaller AAAs.5,6 However, expansion rates may be nonlinear and unpredictable,7 although currently it seems to be the best predictor of aneurysm rupture.8 Therefore, there is a need for a better predictor of aneurysm expansion and possible rupture.
Clinical Perspective on p 1822
There is growing evidence that stress measurement within the AAA wall may aid in identification of a high risk of rupture with rapidly expanding aneurysms.9,10 A patient-specific study previously demonstrated that maximum wall stress was 12% more specific and 13% more sensitive in predicting AAA rupture than maximum diameter alone.11 In other patient-specific studies, peak stress was found to be significantly higher in ruptured AAAs than nonruptured AAAs.12 Rupture of the aneurysm can be seen as a structural failure when the induced mechanical stresses acting on the weakened AAA wall exceeds its local mechanical failure strength. The external forces include blood pressure and wall shear stress. Stress in the AAA wall is due to the influence of other concomitant factors, including the shape of the aneurysm, the characteristics of the wall material, the shape and characteristics of the intraluminal thrombus (ILT) when present, the eccentricity of the AAA, and the interaction between the fluid and solid domains.13,–,17 Their role has been investigated before.9,18,–,20 Fully coupled fluid-structure interaction of the AAA has also been used to investigate the flow and pressure fields in the aneurysm simultaneously with the wall stresses.14,–,16
Although rupture is determined by the comparison of wall stress and wall strength, accurate wall strength measurement in vivo is not currently possible. Therefore, computed wall stresses at 1 time point may not necessarily provide an estimation of the risk of rupture without knowing the strength value at that time point. However, by following up patients and performing wall stress analysis based on follow-up images, the change in wall stresses may be more useful in identifying AAA stability. Therefore, the main purpose of this study was to evaluate the association of the change of wall stresses with expansion rate of AAAs in a longitudinal follow-up study.
A database of patients who were being followed up in the Cambridge Vascular Unit with routine ultrasound surveillance imaging for AAA was used for this study (which usually may be done every 3 months, 6 months, or 12 months). From this database, a further subset of patients was selected who had an abdominal computed tomography (CT) scan done for other medical reasons. This was to ensure that baseline aortic morphology data were available from a CT scan. The maximum cross-sectional diameter of AAAs was measured at each ultrasound surveillance visit. The expansion rate was calculated from the serial ultrasound scans and CT scans. The growth rate calculated from CT scans was used for analysis. A final CT scan was done just before surgery to assess the optimum technique for treating it (ie, open or endovascular). Axial and 3-dimensional (3D) CT reconstruction images were used to assess the maximum diameter and the location of the aneurysm shoulder at baseline CT scan and at the CT scan before surgery. Only infrarenal AAAs were included in this study. Patients with juxtarenal, aorta-iliac, or inflammatory aortic aneurysms were excluded from the study.
Only those patients were selected from this database who had CT scans done for their abdominal pathologies. (The timing of CT scanning was at the discretion of the relevant consultant surgeon.) Only those patients were included in the study who underwent CT abdomen close to the time of ultrasound. This baseline CT scan was used for stress analysis. The patients continued with their ultrasound surveillance after that. When the aneurysm reached a size at which it was considered operable by the surgeon (which is ≈5.5 cm), a CT scan was done for detailed information about aneurysm morphology, which is used for planning the operation. We calculated the expansion rate from the ultrasound surveillance on a yearly basis and then the average expansion rate over the entire follow-up period. Similarly, the average expansion rate over the follow-up period was also calculated from CT scan (from baseline and final CT). Because the expansion rates calculated from ultrasound or CT were similar, and because CT scan was being used for stress analysis, for sake of standardization, we used CT-calculated expansion rates. For comparing the diameters of the 2 groups, we calculated the baseline diameter from the baseline CT scan. Similarly, we only used the final CT scan for comparison of the final maximum diameter.
Because the location of the shoulder and the maximum diameter of the aneurysm changes with aneurysm expansion, a standardized approach was used to overcome this limitation. From the baseline CT scan, the renal arteries were taken as a constant landmark. The shoulder was defined as the junction of the neck and the aneurysm sac. The maximum diameter was defined as the maximum distance between the outer walls of the aorta in the aneurysm sac. The distances of these 2 locations were measured from the renal arteries. For the final scan, the same distances were measured to define the neck and the maximum diameter locations that were used in the earlier CT scan (so that stress changes could be measured at a constant point together with the diameter changes at each of these locations).
Based on the Oxford Screening Program,21 the patients were divided into 2 groups: those with stable aneurysms (expansion rate <0.4 cm/yr) and those with rapidly expanding aneurysms (expansion rate ≥0.4 cm/yr).
All patients had at least 2 CT examinations (baseline and final) of their aorta using 100 mL of iodinated contrast medium (Iopamidol, Niopam 300, Bracco, United Kingdom) via a power injector (5 mL/s flow rate) on a 16-slice spiral CT machine (Somatom Sensation 4, Siemens Medical Solutions, Erlangen, Germany). The imaging protocol included automatic bolus tracking (scan initiation at the peak of contrast uptake), with a collimation of 16×0.75 mm, a 512×512 matrix, and a 26×26 cm field of view. Other parameters were 200 mAs and 120 KVp.
AAA geometries were reconstructed from the entire set of 2-dimensional (2D) CT slices. In brief, 2D cross-sectional images of the abdominal aorta were obtained from the renal arteries to immediately proximal to the iliac bifurcation. These images were imported into image-processing software ScanIP (Simpleware Ltd, Exeter, United Kingdom) for segmentation. The lumen was the most distinguishable entity in a CT image, due to the bright contrast agent. The noise in the image was reduced by using a gaussian filter, with a 3×3 kernel, to clarify the lumen boundaries. The lumen boundaries were segmented automatically using a threshold based on the pixel intensities. Because the lumen borders were obtained automatically, the geometric models reconstructed were reproducible. The boundary of the arterial wall was traced using a semiautomatic method in the diseased part of the artery. We manually segmented the inner boundary, and by subtly varying the window width, it was possible to visualize only the soft tissue of the uncalcified wall. The thickness of the wall equals to the local wall thickness minus the calcification thickness in the radial direction. The position of the calcification was defined by the distance between the center of the calcification and the centerline of the vessel wall. In the healthy part of the artery, the thickness was assumed to be 1.9 mm.22 The region of thrombus was defined by the area within the inner wall minus the lumen area. The distinction between the healthy and diseased part of the aorta was made by reviewing the stacked CT images and using a diameter of ≤3 cm as a general guide for definition of healthy artery.
On “stacking” of all 2D image data in 3D space, the 3D aneurysm, including artery wall, ILT, and lumen, was produced. Surface smoothing was controlled in ScanIP, and a curvature cutoff and a maximum iteration can be given to reduce surfaces containing sharp corners, which may result in artificial stress concentration. This smoothing was done on all the surfaces of AAA components, including ILT and vessel wall. The 3D reconstructed AAA model was then meshed using ScanFE (Simpleware Ltd). A cutting section is shown to illustrate the detail meshes of ILT and arterial wall (Figure 1). The 3D reconstructed AAA model was then exported to ABAQUS/CAE (v6.8, SIMULIA, Providence, RI) for finite element preprocessing. The investigator responsible for the entire computational analysis (Z.-Y.L.) was blinded to the patient group and time of imaging.
Both ILT and AAA wall were assumed to be hyperelastic, homogeneous, incompressible, and isotropic materials. The AAA arterial wall and ILT were modeled using the nonlinear hyperelastic wall mechanical properties derived by Raghavan and Vorp from uni-axial testing of 69 excised human AAAs.23,24 ILT is actually not homogeneous, but there are too little data available in the literature to describe the nonhomogeneity of this material to be useful for mechanical simulation. The strain energy functions for AAA wall and ILT were: where W is the strain energy, C1 and C2 are material parameters for the wall, and IB and IIB are the first and second invariants of the left Cauchy-Green deformation tensor B (IB=tr B; IIB=1/2[(tr B)2–tr(B)2]). The constants were set to the population mean values C1=174 000 Pa and C2=1 881 000 Pa; D1=26 000 Pa, and D2=26 000 Pa. It has been shown that use of population mean values does not affect the wall stress result in a significant manner.25,26 For calcification, we have chosen the parameters of the Mooney-Rivlin model, which has been previously used.27 Mooney-Rivlin materials can be described by 2 constants, and their values for calcification were taken as A=18 804.5 Pa and B=20.27
The principles of this analysis are similar to those previously used by our laboratory.10,28,–,30 Finite element analysis divides a complex structure into small areas called elements for which the stress distribution can be more easily studied. The systolic blood pressure was taken at the time of the initial CT scan and was applied as a boundary condition in the lumen wall. Ideally it would have been better to have blood pressure at both CT scans, but for the purpose of this study we wanted to keep the loading conditions constant to avoid any affect of varying loading conditions. This allowed us to investigate “structure vulnerability” itself. This pressure was applied to the inner surface of corresponding models as an outward-acting tractional loading condition. The outer surface of the AAA was considered load-free. No contact with the spine and abdominal organs was simulated. The shear stress acting on the wall by flowing blood was neglected in this study because it has been shown that it is several orders of magnitude smaller than wall stresses.14,31,32 Both ends of the models were fixed to simulate the tethering to the rest of the aorta. The residual stress was not considered in this study. A nonlinear large deformation model was used, and the AAA components were simulated using a hyperelastic material formulation. Tetrahedral elements were used for all AAA components (Figure 1).
All computations were performed on a 64-bit 4–dual-core 2.6-GHz processors high-performance computing cluster with a 32 GB of RAM. The Von Mises stresses were recorded for each analysis. The following notions were used: overall stress (σmax): maximum wall stress within the entire 3D AAA; shoulder stress (σS): stress at the shoulder of the AAA; and max-diameter stress (σD): stress at the location of maximum diameter.
σmax, σS, and σD were investigated using the above standardized approach. Please note that at the final visit, the shoulder may have transformed into aneurysm (due to growth/expansion), but for the sake of simplicity, the term “shoulder stress (σS)” has been used in that case.
Statistical analysis was performed with SPSS 16.0 (SPSS Inc, Chicago, Ill). The normality of the data was assessed using the Shapiro–Wilk test. For categorical variables, the Fisher exact test was used. For continuous variables the following tests were used: Paired t test was used for paired variables with normal distribution, and Wilcoxon matched pairs test was used for non-normal data. For nonpaired variables, the Mann-Whitney test was used for non-normal data and unpaired t test for data that were approximately normal. The relationships between AAA size, expansion rate, and wall stresses were tested using the Pearson coefficient. A P value <0.05 was used to determine statistical significance. All values are 2-sided.
Forty-four patients were included in this study. The patient demographics and comorbidities have been tabulated in Tables 1 and 2. Fourteen patients had slowly expanding aneurysms (expansion rate <0.4 cm/yr), and 30 patients had rapidly expanding aneurysms (expansion rate ≥0.4 cm/yr). The median overall follow-up period was 20 months (interquartile range [IQR], 16 to 29 months), with slowly expanding AAAs followed up for 32 months (IQR, 17 to 52 months) and rapidly expanding AAAs followed up for 16 months (IQR, 8 to 21 months), P =0.004, before they reached a size at which surgical intervention was offered.
Figure 1 shows the reconstructed 3D AAA model from CT slices. The cross-sectional view shows the components (ILT and arterial wall) of the AAA. The 3D stress contour demonstrated stress distributions in the AAA wall. Areas of high stress were found in most cases in the shoulder region of the aneurysm (Figure 1D).
There was no significant difference between the 2 groups for maximum aneurysm diameter at baseline (median, 4.35 cm [IQR, 4.12 to 5.0 cm] versus 4.6 cm [IQR, 4.2 to 5.0 cm]; P=0.32). The overall maximum diameter increased from 4.6 cm (IQR, 3.2 to 5.5 cm) to 5.7 cm (IQR, 5.0 to 7.0 cm) during the follow-up (P=0.002; Table 3). A decrease in the overall shoulder stress from baseline was observed; that is, 279 kPa (IQR, 200 to 376 kPa) to 274 kPa (IQR, 179 to 374 kPa), but it was not statistically significant (P=0.64). A nonsignificant increase in overall stress and maximum diameter stress was observed; that is, overall stress, 296 kPa (IQR, 193 to 420 kPa) versus 309 kPa (IQR, 203 to 463 kPa) (P=0.32) and max-diameter stress, 215 kPa (IQR, 109 to 360 kPa) versus 219 kPa (IQR, 101 to 373 kPa) (P=0.71). See Figure 2 for a representative patient.
Correlations between baseline maximum diameter, expansion rate, σmax, σS, and σD were assessed in order to determine their ability to predict the expansion of the aneurysm (Table 4). This study failed to find a relationship between expansion rate and baseline aortic diameter for all patients (r=0.13, P=0.36). This may be a type II error. A statistically significant positive correlation was found however between overall shoulder stress and expansion rate (r=0.71; P=<0.001) (Figure 3).
Slowly and rapidly expanding aneurysms had comparable baseline maximum diameters (median, 4.35 cm [IQR, 4.12 to 5.0] versus 4.6 cm [IQR, 4.2 to 5.0]; P=0.32). At the end of follow-up, a significant difference in the diameters of the 2 groups was observed (5.2 cm [IQR, 5.0 to 5.6 cm] versus 5.8 [IQR, 5.52 to 6.0 cm], P=0.001). σmax, σS, and σD were compared between stable and rapidly expanding aneurysms (expansion rates calculated from serial ultrasound scans) (Table 2). A statistically significant difference was observed for overall stress and shoulder stress between the 2 groups (P=0.03 and P=0.0001, respectively) at baseline. Correlations between baseline maximum diameter, expansion rate, σmax, σS, and σD were assessed in order to determine their ability to predict the expansion of slowly (Table 5 and Figure 4) and rapidly expanding aneurysms (Table 6 and Figure 5). A positive correlation was observed for rapidly expanding aneurysms between expansion rate and shoulder stress (r=0.53, P=0.003).
The process of AAA rupture is thought to be a multifactorial process that includes biological, biomechanical, and biochemical processes. The biological and biochemical factors have been widely studied and reviewed,33 whereas the biomechanical factors are still not fully understood. It is generally recognized that rupture of an AAA occurs when the stress acting on the wall exceeds the strength of the wall. Wall-stress simulation based on a patient-specific AAA model appears to give a more accurate rupture risk assessment than AAA diameter alone.
This was a longitudinal study in which serial stress changes in the aneurysm wall were monitored and correlated with the aneurysm expansion rate. Wall stress is associated with AAA geometry and components. High stress is often found at the shoulders of the aneurysm because of the abrupt change in the shape of the aorta. This leads to the upregulation of different matrix metalloproteinases from the mechanotransduction of smooth muscle cells. Matrix metalloproteinases result in increased matrix degradation, leading to aneurysmal dilatation.34,–,37
We set out to determine the stress changes at the shoulder and maximum diameter regions of the aneurysm. It was found that areas of high stress were present at the shoulder region of the aneurysm. Another interesting observation was that during the follow-up period there was some decrease in the stress at the shoulder region. It was accompanied by an increase in the diameter at the shoulder region. This indicates that with increasing diameter at the shoulder, stress decreases. This leads to the moving up of the shoulder region and a lengthening of the aneurysm. It may well result from the formation of ILT at the previous “shoulder area,” which tends to reduce the stress in the AAA.10
Although no concomitant increase from baseline for the overall stress, overall maximum diameter stress, and overall shoulder stress was observed, a positive correlation between the expansion rate and the shoulder stress was identified. Further analysis of the 2 groups revealed that this relationship exists for rapidly expanding aneurysms only and not for slowly expanding aneurysms. The lack of correlation for slowly expanding aneurysms may be due to small numbers of research subjects in this group. Thus shoulder stress seems to be a strong predictor of rapid aneurysm expansion. The finding that rapidly expanding aneurysms had significantly higher shoulder stresses at baseline compared with slow expanding aneurysms, despite having comparable maximum aneurysm diameter, and reached the final maximum diameter (at which surgery was offered to patients) in approximately half the time, also supports our hypothesis. We also tested the relationship of maximum diameter of the aneurysm with its expansion rate, but contrary to common belief, we found that there was no correlation. This is an important finding because in today's clinical practice the maximum diameter is used as a guide for offering repair of the aneurysm.
This study concentrated on the wall stress using a computational simulation to demonstrate the stress distributions within the patient-specific AAAs. Although we have used state-of-the-art image segmentation and reconstruction methods and complex nonlinear material models in our analysis, there are still several assumptions and limitations that need to be discussed.
Each single material was assigned a set of parameters in order to govern the stress/strain relationship. In vivo materials have more complex characteristics than those used in this study. Therefore, the stress values may not represent the actual stress condition within the AAAs, but the relative stress changes. The use of an anisotropic model can overcome this limitation, but this requires determining the material properties of aorta, which is not currently possible in living humans. Autopsy studies could be designed to get a broad range of material properties, but even this is not ideal. The uncertainties in image segmentation, 3D reconstruction, definition of the boundary conditions, and the material properties of the AAA model may affect the results of an finite element analysis model derived from CT data. The sensitivity of image-based finite element analysis modeling has been studied previously.38,39 It has been demonstrated that the coefficients of variation of the output variables from finite element analysis modeling never exceed 9%. Further improvement in CT image resolution and automatic image processing techniques will certainly reduce the uncertainties in the patient-specific modeling in the future.
Future work is needed in the assessment of the mechanical properties of AAA components. The use of maximum stress alone may not be enough in the consideration of AAA stability. There are 2 major determinants for AAA rupture: wall stress and wall strength. An AAA ruptures only when the local stress exceeds the local wall strength. However, lack of AAA material strength data made it impossible to predict local strength value for comparison with local stress value. It remains difficult to determine the failure strength of a particular AAA without destructively testing a piece of tissue excised from it. Although wall strength equations exist, they add to the complexity of the model. Moreover, they may be more important for rupture risk than for predicting future growth rate. Another limitation is that the clinical use of wall stress calculations has been hindered by long computational time. It took approximately 4 hours to calculate the wall stress using our high-performance computer cluster. However, with reducing costs, better accessibility, and increasing computational power, this will be less of a problem in the future.
Should all aneurysms undergo stress analysis? The answer is probably no. Patients who are fit and healthy with large aneurysms (>5.5 cm) will continue to undergo aneurysm repair without stress analysis. This is because the risk-to-benefit ratio clearly favors surgical intervention, and stress analysis will not add much. However, patients with smaller aneurysms, who are usually followed up with routine surveillance programs, may benefit from stress analysis. This is because of the already mentioned fact that the stress in small aneurysms may be quite high, exposing them to rupture risk. Identification of such high-stress small-diameter aneurysms can effectively select high-risk vulnerable patients who have a high risk of aneurysm rupture. Stress analysis has shown a relationship between stress and expansion rate. In conjunction with other factors, this information may help to guide our management of medium-sized AAAs (4 to 5.5 cm) in the future.
High stress at the shoulder appears to have an association with a rapidly expanding AAA. Therefore, it may be useful for estimating the rapid expansion of an AAA. This follow-up stress study again highlights that patient-specific stress analysis may be a useful tool for identification of vulnerable AAAs in the future. Work is needed on an improvement in the understanding of the mechanical properties of AAA components. Finally, further investigation, including a better understanding of AAA material properties and failure strength, may help in creating more realistic computational models to be used as a clinical adjunct in the future for effective decision making for surgical and endovascular AAA repair.
Continuing medical education (CME) credit is available for this article. Go to http://cme.ahajournals.org to take the quiz.
- Received January 20, 2010.
- Accepted August 13, 2010.
- © 2010 American Heart Association, Inc.
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By convention, abdominal aortic aneurysm (AAA) diameter has been used as an indicator of the potential risk of rupture. Advances in biomechanics have enabled us to assess the inherent stresses within the aneurysm wall, which are thought to play a role in aneurysm expansion. From the structural view point, aneurysm expansion and rupture results from material fatigue and failure of the aneurysm wall. In this study we assessed the association of AAA wall stresses with their expansion rates and found that stresses at the shoulder of the rapidly expanding aneurysms had good correlation with the expansion rates compared with slowly expanding aneurysms. We also tested the relationship of maximum diameter of the aneurysm to its expansion rate, but although such a relationship is widely believed to exist, we found no such relationship. This highlights the fact that biomechanical stress analysis of AAAs may be useful for estimating their expansion rather than relying only on maximum AAA diameter for assessment of potential risk of rupture.