Abstract
Objective
Abdominal aortic aneurysm rupture (AAA) is believed to occur when the local mechanical stress exceeds the local mechanical strength of the wall tissue. Based on this hypothesis, the knowledge of the stress acting on the wall of an unruptured aneurysm could be useful in determining the risk of rupture. The role of asymmetry has previously been identified in idealised AAA models, and is now studied using realistic AAAs in the current work.
Methods
Fifteen patient-specific AAAs were studied to estimate the relationship between wall stress and geometrical parameters. 3D AAA models were reconstructed from CT scan data. The stress distribution on the AAA wall was evaluated by the finite element method, and peak wall stress was compared to both diameter and centreline asymmetry. A simple method of determining asymmetry was adapted and developed. Statistical analyses were also performed to determine potential significance of results.
Results
Mean von Mises peak wall stress ± standard deviation was shown to be 0.4505 ± 0.14 MPa, with a range of 0.3157 – 0.9048 MPa. Posterior wall stress increases with anterior centreline asymmetry. Peak stress increased by 48% and posterior wall stress increased by 38% when asymmetry was introduced into a realistic AAA model.
Conclusion
The relationship between posterior wall stress and AAA asymmetry showed that excessive bulging of one surface results in elevated wall stress on the opposite surface. Assessing the degree of bulging and asymmetry that is experienced in an individual AAA may be of benefit to surgeons in the decision making process, and may provide a useful adjunct to diameter as a surgical intervention guide.
INTRODUCTION
This is currently much debate as to the most appropriate time to surgically intervene and repair an abdominal aortic aneurysm (AAA).1–7 Surgery is often performed when the detected AAA exceeds 5.0–5.5cm in maximum diameter. Previous research8,9 has shown how AAAs smaller than 55mm in maximum diameter can also rupture. The reliability of the maximum diameter as the main criterion for rupture has been questioned recently, and a need for a more reliable clinical predictor of AAA rupture has been identified.1–7,10–12 Previous work12,13 has identified the importance of asymmetry in idealised AAA models, and also indicated the need to investigate this aspect in realistic models. In this study, we have examined the role of asymmetry and resulting wall stress in realistic patient-specific AAA cases.
METHODS
Computed tomography (CT) scan data was obtained for 22 patients. For this study, AAAs that were asymmetric in the anterior-posterior plane were deemed applicable. Using this criteria, seven of the 22 cases were excluded from the analysis as these case were asymmetric in other directions. The resulting cohort of 15 cases comprised of 10 males and 5 females. Mean age ± standard deviation of the case subjects was 73.2 ± 6.7 years. These patient scans were obtained from the Midwestern Regional Hospital, Limerick, Ireland, and the University of Pittsburgh Medical Centre, Pittsburgh, PA, USA. All 15 patients were awaiting AAA repair, as AAA diameters had reached or exceeded the current 5cm threshold for repair. CT scans were acquired using both the Somatom Plus 4 (Siemens AG, D-91052 Erlangen, Germany) and LightSpeed Plus (GE Medical Systems, General Electric Company) range of imaging equipment. All scans were single slices with a standard width × height of 512 × 512 pixels. Mean pixel size of scans was 0.742 ± 0.072 mm. The bodily structures of each subject were made visible using the non-ionic contrast dye, Optiray® (Mallinckrodt Inc., Convidien, MO, USA). This CT data was then reconstructed using the commercially available software, Mimics v10.0 (Materialise, Belgium), and these reconstructions allowed the computation of stress distributions within the geometries. The patient-specific details for the cases studied can be seen in Table I, which were obtained using the schematic of Figure 1.
Table I.
Patient details for each study subject.
| Patient | Sex | Age | Max Diameter (cm) | Total Length (cm) | Total Volume (cm3) | Total S.A. (cm2) | Dia/Length | ROD |
|---|---|---|---|---|---|---|---|---|
| 1 | Male | 66 | 5.6 | 13.2 | 176.7 | 19.8 | 0.425 | 1.533 |
| 2 | Male | 78 | 6.1 | 11.2 | 192.4 | 18.5 | 0.544 | 2.071 |
| 3 | Male | 70 | 5.7 | 13 | 194.9 | 19.1 | 0.439 | 1.752 |
| 4 | Female | 65 | 5.6 | 9.3 | 136.9 | 14.8 | 0.606 | 2.474 |
| 5 | Male | 81 | 5.9 | 12.8 | 220.9 | 21.8 | 0.463 | 1.772 |
| 6 | Female | 68 | 5.7 | 10 | 148.2 | 16.3 | 0.570 | 2.953 |
| 7 | Female | 67 | 5.3 | 10.5 | 137.9 | 15.5 | 0.505 | 2.000 |
| 8 | Male | 70 | 6.0 | 11.1 | 216.7 | 20.4 | 0.541 | 1.508 |
| 9 | Female | 77 | 5.8 | 8.8 | 94.2 | 12.6 | 0.661 | 2.535 |
| 10 | Male | 87 | 9.0 | 11.7 | 445.5 | 32.4 | 0.769 | 1.768 |
| 11 | Male | 66 | 6.5 | 10.5 | 207.6 | 19.2 | 0.617 | 1.952 |
| 12 | Male | 81 | 6.8 | 14 | 267.6 | 25.2 | 0.484 | 1.994 |
| 13 | Male | 77 | 6.2 | 16.8 | 320.8 | 27 | 0.371 | 1.757 |
| 14 | Female | 72 | 5.7 | 11.4 | 143.8 | 16.7 | 0.497 | 2.675 |
| 15 | Male | 73 | 7.9 | 11.8 | 286.5 | 24.3 | 0.671 | 2.865 |
Note that S.A. is total AAA surface area, Dia/Length is the ratio of maximum diameter to total AAA length, and ROD is the ratio of maximum AAA diameter to infrarenal diameter of that patient.14
Figure 1.
Schematic of representative AAA showing how dimensions are obtained from each AAA model. Surface area and volume both encompass the total surface area or volume of the AAA from immediately below the renal arteries to immediately prior to the iliac bifurcation. Dianorm is the infrarenal aortic diameter of the particular case.
3D Reconstruction Procedure
Spiral CT data was used to reconstruct the infrarenal section of the aorta. As CT scanning is routinely performed on AAA patients scheduled for repair, collection of this information involved no extra participation by the study subjects. Digital files in Digital Imaging and Communications in Medicine (DICOM) file format, containing cross-sectional information was imported to the software, Mimics v10.0 for reconstruction. All reconstructions were developed from scan positions immediately distal to the lowest renal artery to immediately proximal to the iliac bifurcation. The intraluminal thrombus (ILT) was neglected in this study as with previous approaches.6,7,11–13,15 The thickness of the aorta wall is not easily identifiable from CT scans, therefore the wall was assumed to be uniform throughout the model and set to 2mm.16 Once regions of interest were identified, 3D reconstructions were generated. The reconstruction method employed here was validated and reported in previous work performed by our group,17–19 along with the effect of geometry smoothing on resulting wall stress.20 All AAAs underwent the same degree of smoothing. The iliac bifurcation was omitted from this study, as in previous stress analysis work as it has been shown to not significantly affect the wall stress results of the AAA.7 The influence of asymmetry compared to a symmetric AAA was also examined. The reconstruction of Patient 2 was modified using ProEngineer Wildfire 3.0 (Parametric Technology Corporation, Needham, MA, USA) so that the AAA now formed along a straight central axis, becoming a axisymmetric fusiform aneurysm. This symmetric AAA was created using the same diameter information as the original case. The two forms of this AAA can be seen in Figure 2.
Figure 2.
Original asymmetric AAA of Patient 2 (left) and the modified axisymmetric AAA (right).
Biomechanical Material Properties
The AAA material was assumed to be homogenous and isotropic with non-linear realistic material properties5 that have been implemented in many previous publications.3,6,7,10,11,20–22 The aorta is also known to be nearly incompressible with a Poisson’s ratio of 0.49.
FEA Mesh Generation
Once the AAA surfaces were imported into ABAQUS v.6.6-2 (Dassault Systemes, SIMULIA, Rhode Island, USA) for stress analysis, a mesh was generated on the AAA model. As wall thickness cannot be fully determined from the AAA scan data, each shell element was assigned a uniform thickness of 2mm.16 Mesh independence was performed by increasing the number of elements in the mesh until the difference in peak stress was less than 2% of the previous mesh.10,20,23
Forces and Boundary Conditions
The blood pressure within the AAA acts on the AAA inner wall and therefore, pressure was applied to the inner surface of the computational AAA model. A static peak systolic pressure of 120mmHg (16KPa) was used. In order to simulate the tethering of the AAA to the aorta at the renal junction and iliac bifurcation, the AAA model was fully constrained in the proximal and distal regions.
Asymmetry Definition
Most AAAs are constrained from radial expansion in the posterior direction due to the spinal column, therefore, AAAs predominantly dilate in the anterior plane. All cases studied in this analysis were naturally asymmetric in the anterior-posterior direction. In order to examine the effect asymmetry has on wall stress, the centreline of each AAA was automatically found using the software Mimics v10.0. The centreline passes through the centroid of each polyline slice in the series. Asymmetry is defined, in this case, as the perpendicular distance from the proximal and distal points of the centreline to a defined point on the centreline. Figures 3–5 show how these asymmetry measures are obtained. This method of determining asymmetry was adapted from previous work by Young Suh et al.24 Starting with the 3D AAA model in Figure 3A, a centreline is automatically created through the polyline centroids of Figure 3B, thus creating Figure 3C. Then these polylines are exported from Mimics v10.0 to ProEngineer Wildfire 3.0. Next, using the software, the end points of the centreline are connected with a straight line (Figure 3D) and a perpendicular line is extended from this connecting line, to predetermined points along the centreline (Figure 3E and 3F). The asymmetry at a specified distance along the AAA model is regarded as this perpendicular distance, and is measured in millimetres (mm). This method of determining AAA asymmetry is shown for Patient 3 in Figures 4 and 5. Figure 4 shows the creation of the polylines on the CT scan after the thresholding and segmentation process in Mimics v10.0, and also the resulting model of polylines and AAA centreline. Figure 5 shows the measurement process of asymmetry for Patient 3, and the resulting asymmetry plot. Maximum asymmetry for this case was 24.5mm.
Figure 3.
Simple illustration showing method of obtaining asymmetry measurements.
Figure 5.
Diagram depicting how measurements of asymmetry are determined once AAA centreline is created. Example shown is for Patient 3.
Figure 4.
Example CT scans showing the creation of polylines on each slice, together with the centre point of each polyline. Once polylines are created on each scan in the series, the slices are stacked together to form the model on the right. Example shown is for Patient 3.
Statistical Analysis
In order to evaluate the statistical significance of the wall stress results, the software SPSS 14.0 (SPSS Inc., Chicago, IL, USA) was utilised. This allowed any significant correlations within the results to be identified. Correlations between various geometrical parameters with both peak wall stress and posterior wall stress were assessed for significance.
RESULTS
The results from the geometrical examination of each case are shown in Table I. The finite element analysis using ABAQUS v6.6-2 produced a detailed stress pattern on each of the aneurysmal models under the pressure loading.25 From these stress results, factors affecting wall stress could be examined, in particular, the role of asymmetry.
Peak Wall Stress
It was noted from the computed stress results that the regions of peak wall stress occurred at regions of inflection on the surface of the AAA models. Inflection points are defined as points on the AAA surface at which the local AAA wall shape changes from concave outward to concave inward.12 The peak stress occurring at regions of inflection was also observed by previous researchers in idealised models.12,13,26,27 The von Mises peak wall stress, diameter at peak stress, and location were recorded for each case and were compared to the maximum diameter in Table II. All peak stress values are recorded at the peak systolic pressure of 120mmHg (16KPa). Shown also is the diameter of the region through which the peak wall stress occurred. Mean von Mises peak wall stress ± standard deviation was shown to be 0.4505 ± 0.14 MPa, with a range of 0.3157 – 0.9048 MPa. The circumferential stress was also recorded for each case. Mean circumferential stress ± standard deviation was 0.1176 ± 0.061 MPa, with a range of 0.07 – 0.3271 MPa.
Table II.
Maximum diameter, peak wall stress, location of peak stress, and diameter at peak wall stress for each patient studied.
| Patient | Max Diameter (cm) | Peak Wall Stress (MPa) | Location of Peak Wall Stress | Diameter at Peak Wall Stress (cm) |
|---|---|---|---|---|
| 1 | 5.6 | 0.4018 | Anterior-Right | 3.8 |
| 2 | 6.1 | 0.4213 | Anterior-Right | 4.1 |
| 3 | 5.7 | 0.5524 | Posterior | 5.3 |
| 4 | 5.6 | 0.3157 | Posterior | 4.9 |
| 5 | 5.9 | 0.3822 | Posterior | 5.3 |
| 6 | 5.7 | 0.3823 | Left | 5.8 |
| 7 | 5.3 | 0.3621 | Left | 4.8 |
| 8 | 6.0 | 0.3872 | Posterior | 4.6 |
| 9 | 5.8 | 0.4093 | Posterior-Right | 5.5 |
| 10 | 9.0 | 0.9048 | Posterior | 6.2 |
| 11 | 6.5 | 0.4608 | Left | 5.8 |
| 12 | 6.8 | 0.4991 | Left | 5.6 |
| 13 | 6.2 | 0.4523 | Left | 6 |
| 14 | 5.7 | 0.3703 | Posterior | 5.4 |
| 15 | 7.9 | 0.4747 | Left | 7.6 |
Wall Stress – Asymmetry Relationship
Figures 6–8 show how the von Mises wall stress varies with respect to the asymmetry of the AAA centreline. It was noted that regions of elevated centreline asymmetry experienced a region of elevated posterior wall stress.
Figure 6.
Relationships between posterior wall stress and anterior asymmetry (left column) and posterior wall stress and diameter (right column) for Patients 1–5.
Figure 8.
Relationships between posterior wall stress and anterior asymmetry (left column) and posterior wall stress and diameter (right column) for Patients 11–15.
Effect of Asymmetry on Wall Stress
In order to gauge the effect of asymmetry on resulting wall stress, the AAA of Patient 2 was modified into a symmetric aneurysm as described earlier. The symmetric wall stress can be seen compared to that of the posterior wall stress in the asymmetric case in Figure 9. Peak stress increased from 0.2186 MPa to 0.4213 MPa when asymmetry was introduced into the AAA. This resulted in a 48% increase in peak wall stress in the asymmetric model. There was also a noticeable increase of 38% from 0.2186 MPa to 0.3527 MPa in posterior wall stress between the two models.
Figure 9.
Comparison of the posterior wall stress for the symmetric and asymmetric AAA case for Patient 2. Peak stress for this asymmetric case was located on the anterior-right wall.
Statistical Analysis
A Spearman’s Rho correlation test was considered in order to assess any relationships evident between both peak and posterior wall stress and various patient-specific measurable parameters. Correlations are deemed significant when P<0.05. The P values of this study can be seen in Tables III and IV. There was no significant correlation between peak circumferential stress and either maximum asymmetry (P=0.0708) or maximum diameter (P=0.5197). The relationship between posterior wall stress with both asymmetry and diameter was also examined using a Spearman’s Rho correlation test. Coefficients were found using a bivariate correlation test to compare posterior wall stress with both asymmetry and diameter at 10mm intervals along the longitudinal distance of each patient. These results can be seen in Table V. The significance of the relationship between asymmetry and diameter was also assessed using a nonparametric correlation test. The results are shown in Table VI. Eleven of the fifteen cases revealed that there was a significant correlation between asymmetry and diameter. Patient age also correlated well with both maximum diameter (P=0.009) and peak posterior wall stress (P=0.028).
Table III.
Statistical analysis of patient-specific parameters and peak wall stress.
| P | |
|---|---|
| Max Diameter | 0.0003 |
| Peak Posterior Stress | 0.0021 |
| Asymmetry at Peak Circ Stress | 0.0036 |
| AAA Volume | 0.0043 |
| Sex | 0.0061 |
| Max CSA | 0.0126 |
| AAA Surface Area | 0.0130 |
| ILT Volume | 0.0232 |
| AAA Length | 0.0961 |
| Peak Circ Stress | 0.1580 |
| Lumen Volume | 0.1658 |
| ROD | 0.3307 |
| Asymmetry at Peak VM Stress | 0.4384 |
| AAA Diameter/AAA Length | 0.5409 |
| Peak Stress Location | 0.5814 |
| Peak Asymmetry | 0.6384 |
| AAA Volume/ILT Volume | 0.8994 |
| Average Asymmetry | 0.9345 |
Table IV.
Statistical analysis of patient-specific parameters and posterior wall stress.
| P | |
|---|---|
| AAA Volume | 0.0002 |
| AAA Surface Area | 0.0008 |
| Lumen Volume | 0.0012 |
| Max CSA | 0.0013 |
| Peak Stress | 0.0021 |
| Max Diameter | 0.0028 |
| Sex | 0.0081 |
| Asymmetry at Peak Circ Stress | 0.0136 |
| AAA Length | 0.0144 |
| Peak Circ Stress | 0.0378 |
| AAA Volume/ILT Volume | 0.0983 |
| ILT Volume | 0.1728 |
| ROD | 0.2597 |
| Peak Stress Location | 0.5399 |
| Peak Asymmetry | 0.6025 |
| Asymmetry at Peak VM Stress | 0.7466 |
| AAA Diameter/AAA Length | 0.9295 |
| Average Asymmetry | 0.9496 |
Table V.
Correlation coefficients for posterior wall stress and both asymmetry and diameter.
| Patient | Asymmetry | P | Diameter | P |
|---|---|---|---|---|
| 1 | 0.574 | 0.032 | 0.420 | 0.135 |
| 2 | 0.781 | 0.003 | 0.895 | 0.000 |
| 3 | 0.175 | 0.587 | 0.755 | 0.005 |
| 4 | 0.37 | 0.293 | 0.733 | 0.016 |
| 5 | 0.862 | 0.000 | 0.820 | 0.000 |
| 6 | 0.82 | 0.002 | 0.609 | 0.047 |
| 7 | 0.464 | 0.151 | 0.573 | 0.066 |
| 8 | 0.834 | 0.001 | 0.573 | 0.051 |
| 9 | 0.474 | 0.166 | 0.529 | 0.116 |
| 10 | 0.443 | 0.130 | 0.505 | 0.078 |
| 11 | 0.683 | 0.014 | 0.811 | 0.001 |
| 12 | 0.411 | 0.128 | 0.593 | 0.020 |
| 13 | 0.411 | 0.128 | 0.593 | 0.020 |
| 14 | 0.834 | 0.000 | 0.709 | 0.007 |
| 15 | 0.667 | 0.013 | -0.132 | 0.668 |
Table VI.
Correlation between asymmetry and diameter for each case examined.
| Patient | Coefficient | P |
|---|---|---|
| 1 | 0.801 | 0.001 |
| 2 | 0.823 | 0.001 |
| 3 | 0.755 | 0.005 |
| 4 | 0.612 | 0.060 |
| 5 | 0.935 | 0.000 |
| 6 | 0.752 | 0.008 |
| 7 | 0.9 | 0.000 |
| 8 | 0.806 | 0.002 |
| 9 | 0.799 | 0.006 |
| 10 | 0.627 | 0.022 |
| 11 | 0.746 | 0.005 |
| 12 | 0.391 | 0.150 |
| 13 | 0.391 | 0.150 |
| 14 | 0.889 | 0.000 |
| 15 | 0.066 | 0.830 |
The statistical significance between peak stress and other relevant parameters were also assessed. The rate of change of both asymmetry and diameter along the length of the AAA were not statistically significant (P=0.089 and P=0.501, respectively). The diameter at which peak stress occurred proved to be significant with a P value of 0.039.
DISCUSSION
In this study, fifteen patient-specific AAAs were reconstructed, and wall stress distributions in each aneurysm were estimated using the finite element method. From the von Mises wall stress distributions, the peak stress was found to occur at regions of inflection. This finding is consistent with previous research, both numerical12,26 and experimental.27 The peak wall stresses found in this study ranged from 0.3157 – 0.9584 MPa, with a mean ± standard deviation value of 0.482 ± 0.197 MPa. The AAA with the lowest peak wall stress (0.3157 MPa), Patient 4, also had the second smallest maximum AAA diameter (5.6cm), whereas, the AAA with the highest peak stress (Patient 10) of 0.9048 MPa had the largest AAA diameter (9cm). These finding may suggest that the maximum diameter criterion may be a good predictor of AAA rupture. From the previous research into this hypothesis9 it is known that this may not always be the case, as small AAAs can also rupture. Fillinger et al.7 performed stress analysis on an AAA which had a smaller diameter than the current 5.5cm threshold (diameter = 4.8cm). This particular AAA experienced a peak wall stress of 0.335 MPa, which is within 10% of the peak stress found in Patient’s 4, 7 and 14 of this study.
It is important to note that ruptures do not necessarily occur at the region of peak wall stress, but in fact occur where the locally acting wall stress exceeds the locally acting wall strength. This study examined the role of realistic asymmetry on posterior wall stress in patient-specific cases. In order to determine the affect the asymmetry of the AAA has on posterior wall stress, a simple method of calculating asymmetry was established. Figures 3–5 show the approach used to plot the degree of asymmetry in each case, which were then coupled with the posterior wall stress results. These stress-asymmetry relationships are shown in Figures 6–8, which also show the relationship between diameter and posterior wall stress. It was stated by Raghavan et al.28 that the posterior wall tends to be the higher stressed region, and also the rupture site, even though the bulge is predominantly anterior. Vorp et al.12 identified the link between asymmetry and wall stress in idealised AAA models using FEA, with Scotti et al.13 using a fluid-structure interaction (FSI) approach to highlight the relationship in idealised models. It was concluded in the work of Scotti et al.13 that AAAs experiencing asymmetry may be exposed to higher mechanical stresses and increased risk of rupture than more fusiform AAAs. This current work agrees with this hypothesis, and has furthered the work of idealised AAAs to that of realistic AAA geometries with results suggesting that there may be an intrinsic relationship between asymmetry and posterior wall stress.
Darling et al.9 determined from 118 AAA autopsies that 82% of ruptures occur on the posterior wall, indicating that these ruptures may have been as a result of elevated posterior wall stress. Approximately 68% of cases (15 of 22 patients) examined for this study experienced posterior-anterior bowing, resulting in elevated posterior wall stress. It has been recently reported29 that the posterior and right regions of AAAs are regionally thinner than the anterior and left regions. Raghavan et al.29 also reported that failure tension may be a better indicator of rupture rather than failure stress, with failure tension described as; peak wall tension = peak wall stress × wall thickness. Applying this failure tension to this study results in failure tensions ranging from 0.6314 – 1.8096 N/mm, compared to the range of 0.42 – 1.48 N/mm observed by Fillinger et al.6 Actual failure stress of AAA tissue has been shown to range from 0.336 – 2.351 MPa (median = 1.266 MPa).29
Giannoglou et al.30 also determined that mean AAA curvature may be a better predictor of AAA rupture risk, although, this previous study implemented linearly elastic material properties. AAA centreline curvature was also analysed as part of this present study using the curvature analysis function in ProEngineer Wildfire 3.0. The resulting centreline curvature readings are difficult to interpret as minor changes in the centreline result in large spikes of curvature. Gaussian surface curvature was also examined using ProEngineer Wildfire 3.0, as previously reported.22 It has been shown that rapid changes in surface curvature may indicate regions of high wall stress.22 As with centreline curvature, the model geometries are too complex to achieve surface curvature results with any quantifiable meaning. The definition of asymmetry in this study is a measurement that is easy to interpret and calculate, and shows good agreement with wall stress results.
As the anterior region of the AAA bulges outwards, the posterior region is often constrained from radial expansion by the spinal column, and results in elevated posterior wall stress. AAAs may also rupture at regions experiencing a wall stress less than that of the peak wall stress as AAA are known to rupture when the local stress exceeds the local wall strength, with AAAs experiencing regional variations in wall strength.29 In this study, two cases experienced peak wall stress on the anterior-right wall. Peak stress can occur at any region along the AAA surface, but is predominantly found at regions where there is high local surface curvature or asymmetry. Therefore, when analysing patient-specific AAA cases, it is difficult to pre-determine the location of peak stress. Six cases resulted in peak stress on the left wall of the AAA. Again, these locations of elevated stress are due to the local topology of the surface. Even though peak stress does not necessarily occur along the posterior wall, in all cases examined there was an increase in posterior stress along the length of the particular AAA in relation to anterior asymmetry.
From the results of the statistical analysis shown in Tables III and IV, one can determine that the significant parameters that relate to peak wall stress are maximum diameter (P=0.0003), peak posterior wall stress (P=0.0021), asymmetry at the region of peak circumferential stress (P=0.0036), AAA volume (P=0.0043), sex (P=0.061), maximum cross-sectional area (P=0.0126), AAA surface area (P=0.013), and also the ILT volume (P=0.0232). In comparison, the significant relationships with posterior wall stress are AAA volume (P=0.0002), AAA surface area (P=0.0008), lumen volume (P=0.0012), maximum cross-sectional area (P=0.0013), peak wall stress (P=0.0021), maximum diameter (P=0.0028), sex (P=0.0081), asymmetry at the region of peak circumferential stress (P=0.0136), AAA length (P=0.0144), and also peak circumferential stress (P=0.0378). From these results, maximum diameter appears to be significantly related to peak stress, but if the sample size of 15 used in this study was increased to much larger numbers this relationship may not be as strong. The majority of these parameters are also based on diameter, and therefore, if diameter returns a strong correlation with peak stress, it may be obvious that similar parameters will also score highly. There was no statistical significance between peak wall stress and the rate of change of diameter (P=0.501) or rate of change of asymmetry (P=0.089).
Closer examination of the relationship between both asymmetry and diameter with posterior wall stress involved analyses using a nonparametric Spearman Rho correlation. These results are presented in Table V and show how both asymmetry and diameter are both comparable in their significance towards posterior wall stress. From the resulting correlations, 8/15 cases show asymmetry is significant and 9/15 cases show that diameter is significant. These results suggest that if posterior wall stress is to gain clinical acceptance as a possible high-risk rupture indicator, that both asymmetry and diameter may be as important in determining the posterior wall stress, and therefore may both equally contribute to AAA rupture. It has been previously postulated by Vorp et al.25 and also by Fillinger et al.6,7 that the biomechanics of the AAA may provide useful clinical guidance over the maximum diameter criteria. This work supports this biomechanics-based approach and in particular suggests that posterior wall stress may be clinically important. The results presented also suggest that if peak wall stress is to remain the primary purpose of AAA stress analyses, then diameter remains a significant factor.
Although, ideally, stress analysis should be carried out on every AAA detected, the reality is that the decision to repair lies with the surgeon. The use of the maximum diameter criterion is very easy to implement for the surgeon, in that they must simply measure the maximum diameter from CT scans. The asymmetry condition described in this study could also be readily incorporated into the surgeon’s decision making. This dilation, and ultimately asymmetry, can be identified by the clinician from basic 3D reconstruction, and could greatly aid in their decision to surgically intervene. A method of determining asymmetry from 2D CT scans is also currently under development within our group. Also, our group is developing an approach that accounts for asymmetry in all directions, and therefore the relationship between asymmetry and wall stress can be assessed in all AAAs, regardless of orientation. Once detected, the degree of bulging could be incorporated into the decision making process of the surgeon, and may refine and improve the current system of deciding on surgical intervention solely on the basis of maximum diameter. It is suggested that, to include AAA asymmetry as another means of assessing the rupture potential of AAAs could serve as a useful adjunct to the maximum diameter criterion, and may ultimately lead to improved surgical decision making.
Limitations
Like previous work,6,7,11–13,15 this study did not include ILT in the AAA 3D reconstructions. The ILT has been shown to reduce wall stress by up to 30%10,30 and can act as a “mechanical cushion” 31 for the AAA wall. It is known that the realistic AAA has a non-uniform wall thickness29 varying regionally from 0.23mm at a rupture site to 4.26mm at a calcified site (median = 1.48mm), and also non-uniform material properties due to regions of calcifications,32 which can lead to alterations in stress distributions.32,33 This study examined AAA wall stress using a static analysis. It is possible that a dynamic loading, such as a realistic infrarenal aortic pulse may influence the stress distributions. Researchers have shown that the use of fluid-structure interaction methods to determine wall stress can give more accurate results.3,13 Computational time is increased by as much as 2500-fold13 from that of a static pressure finite element analysis, with maximum stress locations found to be the same using both methods. Variations in maximum wall stress in realistic models have been reported to range from 1–25%, according to prior studies.3,21,33 In order to establish the suitability of this method for clinical applications, a larger cohort of patient data is required. The authors are investigating the possibility of applying this method to a database of previously screened patients, with a view to enhancing confidence in the asymmetry approach. Applying this study to a larger cohort may also significantly alter the statistical results as only 15 patients are studied here.
CONCLUSIONS
Most AAA ruptures occur on the posterior wall. It has been shown here how the posterior wall stress can be related to anterior asymmetry in patient-specific cases. Results suggest that an increase in asymmetry may cause increases in posterior wall stress. Statistical analyses revealed that maximum diameter still significantly influences wall stress, particularly peak wall stress, but that asymmetry may also have a significant role in posterior wall stress. This study suggests that AAA asymmetry may be an important criteria in AAA assessment, and could possibly be included as a factor in the clinicians’ decision to surgically intervene. Further evaluation is needed to determine clinical applicability.
Figure 7.
Relationships between posterior wall stress and anterior asymmetry (left column) and posterior wall stress and diameter (right column) for Patients 6–10.
Acknowledgments
The authors would like to thank (i) the Irish Research Council for Science, Engineering and Technology (IRCSET) Grant RS/2005/340 (ii) Grant #R01-HL-060670 from the US National Heart Lung and Blood Institute (iii) the Department of Vascular Surgery in the Midwestern Regional Hospital, Ireland (iv) Dr. Liam Morris in the Galway Medical Technology Centre, Galway and Mayo institute of Technology, Ireland (v) Samarth Shah from the Centre for Vascular Remodelling and Regeneration and (vi) Michel S. Makaroun, MD, University of Pittsburgh, Department of Surgery.
Footnotes
Clinical Relevance: There is much debate as to the most appropriate time to intervene with surgical treatment of abdominal aortic aneurysms. Currently, maximum diameter is deemed the most accurate indicator of rupture potential, as not only is size an obvious factor in the decision-making process, but it is also easy for the clinician to determine from CT scans. The method of determining vessel asymmetry proposed here is easy to interpret, and was shown to be as significant as diameter in the cases examined. Therefore, asymmetry could become a useful adjunct to diameter in the decision-making process of the clinician.
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