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Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm
Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm Zhi-Yong Li, PhD,a,b Jean U-King-Im, MRCS, FRCR,a Tjun Y. Tang, MRCS,a,c Edmund Soh, MRCP, FRCR,a Teik Choon See, FRCR,a and Jonathan H. Gillard, MD, FRCR,a Cambridge, United Kingdom Background: Increased biomechanical stresses within the abdominal aortic aneurysm (AAA) wall contribute to its rupture. Calcification and intraluminal thrombus can be commonly found in AAAs, but the relationship between calcification/ intraluminal thrombus and AAA wall stress is not completely described. Methods: Patient-specific three-dimensional AAA geometries were reconstructed from computed tomographic images of 20 patients. Structural analysis was performed to calculate the wall stresses of the 20 AAA models and their altered models when calcification or intraluminal thrombus was not considered. A nonlinear large-strain finite element method was used to compute the wall stress distribution. The relationships between wall stresses and volumes of calcification and intraluminal thrombus were sought. Results: Maximum stress was not correlated with the percentage of calcification, and was negatively correlated with the percentage of intraluminal thrombus (r ⴝ ⴚ0.56; P ⴝ .011). Exclusion of calcification from analysis led to a significant decrease in maximum stress by a median of 14% (range, 2%-27%; P < .01). When intraluminal thrombus was eliminated, maximum stress increased significantly by a median of 24% (range, 5%-43%; P < .01). Conclusion: The presence of calcification increases AAA peak wall stress, suggesting that calcification decrease the biomechanical stability of AAA. In contrast, intraluminal thrombus reduces the maximum stress in AAA. Calcification and intraluminal thrombus should both be considered in the evaluation of wall stress for risk assessment of AAA rupture. ( J Vasc Surg 2008;47:928-35.)
Abdominal aortic aneurysm (AAA) is a degenerative disease that involves the dilation and weakening of the aorta. The prevalence of AAA is 8.8% in the population aged ⬎65 years, and about 10,000 people in the United Kingdom (UK)1 and 15,000 people in the United States2 die from the rupture of AAA each year. The main clinical indicators used to assess the risk of rupture are the maximum diameter and expansion rate of the AAA obtained from ultrasound or computed tomography (CT) scanning. Surgery is recommended when the maximum diameter of AAA measures ⱖ55 mm or when maximum diameter expands ⬎10 mm/y for smaller AAAs.3,4 Small aneurysms can also rupture, however, and the overall mortality rate associated with these may exceed 50%.5 Therefore, more reliable criteria associated with the actual rupture potential of the AAAs are needed to improve patient selection for surgery or endovascular stenting. AAA rupture can be seen as a structural failure when the mechanical stresses acting on the dilated arterial wall exceed its mechanical failure strength. The external forces that From the University Department of Radiology,a and Cambridge Vascular Unit,c Cambridge University Hospitals Foundation Trust; and Department of Engineering, University of Cambridge.b Competition of interest: none. Reprint requests: Zhi-Yong Li, PhD, Box 219; Level 5, University Department of Radiology, Cambridge University Hospitals Foundation Trust, Hills Rd, Cambridge CB2 2QQ, UK (e-mail: [email protected]). 0741-5214/$34.00 Copyright © 2008 by The Society for Vascular Surgery. doi:10.1016/j.jvs.2008.01.006
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exert on an AAA include blood pressure and wall shear stress. Stress analysis can be used to study the stress distributions within the AAA. If the local stress is high or there is a stress concentration, the AAA can be considered as vulnerable or prone to rupture.6 Stresses in AAA wall are due to the concomitant influence of many 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 patent lumen, and the interaction between the fluid and solid domains.7-11 Such biomechanical approaches toward assessing the likelihood of AAA rupture have been previously described.12-15 A patient-specific study has previously demonstrated that maximum wall stress was 12% more specific and 13% more sensitive in predicting AAA rupture than maximum diameter alone.16 In other patient-specific studies, peak stress was significantly higher in ruptured AAAs than in nonruptured AAAs.17 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.8-10 Calcification is commonly found within the aneurysm wall. Although AAA calcification is associated with a worse cardiovascular prognosis, the influence of calcification on biomechanical wall stress in AAAs has not been fully studied.18,19 Because calcification generally has a higher stiffness than the surrounding arterial wall, it is postulated that
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Fig 1. A, Cross-sectional computed tomography image shows an abdominal aortic aneurysm. B, Segmentation of calcification, intraluminal thrombosis, arterial wall, and lumen.
it can establish an adverse stress distribution, increasing the propensity to rupture.20 Approximately 75% of all AAAs have varying degrees of ILT,21 which is a three-dimensional (3-D) fibrin structure incorporated with blood cells, platelets, blood proteins, and cellular debris. The role of ILT within AAA on the risk of rupture has been highly controversial. Some investigators have suggested that ILT increases the risk of rupture,22-24 whereas others believe that ILT may significantly reduce AAA wall stress and therefore protect the AAA from rupture.13,14,25,26 Still other investigators suggest that ILT has no effect on the rupture risk.27,28 The main aim of this study was to evaluate the impact of calcification and ILT on AAA structural stability. The finite element analysis method, which allows the study of complex geometries and the determination of the impact of specific material properties on stress magnitudes and distribution, was applied to 20 human AAA lesions in this patient-specific study. METHODS The method included (1) reconstruction of 3-D AAA geometry (arterial wall, ILT, calcification, and lumen) from the CT examinations; (2) assignment of the mechanical properties for arterial wall, ILT, and calcium deposits; and (3) structural analysis. Three models were created for each patient: an unaltered AAA model, a no-calcification model (when calcification was replaced with normal arterial wall), and a no-ILT model (when ILT was eliminated). Each of these procedures will be described subsequently. Patients. Twenty patients (17 men, 3 women; median age, 77; range, 60-89 years) who underwent a CT examination before surgery or endovascular treatment were randomly selected. All patients had a history of hypertension and were either current or ex-smokers. None of the patients were symptomatic or had a ruptured AAA. The maximum median AAA diameter as determined on CT was 5.4 cm (range, 3.8-7.0 cm). This was a retrospective study, and the Local Ethics Committee waived informed consent. Computed tomography imaging. All patients underwent CT examinations of their abdomen and pelvis before
and after the intravenous injection of 100 mL of iodinated contrast medium (Iopimadol, Niopam 300, Bracco UK Ltd., High Wycombe, Bucks, UK) by using a power injector (5 mL/s flow rate) on a 16-slice spiral CT machine (Somatom Sensation 4, Siemens Medical Solutions, Erlangen, The Netherlands). The imaging protocol included automated 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. Abdominal aortic aneurysm reconstruction. Geometries of AAAs were reconstructed from the entire set of 2-D CT slices. In brief, 2-D cross-sectional images of the abdominal aorta were obtained from immediately distal to the renal arteries to immediately proximal to the iliac bifurcation. These images were imported into ScanIP image processing software (Simpleware Ltd, Exeter, Devon, UK) for segmentation. The lumen was the most distinguishable object in a CT image owing 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 threshold based on the pixel intensities. The calcification regions were also picked up automatically during the threshold. The calcification areas were identified by subtracting the lumen region. Because the lumen borders were obtained automatically, the geometric models reconstructed were reproducible. The boundary of the arterial wall was traced using a semi-automatic method in the diseased part of the artery. We manually segmented the inner boundary, and by subtly varying the window width, it was possible only to visualize the soft tissue of the uncalcified wall. The thickness of the wall equals the local wall thickness minus the calcification thickness in the radial direction. The position of the calcification is 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.29 The region of thrombus was defined by the area within the inner wall minus the lumen area (Fig 1). The distinction between healthy and diseased part of the aorta
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Fig 2. Three-dimensional model derived from the computed tomography reconstruction of the abdominal aortic aneurysm (AAA). A, Reconstruction of the AAA shows the AAA components (calcification, intraluminal thrombus, arterial wall, and lumen). B, Three-dimensional mesh of the AAA model. C, Longitudinal cross-section of the AAA model shows the detail meshes of the AAA components.
was made by reviewing the stacked CT images and using a diameter of ⱕ3 cm as a general guide for definition of healthy artery. Upon “stacking” of all 2-D image data in 3-D space, the 3-D aneurysm, including artery wall, ILT, and calcification was produced (Fig 2, A). Surface smoothing was controlled in ScanIP, and a curvature cutoff and a maximal 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, calcification, and vessel wall. The 3-D reconstructed AAA model was then meshed (Fig 2, B) using ScanFE (Simpleware Ltd). A cutting-section is shown to illustrate the detail meshes of ILT and calcification (Fig 2, C). The 3-D reconstructed AAA model was then exported to ABAQUS 6.6 software (ABAQUS Inc, Pawtucket, RI) for finite element preprocessing. Volume ratios of calcifications and intraluminal thrombus. The total volumes of AAA, calcium deposit, and ILT were calculated in ScanFE by summing the pixel elements. The percentage volume of calcification was calculated as [Ca ⫽ (VCa /VAAA) ⫻ 100%] and ILT was calculated as [ILT ⫽ (VILT /VAAA) ⫻ 100%], where VCa and VILT indicated the volumes of calcification and ILT, and VAAA was the volume of the AAA. To gauge the amount of increase in internal stress, a percentage change in stress was calculated. The percentage changes in stresses when calcification was removed was calculated by the equation [⌬ILT ⫽ ( ⫺ nCa)/ ⫻ 100%], and when ILT was eliminated, by the equation [⌬ILT ⫽ ( ⫺ nILT)/ ⫻ 100%], where was the maximum von Mises stress of the unaltered model, and
nCa and nILT were the maximum von Mises stress of the no-calcification model and no-ILT model, respectively. Material properties. Calcification, ILT, and AAA wall were assumed to be hyperelastic, homogenous, incompressible, and isotropic materials. The AAA arterial wall and ILT were modeled using the nonlinear hyperelastic wall mechanical properties derived by Wang et al30 and Raghvan and Vorp31 from uniaxial testing of 69 excised human AAAs. The strain energy functions for AAA wall and ILT were [W ⫽ C1(IB ⫺ 3) ⫹ C2(IB ⫺ 3)2] for the arterial wall and [W ⫽ D1(IIB ⫺ 3) ⫹ D2(IIB ⫺ 3)2] for ILT, where W was the strain energy, C1 and C2 were material parameters for the wall, and IB, and IIB were 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.32,33 Experimental study in mechanical properties of calcification in AAAs is very limited, to our knowledge. One study, by Marra et al,34 investigated the elastic modules and hardness of calcified deposits from AAAs34; and in the other, Loree et al35 studied calcified aortic atherosclerotic tissue and found a circumferential tangential modulus of calcified aortic plaque.35 For our study, we chose the parameters of the Mooney-Rivlin model, which has been previously used in a study of plaque calcification.36 Mooney-Rivlin materials can be described by two constants, and their values for calcification were taken as A ⫽ 18,804.5 Pa and B ⫽ 20.36
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Structural analysis. The principles of this analysis are similar to those previously used by our laboratory to study carotid plaque stability.37,38 Finite element analysis divides a complex structure into small areas, called “elements,” for which the stress distribution can be more easily studied. A mean systolic blood pressure was used by averaging the systolic pressure measurements of each of the 20 patients. This is appropriate, because we wanted only to examine the impact of calcification and ILT on the AAA wall stress and not introduce another variable in the equation. 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 research has shown that it is several orders of magnitude smaller compared with wall stresses.8,39,40 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, and the minimal number of elements, 894,000, was used. Two other meshes of differing mesh refinement were tested to assess the solution grid independency. The maximum von Mises stress was compared in the three cases and a relative error of ⬍2% was found. The stress distribution in each AAA was computed with the well-validated ABAQUS 6.6 finite element analysis software. For each patient, analyses were done on the three models (unaltered model, no-calcification model, and noILT model). All computations were performed on a 64-bit, 4 duel-core, 2.6-GHz processors, high performance computing cluster with a 32GB RAM. The maximum von Mises stresses were recorded for each analysis. Image segmentation is semi-automatic, and it takes approximately 3 hours to reconstruct a 3-D AAA model. It takes a further 30 minutes of computer simulation time. Statistics. Statistical analysis was performed with SPSS 13.0 software (SPSS Inc, Chicago, Ill). To compare the differences between maximum stresses of the three models, a paired t test was used. P ⬍ .05 was considered significant for concluding that the two sets of data had different means (t test). Two approaches were used to study the association between the percentage volume of calcification or ILT and changes in wall stresses. First, we tested for a correlation between the amount of calcification or ILT and the maximum stress levels in the AAA using the nonparametric Spearman correlation test. Second, we used the Spearman test to test for a correlation between the amount of calcification or ILT and the changes in stress. RESULTS Each patient had different degrees of calcification (median percentage volume, 4.6%; range, 0.3%-13%) or ILT (median percentage volume, 49%; range, 11%-78%). The
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Table I. Characteristics and maximum von Mises stresses of the abdominal aortic aneurysms Variable AAAs Age, years Maximum AAA diameter, cm Percent volume of calcification Percent volume of ILT Maximum von Mises stress (kPa)
No. or median (range) 20 77.0 (60.0-89.0) 5.4 (3.8-7.0) 4.6 (0.3-13.0) 49.0 (11.0-78.0) 199.5 (152.0-365.0)
AAA, Abdominal aortic aneurysm; ILT, intraluminal thrombosis.
maximum AAA diameter and maximum von Mises stresses are reported in the Table. The maximum AAA diameter and maximum stresses did not correlate (P ⫽ .734), and neither did the amount of calcification and ILT (P ⫽ .337). The stress distribution within each AAA was largely dependent on the thickness of arterial wall and the AAA surface curvature, which supports the findings of other similar studies.15,41 The maximum stresses occurred in very small regions, and wall stresses in most regions were generally ⬍30% of the maximum stresses (Fig 3). A comparison of 3-D wall stress distributions between the three AAA models is shown in Fig 3. The stress contours in the no-calcification model (Fig 3, B) were smooth and the stress variation was caused by the AAA geometry alone, whereas the contours in the unaltered model (Fig 3, A) were less smooth due to the local stress concentration at the locations of calcifications. A high stress or stress concentration can be often found at the location of calcification (Fig 3, A). This result shows the presence of calcification changes the stress distribution within AAA. Stresses were higher in the no-ILT model (Fig 3, C), which adhered to the commonly used law of Laplace. Fig 4 shows a box-plot of maximum stresses within the three models for the 20 AAAs. Maximum wall stresses increased when the calcification-included models and noncalcification models were compared. The median increase in maximum stress due to calcification for the group was 14% (range, 2%-27%). This change was significant (P ⬍ .01). A similar test was performed for ILT, and maximum stresses decreased when ILT was included in the analysis. The median decrease in maximum stress due to ILT for the group was 24% (range, 5%-43%). This change was also significant (P ⬍ .01). No significant correlation was, however, found between stress and the percentage volume of calcification in the group (P ⫽ .45; Fig 5, A). This result suggests that having more calcification does not indicate the presence of higher stresses in the AAA. A similar approach was applied on ILT to test the correlation between the amount of ILT and the maximum stresses. A significant negative correlation was found between stress and the percentage volume of ILT in this group (r ⫽ ⫺0.56; P ⫽ .011; Fig 5, B). The relationship between changes in stress and the percentage of calcification and ILT was also tested. The correlation between changes in stress and the percentage volume of calcification was significant for the group (r ⫽
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Fig 3. Three-dimensional wall stress distributions among the three abdominal aortic aneurysm models are compared: (A) unaltered model, (B) no-calcification model, (C) no-intraluminal thrombus (ILT) model.
0.685; P ⫽ .001; Fig 6, A). This finding suggests that a larger amount of calcification results in a bigger increase of AAA wall stresses. For ILT, there was a significant positive correlation between the amount of ILT and stress changes in the group (r ⫽ 0.863; P ⬍ .001; Fig 6, B). DISCUSSION It is generally recognized that rupture of an AAA occurs when the stress acting on the wall during the cardiac cycle 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. Wall stress is associated with AAA geometry and its components. Insight into the individual factors of AAA stability is important because strategies to prevent AAA rupture may rely on identifying factors that contribute prominently to AAA stability. This study evaluated the effect of calcification and ILT on the computed AAA wall stress.
Calcification is commonly found in AAAs, and the effect of calcification on the stability of AAAs is unclear. We used patient-specific models to study its effect on wall stress, and the results show that the presence of calcification increases maximum wall stresses and alters stress distribution. Calcification can result in local stress increase and stress concentration at the locations of calcification. The finding on the relationship between amount of calcification and maximum wall stresses suggests that more calcification does not necessarily mean a higher wall stress. The location of calcification may be more important in evaluating its effect on wall stress than the relative amount of calcification. The location of calcification is also of particular interest in the studies in the carotid circulation; for instance, previous work has shown that the presence of calcium deposits within atheroma tended to decrease the stress within the plaque and was therefore protective.36 However, the location of calcium deposits just adjacent to the lumen within the fibrous cap was a risk factor for
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Fig 4. Box and whisker plot of maximum von Mises stresses within the unaltered, no-calcification, and no-intraluminal thrombosis models of abdominal aortic aneurysms. The horizontal line in the middle of each box indicates the median; the top and bottom borders of the box mark the 75th and 25th percentiles, respectively. The whiskers mark the 90th and 10th percentiles. The circle represents an outlier.
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Fig 6. Relationship of abdominal aortic aneurysm (AAA) components to maximum ad minimum stresses. A, Correlation between changes in stress when calcification was replaced within arterial wall and percentage volume of calcification in unaltered AAA. A significant correlation was found (r ⫽ 0.685; P ⫽ .001). B, Correlation between changes in stress with and without intraluminal thrombosis (ILT) and percentage volume of ILT in unaltered AAA. This correlation was also significant (r ⫽ 0.863; P ⬍ .001).
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Fig 5. Relationship of abdominal aortic aneurysm components to maximum von Mises stresses. A, Correlation of stress (in kPa) with percentage volume of calcification. The correlation between percentage volume of calcification and stress was not significant (P ⫽.450). B, Correlation of stress with percentage volume of intraluminal thrombus (ILT). There was a significant moderate negative correlation between stress and percentage volume of ILT (r ⫽ ⫺0.56; P ⫽.011).
increased risk of rupture, suggesting that location was of particular importance.42-44 In our model of AAA, the presence of calcium increased the wall stress. This is because in AAA, calcification is usually found as rim calcification within the adventitia rather than within ILT; whereas in atheroma, calcification can be found at the lipid core at which plaque stress can be decreased. Intraluminal thrombosis is present in most large AAAs.21 The formation of ILT has been linked with platelet exposure to a high and low sequence of wall shear stress, a common characteristic in AAA.45 The role of ILT on the rupture risk of AAA has been controversial. Intraluminal thrombus was shown to reduce oxygen diffusion to the AAA wall, which may cause local hypoxia and wall weakening.24 Kazi et al46 demonstrated that the AAA wall adjacent to the ILT was thinner and there were more macrophages and other inflammatory cells than in walls without ILT. Experimental studies suggest that ILT does not reduce pressure on the aneurysm wall.28,47 However, computational analyses have shown that ILT reduces peak wall stress.26,32 Our study has also shown that a large relative amount of ILT is associated with a lower wall stress and that more ILT leads to a larger wall stress reduction. Furthermore, ILT is likely not a homogeneous material and is a very complex component (maybe organized or
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wet); however, because of lack of information about the material mechanical properties of ILT, the current assumption is the best effort in the computational simulation. A large ex vivo experimental test is needed for future study in this area. A realistic material model is crucial in the modelling of AAA wall stress, and this is a basis of the computational simulation of AAA stability. In aortic aneurysms, the thrombus is usually more lamellated and perhaps of more organized chronic type,48 In the future, this model can of course be improved by considering the variation of ILT properties. Higher stresses can often be found at the shoulders of the AAAs, where a big change of AAA shape presents. It can be easily explained by using Laplace’s Law. The thickness of artery is smaller where the vessel is healthy; so given the same pressure load, the resulted wall stress is higher at this location. From a purely structural engineering point of view, bending is higher at the junction between the healthy and the diseased part of the vessel. Risk stratification of AAA rupture is thought to be a multifactorial process that includes biologic, biomechanical, and biochemical factors. The biologic factors have been widely studied and reviewed,49 but the biomechanical factors are still not fully understood. This study concentrated on the wall stress using a computational simulation to demonstrate the stress distributions within the patientspecific AAAs. Although we have used state-of-the-art image segmentation and reconstruction methods along with complex nonlinear material models in our analysis, several assumptions and limitations still need to be discussed. The AAA component materials were assumed to be isotropic, incompressible, and homogenous. Each single material was assigned a set of parameters to govern for 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. The purpose of this study, however, was to examine the contribution of calcification and ILT on AAA wall stress. The relative stress changes rather than the exact stress magnitudes were examined. Future work is needed in the assessment of the mechanical properties of AAA components. The use of the maximum stress alone may not be enough in the consideration of AAA stability. The two major determinants for AAA rupture are 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 the 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. Another limitation is that the clinical use of wall stress calculations has been hindered by long computational time. It took about 4 hours to calculate the wall stress using our high performance computer cluster; however, with the fast improvements in costs and accessibility of computational power, this will be less of a problem in the future.
CONCLUSIONS The presence of calcification increases wall stress in AAA, suggesting that calcification decreases the biomechanical stability of AAA. The location of calcification rather than the amount of calcification plays a role in determining the maximum wall stress. In contrast, the presence of ILT reduces the maximum stress in AAA, and wall strength may need to be considered to assess AAA stability. The relative amount of ILT is associated with AAA wall stress. Calcification and ILT should both be considered in the evaluation of wall stresses for AAA rupture risk assessment. Future work is needed on the understanding of the mechanical properties of AAA components. The addition of calcified plaque and thrombus may further improve estimation of aneurysm rupture risk using finite element modelling. Further investigation including a better understanding of AAA material properties and failure strength may finally help in creating more realistic computational models to be used as a clinical adjunct in the future for effective decision making in AAA surgical and endovascular repair. AUTHOR CONTRIBUTIONS Conception and design: ZYL, JU, JG Analysis and interpretation: ZYL, JU Data collection: ZYL, ES Writing the article: ZYL, TS Critical revision of the article: ZYL, JU, TT, TS Final approval of the article: ZYL, JU, TT, ES, TS, JG Statistical analysis: ZYL Obtained funding: JG Overall responsibility: ZYL, JU, TT, ES, TS, JG REFERENCES 1. Sayers RD. Aortic aneurysms, inflammatory pathways and nitric oxide. Ann R Coll Surg Engl 2002;84:239-46. 2. Bush RL, Lin PH, Lumsden AB. Endovascular management of abdominal aortic aneurysms. J Cardiovasc Surg (Torino) 2003;44:527-34. 3. Lederle FA, Wilson SE, Johnson GR, Reinke DB, Littooy FN, Acher CW, et al. Immediate repair compared with surveillance of small abdominal aortic aneurysms. N Engl J Med 2002;346:1437-44. 4. Mortality results for randomised controlled trial of early elective surgery or ultrasonographic surveillance for small abdominal aortic aneurysms. The UK Small Aneurysm Trial Participants. Lancet 1998;352:1649-55. 5. Valentine RJ, Decaprio JD, Castillo JM, Modrall JG, Jackson MR, Clagett GP. Watchful waiting in cases of small abdominal aortic aneurysmsappropriate for all patients? J Vasc Surg 2000;32:441-8; discussion 448-50. 6. Vorp DA, Vande Geest JP. Biomechanical determinants of abdominal aortic aneurysm rupture. Arterioscler Thromb Vasc Biol 2005; 25:1558-66. 7. Li Z, Kleinstreuer C. Effects of blood flow and vessel geometry on wall stress and rupture risk of abdominal aortic aneurysms. J Med Eng Technol 2006;30:283-97. 8. Leung JH, Wright AR, Cheshire N, Crane J, Thom SA, Hughes AD, Xu Y. Fluid structure interaction of patient specific abdominal aortic aneurysms: a comparison with solid stress models. Biomed Eng Online 2006;5:33. 9. Wolters BJ, Rutten MC, Schurink GW, Kose U, de Hart J, van de Vosse FN. A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. Med Eng Phys 2005;27:871-83.
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10. Scotti CM, Shkolnik AD, Muluk SC, Finol EA. Fluid-structure interaction in abdominal aortic aneurysms: effects of asymmetry and wall thickness. Biomed Eng Online 2005;4:64. 11. Fillinger MF, Raghavan ML, Marra SP, Cronenwett JL, Kennedy FE. In vivo analysis of mechanical wall stress and abdominal aortic aneurysm rupture risk. J Vasc Surg 2002;36:589-97. 12. Stringfellow MM, Lawrence PF, Stringfellow RG. The influence of aorta-aneurysm geometry upon stress in the aneurysm wall. J Surg Res 1987;42:425-33. 13. Inzoli F, Boschetti F, Zappa M, Longo T, Fumero R. Biomechanical factors in abdominal aortic aneurysm rupture. Eur J Vasc Surg 1993;7: 667-74. 14. Mower WR, Quinones WJ, Gambhir SS. Effect of intraluminal thrombus on abdominal aortic aneurysm wall stress. J Vasc Surg 1997;26: 602-8. 15. Vorp DA, Raghavan ML, Webster MW. Mechanical wall stress in abdominal aortic aneurysm: influence of diameter and asymmetry. J Vasc Surg 1998;27:632-9. 16. Fillinger MF, Marra SP, Raghavan ML, Kennedy FE. Prediction of rupture risk in abdominal aortic aneurysm during observation: wall stress versus diameter. J Vasc Surg 2003;37:724-32. 17. Venkatasubramaniam AK, Fagan MJ, Mehta T, Mylankal KJ, Ray B, Kuhan G, et al. A comparative study of aortic wall stress using finite element analysis for ruptured and non-ruptured abdominal aortic aneurysms. Eur J Vasc Endovasc Surg 2004;28:168-76. 18. Detrano RC, Wong ND, Doherty TM, Shavelle RM, Tang W, Ginzton LE, et al. Coronary calcium does not accurately predict near-term future coronary events in high-risk adults. Circulation 1999;99:2633-8. 19. Schmermund A, Denktas AE, Rumberger JA, Christian TF, Sheedy PF, 2nd, Bailey KR, et al. Independent and incremental value of coronary artery calcium for predicting the extent of angiographic coronary artery disease: comparison with cardiac risk factors and radionuclide perfusion imaging. J Am Coll Cardiol 1999;34:777-86. 20. Speelman L, Bohra A, Bosboom EM, Schurink GW, van de Vosse FN, Makaorun MS, et al. Effects of wall calcifications in patient-specific wall stress analyses of abdominal aortic aneurysms. J Biomech Eng 2007; 129:105-9. 21. Harter LP, Gross BH, Callen PW, Barth RA. Ultrasonic evaluation of abdominal aortic thrombus. J Ultrasound Med 1982;1:315-8. 22. Wolf YG, Thomas WS, Brennan FJ, Goff WG, Sise MJ, Bernstein EF. Computed tomography scanning findings associated with rapid expansion of abdominal aortic aneurysms. J Vasc Surg 1994;20:529-35; discussion 535-8. 23. Satta J, Laara E, Juvonen T. Intraluminal thrombus predicts rupture of an abdominal aortic aneurysm. J Vasc Surg 1996;23:737-9. 24. Vorp DA, Lee PC, Wang DH, Makaroun MS, Nemoto EM, Ogawa S, et al. Association of intraluminal thrombus in abdominal aortic aneurysm with local hypoxia and wall weakening. J Vasc Surg 2001;34: 291-9. 25. Di Martino E, Mantero S, Inzoli F, Melissano G, Astore D, Chiesa R, et al. Biomechanics of abdominal aortic aneurysm in the presence of endoluminal thrombus: experimental characterisation and structural static computational analysis. Eur J Vasc Endovasc Surg 1998;15: 290-9. 26. Wang DH, Makaroun MS, Webster MW, Vorp DA. Effect of intraluminal thrombus on wall stress in patient-specific models of abdominal aortic aneurysm. J Vasc Surg 2002;36:598-604. 27. Dobrin PB. Pathophysiology and pathogenesis of aortic aneurysms. Current concepts. Surg Clin North Am 1989;69:687-703. 28. Schurink GW, van Baalen JM, Visser MJ, van Bockel JH. Thrombus within an aortic aneurysm does not reduce pressure on the aneurysmal wall. J Vasc Surg 2000;31:501-6. 29. Raghavan ML, Vorp DA, Federle MP, Makaroun MS, Webster MW. Wall stress distribution on three-dimensionally reconstructed models of human abdominal aortic aneurysm. J Vasc Surg 2000;31:760-9. 30. Wang DH, Makaroun M, Webster MW, Vorp DA. Mechanical properties and microstructure of intraluminal thrombus from abdominal aortic aneurysm. J Biomech Eng 2001;123:536-9.
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31. Raghavan ML, Vorp DA. Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. J Biomech 2000;33:475-82. 32. Di Martino ES, Vorp DA. Effect of variation in intraluminal thrombus constitutive properties on abdominal aortic aneurysm wall stress. Ann Biomed Eng 2003;31:804-9. 33. Vande Geest JP, Wang DH, Wisniewski SR, Makaroun MS, Vorp DA. Towards a noninvasive method for determination of patient-specific wall strength distribution in abdominal aortic aneurysms. Ann Biomed Eng 2006;34:1098-106. 34. Marra SP, Daghlian CP, Fillinger MF, Kennedy FE. Elemental composition, morphology and mechanical properties of calcified deposits obtained from abdominal aortic aneurysms. Acta Biomater 2006;2: 515-20. 35. Loree HM, Grodzinsky AJ, Park SY, Gibson LJ, Lee RT. Static circumferential tangential modulus of human atherosclerotic tissue. J Biomech 1994;27:195-204. 36. Huang H, Virmani R, Younis H, Burke AP, Kamm RD, Lee RT. The impact of calcification on the biomechanical stability of atherosclerotic plaques. Circulation 2001;103:1051-6. 37. Li ZY, Howarth SP, Tang T, Gillard JH. How critical is fibrous cap thickness to carotid plaque stability? A flow-plaque interaction model. Stroke 2006;37:1195-9. 38. Li ZY, Howarth S, Trivedi RA, U-King-Im JM, Graves MJ, Brown A, et al. Stress analysis of carotid plaque rupture based on in vivo high resolution MRI. J Biomech 2006;39:2611-22. 39. Budwig R, Elger D, Hooper H, Slippy J. Steady flow in abdominal aortic aneurysm models. J Biomech Eng 1993;115:418-23. 40. Peattie RA, Asbury CL, Bluth EI, Riehle TJ. Steady flow in models of abdominal aortic aneurysms. Part II: wall stresses and their implication for in vivo thrombosis and rupture. J Ultrasound Med 1996;15:689-96. 41. Di Martino ES, Guadagni G, Fumero A, Ballerini G, Spirito R, Biglioli P, et al. Fluid-structure interaction within realistic three-dimensional models of the aneurysmatic aorta as a guidance to assess the risk of rupture of the aneurysm. Med Eng Phys 2001;23:647-55. 42. Naghavi M, Libby P, Falk E, Casscells SW, Litovsky S, Rumberger J, et al. From vulnerable plaque to vulnerable patient: a call for new definitions and risk assessment strategies: part I. Circulation 2003;108:1664-72. 43. Li ZY, Howarth S, J UK-I, Gillard J. Atheroma: is calcium important or not? A modelling study of stress within the atheromatous fibrous cap in relation to position and size of calcium deposits. Conf Proc IEEE Eng Med Biol Soc 2005;3:2236-9. 44. Vengrenyuk Y, Carlier S, Xanthos S, Cardoso L, Ganatos P, Virmani R, et al. A hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications in thin fibrous caps. Proc Natl Acad Sci U S A 2006;103:14678-83. 45. Bluestein D, Niu L, Schoephoerster RT, Dewanjee MK. Steady flow in an aneurysm model: correlation between fluid dynamics and blood platelet deposition. J Biomech Eng 1996;118:280-6. 46. Kazi M, Thyberg J, Religa P, Roy J, Eriksson P, Hedin U, et al. Influence of intraluminal thrombus on structural and cellular composition of abdominal aortic aneurysm wall. J Vasc Surg 2003;38:1283-92. 47. Thubrikar MJ, Robicsek F, Labrosse M, Chervenkoff V, Fowler BL. Effect of thrombus on abdominal aortic aneurysm wall dilation and stress. J Cardiovasc Surg (Torino) 2003;44:67-77. 48. Kazi M, Zhu C, Roy J, Paulsson-Berne G, Hamsten A, Swedenborg J, et al. Difference in matrix-degrading protease expression and activity between thrombus-free and thrombus-covered wall of abdominal aortic aneurysm. Arterioscler Thromb Vasc Biol 2005;25:1341-6. 49. Choke E, Cockerill G, Wilson WR, Sayed S, Dawson J, Loftus I, et al. A review of biological factors implicated in abdominal aortic aneurysm rupture. Eur J Vasc Endovasc Surg 2005;30:227-44.
Submitted Jul 9, 2007; accepted Jan 6, 2008.
Abdominal aortic aneurysm (AAA) is a degenerative disease that involves the dilation and weakening of the aorta. The prevalence of AAA is 8.8% in the population aged ⬎65 years, and about 10,000 people in the United Kingdom (UK)1 and 15,000 people in the United States2 die from the rupture of AAA each year. The main clinical indicators used to assess the risk of rupture are the maximum diameter and expansion rate of the AAA obtained from ultrasound or computed tomography (CT) scanning. Surgery is recommended when the maximum diameter of AAA measures ⱖ55 mm or when maximum diameter expands ⬎10 mm/y for smaller AAAs.3,4 Small aneurysms can also rupture, however, and the overall mortality rate associated with these may exceed 50%.5 Therefore, more reliable criteria associated with the actual rupture potential of the AAAs are needed to improve patient selection for surgery or endovascular stenting. AAA rupture can be seen as a structural failure when the mechanical stresses acting on the dilated arterial wall exceed its mechanical failure strength. The external forces that From the University Department of Radiology,a and Cambridge Vascular Unit,c Cambridge University Hospitals Foundation Trust; and Department of Engineering, University of Cambridge.b Competition of interest: none. Reprint requests: Zhi-Yong Li, PhD, Box 219; Level 5, University Department of Radiology, Cambridge University Hospitals Foundation Trust, Hills Rd, Cambridge CB2 2QQ, UK (e-mail: [email protected]). 0741-5214/$34.00 Copyright © 2008 by The Society for Vascular Surgery. doi:10.1016/j.jvs.2008.01.006
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exert on an AAA include blood pressure and wall shear stress. Stress analysis can be used to study the stress distributions within the AAA. If the local stress is high or there is a stress concentration, the AAA can be considered as vulnerable or prone to rupture.6 Stresses in AAA wall are due to the concomitant influence of many 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 patent lumen, and the interaction between the fluid and solid domains.7-11 Such biomechanical approaches toward assessing the likelihood of AAA rupture have been previously described.12-15 A patient-specific study has previously demonstrated that maximum wall stress was 12% more specific and 13% more sensitive in predicting AAA rupture than maximum diameter alone.16 In other patient-specific studies, peak stress was significantly higher in ruptured AAAs than in nonruptured AAAs.17 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.8-10 Calcification is commonly found within the aneurysm wall. Although AAA calcification is associated with a worse cardiovascular prognosis, the influence of calcification on biomechanical wall stress in AAAs has not been fully studied.18,19 Because calcification generally has a higher stiffness than the surrounding arterial wall, it is postulated that
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Fig 1. A, Cross-sectional computed tomography image shows an abdominal aortic aneurysm. B, Segmentation of calcification, intraluminal thrombosis, arterial wall, and lumen.
it can establish an adverse stress distribution, increasing the propensity to rupture.20 Approximately 75% of all AAAs have varying degrees of ILT,21 which is a three-dimensional (3-D) fibrin structure incorporated with blood cells, platelets, blood proteins, and cellular debris. The role of ILT within AAA on the risk of rupture has been highly controversial. Some investigators have suggested that ILT increases the risk of rupture,22-24 whereas others believe that ILT may significantly reduce AAA wall stress and therefore protect the AAA from rupture.13,14,25,26 Still other investigators suggest that ILT has no effect on the rupture risk.27,28 The main aim of this study was to evaluate the impact of calcification and ILT on AAA structural stability. The finite element analysis method, which allows the study of complex geometries and the determination of the impact of specific material properties on stress magnitudes and distribution, was applied to 20 human AAA lesions in this patient-specific study. METHODS The method included (1) reconstruction of 3-D AAA geometry (arterial wall, ILT, calcification, and lumen) from the CT examinations; (2) assignment of the mechanical properties for arterial wall, ILT, and calcium deposits; and (3) structural analysis. Three models were created for each patient: an unaltered AAA model, a no-calcification model (when calcification was replaced with normal arterial wall), and a no-ILT model (when ILT was eliminated). Each of these procedures will be described subsequently. Patients. Twenty patients (17 men, 3 women; median age, 77; range, 60-89 years) who underwent a CT examination before surgery or endovascular treatment were randomly selected. All patients had a history of hypertension and were either current or ex-smokers. None of the patients were symptomatic or had a ruptured AAA. The maximum median AAA diameter as determined on CT was 5.4 cm (range, 3.8-7.0 cm). This was a retrospective study, and the Local Ethics Committee waived informed consent. Computed tomography imaging. All patients underwent CT examinations of their abdomen and pelvis before
and after the intravenous injection of 100 mL of iodinated contrast medium (Iopimadol, Niopam 300, Bracco UK Ltd., High Wycombe, Bucks, UK) by using a power injector (5 mL/s flow rate) on a 16-slice spiral CT machine (Somatom Sensation 4, Siemens Medical Solutions, Erlangen, The Netherlands). The imaging protocol included automated 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. Abdominal aortic aneurysm reconstruction. Geometries of AAAs were reconstructed from the entire set of 2-D CT slices. In brief, 2-D cross-sectional images of the abdominal aorta were obtained from immediately distal to the renal arteries to immediately proximal to the iliac bifurcation. These images were imported into ScanIP image processing software (Simpleware Ltd, Exeter, Devon, UK) for segmentation. The lumen was the most distinguishable object in a CT image owing 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 threshold based on the pixel intensities. The calcification regions were also picked up automatically during the threshold. The calcification areas were identified by subtracting the lumen region. Because the lumen borders were obtained automatically, the geometric models reconstructed were reproducible. The boundary of the arterial wall was traced using a semi-automatic method in the diseased part of the artery. We manually segmented the inner boundary, and by subtly varying the window width, it was possible only to visualize the soft tissue of the uncalcified wall. The thickness of the wall equals the local wall thickness minus the calcification thickness in the radial direction. The position of the calcification is 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.29 The region of thrombus was defined by the area within the inner wall minus the lumen area (Fig 1). The distinction between healthy and diseased part of the aorta
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Fig 2. Three-dimensional model derived from the computed tomography reconstruction of the abdominal aortic aneurysm (AAA). A, Reconstruction of the AAA shows the AAA components (calcification, intraluminal thrombus, arterial wall, and lumen). B, Three-dimensional mesh of the AAA model. C, Longitudinal cross-section of the AAA model shows the detail meshes of the AAA components.
was made by reviewing the stacked CT images and using a diameter of ⱕ3 cm as a general guide for definition of healthy artery. Upon “stacking” of all 2-D image data in 3-D space, the 3-D aneurysm, including artery wall, ILT, and calcification was produced (Fig 2, A). Surface smoothing was controlled in ScanIP, and a curvature cutoff and a maximal 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, calcification, and vessel wall. The 3-D reconstructed AAA model was then meshed (Fig 2, B) using ScanFE (Simpleware Ltd). A cutting-section is shown to illustrate the detail meshes of ILT and calcification (Fig 2, C). The 3-D reconstructed AAA model was then exported to ABAQUS 6.6 software (ABAQUS Inc, Pawtucket, RI) for finite element preprocessing. Volume ratios of calcifications and intraluminal thrombus. The total volumes of AAA, calcium deposit, and ILT were calculated in ScanFE by summing the pixel elements. The percentage volume of calcification was calculated as [Ca ⫽ (VCa /VAAA) ⫻ 100%] and ILT was calculated as [ILT ⫽ (VILT /VAAA) ⫻ 100%], where VCa and VILT indicated the volumes of calcification and ILT, and VAAA was the volume of the AAA. To gauge the amount of increase in internal stress, a percentage change in stress was calculated. The percentage changes in stresses when calcification was removed was calculated by the equation [⌬ILT ⫽ ( ⫺ nCa)/ ⫻ 100%], and when ILT was eliminated, by the equation [⌬ILT ⫽ ( ⫺ nILT)/ ⫻ 100%], where was the maximum von Mises stress of the unaltered model, and
nCa and nILT were the maximum von Mises stress of the no-calcification model and no-ILT model, respectively. Material properties. Calcification, ILT, and AAA wall were assumed to be hyperelastic, homogenous, incompressible, and isotropic materials. The AAA arterial wall and ILT were modeled using the nonlinear hyperelastic wall mechanical properties derived by Wang et al30 and Raghvan and Vorp31 from uniaxial testing of 69 excised human AAAs. The strain energy functions for AAA wall and ILT were [W ⫽ C1(IB ⫺ 3) ⫹ C2(IB ⫺ 3)2] for the arterial wall and [W ⫽ D1(IIB ⫺ 3) ⫹ D2(IIB ⫺ 3)2] for ILT, where W was the strain energy, C1 and C2 were material parameters for the wall, and IB, and IIB were 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.32,33 Experimental study in mechanical properties of calcification in AAAs is very limited, to our knowledge. One study, by Marra et al,34 investigated the elastic modules and hardness of calcified deposits from AAAs34; and in the other, Loree et al35 studied calcified aortic atherosclerotic tissue and found a circumferential tangential modulus of calcified aortic plaque.35 For our study, we chose the parameters of the Mooney-Rivlin model, which has been previously used in a study of plaque calcification.36 Mooney-Rivlin materials can be described by two constants, and their values for calcification were taken as A ⫽ 18,804.5 Pa and B ⫽ 20.36
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Structural analysis. The principles of this analysis are similar to those previously used by our laboratory to study carotid plaque stability.37,38 Finite element analysis divides a complex structure into small areas, called “elements,” for which the stress distribution can be more easily studied. A mean systolic blood pressure was used by averaging the systolic pressure measurements of each of the 20 patients. This is appropriate, because we wanted only to examine the impact of calcification and ILT on the AAA wall stress and not introduce another variable in the equation. 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 research has shown that it is several orders of magnitude smaller compared with wall stresses.8,39,40 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, and the minimal number of elements, 894,000, was used. Two other meshes of differing mesh refinement were tested to assess the solution grid independency. The maximum von Mises stress was compared in the three cases and a relative error of ⬍2% was found. The stress distribution in each AAA was computed with the well-validated ABAQUS 6.6 finite element analysis software. For each patient, analyses were done on the three models (unaltered model, no-calcification model, and noILT model). All computations were performed on a 64-bit, 4 duel-core, 2.6-GHz processors, high performance computing cluster with a 32GB RAM. The maximum von Mises stresses were recorded for each analysis. Image segmentation is semi-automatic, and it takes approximately 3 hours to reconstruct a 3-D AAA model. It takes a further 30 minutes of computer simulation time. Statistics. Statistical analysis was performed with SPSS 13.0 software (SPSS Inc, Chicago, Ill). To compare the differences between maximum stresses of the three models, a paired t test was used. P ⬍ .05 was considered significant for concluding that the two sets of data had different means (t test). Two approaches were used to study the association between the percentage volume of calcification or ILT and changes in wall stresses. First, we tested for a correlation between the amount of calcification or ILT and the maximum stress levels in the AAA using the nonparametric Spearman correlation test. Second, we used the Spearman test to test for a correlation between the amount of calcification or ILT and the changes in stress. RESULTS Each patient had different degrees of calcification (median percentage volume, 4.6%; range, 0.3%-13%) or ILT (median percentage volume, 49%; range, 11%-78%). The
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Table I. Characteristics and maximum von Mises stresses of the abdominal aortic aneurysms Variable AAAs Age, years Maximum AAA diameter, cm Percent volume of calcification Percent volume of ILT Maximum von Mises stress (kPa)
No. or median (range) 20 77.0 (60.0-89.0) 5.4 (3.8-7.0) 4.6 (0.3-13.0) 49.0 (11.0-78.0) 199.5 (152.0-365.0)
AAA, Abdominal aortic aneurysm; ILT, intraluminal thrombosis.
maximum AAA diameter and maximum von Mises stresses are reported in the Table. The maximum AAA diameter and maximum stresses did not correlate (P ⫽ .734), and neither did the amount of calcification and ILT (P ⫽ .337). The stress distribution within each AAA was largely dependent on the thickness of arterial wall and the AAA surface curvature, which supports the findings of other similar studies.15,41 The maximum stresses occurred in very small regions, and wall stresses in most regions were generally ⬍30% of the maximum stresses (Fig 3). A comparison of 3-D wall stress distributions between the three AAA models is shown in Fig 3. The stress contours in the no-calcification model (Fig 3, B) were smooth and the stress variation was caused by the AAA geometry alone, whereas the contours in the unaltered model (Fig 3, A) were less smooth due to the local stress concentration at the locations of calcifications. A high stress or stress concentration can be often found at the location of calcification (Fig 3, A). This result shows the presence of calcification changes the stress distribution within AAA. Stresses were higher in the no-ILT model (Fig 3, C), which adhered to the commonly used law of Laplace. Fig 4 shows a box-plot of maximum stresses within the three models for the 20 AAAs. Maximum wall stresses increased when the calcification-included models and noncalcification models were compared. The median increase in maximum stress due to calcification for the group was 14% (range, 2%-27%). This change was significant (P ⬍ .01). A similar test was performed for ILT, and maximum stresses decreased when ILT was included in the analysis. The median decrease in maximum stress due to ILT for the group was 24% (range, 5%-43%). This change was also significant (P ⬍ .01). No significant correlation was, however, found between stress and the percentage volume of calcification in the group (P ⫽ .45; Fig 5, A). This result suggests that having more calcification does not indicate the presence of higher stresses in the AAA. A similar approach was applied on ILT to test the correlation between the amount of ILT and the maximum stresses. A significant negative correlation was found between stress and the percentage volume of ILT in this group (r ⫽ ⫺0.56; P ⫽ .011; Fig 5, B). The relationship between changes in stress and the percentage of calcification and ILT was also tested. The correlation between changes in stress and the percentage volume of calcification was significant for the group (r ⫽
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Fig 3. Three-dimensional wall stress distributions among the three abdominal aortic aneurysm models are compared: (A) unaltered model, (B) no-calcification model, (C) no-intraluminal thrombus (ILT) model.
0.685; P ⫽ .001; Fig 6, A). This finding suggests that a larger amount of calcification results in a bigger increase of AAA wall stresses. For ILT, there was a significant positive correlation between the amount of ILT and stress changes in the group (r ⫽ 0.863; P ⬍ .001; Fig 6, B). DISCUSSION It is generally recognized that rupture of an AAA occurs when the stress acting on the wall during the cardiac cycle 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. Wall stress is associated with AAA geometry and its components. Insight into the individual factors of AAA stability is important because strategies to prevent AAA rupture may rely on identifying factors that contribute prominently to AAA stability. This study evaluated the effect of calcification and ILT on the computed AAA wall stress.
Calcification is commonly found in AAAs, and the effect of calcification on the stability of AAAs is unclear. We used patient-specific models to study its effect on wall stress, and the results show that the presence of calcification increases maximum wall stresses and alters stress distribution. Calcification can result in local stress increase and stress concentration at the locations of calcification. The finding on the relationship between amount of calcification and maximum wall stresses suggests that more calcification does not necessarily mean a higher wall stress. The location of calcification may be more important in evaluating its effect on wall stress than the relative amount of calcification. The location of calcification is also of particular interest in the studies in the carotid circulation; for instance, previous work has shown that the presence of calcium deposits within atheroma tended to decrease the stress within the plaque and was therefore protective.36 However, the location of calcium deposits just adjacent to the lumen within the fibrous cap was a risk factor for
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Fig 4. Box and whisker plot of maximum von Mises stresses within the unaltered, no-calcification, and no-intraluminal thrombosis models of abdominal aortic aneurysms. The horizontal line in the middle of each box indicates the median; the top and bottom borders of the box mark the 75th and 25th percentiles, respectively. The whiskers mark the 90th and 10th percentiles. The circle represents an outlier.
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Fig 6. Relationship of abdominal aortic aneurysm (AAA) components to maximum ad minimum stresses. A, Correlation between changes in stress when calcification was replaced within arterial wall and percentage volume of calcification in unaltered AAA. A significant correlation was found (r ⫽ 0.685; P ⫽ .001). B, Correlation between changes in stress with and without intraluminal thrombosis (ILT) and percentage volume of ILT in unaltered AAA. This correlation was also significant (r ⫽ 0.863; P ⬍ .001).
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Percent Volume of ILT
Fig 5. Relationship of abdominal aortic aneurysm components to maximum von Mises stresses. A, Correlation of stress (in kPa) with percentage volume of calcification. The correlation between percentage volume of calcification and stress was not significant (P ⫽.450). B, Correlation of stress with percentage volume of intraluminal thrombus (ILT). There was a significant moderate negative correlation between stress and percentage volume of ILT (r ⫽ ⫺0.56; P ⫽.011).
increased risk of rupture, suggesting that location was of particular importance.42-44 In our model of AAA, the presence of calcium increased the wall stress. This is because in AAA, calcification is usually found as rim calcification within the adventitia rather than within ILT; whereas in atheroma, calcification can be found at the lipid core at which plaque stress can be decreased. Intraluminal thrombosis is present in most large AAAs.21 The formation of ILT has been linked with platelet exposure to a high and low sequence of wall shear stress, a common characteristic in AAA.45 The role of ILT on the rupture risk of AAA has been controversial. Intraluminal thrombus was shown to reduce oxygen diffusion to the AAA wall, which may cause local hypoxia and wall weakening.24 Kazi et al46 demonstrated that the AAA wall adjacent to the ILT was thinner and there were more macrophages and other inflammatory cells than in walls without ILT. Experimental studies suggest that ILT does not reduce pressure on the aneurysm wall.28,47 However, computational analyses have shown that ILT reduces peak wall stress.26,32 Our study has also shown that a large relative amount of ILT is associated with a lower wall stress and that more ILT leads to a larger wall stress reduction. Furthermore, ILT is likely not a homogeneous material and is a very complex component (maybe organized or
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wet); however, because of lack of information about the material mechanical properties of ILT, the current assumption is the best effort in the computational simulation. A large ex vivo experimental test is needed for future study in this area. A realistic material model is crucial in the modelling of AAA wall stress, and this is a basis of the computational simulation of AAA stability. In aortic aneurysms, the thrombus is usually more lamellated and perhaps of more organized chronic type,48 In the future, this model can of course be improved by considering the variation of ILT properties. Higher stresses can often be found at the shoulders of the AAAs, where a big change of AAA shape presents. It can be easily explained by using Laplace’s Law. The thickness of artery is smaller where the vessel is healthy; so given the same pressure load, the resulted wall stress is higher at this location. From a purely structural engineering point of view, bending is higher at the junction between the healthy and the diseased part of the vessel. Risk stratification of AAA rupture is thought to be a multifactorial process that includes biologic, biomechanical, and biochemical factors. The biologic factors have been widely studied and reviewed,49 but the biomechanical factors are still not fully understood. This study concentrated on the wall stress using a computational simulation to demonstrate the stress distributions within the patientspecific AAAs. Although we have used state-of-the-art image segmentation and reconstruction methods along with complex nonlinear material models in our analysis, several assumptions and limitations still need to be discussed. The AAA component materials were assumed to be isotropic, incompressible, and homogenous. Each single material was assigned a set of parameters to govern for 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. The purpose of this study, however, was to examine the contribution of calcification and ILT on AAA wall stress. The relative stress changes rather than the exact stress magnitudes were examined. Future work is needed in the assessment of the mechanical properties of AAA components. The use of the maximum stress alone may not be enough in the consideration of AAA stability. The two major determinants for AAA rupture are 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 the 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. Another limitation is that the clinical use of wall stress calculations has been hindered by long computational time. It took about 4 hours to calculate the wall stress using our high performance computer cluster; however, with the fast improvements in costs and accessibility of computational power, this will be less of a problem in the future.
CONCLUSIONS The presence of calcification increases wall stress in AAA, suggesting that calcification decreases the biomechanical stability of AAA. The location of calcification rather than the amount of calcification plays a role in determining the maximum wall stress. In contrast, the presence of ILT reduces the maximum stress in AAA, and wall strength may need to be considered to assess AAA stability. The relative amount of ILT is associated with AAA wall stress. Calcification and ILT should both be considered in the evaluation of wall stresses for AAA rupture risk assessment. Future work is needed on the understanding of the mechanical properties of AAA components. The addition of calcified plaque and thrombus may further improve estimation of aneurysm rupture risk using finite element modelling. Further investigation including a better understanding of AAA material properties and failure strength may finally help in creating more realistic computational models to be used as a clinical adjunct in the future for effective decision making in AAA surgical and endovascular repair. AUTHOR CONTRIBUTIONS Conception and design: ZYL, JU, JG Analysis and interpretation: ZYL, JU Data collection: ZYL, ES Writing the article: ZYL, TS Critical revision of the article: ZYL, JU, TT, TS Final approval of the article: ZYL, JU, TT, ES, TS, JG Statistical analysis: ZYL Obtained funding: JG Overall responsibility: ZYL, JU, TT, ES, TS, JG REFERENCES 1. Sayers RD. Aortic aneurysms, inflammatory pathways and nitric oxide. Ann R Coll Surg Engl 2002;84:239-46. 2. Bush RL, Lin PH, Lumsden AB. Endovascular management of abdominal aortic aneurysms. J Cardiovasc Surg (Torino) 2003;44:527-34. 3. Lederle FA, Wilson SE, Johnson GR, Reinke DB, Littooy FN, Acher CW, et al. Immediate repair compared with surveillance of small abdominal aortic aneurysms. N Engl J Med 2002;346:1437-44. 4. Mortality results for randomised controlled trial of early elective surgery or ultrasonographic surveillance for small abdominal aortic aneurysms. The UK Small Aneurysm Trial Participants. Lancet 1998;352:1649-55. 5. Valentine RJ, Decaprio JD, Castillo JM, Modrall JG, Jackson MR, Clagett GP. Watchful waiting in cases of small abdominal aortic aneurysmsappropriate for all patients? J Vasc Surg 2000;32:441-8; discussion 448-50. 6. Vorp DA, Vande Geest JP. Biomechanical determinants of abdominal aortic aneurysm rupture. Arterioscler Thromb Vasc Biol 2005; 25:1558-66. 7. Li Z, Kleinstreuer C. Effects of blood flow and vessel geometry on wall stress and rupture risk of abdominal aortic aneurysms. J Med Eng Technol 2006;30:283-97. 8. Leung JH, Wright AR, Cheshire N, Crane J, Thom SA, Hughes AD, Xu Y. Fluid structure interaction of patient specific abdominal aortic aneurysms: a comparison with solid stress models. Biomed Eng Online 2006;5:33. 9. Wolters BJ, Rutten MC, Schurink GW, Kose U, de Hart J, van de Vosse FN. A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. Med Eng Phys 2005;27:871-83.
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Submitted Jul 9, 2007; accepted Jan 6, 2008.