Download Imaging - Circulation

Imaging
Association Between Aneurysm Shoulder Stress and
Abdominal Aortic Aneurysm Expansion
A Longitudinal Follow-Up Study
Zhi-Yong Li, PhD; Umar Sadat, MPhil, MRCS; Jean U-King-Im, PhD, FRCR;
Tjun Y. Tang, MD, MRCS; David J. Bowden, MB, BChir;
Paul D. Hayes, MD, FRCS; Jonathan H. Gillard, MD, FRCR
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Background—Aneurysm expansion rate is an important indicator of the potential risk of abdominal aortic aneurysm
(AAA) rupture. Stress within the AAA wall is also thought to be a trigger for its rupture. However, the association
between aneurysm wall stresses and expansion of AAA is unclear.
Methods and Results—Forty-four patients with AAAs were included in this longitudinal follow-up study. They were
assessed by serial abdominal ultrasonography and computed tomography scans if a critical size was reached or a rapid
expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up computed
tomography images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline
and final visit. A nonlinear large-strain finite element method was used to compute the wall-stress distribution. The
relationship between wall stresses and expansion rate was investigated. Slowly and rapidly expanding aneurysms had
comparable baseline maximum diameters (median, 4.35 cm [interquartile range, 4.12 to 5.0 cm] versus 4.6 cm
[interquartile range, 4.2 to 5.0 cm]; P⫽0.32). Rapidly expanding AAAs had significantly higher shoulder stresses than
slowly expanding AAAs (median, 300 kPa [interquartile range, 280 to 320 kPa] versus 225 kPa [interquartile range, 211
to 249 kPa]; P⫽0.0001). A good correlation between shoulder stress at baseline and expansion rate was found (r⫽0.71;
P⫽0.0001).
Conclusion—A higher shoulder stress was found to have an association with a rapidly expanding AAA. Therefore, it may
be useful for estimating the expansion of AAAs and improve risk stratification of patients with AAAs. (Circulation.
2010;122:1815-1822.)
Key Words: aorta 䡲 aneurysm 䡲 mechanics 䡲 tomography
A
bdominal aortic aneurysm (AAA) rupture continues to
be a major source of morbidity and mortality. Rupture
of the aneurysm is fatal in 70% to 90% of cases. It is the 13th
leading causing of death in Western societies.1 According to
the National Vital Statistics Report published in 2007, 14 000
patients had aneurysm-related deaths in 2004.2 The main
clinical indicators used to assess the risk of rupture are the
maximum diameter and expansion rate of the AAA. Surgery
is recommended when the maximum diameter of an AAA is
ⱖ5.5 cm. However, small aneurysms can also rupture, and
the overall mortality associated with these may exceed 50%3;
for example, the 12-year follow-up of the UK Small Aneurysm Trial has also shown a mortality rate of 67.3% in the
surveillance group.4 Expansion rate is also considered to be
an important indicator, and surgery is recommended when
maximum diameter expands above 10 mm/yr for smaller
AAAs.5,6 However, expansion rates may be nonlinear and
unpredictable,7 although currently it seems to be the best
predictor of aneurysm rupture.8 Therefore, there is a need for
a better predictor of aneurysm expansion and possible
rupture.
Clinical Perspective on p 1822
There is growing evidence that stress measurement within
the AAA wall may aid in identification of a high risk of
rupture with rapidly expanding aneurysms.9,10 A patientspecific study previously demonstrated that maximum wall
stress was 12% more specific and 13% more sensitive in
predicting AAA rupture than maximum diameter alone.11 In
other patient-specific studies, peak stress was found to be
significantly higher in ruptured AAAs than nonruptured
Continuing medical education (CME) credit is available for this article. Go to http://cme.ahajournals.org to take the quiz.
Received January 20, 2010; accepted August 13, 2010.
From the School of Biological Science and Medical Engineering (Z.-Y.L.), Southeast University, Nanjing, China; and University Department of
Radiology (Z.-Y.L., U.S., J.U.-K.-I., T.Y.T., D.J.B., J.H.G.), and Cambridge Vascular Unit (U.M., P.D.H.), Cambridge University Hospitals Foundation
Trust, Cambridge, United Kingdom.
Correspondence to Professor Zhi-Yong Li, School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China.
E-mail [email protected]
© 2010 American Heart Association, Inc.
Circulation is available at http://circ.ahajournals.org
DOI: 10.1161/CIRCULATIONAHA.110.939819
1815
1816
Circulation
November 2, 2010
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AAAs.12 Rupture of the aneurysm can be seen as a structural
failure when the induced mechanical stresses acting on the
weakened AAA wall exceeds its local mechanical failure
strength. The external forces include blood pressure and wall
shear stress. Stress in the AAA wall is due to the influence of
other concomitant factors, including the shape of the aneurysm, the characteristics of the wall material, the shape and
characteristics of the intraluminal thrombus (ILT) when
present, the eccentricity of the AAA, and the interaction
between the fluid and solid domains.13–17 Their role has been
investigated before.9,18 –20 Fully coupled fluid-structure interaction of the AAA has also been used to investigate the flow
and pressure fields in the aneurysm simultaneously with the
wall stresses.14 –16
Although rupture is determined by the comparison of wall
stress and wall strength, accurate wall strength measurement
in vivo is not currently possible. Therefore, computed wall
stresses at 1 time point may not necessarily provide an
estimation of the risk of rupture without knowing the strength
value at that time point. However, by following up patients
and performing wall stress analysis based on follow-up
images, the change in wall stresses may be more useful in
identifying AAA stability. Therefore, the main purpose of
this study was to evaluate the association of the change of
wall stresses with expansion rate of AAAs in a longitudinal
follow-up study.
diameter from the baseline CT scan. Similarly, we only used the final
CT scan for comparison of the final maximum diameter.
Because the location of the shoulder and the maximum diameter of
the aneurysm changes with aneurysm expansion, a standardized
approach was used to overcome this limitation. From the baseline CT
scan, the renal arteries were taken as a constant landmark. The
shoulder was defined as the junction of the neck and the aneurysm
sac. The maximum diameter was defined as the maximum distance
between the outer walls of the aorta in the aneurysm sac. The
distances of these 2 locations were measured from the renal arteries.
For the final scan, the same distances were measured to define the
neck and the maximum diameter locations that were used in the
earlier CT scan (so that stress changes could be measured at a
constant point together with the diameter changes at each of these
locations).
Based on the Oxford Screening Program,21 the patients were
divided into 2 groups: those with stable aneurysms (expansion rate
⬍0.4 cm/yr) and those with rapidly expanding aneurysms (expansion
rate ⱖ0.4 cm/yr).
CT Imaging
All patients had at least 2 CT examinations (baseline and final) of
their aorta using 100 mL of iodinated contrast medium (Iopamidol,
Niopam 300, Bracco, United Kingdom) via a power injector (5 mL/s
flow rate) on a 16-slice spiral CT machine (Somatom Sensation 4,
Siemens Medical Solutions, Erlangen, Germany). The imaging
protocol included automatic bolus tracking (scan initiation at the
peak of contrast uptake), with a collimation of 16⫻0.75 mm, a
512⫻512 matrix, and a 26⫻26 cm field of view. Other parameters
were 200 mAs and 120 KVp.
AAA Reconstruction
Methods
Patients
A database of patients who were being followed up in the Cambridge
Vascular Unit with routine ultrasound surveillance imaging for AAA
was used for this study (which usually may be done every 3 months,
6 months, or 12 months). From this database, a further subset of
patients was selected who had an abdominal computed tomography
(CT) scan done for other medical reasons. This was to ensure that
baseline aortic morphology data were available from a CT scan. The
maximum cross-sectional diameter of AAAs was measured at each
ultrasound surveillance visit. The expansion rate was calculated from
the serial ultrasound scans and CT scans. The growth rate calculated
from CT scans was used for analysis. A final CT scan was done just
before surgery to assess the optimum technique for treating it (ie,
open or endovascular). Axial and 3-dimensional (3D) CT reconstruction images were used to assess the maximum diameter and the
location of the aneurysm shoulder at baseline CT scan and at the CT
scan before surgery. Only infrarenal AAAs were included in this
study. Patients with juxtarenal, aorta-iliac, or inflammatory aortic
aneurysms were excluded from the study.
Only those patients were selected from this database who had CT
scans done for their abdominal pathologies. (The timing of CT
scanning was at the discretion of the relevant consultant surgeon.)
Only those patients were included in the study who underwent CT
abdomen close to the time of ultrasound. This baseline CT scan was
used for stress analysis. The patients continued with their ultrasound
surveillance after that. When the aneurysm reached a size at which it
was considered operable by the surgeon (which is ⬇5.5 cm), a CT
scan was done for detailed information about aneurysm morphology,
which is used for planning the operation. We calculated the expansion rate from the ultrasound surveillance on a yearly basis and then
the average expansion rate over the entire follow-up period. Similarly, the average expansion rate over the follow-up period was also
calculated from CT scan (from baseline and final CT). Because the
expansion rates calculated from ultrasound or CT were similar, and
because CT scan was being used for stress analysis, for sake of
standardization, we used CT-calculated expansion rates. For comparing the diameters of the 2 groups, we calculated the baseline
AAA geometries were reconstructed from the entire set of
2-dimensional (2D) CT slices. In brief, 2D cross-sectional images of
the abdominal aorta were obtained from the renal arteries to
immediately proximal to the iliac bifurcation. These images were
imported into image-processing software ScanIP (Simpleware Ltd,
Exeter, United Kingdom) for segmentation. The lumen was the most
distinguishable entity in a CT image, due to the bright contrast agent.
The noise in the image was reduced by using a gaussian filter, with
a 3⫻3 kernel, to clarify the lumen boundaries. The lumen boundaries
were segmented automatically using a threshold based on the pixel
intensities. Because the lumen borders were obtained automatically,
the geometric models reconstructed were reproducible. The boundary of the arterial wall was traced using a semiautomatic method in
the diseased part of the artery. We manually segmented the inner
boundary, and by subtly varying the window width, it was possible
to visualize only the soft tissue of the uncalcified wall. The thickness
of the wall equals to the local wall thickness minus the calcification
thickness in the radial direction. The position of the calcification was
defined by the distance between the center of the calcification and
the centerline of the vessel wall. In the healthy part of the artery, the
thickness was assumed to be 1.9 mm.22 The region of thrombus was
defined by the area within the inner wall minus the lumen area. The
distinction between the healthy and diseased part of the aorta was
made by reviewing the stacked CT images and using a diameter of
ⱕ3 cm as a general guide for definition of healthy artery.
On “stacking” of all 2D image data in 3D space, the 3D aneurysm,
including artery wall, ILT, and lumen, was produced. Surface
smoothing was controlled in ScanIP, and a curvature cutoff and a
maximum iteration can be given to reduce surfaces containing sharp
corners, which may result in artificial stress concentration. This
smoothing was done on all the surfaces of AAA components,
including ILT and vessel wall. The 3D reconstructed AAA model
was then meshed using ScanFE (Simpleware Ltd). A cutting section
is shown to illustrate the detail meshes of ILT and arterial wall
(Figure 1). The 3D reconstructed AAA model was then exported to
ABAQUS/CAE (v6.8, SIMULIA, Providence, RI) for finite element
preprocessing. The investigator responsible for the entire computational analysis (Z.-Y.L.) was blinded to the patient group and time of
imaging.
Li et al
Shoulder Stress and Aneurysm Growth
1817
Figure 1. Reconstruction of 3D AAA
model based on CT and computed wall
stress distributions. A, Threedimensional AAA model and mesh; B,
axial CT slice; C, cross-section of AAA
model showing the AAA components
(ILT, arterial wall, and lumen); D, 3D
stress contours showing von Mises
stress distribution. High stresses can
often be found at the shoulder region.
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Material Properties
Both ILT and AAA wall were assumed to be hyperelastic, homogeneous, incompressible, and isotropic materials. The AAA arterial
wall and ILT were modeled using the nonlinear hyperelastic wall
mechanical properties derived by Raghavan and Vorp from uni-axial
testing of 69 excised human AAAs.23,24 ILT is actually not homogeneous, but there are too little data available in the literature to
describe the nonhomogeneity of this material to be useful for
mechanical simulation. The strain energy functions for AAA wall
and ILT were:
W⫽C 1 共I B ⫺3兲⫹C 2 共I B ⫺3兲 2 for the arterial wall
W⫽D 1 共II B ⫺3兲⫹D 2 共II B ⫺3兲 2 for ILT
where W is the strain energy, C1 and C2 are material parameters for
the wall, and IB and IIB are the first and second invariants of the left
Cauchy-Green deformation tensor B (IB⫽tr B; IIB⫽1/2[(tr B)2–
tr(B)2]). The constants were set to the population mean values
C1⫽174 000 Pa and C2⫽1 881 000 Pa; D1⫽26 000 Pa, and
D2⫽26 000 Pa. It has been shown that use of population mean values
does not affect the wall stress result in a significant manner.25,26 For
calcification, we have chosen the parameters of the Mooney-Rivlin
model, which has been previously used.27 Mooney-Rivlin materials
can be described by 2 constants, and their values for calcification
were taken as A⫽18 804.5 Pa and B⫽20.27
Structural Analysis
The principles of this analysis are similar to those previously used by
our laboratory.10,28 –30 Finite element analysis divides a complex
structure into small areas called elements for which the stress
distribution can be more easily studied. The systolic blood pressure
was taken at the time of the initial CT scan and was applied as a
boundary condition in the lumen wall. Ideally it would have been
better to have blood pressure at both CT scans, but for the purpose
of this study we wanted to keep the loading conditions constant to
avoid any affect of varying loading conditions. This allowed us to
investigate “structure vulnerability” itself. This pressure was applied
to the inner surface of corresponding models as an outward-acting
tractional loading condition. The outer surface of the AAA was
considered load-free. No contact with the spine and abdominal
organs was simulated. The shear stress acting on the wall by flowing
blood was neglected in this study because it has been shown that it
is several orders of magnitude smaller than wall stresses.14,31,32 Both
ends of the models were fixed to simulate the tethering to the rest of
the aorta. The residual stress was not considered in this study. A
nonlinear large deformation model was used, and the AAA components were simulated using a hyperelastic material formulation.
Tetrahedral elements were used for all AAA components (Figure 1).
All computations were performed on a 64-bit 4 – dual-core 2.6GHz processors high-performance computing cluster with a 32 GB
of RAM. The Von Mises stresses were recorded for each analysis.
The following notions were used: overall stress (␴max): maximum
wall stress within the entire 3D AAA; shoulder stress (␴S): stress at
the shoulder of the AAA; and max-diameter stress (␴D): stress at the
location of maximum diameter.
␴max, ␴S, and ␴D were investigated using the above standardized
approach. Please note that at the final visit, the shoulder may have
transformed into aneurysm (due to growth/expansion), but for the
sake of simplicity, the term “shoulder stress (␴S)” has been used in
that case.
Statistics
Statistical analysis was performed with SPSS 16.0 (SPSS Inc,
Chicago, Ill). The normality of the data was assessed using the
Shapiro–Wilk test. For categorical variables, the Fisher exact test
was used. For continuous variables the following tests were used:
Paired t test was used for paired variables with normal distribution,
and Wilcoxon matched pairs test was used for non-normal data. For
nonpaired variables, the Mann-Whitney test was used for nonnormal data and unpaired t test for data that were approximately
normal. The relationships between AAA size, expansion rate, and
wall stresses were tested using the Pearson coefficient. A P value
⬍0.05 was used to determine statistical significance. All values
are 2-sided.
Results
Forty-four patients were included in this study. The patient
demographics and comorbidities have been tabulated in
Tables 1 and 2. Fourteen patients had slowly expanding
aneurysms (expansion rate ⬍0.4 cm/yr), and 30 patients had
rapidly expanding aneurysms (expansion rate ⱖ0.4 cm/yr).
The median overall follow-up period was 20 months (interquartile range [IQR], 16 to 29 months), with slowly expanding AAAs followed up for 32 months (IQR, 17 to 52 months)
and rapidly expanding AAAs followed up for 16 months
1818
Circulation
November 2, 2010
Table 1.
Patient Demographics
Table 3.
No. of AAAs
Change of Diameter and Stress in the AAAs
44
Age, y (range)
78 (60–90)
Sex, n
Baseline
Follow-Up
P
AAA diameter, cm (IQR)
Overall maximum
4.6 (3.2–5.5)
5.7 (5.0–7.0)
0.002
Male
34
Slowly expanding
4.35 (4.12–5.0)
5.2 (5.0–5.6)
0.002
Female
10
Rapidly expanding
4.6 (4.2–5.0)
5.8 (5.52–6.0)
0.0001
Overall stress ␴max,
kPa (IQR)
296 (193–420)
309 (203–463)
0.32
Total shoulder stress ␴S,
kPa (IQR)
279 (200–376)
274 (179–374)
0.64
Total max-diameter stress ␴D,
kPa (IQR)
215 (109–360)
219 (101–373)
0.71
AAAs, n
Stable
14
Rapidly expanding
30
Expansion rate, cm/y (IQR)
0.66 (0.36–0.96)
Follow-up time, months (IQR)
20 (16–29)
Blood pressure, mm Hg (range)
Systolic
Diastolic
Volume of calcification, % (range)
Volume of ILT, % (range)
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149 (100–184)
AAA shoulder stress ␴S,
kPa (IQR)
82 (70–105)
Slowly expanding
225 (211–249)
242 (211–281)
0.22
4.1 (0.1–14.0)
Rapidly expanding
300 (280–320)
279 (267–324)
0.10
Slowly expanding
187 (138–284)
213 (171–274)
0.06
Rapidly expanding
203 (185–237)
220 (182–240)
0.51
46.0 (1.2–79.0)
(IQR, 8 to 21 months), P⫽0.004, before they reached a size
at which surgical intervention was offered.
Figure 1 shows the reconstructed 3D AAA model from CT
slices. The cross-sectional view shows the components (ILT
and arterial wall) of the AAA. The 3D stress contour
demonstrated stress distributions in the AAA wall. Areas of
high stress were found in most cases in the shoulder region of
the aneurysm (Figure 1D).
There was no significant difference between the 2 groups
for maximum aneurysm diameter at baseline (median, 4.35
Table 2. Patient Comorbidities and Abdominal Aortic
Aneurysm Characteristics
Comorbidities
Smoking
Slowly
Expanding
Aneurysms
(n⫽14)
Rapidly
Expanding
Aneurysms
(n⫽30)
P
10
20
1.00
Diabetes mellitus
6
20
0.19
Hypertension
7
22
0.17
Family history of AAA
4
7
0.72
Ischemic heart disease
12
0.19
Median baseline maximum
diameter, cm (IQR)
4.3 (4.1–5.0)
9
4.6 (4.2–5.0)
0.32
Median final maximum
diameter, cm (IQR)
5.2 (5.0–5.6)
5.8 (5.5–6.0)
0.001
Median baseline shoulder
stress, kPa (IQR)
225 (211–249)
300 (280–320)
0.0001
Median final shoulder
stress, kPa (IQR)
242 (211–281)
279 (267–324)
0.02
Median baseline maximum
diameter stress, kPa (IQR)
187 (138–284)
203 (185–237)
0.39
Median final maximum
diameter stress, kPa (IQR)
213 (171–274)
220 (182–240)
0.70
Median baseline overall
stress, kPa (IQR)
266 (230–380)
313 (274–347)
0.03
Median final overall
stress, kPa (IQR)
266 (227–317)
323 (279–371)
0.02
AAA max diameter stress ␴D,
kPa (IQR)
AAA overall stress ␴max,
kPa (IQR)
Slowly expanding
266 (230–380)
266 (227–317)
0.22
Rapidly expanding
313 (274–347)
323 (279–371)
0.01
␴max indicates overall stress; ␴S, shoulder stress; and ␴D, max-diameter
stress.
cm [IQR, 4.12 to 5.0 cm] versus 4.6 cm [IQR, 4.2 to 5.0 cm];
P⫽0.32). The overall maximum diameter increased from 4.6
cm (IQR, 3.2 to 5.5 cm) to 5.7 cm (IQR, 5.0 to 7.0 cm) during
the follow-up (P⫽0.002; Table 3). A decrease in the overall
shoulder stress from baseline was observed; that is, 279 kPa
(IQR, 200 to 376 kPa) to 274 kPa (IQR, 179 to 374 kPa), but
it was not statistically significant (P⫽0.64). A nonsignificant
increase in overall stress and maximum diameter stress was
observed; that is, overall stress, 296 kPa (IQR, 193 to 420
kPa) versus 309 kPa (IQR, 203 to 463 kPa) (P⫽0.32) and
max-diameter stress, 215 kPa (IQR, 109 to 360 kPa) versus
219 kPa (IQR, 101 to 373 kPa) (P⫽0.71). See Figure 2 for a
representative patient.
Correlations between baseline maximum diameter, expansion rate, ␴max, ␴S, and ␴D were assessed in order to
determine their ability to predict the expansion of the aneurysm (Table 4). This study failed to find a relationship
between expansion rate and baseline aortic diameter for all
patients (r⫽0.13, P⫽0.36). This may be a type II error. A
statistically significant positive correlation was found however between overall shoulder stress and expansion rate
(r⫽0.71; P⫽⬍0.001) (Figure 3).
Slowly and rapidly expanding aneurysms had comparable
baseline maximum diameters (median, 4.35 cm [IQR, 4.12 to
5.0] versus 4.6 cm [IQR, 4.2 to 5.0]; P⫽0.32). At the end of
follow-up, a significant difference in the diameters of the 2
groups was observed (5.2 cm [IQR, 5.0 to 5.6 cm] versus 5.8
[IQR, 5.52 to 6.0 cm], P⫽0.001). ␴max, ␴S, and ␴D were
compared between stable and rapidly expanding aneurysms
(expansion rates calculated from serial ultrasound scans)
Li et al
Shoulder Stress and Aneurysm Growth
1819
Figure 2. Comparisons of shoulder
stress and max-diameter stress between
baseline and follow-up for a patient.
Two-dimensional cross-sectional stress
distributions at both levels are shown (in
kPa).
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(Table 2). A statistically significant difference was observed
for overall stress and shoulder stress between the 2 groups
(P⫽0.03 and P⫽0.0001, respectively) at baseline. Correlations between baseline maximum diameter, expansion rate,
␴max, ␴S, and ␴D were assessed in order to determine their
ability to predict the expansion of slowly (Table 5 and Figure 4)
and rapidly expanding aneurysms (Table 6 and Figure 5). A
positive correlation was observed for rapidly expanding
aneurysms between expansion rate and shoulder stress
(r⫽0.53, P⫽0.003).
Discussion
The process of AAA rupture is thought to be a multifactorial
process that includes biological, biomechanical, and biochemical processes. The biological and biochemical factors
have been widely studied and reviewed,33 whereas the biomechanical factors are still not fully understood. It is generally recognized that rupture of an AAA occurs when the stress
acting on the wall exceeds the strength of the wall. WallTable 4. Correlation Between Baseline Maximum Diameter,
Expansion Rate, Overall Stress, Shoulder Stress, and
Max-Diameter Stress for All Patients
Expansion
Rate
(cm/y)
stress simulation based on a patient-specific AAA model
appears to give a more accurate rupture risk assessment than
AAA diameter alone.
This was a longitudinal study in which serial stress changes
in the aneurysm wall were monitored and correlated with the
aneurysm expansion rate. Wall stress is associated with AAA
geometry and components. High stress is often found at the
shoulders of the aneurysm because of the abrupt change in the
shape of the aorta. This leads to the upregulation of different
matrix metalloproteinases from the mechanotransduction of
smooth muscle cells. Matrix metalloproteinases result in
increased matrix degradation, leading to aneurysmal
dilatation.34 –37
We set out to determine the stress changes at the shoulder
and maximum diameter regions of the aneurysm. It was found
that areas of high stress were present at the shoulder region of
the aneurysm. Another interesting observation was that during the follow-up period there was some decrease in the stress
at the shoulder region. It was accompanied by an increase in
the diameter at the shoulder region. This indicates that with
increasing diameter at the shoulder, stress decreases. This
leads to the moving up of the shoulder region and a
Shoulder
Stress, Max-Diameter Max-Overall
Initial
Stress, Initial Stress, Initial
(kPa)
(kPa)
(kPa)
Expansion rate, cm/y
Pearson correlation
coefficient, r
1
P, 2-tailed
0.717*
0.017
0.249
⬍0.001*
0.915
0.103
Baseline maximum
diameter, cm
Pearson correlation
coefficient, r
0.139
0.166
0.120
0.385*
P, 2-tailed
0.368
0.281
0.438
0.010*
*Correlation coefficient (r) and significant level P values.
Figure 3. Association of expansion rate with shoulder stress for
all patients with Pearson correlation. A strong positive correlation was observed (r⫽0.71).
1820
Circulation
November 2, 2010
Table 5. Correlation Between Baseline Maximum Diameter,
Expansion Rate, Overall Stress, Shoulder Stress, and
Max-Diameter Stress for Patients With Slowly
Expanding Aneurysms
Expansion
Rate,
cm/y
Shoulder
Stress, Max-Diameter Max-Overall
Initial,
Stress, Initial, Stress, Initial,
kPa
kPa
kPa
Expansion rate, cm/y
Pearson correlation
coefficient, r
1
⫺0.063
⫺0.288
⫺0.098
0.832
0.319
0.739
Baseline maximum
diameter, cm
P, 2-tailed
Expansion
Rate,
cm/y
Shoulder
Stress, Max-Diameter Max-Overall
Initial,
Stress, Initial, Stress, Initial,
kPa
kPa
kPa
Expansion rate, cm/y
P, 2-tailed
Pearson correlation
coefficient, r
Table 6. Correlation Between Baseline Maximum Diameter,
Expansion Rate, Overall Stress, Shoulder Stress, and
Max-Diameter Stress for Patients With Rapidly
Expanding Aneurysms
Pearson correlation
coefficient, r
1
P, 2-tailed
0.530*
⫺0.102
0.019
0.003*
0.592
0.921
Baseline maximum
diameter, cm
⫺0.417
⫺0.166
⫺0.163
⫺0.157
0.138
0.571
0.578
0.592
Pearson correlation
coefficient, r
0.165
0.178
0.275
0.554*
P, 2-tailed
0.383
0.346
0.142
0.001*
*Correlation coefficient (r) and significant level P value.
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lengthening of the aneurysm. It may well result from the
formation of ILT at the previous “shoulder area,” which tends
to reduce the stress in the AAA.10
Although no concomitant increase from baseline for the
overall stress, overall maximum diameter stress, and overall
shoulder stress was observed, a positive correlation between
the expansion rate and the shoulder stress was identified.
Further analysis of the 2 groups revealed that this relationship
exists for rapidly expanding aneurysms only and not for
slowly expanding aneurysms. The lack of correlation for
slowly expanding aneurysms may be due to small numbers of
research subjects in this group. Thus shoulder stress seems to
be a strong predictor of rapid aneurysm expansion. The
finding that rapidly expanding aneurysms had significantly
higher shoulder stresses at baseline compared with slow
expanding aneurysms, despite having comparable maximum
aneurysm diameter, and reached the final maximum diameter
(at which surgery was offered to patients) in approximately
half the time, also supports our hypothesis. We also tested the
relationship of maximum diameter of the aneurysm with its
expansion rate, but contrary to common belief, we found that
there was no correlation. This is an important finding because
Figure 4. Association of expansion rate with shoulder stress for
slowly expanding aneurysms with Pearson correlation. No correlation was observed (r⫽– 0.06).
in today’s clinical practice the maximum diameter is used as
a guide for offering repair of the aneurysm.
This study concentrated on the wall stress using a computational simulation to demonstrate the stress distributions
within the patient-specific AAAs. Although we have used
state-of-the-art image segmentation and reconstruction methods and complex nonlinear material models in our analysis,
there are still several assumptions and limitations that need to
be discussed.
Each single material was assigned a set of parameters in
order to govern the stress/strain relationship. In vivo materials
have more complex characteristics than those used in this
study. Therefore, the stress values may not represent the
actual stress condition within the AAAs, but the relative
stress changes. The use of an anisotropic model can overcome
this limitation, but this requires determining the material
properties of aorta, which is not currently possible in living
humans. Autopsy studies could be designed to get a broad
range of material properties, but even this is not ideal. The
uncertainties in image segmentation, 3D reconstruction, definition of the boundary conditions, and the material properties
of the AAA model may affect the results of an finite element
analysis model derived from CT data. The sensitivity of
Figure 5. Association of expansion rate with shoulder stress for
rapid expanding aneurysms with Pearson correlation. Correlation was observed (r⫽0.53).
Li et al
Downloaded from http://circ.ahajournals.org/ by guest on June 16, 2017
image-based finite element analysis modeling has been studied previously.38,39 It has been demonstrated that the coefficients of variation of the output variables from finite element
analysis modeling never exceed 9%. Further improvement in
CT image resolution and automatic image processing techniques will certainly reduce the uncertainties in the patientspecific modeling in the future.
Future work is needed in the assessment of the mechanical
properties of AAA components. The use of maximum stress
alone may not be enough in the consideration of AAA
stability. There are 2 major determinants for AAA rupture:
wall stress and wall strength. An AAA ruptures only when the
local stress exceeds the local wall strength. However, lack of
AAA material strength data made it impossible to predict
local strength value for comparison with local stress value. It
remains difficult to determine the failure strength of a
particular AAA without destructively testing a piece of tissue
excised from it. Although wall strength equations exist, they
add to the complexity of the model. Moreover, they may be
more important for rupture risk than for predicting future
growth rate. Another limitation is that the clinical use of wall
stress calculations has been hindered by long computational
time. It took approximately 4 hours to calculate the wall stress
using our high-performance computer cluster. However, with
reducing costs, better accessibility, and increasing computational power, this will be less of a problem in the future.
Should all aneurysms undergo stress analysis? The answer
is probably no. Patients who are fit and healthy with large
aneurysms (⬎5.5 cm) will continue to undergo aneurysm
repair without stress analysis. This is because the risk-tobenefit ratio clearly favors surgical intervention, and stress
analysis will not add much. However, patients with smaller
aneurysms, who are usually followed up with routine surveillance programs, may benefit from stress analysis. This is
because of the already mentioned fact that the stress in small
aneurysms may be quite high, exposing them to rupture risk.
Identification of such high-stress small-diameter aneurysms
can effectively select high-risk vulnerable patients who have
a high risk of aneurysm rupture. Stress analysis has shown a
relationship between stress and expansion rate. In conjunction
with other factors, this information may help to guide our
management of medium-sized AAAs (4 to 5.5 cm) in the
future.
Conclusions
High stress at the shoulder appears to have an association
with a rapidly expanding AAA. Therefore, it may be useful
for estimating the rapid expansion of an AAA. This follow-up
stress study again highlights that patient-specific stress analysis may be a useful tool for identification of vulnerable
AAAs in the future. Work is needed on an improvement in
the understanding of the mechanical properties of AAA
components. Finally, further investigation, including a better
understanding of AAA material properties and failure
strength, may help in creating more realistic computational
models to be used as a clinical adjunct in the future for
effective decision making for surgical and endovascular AAA
repair.
Shoulder Stress and Aneurysm Growth
1821
Disclosures
None.
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CLINICAL PERSPECTIVE
By convention, abdominal aortic aneurysm (AAA) diameter has been used as an indicator of the potential risk of rupture.
Advances in biomechanics have enabled us to assess the inherent stresses within the aneurysm wall, which are thought to
play a role in aneurysm expansion. From the structural view point, aneurysm expansion and rupture results from material
fatigue and failure of the aneurysm wall. In this study we assessed the association of AAA wall stresses with their
expansion rates and found that stresses at the shoulder of the rapidly expanding aneurysms had good correlation with the
expansion rates compared with slowly expanding aneurysms. We also tested the relationship of maximum diameter of the
aneurysm to its expansion rate, but although such a relationship is widely believed to exist, we found no such relationship.
This highlights the fact that biomechanical stress analysis of AAAs may be useful for estimating their expansion rather than
relying only on maximum AAA diameter for assessment of potential risk of rupture.
Go to http://cme.ahajournals.org to take the CME quiz for this article.
Association Between Aneurysm Shoulder Stress and Abdominal Aortic Aneurysm
Expansion: A Longitudinal Follow-Up Study
Zhi-Yong Li, Umar Sadat, Jean U-King-Im, Tjun Y. Tang, David J. Bowden, Paul D. Hayes and
Jonathan H. Gillard
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Circulation. 2010;122:1815-1822; originally published online October 18, 2010;
doi: 10.1161/CIRCULATIONAHA.110.939819
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