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Effect of intraluminal thrombus on wall stress in
patient-specific models of abdominal aortic
aneurysm
David H. J. Wang,a,b Michel S. Makaroun,a Marshall W. Webster,a and David A. Vorp,a,b Pittsburgh, Pa
Purpose: The role of intraluminal thrombus (ILT) on abdominal aortic aneurysm rupture is still not clear. Rupture of an
aneurysm occurs when the wall stress exceeds the wall strength at any location on the wall. The purpose of this study was
to address the hypothesis that the presence of ILT alters the wall stress distribution or wall stress magnitude in AAA.
Methods: Patient-specific 3D AAA geometries were reconstructed from computed tomographic images. Two geometric
features, ILT surface ratio (ILT surface area divided by the total AAA surface area) and ILT volume ratio (ILT volume
divided by the total AAA volume), were calculated for each AAA. Two models were created for each patient: one with ILT
and one without ILT. Systolic pressure measured at the time of computed tomographic imaging was applied to the
internal surface of each model. A nonlinear large deformation algorithm was used to compute wall stress distribution with
the finite element method. The Wilcoxon matched pairs test was used to compare the peak wall stress between the two
models of each patient.
Results: Four patients were studied with ILT surface ratios that ranged from 0.29 to 0.72 and ILT volume ratios that
ranged from 0.12 to 0.66. The peak wall stress was reduced (range, 6% to 38% reduction; P ⴝ .067) for all models with
ILT included (range, 28 to 37 N/cm2) as compared with models with no ILT (range, 30 to 44 N/cm2). Visual inspection
also revealed a marked effect of ILT on the wall stress distribution.
Conclusion: The presence of ILT alters the wall stress distribution and reduces the peak wall stress in AAA.For this reason,
ILT should be included in all patient-specific models of AAA for evaluation of AAA wall stresses. (J Vasc Surg 2002;36:
598-604.)
An untreated abdominal aortic aneurysm (AAA) is at
risk of rupture. Unfortunately, the operative mortality rate
for patients with ruptured AAA remains unacceptably
high.1,2 On the other hand, the elective surgical repair of an
AAA is costly and carries its own significant risks that may
be a more serious threat to life than a stable AAA. Therefore, an accurate identification of patients with AAA at
increased risk of rupture will reduce medical costs and save
lives.
Presently, no reliable criterion exists to predict the risk
of AAA rupture. Rupture is a biomechanical event that
occurs at the instant when the stress in the dilating and
degenerating aneurysm wall exceeds its strength at any
location. Therefore, accurate prediction of wall stress distribution in patient-specific AAA models might be useful in
determining the rupture potential of individual AAAs and
provide improved patient management.
From the Departments of Surgerya and Bioengineering,b University of
Pittsburgh.
Supported by grants (to DAV) from The Whitaker Foundation, The Pittsburgh Foundation, and the NIH (#RO1 HL 060670-01A2).
Competition of interest: nil.
Additional material for this article may be found online at www.mosby.
com/jvs.
Reprint requests: David A. Vorp, PhD, Department of Surgery, Division of
Vascular Surgery, Suite A-1011 PUH, 200 Lothrop St, Pittsburgh, PA
15213 (e-mail: [email protected]).
Published online Jul 9, 2002.
Copyright © 2002 by The Society for Vascular Surgery and The American
Association for Vascular Surgery.
0741-5214/2002/$35.00 ⫹ 0 24/1/126087
doi:10.1067/mva.2002.126087
598
Our laboratory recently introduced the technique of
computational estimation of wall stress in AAA.3 Although
this initial work showed that the wall stress distribution is
quite complex and does not adhere to the commonly used
law of Laplace, it suffers from several significant limitations.
One limitation is that it does not take into account the
effect of the intraluminal thrombus (ILT). ILT is a threedimensional (3D) fibrin structure incorporated with blood
cells, platelets, blood proteins, and cellular debris and is
present in variable degrees between the flowing blood and
the aortic wall in approximately 75% of all AAAs.4
The mechanical role of ILT on wall stress distribution
has been controversial. Dobrin5 suggested that the presence of ILT neither reduces the luminal pressure exerted on
the wall nor offers a retractive force and thus has no effect
on the wall stress. Schurink et al6 performed experimental
measurements and reported that thrombus does not reduce
the pressure near the aneurysmal wall as compared with
luminal pressure. However, recent work in our laboratory
has shown that ILT is a nonlinearly elastic material with
significant mechanical properties.7 Therefore, an ILT with
any significant thickness will likely act as a mechanical
cushion, as predicted with our previous in vivo observation.8 Indeed, stress analyses of AAA with simplified hypothetic models by us and other investigators9-12 have suggested that the presence of ILT reduces stress in the AAA
wall. However, these studies have either assumed the mechanical properties of ILT,10,11 used a simple linear elastic
model for this material,9,11,12 or used simplified shapes for
the AAA and ILT.9-12
JOURNAL OF VASCULAR SURGERY
Volume 36, Number 3
Wang et al 599
The goal of this study was to investigate the effect of
ILT on wall stress distribution and magnitude in realistic
patient-specific models of AAA. To accomplish this, we
used the experimentally determined mechanical behavior
for ILT and AAA wall. Our results suggest that ILT markedly alters wall stress distribution and reduces wall stress
magnitude in AAA.
METHODS
The finite element method was used for computational
stress analysis of the stress distribution on the aneurysmal
wall. An accurate stress analysis of a structure depends on
the following factors: an accurate geometry, realistic
boundary or loading conditions, and accurate mechanical
properties of the materials involved. In this study, realistic
3D AAA geometries, including both wall and ILT, were
reconstructed from each patient’s computed tomographic
(CT) images. Immediately before and after CT scanning,
three measurements of arterial pressure were obtained in
standard fashion with an arm-cuff sphygmomanometer.
For each subject, the systolic values of blood pressure were
averaged, and the mean value was applied as the luminal
pressure. We have shown in a previous study that peripherally measured systolic pressure correlates well with systolic
pressure in the distal aorta, providing an adequate noninvasive estimation.8 Nonlinear elasticity theory developed
specifically for the AAA wall and ILT was used. Two models
were created for each patient for comparison: one with ILT
and one without ILT. Patient-based loading and boundary
conditions were applied to each model. Each of these
procedures are described subsequently.
Abdominal aortic aneurysm reconstruction. The
inner wall surface of each AAA was 3D reconstructed with
a previously reported technique.3 A modification of this
technique was developed to include ILT and wall thickness
in the reconstructed model. In brief, two-dimensional
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 image processing software Scion Image
(Release Beta 3b, Scion Corporation, Frederick, Md) for
segmentation. The boundaries of the luminal surface and
the inner wall were identified with semiautomatic tracing
(Fig 1). After segmentation, a number of coordinate points
were identified on each boundary and assigned coordinate
(X, Y, Z) values associated with their spatial positions (Fig
1). Upon “stacking” of all two-dimensional image data in
3D space, two 3D point clouds were produced: one representing the inner wall surface and the other representing
the luminal surface (Fig 2, A). Each of the 3D point clouds
was triangularized into 3D surfaces. These surfaces contained sharp corners, which were artifacts from the image
processing (Fig 2 , B). Such sharp corners would result in
artificial stress concentration in stress analysis and lead to
erroneous interpretations. The protocol previously reported13 was used for smoothing both the AAA wall and
luminal surfaces. The smoothed surfaces (Fig 2 , C) then
were input to the solid modeling software Pro-Engineer
Fig 1. Edge detection for luminal and inner wall surfaces of AAA.
A, CT scan image obtained at Z ⫽ 3.3-cm level. B, Subsequent
segmentation of image in (A) and placement of coordinate points
on two boundaries.
(Release 20, Parametric Technology Corporation, San
Jose, Calif) for 3D solid reconstruction. The space formed
between the luminal surface and the inner AAA wall surface
was the volume representing the solid mass of ILT. In our
previous method, we assumed a uniform wall thickness for
all AAAs of 1.9 mm.3 In the current work, for each subject,
three wall thickness measurements were made on different
image slices in regions where the wall was clearly defined
from the surrounding tissues. Extrusion of the 3D inner
wall surface outwardly by an amount equal to the average of
the three measurements created the thickness of the AAA
wall in our model. The 3D reconstructed AAA model then
was exported to the meshing software PATRAN (MSC/
PATRAN Version 9.0, MSC Software Corporation, Los
Angeles, Calif) for finite element preprocessing.
Abdominal aortic aneurysm and intraluminal
thrombus geometric features. The total volume of AAA
was calculated with PATRAN as the volume contained
within the 3D reconstructed inner wall surface. The volume
of ILT also was calculated with PATRAN as volume contained between the 3D reconstructed inner AAA wall and
the 3D reconstructed lumen. The ILT volume ratio was
defined as the ILT volume divided by the total AAA volume. Similarly, the surface area of the inner AAA wall and
lumenal surfaces also were calculated with PATRAN. The
JOURNAL OF VASCULAR SURGERY
September 2002
600 Wang et al
Fig 2. Point cloud (A) assembled from smoothed data from
series of CT scan images connected into triangles to form preliminary 3D surface (B). Surface is rough and is processed with
biquintic technique to yield smoothed virtual AAA (C).
ILT surface area ratio was defined as the ILT surface area
divided by the total AAA surface area.
Boundary conditions. Each patient’s blood pressure
was measured at the time of CT scanning following the
previously reported protocol.3 Because we were interested
in evaluating the maximal wall stress during the cardiac
cycle, peak systolic blood 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 possible contact with the spine
and abdominal organs was simulated. The interface between ILT and the AAA wall was assumed to be “nonslip.”
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 compared with wall
stresses.14,15 Residual stresses that may exist within the
aortic wall in vivo also were neglected. Both the proximal
and distal ends were fixed in the axial direction to simulate
tethering at those locations.
Material properties. Both ILT and AAA wall were
assumed to be hyperelastic, homogenous, incompressible,
and isotropic materials. Finite strain constitutive models for
both materials were developed previously by our group.7,16
The pseudostrain energy for the wall was taken as16: W ⫽ ␣
(IB – 3) ⫹  (IB – 3)2, where W is the strain energy density
function (Appendix, online only), ␣ and  are material
parameters for the wall, and IB is the first invariant of the left
Cauchy-Green deformation tensor (B). For ILT, the functional form of W was taken as7: W ⫽ c1 (IIB – 3) ⫹ c2 (IIB
– 3)2, where c1 and c2 are material parameters for the ILT
and IIB is the second invariant of B. Population mean
values of each of the material parameters (ie, ␣, , c1, and
c2) were determined from previous experimentation7,16
and were input to the finite element models of each AAA.
Specifically, we used ␣ ⫽ 17.4 N/cm2,  ⫽ 188.1 N/cm2,
c1 ⫽ 2.6 N/cm2, and c2 ⫽ 2.6 N/cm2. Previous and
ongoing studies in our laboratory revealed that use of
population mean values does not affect the wall stress result
in a significant manner.16,17
Finite element analysis. The stress distribution in
each AAA was computed with the well-validated finite
element analysis software ABAQUS (v 6.0, Hibbit, Karlsson and Sorensen, Inc, Pawtucket, RI). The “NLGOM”
algorithm within ABAQUS was used to account for both
the material and geometric nonlinearities (ie, hyperelasticity and large deformation). For each patient, two analyses
were carried out: one with the 3D reconstructed ILT
included in the geometry and the other without the ILT.
For each model, a mesh independency study was carried
out to assure an optimally sized mesh. This was accomplished by increasing the number of elements until the peak
wall stress and wall stress distribution did not change appreciably (⬍2%). Each “virtual AAA” was meshed with
10,000 to 20,000 quadratic, 10-noded, tetrahedral hyperelastic elements. Generated results included a von Mises
stress mapping on the inner wall of the 3D virtual AAA and
on the outer ILT wall (ie, at the interface between ILT and
AAA wall), where applicable.
RESULTS
Four patients (three male and one female) for whom
CT images were collected for analysis in our previous work3
were studied here. Each of these patients had ILT in their
AAA. Age ranged from 73 to 86 years, and the maximal
AAA diameter ranged from 6.0 cm to 6.4 cm (Table I). The
reconstructed virtual AAA including ILT is shown for each
subject in Fig 3. Each geometry was quite irregular and was
different from patient to patient. The ILT in AAA 1 covered only the lower half of the aneurysm, whereas AAAs 2
and 4 were fully covered by ILT. AAA 3 had a small amount
of ILT that covered only a part of the upper half of the
aneurysm. The geometric features of AAA and contained
ILT varied widely among selected subjects and are given in
Table II.
All finite element stress analyses reached convergence.
The von Mises stress distributions are shown in Fig 4 for
each AAA with and without ILT included in the analysis.
JOURNAL OF VASCULAR SURGERY
Volume 36, Number 3
Wang et al 601
Fig 3. Four AAA models. Note different ILT conıgurations. Lumen through ILT is indicated with black mesh, so that
material between mesh and AAA wall is ILT.
Table I. Information on subjects in study
Patient
Gender
Age (y)
Systolic pressure
(mm Hg)
AAA
diameter (cm)
Wall thickness (mm)
1
2
3
4
Male
Male
Female
Male
85
86
74
73
120
128
155
128
6.0
6.1
6.4
6.4
1.95 (1.95,1.92,1.98)
1.84 (1.93,1.72,1.87)
1.75 (1.8, 1.83,1.62)
1.86 (1.82,1.84, 1.9)
Wall thickness values given as mean followed parenthetically by three individual measurements.
Table II. Geometric features of four AAAs and contained ILT
Patient
1
2
3
4
Length
(cm)
Wall
surface area
(cm2)
AAA volume
(cm3)
ILT
surface area
ratio
ILT volume
ratio
14.0
8.8
9.2
15.0
144
150
168
241
142
156
209
266
0.41
0.54
0.29
0.72
0.47
0.66
0.12
0.49
Compared with the companion models that neglected ILT,
the peak wall stress in the model including ILT was decreased to varying degrees (P ⫽ .067, with Wilcoxon paired
test; Table III). Patients 2 and 4 had the largest amount of
ILT and also had the most profound decrease in peak wall
stress. In all cases, the presence of ILT markedly altered wall
stress distribution (Fig 4). Incidentally, the magnitude of
von Mises stress in ILT was much lower than the stress in
the walls in all AAAs (Table III). In each case, this peak
stress was well below what we have shown to be the failure
strength of ILT, 54 N/cm2.7
DISCUSSION
In this paper, we examined the hypothesis that the
presence of ILT affects AAA wall stress magnitude and
distribution in patient-specific models. On the basis of the
four representative aneurysms studied, the presence of ILT
appears to reduce peak wall stress and markedly alter wall
stress distribution (Fig 3; Table III). The degree or significance of this effect depends on the unique ILT within each
AAA. Both models with and without ILT predicted that the
peak stress would be on the posterior surface of the AAA.
When the ILT was taken into account, the location of peak
stress shifted toward the region where ILT was located.
This is consistent with autopsy studies that showed that
ILT was usually found at the site of AAA rupture.18
To our knowledge, this is the first study to evaluate the
effect of ILT on wall stress in actual 3D reconstructed AAA.
Our approach differs from previous studies in three important ways. First, a realistic patient-specific 3D virtual AAA
model was used instead of hypothetic models.9-12 Second,
nonlinear mathematic models developed specifically for
AAA tissue and ILT were used instead of linear elastic
models.9-12 Finally, patient-specific values of AAA wall
thickness were used instead of one value for all AAA models.16
Although these improvements have increased the accuracy of computational stress analyses of AAA, several limitations remain that should be kept in mind. First, the static
simulation used here does not mimic the dynamic application of intraluminal pressure, and resulting wall deformation and stress distribution, during the cardiac cycle in vivo.
JOURNAL OF VASCULAR SURGERY
September 2002
602 Wang et al
Fig 4. Comparison of 3D wall stress distribution between AAA models with and without ILT. Individual color scales
(right) indicate von Mises stress for each AAA. Both posterior and anterior views are shown for each case.
Table III. Peak wall stress for each patient with and without ILT and peak ILT stress for models with ILT
Patient
1
2
3
4
Peak stress
without ILT
(N/cm2)
Peak stress*
with ILT
(N/cm2)
Decrease
of peak
stress
ILT peak stress
(N/cm2)
Peak ILT stress to
peak wall stress
36
30
40
44
34
19
37
28
6%
36%
6%
38%
11
5
3
8
32%
26%
8%
29%
*P ⫽ .067 with Wilcoxon paired test compared with AAA without ILT.
Ideally, a model for AAA wall stress distribution would use
a dynamic pressure loading condition. However, this would
result in greatly increased mathematic complexity and computational demands yet would not alter our current conclusions. That is, for the purposes of comparison of wall
stress distribution in AAA models with and without ILT,
the worse case scenario, or maximal stress distribution in
the wall, is of more relevance than the actual temporal
variation of the stress. In addition, previous work in our
laboratory19 suggests that ILT is porous, and therefore, a
poroelastic constitutive model for ILT might be more
appropriate than a hyperelastic model. Also neglected in
our model is the likelihood that the AAA is under a degree
of longitudinal tension in vivo. However, no quantitative
information about this is available. Therefore, residual or
pre-stresses were not included in our model. Neither the
presence of calcified plaques nor the contact of AAA with
the vertebral column and other internal organs were included in our models. However, although the presence of
longitudinal tension, calcified plaques, and vertebral contact is likely to effect the wall stress in AAA,10 the purpose
of this study was to investigate the effect of ILT on wall
stress distribution. Therefore, the effect of neglecting these
would be similar in both models with and without ILT, and
our conclusion would remain valid. The AAA wall and ILT
were assumed to be homogeneous isotropic materials in
JOURNAL OF VASCULAR SURGERY
Volume 36, Number 3
this study. Preliminary evidence from our group suggests
that AAA wall may be an aniso …
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