This document discusses a computational model that was created using finite element analysis to evaluate mechanical wall stresses in abdominal aortic aneurysms (AAA). The model was created using CT scans from 6 patients and 1 control subject. The results found that normal aortic wall stresses are around 12 N/cm2, while AAA patients ranged from 29-45 N/cm2. AAA volume was found to be the best indicator of peak wall stress. This analysis could help evaluate individual AAA rupture risk and improve clinical treatment for the disease.

1.
COMPUTATIONAL MODEL EVALUATING THE MECHANICAL
EFFECTS OF ABDOMINAL AORTIC ANEURYSM
Word Count: (1780)
Prepared for
Scott Hazelwood
Biomechanics Professor
California Polytechnic State University
San Luis Obispo, California
Prepared by
Keyon Keshtgar
Biomedical Engineer
March 11 , 2015

2. 1
Abstract
With more than 17,215 deaths in the United States alone, according to a 2009 statistic conducted
by the CDC, abdominal aortic aneurysm (AAA) continues to be a problematic issue in regards to
human health. Computational models of AAA have been created to further analyze the
mechanical wall stresses in hopes to better understand this disease. Finite element analysis (FEA)
is a sophisticated numerical scheme intended to approximate the solution to common boundary
problems. The focus of this report is to highlight and discuss how FEA was used as a
methodology to demonstrate a noninvasive procedure to estimate AAA wall stress distributions
prior to rupturing. It was found that, while normal abdominal aortic wall stresses are around ​12
N/cm​2​
, the wall stresses in patients with AAA ranged from 29 N/​cm​2​
to 45 N/​cm​2​
. In addition,
the results suggest that ​AAA volume was the best indicator of peak wall stresses. This
methodology may allow for the evaluation of an individual AAA’s rupture risk on a more
biophysical level, which can help with research in the world of medicine.
Word Count (180)

3. 2
Introduction
Your heart is one of the most important organs in the human body. Essentially a pump,
the heart’s role is to direct blood flow through the circulatory system. Unfortunately, this system
may have potential complications that could ultimately be fatal if not treated. Abdominal aortic
aneurysm (AAA) is just one problematic issue in relation to the cardiovascular system. The
ability to evaluate the susceptibility of an AAA to rupture using finite element analysis could
vastly improve the clinical treatment of patients with this disease. A working principle of the
cardiovascular system and AAA will first be discussed. This report will then focus on a
methodology to noninvasively estimate wall stress distributions for patients with AAA.
Circulatory System
The heart is a muscle made up of four chambers separated by
valves, which open and close, to direct blood flow. Each half of the heart
contains one chamber called the atrium and one called the ventricle,
which can be seen in ​figure 1​. The
atria collect blood, while the
ventricles propel blood out of the heart. The right half of the
heart receives and sends deoxygenated blood to the lungs
where blood cells get replenished with new oxygen. The blood
then returns to the left half and gets propelled to the cells of
major organs to supply oxygen and nutrients. This cycle
gets repeated and is known as the circulatory system. The circulatory system consists of a

4. 3
network of blood vessels that all work coherently. The vessels that carry blood to the heart are
known as veins, while those that carry blood away from the heart are known as arteries. For the
purpose of this report, an emphasis on the abdominal aorta will be placed. It is the largest artery
in the abdominal cavity and is a direct continuation of of the descending aorta, which can be seen
in ​figure 2.
Abdominal Artery Aneurysm
An Abdominal Aortic Aneurysm (AAA) is often
defined as a dilation of the aorta artery with dilations greater
than 3 cm in diameter. This could lead to a serious and
alarming health issue. According to the CDC, aortic
aneurysms were the primary cause of 10,597 deaths and
contributed to more than 17,215 deaths in the United States
alone in 2009. Approximately two­thirds of people who
have aortic dissection are male. Showin in ​figure 3​ is a
comparison between a normal abdominal aorta versus an abdominal aortic aneurysm.
Typically, AAAs can develop slowly and are asymptomatic until they expand or rupture.
An expanding AAA causes sudden, severe, and constant low back, flank, abdominal, or groin
pain. Patients with a rupture abdominal aorta may experience symptoms, such as pain in the
abdomen or back, passing out, clammy skin, dizziness, nausea, and vomiting, rapid heart rate,
and shock.

5. 4
Historically, AAAs were repaired by ​Endovascular aneurysm repair (EVAR)​ where the
aneurysmal segments of blood vessel were replaced with vascular grafts. EVAR, however is
associated to an increased morbidity and mortality rate in comparison to other minimally
invasive endovascular repair procedures. Limitations of endovascular grafts include graft
migration, which can result in aneurysmal sac expansion. Reintervention for EVAR graft patients
typically occurs in about 15% to 19% of cases after an average of 34 months. FEA could be
applied to further understand a particular AAA and to improve the clinical treatment associated
with this disease.
Methods
Finite element analysis (FEA) is a sophisticated numerical scheme intended to
approximate the solution to common boundary problems. This method helps to predict whether a
model will break or wear out by determining mechanical stresses, vibrations, fatigue, motion,
heat transfer, fluid flow, electrostatics, etc. The typical process behind using FEA is to define the
problem, define the model, mesh the model, choose an analysis method (static/dynamic or
linear/nonlinear), and finally use a software of preference to solve the problem.
One study focused on comparing the mechanical wall stresses of six patients at the
University of Pittsburgh Medical Center to that of a healthy control subject for further analyzing
of AAA prior to rupture occurring. The 3­dimensional infrarenal aorta model geometry was
created using a spiral computed tomography (CT). Before scanning, 150 mL of standard
nonionic contrast was administered at 4mL/s. In addition, the patients were asked to hold their
breath to reduce respiratory­induced motion in the imaging. Next, a cross­sectional slicing of 2­3

6. 5
mm along the infrarenal aorta were made. The spatial coordinates of about 60 points along the
wall boundary were recorded on each cross section, which collectively made a point cloud. This
point cloud, shown in ​figure 4a​, ​allows for
a mathematical representation of the AAA
wall surface, which is used in the
computation. After further image
processing, the aortic wall was created,
shown in ​figure 4b.​ This representation,
however, includes sharp corners and would result in
artificial stress concentrations in the stress analysis. To correct this, a face­smoothing technique
in AutoCAD was used to smooth the surface of the aortic walls.
In order to be suitable for biologic soft tissue, a nonlinear mathematical model was
utilized for this study. Next, mechanical properties of a typical AAA wall were determined and
recorded. Finally, the forces and constraints on the AAA were calculated. A sphygmomanometer
was used to measure the systolic blood pressure. The proximal and distal ends of the
computerized AAA model were constrained from deforming in the longitudinal direction in
order to simulate the tethering of the AAA at the renal artery and the iliac junction. Residual
stresses that may exist in the aortic wall and forces on the posterior surface caused by the lumbar
arteries were neglected for this study. Additionally, the assumption that there was a constant
aortic wall thickness of 1.9mm for the patients with AAA and a uniform thickness of 1.5mm for
the nonaneurysmal patient was made.

7. 6
A linear correlation between peak wall stress and the clinically measureable factors, such
as AAA diameter, height, and volumes shown in ​Table I,​ were conducted through various
approaches. The diameter was defined as the maximum transverse dimension of the cross section
at any part of the model through CT scanning. The height was defined as the straight­line
distance between the centroid of the model to that of the iliac branch. Finally, the volume was
determined by calculating the area of each cross section and integrating that value over the
height of the abdominal aorta.
Results
The von Mises stress distribution on the AAA for
each subject was plotted in order to visually interpret the
computational stress analysis. The von Mises stress is a
stress index composed of nine components, which is
especially suited for failure analysis. The 3­dimensional
von Mises stress distribution on the aortic wall for each
subject is shown in ​figure 5​. It is important to note that the
artificial stress concentrations, that were created through

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longitudinal constraints at the proximal and distal edges, existed in some AAAs. These values
were much higher than the stresses in other regions of the same aneurysms. This was simply
neglected as edge effects. The grey regions in the figure represent those with artificially high
stress concentrations because of edge effects. The stress magnitude is represented by the
individual color scale with blue being the lowest magnitude and red representing the highest
magnitude.
Figure 6 ​shows the peak wall stress for
each subject and the effect of wall thickness.
Various stress analyses were done for each
subject’s aortic wall, which were when the
wall thickness was set equal to the population
mean and at the lower and upper 99% of the
confidence level. The error bars seen in the figure show the range of peak wall stress for each
case. Finally, the dashed line indicates the maximum allowable stress in a typical AAA before
it’s rupture.
Table II ​shows the statistical correlation of peak wall
stress in the AAAs of each subject with the measurable
factors, such as height, diameter, and volume. The control
aorta was excluded from these calculations. This
information is important when determining the factors that
may potentially lead to abdominal aortic rupturing.

9. 8
Discussion
In review, this study had developed and demonstrated a noninvasive method to estimate
AAA wall stress distributions between 6 patients and a control, which was a subject with a
healthy aorta. This was done by using techniques in imaging, image processing, 3D
reconstruction, and engineering mechanics. Based on the results from the FEA, AAA was
indicated to be complexly distributed with large regional variations. Peak wall stresses for for the
experimental group ranged from 29 N/​cm​2​
to 45 N/​cm​2​
, while that of the control was 12 N/cm​2​
.
From ​Table II, ​it was suggested that AAA volume was the best indicator of peak wall stresses,
which may lead to abdominal aortic rupturing.
Some of the limitations to this methodology is present mainly due to contemporary
imaging technology and a lack of experimental information. The more serious assumption made
was that there was uniform and constant wall thickness of the aorta, which isn’t necessarily true.
Some of the other false assumptions was that the mechanical properties do not vary regionally
within a given AAA, shear induced by blood flow was neglected, and possible residual stresses
were not considered. These assumptions were made at an attempt to make the computation for
the study more easily achievable.
Future work is necessary before this methodology can be used clinically to aid in the
management of AAAs. First and foremost, the limitations previously stated may be improved
upon and/or eliminated. Secondly, future studies may incorporate the contribution of thrombus,
rate of change of blood pressure, and other relevant factors to the mechanics of the problem.
Lastly, this method could be used to further understand AAAs and correlate this disease to local

10. 9
expression or suppression of genes. These studies could provide additional insight on the role of
mechanical stresses as it relates to AAAs.
Conclusion
The goal of this paper was to study a computational model relative to any biomedical
engineering application. In particular, finite element analysis (FEA) was used as a methodology
to demonstrate a noninvasive procedure to estimate abdominal aortic aneurysm (AAA) wall
stress distributions. It was found that there were significant increases in the von Mises stresses
associated with an AAA patient. This information may allow for the evaluation of an individual
AAA’s rupture risk on a more biophysically sound basis. The conclusions drawn from using
FEA is that it is a highly acceptable and useful method for analyzing failures in a given system.
This approach may be further applied to the world of medicine. Such examples include using
FEA to understand the cause of failure in total hip replacement surgeries, total shoulder
arthroplasty, and many more biomedical engineering applications.

11. 10
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