COMPUTATIONAL ASSESSMENT OF INTRA-CRANIAL ANEURYSM

DEPARTMENT OF BIOMEDICAL ENGINEERING, THE UNIVERSITY OF IOWA

CFD Analysis of Intracranial Aneurysms

51:155 Cardiovascular Fluid Dynamics

James Arter, Austin Ramme & Brian Walsh 12/4/2009

December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme &

Brian Walsh

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Abstract Intracranial aneurysms are pathologic dilations of the vasculature within the skull that have prevalence between 2-6.5% in the

general population. The severe consequences (i.e. severe disability or death) of aneurysm rupture have motivated research into

factors that may increase the risk of aneurysm rupture. The goal of this study is to relate aneurysm height to neck ratio with

wall shear stress values and changes seen in the fluid dynamics of an intracranial aneurysm. We have developed five fluid

dynamics finite element models to simulate how changes in an aneurysm's geometry affect vascular fluid dynamics and the wall

shear stresses in the aneurysm. Our simulations indicate an increasing pattern of wall shear stress does correspond with the

increasing height to neck ratios. It would be difficult to argue that increased risk of rupture was solely caused by height to neck

ratio increases, but it would be reasonable to suggest an association between an increase in wall shear stress (due to large height

to neck ratio) and rupture risk.

I. Introduction

A. Our Patients

Patient 1: Mrs. X is a 50 year old woman who presents to

her family physician complaining of a three day history of

recurrent stabbing headaches directly behind her eyes. She

also reports photophobia, nausea, and vomiting associated

with the headaches. On further questioning, Mrs. X reveals

that she is a long-term victim of spousal abuse. In fact, the

onset of symptoms aligns with the most recent incident

where her partner stuck her with a closed fist. Her past

medical history is significant for a "small aneurysm in her

head" that had been incidentally identified several years

back. It had been described as "nothing to worry about."

She reveals a family history of three relatives that died

from a ruptured "brain aneurysm." On physical

examination, the patient appears anxious but not in acute

distress. She is oriented to person, time, and place, but

there exists a complete loss of peripheral visual fields. The

remainder of the exam is noncontributory with the

exception of several contusions consistent with the

described assault. Medical imaging studies reveal an

intracranial aneurysm of the anterior communicating artery

with an aneurysm height to neck ratio of 4.0 that appears to

be impinging on the optic chiasm. On comparison to past

medical imaging studies, the aneurysm had significantly

enlarged since the last investigation. Mrs. X desires to

know why the previous "small aneurysm" now requires

such urgent attention.

Patient 2: Mr. Y is a 35 year old man that presents to the

neurology clinic after being referred from his family

physician for an incidental finding of intracranial aneurysm

during workup for an occupational injury. Mr. Y is

completely asymptomatic. He has a family history that is

positive for unruptured "brain aneurysm." He reports

migraine with aura since the age of 3; otherwise, the review

of systems is noncontributory. Physical examination

reveals a healthy male. Medical imaging studies show an

intracranial aneurysm of the anterior communicating artery

with an aneurysm height to neck ratio of 2.6. Mr. Y

understands the tragic consequences of aneurysm rupture

and wants to better understand his rupture risk in order to

make an informed decision about his treatment plan.

B. Intracranial Aneurysms

Intracranial aneurysms are pathologic dilations of the

vasculature within the skull that have prevalence between

2-6.5% in the general population. They have also been

called saccular aneurysms due to their stereotypical

spherical shape that offshoots from a parent vessel. They

have been reported in a variety of locations within the

cerebral vasculature including the middle cerebral artery,

internal carotid artery, basilar artery, and the anterior

communicating artery1. Aneurysms of the anterior

communicating artery are most common and account for

25-38% of all intracranial aneurysms2. The anterior

communicating artery is a small artery that connects the left

and right anterior cerebral arteries and lies in close

proximity to the optic nerves. Regardless of location,

rupture of any intracerebral aneurysm will inevitably lead

to subarachnoid hemorrhage whereby half of patients die

and the other half become severely disabled3.

Most patients with intracranial aneurysms are

asymptomatic, and in most cases they will live normal lives

without complications3. However, some patients may

experience symptoms prior to rupture depending on the

size, location, and orientation of the aneurysm. The

anterior communicating artery belongs to the anterior

circulation of the cerebrum and is in close proximity to the


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optic nerves and optic chiasm. If an aneurysm is present, it

can cause visual symptoms due to compression of the optic

nerves such as visual field loss and visual dimness2.

Compression of surrounding structures can cause stabbing

cluster headaches that are often felt behind the eyes and are

associated nausea and vomiting4.

Histologically, degeneration of the vascular extracellular

matrix and degeneration of the intimal and medial

endothelial cells are indicative of cerebral aneurysms5.

Elevated levels of elastase and matrix mellanoproteinases

have been observed in patients with cerebral aneurysms and

they are believed to be partly responsible for extracellular

matrix degeneration in vascular remodeling. They have

also been shown to induce smooth muscle cell apoptosis,

which leads to arterial wall thinning. It is theorized that

smooth muscle cell apoptosis and the degradation of the

elastin and collagen fibers of the vascular extracellular

matrix are the primary components of arterial wall

weakening.

The exact mechanism of aneurysm initiation and

progression is a debated topic, but many agree they result

from mechanical weakening over time5. A specific inciting

event has not been identified, but an association between

aneurysm initiation and anatomic variation or pathologic

feature has been established. Regions of increased blood

flow (e.g. arteriovenous malformations) or regions of

increased wall shear stress (e.g. arterial bifurcations) have

been shown to have increased rates of aneurysm

development. Some animal models have shown that

increased flow and hypertension are required for aneurysm

development. The progressive weakening of the arterial

wall in aneurysm development has been correlated with

endothelium-dependent nitric oxide (NO), which has been

shown to be released in response to elevated levels of wall

shear stress. Controversy exists as to the exact mechanism,

but it is believed that aneurysm progression is the result of

a NO induced passive yield to blood pressure forces

coupled with reactive healing of the wall. The combination

of elevated forces and wall remodeling can lead to an

increasing aneurysm diameter and thinning vessel wall.

Each aneurysm has two possible outcomes: progression in

size until rupture or maintenance of size.

B. Normal Cerebral Hemodynamics

Many studies have been performed to quantify human

cerebral hemodynamic properties such as wall shear stress,

velocity profiles, and pressure. Customized computational

fluid dynamics (CFD) models, MR imaging, and ultrasound

have been demonstrated as methods of estimating in vivo

values. One of the most important anatomical structures in

cerebral hemodynamics is the Circle of Willis. The Circle

of Willis creates redundancies within the cerebral

circulation such that if part of the circulation becomes

occluded, blood flow from other contributing vessels can

maintain blood flow and prevent major damage. As long as

the Circle of Willis can maintain blood pressure at fifty

percent of normal, no infarction or death of tissue will

occur in an area where a blockage exists1. These

redundancies often introduce some turbulent flow. Flow

rates and especially wall shear stresses vary greatly

depending on location and specific patient vascular

geometries. Flow rates vary from less than 10 cm/s in

some parts of the basilar artery to nearly 100 cm/s in parts

of the middle cerebral artery1. While wall shear stresses

vary from approximately 20 dynes/cm2 in the internal

carotid artery to approximately 200 dynes/cm2 in the

middle cerebral and anterior cerebral arteries. It had been

found that areas of increased and decreased wall shear

stress can be observed in regions of high arterial curvature

and near bifurcations. Arteries with higher degrees of

curvature tend to exhibit higher wall shear stresses6.

C. Intracranial Aneurysm Hemodynamics

Numerous computational and experimental studies of

intracranial aneurysm hemodynamics have been conducted

using patient-specific vasculature geometry. The results of

3D CFD studies reveal flow patterns that range from those

that are simple and stable to those that are complex and

unstable. The simple flow patterns observed

consists largely of a single recirculation or vortex region

within the aneurysm. The complex intra-aneurysmal

hemodynamics may contain more than one recirculation

region, and have been shown to be highly dependent on the

patient-specific vascular geometry. Furthermore, intra-

aneurysmal hemodynamics does not only depend on the

aneurysm shape and size, but also on the inlet and outlet

flow patterns found in the parent vessel(s). For example,

concentrated inflow jets are found to exist when a parent

vessel flows directly into the aneurysm. These inflow jets


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have been shown to directly impact on the aneurysm,

producing local regions of elevated wall shear stress

(WSS)5. In order to allow for in vivo hemodynamic

measurements, 3D phase contrast MR imaging has been

used to view velocity and inflow hemodynamics in and

around aneurysms. The results of these studies correlate

well with most high wall shear stress theories in that the

highest wall shear stresses were found in the inlet flow

region. While both CFD and phase contrast MRI

techniques have revealed a great deal of insight into intra-

aneurysmal hemodynamics, neither technique is practical

for clinical use at this time due to the significant amount of

computational power required7.

D. Treatment Methods for Intracranial Aneurysms

Presently, intracranial aneurysms can be treated with

endovascular or surgical techniques. In 1937, Walter

Dandy performed the first surgical treatment of an

aneurysm using a vascular clip designed by Harvey

Cushing. Surgical clipping involves a craniotomy to expose

the aneurysm, and the placement of a surgical clip to close

the neck of the aneurysm. Advances in neurosurgical

techniques have allowed for the treatment of most cerebral

aneurysms, and surgical clipping remains the best way to

eliminate cerebral aneurysms. Surgical treatment remained

the predominant treatment for nearly four decades until the

development of the detachable coil (shown on the cover

page) by Gglielmi in the late 1980s. Initially, endovascular

treatment was used only in patients who were thought to be

poor candidates for surgical treatment. In the past decade,

however, endovascular treatment has become more

widespread due to new developments in endovascular

techniques. Endovascular coiling is a much less invasive

treatment involving percutaneous access and insertion of

platinum coils into the anuerysm via a catheter. When

placed in the aneurysm, the coils induce thrombogenesis

that, when successful, will eliminate the aneurysm. In

certain cases, stents are inserted as a scaffold for the coils.

While endovascular coiling is a cost effective, minimally

invasive treatment, there exists a major complication of

aneurysm reoccurrence and subsequent bleeding. Treatment

selection depends greatly on the clinical condition of the

patient, the morphology and location of the aneurysm, and

institutional expertise8.

Increased use of medical imaging has led to an increasing

number of incidental discoveries of unruptured intracranial

aneurysms, with some studies reporting prevalence as high

as 6.5% in the general population7. Most often these

incidental findings never cause a problem for the patient,

but the devastating consequences of aneurysm rupture have

made surgical intervention a debated topic. Patients and

physicians must weigh the benefits and risks of the

treatment plan for each patient. Conservative management

is considered the gold standard of treatment for

asymptomatic patients with intracranial aneurysms less

than 7 mm in size3. Treatment of intracranial aneurysm has

been shown to have an 11.5% chance of adverse outcome

with a 2.1% of chance of death during the intervention7.

Endovascular coiling has been shown to have better patient

outcomes than surgical clipping, but both carry an inherent

risk2. A patient-specific evaluation of rupture risk often

guides the management of these patients.

E. Rupture Risk Assessment

Intracranial aneurysms are not uncommon in the general

population, and for the most part will never cause a

problem for most patients. The risk of anterior circulation

intracranial aneurysm rupture, like that of our patients, has

been estimated to be between 0-0.1% per year, a seemingly

small number7. However, the severe consequences (i.e.

severe disability or death) of rupture have motivated

research into factors that may increase the risk of aneurysm

rupture. Unfortunately, aneurysm rupture risk research has

been limited to two specific patient populations: patients

that are unruptured and probably won't rupture and patients

that have already ruptured7. A human investigation of

patients following the natural history of aneurysm rupture

is blatantly unethical. With this limitation, several factors

have been linked to rupture risk using retrospective reviews

of patient medical records. Some of these relationships

include:

Symptomatic aneurysms are 4-5 times more likely to

rupture than asymptomatic aneurysms3.

Intracranial aneurysms found in the posterior

circulation are 2-3 times more likely to rupture than

those found in the anterior circulation3, 7

.

An aneurysm that is greater than 5 mm is 2-3 times

less likely to rupture than an aneurysm that is less than

5 mm in size3, 7

.


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Aneurysms showing evidence of surface irregularities

and daughter sacks are at an increased risk of rupture7.

Aneurysms originating from parent arteries with larger

diameters also tend to rupture at relatively larger

sizes1.

One relationship that has been shown to be clinically useful

and statistically significant is the aneurysm height to neck

ratio7. It has been postulated that intracranial aneurysms

with a height to neck ratio less than 1.4 are at low risk of

rupture, those with a ratio from 1.6-2.2 have a borderline

risk of rupture, and those with a ratio greater than 3.0 have

a high risk of rupture. These risk statistics have been

established based on patient outcomes.

F. Hemodynamic Modeling

Advancements in medical imaging modalities have allowed

for patient-specific reconstruction of aneurysm and

vascular geometries for CFD analysis. Numerous

computational and experimental studies have revealed a

wide variety of complex intra-aneurysmal flow patterns

that are strongly specific to the patient-specific geometries,

and thus may not correlate well with idealized models.

Furthermore, fluid-structure interaction algorithms have

been implemented to incorporate wall compliance into

CFD models. These models reveal that fluid-structure

interactions produce alterations in wall shear stress and

velocity magnitudes, but have minimal affect on flow

patterns5. Despite potential discrepancies in results,

idealized and two dimensional geometries are frequently

used for initial CFD studies due to their predictability and

minimal computational requirements.

G. Goals of This Study

Both of our patient's exhibited the most common type of

intracranial aneurysm, an aneurysm of the anterior

communicating artery; however, the presentations of the

two cases are drastically different. The first patient

definitely exhibits many of the risk factors associated with

aneurysm rupture including a very high height to neck

ratio. The second patient has very few risk factors

associated with his incidentally found aneurysm and has an

intermediate height to neck ratio. In both cases, how do we

best inform the patient of the situation so that they can

make an informed decision in regards to their treatment

plan? We've discussed many of the factors related to

aneurysm growth and rupture. However, we have not seen

a clear presentation of height to neck ratio and it's effect on

wall shear stress and flow patterns in the parent vessel and

aneurysm. The goal of this study is to relate the height to

neck ratio with wall shear stress values and changes seen in

the fluid dynamics of the aneurysm. Our second patient

exhibits a height to neck ratio that is not included on the

risk scale presented earlier. Another goal is to compare the

results using that height to neck ratio to the other values

that appear on the risk scale. We hypothesize that as height

to neck ratio increases, we will also see an increase in wall

shear stress. We all also hypothesize that as the height to

neck ratio increases, changes in fluid flow patterns will

become more apparent.

II. Materials & Methods

A. Overview

The principles of fluid dynamics can be applied to our

evaluation of anterior communicating artery aneurysms.

We have developed five fluid dynamics finite element

models to simulate how changes in an aneurysm's geometry

affect vascular fluid dynamics and the wall shear stresses in

the aneurysm. The first model simulates flow in the normal

anterior communicating artery, while the remaining models

simulate flow in saccular aneurysms with varying height to

neck ratios. In this section, we discuss the simplifying

assumptions and initial conditions used in the model. We

also discuss the model's geometry, theoretical calculations,

and the methods used to generate and simulate the five

different situations.

B. Governing Assumptions & Initial Conditions

To determine the hemodynamic characteristics associated

with anterior communicating artery aneurysms of varying

aspect ratio, idealized two dimensional models were

utilized. For each model, flow was assumed to be steady,

laminar, and fully developed in segment of the anterior

communicating artery upstream of the aneurysm. When

viewed instantaneously, flow in the human circulation is

considered pulsatile; however, when the flow is averaged

over time, it can be considered steady. In addition, laminar

flow can be considered a valid assumption as there is no

experimental evidence to suggest that sustained turbulent

flow exists in the human circulation9. While the

assumptions of steady, laminar flow are generally satisfied

in circulation, fully developed flow does not exist in

circulation. Frequent branching, curvature, and tapering of


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blood vessels do not permit flow to become fully developed

and this assumption is invalid for circulatory flow. Blood

was also assumed to behave as a Newtonian fluid. While

blood exhibits non-Newtonian behavior at low shear rates,

blood has been shown to behave as a Newtonian fluid in

relatively large blood vessels, where shear rates in excess

of 50 sec-1

exist9. Two dimensional, idealized vessel and

aneurysm geometries were also assumed to minimize

computational requirements.

The initial conditions for our models were taken from

quantitative hemodynamic studies performed by Chien, et

al.1 and Chandran, et al

9. Using computational models

reconstructed from 3D rotational angiographic images

taken from six patients with aneurysms of the anterior

communicating artery, Chien, et al. found the average

parent vessel diameter to be 2.1 mm, with an average

aneurysm neck diameter of 3.5 mm. The study also found

the average blood flow velocity through the anterior

communicating artery to be 30 cm/s. Furthermore, the

intrinsic blood properties density and viscosity were

assumed to be 1.06 g/cc and 0.035 Poise, respectively9.

C. Theoretical Calculations

As a means of comparison and for the purposes of

experimental setup, theoretical calculations were performed

to establish values for entrance length, Reynold's number

for the normal vessel, and expected wall shear stress in the

normal vessel. Reynold's number can be calculated using

equation 19:

𝑅𝑒 = ρ × 𝑉 × 𝑑

µ (1)

The Reynold's number was calculated to be 190.08 using a

blood density of 1.056 g/cm3, velocity of 30 cm/sec,

diameter of 0.21 cm, and blood viscosity coefficient of

0.035 P. The theoretical entrance can be calculated using

equation 29:

𝐿𝑒 = .06 × 𝑑 × 𝑅𝑒 (2)

The theoretical entrance length was calculated to be

approximately 2.4 cm using the calculated Reynold's

number and a diameter of 0.21 cm. The theoretical wall

shear stress in fully developed flow was determined from

using equation 39:

𝜏 = −d × ∆𝑃

4 ×L =

4 × µ ×Q

π ×R3 (3)

The theoretical maximum wall shear stress in the normal

vessel was calculated to be 40 Pa using a diameter of 0.21

cm, inlet velocity of 30 cm/s, and blood viscosity

coefficient of 0.035 P. Assuming the aneurysm to be a thin

walled, spherical vessel theoretical wall stresses within the

aneurysm can be approximated using Laplace’s Equation,

where 𝜎 is the circumferential wall stress [N/m2], t is the

wall thickness [m], and R is the radius [m]9.

𝜎 = p×R

𝑡 (4)

Thus the wall stress will increase directly with aneurysm

diameter; assuming pressure and wall thickness remain

constant. However, due to conservation of mass, wall

thinning occurs with increasing diameter, and thus this

calculation cannot be performed due to the variability in

wall thickness.

D. Model Geometry

To realistically develop a two-dimensional model of

saccular aneurysms of the anterior communicating artery,

average dimensions for that vessel were identified. The

anterior communicating artery has been described as

having an average diameter(d) of 2.1 mm with an average

aneurysm neck length(n) of 3.5 mm1. To establish fully

developed flow prior to entering the aneurysm, the

aforementioned theoretical calculations were used to

determine an entrance of length (s1, s2) of 2.4 cm which

was applied before and after the aneurysm. The length(l)

of our theoretical vessel was then equal to twice the

entrance length plus the aneurysm neck length. Our study

investigates four different aneurysms of the anterior

communicating artery with a normal anterior

communicating artery for comparison purposes. The

aneurysm height(h) was the only variable that was varied

between the cases, and this was based on the height to neck

ratio described earlier. The normal case had a height of

zero, while the four aneurysm cases were given heights of

3.5 mm, 7.0 mm, 9.1mm, and 14 mm to represent height to

neck ratios of 1.0, 2.0, 2.6, and 4.0, respectively. Figure 1

demonstrates a "generic" aneurysm with the variables

assigned.


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Figure 1: A generic 2D aneurysm displaying variables for our

four aneurysms and normal case where h = aneurysm height,

d = vessel diameter, l = length of vessel, s1 = length of

segment one, s2 = length of segment 2, and n = aneurysm neck

length. For all cases, the following values were used: d = 2.1

mm, s1 = 2.4 cm, s2 = 2.4 cm, n = 3.5 mm, and l = 5.15 cm.

The height (h) was varied between each of the cases as

follows: h = 0 cm for the normal case, h = 0.35 cm for the 1.0

height to neck ratio, h = 0.70 cm for the 2.0 height to neck

ratio, h = 0.91 cm for the 2.6 height to neck ratio, and h = 1.4

cm for the 4.0 height to neck ratio.

E. Computer Simulations

Using Gambit, the five 2D planar geometries, previously

discussed, were created to study the effects of varying

height to neck ratio on intra-aneurysm hemodynamics. For

each model created, three meshes of varying densities were

created in GAMBIT and imported into FLUENT for CFD

analysis. The initial conditions were applied in FLUENT

and a convergence study was performed for each case to

ensure appropriate mesh density. For each simulation, the

solutions were iterated until the residual for each governing

equation fell below 1E-6. From the convergence study,

mesh densities of 4000, 6883, 6863, 7000, and 6790

elements were selected for the normal, 1.0 ratio, 2.0 ratio,

2.6 ratio, and 4.0 ratio cases, respectively. The wall shear

stresses, velocity magnitudes, flow profiles, and pressures

were then analyzed for each of the five selected meshes.

III. Results

The simulation of the anterior communicating artery

without aneurysm showed a maximum wall shear stress of

approximately 3.0 Pa, a maximum axial velocity of 0.4 m/s,

and full developed flow being reached at 2.2cm

downstream (Appendix Figure A-5). A steady pressure

drop was also observed along the length of the vessel.

Figure 2: Plot of maximum wall shear stress versus height

to neck ratio of each aneurysm case. A logarithmic

trendline was fit to the data points with a correlation

coefficient of .9977.

When the various aneurysm cases were included into the

simulations, many changes related to the fluid dynamics

were noted. Uniformly across the aneurysms, the

maximum wall shear stress occurred at 2.75 cm

downstream of the vessel inlet, which corresponds to the

distal aspect of the aneurysm neck, labeled Point A in

Appendix Figure A-4. The maximum wall shear stress was

shown to increase with increasing height to neck ratio as

shown in Figure 2. The maximum wall shear stress for the

aneurysms ranged between 5.25 Pa and 5.63 Pa. When

plotted against aspect ratio, maximum WSS exhibited a

logarithmic response, as shown in Figure 2.

While elevated wall shear stresses were observed at the

distal aspect of the aneurysm neck, the wall shear stress in

the aneurysm dome significantly dropped in each of the

aneurysm cases. Larger height to neck ratios were

observed to have larger regions of low wall shear stress as

depicted in an overlap diagram in Appendix Figure A-1. It

was also noted that the vessel wall opposing the aneurysm

exhibited a drop in wall shear stress of approximately 0.5

Pa in all four cases. Figure 3 shows a typical wall shear

stress versus position plot for our aneurysm cases; the

vessel wall including the aneurysm is represented in red

and the opposing wall is represented in black.

Our simulations revealed that the pressure within the

aneurysm ranged from 80 mmHg to 90 mmHg for the

y = 0.1877ln(x) + 5.1683R² = 0.9977

0

1

2

3

4

5

6

0 1 2 3 4 5

Max

imu

m W

SS (

Pa)

Height to Neck Ratio


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examined height to neck ratios, as demonstrated in

Appendix Figure A-2. For each of the aneurysm

simulations, a maximum axial velocity of 40 cm/s was

found at the center of the artery and axial velocity

decreased as the position became closer to the wall. The

addition of an aneurysm caused a skewing of the velocity

profile as demonstrated in Appendix Figure A-3. The

amount of skew was observed to increase as the height to

neck ratio increased.

Each simulated aneurysm also demonstrated a single

recirculation zone as shown in Figure 4. Increasing height

to neck ratio affected the velocity magnitudes within the

recirculation zone with larger height to neck ratios

corresponding to larger velocity magnitudes within the

recirculation zone. The velocity within the aneurysm

ranged from 0-0.1 m/s. Appendix Table A-1 summarizes

the results of our simulation.

Figure 3: Plot of wall shear stress vs. position along longitudinal axis of the vessel. The vessel wall including the aneurysm is

shown in red, while the opposing vessel wall is shown in black. The peak wall shear stress corresponds to the neck of the aneurysm. A drop in wall shear stress is also shown at the vessel wall opposing the aneurysm.


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Figure 4: Vector diagram showing flow velocity magnitudes (m/s) and vectors for anterior communicating aneurysm of height

to neck ratio of 4.0. A large, single recirculation zone is observed within the aneurysm with minimal velocity magnitudes found

in the dome region, and larger inlet flows found at the neck.

IV. Discussion

Due to the asymmetric nature of saccular aneurysms, a 2D

axisymmetric simulation was not applicable. Thus, a 2D

planar model was used in Fluent for our simulations. The

theoretical calculations were based on the assumption that

the cross-sections of the arteries were circular, which was

not the case in Fluent. Thus, our theoretical wall shear

stress did not match well with the theoretical values for the

normal anterior communicating artery case. However, the

theoretical entrance length for the normal case did

reasonably match, within a 10% margin of, that found in

the simulation. This confirmed that fully developed flow

should be reached in our aneurysm simulations.

The normal anterior communicating artery simulation was

performed as a means of comparison for the aneurysm

cases. All simulations exhibited a pressure drop over the

length of the artery, which would be expected. However,

an interesting finding was that the pressure within the

aneurysm was uniform and did not vary based on the height

to neck ratio of the aneurysm (Figure A-2). It appeared to

correspond with the pressure found within the parent artery

at the origin of the aneurysm.

The normal anterior communicating artery reached fully

developed flow and had a velocity profile corresponding to

this. The maximum axial velocity reached in all

simulations was uniformly 40 cm/s; however, the presence

of the aneurysm resulted in a skewed flow profile with an

increased amount of skew towards the aneurysm

corresponding to an increasing height to neck ratio. The

skew is likely caused by increased flow into the aneurysm

caused by the low intra-aneurysmal pressures observed.

Furthermore, it was observed that the skewing of the flow

profile induced a WSS drop in the opposing arterial wall, as

shown by the black line in Figure 3. A detailed view of the

velocity vector profile, shown in Figure A-3, reveals that

the increase in flow into the aneurysm minimizes flow at

the opposing arterial wall, thus inducing low WSS. This is

significant in that low arterial WSS has attributed to the

formation of arteriosclerosis, which is the leading cause of

death in the United States9.


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Another common trait found in each of the aneurysm cases

was the prevalence of a single recirculation zone found

entirely within the aneurysm, as shown in Figure 4. The

velocity magnitudes found within the aneurysm were

significantly smaller (<15%) than those found within the

parent vessel. The largest intra-aneurysmal velocities were

found at the start of the recirculation zone located at the

downstream region of the aneurysm inlet. These velocities

were consistent between each aneurysm case ranging

between 4.45 and 5.55cm/s, and no direct correlation was

observed between aspect ratio and maximum intra-

aneurysmal velocity. Minimal intra-aneurysmal velocities

were found at the center of the aneurysm, where the

recirculation flow diminished. Minimal intra-aneurysmal

velocities ranged between 0.0398 and 0.0791 cm/s with

lower aspect ratios correlating to larger velocities. This is

significant in that low flow velocities induce low WSS,

which are associated with thrombus and lesion formation,

as mentioned previously. This indicates that there may exist

an association between aneurysm height to neck ratio and

thrombus formation, however, further studies will be

required to confirm this.

In the normal artery simulation, a uniform WSS of 3Pa was

observed across the vessel. However, this was not the case

in the aneurysm as demonstrated in Figures 2 and 3. Figure

2 demonstrates the maximum wall shear stress exhibited by

the normal case and the four aneurysm cases. A

logarithmic trend line best fit the data with a correlation

coefficient of 0.998. It should be noted that the normal

artery had a maximum wall shear stress that was 42.9-

44.4% lower than that of the aneurysm cases. The

maximum wall shear stress in our simulation was on the

same order of magnitude as reported in at least one other

study1. The height to neck ratio of 4.0, exhibited the largest

wall shear stress; however, there was minimal differences

in maximum wall shear stresses between the aneurysms

with a maximum of 3% variability. Despite these results, a

general trend of increasing height to neck ratio did exist.

The special case of a height to neck ratio of 2.6 was found

to have a maximum wall shear stress that was the same as

the height to neck ratio of 2.0. Based on this observation, a

ratio of 2.6 could be classified as intermediate risk if only

the wall shear stress values were considered.

As aforementioned, the maximum wall shear stress was

consistently located at the distal aspect of the neck of the

aneurysm. Our results correspond well with published CFD

experiments, which have shown that focal elevations in

WSS are largely confined to the downstream lip of an

aneurysm5. The velocity vector profiles shown in Figure 4

reveal increased flow in that region putting additional force

on the vessel wall. As previously mentioned, the minimum

wall shear stress in the aneurysm cases was found to be in

the dome of the aneurysm where values close to 0 Pa were

recorded. The flow patterns exhibited in these regions were

close to stagnant, which resulted in low forces applied to

the aneurysm dome and thus low wall shear stresses.

Our results do not support the high WSS theory of

aneurysm progression and rupture as the dome is the most

common site of rupture and our results show this to be a

location of low WSS. Furthermore, angiographically

documented cases of aneurysm growth generally show

progression of the dome with rare changes in the neck

region5. This observation is further reinforced by the low

WSS and minimal velocity magnitudes found within the

dome region, shown in Figures 4 and A-1. Figure A-1, in

particular, displays an increase in the region of low WSS

and stagnant flow with increasing aneurysm aspect ratio. It

has been shown that, due to the stagnant blood flow, in the

aneurysm dome, thrombus deposition and growth can

occur. This can be particularly dangerous as pseudo flow

patterns similar to that of non-diseased vessels may form,

which may appear normal when viewed with radiographic

angiography when, in fact, the vessel wall is highly

weakened and distended9.

As previously discussed, this study was a simplification of

reality; however, this simplification allowed our

investigation to focus on how varying the aneurysm height

to neck ratio affected the fluid dynamics of the anterior

communicating artery. In the future, additional factors

could be investigated including varying the neck width as

opposed to the aneurysm height. Pulsatile flow patterns,

curved vascular geometries, material properties of the

vessels, and aneurysms located at vascular junctions would

also be of interest. Extending our analysis to 3D patient-

specific geometries could also allow for patient-specific

risk assessment.


Brian Walsh

11 | P a g e

V. Conclusions

The maximum wall shear stress at the aneurysm neck was

noted to slightly increase with increasing height to neck

ratios. While an increasing pattern of wall shear stress does

correspond with the increasing rupture risk based on height

to neck ratios, our study does not indicate a significant

increase in wall shear stress strictly based on the increasing

height to neck ratio. It would be difficult to argue that

increased risk was solely caused by height to neck ratio, but

it would be reasonable to suggest an association between an

increase in wall shear stress (due to large height to neck

ratio) and rupture risk.

However, this study has shown that large height to neck

ratios exhibit more exaggerated effects than lower height to

neck ratios. This was directly seen in the velocity

magnitudes within the recirculation zone of the aneurysm

and the amount of the aneurysm wall exhibiting decreased

wall shear stress values. This study has also shown that

regardless of height to neck ratio, the presence of a saccular

aneurysm will cause skewing of the axial velocity profile

and a decrease in the wall shear stress in the wall opposite

the aneurysm.

Return to Our Patients:

Our results do not give a clear answer to the questions

posed by our patients. Based on our discussion of risk

factors for rupture, Mrs. X is at significant risk for

aneurysm rupture due to her family history, past medical

history, aneurysm height to neck ratio, and recent

appearance of symptoms correlated with traumatic insult.

It would be reasonable to explain that her aneurysm had

likely slowly increased in size over time. The direct blow

to her head may have further weakened the aneurysm wall,

which may have caused a recent increase in size and

sequela of symptoms. Immediate intervention is necessary

to avoid a tragic outcome. Either surgical clipping or

endovascular coiling of the aneurysm would be suitable,

but this decision would be left to a medical professional.

Studies have shown that surgical intervention will likely

resolve her symptoms2,4

.

Mr. Y appears to have a benign case of intracranial

aneurysm that is common in the general population. His

family history of unruptured aneurysm and lack of

symptoms argues against the necessity of an immediate

treatment plan. The results of our study show that his

height to neck ratio would have a similar maximum wall

shear stress to that of the intermediate risk group based on

height to neck ratios. Unless, Mr. Y is experiencing

extreme anxiety related to the aneurysm, it would be

plausible to simply follow-up with him on a regular basis to

ensure that the aneurysm is not increasing in size through

MR imaging. Again, the determination of aneurysm

rupture risk and treatment method should left to a medical

professional.


Brian Walsh

12 | P a g e

VI. References

1. Chien A, Castro MA, Tateshima S, et al. Quantitative

hemodynamic analysis of brain aneurysms at different

locations. AJNR Am J Neuroradiol. 2009;30:1507-1512.

2. Park JH, Park SK, Kim TH, et al. Anterior communicating

artery aneurysm related to visual symptoms. J Korean

Neurosurg Soc. 2009;46:232-238.

3. Lysack JT, Coakley A. Asymptomatic unruptured

intracranial aneurysms: Approach to screening and

treatment. Can Fam Physician. 2008;54:1535-1538.

4. Gentile S, Fontanella M, Giudice RL, et al. Resolution of

cluster headache after closure of an anterior communicating

artery aneurysm: The role of pericarotid sympathetic fibres.

Clin Neurol Neurosurg. 2006;108:195-198.

5. Sforza DM, Putman CM, Cebral JR. Hemodynamics of

cerebral aneurysms. Annu Rev Fluid Mech. 2009;41:91-107.

6. Cebral JR, Putman CM, Alley MT, et al. Hemodynamics in

normal cerebral arteries: Qualitative comparison of 4D phase-

contrast magnetic resonance and image-based computational

fluid dynamics. J Eng Math. 2009;64:367-378.

7. Lall RR, Eddleman CS, Bendok BR, et al. Unruptured

intracranial aneurysms and the assessment of rupture risk

based on anatomical and morphological factors: Sifting

through the sands of data. Neurosurg Focus. 2009;26:E2.

8. Qureshi AI, Janardhan V, Hanel RA, et al. Comparison of

endovascular and surgical treatments for intracranial

aneurysms: An evidence-based review. Lancet Neurol.

2007;6:816-825.

9. Chandran KB, Yoganathan AP, Rittgers SE. Biofluid

Mechanics: The Human Circulation. 2007.


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VII. Appendix

Table A-1: This table summarizes the most pertinent results from our study including velocity, wall shear stress (WSS), and

pressure values.

Case

Maximum Intra-

Aneurysmal Velocity

Magnitude (m/s)

Minimum Intra-

Aneurysmal Velocity

Magnitude (m/s)

Maximum

WSS (Pa)

Minimum

WSS (Pa)

Intra-

aneurysmal

Pressure

(mmHg)

Normal n/a n/a 3 n/a

Height to Neck Ratio 1.0 4.48E-02 7.91E-04 5.25 0 80




Figure A-1: Plots of WSS vs. longitudinal position along vessels with anuerysm of aspect ratios 1, 2, 2.6, and 4 are shown. A

schematic of the aneurysm has been incorporated to visualize location of WSS fluctuations. An increasing region of low WSS within

the aneurysm dome are observed with increasing aneurysm aspect ratio. Elevated regions of WSS are also seen at the downstream lip

of the aneurysm neck.


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14 | P a g e

Figure A-2: Static pressure profile for aneurysm of aspect ratio 4. Intra-aneurysmal pressures were consistently observed between 80

and 90 mmHg, and are greatly dependent upon inlet pressure of the parent artery.

Figure A-3: Velocity vectors colored by magnitude for an of aneurysm aspect ratio of 4. A skewing of the parent vessel flow profile is

observed toward the aneurysm, and velocity flows of 1.33m/s are observed at the inlet to the aneurysm.


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Figure A-4: Vector diagram showing wall shear stress (Pa) for the anterior communicating artery aneurysm of height to neck

ratio of 4.0. Point A displays an elevation in wall shear stress of 5.63Pa at the downstream area of the neck.

Figure A-5: Velocity magnitudes and fully developed flow profile for non-diseased anterior communicating artery observed 2.2cm

downstream of inlet. Maximum velocity magnitudes of 4.48 m/s are observed at the vessel center with decreasing velocity magnitude observed with increases radial distance, indicative of fully developed flow.

COMPUTATIONAL ASSESSMENT OF INTRA-CRANIAL ANEURYSM

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