THE ROLE OF HEMODYNAMICS ON INTRALUMINAL THROMBUS ACCUMULATION
AND ABDOMINAL AORTIC ANEURYSM EXPANSION: A LONGITUDINAL PATIENT
SPECIFIC STUDY
By
Byron A. Zambrano

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering - Doctor of Philosophy
2017

ABSTRACT
THE ROLE OF HEMODYNAMICS ON INTRALUMINAL THROMBUS ACCUMULATION
AND ABDOMINAL AORTIC ANEURYSM EXPANSION: A LONGITUDINAL PATIENT
SPECIFIC STUDY
By
Byron A. Zambrano
Abdominal aortic aneurysm (AAA), the ongoing growth of the abdominal aorta at the
abdominal level is a cardiovascular disease that affects a large part of the elderly
population. Among factors affecting the AAA disease, hemodynamic forces and
intraluminal thrombus (ILT) are suggested to play important roles. Despite the effort made
to understand these roles, much remain to be learned. This suggests a need to better
understand relationships among the three factors: hemodynamics, ILT accumulation, and
AAA expansion. Specially using patient-specific information of AAA patients at different
times throughout the progression of the disease. Hence, this study used 59 computer
tomography (CT) scans from longitudinal studies of 14 different AAA patients to analyzed
the relationship between them. Various hemodynamic variables were obtained from
performing computational fluid dynamics (CFD) and Lagrangian particle method on
patient-specific lumen volumes of each AAA at each scan; ILT accumulation was
estimated by mapping changes of ILT thickness (∆ILT) between two consecutives AAA
scans, and ILT accumulation and AAA expansion rates were estimated from changes in
ILT and AAA volume, respectively. Ultimately, the relationship between local values of
hemodynamic parameters and ∆ILT was tested on each scan of each patient using
Pearson correlation coefficients. Results showed that, while low WSS was observed at
regions where ILT accumulated, the rate at which ILT accumulated occurred at the same

  = 1 ∗ 
  + 2; 	1 =
rate as the aneurysm expansion rate (Rsq=0.738;	

0.87 Âą 0.203, 2 = 10440 Âą 4335). Comparison between AAAs with and without thrombus
showed that aneurysm with ILT recorded lower values of WSS and higher values of AAA
expansion than those without thrombus. In fact, correlation analysis showed that among
all local hemodynamic parameter tested, WSS showed to be inversely correlated to ∆ILT
in approximately half of the scans from all AAA tested (52.5% of n number of scans;
n=40). Vortical structures were also studied in all AAAs (with and without ILT). Results
from this analysis showed that in aneurysms that developed thick ILTs, vortices
consistently dissipated near zones of positive ∆ILT during the diastolic phase. In these

AAAs, level of activation of platelets exposed to these vortices were estimated and results
showed that none of the highest activation level recorded in any AAAs tested reached or
exceeded the proposed activation threshold.
These finding suggest that while vortical structures might be important in convecting and
concentrating platelets and other main coagulation species (e.g. Thrombin) on regions
where positive ∆ILT is observed, these vortices might not be responsible of activating
platelets. Findings also suggest, that regardless of the platelet activation pathway, low
values of WSS might be promoting the formation of thrombus and submits the idea that
by increasing WSS levels ILT accumulation may be prevented.

Copyright by
BYRON A. ZAMBRANO
2017

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... vii
LIST OF FIGURES........................................................................................................ viii
CHAPTER 1 .................................................................................................................... 1
Introduction ................................................................................................................... 1
1.1 Specific aims ........................................................................................................ 1
1.2 Background and hypothesis .............................................................................. 4
CHAPTER 2 .................................................................................................................... 9
Construction of patient specific models of AAAs, calculation of global
geometrical parameters, and estimation of time-averaged hemodynamic
parameters ..................................................................................................................... 9
2.1 Introduction ............................................................................................................. 9
2.2 Methods ................................................................................................................. 10
2.2.1 Volumes, diameter and cross section area calculations ............................ 12
2.2.2 Growth measurements ................................................................................... 13
2.2.3 ILT morphology............................................................................................... 13
2.2.4 AAA classification accordantly to thrombus content ................................. 14
2.2.5 Computational fluid dynamic (CFD) analysis ............................................... 15
2.2.6 Relations between measurements and statistical analysis ........................ 18
2.3 Results ................................................................................................................... 18
2.3.1 Classification according to the AAA wall area covered by ILT .................. 18
2.3.2 ILT accumulation process ............................................................................. 19
2.3.3. CFD analysis .................................................................................................. 21
2.3.3.1 Blood flow pattern ...................................................................................... 21
2.3.3.2 Wall shear stress ........................................................................................ 22
2.3.4 ILT accumulation and wall shear stress relationship .................................. 24
2.3.5 AAA expansion rates and ILT accumulation rates analysis ....................... 25
2.3.6 Relationships between mean TAWSS, AAA expansion rate, and ILT
accumulation rate .................................................................................................... 27
2.4 Discussion ............................................................................................................. 28
CHAPTER 3 .................................................................................................................. 33
Association of regional ILT changes with local hemodynamic variables: TAWSS,
OSI, and vortical structures ....................................................................................... 33
3.1 Introduction ........................................................................................................... 33
3.2 Methods ................................................................................................................. 34
3.2.1 ILT thickness and its changes ....................................................................... 34
3.2.2 Vortex eduction............................................................................................... 35
3.2.3 Local hemodynamic parameters calculations ............................................. 36
3.2.4 Statistical analysis of the relationship among parameters ......................... 37
3.3 Results ................................................................................................................... 38

v

3.3.1 Vortical structures .......................................................................................... 38
3.3.2 Statistical analysis.......................................................................................... 41
3.3.3 Regional relations among hemodynamic parameters and thrombus
thickness changes .................................................................................................. 42
3.4 Discussion ............................................................................................................. 46
CHAPTER 4 .................................................................................................................. 49
Quantification of the shear history of platelets, and their association with local
changes of ILT thickness ........................................................................................... 49
4.1 Introduction ........................................................................................................... 49
4.2 Methods ................................................................................................................. 51
4.2.1 Lagrangian particle tracking method ............................................................ 51
4.3 Results ................................................................................................................... 53
4.3.1 Local association between PLAP, TFP and local changes in thrombus
thickness .................................................................................................................. 53
4.3.2 Platelet activation potential levels ................................................................ 56
4.4 Discussion ............................................................................................................. 57
CHAPTER 5 .................................................................................................................. 60
5.1 Summary of results ............................................................................................... 60
BIBLIOGRAPHY ........................................................................................................... 66

vi

LIST OF TABLES

Table 2.1 Time inverval between two consecutive scans for 14 AAAs used................. 11
Table 3.1 Correlations between ∆ILT and (a) TAWSS, (b) OSI, and (c) ECAP for each
scan of each AAA................................................................................................... 41
Table 4.1 Correlation between ∆ILT and (a) PLAP, (b) TFP for each scan of each AAA
...................................................................................................................................... 54

vii

LIST OF FIGURES

Figure 2.1 Outer volume of each of the 14 AAAs at each time-step (scan) .................. 12
Figure 2.2 AAA outer and lumen surfaces depicting the minimum distance approximation
method between these two surfaces ...................................................................... 14
Figure 2.3 Volume flow rate and pressure outlet waves imposed at the inlet and outlet,
respectively. This figure also shows the inlet and outlet extension made to the inlet
and outlet boundaries in order to avoid numerical instabilities ............................... 16
Figure 2.4 Viscosity vs shear rate predicted by using the Carreau-Yasuda viscosity model
used to capture the non-Newtonian behavior ......................................................... 17
Figure 2.5 (a) Fraction of AAA wall area covered by ILT showing classification between
AAAs with and without ILT according to the 0.2 threshold (---) (b) The ILT thickness
distribution of all AAAs at their respective last scan for each patient. .................... 19
Figure 2.6 The ILT accumulation process using: (a) Spatial distribution of ILT thickness
for patients P-8, and P-9 at all their scans, and (b) the circumferentially averaged
values of ILT along centerline. ............................................................................... 20
Figure 2.7 Color contour of magnitude of time-averaged velocity plotted at particular
longitudinal cross sections for P01, P06 and P08; respectively. Plots qualitatively
show regions of low time-averaged velocity coincide with regions that experienced
an ILT. .................................................................................................................... 21
Figure 2.8 Color-coded time averaged wall shear stress (TAWSS) for patients with and
without ILT showing lower TAWSS values on AAAs with an ILT accumulation from
those that did not developed thrombus. ................................................................. 23
Figure 2.9 mean TAWSS as function of maximum diameter of patients with (a) and
without (b) ILT deposition. ...................................................................................... 24
Figure 2.10 TAWSS of all nodal points at each scan of P08 and P09. high TAWSS and
low (cyan) or high (red) ILT thickness, and low TAWSS and low (green) or high
(yellow) ILT thickness. (It shows that ILT accumulated at areas of low TAWSS
(yellow). .................................................................................................................. 25
Figure 2.11 Linear regression shows the linear positive correlation between ILT
accumulation rate and AAA expansion rate (Rsq=0.738). (This plot shows that for
these AAAs, ILT accumulates at the same rate that aneurysm) ............................ 26

viii

Figure 2.12 Lumen and outer cross-sectional areas at regions of maximum diameter for
AAAs P6, P7, P9, and P11. (a) region of maximum diameter, (b) increasing of the
AAA cross-sectional outer area while the lumen area remained nearly constant, (c)
Values of both cross-sectional areas at different times showing the same effect. . 27
Figure 2.13 Mean wall shear stress (TAWSS) values associated for AAAs with and
without ILT associated with: (a) AAA expansion rate and (b) ILT accumulation rate.
Here it can be seen that AAAs with no ILT have an overall higher mean TAWSS
values than AAAs with an ILT accumulation. Conversely, higher values of ILT
accumulation and AAA expansion rates were recorded in AAAs with an ILT
accumulation that in turn also showed a lower mean TAWSS values. ................... 28
Figure 3.1 Estimation of ∆ILT by mapping a subset of MxN (M= centerpoints along C and
M=360) points x1 ∈ Γl using a 2D parametrization xi = xi(C, θ) which was expressed
in the 3D spatial coordinate	∆ILT(x, y, z) = ∆ILTSs, θ, θs, θ	 ..................................... 35
Figure 3.2 Locations of ∆ILT associated to local hemodynamic conditions of TAWSS,
OSI and ECAP for P10 at time-point 2 (scan 2) ..................................................... 37
Figure 3.3 Eduction of vortical structures in AAAs that showed a thrombus deposition
(P10-S01 and P05-S05). In these AAAs vortical structures form at the proximal
regions and dissipates at zones of thrombus accumulation at approximately end
diastolic. ................................................................................................................. 39
Figure 3.4 Eduction of vortical structures in AAA without an ILT accumulation (P10-S01).
In this AAA, a strong vortical structure is formed due to an stenotic area at the
proximal region. This vortex swipes the entire lumen surface promoting a high wss
environment ........................................................................................................... 40
Figure 3.5 Spatial distribution for P01-S01 and P10-S01 showing the effect of the vortical
structures on TAWSS values. ................................................................................ 40
Figure 3.6 Percentage of number of scans showing an (a) overall and a (b) strong,
moderate and weak correlations between ∆ILT and TAWSS (Pa), OSI and ECAP
(1/Pa), respectively ................................................................................................ 42
Figure 3.7 Spatial distribution of ∆ILT and TAWSS for P12 at scan 3 showing deposition
occurring at regions of low TAWSS. Here, regions of largest ∆ILT occurs within
region of lowest TAWSS ........................................................................................ 43
Figure 3.8 Spatial distribution of ∆ILT and ECAP for P12 at scan 3 showing deposition
occurring at regions of high ECAP. Here, regions of largest ∆ILT occurs within region
of higher ECAP zones. ........................................................................................... 44
Figure 3.9 Spatial distribution of ∆ILT, OSI, TAWSS and ECAP for P08 at scan 2 showing
deposition occurring at regions of high b) OSI, c) ECAP and b) low TAWSS ........ 45

ix

Figure 3.10 Spatial distribution of ∆ILT and OSI for P05 at scan 1 showing deposition
occurring at regions of high and relatively low OSI. ............................................... 45
Figure 4.1 Percentage of number of scans showing an (a) overall and a (b) strong,
moderate and weak correlations between ∆ILT and PLAP and TFP...................... 54
Figure 4.2 Spatial distribution of ∆ILT, PLAP, and TFP for P08 at scan 2 showing that
although no specific trend was found in PLAP distribution, high values of TFP
coincided with regions of positive ILT thickness changes. ..................................... 55
Figure 4.3 95th percentile values of PLAP for all the scans of PLAP for all the scans of
all AAAs ................................................................................................................. 56
Figure 4.4 Mean values of PLAP for all the scans of PLAP for all the scans of all AAAs
............................................................................................................................... 57

x

CHAPTER 1
Introduction
1.1 Specific aims
Abdominal aortic aneurysm (AAA) is the normal growth of the aorta at the abdominal
level. This cardiovascular disease that affects a large part of the elderly population can
cause death when it ruptures. In clinical practice, a maximum diameter of 5.5 cm or a
growth of 1 cm/year are thresholds that assess whether a conservative (e.g. monitoring
AAA growth) or a more aggressive (e.g. open surgery, endovascular repair) treatment
should be performed. The selection these rupture-risk assessment variables are based
on biomechanical calculations that relates variables with the probability of the wall stress
to overcome the arterial wall strength 60. Unfortunately, there have been reported cases
of aneurysms rupturing under these thresholds 21 while other AAAs remained un-rupture
despite their large size

58.

This highlights a pressing need to develop a more profound

understanding of the different aspects influencing the progression of this disease.
Hemodynamic forces that under physiological conditions are key players of the
46,

are being suggested to play an important role in the

29,33,51,66,81.

In fact, the hemodynamic tangential force or shear has

vascular arterial remodeling
progression of AAAs

been inversely associated to the progression of other aneurysms 12. For AAAs, however,
the relationship between hemodynamics and the vascular adaptation of AAA arterial wall
may not be simple in some AAAs since 75% of them are partially or fully covered by a
layer of thrombus (ILT) 44.
This layer of thrombus disrupts the direct interaction between blood flow and
vessel wall, potentially affecting the AAA wall strength and stress. In fact, some studies

1

have suggested thrombus might be promoting weakening of the arterial wall by inducing
hypoxia 74,75, leading to wall thinning, cell inflammation, apoptosis of smooth muscle cells,
and degradation of the extracellular matrix
redistributing the wall stress

10,25,34,52,54,72,77.

49,

while acting as shield, lowering and

These effects, however, are still being

debated.
Despite the potential role of ILT on the progression of the AAA disease, very little
is known about the mechanisms leading to its formation. Interestegly, all theories agree
that hemodynamic forces are important in the formation of thrombus 13,26. For instance, a
widely accepted hypothesis suggests that thrombus forms after platelets get activated
due to shear sensing and later adhere onto lumen surfaces exposed to low wall shear
stress 7. This hypothesis, however, was lately challenged, and instead a thromboactive
area activating and recruiting platelets on regions of low wall shear stress has been
postulated 9,43. Nevertheless, none of these theories are being confirmed or denied.
All these studies highlight a need to analyze the complex relationship between
hemodynamics, ITL and AAA growth that perhaps due to the lack of patient-specific
information is still poorly understood.
The Cardiovascular Tissue and Mechanics Research Laboratory (CVTM), in
collaboration with Dr. Whal Lee from Radiology department at the Seoul National
University Hospital, has gathered longitudinal CT scan images of 14 patients
retrospectively. Using the medical image data, the main objective is to elucidate:
1) The main hemodynamic variables that influence ILT accumulation and AAA
expansion rates and their relationship between them using the longitudinal images
of AAAs, with and without ILT.

2

2) The process of local thrombus accumulation and its association with local
hemodynamic conditions. Specific local hemodynamic conditions such as wall
shear stress (WSS), oscillatory shear index (OSI) and endothelium activation
potential (ECAP) will be accurately estimated by using patient specific anatomic
geometries and associated to local changes of thrombus thickness.
3) The shear history of platelets inside AAAs and their relationship with local
thrombus accumulation. This would help to investigate the origin of thrombus and
thus the role of platelets on the regional thrombus accumulation.
These objectives will be achieved by successfully completing the following aims:

Aim 1. Construction of AAA patient specific models, calculation of global geometrical
parameters and estimation of time-averaged hemodynamic parameters. This aim will
allow us to identify the main hemodynamic differences between AAAs that developed
thrombus from those that remained without significant ILT accumulation and their
relationship with ILT accumulation and AAA expansion rates. Also, by observing the
thrombus content at each time point (scan), we would be able to describe the thrombus
accumulation process.

Aim 2. Estimation and association of regional ILT changes with local hemodynamic
variables as time averaged wall shear stress (TAWSS), oscillatory shear index (OSI) and
vortical structures. This will help to associate the changes of thrombus thickness with
local hemodynamic environment. Using a correlation analysis, their association will be

3

validated with computational fluid dynamic (CFD) constructed from the retrospective data
set.
Aim 3. Quantification of the shear history of platelets, and their association with
local changes of ILT thickness This aim would help us to determine whether platelets are
activated inside AAAs (and to confirm or deny the mechanically induced platelet activation
hypothesis) and if so, the role of these platelets on the local thrombus accumulation.
By the successful completion of the presented research and with better
understanding of hemodynamics and thrombus roles in the natural history of AAAs, we
will be able to develop a reliable predictive model for AAAs, which are an essential tool in
clinical management, risk assessment, and surgical treatment of the disease.

1.2 Background and hypothesis
Abdominal aortic aneurysms, the ongoing expansion of the aorta can cause death when
it ruptures. Mechanically speaking, the rupture of an AAA occurs when the wall stresses
exerted by the hemodynamic forces overcome the wall strength of the aneurysm 60. These
hemodynamic forces that consist of two components, normal and shear, have a profound
impact on mechano-homeostasis of arterial and vascular remodeling 46. Both components
of these forces are also believed to play a key role in AAA pathogenesis 29,33,51,66,81.
Under normal hemodynamic shear levels (>1.5 Pa) [12], changes in wall shear
stress are sensed by endothelium cells on the arterial wall modifying the surface’s antiinflammatory and anti-thrombogenic response, vasoactive tone and fibroblast activity,
and extracellular remodeling

16,20,38,53,55.

Under low wall shear stress loads (<0.4 Pa),

however, wall shear stress promotes atherogenic phenotype and wall degenerative

4

processes

53,71.

Low wall shear stress and oscillatory flow are commonly found at the

distal aorta in patients with special conditions as limb amputation and spinal cord injuries,
or in patients with low physical activities. These patients have been proven to have higher
risk of AAA progression

27.

Interestingly, abnormal flow patterns such as low wall shear

stress levels, flow separation, and formation of vortex rings are flow characteristics found
even at the earliest stages of aneurysm development 8. In addition, a lowering of
hemodynamic shear stress levels were described as AAA enlarged

63.

In other types of

aneurysms, for instance intracranial, a negative correlation between hemodynamic wall
shear and surface displacement during expansion were found

12.

This negative direct

correlation, however, may not be simple to test in AAAs since 75% of them are partially
or fully covered by intraluminal thrombus (ILT) layers 44.
ILT disrupts the direct interaction between hemodynamic forces and the aneurysm
wall, and potentially affecting the AAA wall strength and stress. In fact, studies that have
compared AAA wall characteristics between those aneurysms with and without ILT
suggested that ILT may cause hypoxia

74,

wall thinning, cell inflammation, apoptosis of

SMCs, and degradation of the extracellular matrix of walls covered by thick thrombus 49,
thus weakening the wall and potentially lowering the wall tensile strength. It is suggested
though that wall weakening in regions covered by a thick thrombus is not caused by ILT
released proteases that are capable of cell degradation. It has been shown that these
enzymes released by ILT at the abluminal layer are inactive

31,

therefore, may not affect

wall strength. Similar to its influence on wall strength, ILT is also been thought to affect
wall stress. Numerical studies have found ILT to lower wall stress

10,25,34,52,54,72,77,

suggesting that its presence could prevent AAA rupture. An in vivo study, however,

5

challenged this beneficial effect of the ILT since it found no significant pressure reduction
at wall regions covered by the thrombus, suggesting no reduction in wall stress28.
Physiologically speaking, ILT is found covering the aneurysm lumen wall,
increasing its prevalence as AAA enlarges

67.

The mechanism that leads to the platelet

activation and subsequent thrombus deposition are still not well understood; however, it
is known that hemodynamic forces may also play an important role. Therefore, aim 1 will
focus in the analysis on the hemodynamic differences between AAAs with a thrombus
accumulation from those that remained free of thrombus. Additionally, since the
hemodynamic conditions are also dependent on the geometry, global values of AAA
growth rate would be used to associated these three variables.
Within the last decade, the thrombus formation and accumulation in AAAs was
thought to be caused by vortical structures that are commonly found inside AAAs

8

and

that may activate platelets by exposing them to high shear stresses 7. These activated
platelets would later adhere at lumen walls exposed to low wall shear stress near flow
recirculation zones. This theory motivated researchers to suggest potential variables to
predict the accumulation of thrombus by combining the already proposed time average
wall shear stress (TAWSS), Oscillatory shear index (OSI) and estimated the effect of the
shear history of platelets

22.

Unfortunately, these variables have not been tested

quantitatively using patient data. For this reason, aim 2 will focus on the quantitative local
association between thrombus accumulation and hemodynamic variables (as TAWSS
and OSI).
Latest studies, however, are suggesting that the activation of platelets could be
due to a thromboactive surface 9, conversely to what it was previously thought. This

6

hypothesis suggests that platelets would activated once they pass by near thromboactive
wall regions and those active particles would be carried by the main flow (vortical
structures)

8

to regions of persistent recirculation and relatively low TAWSS [37] where

they would adhere to the wall. Unfortunately, this theory is being only tested on idealized
geometries. Therefore, aim 3 would track the shear history of platelets to determine
whether platelets activates inside AAAs and thus confirm or deny the origin of the platelet
accumulation.
Biochemically and biomechanically speaking, it is known that low values of wall
shear stress would induce endothelium cells (ECs) dysfunction 18, with impairment of nitric
oxide (NO) production 5. NO has shown to be an effective inhibitor of platelet function

39

and the absent of it on the endothelium would lead to an initial thrombotic event 4.
However, it is still unknown whether the endothelium cell dysfunction would host or to
promote a thrombus accumulation.
Once the initial ILT accumulation has taken place and the thrombus has covered
lumen surface, the platelet aggregation occurs at different shear rates. At high shear rates
(> 800 sec-1), von Willebrand factor (vwf) plays a critical role due to the strong bonding
provided

32.

At low shear rates (< 600 sec-1), the aggregation mechanisms would be

highly dependent on fibrinogen biding GPIIb/IIa 40. This aggregation process, however, is
being regulated by many antithrombotic agents that have proved to be effective and shear
dependent

62.

Studies have found that fibrin surfaces degrade faster as the shear rate

increases (this has been shown to be true for the range below the 500 sec-1 shear rate)
50.

The action of these antithrombotic agents and the fact that erythrocytes-like type of

thrombus, which is usually found at the luminal layer of ILTs 1,78, is less resistance against

7

tPA-induced thrombolysis 47. The antithrombotic agents would, then, regulate the platelet
aggregation mechanism mediated by fibrinogen and would inhibit platelet accumulation
at those shear rate ranges (~500 sec-1 ). Therefore, aggregation and subsequently
thrombus accumulation would be regulated by local hemodynamic forces.
Therefore, aim 3 would also study the association between their activation level,
hemodynamic forces and regional thrombus accumulation. This would help us to
determine the role of the interaction between platelets activation and hemodynamic
conditions.

8

CHAPTER 2
Construction of patient specific models of AAAs, calculation of global geometrical
parameters, and estimation of time-averaged hemodynamic parameters
2.1 Introduction
Hemodynamic forces, intraluminal thrombus (ILT) and abdominal aortic aneurysms
(AAAs) expansion are believed to interact with each other in a complex manner during
the progression of this disease.
Regarding the hemodynamic forces-aneurysm expansion relationship, wall shear
stress or tangential hemodynamic force is being associated with atherosclerosis in human
abdominal aortas, which shares many of the mechanisms as AAAs. It has also been
associated with aneurysms growth in intracranial aneurysms

12.

However, for AAA this

relationship is not that simple because of the formation of thrombus.
Interestedly, the thrombus accumulation is also associated with low

22,82

and

oscillatory 5 wall shear stress environment and despite this hemodynamic environment is
being found in all AAAs, just 75% of them experience a thrombus deposition 44.
On the other hand, once the ILT deposition occurs, it disrupts the direct
hemodynamic-vessel wall direct relationship, not just affecting the wall stress
10,25,34,52,54,72,77

and strength 49,74,75 but also promoting AAA expansion. This expansion in

turn would change the main AAA geometrical features and thus modifying the
hemodynamic environment.
All these previous findings have been obtained by studying the relationship
between two of these three factors, indicating a close dependent among these and
highlighting the importance of studying them together. The same studies have also
indicated a need to analyze the main hemodynamic differences among AAAs without ILT

9

accumulation from those that developed thick ILTs. Hence, this chapter used longitudinal
CT scans from 14 patients to investigate the relationship among hemodynamic forces,
ILT accumulation and AAA expansion and the main hemodynamic differences between
AAAs with and without ILT accumulation. Hemodynamic forces, represented by wall
shear stress (WSS), were obtained from computational fluid dynamics; ILT accumulation
was described by ILT thickness distribution changes between consecutives scans, and
ILT accumulation and AAA expansion rates were estimated from changes in ILT and AAA
volume. Results of this analysis showed that, while low WSS was observed at regions
where ILT accumulated, the rate at which ILT accumulated occurred at the same rate as
the aneurysm expansion. Comparison between AAAs with and without thrombus showed
that aneurysm with ILT recorded lower values of WSS and higher values of AAA
expansion than those without thrombus. Findings suggest that low WSS may promote
ILT accumulation and submit the idea that by increasing WSS levels ILT accumulation
may be prevented.
2.2 Methods
Sixty-two CT scans from longitudinal follow-up studies of 14 patients (Figure 2.1), taken
at Seoul National University Hospital, were used for the present analysis.

10

Table 2.1 Time interval between two consecutive scans for 14 AAAs used
Each patient had a set of 2 to 7 CT scans. The study had access to the time interval
between scans (table 2.1). All data collection and usage were in compliance with
guidelines established by the Institutional Review Board at Seoul National University
Hospital and at Michigan State University.

11

Figure 2.1 Outer volume of each of the 14 AAAs at each time-step (scan)

2.2.1 Volumes, diameter and cross section area calculations
Each patient’s CT scan was imported to the biomedical imaging software Mimics
(Materialise, Leuven, Belgium) where lumen and AAA outer volumes (Ί0 	1nd	Ί4 ;

respectively) were segmented, and the luminal and outer wall surfaces Γ0 	and Γ4 were

extracted. Once extracted, lumen and AAA volumes were calculated between orthogonal
planes to the centerline between the lower renal branch and the iliac bifurcation levels.
The ILT volume was then estimated by subtracting the AAA outer volume (Ί4 ) minus
Lumen volume (Ί0 ).
For the maximum diameter calculation, the method of inscribed spheres [19],
which consist of calculating diameters of maximally inscribed spheres along the

12

centerline, was used. Therefore, the largest value of the diameter along the centerline
was defined as the maximum diameter.
To calculate AAA’s outer and lumen cross-section areas at the location of
maximum diameter, an orthogonal plane to the centerline at the location of the maximum
diameter was first generated 35. The intersection between the orthogonal plane, the AAA’s
outer wall and lumen wall surface were used to delineate cross section areas. After
delineating the cross-section contour, the cross-section areas for AAA and lumen were
generated and calculated.

2.2.2 Growth measurements
AAA expansion and ILT accumulation rates were estimated based on the changes in AAA
and ILT volumes between two consecutives scans as follows:
∆5
∆6

=

5789 :	57

(2.1)

6 789 :6 7

2.2.3 ILT morphology
Characterization of the thrombus content on each AAA at each time-point was performed
by using lumen and AAA outer surfaces (Γ0 	and Γ4 ; respectively). Specifically, ILT
thickness at a given point was defined as the minimum distance between these two
surfaces (Figure 2.2).
Since it was challenging to delineate the boundaries between the aneurysmal wall
and the thrombus layer using CT scans, the minimum distance approximation method
would include the aneurysmal wall thickness. Previous studies have estimated the AAA
wall thickness to be between 0.23 mm and 4.23 mm

13

24,59,72.

Therefore, a constant value

of 3.5 mm was subtracted to the initial calculation. Therefore, for given ;< ∈ 	 Γ0 	and	;= ∈
Γ4 , ILT thickness is defined as:


 > (;< )= min	‖(;= A ;< )‖ – 3.5mm,

whereas if 
 > (;< ) is positive, otherwise 
 > (;< ) is zero.

∀	;= ∈ Γ4 ,

(2.2)

Figure 2.2 AAA outer and lumen surfaces depicting the minimum distance
approximation method between these two surfaces
2.2.4 AAA classification accordantly to thrombus content
To study the relationship between hemodynamic forces, AAA growth and ILT
accumulation, each scan of each patient was classified as one with or without an ILT
content using the wall fraction of area covered by ILT criteria. The fraction was calculated
by dividing the measure of the AAA wall area covered by ILT over the surface
measurement of the AAA wall. A surface fraction threshold of 0.2 was assumed and used
as a threshold to classify AAAs in two groups: “AAAs with ILT” and “AAAs without ILT”.
Classifying scans independently rather than patients helped to increase the accuracy of
our observations since ILT can be accumulated at any time during the surveillance period.

14

2.2.5 Computational fluid dynamic (CFD) analysis
Hemodynamic variables were estimated by performing computational fluid dynamics
(CFD) simulations on each AAA’s lumen volume (Ω0 ) at each time-point (or scan). For
each computational domain, renal branches were trimmed and model were truncated
above the renal level and after iliac bifurcation to define inlet and outlets boundaries;
respectively. Since a fully developed flow assumption was used at the inlet and outlet
boundaries, the specific location of these truncations for the CFD analysis changed from
patient to patient.
Additionally, extended boundaries were created at the inlet and outlets of the flow
by approximately three times the inflow diameter in order to avoid numerical instabilities
(Figure 2.3) 6. The estimation of the extension length was done using the relationship
suggested by Wood and colleagues 79.
All lumen volumes of all patients were used except patient 4. The CT image
resolution required to obtain an accurate estimation of the WSS values for patient 4 was
not optimal; and, therefore, this patient was excluded just from the CFD analysis.
Once the computational domain was defined, models were meshed using ICEM
(ANSYS Inc, Lebanon, NH, USA). A sensitivity analysis was performed by using 4
different element sizes (0.95, 0.8, 0.6, and 0.55 mm) and by testing our variables of
interest (i.e., WSS). From this preliminary CFD analysis, a mesh of an element size of 0.6
mm was found to be optimal for this analysis. This edge length resulted in a mesh size
that ranged between approximately 5-8 millions of elements. The element size and
computational size domain obtained from this analysis are similar to what others have
reported for similar CFD analysis 5,14,22.

15

Figure 2.3 Volume flow rate and pressure outlet waves imposed at the inlet and outlet,
respectively. This figure also shows the inlet and outlet extension made to the inlet and
outlet boundaries in order to avoid numerical instabilities
Once defined the computational domain	Ί0 , continuity and the incompressible
Navier-Stoke equations were solved for velocity (C) and pressure () (Eq. 2.3 and 2.4).

GC

D∙C=0,

F( G6 + C ∙ DC) = D ∙ H + I ,

(2.3)
(2.4)

where	F, C, H and I represent the blood density, the velocity vector, the stress tensor and
the external or body force, respectively. For these simulations, the external and body
force were assumed to be zero. The stress tensor can be decomposed into: hydrostatic
() and deviatoric stress (J)
H = AK + J,
J = LM,

(2.5)
(2.6)

where the deviatoric stress can be represented as a function of the shear rate tensor (M)
and the viscosity (L). The disaggregation of red blood cells (RBCs) due to shear stresses
16

makes blood to be considered a non-Newtonian fluid with high shear-thinning. This shearthinning behavior has an impact on the flow structure, including in the fluid circulation
near the surface 37 and it was captured in the present study by using the Carreau-Yasuda
model (Figure 2.4) 36. This is mathematical defined as:
N:NO

NP :NO

= Q1 + (RS) T

UV9
W

,

S = √2M: M ,

(2.7)
(2.8)

where S , M, L4 	, LZ , R, [, 1 represent the scalar shear stress, symmetric part of the
velocity gradient, lower and higher spectrum of viscosity, the power index and the
Yasuda exponent, respectively.

Figure 2.4 Viscosity vs shear rate predicted by using the Carreau-Yasuda viscosity
model used to capture the non-Newtonian behavior

Hemodynamic simulations using FLUENT (ANSYS Inc, Lebanon, NH, USA) were
performed on each lumen model under the assumption of laminar incompressible flow
(ρ=1060 Kg/m3) with rigid walls. Idealistic time-dependent volume flow rate and pressure

17

waves were imposed at the inlet and outlets based on data presented by Olufsen and
colleagues 57 (Figure 2.3).
A time step of 0.001s (1000 time step per cardiac cycle) was chosen and the flow
field was saved every 5 time steps (200 time steps per cardiac cycle). In order to minimize
the error due to the initial condition, the first two cardiac cycles were discarded from the
analysis and the third cardiac cycle was averaged to obtain a time-average wall shear
stress (TAWSS) values. This variable is mathematically defined as follows:
\ = H]^_
`aa = \ A b\ ∙ ]^c d]^_
g

hm


eff = (h :h ) jhg ‖`aa‖	kl
i

9

(2.9)
(2.10)
(2.11)

2.2.6 Relations between measurements and statistical analysis
Statistical analyses were performed using the Matlab software (Mathwork, Natick, USA).
A linear regression was used to examine the relationship between the ILT accumulation
rate and the AAA expansion rate on AAA’s CT scans classified as with an ILT
accumulation. Additionally, the relationship between the maximum equivalent diameter
and maximum ILT thickness at the region of maximum diameter was investigated using
Pearson’s correlation coefficient for all patients.
2.3 Results
2.3.1 Classification according to the AAA wall area covered by ILT
In order to understand hemodynamic differences between AAAs with an ILT accumulation
from those that did not show ILT, each patient was analyzed according to the area
covered by thrombus. Results from this analysis showed that 5 patients presented a

18

significant ILT accumulation from the beginning of the surveillance study (P4, P10, P11,
P13, P14), 4 patients showed an ILT buildup while AAAs were under surveillance (P5,
P6, P8, and P9), and 5 patients were found not to show any significant ILT accumulation
(P1-P3, P7, and P12; Figure 2.5 a). The ILT thickness distributions of patients at their last
scans are shown in Figure 2.5 b.

Figure 2.5 (a) Fraction of AAA wall area covered by ILT showing classification between
AAAs with and without ILT according to the 0.2 threshold (---) (b) The ILT thickness
distribution of all AAAs at their respective last scan for each patient.

2.3.2 ILT accumulation process
In AAAs that showed an ILT buildup, observed spatial distribution of the ILT
thickness through time showed that all followed a common development pattern (Figure
2.6). Specifically, all ILTs began as a localized buildup at the region of maximum diameter.
From this region, ILTs spread to the surrounding areas at the same time as an increase
in ILT thickness was observed on areas previously covered by ILT. This process occurred
gradually as the aneurysm expanded. Sequential 3-D images (Figure 2.6a) and
circumferentially averaged values of ILT thickness plotted in the longitudinal direction

19

(Figure 2.6b) demonstrate this ILT growth pattern in patients P-8 and P-9 as an example
of the common pattern found in all patients with an ILT buildup. Note that in both patients,
the location where the thrombus was the thickest varied throughout the scans but was
located within regions of maximum diameter.

Figure 2.6 The ILT accumulation process using: (a) Spatial distribution of ILT thickness
for patients P-8, and P-9 at all their scans, and (b) the circumferentially averaged values
of ILT along centerline.
A positive correlation coefficient between maximum ILT thickness and maximum
diameter was found for all patients with ILT, which agrees with the above described
accumulation process (r=0.681, P<.001).

20

2.3.3. CFD analysis
2.3.3.1 Blood flow pattern
Results from CFD analysis performed on all aneurysms showed some similarities and
differences in the blood flood pattern between AAA’s that showed an ILT deposition from
those that did not develop it. While recirculation zones inside the sac region that formed
after peak systolic and in some cases remaining through the cardiac cycle was commonly
observed among them, the magnitude of the velocity of these recirculation zones near
the lumen wall showed to be lower in AAAs that developed ILT from those that remained
without a significant accumulation.

Figure 2.7 Color contour of magnitude of time-averaged velocity plotted at particular
longitudinal cross sections for P01, P06 and P08; respectively. Plots qualitatively show
regions of low time-averaged velocity coincide with regions that experienced an ILT.

An illustration of this is shown in Figure 2.7 when the magnitude of time-averaged
velocity is plotted at specific longitudinal cross sections for 3 AAAs (P01 at scans 1 and
2, P06 at scans 2 and 3, and P08 at scans 4 and 5). From P06 and P08 it can be clearly
seen that regions of low time-averaged velocity coincided with the regions of ILT
accumulation. Another illustration of this trend is showed by P01 that experienced high
21

magnitude of time-averaged velocity near the wall in most of its lumen surface except at
a small region; the same region at which, ILT accumulation was later seen. From the
cross-sectional analysis (not shown here), it was also found that the direction of the flow
at regions near the wall areas covered by ILT was dominantly aligned with the normal
flow direction (from proximal to distal). However, reverse flow was seen at these areas at
certain scans; nevertheless, these reverse flows realign with the normal flow direction at
the following scans.
2.3.3.2 Wall shear stress
Differences in flow pattern found between AAAs with and without significant thrombus
depositions were reflected in the TAWSS values. Figure 2.8 illustrated this effect by
comparing TAWSS between 4 AAAs and a Healthy aorta. Results show that despite the
fact that low TAWSS values were found in all AAAs in comparison to the healthy aorta;
these values were lower in those aneurysms at the time that they developed a thick ILT.
This trend was also captured when values of TAWSS at all AAAs’ time points (scans)
were average over the entire lumen surface, namely called “mean TAWSS”, and plotted
as a function of its maximum diameter.

22

Figure 2.8 Color-coded time averaged wall shear stress (TAWSS) for patients with and
without ILT showing lower TAWSS values on AAAs with an ILT accumulation from
those that did not developed thrombus.

Figure 2.9a and Figure 2.9b shows these mean TAWSS values for groups of AAAs
without and with ILT accumulation respectively. From these plots, it can be observed that
AAAs with ILT deposition recorded lower mean TAWSS values than those without an ILT.
Also, while a decreasing mean TAWSS trend as diameter increases was found in all AAAs

23

without ILT but patient P12 (Figure 2.9a), AAAs with ILT accumulation showed nearly
constant values of TAWSS at larger diameters (Figure 2.9b).

Figure 2.9 mean TAWSS as function of maximum diameter of patients with (a) and
without (b) ILT deposition
2.3.4 ILT accumulation and wall shear stress relationship
The relationship between the ILT accumulation process and TAWSS was studied by
plotting TAWSS values and ILT thickness for all lumen surfaces’ nodal points of each
AAA at each scan. Figure 2.10 illustrates the results for P8 and P9 and shows that ILT
accumulated at areas of low TAWSS (yellow). It also showed that as ILT accumulates,
the values of wall shear stress fluctuate within a low range. This trend was followed for
all AAAs that developed significant ILT.

24

Figure 2.10 TAWSS of all nodal points at each scan of P08 and P09. high TAWSS and
low (cyan) or high (red) ILT thickness, and low TAWSS and low (green) or high (yellow)
ILT thickness. (It shows that ILT accumulated at areas of low TAWSS (yellow).
2.3.5 AAA expansion rates and ILT accumulation rates analysis
Using 29 samples from the group of AAA scans classified as “with an ILT”, a linear
regression was conducted for the ILT accumulation rate and AAA expansion rate, which
  = 1 ∗ 
  + 2; 	1 =
revealed a positive linear correlation (Rsq=0.738;	
0.87 Âą 0.203, 2 = 10440 Âą 4335; Figure 2.11). A statistical test of the null hypothesis

that the slope of ILT accumulation rate is 1 from the result of linear regression gives us
the value of t-statistics as 0.591 with the corresponding p-value as 0.559. This indicates
that the ILT accumulation rate is statistically not different from the aneurysm expansion

25

rate (t=0.591, P=0.559). In other words, it was found that ILT accumulates at the same
rate as the aneurysm expands.

Figure 2.11 Linear regression shows the linear positive correlation between ILT
accumulation rate and AAA expansion rate (Rsq=0.738). (This plot shows that for these
AAAs, ILT accumulates at the same rate that aneurysm)
This finding and the positive correlation between ILT thickness and diameter reported
above suggest that ILT might be occupying the expanded AAA areas, thus maintaining
the lumen cross-section nearly constant. To confirm this, AAA and lumen cross-sectional
areas at the region of maximum diameter were determined (Figure 2.12a). Analysis
showed that, while the AAA cross-section area increased, the lumen cross-section area
remained nearly constant. This relation is qualitatively (Figure 2.12b) and quantitatively
(Figure 2.12c) shown for sequential scans at the region of maximum diameter for patients
P-6, P-8, P-9 and P-11

26

Figure 2.12 Lumen and outer cross-sectional areas at regions of maximum diameter for
AAAs P6, P7, P9, and P11. (a) region of maximum diameter, (b) increasing of the AAA
cross-sectional outer area while the lumen area remained nearly constant, (c) Values of
both cross-sectional areas at different times showing the same effect.

2.3.6 Relationships between mean TAWSS, AAA expansion rate, and ILT
accumulation rate
Results from mean TAWSS confirmed that AAAs classified as with an ILT showed lower
mean TAWSS values than those that were classified as without ILT (Figure 2.13a-b).

27

(a)

(b)

Figure 2.13 Mean wall shear stress (TAWSS) values associated for AAAs with and
without ILT associated with: (a) AAA expansion rate and (b) ILT accumulation rate. Here
it can be seen that AAAs with no ILT have an overall higher mean TAWSS values than
AAAs with an ILT accumulation. Conversely, higher values of ILT accumulation and
AAA expansion rates were recorded in AAAs with an ILT accumulation that in turn also
showed a lower mean TAWSS values.

Comparing the results of mean TAWSS and the AAA expansion rate for these two
groups of AAAs, it was observed that the highest expansion rates were recorded in
patients that showed an ILT accumulation and lowest mean TAWSS values (Figure
2.13a).
A similar pattern was found when mean TAWSS values were compared to ILT
accumulation rates (Figure 2.13b). Similar to the AAA expansion rates, the highest ILT
accumulation rates were recorded at aneurysms with low mean TAWSS.
2.4 Discussion
This study used longitudinal CT images from 14 different patients and analyzed the
relationship between the ILT accumulation process, wall shear stress changes, and AAA
expansion. Results showed that the ILT accumulation process began at a localized region
of maximum diameter and spread to neighboring regions while ILT continued to thicken
at previously covered areas. While low wall shear stress showed to be a common feature
on the regions where ILT deposition occurred, the rate at which ILT accumulated occurred

28

at the same rate as the aneurysm expansion. Comparison between AAAs with and
without thrombus showed that aneurysm with ILT recorded lower values of wall shear
stress and higher values of AAA expansion than those AAAs free of thrombus.
The dynamics of the ILT accumulation process is here described for the first time
using a macroscopic perspective. Briefly, ILTs were most often found accumulating
eccentrically in the AAA

42,

and their localization and initial accumulation were both

observed in regions of maximum diameter. The continuous ILT thickening and outward
spreading pattern described here agrees with the hypothesis that the luminal layer is
active and interacts with the main blood flow, which might enhance further thrombus
accumulation 31.
The ILT accumulation process described above for AAAs that showed an ILT
buildup in conjunction with the positive correlation seen between ILT thickness and
diameter suggests that ILT accumulates at the AAA regions that have expanded,
agreeing with what Wilson and colleagues

78

hypothesized. Therefore, it is expected to

find larger ILT volumes at larger diameters, as it was found by Hans and colleagues

42.

This trend, however, cannot be generalized for all aneurysms since our results showed a
few AAAs that despite their large size, were found free of thrombus. Interestingly, in these
AAAs, mean TAWSS values were higher than in those AAAs that developed a thick ILT.
This result suggests that high values of wall shear stress would prevent the ILT from
accumulating. It has been previously proposed that increasing the values of wall shear
stress would attenuate AAA growth

51.

Our results would additionally suggest that by

increasing wall shear stress values e.g., by exercising, ILT deposition could also be
prevented.

29

On the other hand, once this ILT process begins, it accumulates at the same rate
that AAA expands; maintaining the lumen area nearly constant. This nearly constant area
would also impact hemodynamic conditions. In fact, our results showed that values of
TAWSS on average would remain nearly constant on aneurysms of larger diameters. In
other words, all these findings indicate that while low values of wall shear stress are
promoting ILT accumulation; the thrombus accumulation may be at the same time
modifying values of wall shear stress.
The effect of ILT on AAA prognosis has also been studied by other using different
approaches10,25,34,49,52,54,72,74,77 and the possible association between thrombus
accumulation and AAA growth has been proposed

70.

Our results agree with the

suggestion of an association between ILT and AAA growth since higher values of
aneurysm expansion rate were recorded on AAAs with an ILT accumulations in
comparison to those that remained free of thrombus. It is worth noting that these AAAs
that showed higher expansion rate values were in turn AAAs that showed lower values of
wall shear stress.
The positive association between aneurysm size and AAA expansion has been
widely proposed and the relationship between wall stress and strength is expected to be
linear and gradually changing as the aneurysm progresses

14,73.

The hemodynamic

forces, however, responsible of imposing the wall shear stress also change 29,30,63. Albeit
multiple hemodynamic factors (oscillatory shear index, endothelial cell activation potential
or thrombus activation potential5,22) along with the wall shear stress have been proposed
as key factors in the accumulation process and further AAA expansion.

30

Once ILT is initially adhered to the lumen wall, it would enhance the adhesion of
new fresh thrombus at regions where wall shear stress is favorable for its adhesion (low
WSS regions). This adhesion would in turn activate proteolytic degradation with stressmediated growth

7

that modifies the AAA wall stress and strength

10,25,34,49,52,54,72,74,77.

Therefore, as AAA expands, ILT would accumulate and spread throughout the AAA sac
modifying the wall stress-strength relationship strongly. At the same time, the ILT
accumulation would promote a reduction of the lumen passage, which in turn would have
an impact in the hemodynamic conditions. These hemodynamic conditions would be
lowering gradually as AAA expands and thus promoting further accumulation. In
summary, once ILT begins to accumulates, it would slowly impact the wall-strength
relationship and potentially enhancing AAA expansion while modifying wall shear stress
levels. This WSS level would be also modified by AAA expansion
Like most human studies, this investigation had limitations that need to be
considered while interpreting the results. This study used sequential CT scans from 14
patients, and it would be ideal to increase the sample size to reach stronger conclusions.
Additionally, it was difficult to accurately differentiate the aneurysm wall from the thrombus
layer 68. This required the summation of ILT and AAA wall thicknesses and that a uniform
3mm AAA wall thickness was assumed for analysis. This assumption could have over- or
underestimated the value of the ILT thickness. The results for hemodynamic simulations
of this study were obtained based on volumetric flow rate of a young healthy aorta.
Although the volumetric flow rate and pressure wave as inlet and outlet are commonly
used for setting up the boundary conditions 6,7, the evolution of AAA may have effects on
the total rate or profiles of inlet and outlet flow and quantitative measurements of flow

31

rates for individual patients will be needed for better estimation of the blood flow. Also,
while a laminar flow assumption was made in these hemodynamic simulations relying on
a global Reynolds number estimated at the inlet, there is a possibility that flow might
become turbulent at some regions during cardiac cycle. Despite the limitations that these
assumptions could have instilled, results in this study are consistent with previous
findings.
In closing, this study used longitudinal studies of 14 patients and analyzed the
relationship between ILT accumulation, wall shear stress and AAA expansion. The
findings presented explained the ILT accumulation process and showed that ILT
accumulated at the same rate as the AAA expansion rate. Additionally, our results support
the idea that suggests that low wall shear stress level would promote ILT deposition and
submits the hypothesis that by increasing wall shear stress levels thrombus accumulation
inside AAA can be avoided.

32

CHAPTER 3
Association of regional ILT changes with local hemodynamic variables: TAWSS,
OSI, and vortical structures
3.1 Introduction
In our previous analysis, we showed that lower values of mean TAWSS were recorded in
AAAs with ILT deposition in comparison to those without ILT. This suggests a potential
relationship between TAWSS and ILT deposition. Motivated by this finding, a local
association between the local hemodynamic environment and local changes in thrombus
was explored.
Previous studies have analyzed this association at specific AAA regions5,22,23,
proposing different hemodynamic variables to be important in the ILT accumulation
process. For instance, some studies have suggested that variables as TAWSS
oscillatory shear index (OSI) 5, and endothelium activation potential (ECAP)

22

26,82,

could

potentially being used to predict the ILT accumulation process.
Recent other studies suggested that vortical structures might play an important
role in thrombus accumulation [27]. However, it is not well understood mechanisms by
which the vertical structure enhances to transport the activated platelets to distal AAA
regions where thrombus accumulation and how those vortical structure is related to
hemodynamics parameters.
Those previous results from these analysis, however, are still inconclusive
because of the small data. There is, hence, a need to test multiple hypotheses on various
hemodynamic variables using a large data set and thus clarify the potential association
between each local hemodynamic variable and local changes in ILT. Specially using high-

33

resolution patient-specific information of the changes in thrombus accumulation
associated to local hemodynamic conditions.
In this chapter, the local association among all the above proposed parameters
(i.e. vortical structures, WSS, OSI, and ECAP) and local changes of thrombus thickness
was analyzed to test their potential associations to the thrombus accumulation process.
Results from the analysis in this chapter revealed that vortical structures that typically
form at the proximal AAA regions were found to consistently dissipate near zones where
positive changes in ILT thickness were recorded. On these lumen wall regions, correlation
analysis showed that among all tested hemodynamic variables, TAWSS showed to be
the most correlated.
3.2 Methods
3.2.1 ILT thickness and its changes
The ILT thickness distribution (	
 > (;< )) projected on either AAA outer or lumen surface
at each scan “n” of each AAA was estimated in our previous analysis. Here, we used these
values to quantify the changes of ILT thickness (∆
). These changes (∆
(;< ) =

	
 >og (;< ) A 
 > (;< )) were estimated by mapping 
 > (;< ) at time-point “n” to


 >og (;< ) at the next time point “n + 1” (Figure 3.1). To map from the point ;> to ;>og ,
we utilize the AAA centerlines previously generated and a 2D parametrization ;> =

;> (f, p). Here coordinates S and p represents the length along the centerline and

circumferential angle; respectively. Thus, a subset of MxN points ;< ∈ Γ0 were chosen,
(where M=number of center-points along the centerline and N=360) to estimated and
express ∆
 in the 3D spatial coordinate ∆Kqr(;, s, t) = ∆Kqr(f(u, θ), θ(s, θ)	).

34

Figure 3.1 Estimation of ∆ILT by mapping a subset of MxN (M= centerpoints along C
and M=360) points vg ∈ w0 using a 2D parametrization v > = v > (x, p) which was
expressed in the 3D spatial coordinate	∆
(v, y, z) = ∆
(f(u, p), p(u, p)	)
3.2.2 Vortex eduction
These are coherent structures that commonly appear in large arteries (Re > 100)

8

and

might be responsible for the particle transport (like RBC, WBC and platelets) and for the
mixing chemical species in AAAs. These particle transports might influence the thrombus
accumulation process. Up to date, the exact mathematical expression that defines these
vortices are still debated. The most common method used to characterize vortical
structures is known as “λ2 method” 48. This method defines vortical structures as regions
of non-zero vorticity surrounding a pressure minimum. This is achieved by using the
reduced form of the Navier Stoke equation (Eq. 6). This reduced form is obtained by
taking the gradient of the Navier-Stoke equation and by dropping the inertial and viscous
terms:

g

Mm + {m = A | D(D),

35

(3.1)

where:
DC = M + { ,

g

g

M = (DC + DCh )										and													{ = (DC A DCh ),
m

m

(3.2)
(3.3 a-b)

where M	and	{ represent the symmetric and antisymmetric parts of the velocity gradient
tensor. This method defines vortices as regions with negative eigenvalues of the
tensor	Mm + {m . Since this tensor is symmetric, eigenvalues will be always real. Then if

Rg , Rm , R~ 		are the eigenvalues of this tensor and ranking these eigenvalues as	Rg > 	 Rm >

	R~ 		, the vortices is visualized when Rm < 0.

3.2.3 Local hemodynamic parameters calculations
Estimation of local hemodynamic variables such as TAWSS and oscillatory shear index
(OSI) were obtained through computational fluid dynamics (CFD) to lumen all volumes
from all AAA’ scans (n=40; Figure 1.1). These variables represent the time averaged
magnitude and direction of the shear stress vector; respectively. The mathematical
definition of OSI is defined as follows:
g

€f = m 1 A

„i

‚j„9 `aa	ƒ6‚
„i

j„9 ‖`aa‖	ƒ6

…

(3.4)

this variable ranges between 0 and 0.5, where Its maximum value represents a purely
oscillatory flow with equal magnitude of WSS in both direction, while its lower value
represents unidirectional flow condition.
An additional parameter that measures susceptibility of the endothelium cell to
promote thrombus accumulation called “endothelial cell activation potential” (ECAP) 22,23
is being proposed to better predict the accumulation of thrombus. This metric is defined
as the ratio of the two previously defined indexes (e.g. TAWSS and OSI) as follows:

36

†x‡ =

ˆ‰Š

h‹Œ‰‰

.

(10)

Figure 3.2 Locations of ∆ILT associated to local hemodynamic conditions of TAWSS,
OSI and ECAP for P10 at time-point 2 (scan 2)

The hemodynamic parameters (TAWSS, OSI, and ECAP) were plotted for P10 in
S02 and ∆Kqr is estimated from S02 to S03, shown in Figure 3.2.

3.2.4 Statistical analysis of the relationship among parameters
The relationship between local hemodynamic parameters at time point “n” and changes
in thrombus thickness from 
 > (;< ) to 
 >og (;< ) (Figure 3.2) was tested on each AAA
at each time-point. AAA at each time-point. A Pearson correlation coefficient per scan
was computed using a subset of nodal points that was used to record changes in ILT
thickness (∆
  0). This resulted in a table of 40 correlation coefficients describing the
relationship between hemodynamic and thrombus parameters at each time-point. The
calculation of coefficients is performed using the Matlab software (Mathwork, Natick,

37

USA). Each correlation coefficients was classified as strong (r >0.5), moderate
(0.3<r<=0.5), and weak (0.1<r<=0.3) according to guidelines provided by Cohen et al 19.
3.3 Results
3.3.1 Vortical structures
Our results showed that vortices that formed at the proximal regions during the systolic
phase (figure 5), were later detached from the wall, transported downstream where they
broke-up and dissipated during the diastolic phase. An illustration of these vortical
structure pattern is shown in Figure 3.3a for AAA P10 at scan 01. Here it can be seen a
large vortical structure that formed at the proximal region, translated while splits in smaller
vortices, and dissipated at regions where positive changes in ILT thickness was observed.
Another similar example is shown for AAA P05 at scan 05 (figure 3.3b.), however, this
AAA showed multiple large vortices forming at the proximal region that split in smaller
vortices. Nevertheless, all these vortices also dissipated at regions of positive ILT
thickness changes.

38

Figure 3.3 Eduction of vortical structures in AAAs that showed a thrombus deposition
(P10-S01 and P05-S05). In these AAAs vortical structures form at the proximal regions
and dissipate at zones of thrombus accumulation at approximately end diastolic.

Similarly to AAAs that showed an ILT accumulation, vortical structures were also
seen in AAAs that did not show thrombus deposition. In these AAAs, however, vortical
structures showed to be stronger than in AAAs that showed thrombus accumulation,
swiping the majority of the AAA luminal wall. Figure 3.4 shows vortical structures pattern
for P01 at scan 01. This AAAs showed that due to the stenotic region found at the proximal
part, a strong vortex forms during the peak systolic (t=0.25). This vortex moves and
sweeps most of the lumen surface during the rest of the cardiac cycle.

39

Figure 3.4 Eduction of vortical structures in AAA without an ILT accumulation (P10S01). In this AAA, a strong vortical structure is formed due to an stenotic area at the
proximal region. This vortex swipes the entire lumen surface promoting a high wss
environment
These differences vortical structure patterns could affect TAWSS values. This is seen in
figure 3.5 in which spatial distribution of TAWSS is shown for AAAs with (P10 S02) and
without (P01 S01) a thrombus accumulation. Here it can be seen that while P01 the
vortices that swipes the entire lumen surface influence values of TAWSS in comparison
to the AAA that experience a dissipation of the vortex formed at the proximal region.

Figure 3.5 Spatial distribution for P01-S01 and P10-S01 showing the effect of the
vortical structures on TAWSS values.

40

3.3.2 Statistical analysis
Results from the correlation coefficient analysis to test the local relationships between
hemodynamic parameters (TAWSS, OSI, ECAP) and ∆
 on each AAA at all time-points
was performed and it is presented in Table 3.1

Table 3.1 Correlations between ∆ILT and (a) TAWSS, (b) OSI, and (c) ECAP for each
scan of each AAA

Results from the analysis showed that among all the proposed parameters,
TAWSS not just showed an overall inverse correlation in most of AAAs’ scans, but also
recorded stronger correlations in comparison to the other variables. Specifically, from all
the scan tested (n=40), approximately half of them (52.5%) depicted an overall inverse
correlation (Figure 3.6a). This overall correlation included strong, moderate and weak
correlations (7.5, 10 and 35%; respectively; Figure 3.6b).

41

Figure 3.6 Percentage of number of scans showing an (a) overall and a (b) strong,
moderate and weak correlations between ∆ILT and TAWSS (Pa), OSI and ECAP
(1/Pa), respectively
Another variable that showed similar results was ECAP. Correlation coefficients
also showed an overall direct correlation in 52.5% of the tested scans, however, less
scans showed to be strongly correlated (2.5% of scans; 3 vs 1 strongly correlated scans)
in comparison to the correlations found when ∆
-TAWSS relationship was tested.

Lastly, results from the correlation analysis performed to test the ∆
-OSI relationship
showed that 30% of the tested scans showed an overall direct correlation.

3.3.3 Regional relations among hemodynamic parameters and thrombus
thickness changes
Spatial distribution of the proposed hemodynamic quantities estimated at times n were

qualitative analyzed in regions where positive changes in thrombus thickness (∆
 > 0)

between times n and n + 1 were observed. This analysis revealed common trends in some

hemodynamic parameters. This is the case of the TAWSS that showed to be consistently
low in regions of positive ∆
 (TAWSS < 0.4 Pa; Figure 3.7). As an example, we have
P12 at scan 3 showed that regions of positive thrombus accumulation (∆
>0) correlated

42

with regions of low TAWSS. Interestingly, some of the region largest accumulation
occurred at region of lowest TAWSS (Figure 3.7).

Figure 3.7 Spatial distribution of ∆ILT and TAWSS for P12 at scan 3 showing
deposition occurring at regions of low TAWSS. Here, regions of largest ∆ILT occurs
within region of lowest TAWSS
Similar to the relationship to TAWSS, local changes in thrombus were also
qualitative associated to estimated values of ECAP. Results of this analysis showed that
in some scans of some AAAs, regions of positive ∆ILT were associated to high values of
ECAP. As an illustration, we have P10 at scan 2 (Figure 3.8) that shows regions of
positive accumulation at zones where high values of ECAP were recorded. Similar to
TAWSS, higher values of ECAP also coincided with regions of larger accumulation on
these AAAs (Figure 3.8).

43

Figure 3.8 Spatial distribution of ∆ILT and ECAP for P12 at scan 3 showing deposition
occurring at regions of high ECAP. Here, regions of largest ∆ILT occurs within region of
higher ECAP zones.
Spatial distribution of OSI was also qualitative associated to ∆ILT.

As an

illustration of the association found we have P08 at scan 2 (Figure 3.9). This AAA at that
specific scan (S02) shows that positive values of ∆ILT are seen at regions where high
values of OSI were also observed. This AAA also showed to be qualitative associated to
regions of low values of TAWSS (Figure 3.9c) and high values of ECAP (figure 3.9d);
respectively. Observation on this AAA scan agree with the strong correlation coefficients
found between ∆ILT and all tested variables.

44

Figure 3.9 Spatial distribution of ∆ILT, OSI, TAWSS and ECAP for P08 at scan 2
showing deposition occurring at regions of high b) OSI, c) ECAP and b) low TAWSS
Some scans, however, large changes in ILT thickness at both high and low OSI.
This is the case of P05 at scan 1 (Figure 3.10) that depicted two regions of large
accumulation occurring either at high and relatively low OSI zones.

Figure 3.10 Spatial distribution of ∆ILT and OSI for P05 at scan 1 showing deposition
occurring at regions of high and relatively low OSI.

45

3.4 Discussion
In this chapter, local changes in thrombus thickness were estimated and associated to
vortical structures and local hemodynamic variables, qualitatively and quantitatively.
Local ILT changes were estimated by mapping points between time-point “n" to time-point
“n + 1”, while vortical structures and local hemodynamic variables such as TAWSS, OSI
and ECAP were derived from CFD simulations at time point “n". These variables were
ultimately used to perform a correlation study using Pearson correlation coefficients.
Results revealed that vortical structures that typically form at the proximal AAA regions
were found to consistently dissipate near zones where positive changes in ILT thickness
were recorded. On these lumen wall regions, correlation analysis showed that among all
tested hemodynamic variables, TAWSS showed to be the most correlated.
Vortical structures are characteristic flow patterns that describes a non-organized
flow. These coherent structures are being suggested to play an important role in the
thrombus accumulation process 17. In a normal aorta, small spanwise vortices that roll up
due to the aortic undulation are commonly seen during the early stages of the systolic
phase 8. In AAAs, our results also showed spanwise vortices forming at the proximal
region during the systolic phase. These vortices, however, became stronger as they
detached from the aortic wall right before entering the aneurysm bulge and dissipated
during the diastolic phase at specific near wall regions. Interestingly, our results found
that the dissipation regions coincided with those zones where positive changes in ILT
thickness was observed. This finding agrees with the hypothesis that suggests that
vortical structures would convect and concentrate platelets and other blood factors (e.g.
Thrombin) on regions of ILT accumulation 9.

46

While vortical structures are being suggested to have an influence on the local
hemodynamic environment 8, potentially affecting the accumulation of thrombus

17,

it is

not always the case. In the flow pattern of P01-S01 (Figure 3.4, 3.5), the vortex moves
and sweeps most of the lumen surface during the rest of the cardiac cycle, contrast to the
impinging flow in Fig. 3.3 in which the sweeping flow on the lumen surface could
potentially prevent the accumulation of thrombus. This was found when vortices in AAAs
with and without ILT were compared. Specifically, this comparison found that while both
AAAs were affected by strong vortical structures, vortices in the AAA without ILT swiped
most of the lumen surface, promoting higher levels of WSS. Those pattern of vertical
structure with high WSS levels could, potentially avoid the accumulation of thrombus.
This finding motivated us to perform a correlation analysis to study the relationship
between local values of time averaged WSS (TAWSS) and other hemodynamic
parameters (OSI and ECAP) with local changes of thrombus thickness. These
relationships were tested on each AAA at all time-point available. Results from the
analysis showed that among these parameters, TAWSS showed an overall inverse
correlation in about half of the scan tested (52,5% of all scans tested), shown in Figure
3.6a. At those low wall shear stress levels, antithrombotic agents have been proven to be
effective and shear dependent (< 600sec-1)

62.

aggregation mediate by fibrinogen biding GPIIb/IIa

This would regulate the platelet
40

and therefore the formation of

thrombus.
Another parameter that has being lately proposed as potential predictor of ILT
accumulation is ECAP 22,23. This variable defined as the ratio between TAWSS and OSI
was proposed from the premise that activated platelets would adhere onto low WSS

47

regions near recirculation zones (high OSI) 7. This variable was also correlated with ∆ILT
and results showed that, similarly to the results found with TAWSS, about half of the
scans also showed a correlation.
As any other analysis, this study also encounter some limitations. For instance, at
the time of mapping nodal points between two consecutives scans. The mapping was
achieved by assuming that centerline angles and lengths were constant between two
consecutives scans. Although sensitivity analysis previously performed showed not
significant differences in centerline length and angle, these small changes could
potentially affect the ∆ILT calculation. Another limitation arise at the time longitudinal
studies were acquired. Since these studies were acquire retrospectively the time between
consecutives scans could not be controlled. This could also potentially weaken our
statistical analysis. Despite these limitation, correlation trends between local
hemodynamic parameters and changes in thrombus thickness were achieved and those
agree with suggested hypothesis.
In summary, this analysis used CFD and ILT thickness information from our
previous analysis and study the relationship between hemodynamic parameters with local
quantified changes in ILT thickness. These results suggest that vortical structures might
be concentrating platelets and chemical species responsible for the formation of thrombus
(e.g. Thrombin) at regions where ILT accumulation takes place. Results also submits the
idea that although TAWSS is not the only parameters involved in the formation of
thrombus, in some cases, this variable could regulate its accumulations.

48

CHAPTER 4
Quantification of the shear history of platelets, and their association with local
changes of ILT thickness
4.1 Introduction
The specific mechanisms leading to the initiation of thrombus inside AAAs is still
unknown. A widely accepted hypothesis suggests that platelets, due to the recirculation
regions commonly found inside AAAs, would be exposed to high shear environments and
as a result would activate. Chap 3, however, found that thrombus accumulation occurred
in a low TAWSS and other studies proposed that activated platelets would recirculate at
low velocity regions where accumulation occurs 22,23. This hypothesis, however, has been
lately challenged and instead an activation of platelets due to a thrombo-active surface is
being proposed

5,9,43.

With conflicting two different hypotheses, there is a need to

elucidate whether mechanically induced platelet activation is a key mechanism leading to
the formation of thrombus.
The activation of platelets due to high shear rates comes from a theory of damage
2.

The theory, initially proposed while studying of hemolysis due to high shear

found to have a similar phenomenological effect on platelets

65.

15,69,

was

Specifically, once a

platelet reaches these activation/damage shear stress levels, it would release adenosine
diphosphate (ADP), serotonin, von willebrand factor (vWF) among other chemical
species, many of which, would promote platelet activation and aggregation 56.
The mechanical activation of platelets has been experimentally studied and all
agree that an activation of platelet would not be just a function of the stress but also of
the time a platelet is being exposed to such stresses61,80. This cumulative effect is being

49

study by Hellum et al 45 and they have presented a plot that depict the activation locus at
different stress and times using a power law relationship.
Many computational models have also tried to model this effect. For example, an
early model, approached the activation by using a linear stress-exposure time model

11.

These models are being lately replaced by power law model that according to literature
better reflects results obtained through experimentation 41.
In AAAs, several approaches have been used to test this hypothesis

6,22,23,43.

For

instance, a hemodynamic parameter such as platelet activation potential (PLAP) and
thrombus formation potential (TFP) based on this theory are being proposed to be better
predictors of ILT accumulation

22.

However, none of these parameters have been

estimated using a more complex platelet activation model (power law) nor validated using
a large patient-specific data set. In addition, there is still uncertain whether shear rates
levels and the time that platelets are exposed to such stresses would promote platelet
activation.
Hence, in this chapter, levels of activation will be estimated using a Lagrangian
particle method with a power law platelet activation model. Also, spatial distribution of
PLAP and TFP on regions where changes in ILT was observed will be correlated using a
Pearson correlation coefficients. Results from the analysis in this chapter revealed that
just 22.5% and 30.0% of the scans showed an overall correlation between changes in
ILT, PLAP and TFP, respectively. Also, results from measuring the activation levels in all
AAAs showed that none of the aneurysms tested showed activation levels higher than
the suggested activation threshold

50

4.2 Methods
4.2.1 Lagrangian particle tracking method
The CFD method under the Eulerian framework is an excellent tool to analyze averaged
flow pattern inside AAAs. However, due to the unsteady nature of the flow, the effect of
the instantaneous flow field in AAAs becomes challenging to be analyzed. This
unsteadiness is believed to play a role in the activation of platelets that is believed to be
responsible for the thrombus accumulation. Furthermore, it can also affect the dynamic
of platelets and chemical species responsible for the formation and accumulation of
thrombus 9. Here, the Lagrangian particle tracking method is used to estimate the level
of activation of platelets in AAAs and study its relationship with the accumulation of
thrombus. Platelets, represented by Lagrangian particles, were tracked by solving the
particle equation:
ƒ;
ƒ6

= C ,

(4.1)

where ; 	1[k	C represent the position and velocity of the particle, respectively. The
particles are assumed to be massless and particles’ velocities are interpolated from the
CFD flow field calculation using shape functions. These particles were seeded every
0.005s (200 release times throughout one cycle) from a plane normal to the centerline at
the level of the lower renal branch. Approximately, 3 million particles were released per
cardiac cycle, which accounts for 0.1% of the normal platelet concentration in humans
(150,000 platelets/mm3). The number of particle released per time step depended on the
volumetric flow rate in order to preserve a uniform concentration at all times.
Each particle was tracked using a parallel in-house code, where an Euler method
was used to discretize the particle equation Eq. 4.1 To maintain numerical stability, all

51

particles were constrained to move a distance of 1/10th of the element’s characteristic
length that contained them; therefore, each particle time step was independently adapted
to meet this criterion. Particles were continuously released until time averaged values of
interest (platelet activation potential) did not changed between cardiac cycles. At each
time step, the shear stress exerted on each particle was calculated and used for the
estimation of the platelet activation potential (PLAP). PLAP was calculated using a power
law exposure time model 11
h

 
‡‡(;;	; , l4 ) = j6  Q‘  (	; (l), l)T	’ kl ,
P

(4.2)

where ; , l4 , ‘  , ;, T, and “ represent the initial seeding position, initial seeding time, the

scalar value of the stress, particle position, time at position ;, and the power law

coefficient constant (“ = 2.28) chosen to compare values to Hellums locus

45;

respectively. The scalar value of the stress is defined as:
‘  = √2L ‖M‖”

and

‖M‖” = •l–(MMh ) ,

(4.3)

where ‖M‖” represents the Forbenius norm of the symmetric part of the velocity gradient
tensor at the particle position.
‖M‖” = •l–(MMh )

(4.4)

While Eq. 4.2 provides an estimation of the activation levels on each seeded
platelet at any time, does not provide meaningful information about activation levels on
specific near wall regions that experienced ILT accumulation. To enable this analysis,
platelet activation levels at near wall regions were extracted from the Lagrangian analysis
by dividing the lumen volume (Ί0 ) into small control volumes or subdomains (Ί0 =

˜
š›œœ
∑™
>g Ί0 ) and averaging the contribution of each particle visiting each subdomain over a

cardiac cycle:
52

˜
žžžžžžž
‡‡ bΩ0 d =

g

™Ÿ

Ÿ
∑™
¢g ∑¡‰

g
‡‡(l¢ ; v4 , l4 ),
|‰|

(4.5)

˜

where Ί0 is the subdomain corresponding to the cell used for the CFD flow field
˜





˜

calculation, fbΊ0 , l¢ d = £¤|	vbl¢ ; v , l d	¼	Ί0 Œ is the set of particles visiting the subdomain
˜
˜
Ί0 at time l, |f| number of particles visiting Ί0 at time l, §6 is the number of time steps

per cardiac cycle, and ‡‡(l¢ ; v4 , l4 ) is the platelet activation potential of the platelet

“¤” from time l4 to time l¢ . The value of the activation potential associated to each vessel

nodal point on the lumen surface was assigned to the one from the subdomain or cell
located at a normal distance “d” from the lumen wall (d=0.5 mm).
In addition to the PLAP parameters, a variable called “thrombus formation potential
(TFP)” was also estimated and included for the present analysis. This metrics combines
the effect of the flow-induced platelet activation with the susceptibility of the endothelium
to adhere thrombus 22;
žžžžžžž(v)

¨‡(v) = †x‡(v)‡‡

(4.6)

4.3 Results
4.3.1 Local association between PLAP, TFP and local changes in thrombus
thickness
Correlation analysis performed to test the local association between regional changes in
thrombus thickness and local hemodynamic parameters derived from a Lagrangian
particle method such as PLAP and TFP are presented in this chapter (Table 4.1).

53

Table 4.1 Correlation between ∆ILT and (a) PLAP, (b) TFP for each scan of each AAA
Results from the analysis revealed that from all the scans of all AAAs tested, 22.5
and 30% of them showed a direct ∆ILT-PLAP and ∆ILT-TFP relationships, respectively
(Figure 4.1a). In both variables, the number of scans showing a weak correlation was
approximately the same, but TFP showed larger number of scans with a moderated and
strong correlations in comparison to the correlation found with PLAP (Figure 4.1b).

Figure 4.1 Percentage of number of scans showing an (a) overall and a (b) strong,
moderate and weak correlations between ∆ILT and PLAP and TFP.

54

Qualitative examination of the spatial distribution of hemodynamic variables such
as PLAP and TFP at time point “n” on regions where positives changes in thrombus
thickness (∆
 > 0) between times n and n + 1 was performed. This analysis showed
some trends in some patients at specific scans. This is the case of P08 at scan 2 that
despite regions of high PLAP coincided with regions of ∆ILT, high values of TFP were
able to clearly depict regions of positive thrombus accumulation in this scan. (Figure 4.2).

Figure 4.2 Spatial distribution of ∆ILT, PLAP, and TFP for P08 at scan 2 showing that
although no specific trend was found in PLAP distribution, high values of TFP coincided
with regions of positive ILT thickness changes.

55

4.3.2 Platelet activation potential levels
Levels of platelet activation were tested in all AAAs different time point. This cumulative
shear rate calculation was performed using a power law model with a coefficient “=2.28.

the power low coefficient “ was selected in order to compare the estimated activation

levels with the locus of activation proposed by Hellums and colleagues 45. Results of the
mean and 95th values of the activation potential recorded in all scan are presented here
(Figure 4.3, 4.4).

Figure 4.3 95th percentile values of PLAP for all the scans of all AAAs

These results showed that none of the AAAs tested at any time-point recorded
values close to the threshold activation. The highest activation potential found among all
AAAs was recorded in P01. Interestegly, in this AAAs, a very small accumulation of
thrombus was seen in comparison to others AAAs that developed thicker thrombus layers
(e.g. P09, P13). Also, by comparing average (Figure 4.4) from 95th (Figure 4,3) percentile

56

it can be seen a large difference between both values, which suggests that platelets inside
these AAAs are exposed to large ranges of activation potential.

Figure 4.4 Mean values of PLAP for all the scans of PLAP for all the scans of all AAAs

4.4 Discussion
The mechanisms leading to the initiation of thrombus were investigated here. Specifically,
the theory that suggests that platelet activation is mechanically induced due to the high
shear these particles are exposed while being convected to regions suitable for
accumulation. The analysis was performed by measuring platelet activation levels in all
AAAs at all available time-points (scans) and recording averaged and 99th percentile
values of PLAP within the aneurysms. Results from this analysis showed that none of the
AAAs reached the suggested activation potential. Also, local hemodynamic parameter
measured on the lumen wall (e.g. PLAP and TFP) derived from analysis were also
calculated. These values were later correlated to measured changes in thrombus

57

thickness between two consecutives scans. Results from the analysis showed that just
22.5% and 30.0% of the scans showed an overall correlation between the aforementioned
parameters and ∆ILT, respectively.
This study used a power law platelet activation model. This model is suggested to
better reflect the activation of platelets in comparison to a linear stress-time cumulative
model. Here, the exponent (Îą) was set to 2.28 to allow to compare results with the locus
of platelets activation proposed by Hellums and colleagues

45.

Results from

measurements showed that 95th percentile values of all AAAs (xx scans) tested here
showed that none of them at any time-point reached nor exceeded the activation
potential. A recent study also measured this activation potential in 10 small AAAs
reaching similar results as the one found in this study

43.

These finding would suggest

that mechanically induced platelet activation might not be a kay mechanisms in the
formation of thrombus inside AAAs
Despite PLAP values did not reach the activation potential, there was still a
possibility that the PLAP variable along or in conjunction with other hemodynamic
parameters (e.g. TFP) could be associated to ∆ILT. This was tested first using Pearson
correlation coefficients and ultimately qualitatively by observing at the spatial distribution
of PLAP and TFP on regions where positive ∆ILT was observed. Correlation studies,
revealed, that among all scans of all AAAs tested, just 22.5 % of them showed weak or
moderated correlation between ∆ILT and PLAP. Similarly, results from testing the ∆ILTTFP relationship showed that 30.0% showed an overall correlation. For the TFP variable,
however, more scans showed a moderated and a strong correlation in comparison to
correlations using PLAP.

58

Qualitatively examination performed to TFP on regions of ILT accumulations,
however, showed that in some scans of some AAAs, high values of TFP could predict the
accumulation of thrombus (P08 at S02). These findings agree with previous studies that
have qualitative associated 90th percentile values of TFP with regions of positive
accumulation 22.
It is important to mention that PLAP values were measured at the abdominal level
area; specifically, between the renal level and the common iliacs. There is a probability
that particles might be exposed to high stresses before entering our area of interest.
Although a sensitivity analysis should be performed to estimate this effect, values found
in this study were much lower than the suggested activation threshold.
In closing, this chapter tested the hypothesis of a mechanically induced platelet
activation as a mechanism responsible of the formation of thrombus inside AAAs

22.

To

test the hypothesis, platelet activation levels between the renal level and the common
iliac arteries were measured in all AAAs using a Lagrangian particle method. Thus,
approximately 3 millions of particles per cardiac cycle, which accounts for about 0.1% of
normal platelet concentration in humans were used. On each particle, cumulative
activation levels were measured using a power law stress-time model. Results showed
that none of particle released in all AAAs reached or exceeded the activation potential.
Additionally, the relationship between local changes of thrombus thickness and
hemodynamic parameters as PLAP and TFP and results showed that just 22.5 and
30.00% of the scan testes showed an overall correlation. These finding suggests that,
although vortical structure might be convecting platelets to regions of activation, platelets
are not being activated.

59

Chapter 5

5.1 Summary of results
Abdominal aortic aneurysms, the permanent focal dilatation of the abdominal aorta 76, is
a cardiovascular disease responsible of at least 15.000 deaths. This disease was the 10th
leading cause of death within elderly white males in the united states along
Hemodynamics is one of the main contributor to the AAA growth
of the intraluminal thrombus (ILT)

13;

51

3.

and to the formation

another important factor that influence the

pathogenesis of the disease. Despite the effort to understand the role of each one of
these factors to the progression of AAAs, these roles are still poorly understood. This
study, used 59 CT scans from a longitudinal CT data set from 14 patients diagnosed with
AAA and study the role of hemodynamics in the progression of AAAs and the formation
of the intraluminal thrombus.
In chapter 2, we explored this complex relationship by comparing global values of
mean TAWSS, AAA expansion and ILT accumulation rates, between AAAs with and
without a thrombus accumulation. The amount of ILT accumulation was initially estimated
by calculating the spatial distribution of ILT thickness and later measured by using a
fraction of lumen area covered by thrombus. The results of this analysis showed that
lower values of mean TAWSS and higher values of AAA expansion rates were found in
AAAs with ILT in comparisons to those without thrombus. Also, by estimating the spatial
distribution of ILT thickness at different time-points, the ILT accumulation process could
be described. The ILT showed to initially accumulates on regions of maximum diameter
and from there it spread to surrounding regions while thicken on previously covered

60

regions. Interestedly, this accumulation occurred at the same rate as the AAA expansion
rate.
In Chapter 3, we further explored the relationship between hemodynamic and ILT
accumulation.

Specifically,

the

relationship

between

vortical

structures,

local

hemodynamic parameters such as TAWSS, OSI, and ECAP and local changes in
thrombus thickness, were qualitative and quantitative studied, respectively. Results of the
analysis showed that while AAAs with and without ILT experienced strong vortical
structures, vortices on AAAs that experienced ILT consistently dissipated near
accumulation regions. Also, by performing a correlation analysis among all local
hemodynamic variables measured on the lumen wall, it was found TAWSS showed to be
mostly correlated.
Finally, a hypothesis that suggests that mechanically activated platelets might be
the leading mechanism promoting thrombus accumulation inside AAA was tested in
Chapter 4. Thus, a Lagrangian particle method was used to record shear stress history
of a large number of particles (~ 3 millions). In addition, the association between
suggested hemodynamic parameters, derived from the particle analysis such as PALP
and TFP, and local changes in thrombus thickness was investigated. Results showed that
among all scans tested just 22.5% and 30% of them, showed a ∆ILT-PLAP and ∆ILT-TFP
relationship (Figure 4.1a), respectively. Also, by measuring the platelet activation levels
it was found that none of the AAAs at any time-point either reached or exceeded the
proposed activation potential (Figure 4.3 ,4.4).
The findings presented in this work suggests that ILT formation due to a
mechanically induced platelet activation might not be a key mechanism leading to the

61

formation of thrombus. A recent theory submits the idea that platelets might become
activated due to a thromboactive surface. Arguably, thromboactive surfaces form due to
abnormal flow patterns and low values of wall shear stress environment that induce
endothelium cells (ECs) dysfunction, with impairment of nitric oxide (NO) production

18.

NO has shown to be an effective inhibitor of platelet function 39 and the absent of it on the
endothelium would lead to an initial thrombotic event 4. Our results showed that lower
values of wall shear stress were found in AAAs that developed thick ILTs in comparison
to those that did not developed thrombus; agreeing with this hypothesis.
Once the initial accumulation occurs, the recruitment and activation of platelets
onto thromboactive surfaces can occur at high (> 800 sec-1) and low shear rates
(<600sec-1). At high shear rates (> 600-800 sec-1), von Willebrand factor (vwf) plays a
critical role due to the strong bonding provided 32. On the other hand, at low shear rates,
the aggregation mechanisms would be highly dependent on fibrinogen biding GPIIb/IIa
40.

Other studies have suggested that platelets would adhere to the AAA lumen surfecs

due to the bonding to vWF (at moderate WSS). Shear rates calculated in all AAAs in this
study, however, were found be under 600 sec-1 range. At this range, antithrombotic
agents have proved to be effective and shear dependent

62.

Our correlation analysis

depicted this shear dependency when an inverse correlation between TAWSS and ∆ILT
was found within regions that experienced thrombus deposition (∆ILT0).
However, despite the ∆ILT-TAWSS inverse relationship found on such regions, not
all zones of low wall shear stress experienced accumulation of thrombus. This suggests
that WSS might be an important but not the only factor influencing the accumulation of
thrombus. Vortical structures have been suggested to convect platelets and other

62

chemical species (e.g. Thrombin) to distal regions where thrombus accumulation has
been reported 9. Although our results have shown that ILT accumulation can occur also
at proximal regions, the fact vortices on AAAs that developed thrombus consistently
dissipated in regions where positive ∆ILT were observed suggest that these coherent
structures might be also important in the accumulation of thrombus.
These vortical structure would not just convect platelets to regions of accumulation,
but potentially influence the near wall hemodynamic environment 17. Our results showed
this in some AAA that despite their large size, experienced high levels of WSS promoted
by a vortical structure swiping the entire lumen surface (P01-S01; Figure 3.6) and this
hemodynamic differences could potentially prevent the accumulation of thrombus.
This study also analyzed the role of the ILT accumulation on AAA expansion, which
is being debated. Results showed higher AAA expansion rates recorded in AAAs with
thick thrombus compared to those that remained without ILT. This results suggests thick
ILT layer might be weakening the arterial wall through inducing hypoxia 74, wall thinning,
cell inflammation, apoptosis of SMCs, and degradation of the extracellular matrix in walls
covered by thick thrombus

49,

promoting AAA growth. Interestedly, AAA expansion rate

was the same as ILT accumulation rate, suggesting that ILT might be occupying
expanded areas, maintaining a nearly constant lumen cross section, which arguably
would promote a nearly constant low WSS levels.
In closing, hemodynamic forces are being showed to influence the AAA expansion
and ILT accumulation rates. While high WSS values would prevent ILT accumulation, low
values of WSS would arguably promote thromboactive surface, which in turn would
promote the formation of thrombus. Once these surfaces become thromboactive, the ILT

63

accumulation would be greatly influenced by vortical structure and local hemodynamic
conditions (e.g. WSS). Specifically, Vortical structures would convect platelets and main
chemical species (e.g. thrombin) to regions of accumulation, while local hemodynamic
variables such as wall shear stress would regulate the platelet recruitment and the
formation of thrombus.

The main contribution of this study are the followings:

1. By depicting the ILT thickness distribution at different time-points (scans), the
accumulation of thrombus could be described and thus many hypothesis about the
location of the initial thrombus deposition and subsequently accumulation were
clarified.
2. By comparing AAAs with and without a significant thrombus accumulation, our
finding supports the idea of thick ILTs promoting AAA expansion rates.
3. Among all local hemodynamic variables suggested, TAWSS showed to be an
important parameter in the accumulation of thrombus.
4. Vortical Structures showed to be a factor in the accumulation of thrombus by
convecting platelets and main chemical species (e.g. thombin) on regions suitable
for thrombus accumulation.
5. Measuring platelet activation levels, our study found that none of the AAAs studied
reached high levels for platelets to activates, suggesting the mechanically induced
platelet activation not to be an important mechanism in the accumulation of
thrombus.

64

Some of these findings are being already incorporated in the development of a datadriven approaches for the estimation of the initiation and accumulation of ILT and its effect
of AAA expansion. For instance, Farsad et al 28 , incorporated the relationship between
AAA expansion and ILT accumulation rates to developed a data-driven growth and
remodeling (G&R) formation that included the effect of ILT accumulation. As a future
direction, the Cardiovascular Tissue and Mechanics Laboratory will use the findings of
this study and develop more enhanced models to integrate hemodynamics into AAA
growth (G&R), which enables us to investigate the influence of the hemodynamic
environment onto the production of main chemical species for the thrombus formation.

65

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