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Carotid wall shear stress characterization using echo particle image velocimetry

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Title:
Carotid wall shear stress characterization using echo particle image velocimetry
Creator:
Gurung, Arati ( author )
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English
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1 electronic file (136 pages). : ;

Thesis/Dissertation Information

Degree:
Doctorate ( Doctor of Philosophy)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Bioengineering, CU Denver
Degree Disciplines:
Bioengineering

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Subjects / Keywords:
Echocardiography ( lcsh )
Carotid artery -- Imaging ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Review:
Cardiovascular disease, including stroke, is the leading cause of death worldwide. The most common trigger of ischemic stroke is the rupture of atherosclerotic plaques and subsequent obstruction of blood flow. Atherosclerosis is a systemic disease characterized by chronic inflammation and local accumulations of macrophages, smooth muscle cells, lipids and fibrous proteins (collectively called plaques) in the arterial wall. Strikingly, atherosclerotic plaques affect only some regions of the arterial system, a property that has been attributed to local variation in blood flow. Flow induces a frictional force on the arterial wall and the magnitude, direction and pattern of this induced wall shear stress (WSS) are known to differentially affect the endothelial structure and function. It has been postulated that low and oscillatory WSS predisposes arteries to develop atherosclerosis, while high WSS may increase the vulnerability of plaque to rupture. However, in vivo WSS measurement is difficult and the accuracy of current WSS measurements is questionable. This has limited our understanding of the exact role and patterns of WSS involved in the initiation and progression of atherosclerosis. In vivo WSS so far has been measured using phase contract magnetic resonance imaging (PC-MRI) and ultrasound Doppler velocimetry (UDV). While PC-MRI provides three dimensional (3D) flow visualization, its spatial and temporal resolution is too limited to allow reliable measurement of blood flow velocities and WSS near the vessel wall endothelium, specifically in small to medium sized arteries. Ultrasound Doppler based estimate of WSS requires very strict placement of the transducer, is limited to velocity measurement only along the ultrasound beam line, depends on unrealistic flow assumptions and its spectral broadening along the angular dependence introduces measurements inaccuracies. In contract, echo PIV can accurately measure velocity fields with high temporal (1 ms) and spatial resolution within 250-200 microns of the vessel wall, and makes no assumptions about the flow pattern. The present study demonstrated the reliability and reproducibility of echo-PIV for measuring detailed markers of carotid WSS in comparison to PC-MRI and UDV both of which underestimated WSS (by 40 percent and 28 percent respectively). Our clinical study involving 24 health individuals and 12 individuals with a recent transient ischemic attack (TIA) showed that WSS was reduced by 50 percent in the TIA cohort and that the spatio-temporal patterns of WSS were significantly different between the two groups. Echo PIV holds significant potential for quantifying spatio-temporal WSS data in human arteries and provides detailed markers of WSS in physiological and pathological flow environments which may improve our understanding of the relationship between WSS and atherosclerosis. Our study was limited by small sample size. A larger clinical study is need to further validate and redefine these WSS characteristics and to fully exploit their utility.
Thesis:
Thesis (Ph.D.)--University of Colorado Denver.
Bibliography:
Includes bibliographic references.
General Note:
Department of Bioengineering
Statement of Responsibility:
by Arati Gurung.

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University of Colorado Denver
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Full Text
CAROTID WALL SHEAR STRESS CHARACTERIZATION USING
ECHO PARTICLE IMAGE VELOCIMETRY
By
ARATI GURUNG
B.S. University of Colorado, Denver, 2003
M.S. University of Maryland, Baltimore, 2006
M.S. Johns Hopkins University, Baltimore, 2009
A thesis submitted to the Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirement for the degree of
Doctor of Philosophy
Bioengineering Program
2014


This thesis for the Doctor of Philosophy degree by
Arati Gurung
has been approved for the
Bioengineering Program
By
Kendal Hunter, Chair
Robin Shandas, Advisor
Yiming Deng
Jean Hertzberg
Karen Moulton
November 21,2014


Gurung, Arati (Ph.D., Bioengineering)
Carotid Wall Shear Stress Characterization Using Echo Particle Image
Velocimetry
Thesis directed by Professor Robin Shandas
ABSTRACT
Cardiovascular disease, including stroke, is the leading cause of death
worldwide. The most common trigger of ischemic stroke is the rupture of
atherosclerotic plaques and subsequent obstruction of blood flow.
Atherosclerosis is a systemic disease characterized by chronic inflammation and
local accumulations of macrophages, smooth muscle cells, lipids and fibrous
proteins (collectively called plaques) in the arterial wall. Strikingly, atherosclerotic
plaques affect only some regions of the arterial system, a property that has been
attributed to local variation in blood flow. Flow induces a frictional force on the
arterial wall and the magnitude, direction and pattern of this induced wall shear
stress (WSS) are known to differentially affect the endothelial structure and
function. It has been postulated that low and oscillatory WSS predisposes
arteries to develop atherosclerosis, while high WSS may increase the
vulnerability of plaque to rupture. However, in vivo WSS measurement is difficult
and the accuracy of current WSS measurements is questionable. This has
limited our understanding of the exact role and patterns of WSS involved in the
initiation and progression of atherosclerosis.
In vivo WSS so far has been measured using phase contrast magnetic
resonance imaging (PC-MRI) and ultrasound Doppler velocimetry (UDV). While


PC-MRI provides three dimensional (3D) flow visualization, its spatial and
temporal resolution is too limited to allow reliable measurement of blood flow
velocities and WSS near the vessel wall endothelium, specifically in small to
medium sized arteries. Ultrasound Doppler based estimate of WSS requires very
strict placement of the transducer, is limited to velocity measurement only along
the ultrasound beam line, depends on unrealistic flow assumptions and its
spectral broadening along with the angular dependence introduces measurement
inaccuracies.
In contrast, echo PIV can accurately measure velocity fields with high
temporal (1 ms) and spatial resolution within 250-300 microns of the vessel wall,
and makes no assumptions about the flow pattern. The present study
demonstrated the reliability and reproducibility of echo PIV for measuring detailed
makers of carotid WSS in comparison to PC MRI and UDV both of which
underestimated WSS (by 40% and 28% respectively). Our clinical study involving
24 healthy individuals and 12 individuals with a recent transient ischemic attack
(TIA) showed that WSS was reduced by 50% in the TIA cohort and that the
spatio-temporal patterns of WSS were significantly different between the two
groups.
Echo PIV holds significant potential for quantifying spatio-temporal WSS
data in human arteries and provides detailed markers of WSS in physiological
and pathological flow environments which may improve our understanding of the
relationship between WSS and atherosclerosis. Our study was limited by small


V
sample size. A larger clinical study is needed to further validate and refine these
WSS characteristics and to fully exploit their utility.
The form and content of this abstract are approved. I recommend its
publication.
Approved : Robin Shandas


DEDICATION
vi
Dedicated to my late sister Asha and to study participants whose valuable time
will someday save the lives of many others.


ACKNOWLEDGEMENTS
I am grateful to my mentor and advisor, Professor Robin Shandas.
Without his mentorship, patience, timely advice and generous grant support, I
would not have this opportunity to actually live my dream. I am also grateful to
Dr. Phil Gates for his tireless and consistent efforts in helping build my critical
thinking skills in my research. I thank Luciano Mazzaro for his mentorship early
on in the training. I wholeheartedly thank my advisors: Dr. Kendall Hunter, Dr.
Jean Hertzberg, Dr. Karen Moulton and Dr. Yiming Deng for their sage advice,
critiques, time and constant encouragement. I would like to thank Dr. Michael
Yeager for his invaluable advice, teaching and motivation throughout my training.
My sincere thanks and gratitude to NIH (through Professor Shandas T32)
and IlEA/Vhitaker for their generous funding that made my research possible.
I am grateful to Dr. Stefania Petra and Dr. Florian Becker at HCI/IPA for
their constant inquisition and push for excellence that helped me move forward
and onward. I thank my friends at HCI for making me feel at home in Heidelberg
and Nancy Tsen for taking care of me when sick at work. I would like to thank Dr.
Christian Poelma for being an inspiration and making a difference. Many thanks
to my family and friends whose love and support remain the backbone of my
personal and professional career. Special thanks to Martin Schiffner for
introducing me to inverse scattering and theoretical frameworks of quantitative
ultrasound imaging; but most importantly thank you for sharing with me your
enthusiasm and commitment to science, innovation and excellence. Thank you
God for your unconditional love and unwavering presence.


viii
TABLE OF CONTENTS
Chapter
1.Introduction........................................................................1
2. Cardiovascular Fluid Dynamics and Pathophysiology..................................7
3. Fundamentals of Ultrasound Imaging................................................16
4. Fundamentals of Ultrasound Echo Particle Image Velocimetry........................25
5. Reliability and Accuracy of Echo PIV for WSS Measurement..........................32
6. Characterization of Carotid WSS in Healthy Subjects...............................64
7. Characterization of Carotid WSS in TIA Subjects...................................87
8. Summary and Future Work..........................................................110
Bibliography........................................................................115


LIST OF TABLES
Table
6.1. Participants Characteristics....................................................73
6. 2. Descriptive statistics of WSS parameters for upper and lower walls and the average
of the two............................................................................75
6. 3. Percent difference between echo PIV- and ultrasound Doppler- derived wall shear
stress at the upper wall, lower wall and the average of both walls....................76
7.1. Participant Characteristics.....................................................95


X
LIST OF FIGURES
Figure
1.1. Plaque deposits at the bifurcation of the common carotid artery and disturbed flow
as a result [3]......................................................................1
2.1. WSS mechanotransduction by the endothelial cells [2]..........................7
2. 2. Disturbed flow patterns and low shear stress are known to initiate and promote
atherosclerosis......................................................................8
2. 3 aminar flow in a straight cylindrical tube[4]...............................12
3.1.Schematic of ultrasound image formation.........................................17
3. 2. Image reconstruction from RF signals using a linear phase array transducer...20
3. 3. Doppler velocity spectrum....................................................22
4.1. A flow chart illustrating the working principles of echo PIV. 25
4. 2. Cross-correlation based estimation of particle displacement..................26
4. 3. Pixel intensity distribution as a function of particle displacement [35].....28
4. 4. Two dimensional velocity and gradient (shear rate) vector fields.............30
5.1. Repeatability.................................................................47
5. 2. Reproducibility..............................................................48
5. 3. Inter-scan variability.......................................................49
5. 4. Measurement uncertainty from measurement variability.........................50
5. 5. Percent uncertainty...........................................................51
5. 6. Uncertainty contribution from individual velocity components..................51
5. 7. Uncertainty in WSS measurement................................................52
5. 8. WSS measurement comparison between echo PIV and PC-MRI........................52
5. 9. Temporal distribution of WSS..................................................53
5.10. Point-wise correlation analysis..............................................54
5.11. Maximum percent differences in peak systolic WSS measurements were observed
when the vessel diameters were smaller..............................................55


xi
5.12. For a Given Diameter, Echo PIV Measures peak systolic WSS Within the Same
Magnitude Range whereas PC MRI Underestimates in the second case (subject number
8)..................................................................................56
6.1. Comparison between Doppler velocimetry and echo PIV...........................68
6. 2. Instantaneous WSS Measurement................................................74
6. 3. Example of a parabolic systolic velocity profile.............................77
6. 4. Examples of a blunt systolic velocity profile................................77
6. 5. Spatial and temporal variation in velocity profiles at C1-C5 for each participant78
6. 6. Ensemble averaged WSS profile.................................................79
6. 7. Temporal variation in the WSS profile between individual participants........80
7.1. Time-averaged wall shear stress is reduced by 50% in individuals with transient
ischemic attack compared to healthy controls........................................96
7. 2. Differences in WSS between the healthy and TIA cohorts measured at five different
time points in the cardiac cycle....................................................97
7. 3. Temporal distribution of spatial and phase averaged WSS in the TIA cohort.....98
7. 4. Differences in temporal waveforms of WSS in TIA and HC.......................99
7. 5. Ensemble averaged WSS waveforms.............................................101
7. 6. Differences in spatio-temporal WSS patterns between TIA and HC...............103


xii
LIST OF ABBREVIATIONS
wss Wall shear stress
UDV Ultrasound Doppler velocimetry
Echo PIV Ultrasound particle imaging velocimetry
PC-MRI Phase-contrast magnetic resonance imaging
PRF Pulse repetition frequency
WSSvmax UDV derived WSS estimate
Vmax Centerline peak velocity
CCA Common carotid artery
2D Two-dimensional
Dynamic viscosity
D Inner diameter of the carotid artery
s s-index
V Instantaneous velocity
y Radial position
R Inner radius of the carotid artery
C1 Accelerating systolic cardiac phase
C2 Peak systolic time point
C3 Decelerating systolic cardiac phase
C4 Mid diastolic time point
C5 End diastolic time point
Re Reynolds number
A Womerlseys number
P Blood density
T Time period of the cardiac cycle
3v/3y Spatial gradient of the velocity (shear rate)
WSSi lnst3nt3ri6us WSS
FDHM Full duration half maximum
A Exponential decay constant
PI Pulsatility index
Rl Resistivity index


1.Introduction
1
Overview
Heart attacks and strokes are the leading causes of death worldwide [1].Carotid
atherosclerotic plaque accounts for more than eighty percent of ischemic stroke
that occurs each year [1].Atherosclerosis is a systemic disease characterized by
chronic inflammation, fibro-proliteration and lipid deposits that are localized in
arterial segments with branching, curvatures and complex geometry [2].
Figure 1.1.Plaque deposits at the bifurcation of the common carotid artery
and disturbed flow as a result [3].
Plaque deposits are mostly seen in arterial segments with branches and
curvatures. As the plaque formation progresses, it occludes blood flow that
affects exchange of blood nutrients with the endothelial cells. _________________
Despite being a systemic disease, the localized behavior of atherosclerotic
plaques indicates that certain flow patterns might be involved in the distribution of
blood elements that make up the plaque deposits (Figure 1.1). Flow induces a


2
frictional force on the arterial wall known as wall shear stress (WSS) which
results from the resistance exerted by blood viscosity [4]. Endothelial cells lining
the inner walls of the arterial vasculature are the principal sensors of WSS [5]. It
has been well established that endothelial function and dysfunction is associated
with the magnitude and directionality of WSS imparted by the blood flow [6]. A
growing body of studies has demonstrated that WSS can transcriptically induce
structural and functional changes in the endothelium that lines the arterial walls
[7-11]. While low and oscillatory WSS predisposes arteries to develop
atherosclerosis [2], [6], [12], high WSS may perpetuate transient ischemic stroke
(TIA) or stroke by causing the plaques to rupture [13-17], However, the
mechanism by which low and/or oscillatory flow contributes to endothelial
dysfunction remains uncertain [8], [10], [18-20], primarily because WSS is
difficult to measure in vivo. In particular, the present imaging modalities are
unable to measure flow with sufficient spatial and temporal resolution to
determine accurate estimates of WSS. High spatio-temporal resolution means
flow patterns can be measured near the vessel walls throughout the cardiac
cycle to determine any time-varying characteristics in WSS that might be
physiologically and clinically important.
Measurement of hemodynamic WSS has both physiologic and clinical
applications. WSS profiles may determine initiation and progression rates of
atherosclerosis. The distribution of WSS in clinically interesting population groups
could be used to monitor symptoms of progressing pathology or identify risk for
future ischemic events. Current methods to estimate in vivo WSS are primarily


3
based on two imaging modalities: phase-contrast magnetic resonance imaging
(PC-MRI) and ultrasound imaging. PC-MRI provides volumetric flow visualization
but is relatively expensive, time consuming, and has limited spatial and temporal
resolution [6], [21-25], Because of this, ultrasound Doppler velocimetry (UDV)
has become a popular method to estimate WSS in studies of endothelial function
and the natural history of atherosclerotic plaque. This method is inexpensive,
readily available and relatively cheap. However, it is uncertain whether it provides
an accurate estimate of WSS. The main threat to accuracy is that it uses a one
dimensional velocity component rather than measuring the whole velocity vector
field. This introduces error as it is not possible to measure the spatial gradient of
the velocity distribution near the vessel walls, which is required to accurately
calculate WSS [6], [23], [26-28],
Unmet Needs and Contribution of Dissertation
Despite the fact that hemodynamic WSS is emerging as an important metric
of endothelial dysfunction and associated atherosclerotic carotid stroke, accuracy
of WSS measurement remains an open problem [6], [12], [29], [30]. To address
the limitations of the commonly existing measurement methods, we propose the
use of a novel ultrasound based particle image velocimetry technique (echo PIV)
to compute spatially local time-resolved two-dimensional velocity vector fields,
which can be easily and directly converted into WSS data.
In this thesis, we evaluated the clinical utility of a previously validated [31-34]
ultrasound based echo particle imaging velocimetry (echo PIV) for quantification
of WSS in vivo among different population group. Particle image velocimetry is


4
an optical technique that uses an optical laser system to illuminate the fluid
seeded with particles the intensity patterns of which are tracked over time to
produce a time dependent velocity-vector field. The vector field is then used to
derive hemodynamic information in the entire region of interest (ROI) [31-35],
Translation of this technology into medical imaging has been achieved by using
contrast enhanced ultrasound, where a velocity vector field is produced in blood
seeded with contrast agent microbubbles. Echo PIV uses the two-dimensional
(2D) ultrasound image of the arterial segment to measure the local flow velocity
distribution from which a 2D velocity vector field is generated and converted into
WSS data.
Given the limitations of the current modalities and the importance of WSS in
vascular physiology and pathology, we identified three aims to determine
whether echo PIV can produce a reliable, reproducible and accurate clinical
measure of WSS.
Specific Aim 1:Evaluate the reliability and accuracy of echo PIV for measuring
WSS in human carotid arteries in vivo.
Rationale: Our in-vitro work has shown that echo PIV provides detailed
hemodynamic information in two dimensions with high temporal (0.7ms) and
spatial resolution (0.15mm) [36]. The in-vitro analysis demonstrated that echo
PIV provides accurate measurement of hemodynamic in a single acquisition. We
have also previously validated the in vivo use of echo PIV in human carotid
arteries [36]. In this study, we wanted to further investigate the repeatability and
reproducibility of echo PIV for WSS measurement in human carotid arteries and


5
evaluate its measurement uncertainty. Phase contrast magnetic resonance
image velocimetry (PC-MRI) is the state of the art imaging modality for volumetric
flow visualization. However, its relatively limited spatial (-0.6 mm3) and temporal
resolution (2 ms) [34] has raised questions with regards to its accuracy in
measuring local WSS particularly in small to medium sized arteries such as the
carotid arteries [22], [25], [37]. This motivated us to compare the PC MRI data
against the echo PIV data.
Specific Aim 2: Characterize carotid WSS in healthy population samples
Rationale: Echo PIV uses the 2D ultrasound image of the arterial segment to
measure the local flow velocity distribution, producing a 2D velocity vector field
from which WSS is derived. WSS measurement based on UDV is being used
extensively in physiological studies, yet its accuracy and utility are uncertain. As
such, information about the usefulness of these estimates and their limitations
are needed for better interpretation of WSS data. Our purpose was to compare
arterial WSS measurements estimated from ultrasound Doppler with those from
echo PIV.
Specific Aim 3: Characterize carotid WSS in TIA patients
Rationale: The TIA cohort is of particular interest because several studies have
shown that the presence of endothelial dysfunction in the coronary or peripheral
circulation increases the risk of stroke or TIA in patients with various stages of
atherosclerosis [38]. Several computational and biological studies have analyzed
flow patterns in arterial regions susceptible to atherosclerosis or with varying
degree of stenosis and have demonstrated the various mechanisms by which


6
WSS regulates endothelial function and structure^]. Recent studies have shown
that the endothelial function depends not only on the magnitudes of arterial WSS
but also on its spatial and temporal variations introduced by the pulsatile nature
of blood flow in interaction with the arterial geometry [7-10], [39]. They
demonstrated that the endothelial cells respond to both the spatial [7], [8], [16],
[40] and temporal [9], [10], [29], [39], [41] shear patterns by differentially
activating endothelial transcription factors and independent mechanotransduction
pathways. While these detailed analyses of endothelial responses to fluid
mechanics in atherosclerosis susceptible regions have advanced our
understanding of the mechanisms by which shear stresses regulate endothelial
behavior, the exact role and spatio-temporal patterns of shear in the
pathogenesis of atherosclerosis remain poorly defined because of the complexity
and difficulty of measuring WSS in vivo, which limits its utility as an early marker
of atherosclerosis[2], [10],[16].
In this study, we examined the time varying characteristics of wall shear
stresses in the apparently healthy individuals without any known disease and
participants who were recently diagnosed with a TIA. The objective was to
evaluate the prevailing hypothesis that WSS in individuals susceptible to
atherosclerosis differs from healthy individuals both in terms of its magnitude and
its spatio-temporal distribution patterns.


2. Cardiovascular Fluid Dynamics and Pathophysiology
7
Pathological hemodynamic wall shear stress (WSS) is known to trigger
atherogenesis that involves dysfunction of the vascular endothelium. Endothelial
cells lining the arterial walls respond differentially to WSS induced by the blood
flow [18]. Depending on the type of induced shear stress, endothelial genes such
as vascular cell adhesion molecule-1 (VCAM-1) are either up- or down- regulated
[6]. Li et al. (2009) showed that high pulsatility flow with a constant mean WSS
upregulates pro-inflammatory gene expression and enhances leukocyte
TKRft
Figure 2.1.WSS mechanotransduction by the endothelial cells [2].
Endothelial shear stress (ESS) induced by blood flow triggers a series of
signaling cascade in the endothelium that eventually affects the morphology and
physioloqy of endothelial cells. _________________________________
adhesion and cell proliferation implicating a dynamic relationship between the
temporal gradients in WSS distribution and the responses of the endothelial cells
experiencing them [19]. As shown in Figure 2.1, wall shear stress (referred to as
ESS in the figure) activates a range of mechanoreceptors thereby triggering a
complex range of intracellular pathways [2]. The mechanotransduction pathway
generally involves activation of the mitogen-activated protein kinase (MAPKs).


8
These activated proteins then orchestrate a range of signaling messages
responsible for activating transcription factors that are either atherogenic or
atheroprotective [2], [8]. This concert of signaling cascades causes structural and
functional remodeling of the arterial bed.
Reduced mass transport
LDL uptake and synthesis
Apoptosis and Proliferation
t VCAM-1,ICAM-1,E-Selectin, TNF
LDL and monocyte permeability
Bone morphogenic protein-4
l^MCP-l. IL-1. TNF-a, IFN-y
I eNOS/NO Synthesis
Blood flow reversal
and stagnation
Endothelial cells align
in random direction
PATHOLOGICAL (LOW) WSS
PHYSIOLOGICAL (HIGH) WSS
Endothelial cells
align parallel to flow
Figure 2. 2. Disturbed flow patterns ancMow shear stress are known to
initiate and promote atherosclerosis.
aminar flow and high WSS (15-70 dyn/cm2) are known to be atheroprotective. In
contrast, disturbed flow with low WSS (< 10-12 dyn/cm2) cause cells to align in a
random fashion compromising the endothelial cellular functions: e.g. reduced
eNOS synthesis leads to vasoconstriction; increased VCAM-1, BMP-4
expression, LDL uptake and permeability leads to cellular proliferation, plaque
formation and calcification; increased MCP-1, TNF-a promotes inflammation, all
leading to onset and progression of atherosclerosis [2], [42].__________________
It is shown that endothelial genetic expression unique to arterial regions
with laminar, undisturbed flow patterns tends to be atheroprotective; for example
by inducing increased endothelial synthesis of nitric oxide synthase (eNOS)
which is a vasoregulator or by suppressing pro-atherogenic genes such as


9
VCAM-1. In contrast, increased expression of pro-atherogenic and mitogenic
genes and reduced eNOS are associated with regions where low and disturbed
flow patterns are found [2], [6], [43].
Cardiovascular Flow Dynamics
Blood is an isotropic, non-Newtonian, incompressible fluid carried by the
arterial system away from the heart to the rest of the body. As the heart pumps
during systole, the flow velocity increases and so does the strain rate. Blood
becomes Newtonian at larger strain rates. This allows us to consider blood flow
in medium to large sized arteries, such as the common carotid arteries (CCA;
Figure 1.1) to be Newtonian. Thus, its flow characteristics can be approximated
by a Newtonian constitutive equation [4]:
Equation (2.1) expresses the three-dimensional stress tensor, ", as a
linear combination of the hydrostatic pressure, p, and the three-dimensional
Here, v represents the three-dimensional three-component velocity vector with
vij components in the Cartesian coordinates. The Dirac delta function, 5,y ensures
that the pressure term is defined only at the surface point, AS where / = j, i.e.
pressure is a normal stress.
(2.1)
strain-rate tensor, en-
sealed by the fluid dynamic viscosity,
Blood flow can then be analyzed using the differential equations of fluid
mechanics that obey the principles of mass and momentum conservation of fluid.


10
We obtain the Euler's equation of motion from the Newtons second law of
motion per unit volume (Eqn. 2.2) while obeying the equation of continuity for an
incompressible fluid (2.3):
Dpv =F (2.2)
Dt
V.v = 0 (2.3)
Equation 2.2 expresses conservation of momentum by stating that the
material rate of change of momentum equals the force acting on the body,F
which is defined on the right hand side of equation (2.4) as a sum of the surface
forces and the body forces acting on the fluid:
Dv
pm=+ x
(2.4)
where ^ measures the surface forces acting normal (pressure, p) and
dxj
tangential (stress, p) to the surface of the fluid and X= X,Y&c\6 Z measures the
body forces (e.g. gravity and viscous forces) per unit volume in the x, y and z
directions respectively [44]. Here, the material derivative is defined by the
operator: =-^ + v. V where the gradient operator V=evaluates the spatial
derivative of the three velocity components: u, v and w in the x, y and z
directions respectively. From equation (2.4), we subsequently obtain the Navier-
Stokes equations that govern the flow characteristics of an incompressible
viscous flow in three dimensions:


11
du du du du
(2.5)
dco dco dco dco
And in a compact form (neglecting the body
forces) as: p = Vp + fiV2v
The simplest model of blood flow that satisfy the Navier-Stokes equation
can be derived based on the following assumptions: fluid is homogenous =
constant); flow is laminar (layers of fluid are parallel to each other and the walls);
flow is steady (fluid velocity, v and density, p remain constant with time); flow is
axial (in the cylindrical polar coordinates {r,Q,z), there is no circumferential
variation: vr = 0; vg = 0; pressure, p(r,z) is a function of the radial position,
rand the tube length, z; and vz(r) is a function ofr only); flow is axisymmetric
(p(r,z) and vz(r) are independent of the azimuthal direction, Q)\ flow is fully
developed (vz(r) is independent of the tube length, z); and the tube is uniformly
straight, rigid, cylindrical and long relative to the fluid volume studied such that
Newtonian [44]. These assumptions describe the behavior of a steady viscous
flow in a uniformly straight and axisymmetric tube with the no-slip boundary
condition on the surface (vr=R = 0), i.e. the flow shares the same velocity as that
of the wall and is therefore zero at the wall. Due to viscosity, the velocity of flow


12
away from the walls increases reaching a maximum value in the center as shown
in Figure 2.3. This profile of the flow as a function of its spatial position with
respect to the wall approximates a parabola and is colloquially known as a
parabolic or Poiseuille's flow.
Pi 'Pi
Figure2.3.Laminarflowinastraightcylindricaltube[4].
Considering the blood vessels to be uniform and cylindrical, viscosity causes the
flow velocity profile to become parabolic with the maximum velocity at the center
of the b 100d vessel._______________________________________________________
The resulting generalized solution to the Navier-Stokes equation is known
as the Hagen-Poiseuilles flow named after the German engineer G.H.Hagen
(1839) and the French physician J.L.M. Poiseuille (1840) for their work on the
pressure-drop (AP = Pi-P2) law governing a laminar pipe-flow whose velocity
profile is a parabola given by equation (2.6) where
u(r) = (R2 r2) (2.6)
Here, fj is the blood viscosity, R is the radius of the vessel, and r is the radial
position at which the velocity component, u(r) is computed (i.e. the axial flow
velocity u along the x-axis in the Cartesian coordinates or vz(r) along the tube
length (z) in the cylindrical polar coordinates) varies spatially as a function of
position (r) along the vessel cross section such that it reaches zero at the wall
with a maximum at the center. However, Poiseuille's flow is not a very realistic


13
model for studying physiological flow where one observes non-steady flow due to
cardiac pulsatility. Womersley solution to the pulsatile Navier-Stokes flow
equations takes into account the time-dependence of the pressure gradient and
more realistically characterize the blood flow observed in a moderately sized
vessel such as the CCA.
J.R. Womersley solved the Navier's Stokes equation for pulsatile blood
flow in 1955 [45]. His solution, commonly known as the Womersley's solution,
describes the pulsatile nature of arterial blood flow approximated by an
incompressible Newtonian characteristics. Considering only the motion parallel to
the axis of the vessel a cylindrical tube and with the assumptions that the
vessel is axisymmetric with no radial component, the Womersley's solution to the
reduced Navier-Stokes equation for the axial velocity (along the axis of the tube
in the x-direction) with a sinusoidally modulated pressure gradient is given by:
(2.7)
where w is the frequency and A is the amplitude of the sinusoidal pressure
gradient, y is the nondimensional radial position given by y = ^ and Jis a zeroth-
order Bessel function of the first kind accounting for the periodic pressure
gradient that drives the pulsatile flow.
These fundamental principles of hemodynamics therefore form the basis
for the various measurement techniques available today to estimate flow
properties such as blood flow velocity and WSS in both the experimental and the


14
clinical measurement setups. The key parameter of interest is the
nondimensional Womersley number a that defines the pulsatility and bluntness of
the flow profile in relation to viscous effects. The non-dimensional Womersley
a = R (2.8)
number is a ratio of the unsteady inertial force governed by the fluid density (p) and the
angular frequency (co) defined as ^ where T is the time period over which one cardiac
cycle pulsates [4]. At a lower a, the viscous force dominates favoring a parabolic velocity
profile. Therefore, an a of 1 or less indicates a laminar flow with a fully developed
parabolic velocity profile whereas a value larger than 1 indicates a blunter velocity
profile.
Akin to the Womersley number, a second parameter that is commonly used is
the nondimensional Reynolds number (Re). The Reynolds number is the key parameter
used to characterize the range of flow in any fluid mechanics study. It defines the
balance between the inertial force (i.e. kinetic energy per unit volume of flow) and
viscous force (i.e. the product of blood viscosity and velocity gradient):
Re = P-^ (2.9)
where p =1015 kg/m3 is blood density, D is the mean inner diameter of the blood vessel
and U is the mean flow velocity in the streamwise direction. A large Re number indicates
a dominant inertial force leading to increased turbulence whereas a smaller Re number
indicates a dominant viscous force favoring laminar flow with a parabolic velocity profile
[46].
Additional physiological flow related variables include the pulsatility index and the
resistivity index that have been shown to inform about the downstream arterial


15
resistance to pulsatile flow [47], [48]. The pulsatility index (PI) can be calculated as the
velocity pulse (difference between the peak systolic (Vmax) and minimum diastolic
(ymin)values) normalized to its mean value (ean) and is an indicator function of arterial
compliance:
pj Knax ^min (2.10)
^mean
ikewise, the resistivity index (Rl) can be calculated as the velocity pulse normalized to
its peak systolic value and is a measure of arterial resistance:
nr Knax- ^min (2.11)


16
3. Fundamentals of UltrasouncMmaging
Medical ultrasound imaging is a non-destructive technique for quantifying tissue
characteristics based on the velocity response of the insonicated particles in the
perturbed pressure field [5,6,8], The basic principle of image formation via
ultrasonography is schematically illustrated in Figure 3.1. We start with a brief
description of the transducer electronics used in a typical pulse-echo imaging
setup to understand the propagation of ultrasound beam and image formation.
This fundamental understanding will give us some clues on the origin of
challenges that the current 2D echoPIV encounters and will further guide us
towards finding a direct solution.
Linear Array Transducer Electronics
The acoustic pressure field is created in the medium when a linear array of
piezoelectric elements is activated with each activated element, sequentially,
emitting short bursts (two to three cycles) of high frequency sinusoidal pulses
across a medium of interest. An ultrasound transducer consists of 128 to 512
elements of piezoelectric material; these elements act both as the transmitter and
the receiver. The number of elements that is activated at a given time,
determines the aperture width. Typically a sub-array of 16 to 32 elements is
activated at a single point in time emitting spherical waves into the medium at a
radio frequency (RF, 2-10 MHz). These RF waves perturb the pressure field in
the medium, i.e. tissues with varying acoustic impedances (Z = p/c) defined by
the tissue density (p) and speed of sound [5].


17
Received Echo
sm(t)= t)cos(2?r/0t)
Emitted pulse
pg(t) = A(t)e~J27r^t Pixel Intensity: |/l(t)|2 Envelope = |i4(t)[
Figure 3.1.Schematic of ultrasound image formation.
A subarray of transducer elements is excited sequentially to perturb the pressure
field of the medium (p) and generate one beamline per excitation period (t)
recorded at the center of the subarray (s(r)). A delay and sum scheme is
employed to time the emission and reception of the ultrasound pulse echo, i.e.
the center element has the longest delay r compared to the adjacent elements
(T-iand t+1) since the round trip ( i for the echo traveling a depth of (z) with a
sound speed of c for time t is the shortest for corresponding to the center
element (xF). These returning echoes are summed and processed (B(z)) to
obtain the envelope signal A{t) that forms the raw signal for the grayscale
Bmode image.
The same transducer elements record the echo which is post-processed
into a 2D gray-scale digital image of the ROI that can then be investigated for
morphological (i.e. if the ROI is an artery, information such as arterial diameter
and intima media thickness can be extracted) and functional (i.e. blood flow
velocity and WSS) properties. Pressure field perturbation occurs as a series of
compression and rarefaction, i.e. elasticity counteracts a local compression due
to increased pressure amplitudes to return to equilibrium whereby inertia


18
counteracts return to equilibrium at a larger degree causing rarefaction (reduced
pressure amplitudes). This allows acoustic impedance to be expressed as a ratio
of the driving force, i.e. the pressure potential (p(t)) to the particle velocity
response (v(t)) or alternatively as a ratio of the material density (p) and
compressibility (k):

(3.1)
Difference in acoustic impedance between the two media gives rise to the
echo signals useful for image formation. When the boundary between two media
of different acoustic impedances is larger than the incident ultrasound
wavelength, the incident wave is reflected obeying Snell's law (Figure 3.2).
p , 7 7 A 7
te!2 \
R
Pine Zi + Z2 2Z
(3.2)
When the objects in the medium are equal or smaller than the ultrasound
wavelength, acoustic scattering occurs. It is this scattered wave or echo that
carries information intrinsic to the insonated tissues. In essence, a 2D ultrasound
image is an intensity based image, aka reflectivity or brightness mode (Bmode)
image. Each pixel intensity is distributed across a gray scale range from 0 to 255
based on the amplitude of the received echo signal. The echo amplitude
depends on the acoustic impedance difference, the number of scatterers per unit
volume, the sizes of these scatterers and the transducer frequency at which the
ultrasound is emitted. Acoustic scattering increases with ultrasound frequency.
Reflection does not depend on frequency. Referring back to Figure 3.1, the
emitted pulse (p() can be mathematically described as a decaying sinusoidal


19
wave modulated by its center frequency (f) with an initial time-dependent
amplitude {A(t)).
p(t) = A0(t)e~j2nft (3.3)
The amplitude attenuates as a function of the propagation distance (z) or
by an amount (A(z) = /Ae_fyz) due to ultrasound interactions with tissues such as
absorption, scattering and mode conversion (i.e. liquid to solid). Here, the
attenuation coefficient (jj) depends on the medium (i.e. tissue and fluid type) and
provides the relative intensity loss (dB) per centimeter of propagation for the
insonated medium. There is a linear dependence between the ultrasound
frequency and the attenuation coefficient. In other words, a high frequency
ultrasound wave decays more rapidly and therefore has a shorter depth of
insonification than a low frequency ultrasound wave.
This ultrasound pulse returns to the same transducer elements after a
round trip (2z). In an overly simplified example as illustrated in Figure 3.1, let us
consider two scatterers (objects that are smaller than the wavelength of the
ultrasound, e.g. <0.15 mm in size if the modulating frequency is 10 MHz and the
ultrasound speed in the tissue, c =1540 m/s) located at positions zi and z2with
if being the position at the near focal point, the received echo can then be
expressed as:
sm(t) = A(t)cos(2nft) = Re[A(t)e-Jnfot] (3.4)
As shown in Figure 3.1,a time delay of rm(z) is introduced for each
transducer element during both transmit and receive according to its relative
location to the center element (xF) so that the intensity of the echo signal


20
returning from the scatterers zi and z2 are compensated for the depth dependent
beam attenuation. This time gain compensation (TGC) therefore allows the
intensity distribution in the formed image to indicate the acoustic impedance
differences between tissue boundaries and inform about the inhomogeneity
properties therein that could be investigated for both structural and functional
studies (Figure 3.2).
A. Ultrasound scanning B. Dciccicd RF signal C. Envelop detection
LalKal Petition (mm)
Figure 3. 2. Image reconstruction from RF signals using a linear phase
array transducer.
As described in figure 3.1.,a subarray of elements are excited sequentially
resulting in formation of single beamlines per lateral sweep. Each scan lines (RF
lines) are processed (envelope detected, log compressed, filtered) to obtain a 2D
grayscale intensity map of the ROI.
This technique employed in a phased array transducer, as depicted in
Figure 3.2, is known as dynamic focusing that rephases the signals returning to
the individual transducer elements to improve the spatial resolution of the image.


21
The time compensated echoes received by the individual elements are summed
and compressed for an optimal gray-scale display. The compressed signal is
demodulated to extract its envelope, i.e. \A(t)\ that gives rise to the pixel intensity
distribution of the grayscale image, i.e. I = \A(t)\2. The envelop signal is
commonly known as the amplitude-modulated signal or the A-line or the RF
signal. Each A-line corresponds to the number of activated transducer elements
used for imaging the region of interest with its length corresponding to the
imaging depth. These A-lines are arranged together such that the number of
columns provides the lateral view of the ROI whereas the number of rows
provides the axial view thereby forming a 2D image of the ROI (Figure 3.2).
This kind of Bmode image formation via sequential activation of the
transducer elements is commonly known as the Delay and Sum (DAS) pulse-
echo imaging. For EchoPIV, the backscattered pressure field is reconstructed in
this manner, into a time series of two dimensional frames with the frameate
dictating the temporal resolution critical for velocimetry. In the next section we will
discuss how these Bmode images suffer from poor image quality due to
presence of speckles inherent to ultrasound imaging and the frame rate limitation
on the maximum resolvable velocity for arterial blood flow measurement.
Quantification of Arterial Blood Flow
The fundamental principles of hemodynamics and ultrasound imaging drive the
underlying mechanism of ultrasound based velocimetry such as Doppler and
EchoPIV. Ultrasound attenuation is dependent on both the frequency and the
propagation distance; while use of a high frequency ultrasound transducer


22
provides superior spatial resolution of the image at the cost of the imaging depth,
the need to image deeper tissues would require use of a low frequency
ultrasound transducer at the cost of image quality. In lieu of this tradeoff, the
moderately sized CCA therefore presents itself as a clinically desirable vessel for
hemodynamic study due to its superficial location that allows an easy access to
obtain blood flow details such as velocity and WSS. These hemodynamic details
inform clinicians of any impending disease development and/or progression in
Figure 3. 3. Doppler velocity spectrum.
A screenshot of the ultrasound acquisition procedure where the top figure
displays the real time grayscale image of the CCA, displayed on the bottom is the
velocity spectrum measured inside the sample volume seen at the center of the
lumen and the imaging parameters (center frequency of 10 MHz and imaging
depth of 4.0 cm).
the arteries. This way, a non-invasive diagnostic technique could be made
available for screening and stratifying patients at risk for clinical events relating to
arterial diseases such as stroke or heart attack.


23
Ultrasound Doppler velocimetry is based on the shift of the frequency, also
known as the Doppler shift, caused by the moving particles, i.e. the blood cells.
Doppler shift is the difference between the incident frequency and reflected
frequency. The moving reflectors obey the Hugyen's principles, in other words, a
collection of these objects in motion at varying velocities gives a superposition of
the contribution from the individual reflectors giving rise to a power density
spectrum (PDS) (Figure 3.3) [49]. Normalized PDS relates to the density of the
velocity distribution:
G(fd)
2
n
(1 ~~~
(3.5)
where the maximum frequency fmax is adjusted by the cosine of the angle &
between the direction of blood flow and the direction of the sound, known as the
Doppler angle and the center frequency of the transducer fc.
2v
fma
and the resulting doppler shift is given by
-cosd
(3.6)
fd(r)
2un

RJ
%]cos8
(3.7)
that takes into consideration Poiseuille's assumptions of an axisymmetric laminar
flow with a parabolic velocity profile:

1
(3.8)
which is equivalent to equation (2.6) where the exponent term n governs the
profile of the velocity (n = 2 for a parabola).


24
As can be clearly observed from equation (3.8), one of the drawbacks of
Doppler velocimetry is the fact that the field of view (FOV) is limited by the
insonation angle i.e. at a 90 degree angle, the measured frequency shift
becomes zero therefore providing no velocity information. Poiseuiiles
assumption requires relatively straight blood vessel which is not always the case
in real physiological conditions and additionally, calculation of single velocity
component reduces accuracy of WSS estimation which is measured as follows:
Auumax
UJ R (3.9)
There are several advantages to Doppler velocimetry: it is non-invasive,
i.e. it does not require intravenous injection of microbubbles for contrast and it
offers superior temporal and spatial resolution compared to PC-MRI velocimetry.
An alternative method for quantifying blood flow is the Phase Contrast
Magnetic Resonance Velocimetry (PC-MR) that provides three to four
dimensional blood flow characteristics in the arteries such as aorta and CCA[22],
[3], [34], [50].


25
4. Fundamentals of Ultrasound Echo Particle Image Velocimetry
Echo PIV uses ultrasound brightness-mode (Bmode) rather than Doppler for flow
measurement and is inherently capable of measuring two-dimensional (2D)
velocity vector fields. Unlike the Doppler velocimetry, echo PIV makes use of the
pulse-echo imaging to capture the two dimensional gray scale images of the
seeded particles. These particles are small microbubbles with a mean diameter
of 2-4 pcm that are filled with sulphur hexafluoride gas molecules inside a lipid
shell (SonoVue, Bracco Diagnostics, Inc., The Netherlands) thus creating a large
Online Signal Acquisition
VISCOUS FLOW
Figure 4.1.A flow chart illustrating the working principles of echo PIV.
Seeded flow is imaged and 2D grayscale images are constructed form 1D RF
signals. Particle image patterns are matched across the consecutive frames via
the PIV algorithm (described in text) and a 2D local velocity vector field is
obtained. A 1D phase averaged flow is be obtained. Data validation includes
removal of spurious vectors._______________________________________________________


26
acoustic impedance difference that gives rise to strong backscattered echo
signals (cf. Eqn. 3.2). patterns) in the form of the grayscale intensity values
(Figure 4.1).
As guided by our prior work [32-34], [51], microbubbles are injected at a
concentration of ~ 1-2 x 103 per ml to maintain optimal particle image density.
Following the image reconstruction scheme described in Chapter 3, two
dimensional Bmode images of the microbubbles are obtained from one-
dimensional radio-frequency (RF) signal which contains the information about the
location and displacement of these flowing particles (or more precisely their
image patterns; Figure 4.1). The imaging window is typically placed a few
millimeters away from the bifurcation.
1 Cross-correlation peak =1 velocity vector
20 30 40 50
ength of the artery [pixels]
Figure 4. 2. Cross-correlation based estimation of particle displacement.
An interrogation window of size 48x24 is applied to compute one velocity vector.
After scanning the entire FOV, spatially local instantaneous velocity vector fields
are obtained. WSS is then calculated by computing the spatial gradient of the
velocitv near the walls. _______________________________________________________
The long axis of the transducer probe is aligned longitudinally with the
centerline of the blood vessel such that blood flow is orthogonal to ultrasound
beam direction. This alignment provides a longitudinal view of contrast-enhanced


27
flow that is recorded in a time sequence using very high frame rates (480 680
frame per second [34]) with ECG-gating for post-processing synchronization.
The use of microbubbles gives excellent signal discrimination between
tissue and blood and allows velocity measurement close to the vessel walls
(Figure 4.2). Once the vessel walls are segmented in a semi-automated manner,
an interrogation scheme is applied wherein each consecutive image pair is
subdivided into smaller areas known as the interrogation windows [33], [51].
Denoting each image pair as F1 and F2 and the corresponding interrogation
windows as .and F2tJ the image pair is then compared to identify a
displacement of the intensity pattern from F^,J to F2tJ by using a normalized cross-
correlation function as defined in Eqn. (4.1) where R(s,t) denotes the cross-
correlation values when the F2tJis shifted by variables s and t known as the cyclic
lags, M and N are the number of rows and columns for each image frame.
1 M-1N-1
R (s, t) = ^ } F^,] (m, n)F2IJ (m + s,n + t)
771=0 71 = 0
(4.1)
These segments of measurement areas are called interrogation windows. The
size of the interrogation window determines to what degree the recovered
velocity field is spatially smoothed; there exists a tradeoff between the spatial
resolution and the accuracy of velocity estimations, whereby a larger window
improves the image quality but reduces the accuracy due to increased spatial


28
averaging of the velocity magnitudes [34]. In our clinical studies, an interrogation
window of 48 pixels by 28 pixels was employed.
In order to extract the displacement information from the cross-correlation
map, a 3-point Gaussian peak finding subpixel interpolation function is used [52].
Following Willert and Gharib (1991), this interpolation scheme finds the
maximum cross-correlation peak which informs about the two components of
instantaneous displacement vector field, xO and yO (Eqn. 4.2):
= ln(i?(i-l,;))-ln(i?(i + lj)) (4.2)
X 1 + 21n(i?(i -lj)) 41n(i?(i,;)) + 21n(i?(i + lj))
=. ln(i?(ij'-1))-\n(R(i, j + 1))
y =J 2\n(R(i,j -1))-41n(i?(ij)) + 2\n(R(i,j + 1))
where, R(i j) indicates the local coordinate of the peak cross-correlation peak at
the ith row and the jth column. Subsequently, two components of the velocity
vector field: u{xQ,t) and v(y,t) are obtained using the fundamental definition of
velocity (Eqn. 4.3).
.V, A*i


0.0 0.0
Figure 4. 3. Pixel intensity distribution as a function of particle
displacement [35].
An illustration of pattern matching to calculate particle displacement, a special
note is the out of plane displacement (x2') that occurs at large displacement that
cannot be captured at a low frame rate, a serious limitation of the current flow
imaging modality which is related to limited frame rate currently available.


29
Once the interrogation window has spanned the entire rows and columns
of the image pair (using a 50% overlap between each interrogation to improve
the spatial vector resolution), a spatially local instantaneous velocity
measurement is obtained: v(x,y,t) = f(u(x,t),v(y,t)):
Ax(x, y, t)
u(x,y,t) = vx
v{x,y,t) = vy
At
Ay(x,y, t)
At
(4.3)
Where Ax and Ay are the two displacement components calculated from (4.2).
As obvious from Eqn. (4.3), the time lapse between the consecutive image
frames (At) affects accuracy of the velocity measurement. The frame rate
governs the time lag between image frames: At =---------. As schematically
a a a Frame Rate 1
illustrated in Figure 4.3, a larger At due to a low frameate would cause the
displaced particle x2' to leave the measurement volume if the particles are
flowing at a high velocity. This out of plane loss of particle pair introduces error in
the velocity measurement since the particle images cannot be correlated
between successive frames (i.e. I1^ no longer contains the particle images from
required for displacement estimation). To prevent this, an optimal frame rate
is set at about eight times the maximum flow velocity estimated from the
ultrasound Doppler. The desired frame rate is obtained by adjusting the
ultrasound imaging parameters:
Frame Rate
T'f T'lir
N,
ele
(4.4)


30
Lateral Distance [mm]
Figure 4. 4. Two dimensional velocity and gradient (shear rate} vector
fields.
Actual flow measurement data from a healthy individual obtained using the
principles described in Figure 4.2. A uniform laminar flow is observed with
maximum velocity towards the center of the blood vessel and close to zero
velocity towards the walls. Velocity gradient is zero towards the center of the
vessel and maximum at the walls.
where, Tane =13^*D{cm)
Here, Tline is the acquisition time for each scan line, Nele is the number of
transducer elements used to create the ultrasound image of the ROI which
corresponds to the total number of scan lines (cf. Figure 3.2) and D is the
imaging depth [53]. Thus, a high frame rate can be achieved at the expense of a
smaller FOV. Additionally, the PIV standard one-quarter rule can be employed
which dictates that the particle displacement may not exceed more than a quarter
of the interrogation window size.
1450130011501000850700550400250100-50-200-350l-650-800-950-1^
5040302010
4 8
ELU,,90u-SInlBipey


31
A successful implementation of the PIV algorithm on the entire width of the
image for all time sequences results in a spatially local instantaneous velocity
vector field and corresponding shear rate map as shown in Figure 4.4 which was
obtained from a healthy study participant.


32
5. Reliability and Accuracy of Echo PIV for WSS Measurement
Introduction
The local hemodynamic environment, especially wall shear stress (WSS), plays
an important role in the initiation and progression of atherosclerotic plaque at
bifurcations, branch points and bends in the arterial tree [2], [22], [54]. Areas of
arterial wall that are exposed to low and oscillatory WSS exhibit changes in
endothelial cell gene and protein expression that are altered towards a pro-
atherogenic phenotype [12], [42]; these areas correlate with focal atheroma and
plaque [29], [55-57], Low WSS at these locations results from oscillation and
secondary flows that include separation, recirculation, turbulence and vortex flow
formation [2]. The carotid bulb is the main site of plaque development in the
carotid artery, where WSS is low and blood flow may be disturbed at the
bifurcation [55]. Although determinants of plaque progression are uncertain, the
local hemodynamic environment around the plaque surface may influence
whether plaques becomes quiescent, stenotic or more vulnerable to rupture [17],
[3], [55].
Measurement of carotid WSS is thus relevant for both physiological and
clinical purposes; WSS characterization would advance our understanding of the
role it plays in the disease process of atherosclerotic plaque formation whereas
WSS patterns unique to the plaque prone arterial regions could be used as
hemodynamic biomarkers for plaque burden. However, in vivo WSS cannot be
measured easily by current clinical methods and its measurement accuracy thus
far has remained elusive. Two vascular imaging based methods are commonly


33
utilized for measuring WSS in viva, ultrasound Doppler and the phase contrast
magnetic resonance imaging (PC-MRI). In both techniques, WSS is derived from
flow velocity magnitude. Ultrasound Doppler velocimetry (UDV) measures the
flow velocity at the center of the artery and extrapolates this single valued
centerline measurement for velocity estimation close to the vessel walls. WSS is
then derived from this velocity information based on the assumptions that the
vessel walls are uniformly straight and the flow is steady, laminar, non-oscillatory
and axisymmetric with a uniform velocity profile across the vessel cross-section.
These assumptions are not physiologically relevant which makes it difficult to
obtain a clinically useful interpretation from the UDV measured WSS information.
Several studies have evaluated its measurement accuracy and have showed that
unsteady nature of the blood flow, presence of skewed non-axisymmetric velocity
profiles and its technical limitations such as angle-dependent aliasing, spectral
broadening and the inability to resolve multiple velocity components lead to
inaccurate (either over- or under- estimation) of actual flow velocity [23], [27],
[58-60], Physiological studies of arterial WSS and routine clinical assessment of
carotid arterial plaque have so far relied mostly on conventional brightness-mode
(-mode) for structural visualization and Doppler centerline velocity assessment
for velocity and WSS estimation [61],[62].
PC-MRI is the state-of-the-art imaging modality that has emerged as an
essential tool in cardiovascular imaging for the diagnosis, monitoring and
treatment of cardiac diseases as it can measure multi-component flow velocity
profiles in the vasculature including the aorta and carotid arteries [30], [50], [62-


34
65]. PC-MRI provides assessment of vascular structure and morphology as well
as time-resolved three-dimensional blood flow measurement. Analogous to the
Doppler shift employed in ultrasound Doppler velocimetry (UDV), PC-MRI
estimates the velocity shift based on the change in the phase of the proton
magnetization when a magnetic field gradient is applied [66]. Unlike the one
dimensional velocity measurement obtained in UDV, PC-MRI obtains three-
dimensional three-component velocity information and does not rely on any
assumptions about flow. However, spatio-temporal averaging is inherent to PC-
MRI due to its large slice thickness (commonly reported as ~6mm in clinical
literature) and poor spatial (1-3 mm) and temporal (15 to 30 millisecond)
resolution [22], [34], [53]. Thus, the underestimation effect of PC-MRI is likely
more pronounced in small to medium sized arteries such as the common carotid
artery (CCA) compared to the aorta, where PC-MRI is used more frequently [30].
Additionally, PC-MRI requires a long acquisition time to capture one single slice
(-15-20 minutes).
To address the limitations present in the current techniques, we propose a
novel ultrasound based echo particle image velocimetry (echo PIV) for the
measurement of WSS in vivo. As an ultrasound-based imaging modality, echo
PIV offers advantages with regards to rapid acquisition with superior spatial (0.15
mm) and temporal (0.7 ms) resolution compared to PC MRI and its ability to
measure blood flow variables in small to medium sized blood vessels and
quantify multi-dimensional multi-component flow field unlike the UDV method.
We have recently demonstrated in-vitro the feasibility and accuracy of echo PIV


35
to measure two-dimensional (2D), two-component flow velocity information in
both steady and pulsatile flow environments [31-34], Conventionally, PIV is an
optical technique that uses a laser system to illuminate the seeded flow and by
tracking the particle intensity patterns across the imaging frames measures the
velocity field. The use of ultrasound instead of the laser source in the PIV
measurement offers three benefits:1)PIV, a gold standard for measuring a
velocity field, can be applied for in vivo flow measurement, 2) the microbubbles
generate high intensity signals in the vessel lumen and therefore enhance
contrast between the moving blood and stationary tissue improving wall
segmentation accuracy, and 3) tracking the intensity patterns generates a two-
dimensional velocity vector field providing hemodynamic information more
accurate to the actual flow environment [35], [67]. We validated our ultrasound
based PIV technique by measuring the flow velocity and WSS measurements in
a realistic carotid artery phantom and compared against the measurements
obtained from the same phantom using the optical PIV system. We found good
agreement between the two techniques for all variables of flow measurements
including the flow rate, velocity magnitudes and spatial profiles, and
instantaneous WSS distribution [32], [33], [51],[68].
The purpose of the present study was to develop the in vivo use of echo
PIV for measuring flow induced WSS in the human carotid arteries. Having
validated the technique against the standard optical PIV, we examined the
reliability and accuracy of echo PIV for measuring carotid WSS in vivo.
Specifically, we quantified the repeatability and reproducibility of echo PIV,


36
identified the major sources of uncertainty in velocity and WSS measurement
and finally compared its measurements against the reference PC-MRI technique.
Methods
Ethical approval
Participants were apparently healthy men and women recruited at the National
Institute for Health Research Exeter Clinical Research Facility, UK. This study
conformed to the Declaration of Helsinki and was approved by the National
Research Ethics Service Southwest (09/H0202/49). All participants gave written
informed consent.
Study design and research participants
Participants were asked to refrain from food drink, except water, for at least 2
hours before the visit, and to avoid smoking, drinking tea or coffee, alcohol and
strenuous exercise on the study day. Exclusion criteria for patients included
history of uncontrolled hypertension, pulmonary hypertension, renal disease,
hepatic disease, claudication, hypersensitivity to the contrast agent and
individuals outside the age range of 20 to 80 years. Included in the study were
data sets with adequate image density of contrast agent, a clear delineation of
the lumen boundary on the B-mode images and comparable peak velocity
measurements between UDV and echo PIV. The images from twelve participants
were involved in the initial experimentation to determine the optimal micro-bubble
concentration as guided by our prior validation work [32], [33].


37
Screening involved a physical examination and review of the medical
history. Participants were screened for contraindications to the ultrasound
contrast agent (Sonovue, Bracco Diagnostics, Italy). Participants were
considered healthy and asymptomatic if they showed no overt clinical
manifestations of disease.
Study 1.Repeatability and Reproducibility Echo PIV measurements were
randomly selected from 22 out of 28 participants. Repeatability data was derived
from a single observer who analyzed 44 data sets (22 per subject with two
repeats) on two separate occasions. Reproducibility data was derived from two
observers independently analyzing 22 data sets. Additionally, inter-scan
variability, as performed by a single observer, was also assessed by comparing
the analyses of two consecutive scans from each of the 22 participants for a total
of 44 data sets.
Study 2. Uncertainty in velocity measurements and propagation to the estimation
of l/l/SS. Data from 28 participants were used to investigate the sources of errors
in velocity measurement. After identification of the individual uncertainty sources,
the resulting uncertainty in the velocity measurement was calculated for both the
horizontal (streamwise) and the vertical (radial) components. The first order
Taylor series expansion was used to calculated the uncertainty in WSS
measurement resulting from the measurement uncertainties in the velocity
components.
Study 3. Comparison against PC MRI derived l/l/SS. Participants attended the
laboratory for echo PIV and PC MRI on occasions separated in time by one day


38
to six months. PC MRI provides a volumetric measurement of flow and thus the
phase averaged WSS measurements were spatially averaged around the vessel
circumference whereas the phase averaged echo PIV derived WSS
measurements spatially were spatially averaged along the vessel length.
Comparative analysis was conducted using the peak systolic WSS
measurements. Studies have shown that the accuracy of PC MRI for measuring
flow velocity is compromised in vessels of small to medium size diameter [25].
The mean diameter of a common carotid artery is usually around 6 mm, much
smaller than the aortic diameter which is larger than 10 mm. We therefore
measured the arterial diameter and investigated the effect of vessel diameter in
WSS measurements agreement between echo PIV and PC MRI.
Echo PIV procedure
Details regarding the use of this technique have been described previously [SI-
33], [36]. The technique is based on the synthesis of two existing technologies:
particle image velocimetry and contrast enhanced B-mode ultrasound imaging.
The system includes custom-designed computer-controlled ultrasound firing
sequences, a 10 MHz 128-element linear array transducer, radio-frequency data
acquisition and advanced algorithms for echo PIV analysis. Contrast enhanced
ultrasound imaging was performed using small microbubbles (contrast agent)
which were injected intravenously. Echo PIV tracks the motion of microbubbles
from one image frame to the next and uses cross-correlation to determine the
movement (displacement) of the bubbles from frame-to-frame. Frame rate is


39
used to calculate velocity information at any position in the field of view and a
velocity map constructed.
Participants attended the laboratory in the morning after an overnight fast.
Upon lying supine they were instrumented with a vital signs monitor and
cannulated to obtain intra-venous access for infusion of contrast agent. After a
rest period, conventional B-mode Doppler ultrasound was performed on the right
common carotid artery 1~2 cm upstream of the bifurcation [34]. Ultrasound
contrast agent was introduced thoughthecannulaintwosepaate2.4ml_
boluses or infused using a dedicated pump (VueJect pump, Bracco Diagnostics,
Italy). Echo PIV data were collected in 10-second segments using a customized
ultrasound imaging system (Sonix RP, Ultrasonix Medical Corporation, Canada).
Echo PIV data were collected at 500-700 frames per second such that the
desired frame rate was at least eight times the peak velocity magnitude of blood
flow as measured with conventional Doppler ultrasound. Following the infusion of
contrast agent participants were monitored for 30 minutes before being
discharged.
PC-MRI procedure
Protocol for the PC-MRI study has been reported previously [34]. Participants
attended the MRI suite either prior after the echo PIV visit but at around the
same time of day and after an overnight fast. After screening for safe entry into
the scanner they were instrumented with ECG and a neck coil. Scan duration
was 30-40 minutes. PC-MRI was performed using a 1.5 Tesla contrast-enhanced
fast field echo (T1-FFE) gradient echo sequence (Intera, Philips Medical


40
Systems, Cincinnati, OH, USA) to obtain retrospectively-gated tissue intensity
and phase velocity maps. PC MRI data was acquired by two experienced
radiologists. These were encoded in the 3 principle directions (head-foot, left-
right, and anterior-posterior) at five levels perpendicular to the longitudinal axis of
the common carotid artery. The center level slice was located just below the
carotid bifurcation. Two slices were located superiorly and two slices interiorly to
the center slice. The voxel size of MRI scanning was 0.6x0.6 mm2 in the cross-
sectional plane. Slice thickness was 6.0 mm and slices were spaced at 6.0 mm.
The total scan time for each individual was less than 45 minutes. Temporal
interpolation was used to obtain ~40 frames per cardiac cycle.
A 3D paraboloid function was fitted to the measured velocity profile to obtain
a global WSS (i.e. WSS component in the streamwise direction averaged
spatially along the circumference of the vessel) [50], [65]. Assuming that the
blood velocity profile at the boundary layer is parabolic, this algorithm
interpolates the paraboloid using the near wall velocity values with its peak
centerline velocity taken from the average of the central nine pixels [50].
Following ye et al.(1998) [50], the thickness of the boundary layer was
assumed to be 1 mm. Care was taken to match the WSS measurement locations
(approximately 12 cm upstream of bifurcation) by echo PIV and PC-MRI.
Carotid wall shear stress was then obtained via linearized approximation, i.e.
the shear stress (rrz) parallel to the vessel wall is equal to the sum of streamwise
(z-direction) velocity gradient and the spanwise (radial, -direction) velocity
gradient, i.e. ( -\multiplied by the dynamic blood viscosity (). Assuming


41
that the radial component of the velocity gradient is negligible, the axial wall
shear stress was approximated by ~ Following the original work of Oyre et
al.(1998) for measuring carotid WSS using PC MRI, three dimensional (3D)
paraboloid fitting [50] was applied to compute the velocity gradient. Assuming
zero wall velocity and axisymmetric parabolic velocity profile close to the vessel
wall, the velocity profiles were obtained by interpolating the near wall velocities in
the boundary layers of the vessels [50]. Wall shear rate (i.e. the axial velocity
gradient) was then calculated by fitting a parabolic profile to the measured close-
to-wall velocity data points as previously described. The cardiac cycle was
normalized to 1 second for point-wise comparison against the echo PIV
measurements. The axial WSS was interpolated around the entire vessel
circumference and phase averaged (i.e. the WSS measurements at individual
cardiac phase were averaged).
Statistical Analysis
Study 1.Repeatability and Reproducibility
Repeatability and reproducibility of echo PIV were investigated using the Bland-
Altman analysis technique [69]. For the intra-observer variability, the difference in
WSS measurements between the two repeats was plotted against the average of
the two. The scatter plot consisted a mean average difference bounded by its
uncertainty interval, i.e. 2 SD (standard deviation of the difference). The
magnitude of the averaged difference provides the bias in WSS measurement
during repeats. Bias and its standard deviation were calculated at peak systole,
end diastole and time averaged. The inter-observer variability and inter-scan


42
variability were examined using the same analytical procedure. Variables are
reported as mean+SD.
Study 2. Measurement Uncertainty
Echo PIV is a semi-automated measurement technique that requires a range of
user inputs and a fixed automated sequence of image processing operations,
such as an application of median filtering for the removal of background noise.
The algorithm is designed to measure flow characteristics based on a time-series
of ultrasound images of the seeded flow. Factors associated with the ultrasound
image acquisition influence the performance of the PIV algorithm, namely: the
frame rate at which the images are acquired governs the resolvable dynamic
velocity range; the image quality depends on the ultrasound operating frequency,
depth of insonication and field of view; and most importantly the seeding particle
density, size and dynamics [70], [71].The dynamic nature of flow causes image
quality to vary in time and space, which leads to non-uniform uncertainty
distribution throughout the flow field [70]. This makes it challenging to compute
uncertainty in echo PIV measurement since the sources of error relating to
ultrasound imaging and the PIV computation are coupled. In our study, we
measured uncertainty relating to WSS measurement at one spatial point at
different time points.
In echo PIV, the mean particle displacement is computed by means of
spatial cross-correlation of consecutive image pairs (cf. Chapter 4). Rewriting
Eqn. (4.3) in Eqn. (5.2), we note that the uncertainty of u originates from both the
displacement Ax in the streamwise direction (8x) and the time step At and


43
likewise the uncertainty of v originates from both the displacement Ay in the
radial direction (8y) and At.
u(x, t) = VX
dx Ax

dt At
(5.2)
,^ T/ dy
v(x>t) = Vy = -x-
Using the Taylor series method for uncertainty propagation [72], the
displacement uncertainty propagates to the velocity uncertainty as shown in Eqn.
5.3:
(5.3)
2
Key ultrasound imaging parameters that affect the image acquisition rame
rate are the beam line numbers, the depth of focus (single) and the field of view,
all of which are kept constant throughout the experiment. Following Timmins et
al. [70], we assume the uncertainty in the At is small enough to be negligible.
This reduces equation 5.3 to equation 5.4:
Uvx
mUax
(5.4)
Uvy=TtUAy
In this study, the uncertainties Uv (x,t) and Uv (x,t) are both functions of
spatial and temporal points. For simplicity, we computed the random standard
uncertainty at the first spatial point in the vessel length. UVx{l,t) and UVy{l,t)


44
were then computed from the standard deviation of the Vx(t) and Vy(t) at different
time points spanning three to four cardiac cycles. In essence, due to the nature
of the in vivo data under study, random uncertainty in the displacement
measurements was calculated based on the inter-cycle variability in particle
displacements (Ax and Ay).
Finally, the computed uncertainty in the two velocity components was
propagated to uncertainty in the measurement of WSS. WSS is the product of
blood dynamic viscosity, ^ which is considered to be constant at 0.032 Poise,
and the spatial velocity gradient (also known as the wall shear rate, SR), which is
the sum of the radial change of per change in y (i.e. 8y) and the lateral change
o\Vy per change in x (i.e. 5x). The data reduction equation was constructed as
follows to obtain the uncertainty equation for the wall shear rate (USR) (Eqn. 5.5)
_ (5.5)
5y 5x 5y 5x
dSR
^dSR
\ddx
"Sx)
In echo PIV, points are equally spaced at all time points for the given
experiment; i.e. 5x and 5y are constant for each cardiac cycle and thus the
random standard uncertainty in 5x and 5y is zero. This reduces Eqn. 5.5 to Eqn.
5.6:
UsR =
(5.6)


45
Finally, the uncertainty in WSS measurement was computed by multiplying Eqn.
5.5 with the dynamic blood viscosity, ^ = 0.032 P.
Total uncertainty in velocity measurement is the sum of the systematic
standard uncertainty and the random standard uncertainty (Eqn. 5.6) [72]. The
systematic uncertainty (b) of 0.235 pixels in displacement measurement was
obtained from reports on optical PIV that employed the 3-point Gaussian peak
finding sub-pixel interpolation algorithm as described in equation (5.1)[70]. The
displacement systematic uncertainty was propagated to systematic uncertainty in
velocity in a similar manner to random uncertainty propagation (Eqn. 5.4); the
same value was used for both the u and v components of the velocity vector,
V(x,y,t). Total random uncertainty was computed by taking the Pythagorean
sum of the uncertainties in Vx and Vy (Eqn. 5.7) where, Vx and Vy are the average
values of the respective uncertainties.
r = Uv= ^ Ul + (5.7)
The f/95uncertainty was then used to compute the total uncertainty in velocity
measurement:
TUv = 2 + (r)2 (5.8)
where, t95 v is the student's t for a degree of freedom of 27 which equals to 2.056
[72]. Individual contribution of the systematic and random uncertainties were then
calculated as in Eqn. 5.9 [73]:
n b2 (5.9)
lb b2+r2
Study 3. Comparison against PC MRI


46
Percent difference in WSS measurements between the echo PIV (WSSe)
and PC-MRI (14^5^) methods was calculated: % Difference
(WSSg-WSSp)
mean(WSSe+WSSp)

100%. Percent difference was calculated for WSS measurements extracted at
peak systole, end diastole and time averaged magnitudes.
Results
Participant characteristics
The study population comprised of 37 apparently healthy participants. Evaluation
of data from 12 participants was needed to determine the quality and density of
contrast agent required within the arterial lumen for optimal echo PIV analysis.
Application of the exclusion criteria resulted in usable datasets from 28
participants with acceptable UDV data and echo PIV velocity vector field
resolution.
For the repeatability and reproducibility study, 22 subjects were randomly
selected for inter-scan, intra-observer and inter-observer variability analysis. For
comparison against the PC-MRI measurements, all 28 subjects were evaluated.
WSS derived from echo PIV exhibited small intra-observer variability with
a mean bias of -0.05 +1 dyn/cm2 for peak systole, -0.10 + 0.9 for time averaged
magnitude and -0.03 0.5 dyn/cm2 for end diastole (Figure 5.1). Likewise, inter-
observer variability was also found to be low (Figure 5.2): Peak systolic WSS
bias:-1 2 dyn/crrr, time averaged WSS mean: -0.4 1.3 dyn/cm2 and End
diastolic WSS min: -0.4 0.7 dyn/cm2
Study 1.Repeatability and Reproducibility


47
limMtMUMWIIMIIIIIinHHMIMMHIIli
.a..
+2SD=1.1
-2SD=-1.3
10
20
30
..
+2SD=0.91
-2SD=-0.96
10
20
30
Average [dyn/cm2]
Compared to intra- and inter- observer variability, Bland-Altman analysis revealed
increased inter-scan variability with relatively wider limits of agreement (i.e. 2SD)
or peak systolic (-1.2 7 dyn/cm2), time averaged (-0.5 3 dyn/cm2) and end
diastolic WSS measurements (-0.5 + 1.5 dyn/cm2) (Figure 5.3, note the larger y-
scales).
1 1 5
o f
x 0
CO ¢0
CO s -5

+2SD=2.0
----

O
-0-
o
-2SD=-2.1
0
10
20
30
Figure 5.1.Repeatability.
Intra-observer variability was calculated as the difference in WSS measurement
between the repeated analyses by the same observer. Resulting bias was
extracted at peak systole (BiasMax), time averaged (BiasMean) and end diastole
(BiasMin)-
0

'a
5
i

cniujo/uapj ussejg CVIUJO'CAP ises


48
+2SD=1.1
IMBMIHUI
IIHMMMMmillllMIBtillimMmtlWIlBIIIMMBMIl mMIIIIMBBMIWWIIIHWIUMIIWlWIIMI MmilWIBIIBIWIWIHWII
o
c
5
0
2
8
-5
O
+2SD=2
HWHIHI_HWHH_MIWIWIIWWWmmWiWIWmMim_WHWmWHHIWIWIWWBWHMIWimi WHHWIWIIWIWHWIHWII
-0#

-2SD=-3
IIWnHMIHraiHailHNailllliMIlMIIlinHIlIIimiHflllHHailllHMIBHIIipaHHIMIMlIIlMHIHIIMIMIHIMilKlIiminilHIMinHHWni
IIIIM||iHI
0
10
20
30
2

m
CO
m -5
IIMnHMIHinliaiIHNailIIIiMIiIIIIBHIIIIBaiHflIIIiailIimiBHIIIHinHHIIMIIIIMH(HIIMimiHIHilKIIimiHIIHIMIIHnni
o
-2SD=_1.9
0
10
20
30
Average [dyn/cm

Figure 5. 2. Reproducibility.
Inter-observer variability was calculated by plotting the difference in WSS
measurements obtained from two independent observers against the estimate
averaged over the two observers. Resulting bias was extracted at peak systole
(BiasMax), time averaged (BiasMean) and end diastole (BiasMin).

I 0
+2SD=3

o
O
O


fEU/UAPJ
--5I
D-I
-2SI
O
0
#
o
o
o
Au
5
o
XI
SB5


49
20
0
-20.
+2SD=13
WMoniran nwmnMHMmnnmnM_MHWHnBm_nMmniMiwinMm_mwMmn o
o
jO.

IIIMMIK
o
o
o
Q
O -2SD15
IMIUMIIMMIIMHlHIMMVMIIHimMlliNHHMnHHMIHNHIIMIUINIMimilMIIMIIIMniUmiMHtlUMimRHHNIHINniiaillllMUi
10
20
30
20
0
20
oiii
+2SD=2.5


-2SD3.5
10
20
30
Average [dyn/cm
2,
Figure 5. 3nter-scan variability.
Inter-scan variability was calculated by plotting the difference in WSS
measurements calculated for the same individual at two consecutive time points,
i.e. scan 1 and scan 2. Resulting bias was extracted at peak systole (BiasMax),
time averaged (BiasMean) and end diastole (BiasMin).
Study 2. Measurement Uncertainty and Propagation
Variability in WSS measurements due to different observers or acquisition time or
repetitions was included in the investigation of measurement uncertainty in WSS
(Figure 5.4).
eo/uas2se!g 1 ED/UAS s E/UAS5weffi


50
Inter-scan
Intra-observer
Inter-observer
Peak Systole Time Averaged End Diastole
Figure 5. 4. Measurement uncertainty from measurement variability.
Inter-scan variability was the major source of uncertainty in WSS measurement
with the largest influence during peak systole and the lowest during end diastole.
Intra-observer variability contributed the least to WSS uncertainty. The error bars
on each magnitude bars are the standard error of the bias distribution across the
sample population.
Percent contribution of each individual uncertainties revealed that the majority
of uncertainty originated from the random sources of error (median: 84%, Figure
5.5). Likewise, contribution of uncertainty in each individual velocity component
was evaluated. Compared to the uncertainty in the u-component (i.e. UVx), the
uncertainty in the v-component of the velocity vector (i.e. UVy) was negligible over
the entire cardiac cycle (Figure 5.6).
8 6 4 2 0
KrEo/UAaAlEisJ8up


51
t----------------------------------------*
0 0.2 0.4 0.6 0.8 1
Normalized Cardiac Cycle [t/T]
Figure 5. 6. Uncertainty contribution from individual velocity components.
Uncertainty due to the velocity component (i.e. Uv = UVy(Ay,At) was negligible
compared to Uu = UVx^x,M).
Figure 5. 5. Percent uncertainty.
Random uncertainty contributed more to the overall uncertainty in velocity
measurement. The systematic uncertainty only contributed to a median of 15%
uncertainty in velocity measurement.
S/E A-30 0> u -uletsoun


52
Echo PIV
PC-MRI
Figure 5. 8. WSS measurement comparison between echo PIV and PC-MRI.
Significant difference was found in WSS measurements during peak systole
(p<0.001) and time averaged WSS (p=0.02).
The total uncertainty in velocity measurement resulted in a mean
uncertainty of 6.4 cm/s that translated to a mean uncertainty of 1.54 dyn/cm2 in
WSS measurement.
Figure 5. 7. Uncertainty in WSS measurement.
On an average, the WSS measurement uncertainty due to inter-cycle variable
was low (max: 3.1 3 dyn/cm2, mean: 1.541 dyn/cm2 and min: 0.720.3
dyn/cm2).
5 0 5 0 5 0
3 3 2 2 1 1
2E3/UAPSSM


53
Study 3. Comparison with PC-MRI
Normalized Cardiac Cycle
Figure 5. 9. Temporal distribution of WSS.
Both PC MRI (red) and echo PIV (black) measured similar temporal patterns of
WSS though the absolute magnitudes varied significantly for the majority of the
population samples.___________________________________________________________________
Compared to echo PIV, the time averaged WSS was underestimated by PC-MRI
by 40% overall (Figure 5.8). Likewise, PC-MRI underestimated WSS by 37%


54
during peak systole. The maximum discrepancy in WSS measurement between
the two methods was observed during diastole, a percent difference of 62%.
However, the temporal WSS pattern showed good qualitative agreement
between the two methods which was supported by the point-wise correlation
analysis (Figure 5.9) that revealed good agreement (r=0.89, p < 0.001). This
suggests that the percent difference in WSS measurements between the two
originated from a systematic uncertainty in the measurement technique.
0
WSSPC MR[dyn/cm ]
20
Figure 5.10. Point-wise correlation analysis.
WSS Regression between Echo PIV vs. PC MRI. A good correlation was found
between velocity and WSS measurements using PC MRI and echo PIV (both at
r=0.89 at p<0.05). WSS measurement using echo PIV appeared to vary at a
larger proportion to the PC MRI derived WSS values compared to the velocity
measurements between the two methods.
40
API
AldoLP
M
Further investigation in the temporal distribution of phase averaged WSS
revealed significant inter-subject variability in absolute difference in WSS
magnitudes between the two methods (Figure 5.9) but modest point-wise


55
correlation overall (a sample mean Pearson's correlation coefficient, r = 0.89,
p<0.001) as shown in Figure 5.10. The discrepancy in WSS measurements was
investigated by examining the vessel diameter and quantifying its impact on WSS
measurement accuracy.
200
150
100
50
AWSS %
-50
-100
-150
-200.
o
laiimiiii 1111111mil
iiiiiiii 111111111111
D
D:6.5mm
O
..............................""D..........................
o o
1111111^^111111111111 lllllllllllllll1111111lllll]^^lll 1111111
IIIIIIII 1111111 mm
0
D:5mm
0
10 15 20
Number of Subjects [n]
25
100
11111111111mi imiiai
AArea%
30
-100
Figure 5.11.Maximum percent differences in peak systolic WSS
measurements were observed when the vessel diameters were smaller.
Peak systolic WSS measurements were chosen because the vessel diameters
are the largest during systole. Percent differences in WSS (AWSS%) and cross-
sectional area (AArea%) measurements between the two methods were plotted
on the same figure to evaluate the influence of the vessel size in WSS
distribution for each individual. The green dashed lines indicate 1 standard
deviation for the AArea%.
Discrepancy in the measurements of cross-sectional area between PC MRI
and Echo PIV led to a discrepancy in WSS measurements (Figure 5.11). At a
given level of peripheral resistance with constant volume flow, the mean flow
velocity in a straight vessel is determined mainly by lumen cross-sectional area
as shown by the steady state Hagen-Poiseuille's equation: M^55 c Flow i.e.
wall shear stress is least where the diameter is greatest [56]. This translates to
an inverse 3/2 effect of the cross-sectional area in the determination of WSS. In


56
this study, overestimation in cross-sectional area by PC MRI led to
underestimation in WSS by almost a factor of 2. The range of the vessel
diameter also played a role in WSS agreement between the two methods. In our
study, the mean diameter was 7.51 mm. We found that PC MRI severely
underestimates WSS when the vessel diameter is about 5 mm. For the vessel
diameter closer to 10mm, discrepancy in cross-sectional area measurements
between the two methods was lessened.
ID 15 id 8
200
150
100
50
AWSS %
-50
-100
-150
-200.
0
ID 15
1
ID 8
Echo PIV
D:10mm
o
i O e
O
o
1111111111MIMlfflll
D:10.3mrn
o
11111 1111111111
PC MRI
o o w
o
100
AArea%
5 10 15 20
Number of Subjects [n]
25
30
100
Figure 5.12. For a Given Diameter, Echo PIV Measures peak systolic WSS
Within the Same Magnitude Range whereas PC MRI Underestimates in the
second case (subject number 8).
The fact that for a large vessel with about the same diameter 10mm), echo PIV
measured similar WSS magnitudes but PC MRI underestimated WSS in subject
ID 8 compared to ID 15 suggesting that a different independent contributor might
be present.____________________________________________________________
However, the agreement in WSS measurements for a given vessel size was
not entirely a linear phenomenon as can be inferred from the non-linear
distribution of the data points across the zero mean plus the finding that even for


57
a vessel with similar diameter (~10mm), PC MRI underestimated WSS for one
subject compared to the other (Figure 5.12).
Discussion
The main findings of this study are that:1)Echo PIV can be used in humans to
generate WSS with good repeatability and reproducibility; 2) the primary sources
of uncertainty in WSS measurement using echo PIV are image particle density
and lateral resolution; and 3) compared to echo PIV, PC-MRI underestimates
inst3nt3n6us W m63suem6nts ovsr ths cardiac cycls.
Inter-scan variability in WSS measurement is a measure of the difference
in image particle density between two consecutive acquisitions and was found to
be a significant contributor to WSS measurement uncertainty similar to the
standard optical PIV [74], [75]. As guided by our previous in vitro work [32-34],
microbubbles were infused at a concentration of about 2-3 x 10 particles per
milliliters by using a controlled pump. Lateral resolution, which is governed by the
number of scan lines per frame, also significantly contributed to the uncertainty.
Lateral resolution affects the accuracy of computing the displacement vector in
the streamwise direction using the Gaussian peak finding interpolation method
described in equation 5.1[33], [34]. This indeed translated to a greater
contribution in velocity measurement uncertainty from the horizontal component
of the velocity vector (i.e. Vx). Further studies should therefore be focused on
optimizing the lateral resolution and consistency of optimal particle image density
during image acquisition[31-34]. The uncertainty in velocity measurement can


58
thus be reduced by optimizing the contributing factors during both the image
acquisition and post-processing phases.
PIV is a very useful measurement tool for quantifying flow fields. In
biomedical applications, ultrasound based echo PIV offers the same benefits that
optical PIV has provided to the aerospace and mechanical engineering
communities. Measurement uncertainty relating to PIV variables has only been
recently quantified in a rigorous manner by a multi-institutional team led by
Vlachos[70], [76], [77]. PIV measurements are time-resolved and non-linear due
to the nature of the flow field being measured. PIV uncertainty quantification
therefore poses a unique challenge in that the standard uncertainty technique of
measuring the mean and variance is not adequate and furthermore assumes that
the accuracy of a measurement system varies linearly with the uncertainty in the
measurement which is not the case; measurement uncertainty varies nonlinearly
with the variance in the measurand and/or the measurement system [70], [76].
In this study, we presented the measurement uncertainty of echo PIV for
computing the velocity vector field in both the horizontal and vertical directions.
Of importance was how this uncertainty in velocity measurement propagated to
the wall shear stress estimation. Applying the Taylor series expansion, we
quantified the influence of these error sources in WSS calculation. PIV
uncertainties varied within the measurement field due to changes in the local
contributors. Two major sources of random uncertainties were identified: lateral
resolution (i.e. pixel resolution) that depends on the number of beam line


59
numbers used in the each ultrasound frame reconstruction and the dynamic
velocity range that is related to the lateral resolution but also the frame rate.
Timmins et al studied the effects of specific eosources (diameter,
density, displacement and shear) on PIV accuracy which differed depending on
the type of PIV algorithms used for motion estimation [70], [78]. Of the four
sources, displacement gradient with the interrogation window and smaller particle
image diameter were the most significant sources of uncertainties. Given the
nature of our in vivo data, we were not able to run an experiment to quantify the
measurement uncertainty originating from sources such as particle image
diameters and shear. Instead, an alternative approach was employed to identify
the two sources of random uncertainty: particle image density and particle
displacement. As previously described, inter-scan variability was used to
evaluate the effect of particle density in WSS estimation and inter-cycle variability
was used for evaluating the displacement uncertainty.
Hemodynamic flow generates varying levels of uncertainty throughout the
measurement field for PIV because of fluid and structural coupling, and the
pulsatile nature of blood flow in the arterial tree [76], [77], [79]. The pulsatile flow
is characterized by time varying high shear at the edges (vessel walls) and a
core flow with a nearly uniform velocity profile. Wilson et al. [79] showed that
larger amounts of random error are present in regions with higher wall shear
while smaller, systematic uncertainties are more dominant in the center of the
flow where shear stress is close to zero [79]. In agreement with this finding, our
study showed that random standard uncertainty was indeed dominant in WSS


60
measurement. This most possibly arises from the poor lateral resolution 0.5
mm) that currently exists in any ultrasound system including the echo PIV
system. Additionally, fluctuations in the shear layer during each cardiac cycle
also introduce temporal variations in the magnitude of WSS that contribute
uncertainties at different locations and times.
Echo PIV has a better spatial resolution (-0.15 to 0.4 mm) compared to
PC MRI (1 mm). Because of the limited spatial resolution and large slice
thickness (6mm) in PC MRI, flow measurements are spatially averaged across
the lumen. In this study, the echo PIV derived WSS measurements were also
spatial averaged along the length of the vessel. However, in PC MRI, the WSS
measurements are averaged around the circumference of the vessel which
underestimates WSS to a larger degree than an axial averaging along the vessel
length. Spatial averaging over a larger volume with few actual data points (due to
overestimation of luminal area) led to significant underestimation in WSS [22],
[25], [80]. Potters et al. (2014) demonstrated that PC MRI measured WSS has
higher magnitudes at higher spatial resolutions [25]. Additionally, they showed
that the effects of spatial resolution on WSS measurement accuracy differed
between the fitting methods employed for near-wall velocity interpolation. Cheng
et al. (2002) also showed that even in the aorta, the circumferentially averaged
WSS incurred a mean absolute error of 28% at a spatial resolution commonly
observed in an in-vivo imaging which was reduced to 15% when the resolution
was doubled [80]. In addition, the position of the vessel wall within the edge pixel
of the sample volume cannot be determined with certainty due to the limited


61
spatial resolution inherent to PC-MRI [81].This limitation is more problematic in
the smaller or medium sized carotid arteries [25], [37]. We found that, in the
vessels with a larger diameter, i.e. closer to 10mm (here as observed for subject
number, n=15, with a vessel diameter of D=10.3mm and again at n=8 and
D=10mm), the percent difference in diameter measurements between the two
methods tend to be lower though the percent difference in the corresponding
WSS measurements was not linear suggesting presence of a second
independent variable that caused WSS underestimation (3). Except in three
cases (n=1, n=16 and n=19), PC MRI consistently underestimated WSS across
the study population.
Comparison of echo PIV measured hemodynamic variables (diameter and
WSS) against the PC MRI measurements indicated that PC-MRI might not be a
good reference technique for carotid WSS measurement due to inaccuracy in
WSS measurements arising from its limited spatial resolution, circumferential
averaging and diameter overestimation both of which led to significant
underestimation of WSS. Nonetheless, volumetric measurements of in vivo flow
that can be obtained from PC MRI are still useful for qualitative evaluation of the
temporal WSS distribution, as our study showed good agreement in temporal
WSS patterns between the two methods, but it should be noted that the absolute
magnitudes of carotid WSS are underestimated.
Inaccuracy in WSS measurements can also result due to segmentation
errors [25]. WSS measurements can incur an error of 34% if the wall position in
the edge pixel is not correctly estimated [37]. Potters et al. (2014) found a


62
segmentation error of 40% and suggested that at least 8 voxels were required
across the diameter to obtain a WSS accuracy of 5% and a precision of 20% in
simulated data [25]. The use of microbubbles in echo PIV offers easy delineation
of the high intensity moving particle images from the stationary arterial walls
resulting in good segmentation accuracy [32], [33], [36]. In our study, PC MRI
underestimated peak systolic WSS by 38% and time averaged WSS by 40%. A
significantly larger 62% difference was found during diastole. This is possibly
related to the low particle image density during the diastolic phase when the
blood flow is minimum. As a result, echo PIV underestimated the flow velocity
compared to PC MRI and consequently shear stress on the vessel walls.
Our study was limited by the small sample size. Second, the scanning planes
in the measurements by the two modalities were different: echo PIV measured
the longitudinal plane of the right carotid artery whereas PC-MRI measured
global WSS magnitude that was spatially averaged over the cross-sectional
plane. The maximum resolvable velocity in the current echo PIV system is about
2~2.5 cm/s due to the cuirent frameate of ultrasound -mode imaging. Higher
velocities could be measured at the cost of field of view which in turn would affect
the spatial resolution. It should also be noted that unlike PC MRI, the current
echo PIV system is not yet able to measure vascular hemodynamics in three-
dimensions and therefore any effects from secondary flow components are not
realized. These limitations could be overcome by employing advanced
techniques such as interleaved imaging which has been shown to increase the
maximum resolvable dynamic velocity range [82], [83].


63
In summary, echo PIV is a novel ultrasound-based velocimetry technique that
provides spatial, multi-component, and time-resolved velocity and WSS
measurements. Echo PIV is highly repeatable and reproducible with good
reliability for measuring in vivo WSS compared to PC MRI. Given the large
discrepancies in instantaneous WSS measurements between echo PIV and PC
MRI, but not temporal patterns, echo PIV may be more appropriate for
measurement of WSS in small to medium sized arteries such as the common
carotid.


64
6. Characterization of Carotid WSS in Healthy Subjects
Introduction
Hemodynamic wall shear stress (WSS) is implicated in vascular endothelial
dysfunction and atherogenesis [6], [12], [29], [30], [84]. Endothelial cells lining the
arterial walls are mechano-sensitive and respond to different types of WSS
transduced by blood flow [18]. Regions of arterial walls exposed to low and
oscillatory WSS are predisposed to atherosclerosis while high WSS is pro-
atherogenic but increases vulnerability to plaque rupture in the advanced stage
[6],[12]. Since endothelial dysfunction develops much before the clinical
manifestation of atherosclerosis, the mechanism by which low and/or oscillatory
flow contributes to endothelial dysfunction remains an active research area but
several issues remain uncertain [8], [10], [18-20], This is in part because WSS is
difficult to measure in vivo. In particular, it is difficult to measure flow with
sufficient spatial and temporal resolution to determine accurate estimates of
WSS. High spatio-temporal resolution means flow patterns can be measured
near the vessel walls throughout the cardiac cycle to determine any time-varying
characteristics in WSS that might be physiologically and clinically important. This
is relevant because spatial gradients in shear enhance activation of endothelial
transcription factors [8] and temporal gradients caused by high flow pulsatility are
known to stimulate endothelial cell proliferation and inflammatory gene
expression [10],[19].
Current methods to estimate in vivo WSS are primarily based on two imaging
modalities: Phase-contrast magnetic resonance imaging (PC-MRI) and


65
ultrasound imaging. PC-MRI provides volumetric flow visualization but is
relatively expensive, time consuming, and has limited spatial and temporal
resolution [21].Because of this, ultrasound Doppler velocimetry (UDV) has
become a popular method to estimate WSS in studies of endothelial function and
the natural history of atherosclerotic plaque. This method is inexpensive, readily
available and easy to use. However, it is not clear whether it provides an
accurate estimate of WSS. The main threat to accuracy is that it measures a one
dimensional velocity component rather than measuring the whole velocity vector
field. This introduces error as it is not possible to measure the spatial gradient of
the velocity distribution near the vessel walls, which is required to accurately
calculate WSS. Instead UDV measures the centerline peak velocity {Vmax) which
is then extrapolated over a theoretical parabola from upper to lower wall.
However, pulsatile arterial flow does not always exhibit a parabolic velocity
profile, meaning any discrepancy between the actual and the assumed velocity
profiles propagates error in WSS measurement [6], [27], [28].
We have developed and validated [31-34] an ultrasound based method called
echo particle imaging velocimetry (echo PIV) that can be used to more accurately
measure WSS. Echo PIV uses the two-dimensional (2D) ultrasound image of the
arterial segment to measure the local flow velocity distribution, producing a 2D
velocity vector field within an arterial segment. WSS measurement based on
UDV is being used extensively in physiological studies, yet its accuracy and utility
are uncertain. As such, information about the usefulness of these estimates and
their limitations are needed for better interpretation of WSS data. Our purpose


66
was to compare arterial WSS measurements estimated from ultrasound Doppler
with those from echo PIV.
Methods
Ethical approval
Participants were apparently healthy men and women recruited at the National
Institute for Health Research Exeter Clinical Research Facility, UK. This study
conformed to the Declaration of Helsinki and was approved by the National
Research Ethics Service Southwest (09/H0202/49). All participants gave written
informed consent.
Participant screening and baseline characteristics
Participants were asked to refrain from food or drink (except water) at least 2
hours before the visit, and to avoid smoking, drinking tea or coffee, alcohol and
strenuous exercise on the study day. Medical history, electrocardiogram (ECG),
height, body mass, waist circumference, and blood pressure were obtained and
twelve-hour-fasting blood samples were collected in accordance with the U.K.
National Quality Assessment Scheme [34], [68]. Doppler measurements were
collected before contrast agent injection (SonoVue, Bracco, Italy) and echo PIV
imaging. Twelve participants were involved in the initial experimentation to
determine optimal micro-bubble concentration as guided by our prior work [32],
[33]. Inclusion criteria were: Adequate contrast agent density, clear delineation of
the lumen boundary on the B-mode image and comparable peak velocity
measurements between UDV and echo PIV. Exclusion criteria included history of


67
uncontrolled hypertension, pulmonary hypertension, renal disease, hepatic
disease, claudication, hypersensitivity to the contrast agent and individuals
outside the age range of 20 to 80 years.
UDV based WSS measurement
Pulsed wave Doppler imaging (Sonix RP, Ultrasonix, Canada) was used to
measure maximum blood flow velocity (Vmax) from the right common carotid
artery (CCA) at a sample volume placed in the center of the vessel at a recorded
location upstream of the carotid bifurcation. The pulse repetition frequency (PRF)
was set at 5 kHz with the transducer probe (L14-5/38) parallel to the centerline
axis of the artery and Doppler angle set at 60 [53]. WSS was calculated from
the centerline Vmax using the standard Hagen-Poiseuille's equation [28], [85]:
WSSvmax = |i4Vmax/D, where D is carotid artery inner diameter and ^ is dynamic
viscosity assumed constant at 0.032 Poise (Figure 6.1). This equation uses the
Poiseuillean assumptions that flow is steady, fully developed (i.e. shape of the
flow velocity profile does not change and the mean velocity is half the maximum
flow velocity) and has a parabolic velocity profile. The UDV derived WSS
measurement (WSSvmax) provides an estimate of the mean flow WSS within the
Poiseuillean flow assumptions.
Echo PIV derived flow variables
We have previously shown that echo PIV can measure accurate velocity profiles
in the common carotid artery by tracking grayscale image patterns of


68
microbubbles in the flow [31-34], Echo PIV uses ultrasound B-mode rather than
Doppler Velocimetry Echo Particle Image Velocimetry
MMMMT MMMM MMMMt MMMMt 4MMMK 4NMMM MMMM MMMM MMMM IMMMia Steady flow Parabolic Velocity P^i'e , Unsteady flow ,_. Local Velocity Pnofite

Centerline Peak Velocity ¥max Velocity gradient 0

4Vmax WSS = p. g~ du WSS = |y=R
Dashed line = assumptions made u = flow velocity in the streamwise direction
H = dynamic blood viscosity y = position along the vessel cross-section
D = arterial luminal diameter R = interna! radius of the vessel
Figure 6.1.Comparison between Doppler velocimetry and echo PIV.
Ultrasound Doppler Velocimetry calculates flow induced shear stress on the
vessel walls by assuming a parabolic velocity profile across the arterial lumen. In
contrast, echo particle imaging velocimetry measures actual velocity profiles by
statistically tracking ultrasound images of seeded particles (micro-bubble contrast
agent) at consecutive time points. Spatial change in the velocity is calculated
near the upper and lower walls from which wall shear stress (WSS) is computed.
Doppler for flow measurement and is inherently capable of measuring two
-dimensional velocity vector fields. The use of microbubbles gives excellent
signal discrimination between tissue and blood and allows velocity measurement
close to the vessel walls (Figure 4.2).
The echo PIV imaging window was selected to overlap with the location of
the UDV measurements such that both UDV and echo PIV measured a similar
flow region. The long axis of the transducer probe was aligned longitudinally with
the centerline of the blood vessel such that blood flow was orthogonal to


69
ultrasound beam direction. This alignment provides a longitudinal view of
contrast-enhanced flow that is recorded into a time-series of images acquired at
very high frame rates (480 680 frame per second [34]), with ECG-gating for
post-processing synchronization.
The echo PIV velocity vector field was computed by cross-correlating
consecutive frames (1100 to 3200) in the time sequence as reported in our prior
work. The spatially and temporally local velocity vector field was used to
construct the spatial profile of flow velocity from upper to lower wall at different
time points (Figure 4.4). To quantify the shape of this velocity profile, we used the
shape-index (s-index). The s-index (s) was derived by fitting the Hagen-
Poiseuille's analytical velocity profile (Eqn. 6.1) to the measured data points [6]:
V(y) = Vmax [l-|||S] (6-1)
An s-index of 2 generates a parabolic profile representative of fully-
developed laminar flow; this also represents the foundational assumption behind
the UDV-method for calculating WSS. S-index values greater than 2 represent
velocity profiles that are blunted at the center with sharp spatial gradients at the
vessel walls. We extracted the echo PIV measured velocity profiles at five
different time points in the cardiac cycle, as follows:1)accelerating systole past
the time-averaged value (C1),2) peak systole (C2), 3) decelerating systole
coinciding with the first notch (C3), 4) mid-diastole (at 0.6 s in the cardiac cycle;
C4) and 5) end-diastole (C5). These five time points were selected to investigate
WSS distribution at characteristic points in the cardiac cycle where flow patterns
vary significantly, e.g. accelerating flow (C1) is known to be less turbulent


70
compared to mid-late systole (C3) and early-mid diastole (C4) [4], [46], [86], [87].
Characterizing the spatial and temporal variation of these velocity profiles
allowed us to compare the mean flow WSS estimate obtained via the
conventional UDV method with instantaneous echo PIV WSS.
Characterization of flow pulsatility using the Womersley's number
The non-dimensional Womersley (a) number was also obtained for each
participant (Eqn. (6.2)):
a = R
The Womersley number is a ratio of the unsteady inertial force governed by the
fluid density (p) and the angular frequency (co) defined as 2n/T where T is the
time period over which one cardiac cycle pulsates [46]. At a lower a, the viscous
force dominates favoring a parabolic velocity profile. Therefore, a of 1 or less
indicates a fully developed parabolic velocity profile whereas a value larger than
1 indicates a blunter profile. The UDV method of estimating WSS assumes a of
1;thus, echo PIV WSS measurements with values larger than 1 indicate larger
differences between the two methods.
Echo PIV based WSS measurement
WSS was calculated directly from the echo PIV derived local velocity
vector field by computing its spatial gradient (also known as shear rate) at the
radius (R)


71
dv
WSS = ^Yy
(6.3)
estimated at y = R where y is the radial position across the vessel lumen, v is the
radial velocity and dv/dy is the shear rate (Figure 6.2a-b). The time sequence of
velocity vector fields obtained from echo PIV allowed extraction of detailed
temporal and spatial shear rate information (Figure 6.2b). Spatially local WSS
measurements (i.e. WSS measured at one spatial point along the vessel length
within the field of view) were used to compare against the UDV estimates.
Temporal WSS values were extracted at five different points in the cardiac cycle
(i.e, C1-C5) as described above. Mean WSS was calculated as the time-
averaged WSS across one full cardiac cycle. Echo PIV WSS measurements
were obtained from both the upper and lower walls of the CCA and averaged.
Ensemble averaged WSS waveform analysis
Because Echo PIV produces more detailed characterization of WSS than
UDV, we performed a qualitative and quantitative analysis on an ensemble
averaged waveform. To construct the ensemble averaged waveform, WSS
waveforms obtained from each individual in the cohort were spatially and
temporally phase averaged and the following three temporal metrics were then
derived:1)the time-averaged (TA) WSS; 2) the decay rate of the systolic peak
shear calculated by fitting an exponential decay curve to data points extracted
from the systolic peak to the base of the first notch; and 3) the systolic time
duration, i.e. the time difference between the initial upstroke of systole to the time
of arrival of the first prominent notch. Instantaneous WSS measurements were


72
spatially and temporally phase averaged over four cardiac cycles and ensemble
averaged for each study group to construct a healthy and a TIA phenotypical
waveform.
Statistical analysis
Percent difference in WSS measurements between the UDV and the echo PIV
methods was calculated (Eqn. 6.4):
(WSS WSSV ) (6.4)
% Difference = --------------ma 100%
mean(WSSi + WSSVmax)
Here, WSSi (i =[1,5]) indicates the echo PIV WSS measurements extracted at
the five characteristic time points. The percent difference between the two mean
WSS estimates was also calculated in a similar manner. The paired t-test was
used to compare the UDV derived mean WSS estimate (i.e. WSSvmax) with the
echo PIV derived instantaneous WSS measurements. A one-way balanced
ANOVA was conducted to determine differences in WSS at different time points
in the cardiac cycle (C1-C5). A probability of p < 0.05 was considered statistically
significant for both tests. WSS measurements obtained from the two methods are
presented as mean standard deviation.
Results
Participant characteristics
The study population comprised 37 apparently healthy participants. Evaluation of
data from 12 participants was needed to determine the quality and density of


73
Table 6.1.Participants Characteristics
Parameter (n=27) Mean SD
Age (Male, n=18) 55.2 12
Body mass (kg) 72.4 10
Height (m) 1.7 0.1
BMI 24.4 3
Waist circ. (cm) 85.6 9
Hip circ. (cm) 96.3 8
Waist-Hip Ratio 0.9 0.1
Systolic BP (mmHg) 124 13
Diastolic BP (mmHg) 77.5 9
Pulse Pressure (mmHg) 46.4 8.9
Heart Rate (b/min) 63.8 9
Cholesterol (mmol/ 5.4 0.9
iglycerides (mmol/ 1.2 0.5
HDL TG (mmol/L) 1.5 0.4
LDL TG (mmol/L) 3.4 0.8
Chol:HDL 3.9 1
Sodium (mmol/L) 139.3 2
Potassium (mmol/L) 4.5 0.4
Creatinine (mmol/L) 78.8 13
Albumin (g/L) 45.1 3


74
contrast agent required within the arterial lumen for optimal echo PIV analysis.
Application of the exclusion criteria resulted in usable datasets from 27
Participants with acceptable UDV data and echo PIV velocity vector field
resolution. Characteristics from these participants are presented in Table 6.1.
Differences between UDV and echo PIV
Mean WSS calculated from UDV was lower than the time averaged WSS
measured using echo PIV (10.12 dyn/cm2 versus 14.35 dyn/cm2, p<0.001,
Figure 6.2).
Upper Wall (U) Lower Wall (L) Average(U,L) E Doppler
Figure 6. 2. Instantaneous WSS Measurement.
Instantaneous WSS measurements were extracted at five different time points in
the cardiac cycle: accelerating (C1), peak(C2), decelerating(C3) systolic phases
and mid-diastolic (C4) and end-diastolic (C5) phases. These measurements,
along with time averaged (TA) WSS values were compared between the two
methods. Asterisks represent statistical significance (p<0.05).
Compared with echo PIV WSS at C1-C5, the UDV method underestimated WSS


75
at C1,C2 and C3 (22.28 dyn/cm2, 41.212 dyn/cm2and 14.57 dyn/cm2
respectively) and over-estimated at C5 (7.34+4 dyn/cm2, all p<0.005) (Figure
6.2). No significant difference was found between the two WSS estimates at C4
(11.95 dyn/cm2).
Table 6. 2. Descriptive statistics of WSS parameters for upper ancMower
walls and the average of the two.
Upper Wall Shear Stress Lower Wall Shear Stress Averaged Wall Shear Stress
dyn/cm" Range dyn/crrT Range dyn/crrT Range
TA 147 [2,29] 15.76 [5,33] 14.85 [5,30]
C1 22.4 11 [5,42] 23.3 8 [8,43] 22.9 8 [10,43]
C2 41.1 16 [14,72] 44.0 15 [24,89] 42.3 12 [24,81]
C3 16.1 10 [2,40] 15.1 10 [1.7,47] 15.6 8 [2,43]
C4 11.2 9 [0.6,33] 13.27 [3,30] 12.26 [3,25]
C5 7.05 6 [0.3,21] 8.30 5 [0.80,23] 7.68 5 [0.6,22]
Values are meanSD and the range is [Min, Max]. All values were significantly different from the
ultrasound Doppler estimates (p<0.05), except for the mid-diastole.
TA = Time averaged, C1=Accelerating systole, C2 = Peak systole, C3 = Decelerating systole,
C4 = Mid-diastole, C5 = End-diastole, Averaged = WSS averaged over the UW and LW.
These differences remained when WSS at the upper and lower walls of
the artery were derived from echo PIV and compared with UDV WSS (Table 6.2).
There were no differences between WSS measured with echo PIV at the upper
and lower walls at C1-C5 or when time-averaged across the cardiac cycle
(Figure 6.2). Percent differences in WSS measurements between the echo PIV
and UDV methods are presented in Table 6.3. The largest percent difference was
found during peak-systole (C2; underestimation by 119 17%) and the smallest
during mid-diastole (C4; underestimation by 3.7 48/). Compared with echo


76
PIV, the UDV method overestimated WSS values during end-diastole (C5; 43.5
55%).
Table 6. 3. Percent difference between echo PIV- and ultrasound Doppler-
derived wall shear stress at the upper wall, lower wall and the average of
both walls
Upper Wall Shear Stress Lower Wall Shear Stress Averaged Wall Shear Stress
Mean [%] Range [%] Mean [%] Range [%] Mean [%] Range [%]
TA 13.2 54 [-121,93] 32.4 39 [-63,98] 28.2 35 [-51,76]
C1 57.0 45 [-71,147] 70.3 31 [-14,113] 67.8 30 [10,130]
C2 112 26 [54,154] 118 20 [62,154] 118 16 [74,142]
C3 16.6 70 [-117,132] 14.3 69 [-139,95] 24.8 51 [-123,117]
C4 -22.9 76 [-179,102] 9.87 51 [-89,85] 4.30 46 [-104,70]
C5 -61.5 70 [-189,56] -37.3 60 [-167,71] -43.5 55 [-176,40]
Blood flow velocity profiles and shape index
Compared with the parabolic profile assumed in UDV, the shape of the velocity
profile measured using the echo PIV method varied spatially across the cardiac
cycle. In contrast to a constant value of 2 assumed in the UDV method (i.e. a
parabolic velocity profile throughout the cardiac cycle), echo PIV measurements
revealed that the mean s-index was 4.3+3 at C1,7.4+4 at C2, 6.4+5 at C3,
4.5+2 at C4 and 3.6+3 at C5. The s-index significantly varied at different phases
of the cardiac cycle (p < 0.001). S-index distribution and its influence on the
shape of the velocity profile are shown in Figure 6.4. Womersley's numbers (a)
ranged from 3.48 to 6.88, indicating that the actual velocity profile tends to be


77
Figure 6. 3. Example of a parabolic systolic velocity profile.
A parabolic systolic velocity magnitude of 48.5 cm/s generates a systolic WSS of
54 dyn/cm2 for a vessel diameter of 6.4 mm.
Figure 6. 4. Examples of a blunt systolic velocity profile.
Wall shear stress (WSS) measurement depends on the shape of the velocity
profile as well as vessel diameter. Here, a blunt systolic velocity profile for
participant number 13 generates a systolic WSS of 46 dyn/cm2 for a relatively
larger diameter of 7.0 mm (compared to 54 dyn/cm2 for subject 3 in Figure 6.3
whose diameter was 6.4 mm).
less parabolic and more blunt at the center of the blood vessel with sharp
gradients at the walls.


78
Number of Subjects
27
Figure 6. 5. Spatial and temporal variation in velocity profiles at C1-C5 for
each participant.
Distribution of the s-index for all participants extracted at five different time points
(C1-C5) reveals spatio-temporal variation in the velocity profile within a cardiac
cycle. An s-index of 2 indicates a parabolic profile that is symmetric across the
center axis of the vessel, whereas a value larger than 2 indicates a blunted
profile.____________________________________________________________________
Ensemble averaged WSS waveform analysis
The ensemble-averaged WSS waveform is presented in Figure 6.5 and
instantaneous WSS measurements at the upper and lower wall are reported in
Table 6.2. The time-aveaged WSS was 14.8 5 dyn/cm2 The waveform was
characterised by a primary peak with a local maximum of 42.3 12 dyn/cm2
8 8
o
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08 8is1
O O 8p0
O 0 0 0-0
8 0 8 -
O O
0 0 "
0 0 00
8
< 1
8
d
osm ,
o Q
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79
Figure 6. 6. Ensemble averaged WSS profile.
WSS measurements were spatial and phase averaged. The decay constant A
was calculated by fitting an exponential decay curve to data points from the peak
systolic to the first inflection point. The systolic time duration was At was
calculated as the time difference between the upstroke and the first notch.
Approximately half of this maximum shear was sustained for a mean duration of
0.14 0.07 s. Analysis of the systolic descending velocity showed that peak
systolic shear force decelerated towards the first notch of the waveform at a
mean speed of 9 0.07 per second. WSS extracted at this notch ranged 15.6 8
dyn/cm2and a similar WSS was maintained through mid-diastole (12.2 6
dyn/cm2).
The minimum WSS occurred at end-diastole (7.68 5 dyn/cm2). The
accelerating systolic WSS was 22.9 8 dyn/cm2 These differences in WSS at


1
2
3
4
80
0
CO
cc

5
I/V l/^VN__
IK i/C
IN_ 10 INn 11 ijw . 12 l/u.
13 14 IfvW 15 l/V^ 16
17 18 19 20
21 22 23 24 l/V.
25 26 |/Vv^ 27 lA^v.^
One Cardiac Cycle
Figure 6. 7. Temporal variation in the WS5 profile between individual
participants.
Phase averaged WSS revealed the presence of primary and secondary systolic
peaks followed by a diastolic peak within each cardiac cycle. Phase averaging
was performed to obtain a representative WSS waveform instead of an
alternative method of fitting to a spline. The arrival time of the secondary peak
appears to be consistent across the participant group. Except for subject number
9,17 and 20, we observed low variability in the WSS waveform between
individuals.
different phases of the cardiac cycle were significant (p < 0.001). We also
observed some degree of inter-individual variability in the qualitative appearance
of WSS waveforms, particularly subject numbers 9,17 and 20 seemed to have
an increased number of fluctuation during the decelerating systolic phase (Figure
6.6).


81
Discussion
In this study, we measured carotid artery WSS using echo PIV and compared
this with WSS estimated from the commonly used ultrasound Doppler
velocimetry method. To our knowledge this is the first study to characterise time
varying carotid WSS patterns measured in-vivo. The key findings were that:1)
compared with echo PIV, time-averaged WSS was lower using the UDV method;
2) the degree of under- or over- estimation of WSS by UDV varied across the
cardiac cycle because of temporal variation in WSS that is not accommodated by
the UDV method; 3) echo PIV revealed considerable spatio-temporal variation in
the flow velocity profile that is contrary to the assumption that flow is steady and
the velocity profile is parabolic throughout the cardiac cycle.
Hemodynamic WSS is currently measured because of its importance to
vascular endothelial cell shape, size, orientation, function and permeability [2].
Alterations in WSS influence endothelial cell signaling, protein expression and
synthesis of vasoactive molecules[2]. Wall shear stress plays a prominent role in
vessel remodeling and in the process of atherogenesis and atheroma
progression. Endothelial cells discern different hemodynamic WSS stimuli at the
cellular level [2] and independent mechano-chemical transduction pathways are
activated in the endothelial cells depending on the type of shear stress
exerted[9], [88]. For example, turbulent blood flow causes low and oscillatory
WSS that causes endothelial cells to express a pro-atherogenic phenotype [2]. In
adult humans atheroma tends to occur at bends, branches and bifurcations in the
arterial tree where WSS can be low, oscillatory and sometimes turbulent [2]. For


82
this reason, the measurement of WSS has become important in understanding
vascular biology and pathogenesis. The UDV method is convenient and has
become a popular estimate of WSS. However, our data suggest that it does not
accurately estimate mean WSS and illustrates that it misses much of the
important information about WSS that is pertinent to understanding its role in
vascular physiology.
Analysis of WSS at five discrete time points revealed large temporal
variation in the WSS distribution across the cardiac cycle and that WSS was
significantly different at these time points. The UDV method does not estimate
temporal variations in WSS and comparison based on the UDV mean WSS
revealed significant discrepancies at four of the five time points. The largest
discrepancy was in peak systolic WSS; the UDV method underestimated this by
74 to 142%. Mynard et al. (2013) also found that UDV underestimated peak-
systolic WSS, irrespective of profile skewing using either Poiseuilles or
Womersley's profiles (12). They calculated an underestimation of 30 to 50%
using computational fluid dynamics simulations. The discrepancy with our data
may result from their use of spatially averaged image-based simulations of
velocity profiles extracted from the common carotid artery rather than actual
velocity profiles measured in-vivo, as reported here. We also found that the end-
diastolic WSS was overestimated by UDV and that there was considerable
variation in the discrepancy between echo PIV and UDV. This resulted from
wide-ranging, individual-dependent variability in WSS at end diastole detected by
echo PIV. The significance of variability in WSS at specific phases of the cardiac


83
cycle is uncertain, but given the sensitivity of endothelial cells to variation in
WSS, this may reveal important insight into endothelial physiology and the focal
susceptibility to vascular disease.
In this study, we quantified the flow velocity patterns using a shape metric
(s-index) and found that the shape of the local velocity profile varied both
spatially across the vessel lumen and temporally within the cardiac cycle. This
spatial and temporal variation in the velocity distribution translated into variation
in WSS distribution that was not detected using the UDV method. The UDV
method is one-dimensional, necessitating flow assumptions to estimate multi-
dimensional flow velocity and shear stress near the arterial walls, whereas echo
PIV produces actual 2-D velocity vector fields that allow velocity measurement
close to the wall (14-17). A critical assumption of the UDV method is that blood
flow is steady and the shape of the velocity profile is parabolic with its maximum
located at the center of the vessel, but echo PIV showed that this was not always
the case.
The effect of the pulsatile flow pattern on the shape of the local velocity
profile was also quantified using the Womersley's number, a mechanical gauge
for the degree of bluntness present in the velocity profile. Consistent with
previous studies [86], the Womersley's number ranged from 4 to 7, indicating that
the velocity profiles were blunt during most of the cardiac cycle. As noted by
Mynard et al. [28] and also shown in this study, the UDV technique cannot detect
WSS variations caused by profile blunting. Although some new studies
employing the UDV method now use a Womersley's profile to estimate WSS, the


84
underlying assumption remains that flow velocity exhibits an axis-symmetric and
fully-developed profile. Furthermore, this flow assumption neglects any variations
in the arterial diameter during the cardiac cycle which results in compounded
error during WSS estimation, particularly during peak-systole. For example, when
comparing pulsatile flow with similar peak systolic velocity (e.g. 49 cm/s versus
48 cm/s in Figure 3a and 3b respectively) but different inner diameter (6.4 mm
versus 7.0 mm respectively), flow with a parabolic velocity profile (s-index of 2)
during peak-systole exerts a WSS of 54 dyn/cm2 in a smaller artery (Figure 3a),
compared with a flattened systolic flow (s-index of 6) exerting a WSS of 46
dyn/cm2 in the larger artery (Figure 3b). In this example, the UDV method
estimated a mean WSS of 13 dyn/cm2 and 10 dyn/cm2 respectively. This
suggests that the use of parabolic velocity profiles for estimating WSS (mean or
at specific time points), while neglecting pulsatile fluctuations in the arterial
diameter is inaccurate. Our finding is in agreement with that of Tortoli et al (2003)
who showed that velocity distribution during the mid-late systolic phase was
markedly asymmetric ("M-shape") due to the presence of secondary flows during
deceleration [58]. As our data showed, complex velocity patterns resulting from
increased turbulence during the deceleration of systolic flow can result in WSS
distribution that is different from the values predicted by the time-averaged mean
WSS [4], [6]J30].
Instantaneous WSS measurement using echo PIV allowed us to construct
an ensemble averaged WSS phenotype, representing normal carotid
hemodynamics, with detailed time-varying markers. The WSS waveform


85
revealed a highly transient peak systolic WSS decaying at a rate of 9.08 7 per
second with about half of its magnitude sustained for 9.9 6.2 s_1. We found that
the decelerating systolic minimum (17 dyn/cm2) and the mid-diastolic (12
dyn/cm2) WSS values approximated each other (and the time-averaged value of
14 dyn/cm2) showing that the temporal gradient in WSS is followed by a
sustained steady shear stress. White et al.[10] showed that temporal gradient in
shear stress affected endothelial proliferation differently based on the presence
or absence of steady shear stress and the sustained steady WSS suppressed
the proliferative stimulus of the gradient. Because endothelial cells are sensitive
to the spatial and temporal flow patterns experienced at the arterial walls, this
could be an important determinant of endothelial and vascular health. Further
elaboration of WSS characteristics, their consequences and how they change
with age, health and disease is required to fully exploit the utility of WSS
information. To this end, we are currently investigating WSS in patients with a
recent history of transient ischemic attack.
In summary, detailed and accurate markers of physiological and
pathophysiological WSS are needed to fully understand the role of WSS in
vascular biology and vessel disease. Our data show that spatial and temporal
flow patterns are complex, dynamic and do not fit well with traditional
assumptions about blood flow in arteries. Importantly, our data suggest that the
use of ultrasound Doppler and extrapolation from centerline peak velocity
provides limited and largely inaccurate information about WSS. Echo PIV offers a
potentially useful tool to accurately measure detailed markers of wall shear stress


86
in humans in vivo, an important yet poorly understood hemodynamic stimulus
known to regulate endothelial cell physiology and pathophysiology.


87
7. Characterization of Carotid WSS in TIA Subjects
Introduction
Wall shear stress (WSS) is a strong determinant of endothelial dysfunction
present early in atherosclerosis[2], [6], [89]. Although endothelial dysfunction is a
systemic disorder [90], atherosclerotic lesions are localized in arterial regions
with complex geometry, such as curvatures and bifurcations, and disturbed flow
patterns, such as flow separation and turbulence[2], [38]. Given the focal nature
of atherosclerosis, it has been hypothesized that certain patterns of WSS unique
to athero-prone regions may potentiate atherogenesis [2]. However, the exact
role and patterns of WSS that are associated with the pathogenesis of
atherosclerosis remains unclear [2], [10],[16].
Several studies, mostly computational and in vitro, have analyzed flow
patterns in arterial regions susceptible to atherosclerosis or in regions with
varying degrees of stenosis and have demonstrated that WSS regulates
endothelial function and structure by various mechanisms [2]. Results have
shown that the endothelial function depends not only on the magnitudes of
arterial WSS but also on its spatial and temporal variations introduced by the
pulsatile blood flow and is interdependent on the arterial geometry [7-10], [39].
They demonstrated that the endothelial cells respond to both the spatial [7], [8],
[16], [40] and temporal [9], [10], [29], [39], [41] shear patterns by differentially
activating endothelial transcription factors independent of the
mechanotransduction pathways. This data highlights the importance of
identifying different components of WSS that are associated with the endothelial


88
physiology and pathology. While computational and biological analyses of
endothelial responses to fluid mechanics in atherosclerosis susceptible regions
have advanced our understanding of how the endothelial cells respond to flow
induced shear stresses, the exact role and spatio-temporal patterns of WSS
unique to atherogenesis and progression of atherosclerosis remain poorly
defined because of the complexity and difficulty of measuring WSS in vivo [2],
[10],[16]. As a result, a more comprehensive analysis of WSS patterns is needed
to define flow environments in vivo Characterization of in vivo WSS patterns
and integration with other computational and biological findings may identify
WSS patterns that mark different stages of atherosclerosis and enhance our
understanding of mechanisms whereby different WSS patterns modulate
atherosclerosis progression or regression.
In this study, we measured carotid WSS in vivo using an ultrasound based
echo particle image velocimetry (echo PIV) and examined the time varying
characteristics of WSS in apparently healthy individuals and participants who
were recently diagnosed with a transient ischemic attack (TIA). The TIA cohort
was of particular interest because several studies have shown that the presence
of endothelial dysfunction in the coronary or peripheral circulation increases the
risk of stroke or TIA in patients with various stages of atherosclerosis [38]. Using
echo PIV, we were able to measure spatially and time-resolved WSS in the
common carotid artery (CCA) and to quantify spatial and temporal patterns of
WSS in the two study groups [31-33], [36]. We also characterized the carotid
flow environment in these two cohorts using conventional metrics, including the


Full Text

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CAROTID WALL SHEAR STRESS CHARACTERIZATION USING ECHO PARTICLE IMAGE VELOCIMETRY By ARATI GURUNG B.S. University of Colorado, Denver, 2003 M.S. University of Maryland, Baltimore, 2006 M.S. Johns Hopkins University, Baltimore, 2009 A thesis submitted to the Faculty of the Graduate S chool of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy Bioengineering Program 2014

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ii This thesis for the Doctor of Philosophy degree by Arati Gurung has been approved for the Bioengineering Program By Kendal Hunter, Chair Robin Shandas, Advisor Yiming Deng Jean Hertzberg Karen Moulton November 21, 2014

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iii Gurung, Arati (Ph.D., Bioengineering) Carotid Wall Shear Stress Characterization Using Ec ho Particle Image Velocimetry Thesis directed by Professor Robin Shandas ABSTRACT Cardiovascular disease, including stroke, is the le ading cause of death worldwide. The most common trigger of ischemic stro ke is the rupture of atherosclerotic plaques and subsequent obstruction of blood flow. Atherosclerosis is a systemic disease characterized by chronic inflammation and local accumulations of macrophages, smooth muscle c ells, lipids and fibrous proteins (collectively called plaques) in the arter ial wall. Strikingly, atherosclerotic plaques affect only some regions of the arterial sy stem, a property that has been attributed to local variation in blood flow. Flow i nduces a frictional force on the arterial wall and the magnitude, direction and patt ern of this induced wall shear stress (WSS) are known to differentially affect the endothelial structure and function. It has been postulated that low and oscil latory WSS predisposes arteries to develop atherosclerosis, while high WSS may increase the vulnerability of plaque to rupture. However, in vivo WSS measurement is difficult and the accuracy of current WSS measurements is que stionable. This has limited our understanding of the exact role and pat terns of WSS involved in the initiation and progression of atherosclerosis. In vivo WSS so far has been measured using phase contrast m agnetic resonance imaging (PC-MRI) and ultrasound Doppler v elocimetry (UDV). While

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iv PC-MRI provides three dimensional (3D) flow visuali zation, its spatial and temporal resolution is too limited to allow reliabl e measurement of blood flow velocities and WSS near the vessel wall endothelium specifically in small to medium sized arteries. Ultrasound Doppler based est imate of WSS requires very strict placement of the transducer, is limited to v elocity measurement only along the ultrasound beam line, depends on unrealistic fl ow assumptions and its spectral broadening along with the angular dependen ce introduces measurement inaccuracies. In contrast, echo PIV can accurately measure veloci ty fields with high temporal (1 ms) and spatial resolution within 250-3 00 microns of the vessel wall, and makes no assumptions about the flow pattern. Th e present study demonstrated the reliability and reproducibility of echo PIV for measuring detailed makers of carotid WSS in comparison to PC MRI and U DV both of which underestimated WSS (by 40% and 28% respectively). O ur clinical study involving 24 healthy individuals and 12 individuals with a re cent transient ischemic attack (TIA) showed that WSS was reduced by 50% in the TIA cohort and that the spatio-temporal patterns of WSS were significantly different between the two groups. Echo PIV holds significant potential for quantifyin g spatio-temporal WSS data in human arteries and provides detailed marker s of WSS in physiological and pathological flow environments which may improv e our understanding of the relationship between WSS and atherosclerosis. Our s tudy was limited by small

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v sample size. A larger clinical study is needed to f urther validate and refine these WSS characteristics and to fully exploit their util ity. The form and content of this abstract are approved I recommend its publication. Approved : Robin Shandas

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vi DEDICATION Dedicated to my late sister Asha and to study parti cipants whose valuable time will someday save the lives of many others.

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vii ACKNOWLEDGEMENTS I am grateful to my mentor and advisor, Professor R obin Shandas. Without his mentorship, patience, timely advice and generous grant support, I would not have this opportunity to actually live my dream. I am also grateful to Dr. Phil Gates for his tireless and consistent effo rts in helping build my critical thinking skills in my research. I thank Luciano Maz zaro for his mentorship early on in the training. I wholeheartedly thank my advis ors: Dr. Kendall Hunter, Dr. Jean Hertzberg, Dr. Karen Moulton and Dr. Yiming De ng for their sage advice, critiques, time and constant encouragement. I would like to thank Dr. Michael Yeager for his invaluable advice, teaching and moti vation throughout my training. My sincere thanks and gratitude to NIH (through Pro fessor Shandas T32) and IIE/Whitaker for their generous funding that ma de my research possible. I am grateful to Dr. Stefania Petra and Dr. Florian Becker at HCI/IPA for their constant inquisition and push for excellence that helped me move forward and onward. I thank my friends at HCI for making me feel at home in Heidelberg and Nancy Tsen for taking care of me when sick at w ork. I would like to thank Dr. Christian Poelma for being an inspiration and makin g a difference. Many thanks to my family and friends whose love and support rem ain the backbone of my personal and professional career. Special thanks to Martin Schiffner for introducing me to inverse scattering and theoretica l frameworks of quantitative ultrasound imaging; but most importantly thank you for sharing with me your enthusiasm and commitment to science, innovation an d excellence. Thank you God for your unconditional love and unwavering pres ence.

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viii TABLE OF CONTENTS Chapter 1. Introduction ................................... ................................................... ....................................... 1 2. Cardiovascular Fluid Dynamics and Pathophysiolog y ................................................. ............ 7 3. Fundamentals of Ultrasound Imaging ............. ................................................... ................... 16 4. Fundamentals of Ultrasound Echo Particle Image V elocimetry ........................................ ..... 25 5. Reliability and Accuracy of Echo PIV for WSS Mea surement .......................................... ..... 32 6. Characterization of Carotid WSS in Healthy Subje cts ............................................... ............ 64 7. Characterization of Carotid WSS in TIA Subjects ................................................... .............. 87 8. Summary and Future Work ........................ ................................................... ...................... 110 Bibliography ...................................... ................................................... .................................. 115

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ix LIST OF TABLES Table 6. 1. Participants Characteristics ................ ................................................... ................73 6. 2. Descriptive statistics of WSS parameters for upper and lower walls and the average of the two. ....................................... ................................................... ............................75 6. 3. Percent difference between echo PIVand ultr asound Dopplerderived wall shear stress at the upper wall, lower wall and the averag e of both walls .................................76 7. 1. Participant Characteristics ................. ................................................... .................95

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x LIST OF FIGURES Figure 1. 1. Plaque deposits at the bifurcation of the com mon carotid artery and disturbed flow as a result [3]. .................................. ................................................... ............................ 1 2. 1. WSS mechanotransduction by the endothelial ce lls [2]. .......................................... 7 2. 2. Disturbed flow patterns and low shear stress are known to initiate and promote atherosclerosis. .................................. ................................................... ......................... 8 2. 3. Laminar flow in a straight cylindrical tube[4 ]. ................................................ ..........12 3. 1. Schematic of ultrasound image formation. .... ................................................... ......17 3. 2. Image reconstruction from RF signals using a linear phase array transducer. .......20 3. 3. Doppler velocity spectrum.................... ................................................... ...............22 4. 1. A flow chart illustrating the working princip les of echo PIV. 25 4. 2. Cross-correlation based estimation of particl e displacement. .................................26 4. 3. Pixel intensity distribution as a function of particle displacement [35]. ....................28 4. 4. Two dimensional velocity and gradient (shear rate) vector fields. ..........................30 5. 1. Repeatability. .............................. ................................................... ........................47 5. 2. Reproducibility. ............................ ................................................... .......................48 5. 3. Inter-scan variability. ..................... ................................................... ......................49 5. 4. Measurement uncertainty from measurement vari ability. .......................................50 5. 5. Percent uncertainty. ........................ ................................................... ....................51 5. 6. Uncertainty contribution from individual velo city components. ...............................51 5. 7. Uncertainty in WSS measurement. ............. ................................................... ........52 5. 8. WSS measurement comparison between echo PIV a nd PC-MRI. .........................52 5. 9. Temporal distribution of WSS. ............... ................................................... .............53 5. 10. Point-wise correlation analysis. ........... ................................................... ..............54 5. 11. Maximum percent differences in peak systolic WSS measurements were observed when the vessel diameters were smaller. ........... ................................................... ........55

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xi 5. 12. For a Given Diameter, Echo PIV Measures peak systolic WSS Within the Same Magnitude Range whereas PC MRI Underestimates in th e second case (subject number 8). ............................................... ................................................... ................................56 6. 1. Comparison between Doppler velocimetry and ec ho PIV. .....................................68 6. 2. Instantaneous WSS Measurement. .............. ................................................... ......74 6. 3. Example of a parabolic systolic velocity prof ile. .............................................. .......77 6. 4. Examples of a blunt systolic velocity profile ................................................. .........77 6. 5. Spatial and temporal variation in velocity pr ofiles at C1-C5 for each participant. ....78 6. 6. Ensemble averaged WSS profile. .............. ................................................... .........79 6. 7. Temporal variation in the WSS profile between individual participants. ..................80 7. 1.Time-averaged wall shear stress is reduced by 50% in individuals with transient ischemic attack compared to healthy controls. ..... ................................................... .......96 7. 2. Differences in WSS between the healthy and TI A cohorts measured at five different time points in the cardiac cycle. ................. ................................................... .................97 7. 3. Temporal distribution of spatial and phase av eraged WSS in the TIA cohort. ........98 7. 4. Differences in temporal waveforms of WSS in T IA and HC. ...................................99 7. 5. Ensemble averaged WSS waveforms. ............ ................................................... .. 101 7. 6. Differences in spatio-temporal WSS patterns b etween TIA and HC. .................... 103

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xii LIST OF ABBREVIATIONS WSS Wall shear stress UDV Ultrasound Doppler velocimetry Echo PIV Ultrasound particle imaging velocimetry PC-MRI Phase-contrast magnetic resonance imaging PRF Pulse repetition frequency WSSVmax UDV derived WSS estimate Vmax Centerline peak velocity CCA Common carotid artery 2D Two-dimensional m Dynamic viscosity D Inner diameter of the carotid artery s s-index v Instantaneous velocity y Radial position R Inner radius of the carotid artery C1 Accelerating systolic cardiac phase C2 Peak systolic time point C3 Decelerating systolic cardiac phase C4 Mid diastolic time point C5 End diastolic time point Re Reynolds number WomerlseyÂ’s number Blood density T Time period of the cardiac cycle v/ y Spatial gradient of the velocity (shear rate) WSSi Instantaneous WSS FDHM Full duration half maximum Exponential decay constant PI Pulsatility index RI Resistivity index

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1 1. Introduction Overview Heart attacks and strokes are the leading causes of death worldwide [1]. Carotid atherosclerotic plaque accounts for more than eight y percent of ischemic stroke that occurs each year [1]. Atherosclerosis is a sys temic disease characterized by chronic inflammation, fibro-proliferation and lipid deposits that are localized in arterial segments with branching, curvatures and co mplex geometry [2]. Figure 1. 1. Plaque deposits at the bifurcation of the common carotid artery and disturbed flow as a result [3] Plaque deposits are mostly seen in arterial segment s with branches and curvatures. As the plaque formation progresses, it occludes blood flow that affects exchange of blood nutrients with the endoth elial cells. Despite being a systemic disease, the localized beh avior of atherosclerotic plaques indicates that certain flow patterns might be involved in the distribution of blood elements that make up the plaque deposits (Fi gure 1.1). Flow induces a

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2 frictional force on the arterial wall known as wall shear stress (WSS) which results from the resistance exerted by blood viscos ity [4]. Endothelial cells lining the inner walls of the arterial vasculature are the principal sensors of WSS [5]. It has been well established that endothelial function and dysfunction is associated with the magnitude and directionality of WSS impart ed by the blood flow [6]. A growing body of studies has demonstrated that WSS c an transcriptically induce structural and functional changes in the endotheliu m that lines the arterial walls [7–11]. While low and oscillatory WSS predisposes a rteries to develop atherosclerosis [2], [6], [12], high WSS may perpet uate transient ischemic stroke (TIA) or stroke by causing the plaques to rupture [ 13–17]. However, the mechanism by which low and/or oscillatory flow cont ributes to endothelial dysfunction remains uncertain [8], [10], [18–20], p rimarily because WSS is difficult to measure in vivo In particular, the present imaging modalities are unable to measure flow with sufficient spatial and temporal resolution to determine accurate estimates of WSS. High spatio-te mporal resolution means flow patterns can be measured near the vessel walls throughout the cardiac cycle to determine any time-varying characteristics in WSS that might be physiologically and clinically important. Measurement of hemodynamic WSS has both physiologic and clinical applications. WSS profiles may determine initiation and progression rates of atherosclerosis. The distribution of WSS in clinica lly interesting population groups could be used to monitor symptoms of progressing pa thology or identify risk for future ischemic events. Current methods to estimate i n vivo WSS are primarily

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3 based on two imaging modalities: phase-contrast mag netic resonance imaging (PC-MRI) and ultrasound imaging. PC-MRI provides vo lumetric flow visualization but is relatively expensive, time consuming, and ha s limited spatial and temporal resolution [6], [21–25]. Because of this, ultrasoun d Doppler velocimetry (UDV) has become a popular method to estimate WSS in stud ies of endothelial function and the natural history of atherosclerotic plaque. This method is inexpensive, readily available and relatively cheap. However, it is uncertain whether it provides an accurate estimate of WSS. The main threat to acc uracy is that it uses a one dimensional velocity component rather than measurin g the whole velocity vector field. This introduces error as it is not possible to measure the spatial gradient of the velocity distribution near the vessel walls, wh ich is required to accurately calculate WSS [6], [23], [26–28]. Unmet Needs and Contribution of Dissertation Despite the fact that hemodynamic WSS is emerging a s an important metric of endothelial dysfunction and associated atheroscl erotic carotid stroke, accuracy of WSS measurement remains an open problem [6], [12 ], [29], [30]. To address the limitations of the commonly existing measuremen t methods, we propose the use of a novel ultrasound based particle image velo cimetry technique (echo PIV) to compute spatially local time-resolved two-dimens ional velocity vector fields, which can be easily and directly converted into WSS data. In this thesis, we evaluated the clinical utility o f a previously validated [31–34] ultrasound based echo particle imaging velocimetry (echo PIV) for quantification of WSS in vivo among different population group. Particle image v elocimetry is

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4 an optical technique that uses an optical laser sys tem to illuminate the fluid seeded with particles the intensity patterns of whi ch are tracked over time to produce a time dependent velocity-vector field. The vector field is then used to derive hemodynamic information in the entire region of interest (ROI) [31–35]. Translation of this technology into medical imaging has been achieved by using contrast enhanced ultrasound, where a velocity vect or field is produced in blood seeded with contrast agent microbubbles. Echo PIV u ses the two-dimensional (2D) ultrasound image of the arterial segment to me asure the local flow velocity distribution from which a 2D velocity vector field is generated and converted into WSS data. Given the limitations of the current modalities and the importance of WSS in vascular physiology and pathology, we identified th ree aims to determine whether echo PIV can produce a reliable, reproducib le and accurate clinical measure of WSS. Specific Aim 1: Evaluate the reliability and accuracy of echo PIV for measuring WSS in human carotid arteries in vivo Rationale: Our in-vitro work has shown that echo PIV provides detailed hemodynamic information in two dimensions with high temporal (0.7ms) and spatial resolution (0.15mm) [36]. The in-vitro anal ysis demonstrated that echo PIV provides accurate measurement of hemodynamic in a single acquisition. We have also previously validated the in vivo use of e cho PIV in human carotid arteries [36]. In this study, we wanted to further investigate the repeatability and reproducibility of echo PIV for WSS measurement in human carotid arteries and

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5 evaluate its measurement uncertainty. Phase contras t magnetic resonance image velocimetry (PC-MRI) is the state of the art imaging modality for volumetric flow visualization. However, its relatively limited spatial (~0.6 mm3) and temporal resolution (2 ms) [34] has raised questions with re gards to its accuracy in measuring local WSS particularly in small to medium sized arteries such as the carotid arteries [22], [25], [37]. This motivated u s to compare the PC MRI data against the echo PIV data. Specific Aim 2: Characterize carotid WSS in healthy population sam ples Rationale: Echo PIV uses the 2D ultrasound image of the arteri al segment to measure the local flow velocity distribution, produ cing a 2D velocity vector field from which WSS is derived. WSS measurement based on UDV is being used extensively in physiological studies, yet its accur acy and utility are uncertain. As such, information about the usefulness of these est imates and their limitations are needed for better interpretation of WSS data. O ur purpose was to compare arterial WSS measurements estimated from ultrasound Doppler with those from echo PIV. Specific Aim 3: Characterize carotid WSS in TIA patients Rationale: The TIA cohort is of particular interest because se veral studies have shown that the presence of endothelial dysfunction in the coronary or peripheral circulation increases the risk of stroke or TIA in patients with various stages of atherosclerosis [38]. Several computational and bio logical studies have analyzed flow patterns in arterial regions susceptible to at herosclerosis or with varying degree of stenosis and have demonstrated the variou s mechanisms by which

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6 WSS regulates endothelial function and structure[2] Recent studies have shown that the endothelial function depends not only on t he magnitudes of arterial WSS but also on its spatial and temporal variations int roduced by the pulsatile nature of blood flow in interaction with the arterial geom etry [7–10], [39]. They demonstrated that the endothelial cells respond to both the spatial [7], [8], [16], [40] and temporal [9], [10], [29], [39], [41] shear patterns by differentially activating endothelial transcription factors and in dependent mechanotransduction pathways. While these detailed analyses of endothel ial responses to fluid mechanics in atherosclerosis susceptible regions ha ve advanced our understanding of the mechanisms by which shear stre sses regulate endothelial behavior, the exact role and spatio-temporal patter ns of shear in the pathogenesis of atherosclerosis remain poorly defin ed because of the complexity and difficulty of measuring WSS in vivo, which limi ts its utility as an early marker of atherosclerosis[2], [10], [16]. In this study, we examined the time varying charact eristics of wall shear stresses in the apparently healthy individuals with out any known disease and participants who were recently diagnosed with a TIA The objective was to evaluate the prevailing hypothesis that WSS in indi viduals susceptible to atherosclerosis differs from healthy individuals bo th in terms of its magnitude and its spatio-temporal distribution patterns.

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7 2. Cardiovascular Fluid Dynamics and Pathophysiolog y Pathological hemodynamic wall shear stress (WSS) is known to trigger atherogenesis that involves dysfunction of the vasc ular endothelium. Endothelial cells lining the arterial walls respond differentia lly to WSS induced by the blood flow [18]. Depending on the type of induced shear s tress, endothelial genes such as vascular cell adhesion molecule-1 (VCAM-1) are e ither upor downregulated [6]. Li et al. (2009) showed that high pulsatility flow with a co nstant mean WSS upregulates pro-inflammatory gene expression and en hances leukocyte Figure 2. 1. WSS mechanotransduction by the endothe lial cells [2]. Endothelial shear stress (ESS) induced by blood flo w triggers a series of signaling cascade in the endothelium that eventuall y affects the morphology and physiology of endothelial cells. adhesion and cell proliferation implicating a dynam ic relationship between the temporal gradients in WSS distribution and the resp onses of the endothelial cells experiencing them [19]. As shown in Figure 2.1, wal l shear stress (referred to as ESS in the figure) activates a range of mechanorece ptors thereby triggering a complex range of intracellular pathways [2]. The me chanotransduction pathway generally involves activation of the mitogen-activa ted protein kinase (MAPKs).

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8 These activated proteins then orchestrate a range o f signaling messages responsible for activating transcription factors th at are either atherogenic or atheroprotective [2], [8]. This concert of signalin g cascades causes structural and functional remodeling of the arterial bed. Figure 2. 2. Disturbed flow patterns and low shear stress are known to initiate and promote atherosclerosis. Laminar flow and high WSS (15-70 dyn/cm2) are known to be atheroprotective. In contrast, disturbed flow with low WSS (< 10-12 dyn/ cm2) cause cells to align in a random fashion compromising the endothelial cellula r functions: e.g. reduced eNOS synthesis leads to vasoconstriction; increased VCAM-1, BMP-4 expression, LDL uptake and permeability leads to ce llular proliferation, plaque formation and calcification; increased MCP-1, TNFpromotes inflammation, all leading to onset and progression of atherosclerosis [2], [42]. It is shown that endothelial genetic expression uni que to arterial regions with laminar, undisturbed flow patterns tends to be atheroprotective; for example by inducing increased endothelial synthesis of nitr ic oxide synthase (eNOS) which is a vasoregulator or by suppressing pro-athe rogenic genes such as

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9 VCAM-1. In contrast, increased expression of pro-at herogenic and mitogenic genes and reduced eNOS are associated with regions where low and disturbed flow patterns are found [2], [6], [43]. Cardiovascular Flow Dynamics Blood is an isotropic, non-Newtonian, incompressibl e fluid carried by the arterial system away from the heart to the rest of the body. As the heart pumps during systole, the flow velocity increases and so does the strain rate. Blood becomes Newtonian at larger strain rates. This allo ws us to consider blood flow in medium to large sized arteries, such as the comm on carotid arteries (CCA; Figure 1.1) to be Newtonian. Thus, its flow charact eristics can be approximated by a Newtonian constitutive equation [4]: n r (2.1) Equation (2.1) expresses the three-dimensional stre ss tensor, ij, as a linear combination of the hydrostatic pressure, and the three-dimensional strain-rate tensor, scaled by the fluid dynamic viscosity, . Here, represents the three-dimensional three-component ve locity vector with components in the Cartesian coordinates. The Dirac delta function, ij ensures that the pressure term is defined only at the surfa ce point, S where i = j i.e. pressure is a normal stress. Blood flow can then be analyzed using the different ial equations of fluid mechanics that obey the principles of mass and mome ntum conservation of fluid.

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10 We obtain the EulerÂ’s equation of motion from the N ewtonÂ’s second law of motion per unit volume (Eqn. 2.2) while obeying the equation of continuity for an incompressible fluid (2.3): (2.2) # $ (2.3) Equation 2.2 expresses conservation of momentum by stating that the material rate of change of momentum equals the forc e acting on the body, F which is defined on the right hand side of equation (2.4) as a sum of the surface forces and the body forces acting on the fluid: % (2.4) where & measures the surface forces acting normal (pressur e, ) and tangential (stress, ) to the surface of the fluid and X'()and measures the body forces (e.g. gravity and viscous forces) per u nit volume in the + and directions respectively [44]. Here, the material de rivative is defined by the operator: -. #" where the gradient operator / evaluates the spatial derivative of the three velocity components: 0, and 1 in the + and directions respectively. From equation (2.4), we su bsequently obtain the NavierStokes equations that govern the flow characteristi cs of an incompressible viscous flow in three dimensions:

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11 0 0 0 0 + 2 0 3 r 0 (2.5) 0 + 2 ) 3 + r 2 0 2 2 + 2 2 3 r 2 And in a compact form (neglecting the body forces) as: -. "r" The simplest model of blood flow that satisfy the N avier-Stokes equation can be derived based on the following assumptions: fluid is homogenous (r = constant); flow is laminar (layers of fluid are par allel to each other and the walls); flow is steady (fluid velocity, and density, 4 remain constant with time); flow is axial (in the cylindrical polar coordinates (5(6(,, there is no circumferential variation: 7$; 8$; pressure, 5(, is a function of the radial position, 5and the tube length, ,; and 95 is a function of 5 only); flow is axisymmetric ( 5(, and 9 5 are independent of the azimuthal direction, 6); flow is fully developed (9 5 is independent of the tube length, ,); and the tube is uniformly straight, rigid, cylindrical and long relative to t he fluid volume studied such that Newtonian [44]. These assumptions describe the beh avior of a steady viscous flow in a uniformly straight and axisymmetric tube with the no-slip boundary condition on the surface (7:;$), i.e. the flow shares the same velocity as that of the wall and is therefore zero at the wall. Due to viscosity, the velocity of flow

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12 away from the walls increases reaching a maximum va lue in the center as shown in Figure 2.3. This profile of the flow as a functi on of its spatial position with respect to the wall approximates a parabola and is colloquially known as a parabolic or PoiseuilleÂ’s flow. Figure 2. 3. Laminar flow in a straight cylindrical tube [4] Considering the blood vessels to be uniform and cyl indrical, viscosity causes the flow velocity profile to become parabolic with the maximum velocity at the center of the blood vessel. The resulting generalized solution to the Navier-St okes equation is known as the Hagen-PoiseuilleÂ’s flow named after the Germ an engineer G.H.L. Hagen (1839) and the French physician J.L.M. Poiseuille ( 1840) for their work on the pressure-drop <=== law governing a laminar pipe-flow whose velocity profile is a parabola given by equation (2.6) where 0 5 > ? @ AB C 5 (2.6) Here, is the blood viscosity, R is the radius of the vessel, and r is the radial position at which the velocity component, 05 is computed (i.e. the axial flow velocity 0along the x-axis in the Cartesian coordinates or 95 along the tube length (,) in the cylindrical polar coordinates) varies spat ially as a function of position 5 along the vessel cross section such that it reache s zero at the wall with a maximum at the center. However, PoiseuilleÂ’s flow is not a very realistic = =

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13 model for studying physiological flow where one obs erves non-steady flow due to cardiac pulsatility. Womersley solution to the puls atile Navier-Stokes flow equations takes into account the time-dependence of the pressure gradient and more realistically characterize the blood flow obse rved in a moderately sized vessel such as the CCA. J.R. Womersley solved the NavierÂ’s Stokes equation for pulsatile blood flow in 1955 [45]. His solution, commonly known as the WomersleyÂ’s solution, describes the pulsatile nature of arterial blood fl ow approximated by an incompressible Newtonian characteristics. Consideri ng only the motion parallel to the axis of the vessel or a cylindrical tube and wi th the assumptions that the vessel is axisymmetric with no radial component, th e WomersleyÂ’s solution to the reduced Navier-Stokes equation for the axial veloci ty (along the axis of the tube in the x-direction) with a sinusoidally modulated p ressure gradient is given by: 0 5 CD E F D G. C r H 3 I J K 3 L M N I O J+ P L M I Q R S (2.7) where is the frequency and A is the amplitude of the sinu soidal pressure gradient, y is the nondimensional radial position given by +7 ; and J0 is a zerothorder Bessel function of the first kind accounting for the periodic pressure gradient that drives the pulsatile flow. These fundamental principles of hemodynamics theref ore form the basis for the various measurement techniques available to day to estimate flow properties such as blood flow velocity and WSS in b oth the experimental and the

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14 clinical measurement setups. The key parameter of i nterest is the nondimensional Womersley number that defines the pulsatility and bluntness of the flow profile in relation to viscous effects. Th e non-dimensional Womersley J C T UG A (2.8) number is a ratio of the unsteady inertial force go verned by the fluid density and the angular frequency 2 defined as V W where X is the time period over which one cardiac cycle pulsates [4]. At a lower the viscous force dominates favoring a parabolic velocity profile. Therefore, an of 1 or less indicates a laminar flow with a fully developed parabolic velocity profile whereas a value larger t han 1 indicates a blunter velocity profile. Akin to the Womersley number, a second parameter th at is commonly used is the nondimensional Reynolds number (CD). The Reynolds number is the key parameter used to characterize the range of flow in any fluid mechanics study. It defines the balance between the inertial force (i.e. kinetic en ergy per unit volume of flow) and viscous force (i.e. the product of blood viscosity and velocity gradient): CD Y r (2.9) where r = 1015 kg/m3 is blood density, D is the mean inner diameter of the blood vessel and Y is the mean flow velocity in the streamwise direct ion. A large Re number indicates a dominant inertial force leading to increased turb ulence whereas a smaller Re number indicates a dominant viscous force favoring laminar flow with a parabolic velocity profile [46]. Additional physiological flow related variables inc lude the pulsatility index and the resistivity index that have been shown to inform ab out the downstream arterial

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15 resistance to pulsatile flow [47], [48]. The pulsat ility index (PI) can be calculated as the velocity pulse (difference between the peak systoli c Z[\ and minimum diastolic Z[]values) normalized to its mean value Z[^\] and is an indicator function of arterial compliance: =_ Z `ab c Z [] Z [^\] (2.10) Likewise, the resistivity index (RI) can be calcula ted as the velocity pulse normalized to its peak systolic value and is a measure of arteria l resistance: C_ Z `ab c Z [] Z [\ (2.11)

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16 3. Fundamentals of Ultrasound Imaging Medical ultrasound imaging is a non-destructive tec hnique for quantifying tissue characteristics based on the velocity response of t he insonicated particles in the perturbed pressure field [5,6,8]. The basic princip le of image formation via ultrasonography is schematically illustrated in Fig ure 3.1. We start with a brief description of the transducer electronics used in a typical pulse-echo imaging setup to understand the propagation of ultrasound b eam and image formation. This fundamental understanding will give us some cl ues on the origin of challenges that the current 2D echoPIV encounters a nd will further guide us towards finding a direct solution. Linear Array Transducer Electronics The acoustic pressure field is created in the mediu m when a linear array of piezoelectric elements is activated with each activ ated element, sequentially, emitting short bursts (two to three cycles) of high frequency sinusoidal pulses across a medium of interest. An ultrasound transduc er consists of 128 to 512 elements of piezoelectric material; these elements act both as the transmitter and the receiver. The number of elements that is activa ted at a given time, determines the aperture width. Typically a sub-arra y of 16 to 32 elements is activated at a single point in time emitting spheri cal waves into the medium at a radio frequency (RF, 2-10 MHz). These RF waves pert urb the pressure field in the medium, i.e. tissues with varying acoustic impe dances ( Z = /c ) defined by the tissue density () and speed of sound ( c ) [5].

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17 Figure 3. 1. Schematic of ultrasound image formatio n. A subarray of transducer elements is excited sequen tially to perturb the pressure field of the medium d and generate one beamline per excitation period e recorded at the center of the subarray fghg A delay and sum scheme is employed to time the emission and reception of the ultrasound pulse echo, i.e. the center element has the longest delay hg compared to the adjacent elements hcijklhmi since the round trip Nno p P for the echo traveling a depth of o with a sound speed of pfor time e is the shortest for corresponding to the center element /!. These returning echoes are summed and processed q r o s to obtain the envelope signal t e that forms the raw signal for the grayscale Bmode image. The same transducer elements record the echo which is post-processed into a 2D gray-scale digital image of the ROI that can then be investigated for morphological (i.e. if the ROI is an artery, inform ation such as arterial diameter and intima media thickness can be extracted) and fu nctional (i.e. blood flow velocity and WSS) properties. Pressure field pertur bation occurs as a series of compression and rarefaction, i.e. elasticity counte racts a local compression due to increased pressure amplitudes to return to equil ibrium whereby inertia

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18 counteracts return to equilibrium at a larger degre e causing rarefaction (reduced pressure amplitudes). This allows acoustic impedanc e to be expressed as a ratio of the driving force, i.e. the pressure potential ( p ( t )) to the particle velocity response ( v ( t )) or alternatively as a ratio of the material dens ity ( ) and compressibility ( ): (3.1) Difference in acoustic impedance between the two me dia gives rise to the echo signals useful for image formation. When the b oundary between two media of different acoustic impedances is larger than the incident ultrasound wavelength, the incident wave is reflected obeying SnellÂ’s law (Figure 3.2). (3.2) When the objects in the medium are equal or smaller than the ultrasound wavelength, acoustic scattering occurs. It is this scattered wave or echo that carries information intrinsic to the insonated tiss ues. In essence, a 2D ultrasound image is an intensity based image, aka reflectivity or brightness mode (Bmode) image. Each pixel intensity is distributed across a gray scale range from 0 to 255 based on the amplitude of the received echo signal. The echo amplitude depends on the acoustic impedance difference, the n umber of scatterers per unit volume, the sizes of these scatterers and the trans ducer frequency at which the ultrasound is emitted. Acoustic scattering increase s with ultrasound frequency. Reflection does not depend on frequency. Referring back to Figure 3.1, the emitted pulse ( p0( t )) can be mathematically described as a decaying si nusoidal

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19 wave modulated by its center frequency ( f0) with an initial time-dependent amplitude ( A0( t )). M F M D c V u v (3.3) The amplitude attenuates as a function of the propa gation distance ( z ) or by an amount ( A ( z ) = A0ez) due to ultrasound interactions with tissues such as absorption, scattering and mode conversion (i.e. li quid to solid). Here, the attenuation coefficient ( ) depends on the medium (i.e. tissue and fluid type ) and provides the relative intensity loss ( dB ) per centimeter of propagation for the insonated medium. There is a linear dependence betw een the ultrasound frequency and the attenuation coefficient. In other words, a high frequency ultrasound wave decays more rapidly and therefore h as a shorter depth of insonification than a low frequency ultrasound wave This ultrasound pulse returns to the same transduce r elements after a round trip (2 z ). In an overly simplified example as illustrated i n Figure 3.1, let us consider two scatterers (objects that are smaller t han the wavelength of the ultrasound, e.g. < 0.15 mm in size if the modulatin g frequency is 10 MHz and the ultrasound speed in the tissue, c = 1540 m/s) locat ed at positions z1 and z2 with zF being the position at the near focal point, the rec eived echo can then be expressed as: sm( t ) = A ( t ) cos (2fot ) = Re [ Ao( t ) ejfot] (3.4) As shown in Figure 3.1, a time delay of m( z ) is introduced for each transducer element during both transmit and receive according to its relative location to the center element ( xF ) so that the intensity of the echo signal

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20 returning from the scatterers z1 and z2 are compensated for the depth dependent beam attenuation. This time gain compensation (TGC) therefore allows the intensity distribution in the formed image to indic ate the acoustic impedance differences between tissue boundaries and inform ab out the inhomogeneity properties therein that could be investigated for b oth structural and functional studies (Figure 3.2). Figure 3. 2. Image reconstruction from RF signals u sing a linear phase array transducer. As described in figure 3.1., a subarray of elements are excited sequentially resulting in formation of single beamlines per late ral sweep. Each scan lines (RF lines) are processed (envelope detected, log compre ssed, filtered) to obtain a 2D grayscale intensity map of the ROI. This technique employed in a phased array transduce r, as depicted in Figure 3.2, is known as dynamic focusing that repha ses the signals returning to the individual transducer elements to improve the s patial resolution of the image.

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21 The time compensated echoes received by the individ ual elements are summed and compressed for an optimal gray-scale display. T he compressed signal is demodulated to extract its envelope, i.e. | A ( t )| that gives rise to the pixel intensity distribution of the grayscale image, i.e. I = | A ( t )|2. The envelop signal is commonly known as the amplitude-modulated signal or the A line or the RF signal. Each A-line corresponds to the number of ac tivated transducer elements used for imaging the region of interest with its le ngth corresponding to the imaging depth. These A-lines are arranged together such that the number of columns provides the lateral view of the ROI wherea s the number of rows provides the axial view thereby forming a 2D image of the ROI (Figure 3.2). This kind of Bmode image formation via sequential a ctivation of the transducer elements is commonly known as the Delay and Sum (DAS) pulseecho imaging. For EchoPIV, the backscattered pressu re field is reconstructed in this manner, into a time series of two dimensional frames with the frame rate dictating the temporal resolution critical for velo cimetry. In the next section we will discuss how these Bmode images suffer from poor ima ge quality due to presence of speckles inherent to ultrasound imaging and the frame rate limitation on the maximum resolvable velocity for arterial blo od flow measurement. Quantification of Arterial Blood Flow The fundamental principles of hemodynamics and ultr asound imaging drive the underlying mechanism of ultrasound based velocimetr y such as Doppler and EchoPIV. Ultrasound attenuation is dependent on bot h the frequency and the propagation distance; while use of a high frequency ultrasound transducer

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22 provides superior spatial resolution of the image a t the cost of the imaging depth, the need to image deeper tissues would require use of a low frequency ultrasound transducer at the cost of image quality. In lieu of this tradeoff, the moderately sized CCA therefore presents itself as a clinically desirable vessel for hemodynamic study due to its superficial location t hat allows an easy access to obtain blood flow details such as velocity and WSS. These hemodynamic details inform clinicians of any impending disease developm ent and/or progression in Figure 3. 3. Doppler velocity spectrum. A screenshot of the ultrasound acquisition procedur e where the top figure displays the real time grayscale image of the CCA, displayed on the bottom is the velocity spectrum measured inside the sample volume seen at the center of the lumen and the imaging parameters (center frequency of 10 MHz and imaging depth of 4.0 cm). the arteries. This way, a non-invasive diagnostic t echnique could be made available for screening and stratifying patients at risk for clinical events relating to arterial diseases such as stroke or heart attack.

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23 Ultrasound Doppler velocimetry is based on the shif t of the frequency, also known as the Doppler shift, caused by the moving pa rticles, i.e. the blood cells. Doppler shift is the difference between the inciden t frequency and reflected frequency. The moving reflectors obey the HugyenÂ’s principles, in other words, a collection of these objects in motion at varying ve locities gives a superposition of the contribution from the individual reflectors giv ing rise to a power density spectrum (PDS) (Figure 3.3) [49]. Normalized PDS re lates to the density of the velocity distribution: (3.5) where the maximum frequency fmax is adjusted by the cosine of the angle between the direction of blood flow and the directi on of the sound, known as the Doppler angle and the center frequency of the trans ducer fc. (3.6) and the resulting doppler shift is given by (3.7) that takes into consideration PoiseuilleÂ’s assumpti ons of an axisymmetric laminar flow with a parabolic velocity profile: (3.8) which is equivalent to equation (2.6) where the exp onent term n governs the profile of the velocity ( n = 2 for a parabola).

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24 As can be clearly observed from equation (3.8), one of the drawbacks of Doppler velocimetry is the fact that the field of v iew (FOV) is limited by the insonation angle i.e. at a 90 degree angle, the measured frequency shift becomes zero therefore providing no velocity inform ation. PoiseuiileÂ’s assumption requires relatively straight blood vesse l which is not always the case in real physiological conditions and additionally, calculation of single velocity component reduces accuracy of WSS estimation which is measured as follows: (3.9) There are several advantages to Doppler velocimetry : it is non-invasive, i.e. it does not require intravenous injection of m icrobubbles for contrast and it offers superior temporal and spatial resolution com pared to PC-MRI velocimetry. An alternative method for quantifying blood flow is the Phase Contrast Magnetic Resonance Velocimetry (PC-MR) that provide s three to four dimensional blood flow characteristics in the arter ies such as aorta and CCA[22], [30], [34], [50].

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25 4. Fundamentals of Ultrasound Echo Particle Image V elocimetry Echo PIV uses ultrasound brightness-mode (Bmode) ra ther than Doppler for flow measurement and is inherently capable of measuring two-dimensional (2D) velocity vector fields. Unlike the Doppler velocime try, echo PIV makes use of the pulse-echo imaging to capture the two dimensional g ray scale images of the seeded particles. These particles are small microbu bbles with a mean diameter of 2-4 rw that are filled with sulphur hexafluoride gas mole cules inside a lipid shell (SonoVue, Bracco Diagnostics, Inc., The Nethe rlands) thus creating a large Figure 4. 1. A flow chart illustrating the working principles of echo PIV. Seeded flow is imaged and 2D grayscale images are c onstructed form 1D RF signals. Particle image patterns are matched across the consecutive frames via the PIV algorithm (described in text) and a 2D loca l velocity vector field is obtained. A 1D phase averaged flow is be obtained. Data validation includes removal of spurious vectors.

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26 acoustic impedance difference that gives rise to st rong backscattered echo signals (cf. Eqn. 3.2). patterns) in the form of th e grayscale intensity values (Figure 4.1). As guided by our prior work [32–34], [51], microbub bles are injected at a concentration of ~ 1-2 x 103 per ml to maintain optimal particle image density. Following the image reconstruction scheme described in Chapter 3, two dimensional Bmode images of the microbubbles are ob tained from onedimensional radio-frequency (RF) signal which conta ins the information about the location and displacement of these flowing particle s (or more precisely their image patterns; Figure 4.1). The imaging window is typically placed a few millimeters away from the bifurcation. Figure 4. 2. Cross-correlation based estimation of particle displacement. An interrogation window of size 48x24 is applied to compute one velocity vector. After scanning the entire FOV, spatially local inst antaneous velocity vector fields are obtained. WSS is then calculated by computing t he spatial gradient of the velocity near the walls. The long axis of the transducer probe is aligned lo ngitudinally with the centerline of the blood vessel such that blood flow is orthogonal to ultrasound beam direction. This alignment provides a longitudi nal view of contrast-enhanced

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27 flow that is recorded in a time sequence using very high frame rates (480 – 680 frame per second [34]) with ECG-gating for post-pro cessing synchronization. The use of microbubbles gives excellent signal disc rimination between tissue and blood and allows velocity measurement cl ose to the vessel walls (Figure 4.2). Once the vessel walls are segmented i n a semi-automated manner, an interrogation scheme is applied wherein each con secutive image pair is subdivided into smaller areas known as the interrog ation windows [33], [51]. Denoting each image pair as x and x and the corresponding interrogation windows as x (and x (, the image pair is then compared to identify a displacement of the intensity pattern from x ( to x ( by using a normalized crosscorrelation function as defined in Eqn. (4.1) where R(s,t) denotes the crosscorrelation values when the x (is shifted by variables yz{|} known as the cyclic lags, M and N are the number of rows and columns fo r each image frame. These segments of measurement areas are called inte rrogation windows. The size of the interrogation window determines to what degree the recovered velocity field is spatially smoothed; there exists a tradeoff between the spatial resolution and the accuracy of velocity estimations whereby a larger window improves the image quality but reduces the accuracy due to increased spatial C y ( 3 ~ € € x ( w (  x ( w y (  ‚ c ] : M ƒ c [ : M (4.1)

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28 averaging of the velocity magnitudes [34]. In our c linical studies, an interrogation window of 48 pixels by 28 pixels was employed. In order to extract the displacement information fr om the cross-correlation map, a 3-point Gaussian peak finding subpixel inter polation function is used [52]. Following Willert and Gharib (1991), this interpola tion scheme finds the maximum cross-correlation peak which informs about the two components of instantaneous displacement vector field, x0 and y0 (Eqn. 4.2): M „ …{ C „ 3 ( I …{ C „ 3 ( I …{ C „ 3 ( I † …{ C „ ( I …{ C „ 3 ( I (4.2) + M I …{ C „ ( I 3 …{ C „ ( I 3 …{ C „ ( I 3 † …{ C „ ( I …{ C „ ( I 3 where, R(i,j) indicates the local coordinate of the peak cross-correlation peak at the ith row and the jth column. Subsequently, two components of the veloci ty vector field: 0 M( z{|+M( are obtained using the fundamental definition of velocity (Eqn. 4.3). Figure 4. 3. Pixel intensity distribution as a func tion of particle displacement [35] An illustration of pattern matching to calculate pa rticle displacement, a special note is the out of plane displacement ( /n‡ ) that occurs at large displacement that cannot be captured at a low frame rate, a serious l imitation of the current flow imaging modality which is related to limited frame rate currently available.

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29 Once the interrogation window has spanned the entir e rows and columns of the image pair (using a 50% overlap between each interrogation to improve the spatial vector resolution), a spatially local i nstantaneous velocity measurement is obtained: v(x,y,t) = f(u(x,t),v(y,t) ): 0 ( + ( < ( + ( < (4.3) ( + ( ˆ < + ( + ( < Where
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30 where, X Œ]^ 3O AŽ^ [  w Here, XŒ]^ is the acquisition time for each scan line, ^Œ^ is the number of transducer elements used to create the ultrasound i mage of the ROI which corresponds to the total number of scan lines (cf. Figure 3.2) and D is the imaging depth [53]. Thus, a high frame rate can be achieved at the expense of a smaller FOV. Additionally, the PIV standard one-qua rter rule can be employed which dictates that the particle displacement may n ot exceed more than a quarter of the interrogation window size. Figure 4. 4. Two dimensional velocity and gradient (shear rate) vector fields. Actual flow measurement data from a healthy individ ual obtained using the principles described in Figure 4.2. A uniform lamin ar flow is observed with maximum velocity towards the center of the blood ve ssel and close to zero velocity towards the walls. Velocity gradient is ze ro towards the center of the vessel and maximum at the walls.

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31 A successful implementation of the PIV algorithm on the entire width of the image for all time sequences results in a spatially local instantaneous velocity vector field and corresponding shear rate map as sh own in Figure 4.4 which was obtained from a healthy study participant.

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32 5. Reliability and Accuracy of Echo PIV for WSS Mea surement Introduction The local hemodynamic environment, especially wall shear stress (WSS), plays an important role in the initiation and progression of atherosclerotic plaque at bifurcations, branch points and bends in the arteri al tree [2], [22], [54]. Areas of arterial wall that are exposed to low and oscillato ry WSS exhibit changes in endothelial cell gene and protein expression that a re altered towards a proatherogenic phenotype [12], [42]; these areas corre late with focal atheroma and plaque [29], [55–57]. Low WSS at these locations re sults from oscillation and secondary flows that include separation, recirculat ion, turbulence and vortex flow formation [2]. The carotid bulb is the main site o f plaque development in the carotid artery, where WSS is low and blood flow may be disturbed at the bifurcation [55]. Although determinants of plaque p rogression are uncertain, the local hemodynamic environment around the plaque sur face may influence whether plaques becomes quiescent, stenotic or more vulnerable to rupture [17], [30], [55]. Measurement of carotid WSS is thus relevant for bot h physiological and clinical purposes; WSS characterization would advan ce our understanding of the role it plays in the disease process of atheroscler otic plaque formation whereas WSS patterns unique to the plaque prone arterial re gions could be used as hemodynamic biomarkers for plaque burden. However, in vivo WSS cannot be measured easily by current clinical methods and its measurement accuracy thus far has remained elusive Two vascular imaging based methods are commonly

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33 utilized for measuring WSS in vivo : ultrasound Doppler and the phase contrast magnetic resonance imaging (PC-MRI). In both techni ques, WSS is derived from flow velocity magnitude. Ultrasound Doppler velocim etry (UDV) measures the flow velocity at the center of the artery and extra polates this single valued centerline measurement for velocity estimation clos e to the vessel walls. WSS is then derived from this velocity information based o n the assumptions that the vessel walls are uniformly straight and the flow is steady, laminar, non-oscillatory and axisymmetric with a uniform velocity profile ac ross the vessel cross-section. These assumptions are not physiologically relevant which makes it difficult to obtain a clinically useful interpretation from the UDV measured WSS information. Several studies have evaluated its measurement accu racy and have showed that unsteady nature of the blood flow, presence of skew ed non-axisymmetric velocity profiles and its technical limitations such as angl e-dependent aliasing, spectral broadening and the inability to resolve multiple ve locity components lead to inaccurate (either overor underestimation) of a ctual flow velocity [23], [27], [58–60]. Physiological studies of arterial WSS and routine clinical assessment of carotid arterial plaque have so far relied mostly o n conventional brightness-mode (B-mode) for structural visualization and Doppler c enterline velocity assessment for velocity and WSS estimation [61], [62]. PC-MRI is the state-of-the-art imaging modality tha t has emerged as an essential tool in cardiovascular imaging for the di agnosis, monitoring and treatment of cardiac diseases as it can measure mul ti-component flow velocity profiles in the vasculature including the aorta and carotid arteries [30], [50], [62–

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34 65]. PC-MRI provides assessment of vascular structu re and morphology as well as time-resolved three-dimensional blood flow measu rement. Analogous to the Doppler shift employed in ultrasound Doppler veloci metry (UDV), PC-MRI estimates the velocity shift based on the change in the phase of the proton magnetization when a magnetic field gradient is app lied [66]. Unlike the one dimensional velocity measurement obtained in UDV, P C-MRI obtains threedimensional three-component velocity information an d does not rely on any assumptions about flow. However, spatio-temporal av eraging is inherent to PCMRI due to its large slice thickness (commonly repo rted as ~6mm in clinical literature) and poor spatial (~ 1-3 mm) and tempora l (~ 15 to 30 millisecond) resolution [22], [34], [53]. Thus, the underestima tion effect of PC-MRI is likely more pronounced in small to medium sized arteries s uch as the common carotid artery (CCA) compared to the aorta, where PC-MRI is used more frequently [30]. Additionally, PC-MRI requires a long acquisition ti me to capture one single slice (~15-20 minutes). To address the limitations present in the current t echniques, we propose a novel ultrasound based echo particle image velocime try (echo PIV) for the measurement of WSS in vivo As an ultrasound-based imaging modality, echo PIV offers advantages with regards to rapid acquisi tion with superior spatial (0.15 mm) and temporal (0.7 ms) resolution compared to PC MRI and its ability to measure blood flow variables in small to medium siz ed blood vessels and quantify multi-dimensional multi-component flow fie ld unlike the UDV method. We have recently demonstrated in-vitro the feasibility and accuracy of echo PIV

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35 to measure two-dimensional (2D), two-component flow velocity information in both steady and pulsatile flow environments [31–34] Conventionally, PIV is an optical technique that uses a laser system to illum inate the seeded flow and by tracking the particle intensity patterns across the imaging frames measures the velocity field. The use of ultrasound instead of th e laser source in the PIV measurement offers three benefits: 1) PIV, a gold s tandard for measuring a velocity field, can be applied for in vivo flow measurement, 2) the microbubbles generate high intensity signals in the vessel lumen and therefore enhance contrast between the moving blood and stationary ti ssue improving wall segmentation accuracy, and 3) tracking the intensit y patterns generates a twodimensional velocity vector field providing hemodyn amic information more accurate to the actual flow environment [35], [67]. We validated our ultrasound based PIV technique by measuring the flow velocity and WSS measurements in a realistic carotid artery phantom and compared aga inst the measurements obtained from the same phantom using the optical PI V system. We found good agreement between the two techniques for all variab les of flow measurements including the flow rate, velocity magnitudes and sp atial profiles, and instantaneous WSS distribution [32], [33], [51], [6 8]. The purpose of the present study was to develop the in vivo use of echo PIV for measuring flow induced WSS in the human car otid arteries. Having validated the technique against the standard optica l PIV, we examined the reliability and accuracy of echo PIV for measuring carotid WSS in vivo Specifically, we quantified the repeatability and r eproducibility of echo PIV,

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36 identified the major sources of uncertainty in velo city and WSS measurement and finally compared its measurements against the r eference PC-MRI technique. Methods Ethical approval Participants were apparently healthy men and women recruited at the National Institute for Health Research Exeter Clinical Resea rch Facility, UK. This study conformed to the Declaration of Helsinki and was ap proved by the National Research Ethics Service Southwest (09/H0202/49). Al l participants gave written informed consent. Study design and research participants Participants were asked to refrain from food or dri nk, except water, for at least 2 hours before the visit, and to avoid smoking, drink ing tea or coffee, alcohol and strenuous exercise on the study day. Exclusion crit eria for patients included history of uncontrolled hypertension, pulmonary hyp ertension, renal disease, hepatic disease, claudication, hypersensitivity to the contrast agent and individuals outside the age range of 20 to 80 years Included in the study were data sets with adequate image density of contrast a gent, a clear delineation of the lumen boundary on the B-mode images and compara ble peak velocity measurements between UDV and echo PIV. The images f rom twelve participants were involved in the initial experimentation to det ermine the optimal micro-bubble concentration as guided by our prior validation wor k [32], [33].

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37 Screening involved a physical examination and revie w of the medical history. Participants were screened for contraindic ations to the ultrasound contrast agent (Sonovue, Bracco Diagnostics, Italy) Participants were considered healthy and asymptomatic if they showed no overt clinical manifestations of disease. Study 1. Repeatability and Reproducibility – Echo PIV measurements were randomly selected from 22 out of 28 participants. R epeatability data was derived from a single observer who analyzed 44 data sets (2 2 per subject with two repeats) on two separate occasions. Reproducibility data was derived from two observers independently analyzing 22 data sets. Add itionally, inter-scan variability, as performed by a single observer, was also assessed by comparing the analyses of two consecutive scans from each of the 22 participants for a total of 44 data sets. Study 2. Uncertainty in velocity measurements and p ropagation to the estimation of WSS Data from 28 participants were used to investigat e the sources of errors in velocity measurement. After identification of th e individual uncertainty sources, the resulting uncertainty in the velocity measureme nt was calculated for both the horizontal (streamwise) and the vertical (radial) c omponents. The first order Taylor series expansion was used to calculated the uncertainty in WSS measurement resulting from the measurement uncertai nties in the velocity components. Study 3. Comparison against PC MRI derived WSS. Participants attended the laboratory for echo PIV and PC MRI on occasions sep arated in time by one day

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38 to six months. PC MRI provides a volumetric measure ment of flow and thus the phase averaged WSS measurements were spatially aver aged around the vessel circumference whereas the phase averaged echo PIV d erived WSS measurements spatially were spatially averaged alon g the vessel length. Comparative analysis was conducted using the peak s ystolic WSS measurements. Studies have shown that the accuracy of PC MRI for measuring flow velocity is compromised in vessels of small to medium size diameter [25] The mean diameter of a common carotid artery is usu ally around 6 mm, much smaller than the aortic diameter which is larger th an 10 mm. We therefore measured the arterial diameter and investigated the effect of vessel diameter in WSS measurements agreement between echo PIV and PC MRI. Echo PIV procedure Details regarding the use of this technique have be en described previously [31– 33], [36]. The technique is based on the synthesis of two existing technologies: particle image velocimetry and contrast enhanced Bmode ultrasound imaging. The system includes custom-designed computer-contro lled ultrasound firing sequences, a 10 MHz 128-element linear array transd ucer, radio-frequency data acquisition and advanced algorithms for echo PIV an alysis. Contrast enhanced ultrasound imaging was performed using small microb ubbles (contrast agent) which were injected intravenously. Echo PIV tracks the motion of microbubbles from one image frame to the next and uses cross-cor relation to determine the movement (displacement) of the bubbles from frame-t o-frame. Frame rate is

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39 used to calculate velocity information at any posit ion in the field of view and a velocity map constructed. Participants attended the laboratory in the morning after an overnight fast. Upon lying supine they were instrumented with a vit al signs monitor and cannulated to obtain intra-venous access for infusi on of contrast agent. After a rest period, conventional B-mode Doppler ultrasound was performed on the right common carotid artery 1~2 cm upstream of the bifurc ation [34]. Ultrasound contrast agent was introduced through the cannula i n two separate 2.4 mL boluses or infused using a dedicated pump (VueJect pump, Bracco Diagnostics, Italy). Echo PIV data were collected in 10-second s egments using a customized ultrasound imaging system (Sonix RP, Ultrasonix Med ical Corporation, Canada). Echo PIV data were collected at 500-700 frames per second such that the desired frame rate was at least eight times the pea k velocity magnitude of blood flow as measured with conventional Doppler ultrasou nd. Following the infusion of contrast agent participants were monitored for 30 m inutes before being discharged. PC-MRI procedure Protocol for the PC-MRI study has been reported pre viously [34]. Participants attended the MRI suite either prior or after the ec ho PIV visit but at around the same time of day and after an overnight fast. After screening for safe entry into the scanner they were instrumented with ECG and a n eck coil. Scan duration was 30-40 minutes. PC-MRI was performed using a 1.5 Tesla contrast-enhanced fast field echo (T1-FFE) gradient echo sequence (In tera, Philips Medical

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40 Systems, Cincinnati, OH, USA) to obtain retrospecti vely-gated tissue intensity and phase velocity maps. PC MRI data was acquired b y two experienced radiologists. These were encoded in the 3 principle directions (head-foot, leftright, and anterior-posterior) at five levels perpe ndicular to the longitudinal axis of the common carotid artery. The center level slice w as located just below the carotid bifurcation. Two slices were located superi orly and two slices inferiorly to the center slice. The voxel size of MRI scanning wa s ~0.6x0.6 mm2 in the crosssectional plane. Slice thickness was 6.0 mm and sli ces were spaced at 6.0 mm. The total scan time for each individual was less th an 45 minutes. Temporal interpolation was used to obtain ~40 frames per car diac cycle. A 3D paraboloid function was fitted to the measured velocity profile to obtain a global WSS (i.e. WSS component in the streamwise direction averaged spatially along the circumference of the vessel) [5 0], [65]. Assuming that the blood velocity profile at the boundary layer is par abolic, this algorithm interpolates the paraboloid using the near wall vel ocity values with its peak centerline velocity taken from the average of the c entral nine pixels [50]. Following Oyre et al. (1998) [50], the thickness of the boundary layer w as assumed to be 1 mm. Care was taken to match the WSS measurement locations (approximately 1~2 cm upstream of bifurcation) by e cho PIV and PC-MRI. Carotid wall shear stress was then obtained via lin earized approximation, i.e. the shear stress ‘79 parallel to the vessel wall is equal to the sum of streamwise (z-direction) velocity gradient and the spanwise (r adial, r-direction) velocity gradient, i.e. N’“’7 ’”’9 P multiplied by the dynamic blood viscosity r Assuming

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41 that the radial component of the velocity gradient is negligible, the axial wall shear stress was approximated by •r>–—> Following the original work of Oyre et al. (1998) for measuring carotid WSS using PC MRI, thr ee dimensional (3D) paraboloid fitting [50] was applied to compute the velocity gradient. Assuming zero wall velocity and axisymmetric parabolic veloc ity profile close to the vessel wall, the velocity profiles were obtained by interp olating the near wall velocities in the boundary layers of the vessels [50]. Wall shear rate (i.e. the axial velocity gradient) was then calculated by fitting a paraboli c profile to the measured closeto-wall velocity data points as previously describe d. The cardiac cycle was normalized to 1 second for point-wise comparison ag ainst the echo PIV measurements. The axial WSS was interpolated around the entire vessel circumference and phase averaged (i.e. the WSS meas urements at individual cardiac phase were averaged). Statistical Analysis Study 1. Repeatability and Reproducibility Repeatability and reproducibility of echo PIV were investigated using the BlandAltman analysis technique [69]. For the intra-obser ver variability, the difference in WSS measurements between the two repeats was plotte d against the average of the two. The scatter plot consisted a mean average difference bounded by its uncertainty interval, i.e. ™ SD (standard deviation of the difference). The magnitude of the averaged difference provides the b ias in WSS measurement during repeats. Bias and its standard deviation wer e calculated at peak systole, end diastole and time averaged. The inter-observer variability and inter-scan

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42 variability were examined using the same analytical procedure. Variables are reported as mean ™ SD. Study 2. Measurement Uncertainty Echo PIV is a semi-automated measurement technique that requires a range of user inputs and a fixed automated sequence of image processing operations, such as an application of median filtering for the removal of background noise. The algorithm is designed to measure flow character istics based on a time-series of ultrasound images of the seeded flow. Factors as sociated with the ultrasound image acquisition influence the performance of the PIV algorithm, namely: the frame rate at which the images are acquired governs the resolvable dynamic velocity range; the image quality depends on the ul trasound operating frequency, depth of insonication and field of view; and most importantly the seeding particle density, size and dynamics [70], [71]. The dynamic nature of flow causes image quality to vary in time and space, which leads to n on-uniform uncertainty distribution throughout the flow field [70]. This m akes it challenging to compute uncertainty in echo PIV measurement since the sourc es of error relating to ultrasound imaging and the PIV computation are coup led. In our study, we measured uncertainty relating to WSS measurement at one spatial point at different time points. In echo PIV, the mean particle displacement is comp uted by means of spatial cross-correlation of consecutive image pair s (cf. Chapter 4). Rewriting Eqn. (4.3) in Eqn. (5.2), we note that the uncertai nty of u originates from both the displacement < in the streamwise direction (dx) and the time step < and

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43 likewise the uncertainty of v originates from both the displacement <+ in the radial direction (dy) and < 0 ( Z š š • < < (5.2) ( Z ˆ š+ š • < + < Using the Taylor series method for uncertainty prop agation [72], the displacement uncertainty propagates to the velocity uncertainty as shown in Eqn. 5.3: Y ›œ  Z < Y > Z < Y > (5.3) Y ›Ÿ    Z ˆ < + Y >ˆ ¡   Z ˆ < Y > ¡ Key ultrasound imaging parameters that affect the i mage acquisition rame rate are the beam line numbers, the depth of focus (single) and the field of view, all of which are kept constant throughout the exper iment. Following Timmins et al [70], we assume the uncertainty in the < is small enough to be negligible. This reduces equation 5.3 to equation 5.4: Y › œ 3 < Y > (5.4) Y › Ÿ 3 < Y > ˆ In this study, the uncertainties Y›œ ( and Y›Ÿ( are both functions of spatial and temporal points. For simplicity, we com puted the random standard uncertainty at the first spatial point in the vesse l length. Y›œ 3( and Y›Ÿ3(

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44 were then computed from the standard deviation of t he Z and Zˆ at different time points spanning three to four cardiac cycles. In essence, due to the nature of the in vivo data under study, random uncertainty in the displac ement measurements was calculated based on the inter-cycl e variability in particle displacements ( < and <+ ). Finally, the computed uncertainty in the two veloci ty components was propagated to uncertainty in the measurement of WSS WSS is the product of blood dynamic viscosity, r which is considered to be constant at 0.032 Poise, and the spatial velocity gradient (also known as th e wall shear rate, SR), which is the sum of the radial change of Z per change in y (i.e. d+ ) and the lateral change of Zˆ per change in x (i.e. ). The data reduction equation was constructed as follows to obtain the uncertainty equation for the wall shear rate ( Y¢;) (Eqn. 5.5) £C š Z + š Z ˆ • < Z + < Z ˆ (5.5) Y ¢;  £C < Z Y ›œ £C < + Y ˆ   £C < Z ˆ Y ›Ÿ ¡ £C Y b In echo PIV, points are equally spaced at all time points for the given experiment; i.e. and + are constant for each cardiac cycle and thus the random standard uncertainty in and + is zero. This reduces Eqn. 5.5 to Eqn. 5.6: Y ¢;  3 ‰ Y ›œ 3 Y ›Ÿ (5.6)

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45 Finally, the uncertainty in WSS measurement was com puted by multiplying Eqn. 5.5 with the dynamic blood viscosity, r$#$O= Total uncertainty in velocity measurement is the su m of the systematic standard uncertainty and the random standard uncert ainty (Eqn. 5.6) [72]. The systematic uncertainty (b) of 0.235 pixels in displ acement measurement was obtained from reports on optical PIV that employed the 3-point Gaussian peak finding sub-pixel interpolation algorithm as descri bed in equation (5.1) [70]. The displacement systematic uncertainty was propagated to systematic uncertainty in velocity in a similar manner to random uncertainty propagation (Eqn. 5.4); the same value was used for both the u and v components of the velocity vector, Z(+( Total random uncertainty was computed by taking t he Pythagorean sum of the uncertainties in Z and Zˆ (Eqn. 5.7) where, Z and Zˆ are the average values of the respective uncertainties. 5 Y › T Y › œ Y › Ÿ (5.7) The Y¤uncertainty was then used to compute the total unce rtainty in velocity measurement: X ¦ § ¤ ( ¨ 5 (5.8) where, ¤(¨ is the student’s t for a degree of freedom of 27 w hich equals to 2.056 [72]. Individual contribution of the systematic and random uncertainties were then calculated as in Eqn. 5.9 [73]: = 5 (5.9) Study 3. Comparison against PC MRI

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46 Percent difference in WSS measurements between the echo PIV ( ££^) and PC-MRI ( ££) methods was calculated: {q cs `a m  3$$ Percent difference was calculated for WSS measure ments extracted at peak systole, end diastole and time averaged magnit udes. Results Participant characteristics The study population comprised of 37 apparently hea lthy participants. Evaluation of data from 12 participants was needed to determin e the quality and density of contrast agent required within the arterial lumen f or optimal echo PIV analysis. Application of the exclusion criteria resulted in u sable datasets from 28 participants with acceptable UDV data and echo PIV velocity vector field resolution. For the repeatability and reproducibility study, 22 subjects were randomly selected for inter-scan, intra-observer and inter-o bserver variability analysis. For comparison against the PC-MRI measurements, all 28 subjects were evaluated. WSS derived from echo PIV exhibited small intra-obs erver variability with a mean bias of -0.05 ™ 1 dyn/cm2 for peak systole, -0.10 ™ 0.9 for time averaged magnitude and -0.03 ™ 0.5 dyn/cm2 for end diastole (Figure 5.1). Likewise, interobserver variability was also found to be low (Figu re 5.2): Peak systolic WSS bias: -1 ™ 2 dyn/cm2, time averaged WSS mean: -0.4 ™ 1.3 dyn/cm2 and End diastolic WSS min: -0.4 ™ 0.7 dyn/cm2. Study 1. Repeatability and Reproducibility

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47 Compared to intraand interobserver variability, Bland-Altma n analysis revealed increased inter-scan variability with relatively wi der limits of agreement (i.e. 2SD) or peak systolic (-1.2 ™ 7 dyn/cm2), time averaged (-0.5 ™ 3 dyn/cm2) and end diastolic WSS measurements (-0.5 ™ 1.5 dyn/cm2) (Figure 5.3, note the larger yscales). Figure 5. 1. Repeatability. Intra-observer variability was calculated as the di fference in WSS measurement between the repeated analyses by the same observer. Resulting bias was extracted at peak systole (BiasMax), time averaged (BiasMean) and end diastole (BiasMin).

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48 Figure 5. 2. Reproducibility. Inter-observer variability was calculated by plotti ng the difference in WSS measurements obtained from two independent observer s against the estimate averaged over the two observers. Resulting bias was extracted at peak systole (BiasMax), time averaged (BiasMean) and end diastole (BiasMin).

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49 Figure 5. 3. Inter-scan variability. Inter-scan variability was calculated by plotting t he difference in WSS measurements calculated for the same individual at two consecutive time points, i.e. scan 1 and scan 2. Resulting bias was extract ed at peak systole (BiasMax), time averaged (BiasMean) and end diastole (BiasMin). Study 2. Measurement Uncertainty and Propagation Variability in WSS measurements due to different ob servers or acquisition time or repetitions was included in the investigation of me asurement uncertainty in WSS (Figure 5.4).

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50 Figure 5. 4. Measurement uncertainty from measureme nt variability. Inter-scan variability was the major source of unce rtainty in WSS measurement with the largest influence during peak systole and the lowest during end diastole. Intra-observer variability contributed the least to WSS uncertainty. The error bars on each magnitude bars are the standard error of th e bias distribution across the sample population. Percent contribution of each individual uncertainti es revealed that the majority of uncertainty originated from the random sources o f error (median: 84%, Figure 5.5). Likewise, contribution of uncertainty in each individual velocity component was evaluated. Compared to the uncertainty in the u -component (i.e. Y›œ), the uncertainty in the v-component of the velocity vect or (i.e. Y›Ÿ) was negligible over the entire cardiac cycle (Figure 5.6).

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51 Figure 5. 5. Percent uncertainty. Random uncertainty contributed more to the overall uncertainty in velocity measurement. The systematic uncertainty only contri buted to a median of 15% uncertainty in velocity measurement. Figure 5. 6. Uncertainty contribution from individu al velocity components. Uncertainty due to the velocity component (i.e. YY›Ÿ<+(< ) was negligible compared to YY›œ<(<

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52 The total uncertainty in velocity measurement resul ted in a mean uncertainty of 6.4 cm/s that translated to a mean u ncertainty of 1.54 dyn/cm2 in WSS measurement. Figure 5. 7. Uncertainty in WSS measurement. On an average, the WSS measurement uncertainty due to inter-cycle variable was low (max: 3.1 ™ 3 dyn/cm2, mean: 1.54 ™ 1 dyn/cm2 and min: 0.72 ™ 0.3 dyn/cm2). Figure 5. 8. WSS measurement comparison between ech o PIV and PC-MRI. Significant difference was found in WSS measurement s during peak systole (p<0.001) and time averaged WSS (p=0.02).

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53 Study 3. Comparison with PC-MRI Figure 5. 9. Temporal distribution of WSS. Both PC MRI (red) and echo PIV (black) measured sim ilar temporal patterns of WSS though the absolute magnitudes varied significa ntly for the majority of the population samples. Compared to echo PIV, the time averaged WSS was und erestimated by PC-MRI by 40% overall (Figure 5.8). Likewise, PC-MRI under estimated WSS by 37%

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54 during peak systole. The maximum discrepancy in WSS measurement between the two methods was observed during diastole, a per cent difference of 62%. However, the temporal WSS pattern showed good quali tative agreement between the two methods which was supported by the point-wise correlation analysis (Figure 5.9) that revealed good agreement (r=0.89, p < 0.001). This suggests that the percent difference in WSS measure ments between the two originated from a systematic uncertainty in the mea surement technique. Figure 5. 10. Point-wise correlation analysis. WSS Regression between Echo PIV vs. PC MRI. A goo d correlation was found between velocity and WSS measurements using PC MRI and echo PIV (both at r=0.89 at p<0.05). WSS measurement using echo PIV a ppeared to vary at a larger proportion to the PC MRI derived WSS values compared to the velocity measurements between the two methods. Further investigation in the temporal distribution of phase averaged WSS revealed significant inter-subject variability in a bsolute difference in WSS magnitudes between the two methods (Figure 5.9) but modest point-wise

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55 correlation overall (a sample mean PearsonÂ’s correl ation coefficient, r = 0.89, p<0.001) as shown in Figure 5.10. The discrepancy i n WSS measurements was investigated by examining the vessel diameter and q uantifying its impact on WSS measurement accuracy. Figure 5. 11. Maximum percent differences in peak s ystolic WSS measurements were observed when the vessel diameter s were smaller. Peak systolic WSS measurements were chosen because the vessel diameters are the largest during systole. Percent differences in WSS (DWSS%) and crosssectional area (DArea%) measurements between the two methods were pl otted on the same figure to evaluate the influence of the vessel size in WSS distribution for each individual. The green dashed lines indicate 1 standard deviation for the DArea%. Discrepancy in the measurements of cross-sectional area between PC MRI and Echo PIV led to a discrepancy in WSS measuremen ts (Figure 5.11). At a given level of peripheral resistance with constant volume flow, the mean flow velocity in a straight vessel is determined mainly by lumen cross-sectional area as shown by the steady state Hagen-PoiseuilleÂ’s equ ation: ! je i.e. wall shear stress is least where the diameter is gr eatest [56]. This translates to an inverse 3/2 effect of the cross-sectional area i n the determination of WSS. In

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56 this study, overestimation in cross-sectional area by PC MRI led to underestimation in WSS by almost a factor of 2. The range of the vessel diameter also played a role in WSS agreement betwee n the two methods. In our study, the mean diameter was 7.5 ™ 1 mm. We found that PC MRI severely underestimates WSS when the vessel diameter is abou t 5 mm. For the vessel diameter closer to 10mm, discrepancy in cross-secti onal area measurements between the two methods was lessened. Figure 5. 12. For a Given Diameter, Echo PIV Measur es peak systolic WSS Within the Same Magnitude Range whereas PC MRI Unde restimates in the second case (subject number 8). The fact that for a large vessel with about the sam e diameter (~10mm), echo PIV measured similar WSS magnitudes but PC MRI underest imated WSS in subject ID 8 compared to ID 15 suggesting that a different independent contributor might be present. However, the agreement in WSS measurements for a gi ven vessel size was not entirely a linear phenomenon as can be inferred from the non-linear distribution of the data points across the zero mea n plus the finding that even for

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57 a vessel with similar diameter (~10mm), PC MRI unde restimated WSS for one subject compared to the other (Figure 5.12). Discussion The main findings of this study are that: 1) Echo P IV can be used in humans to generate WSS with good repeatability and reproducib ility; 2) the primary sources of uncertainty in WSS measurement using echo PIV ar e image particle density and lateral resolution; and 3) compared to echo PIV PC-MRI underestimates instantaneous WSS measurements over the cardiac cyc le. Inter-scan variability in WSS measurement is a meas ure of the difference in image particle density between two consecutive a cquisitions and was found to be a significant contributor to WSS measurement unc ertainty similar to the standard optical PIV [74], [75]. As guided by our p revious in vitro work [32–34], microbubbles were infused at a concentration of abo ut 2-3 x 103 particles per milliliters by using a controlled pump. Lateral res olution, which is governed by the number of scan lines per frame, also significantly contributed to the uncertainty. Lateral resolution affects the accuracy of computin g the displacement vector in the streamwise direction using the Gaussian peak fi nding interpolation method described in equation 5.1 [33], [34]. This indeed t ranslated to a greater contribution in velocity measurement uncertainty fr om the horizontal component of the velocity vector (i.e. Z). Further studies should therefore be focused on optimizing the lateral resolution and consistency o f optimal particle image density during image acquisition[31–34]. The uncertainty in velocity measurement can

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58 thus be reduced by optimizing the contributing fact ors during both the image acquisition and post-processing phases. PIV is a very useful measurement tool for quantifyi ng flow fields. In biomedical applications, ultrasound based echo PIV offers the same benefits that optical PIV has provided to the aerospace and mecha nical engineering communities. Measurement uncertainty relating to PI V variables has only been recently quantified in a rigorous manner by a multi -institutional team led by Vlachos[70], [76], [77]. PIV measurements are timeresolved and non-linear due to the nature of the flow field being measured. PIV uncertainty quantification therefore poses a unique challenge in that the stan dard uncertainty technique of measuring the mean and variance is not adequate and furthermore assumes that the accuracy of a measurement system varies linearl y with the uncertainty in the measurement which is not the case; measurement unce rtainty varies nonlinearly with the variance in the measurand and/or the measu rement system [70], [76]. In this study, we presented the measurement uncerta inty of echo PIV for computing the velocity vector field in both the hor izontal and vertical directions. Of importance was how this uncertainty in velocity measurement propagated to the wall shear stress estimation. Applying the Tayl or series expansion, we quantified the influence of these error sources in WSS calculation. PIV uncertainties varied within the measurement field d ue to changes in the local contributors. Two major sources of random uncertain ties were identified: lateral resolution (i.e. pixel resolution) that depends on the number of beam line

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59 numbers used in the each ultrasound frame reconstru ction and the dynamic velocity range that is related to the lateral resol ution but also the frame rate. Timmins et al studied the effects of specific error sources (diameter, density, displacement and shear) on PIV accuracy wh ich differed depending on the type of PIV algorithms used for motion estimati on [70], [78]. Of the four sources, displacement gradient with the interrogati on window and smaller particle image diameter were the most significant sources of uncertainties. Given the nature of our in vivo data, we were not able to run an experiment to quan tify the measurement uncertainty originating from sources su ch as particle image diameters and shear. Instead, an alternative approa ch was employed to identify the two sources of random uncertainty: particle ima ge density and particle displacement. As previously described, inter-scan v ariability was used to evaluate the effect of particle density in WSS esti mation and inter-cycle variability was used for evaluating the displacement uncertaint y. Hemodynamic flow generates varying levels of uncert ainty throughout the measurement field for PIV because of fluid and stru ctural coupling, and the pulsatile nature of blood flow in the arterial tree [76], [77], [79]. The pulsatile flow is characterized by time varying high shear at the edges (vessel walls) and a core flow with a nearly uniform velocity profile. W ilson et al. [79] showed that larger amounts of random error are present in regio ns with higher wall shear while smaller, systematic uncertainties are more do minant in the center of the flow where shear stress is close to zero [79]. In a greement with this finding, our study showed that random standard uncertainty was i ndeed dominant in WSS

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60 measurement. This most possibly arises from the poo r lateral resolution (~ 0.5 mm) that currently exists in any ultrasound system including the echo PIV system. Additionally, fluctuations in the shear lay er during each cardiac cycle also introduce temporal variations in the magnitude of WSS that contribute uncertainties at different locations and times. Echo PIV has a better spatial resolution (~0.15 to 0.4 mm) compared to PC MRI (1 mm). Because of the limited spatial resol ution and large slice thickness (6mm) in PC MRI, flow measurements are sp atially averaged across the lumen. In this study, the echo PIV derived WSS measurements were also spatial averaged along the length of the vessel. Ho wever, in PC MRI, the WSS measurements are averaged around the circumference of the vessel which underestimates WSS to a larger degree than an axial averaging along the vessel length. Spatial averaging over a larger volume with few actual data points (due to overestimation of luminal area) led to significant underestimation in WSS [22], [25], [80]. Potters et al. (2014) demonstrated that PC MRI measured WSS has higher magnitudes at higher spatial resolutions [25 ]. Additionally, they showed that the effects of spatial resolution on WSS measu rement accuracy differed between the fitting methods employed for near-wall velocity interpolation. Cheng et al. (2002) also showed that even in the aorta, the cir cumferentially averaged WSS incurred a mean absolute error of 28% at a spat ial resolution commonly observed in an in-vivo imaging which was reduced to 15% when the resoluti on was doubled [80]. In addition, the position of the vessel wall within the edge pixel of the sample volume cannot be determined with cert ainty due to the limited

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61 spatial resolution inherent to PC-MRI [81]. This li mitation is more problematic in the smaller or medium sized carotid arteries [25], [37]. We found that, in the vessels with a larger diameter, i.e. closer to 10mm (here as observed for subject number, n=15, with a vessel diameter of D=10.3mm an d again at n=8 and D=10mm), the percent difference in diameter measure ments between the two methods tend to be lower though the percent differe nce in the corresponding WSS measurements was not linear suggesting presence of a second independent variable that caused WSS underestimatio n (3). Except in three cases (n=1, n=16 and n=19), PC MRI consistently und erestimated WSS across the study population. Comparison of echo PIV measured hemodynamic variabl es (diameter and WSS) against the PC MRI measurements indicated that PC-MRI might not be a good reference technique for carotid WSS measuremen t due to inaccuracy in WSS measurements arising from its limited spatial r esolution, circumferential averaging and diameter overestimation both of which led to significant underestimation of WSS. Nonetheless, volumetric mea surements of in vivo flow that can be obtained from PC MRI are still useful f or qualitative evaluation of the temporal WSS distribution, as our study showed good agreement in temporal WSS patterns between the two methods, but it should be noted that the absolute magnitudes of carotid WSS are underestimated. Inaccuracy in WSS measurements can also result due to segmentation errors [25]. WSS measurements can incur an error of 34% if the wall position in the edge pixel is not correctly estimated [37]. Pot ters et al. (2014) found a

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62 segmentation error of 40% and suggested that at lea st 8 voxels were required across the diameter to obtain a WSS accuracy of 5% and a precision of 20% in simulated data [25]. The use of microbubbles in ech o PIV offers easy delineation of the high intensity moving particle images from t he stationary arterial walls resulting in good segmentation accuracy [32], [33], [36]. In our study, PC MRI underestimated peak systolic WSS by 38% and time av eraged WSS by 40%. A significantly larger 62% difference was found durin g diastole. This is possibly related to the low particle image density during th e diastolic phase when the blood flow is minimum. As a result, echo PIV undere stimated the flow velocity compared to PC MRI and consequently shear stress on the vessel walls. Our study was limited by the small sample size. Sec ond, the scanning planes in the measurements by the two modalities were diff erent: echo PIV measured the longitudinal plane of the right carotid artery whereas PC-MRI measured global WSS magnitude that was spatially averaged ov er the cross-sectional plane. The maximum resolvable velocity in the curre nt echo PIV system is about 2~2.5 cm/s due to the current frame rate of ultraso und B-mode imaging. Higher velocities could be measured at the cost of field o f view which in turn would affect the spatial resolution. It should also be noted tha t unlike PC MRI, the current echo PIV system is not yet able to measure vascular hemodynamics in threedimensions and therefore any effects from secondary flow components are not realized. These limitations could be overcome by em ploying advanced techniques such as interleaved imaging which has be en shown to increase the maximum resolvable dynamic velocity range [82], [83 ].

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63 In summary, echo PIV is a novel ultrasound-based ve locimetry technique that provides spatial, multi-component, and time-resolve d velocity and WSS measurements. Echo PIV is highly repeatable and rep roducible with good reliability for measuring in vivo WSS compared to PC MRI. Given the large discrepancies in instantaneous WSS measurements bet ween echo PIV and PC MRI, but not temporal patterns, echo PIV may be mor e appropriate for measurement of WSS in small to medium sized arterie s such as the common carotid.

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64 6. Characterization of Carotid WSS in Healthy Subje cts Introduction Hemodynamic wall shear stress (WSS) is implicated i n vascular endothelial dysfunction and atherogenesis [6], [12], [29], [30] [84]. Endothelial cells lining the arterial walls are mechano-sensitive and respond to different types of WSS transduced by blood flow [18]. Regions of arterial walls exposed to low and oscillatory WSS are predisposed to atherosclerosis while high WSS is proatherogenic but increases vulnerability to plaque r upture in the advanced stage [6], [12]. Since endothelial dysfunction develops m uch before the clinical manifestation of atherosclerosis, the mechanism by which low and/or oscillatory flow contributes to endothelial dysfunction remains an active research area but several issues remain uncertain [8], [10], [18–20]. This is in part because WSS is difficult to measure in vivo In particular, it is difficult to measure flow wi th sufficient spatial and temporal resolution to deter mine accurate estimates of WSS. High spatio-temporal resolution means flow pat terns can be measured near the vessel walls throughout the cardiac cycle to determine any time-varying characteristics in WSS that might be physiologicall y and clinically important. This is relevant because spatial gradients in shear enha nce activation of endothelial transcription factors [8] and temporal gradients ca used by high flow pulsatility are known to stimulate endothelial cell proliferation a nd inflammatory gene expression [10], [19]. Current methods to estimate i n vivo WSS are primarily based on two imaging modalities: Phase-contrast magnetic resonance imagi ng (PC-MRI) and

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65 ultrasound imaging. PC-MRI provides volumetric flow visualization but is relatively expensive, time consuming, and has limit ed spatial and temporal resolution [21]. Because of this, ultrasound Dopple r velocimetry (UDV) has become a popular method to estimate WSS in studies of endothelial function and the natural history of atherosclerotic plaque. This method is inexpensive, readily available and easy to use. However, it is not clear whether it provides an accurate estimate of WSS. The main threat to accura cy is that it measures a one dimensional velocity component rather than measurin g the whole velocity vector field. This introduces error as it is not possible to measure the spatial gradient of the velocity distribution near the vessel walls, wh ich is required to accurately calculate WSS. Instead UDV measures the centerline peak velocity ( Z[\) which is then extrapolated over a theoretical parabola fr om upper to lower wall. However, pulsatile arterial flow does not always ex hibit a parabolic velocity profile, meaning any discrepancy between the actual and the assumed velocity profiles propagates error in WSS measurement [6], [ 27], [28]. We have developed and validated [31–34] an ultrasou nd based method called echo particle imaging velocimetry (echo PIV) that c an be used to more accurately measure WSS. Echo PIV uses the two-dimensional (2D) ultrasound image of the arterial segment to measure the local flow velocity distribution, producing a 2D velocity vector field within an arterial segment. W SS measurement based on UDV is being used extensively in physiological stud ies, yet its accuracy and utility are uncertain. As such, information about the usefu lness of these estimates and their limitations are needed for better interpretat ion of WSS data. Our purpose

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66 was to compare arterial WSS measurements estimated from ultrasound Doppler with those from echo PIV. Methods Ethical approval Participants were apparently healthy men and women recruited at the National Institute for Health Research Exeter Clinical Resea rch Facility, UK. This study conformed to the Declaration of Helsinki and was ap proved by the National Research Ethics Service Southwest (09/H0202/49). Al l participants gave written informed consent. Participant screening and baseline characteristics Participants were asked to refrain from food or dri nk (except water) at least 2 hours before the visit, and to avoid smoking, drink ing tea or coffee, alcohol and strenuous exercise on the study day. Medical histor y, electrocardiogram (ECG), height, body mass, waist circumference, and blood p ressure were obtained and twelve-hour-fasting blood samples were collected in accordance with the U.K. National Quality Assessment Scheme [34], [68]. Dopp ler measurements were collected before contrast agent injection (SonoVue, Bracco, Italy) and echo PIV imaging. Twelve participants were involved in the i nitial experimentation to determine optimal micro-bubble concentration as gui ded by our prior work [32], [33]. Inclusion criteria were: Adequate contrast ag ent density, clear delineation of the lumen boundary on the B-mode image and comparab le peak velocity measurements between UDV and echo PIV. Exclusion cr iteria included history of

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67 uncontrolled hypertension, pulmonary hypertension, renal disease, hepatic disease, claudication, hypersensitivity to the cont rast agent and individuals outside the age range of 20 to 80 years. UDV based WSS measurement Pulsed wave Doppler imaging (Sonix RP, Ultrasonix, Canada) was used to measure maximum blood flow velocity (Vmax) from the right common carotid artery (CCA) at a sample volume placed in the cente r of the vessel at a recorded location upstream of the carotid bifurcation. The p ulse repetition frequency (PRF) was set at 5 kHz with the transducer probe (L14-5/3 8) parallel to the centerline axis of the artery and Doppler angle set at $ [53]. WSS was calculated from the centerline Vmax using the standard Hagen-PoiseuilleÂ’s equation [28 ], [85]: WSSVmax = m4Vmax/D, where D is carotid artery inner diameter and r is dynamic viscosity assumed constant at 0.032 Poise (Figure 6 .1). This equation uses the Poiseuillean assumptions that flow is steady, fully developed (i.e. shape of the flow velocity profile does not change and the mean velocity is half the maximum flow velocity) and has a parabolic velocity profile The UDV derived WSS measurement (WSSVmax) provides an estimate of the mean flow WSS within the Poiseuillean flow assumptions. Echo PIV derived flow variables We have previously shown that echo PIV can measure accurate velocity profiles in the common carotid artery by tracking grayscale image patterns of

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68 microbubbles in the flow [31–34]. Echo PIV uses ult rasound B-mode rather than Figure 6. 1. Comparison between Doppler velocimetry and echo PIV. Ultrasound Doppler Velocimetry calculates flow indu ced shear stress on the vessel walls by assuming a parabolic velocity profi le across the arterial lumen. In contrast, echo particle imaging velocimetry measure s actual velocity profiles by statistically tracking ultrasound images of seeded particles (micro-bubble contrast agent) at consecutive time points. Spatial change i n the velocity is calculated near the upper and lower walls from which wall shea r stress (WSS) is computed. Doppler for flow measurement and is inherently capa ble of measuring two -dimensional velocity vector fields. The use of mic robubbles gives excellent signal discrimination between tissue and blood and allows velocity measurement close to the vessel walls (Figure 4.2). The echo PIV imaging window was selected to overlap with the location of the UDV measurements such that both UDV and echo PI V measured a similar flow region. The long axis of the transducer probe was aligned longitudinally with the centerline of the blood vessel such that blood flow was orthogonal to

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69 ultrasound beam direction. This alignment provides a longitudinal view of contrast-enhanced flow that is recorded into a time -series of images acquired at very high frame rates (480 – 680 frame per second [ 34]), with ECG-gating for post-processing synchronization. The echo PIV velocity vector field was computed by cross-correlating consecutive frames (1100 to 3200) in the time seque nce as reported in our prior work. The spatially and temporally local velocity v ector field was used to construct the spatial profile of flow velocity from upper to lower wall at different time points (Figure 4.4). To quantify the shape of this velocity profile, we used the shape-index (s-index). The s-index (s) was derived by fitting the HagenPoiseuille’s analytical velocity profile (Eqn. 6.1) to the measured data points [6]: Z + Z [\ 3 + C Ž (6.1) An s-index of 2 generates a parabolic profile repre sentative of fullydeveloped laminar flow; this also represents the fo undational assumption behind the UDV-method for calculating WSS. S-index values greater than 2 represent velocity profiles that are blunted at the center wi th sharp spatial gradients at the vessel walls. We extracted the echo PIV measured ve locity profiles at five different time points in the cardiac cycle, as foll ows: 1) accelerating systole past the time-averaged value (C1), 2) peak systole (C2), 3) decelerating systole coinciding with the first notch (C3), 4) mid-diasto le (at ~0.6 s in the cardiac cycle; C4) and 5) end-diastole (C5). These five time point s were selected to investigate WSS distribution at characteristic points in the ca rdiac cycle where flow patterns vary significantly, e.g. accelerating flow (C1) is known to be less turbulent

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70 compared to mid-late systole (C3) and early-mid dia stole (C4) [4], [46], [86], [87]. Characterizing the spatial and temporal variation o f these velocity profiles allowed us to compare the mean flow WSS estimate ob tained via the conventional UDV method with instantaneous echo PIV WSS. Characterization of flow pulsatility using the Wome rsley’s number The non-dimensional Womersley (number was also obtained for each participant (Eqn. (6.2)): J C  2 r (6.2) The Womersley number is a ratio of the unsteady ine rtial force governed by the fluid density (r) and the angular frequency (w) defined as 2P/T where T is the time period over which one cardiac cycle pulsates [ 46]. At a lower the viscous force dominates favoring a parabolic velocity profi le. Therefore, of 1 or less indicates a fully developed parabolic velocity prof ile whereas a value larger than 1 indicates a blunter profile. The UDV method of es timating WSS assumes of 1; thus, echo PIV WSS measurements with values larg er than 1 indicate larger differences between the two methods. Echo PIV based WSS measurement WSS was calculated directly from the echo PIV deriv ed local velocity vector field by computing its spatial gradient (als o known as shear rate) at the radius (R)

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71 ££ r + (6.3) estimated at y = R where y is the radial position a cross the vessel lumen, v is the radial velocity and v/y is the shear rate (Figure 6.2a-b). The time sequ ence of velocity vector fields obtained from echo PIV allow ed extraction of detailed temporal and spatial shear rate information (Figure 6.2b). Spatially local WSS measurements (i.e. WSS measured at one spatial poin t along the vessel length within the field of view) were used to compare agai nst the UDV estimates. Temporal WSS values were extracted at five differen t points in the cardiac cycle (i.e, C1 C5) as described above. Mean WSS was cal culated as the timeaveraged WSS across one full cardiac cycle. Echo PI V WSS measurements were obtained from both the upper and lower walls o f the CCA and averaged. Ensemble averaged WSS waveform analysis Because Echo PIV produces more detailed characteriz ation of WSS than UDV, we performed a qualitative and quantitative an alysis on an ensemble averaged waveform. To construct the ensemble averag ed waveform, WSS waveforms obtained from each individual in the coho rt were spatially and temporally phase averaged and the following three t emporal metrics were then derived: 1) the time-averaged (TA) WSS; 2) the deca y rate of the systolic peak shear calculated by fitting an exponential decay cu rve to data points extracted from the systolic peak to the base of the first not ch; and 3) the systolic time duration, i.e. the time difference between the init ial upstroke of systole to the time of arrival of the first prominent notch. Instantane ous WSS measurements were

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72 spatially and temporally phase averaged over four c ardiac cycles and ensemble averaged for each study group to construct a health y and a TIA phenotypical waveform. Statistical analysis Percent difference in WSS measurements between the UDV and the echo PIV methods was calculated (Eqn. 6.4): { q "" s 'z{ q "" s  3$$ (6.4) Here, WSSi (i = [1,5]) indicates the echo PIV WSS measurement s extracted at the five characteristic time points. The percent di fference between the two mean WSS estimates was also calculated in a similar mann er. The paired t-test was used to compare the UDV derived mean WSS estimate ( i.e. WSSVmax) with the echo PIV derived instantaneous WSS measurements. A one-way balanced ANOVA was conducted to determine differences in WSS at different time points in the cardiac cycle (C1-C5). A probability of p < 0.05 was considered statistically significant for both tests. WSS measurements obtain ed from the two methods are presented as mean standard deviation. Results Participant characteristics The study population comprised 37 apparently health y participants. Evaluation of data from 12 participants was needed to determine t he quality and density of

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73 Table 6. 1. Participants Characteristics Parameter (n=27) Mean ™ SD Age (Male, n=18) 55.2 ™ 12 Body mass (kg) 72.4 ™ 10 Height (m) 1.7 ™ 0.1 BMI 24.4 ™ 3 Waist circ. (cm) 85.6 ™ 9 Hip circ. (cm) 96.3 ™ 8 Waist-Hip Ratio 0.9 ™ 0.1 Systolic BP (mmHg) 124 ™ 13 Diastolic BP (mmHg) 77.5 ™ 9 Pulse Pressure (mmHg) 46.4 ™ 8.9 Heart Rate (b/min) 63.8 ™ 9 Cholesterol (mmol/L) 5.4 ™ 0.9 Triglycerides (mmol/L) 1.2 ™ 0.5 HDL TG (mmol/L) 1.5 ™ 0.4 LDL TG (mmol/L) 3.4 ™ 0.8 Chol:HDL 3.9 ™ 1 Sodium (mmol/L) 139.3 ™ 2 Potassium (mmol/L) 4.5 ™ 0.4 Creatinine (mmol/L) 78.8 ™ 13 Albumin (g/L) 45.1 ™ 3

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74 contrast agent required within the arterial lumen f or optimal echo PIV analysis. Application of the exclusion criteria resulted in u sable datasets from 27 Participants with acceptable UDV data and echo PIV velocity vector field resolution. Characteristics from these participants are presented in Table 6.1. Differences between UDV and echo PIV Mean WSS calculated from UDV was lower than the tim e averaged WSS measured using echo PIV (10.1 ™ 2 dyn/cm2 versus 14.3 ™ 5 dyn/cm2, p<0.001, Figure 6.2). Figure 6. 2. Instantaneous WSS Measurement. Instantaneous WSS measurements were extracted at fi ve different time points in the cardiac cycle: accelerating (C1), peak(C2), dec elerating(C3) systolic phases and mid-diastolic (C4) and end-diastolic (C5) phase s. These measurements, along with time averaged (TA) WSS values were compa red between the two methods. Asterisks represent statistical significan ce (p<0.05). Compared with echo PIV WSS at C1-C5, the UDV method underestimated WSS

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75 at C1, C2 and C3 (22.2 ™ 8 dyn/cm2, 41.2 ™ 12 dyn/cm2 and 14.5 ™ 7 dyn/cm2 respectively) and over-estimated at C5 (7.34 ™ 4 dyn/cm2, all p<0.005) (Figure 6.2). No significant difference was found between t he two WSS estimates at C4 (11.9 ™ 5 dyn/cm2). Table 6. 2. Descriptive statistics of WSS parameter s for upper and lower walls and the average of the two. Upper Wall Shear Stress Lower Wall Shear Stress Averaged Wall Shear Stress dyn/cm 2 Range dyn/cm 2 Range dyn/cm 2 Range TA 14 7 [2,29] 15.7 6 [5,33] 14.8 5 [5,30] C1 22.4 11 [5,42] 23.3 8 [8,43] 22.9 8 [10, 43] C2 41.1 16 [14,72] 44.0 15 [24,89] 42.3 12 [24,81] C3 16.1 10 [2,40] 15.1 10 [1.7,47] 15.6 [2,43] C4 11.2 9 [0.6,33] 13.2 7 [3,30] 12.2 6 [3, 25] C5 7.05 6 [0.3,21] 8.30 5 [0.80,23] 7.68 5 [0.6,22] Values are meanSD and the range is [Min, Max]. All values were significantly different from the ultrasound Doppler estimates (p<0.05), except for t he mid-diastole. TA = Time averaged, C1 = Accelerating systole, C2 = Peak systole, C3 = Decelerating systole, C4 = Mid-diastole, C5 = End-diastole, Averaged = WS S averaged over the UW and LW. These differences remained when WSS at the upper an d lower walls of the artery were derived from echo PIV and compared with UDV WSS (Table 6.2). There were no differences between WSS measured with echo PIV at the upper and lower walls at C1-C5 or when time-averaged acro ss the cardiac cycle (Figure 6.2). Percent differences in WSS measuremen ts between the echo PIV and UDV methods are presented in Table 6.3. The lar gest percent difference was found during peak-systole (C2; underestimation by 1 19 17%) and the smallest during mid-diastole (C4; underestimation by 3.7 4 8%). Compared with echo

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76 PIV, the UDV method overestimated WSS values during end-diastole (C5; 43.5 ™ 55%). Table 6. 3. Percent difference between echo PIVan d ultrasound Dopplerderived wall shear stress at the upper wall, lower wall and the average of both walls Upper Wall Shear Stress Lower Wall Shear Stress Averaged Wall Shear Stress Mean [%] Range [%] Mean [%] Range [%] Mean [%] R ange [%] TA 13.2 54 [-121,93] 32.4 39 [-63,98] 28.2 35 [-51,76] C1 57.0 45 [-71,147] 70.3 31 [-14,113] 67.8 30 [10,130] C2 112 26 [54,154] 118 20 [62,154] 118 16 [ 74,142] C3 16.6 70 [-117,132] 14.3 69 [-139,95] 24.8 51 [-123,117] C4 -22.9 [-179,102] 9.87 51 [-89,85] 4.30 † [-104,70] C5 -61.5 70 [-189,56] -37.3 60 [-167,71] -43. 5 55 [-176,40] Blood flow velocity profiles and shape index Compared with the parabolic profile assumed in UDV, the shape of the velocity profile measured using the echo PIV method varied s patially across the cardiac cycle. In contrast to a constant value of 2 assumed in the UDV method (i.e. a parabolic velocity profile throughout the cardiac c ycle), echo PIV measurements revealed that the mean s-index was 4.3 ™ 3 at C1, 7.4 ™ 4 at C2, 6.4 ™ 5 at C3, 4.5 ™ 2 at C4 and 3.6 ™ 3 at C5. The s-index significantly varied at differ ent phases of the cardiac cycle (p < 0.001). S-index distribut ion and its influence on the shape of the velocity profile are shown in Figure 6 .4. Womersley’s numbers ( ) ranged from 3.48 to 6.88, indicating that the actua l velocity profile tends to be

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77 Figure 6. 3. Example of a parabolic systolic veloci ty profile. A parabolic systolic velocity magnitude of 48.5 cm/ s generates a systolic WSS of 54 dyn/cm2 for a vessel diameter of 6.4 mm. Figure 6. 4. Examples of a blunt systolic velocity profile. Wall shear stress (WSS) measurement depends on the shape of the velocity profile as well as vessel diameter. Here, a blunt s ystolic velocity profile for participant number 13 generates a systolic WSS of 4 6 dyn/cm2 for a relatively larger diameter of 7.0 mm (compared to 54 dyn/cm2 for subject 3 in Figure 6.3 whose diameter was 6.4 mm). less parabolic and more blunt at the center of the blood vessel with sharp gradients at the walls.

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78 Figure 6. 5. Spatial and temporal variation in velo city profiles at C1-C5 for each participant. Distribution of the s-index for all participants ex tracted at five different time points (C1-C5) reveals spatio-temporal variation in the ve locity profile within a cardiac cycle. An s-index of 2 indicates a parabolic profil e that is symmetric across the center axis of the vessel, whereas a value larger t han 2 indicates a blunted profile. Ensemble averaged WSS waveform analysis The ensemble-averaged WSS waveform is presented in Figure 6.5 and instantaneous WSS measurements at the upper and low er wall are reported in Table 6.2. The time-averaged WSS was 14.8 5 dyn/c m2. The waveform was characterised by a primary peak with a local maximu m of 42.3 12 dyn/cm2.

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79 Figure 6. 6. Ensemble averaged WSS profile. WSS measurements were spatial and phase averaged. T he decay constant was calculated by fitting an exponential decay curv e to data points from the peak systolic to the first inflection point. The systoli c time duration was e was calculated as the time difference between the upstr oke and the first notch. Approximately half of this maximum shear was sustai ned for a mean duration of 0.14 0.07 s. Analysis of the systolic descending velocity showed that peak systolic shear force decelerated towards the first notch of the waveform at a mean speed of 9 0.07 per second. WSS extracted at this notch ranged 15.6 8 dyn/cm2and a similar WSS was maintained through mid-diasto le (12.2 6 dyn/cm2). The minimum WSS occurred at end-diastole (7.68 5 dyn/cm2). The accelerating systolic WSS was 22.9 8 dyn/cm2. These differences in WSS at

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80 Figure 6. 7. Temporal variation in the WSS profile between individual participants. Phase averaged WSS revealed the presence of primary and secondary systolic peaks followed by a diastolic peak within each card iac cycle. Phase averaging was performed to obtain a representative WSS wavefo rm instead of an alternative method of fitting to a spline. The arri val time of the secondary peak appears to be consistent across the participant gro up. Except for subject number 9, 17 and 20, we observed low variability in the WS S waveform between individuals. different phases of the cardiac cycle were signific ant (p < 0.001). We also observed some degree of inter-individual variabilit y in the qualitative appearance of WSS waveforms, particularly subject numbers 9, 1 7 and 20 seemed to have an increased number of fluctuation during the decel erating systolic phase (Figure 6.6).

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81 Discussion In this study, we measured carotid artery WSS using echo PIV and compared this with WSS estimated from the commonly used ultr asound Doppler velocimetry method. To our knowledge this is the fi rst study to characterise time varying carotid WSS patterns measured in-vivo The key findings were that: 1) compared with echo PIV, time-averaged WSS was lower using the UDV method; 2) the degree of underor overestimation of WSS by UDV varied across the cardiac cycle because of temporal variation in WSS that is not accommodated by the UDV method; 3) echo PIV revealed considerable s patio-temporal variation in the flow velocity profile that is contrary to the a ssumption that flow is steady and the velocity profile is parabolic throughout the ca rdiac cycle. Hemodynamic WSS is currently measured because of it s importance to vascular endothelial cell shape, size, orientation, function and permeability [2]. Alterations in WSS influence endothelial cell signa ling, protein expression and synthesis of vasoactive molecules[2]. Wall shear st ress plays a prominent role in vessel remodeling and in the process of atherogenes is and atheroma progression. Endothelial cells discern different he modynamic WSS stimuli at the cellular level [2] and independent mechano-chemical transduction pathways are activated in the endothelial cells depending on the type of shear stress exerted[9], [88]. For example, turbulent blood flow causes low and oscillatory WSS that causes endothelial cells to express a proatherogenic phenotype [2]. In adult humans atheroma tends to occur at bends, bran ches and bifurcations in the arterial tree where WSS can be low, oscillatory and sometimes turbulent [2]. For

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82 this reason, the measurement of WSS has become impo rtant in understanding vascular biology and pathogenesis. The UDV method i s convenient and has become a popular estimate of WSS. However, our data suggest that it does not accurately estimate mean WSS and illustrates that i t misses much of the important information about WSS that is pertinent t o understanding its role in vascular physiology. Analysis of WSS at five discrete time points reveal ed large temporal variation in the WSS distribution across the cardia c cycle and that WSS was significantly different at these time points. The U DV method does not estimate temporal variations in WSS and comparison based on the UDV mean WSS revealed significant discrepancies at four of the f ive time points. The largest discrepancy was in peak systolic WSS; the UDV metho d underestimated this by 74 to 142%. Mynard et al (2013) also found that UDV underestimated peaksystolic WSS, irrespective of profile skewing using either PoiseuilleÂ’s or WomersleyÂ’s profiles (12). They calculated an under estimation of 30 to 50% using computational fluid dynamics simulations. The discrepancy with our data may result from their use of spatially averaged ima ge-based simulations of velocity profiles extracted from the common carotid artery rather than actual velocity profiles measured in-vivo as reported here. We also found that the enddiastolic WSS was overestimated by UDV and that the re was considerable variation in the discrepancy between echo PIV and U DV. This resulted from wide-ranging, individual-dependent variability in W SS at end diastole detected by echo PIV. The significance of variability in WSS at specific phases of the cardiac

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83 cycle is uncertain, but given the sensitivity of en dothelial cells to variation in WSS, this may reveal important insight into endothe lial physiology and the focal susceptibility to vascular disease. In this study, we quantified the flow velocity patt erns using a shape metric (s-index) and found that the shape of the local vel ocity profile varied both spatially across the vessel lumen and temporally wi thin the cardiac cycle. This spatial and temporal variation in the velocity dist ribution translated into variation in WSS distribution that was not detected using the UDV method. The UDV method is one-dimensional, necessitating flow assum ptions to estimate multidimensional flow velocity and shear stress near the arterial walls, whereas echo PIV produces actual 2-D velocity vector fields that allow velocity measurement close to the wall (14–17). A critical assumption of the UDV method is that blood flow is steady and the shape of the velocity profil e is parabolic with its maximum located at the center of the vessel, but echo PIV s howed that this was not always the case. The effect of the pulsatile flow pattern on the sha pe of the local velocity profile was also quantified using the Womersley’s n umber, a mechanical gauge for the degree of bluntness present in the velocity profile. Consistent with previous studies [86], the Womersley’s number range d from 4 to 7, indicating that the velocity profiles were blunt during most of the cardiac cycle. As noted by Mynard et al. [28] and also shown in this study, the UDV techniq ue cannot detect WSS variations caused by profile blunting. Although some new studies employing the UDV method now use a Womersley’s prof ile to estimate WSS, the

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84 underlying assumption remains that flow velocity ex hibits an axis-symmetric and fully-developed profile. Furthermore, this flow ass umption neglects any variations in the arterial diameter during the cardiac cycle w hich results in compounded error during WSS estimation, particularly during pe ak-systole. For example, when comparing pulsatile flow with similar peak systolic velocity (e.g. 49 cm/s versus 48 cm/s in Figure 3a and 3b respectively) but diffe rent inner diameter (6.4 mm versus 7.0 mm respectively), flow with a parabolic velocity profile (s-index of 2) during peak-systole exerts a WSS of 54 dyn/cm2 in a smaller artery (Figure 3a), compared with a flattened systolic flow (s-index of 6) exerting a WSS of 46 dyn/cm2 in the larger artery (Figure 3b). In this example, the UDV method estimated a mean WSS of 13 dyn/cm2 and 10 dyn/cm2 respectively. This suggests that the use of parabolic velocity profile s for estimating WSS (mean or at specific time points), while neglecting pulsatil e fluctuations in the arterial diameter is inaccurate. Our finding is in agreement with that of Tortoli et al (2003) who showed that velocity distribution during the mi d-late systolic phase was markedly asymmetric (“M-shape”) due to the presence of secondary flows during deceleration [58]. As our data showed, complex velo city patterns resulting from increased turbulence during the deceleration of sys tolic flow can result in WSS distribution that is different from the values pred icted by the time-averaged mean WSS [4], [6], [30]. Instantaneous WSS measurement using echo PIV allowe d us to construct an ensemble averaged WSS phenotype, representing no rmal carotid hemodynamics, with detailed time-varying markers. T he WSS waveform

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85 revealed a highly transient peak systolic WSS decay ing at a rate of 9.08 7 per second with about half of its magnitude sustained f or 9.9 6.2 s-1. We found that the decelerating systolic minimum (17 dyn/cm2) and the mid-diastolic (12 dyn/cm2) WSS values approximated each other (and the timeaveraged value of 14 dyn/cm2) showing that the temporal gradient in WSS is foll owed by a sustained steady shear stress. White et al. [10] showed that temporal gradient in shear stress affected endothelial proliferation dif ferently based on the presence or absence of steady shear stress and the sustained steady WSS suppressed the proliferative stimulus of the gradient. Because endothelial cells are sensitive to the spatial and temporal flow patterns experienc ed at the arterial walls, this could be an important determinant of endothelial an d vascular health. Further elaboration of WSS characteristics, their consequen ces and how they change with age, health and disease is required to fully e xploit the utility of WSS information. To this end, we are currently investig ating WSS in patients with a recent history of transient ischemic attack. In summary, detailed and accurate markers of physio logical and pathophysiological WSS are needed to fully understa nd the role of WSS in vascular biology and vessel disease. Our data show that spatial and temporal flow patterns are complex, dynamic and do not fit w ell with traditional assumptions about blood flow in arteries. Important ly, our data suggest that the use of ultrasound Doppler and extrapolation from ce nterline peak velocity provides limited and largely inaccurate information about WSS. Echo PIV offers a potentially useful tool to accurately measure detai led markers of wall shear stress

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86 in humans in vivo an important yet poorly understood hemodynamic st imulus known to regulate endothelial cell physiology and p athophysiology.

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87 7. Characterization of Carotid WSS in TIA Subjects Introduction Wall shear stress (WSS) is a strong determinant of endothelial dysfunction present early in atherosclerosis[2], [6], [89]. Alt hough endothelial dysfunction is a systemic disorder [90], atherosclerotic lesions are localized in arterial regions with complex geometry, such as curvatures and bifur cations, and disturbed flow patterns, such as flow separation and turbulence[2] [38]. Given the focal nature of atherosclerosis, it has been hypothesized that c ertain patterns of WSS unique to athero-prone regions may potentiate atherogenesi s [2]. However, the exact role and patterns of WSS that are associated with t he pathogenesis of atherosclerosis remains unclear [2], [10], [16]. Several studies, mostly computational and in vitro have analyzed flow patterns in arterial regions susceptible to atheros clerosis or in regions with varying degrees of stenosis and have demonstrated t hat WSS regulates endothelial function and structure by various mecha nisms [2]. Results have shown that the endothelial function depends not onl y on the magnitudes of arterial WSS but also on its spatial and temporal v ariations introduced by the pulsatile blood flow and is interdependent on the a rterial geometry [7–10], [39]. They demonstrated that the endothelial cells respon d to both the spatial [7], [8], [16], [40] and temporal [9], [10], [29], [39], [41] shear patterns by differentially activating endothelial transcription factors indepe ndent of the mechanotransduction pathways. This data highlights the importance of identifying different components of WSS that are as sociated with the endothelial

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88 physiology and pathology. While computational and b iological analyses of endothelial responses to fluid mechanics in atheros clerosis susceptible regions have advanced our understanding of how the endothel ial cells respond to flow induced shear stresses, the exact role and spatio-t emporal patterns of WSS unique to atherogenesis and progression of atherosc lerosis remain poorly defined because of the complexity and difficulty of measuring WSS in vivo [2], [10], [16]. As a result, a more comprehensive analy sis of WSS patterns is needed to define flow environments in vivo Characterization of in vivo WSS patterns and integration with other computational and biolog ical findings may identify WSS patterns that mark different stages of atherosc lerosis and enhance our understanding of mechanisms whereby different WSS p atterns modulate atherosclerosis progression or regression. In this study, we measured carotid WSS in vivo using an ultrasound based echo particle image velocimetry (echo PIV) and exam ined the time varying characteristics of WSS in apparently healthy indivi duals and participants who were recently diagnosed with a transient ischemic a ttack (TIA). The TIA cohort was of particular interest because several studies have shown that the presence of endothelial dysfunction in the coronary or perip heral circulation increases the risk of stroke or TIA in patients with various stag es of atherosclerosis [38]. Using echo PIV, we were able to measure spatially and tim e-resolved WSS in the common carotid artery (CCA) and to quantify spatial and temporal patterns of WSS in the two study groups [31–33], [36]. We also characterized the carotid flow environment in these two cohorts using convent ional metrics, including the

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89 Reynolds number, the Womersley number, the pulsatil ity index and the resistivity index[4], [47]. The objective was to evaluate the h ypothesis that WSS measurements in individuals at an increased risk fo r atherosclerosis differ from those in the healthy individuals, both in terms of the absolute magnitudes and the detailed spatial and temporal patterns of WSS. Methods Participant Screening and Baseline Characteristics Adult men and women participants were recruited at the National Institute for Health Research Exeter Clinical Research Facility, UK. Apparently healthy adults without any known disease were allocated to the hea lthy control group whereas the TIA cohort included participants with a clinica l diagnosis of a recent ischemic insult that resulted in transient cognitive impairm ent. Participants were asked to refrain from food or drink (except water at least 2 hours before the visit), and to avoid smoking, caffeine, alcohol, and strenuous exe rcise on the study day. Doppler measurements were collected before contrast agent injection (Sono Vue, Bracco, Italy) and echo PIV imaging. Inclusion criteria were: Adequate contrast agent density, clear delineation of the lu men boundary on the B-mode image and comparable peak velocity measurements bet ween Doppler and echo PIV. Exclusion criteria included history of uncont rolled hypertension, pulmonary hypertension, renal disease, hepatic disease, claud ication, hypersensitivity to the contrast agent, and individuals outside the age ran ge of 20 to 80 years. This study conformed to the Declaration of Helsinki and was approved by the National

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90 Research Ethics Service Southwest (09/H0202/49). Al l participants gave written informed consent. Ultrasound Imaging Conventional ultrasound B-mode imaging was used to capture images of the carotid blood flow seeded with microbubbles. Detail s on the ultrasound acquisition parameters can be found in our previous reports [32], [33], [51], [68]. By tracking ultrasound image patterns of the seeded particles (microbubbles) between consecutive image frames, echo PIV computes spatially local instantaneous velocity profiles in the common carot id artery. Details on the echo PIV algorithm can be found in our aforementioned re ports. In brief, a sample volume was placed on the right CCA upstream of the carotid bifurcation and ultrasound images were acquired at high frame rates (350 – 680 frame per second). Consecutive frames (1100 to 3200 spanning 3-4 cardiac cycles) were cross-correlated to compute the echo PIV velocity v ector field. These spatially and temporally local velocity vector fields were us ed to construct instantaneous velocity profiles at the upper and lower carotid wa lls. Echo PIV Measurement of WSS Instantaneous WSS was calculated by computing the s patial gradient of the local velocity profiles (also known as shear rate) at the radius (R) as shown in equation (7.1): ££ ( r ( + ( + ˆ : ; (7.1)

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91 where y indicates the radial position across the ve ssel lumen, vx(x,y,t) is the horizontal component (streamwise along the x-axis) of the velocity vector, vx/y is the shear rate and m is blood viscosity assumed constant at 0.032 Poise Instantaneous WSS measurements at the first spatial point (WSS(1,t) denoted hereon as simply WSS(t)) were used for comparative analysis between the two study groups. The first spatial point was selected to reduce any potential effects introduced by complex flow patterns known to exist at or near the carotid bifurcation region. The mean cardiac cycles for ind ividual imaging studies were normalized to equal cycle length, and WSS values we re extracted at five time points across the cardiac cycle defined as: 1) C1, onset of systole; 2) C2, peak systole; 3) C3, decelerating systole (mid-late syst ole) coinciding with the first notch; 4) C4, mid-diastole approximately after 60% of the cardiac cycle; and 5) C5, end-diastole. These five time points were selec ted to investigate WSS distribution at characteristic points in the cardia c cycle where flow patterns change significantly, e.g. accelerating flow in C1 is known to be less turbulent compared to mid-late systole in C3 and early-mid di astole in C4 [4], [46], [86], [87]. Mean WSS was calculated as the time-averaged WSS across one full cardiac cycle. WSS measurements were obtained from both the upper and lower walls of the CCA and averaged. Characterization of Flow Pulsatility The effect of flow pulsatility on WSS distribution was investigated. The flow field in each participant was described by the Reynolds ( Re) number and the Womersley () number. The non-dimensional Reynolds number (Eqn. 7.2)

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92 defines the balance between the inertial force (i.e kinetic energy per unit volume of flow) and viscous force (i.e. the product of blo od viscosity and velocity gradient): CD Y r (7.2) where r = 1015 kg/m3 is blood density, U is the mean flow velocity in t he streamwise direction, D is the mean inner diameter of the blood vessel and r = 0.032 Poise is the dynamic blood viscosity. A large Re number indicates a dominant inertial force leading to increased turbul ence whereas a smaller Re number (<2000) indicates a dominant viscous force f avoring laminar flow with a parabolic velocity profile[46]. Likewise, the Womer sley () number in equation (7.3) J C  r X (7.3) where T is the time period of one cardiac cycle, ch aracterizes the flow velocity profile as well as flow laminarity in a pulsatile f low. A Womersley of 1 or less indicates dominant viscous force favoring a quasi-s teady or fully developed flow with a parabolic velocity profile whereas a value l arger than 1 indicates a dominant influence of unsteady inertial forces blun ting the flow velocity profiles. Additionally, instantaneous velocity measurements w ere used to calculate the pulsatility and resistivity indices were calcul ated using the instantaneous velocity measurements. The pulsatility index (PI) w as calculated as the velocity pulse normalized to its mean value: PI = [Vmax Vmin]/Vmean and the resistivity

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93 index (RI) was calculated as the velocity pulse nor malized to its peak systolic value: RI = [Vmax – Vmin]/Vmax as described in equations (2.10) and (2.11). These metrics are the indicator functions for downstream arterial resistance to pulsatile flow [47], [48]. Time-varying Characteristics of WSS Three temporal markers of WSS were extracted from t he WSS waveform. The temporal gradient in WSS was calculated using forwa rd differences: dWSS(t)/dt [WSS(t+dt) – WSS(t)]/Dt. The peak systolic gradients were determined for each individual and compared between the two groups. The second metric was the systolic decay constant (l) which defined the rate at which the peak systolic WSS decayed to its first notch. The exponential dec ay curve was fitted to data points extracted from the systolic peak to the base of the first notch. In the case where the systolic peak was prolonged, the peak poi nt closest to the diastolic downstroke was selected (see Figure 3, plot number 9). The third metric was the systolic time duration, i.e. the time difference be tween the initial upstroke of systole to the time of arrival of the first promine nt notch. Instantaneous WSS measurements were spatially and temporally phase av eraged over four cardiac cycles and ensemble averaged for each study group t o construct a healthy and a TIA phenotypical waveform. Statistical Analysis Based on the normality test, a non-parametric Wilco xon-Mann-Whitney U test was used to compare WSS measurements between the tw o cohorts. The

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94 measured variables were examined for presence of ou tliers and, if present, each outlier was tested for its significance by applying Grubbs test on the logtransformed data [91]. A one-way balanced ANOVA was conducted to determine differences in WSS at different time points in the cardiac cycle (C1-C5). Both tests reached the statistical significance at p < 0 .05. Measurements are presented as Mean SD. Statistical Analysis Based on the normality test, a non-parametric Wilco xon-Mann-Whitney U test was used to compare WSS measurements between the tw o cohorts. The measured variables were examined for presence of ou tliers and, if present, each outlier was tested for its significance by applying Grubbs test on the logtransformed data [91]. A one-way balanced ANOVA was conducted to determine differences in WSS at different time points in the cardiac cycle (C1-C5). Both tests reached the statistical significance at p < 0 .05. Measurements are presented as Mean SD. Results Participant Characteristics The observational study comprised 39 subjects, incl uding 12 participants with a recent history of TIA (Age: 68.5 11) and 27 appar ently healthy control individuals (HC, Age 55.2 12). The clinical, anth ropometric and hemodynamic variables of the TIA group and healthy controls are summarized in Table 7.1.

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95 The TIA group had significant differences relative to healthy controls in pulse pressure (p=0.01) and IMT (p<0.0001); serological m arkers of cholesterol, LDL Table 7. 1. Participant Characteristics Parameters Healthy (n=27) TIA (n=12) P-value Age 55.2 ™ 12 68.5 11 0.030 Weight (kg) 72.4 ™ 10 84.2 17 0.034 Height (m) 1.7 ™ 0.1 1.7 ™ 0.1 0.945 BMI 24.4 ™ 3 28.6 5 0.016 Waist circ. (cm) 85.6 ™ 9 97.8 14 0.007 Hip circ. (cm) 96.3 ™ 8 105.9 12 0.036 Waist-Hip Ratio 0.9 ™ 0.1 0.9 0.1 0.596 Systolic BP (mmHg) 124 ™ 13 137.8 26 0.062 Diastolic BP (mmHg) 77.5 ™ 9 79.5 16 0.918 Pulse Pressure (mmHg) 46.4 ™ 8.9 58.3 12 0.004 Heart Rate (b/min) 63.8 ™ 9 65.9 10 0.453 Cholesterol (mmol/L) 5.4 ™ 0.9 4.0 0.5 <0.001 Triglycerides (mmol/L) 1.2 ™ 0.5 1.3 0.6 0.514 HDL (mmol/L) 1.5 ™ 0.4 1.3 0.4 0.571 LDL (mmol/L) 3.4 ™ 0.8 2.1 0.4 <0.001 Chol/HDL 3.9 ™ 1 3.4 1 0.409 Sodium (mmol/L) 139.3 ™ 2 141 2.4 0.214 Potassium (mmol/L) 4.5 ™ 0.4 4.3 0.2 0.180 Creatinine (mmol/L) 78.8 ™ 13 92.4 20 0.047 Albumin (g/L) 45.1 ™ 3 44.9 2.5 0.648 Circ = circumference; BP = blood pressure; HDL = hi gh density lipoprotein; LDL = low density lipoprotein; TG = triglycerides; Pulse Pres sure = Systolic-Diastolic BP

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96 and creatinine; and anthropometric metrics includin g weight, BMI, waist and hip circumferences. Compared to controls, TIA group had lower cholesterol and LDL levels possibly due to their statin drug regimen du ring the study. Echo PIV Measurements of Flow and WSS Flow pulsatility was characterized in each individu al by determining the Reynolds (Re) and Womersley ( ) numbers (see Methods). Carotid flow was laminar i n both the healthy (Re of 597 115) and TIA groups ( 354 128; TIA vs HC p > 0.05). Likewise, there was no difference in the Wom ersley number between the two groups (5 0.7 in TIA vs 5 0.7 in HC). The p ulsatility and resistivity indices were not different between the two groups (1.9 0. 7 vs 1.4 0.5 (PI, TIA vs HC) and 0.8 0.1 vs 0.7 0.1 (RI, TIA vs HC), p > 0.0 5). The peak systolic velocity Figure 7. 1.Time-averaged wall shear stress is redu ced by 50% in individuals with transient ischemic attack compared to healthy controls. Instantaneous WSS measurements measured at a single spatial point farthest away from the carotid bifurcation were time average d across the cardiac cycle for both the TIA cohort (n=12) and the healthy control (n=27). Asterisk denotes a statistical significance of p < 0.05. WSS = wall sh ear stress; HC = healthy controls; TIA = Transient ischemic attack. Asterisk denotes statistical significance at p<0.05

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97 was approximately three times the temporal mean vel ocity in both groups. Thus, the TIA and HC groups did not demonstrate significa nt differences by several conventional ultrasound indices of flow field and p eripheral vascular resistance. Compared with the healthy controls, the TIA cohort had lower time averaged WSS (8.1 5 dyn/cm2 vs 14.8 5 dyn/cm2 in HC, p < 0.001; Figure 7.1). Figure 7. 2. Differences in WSS between the healthy and TIA coho rts measured at five different time points in the cardi ac cycle. (A) A representative WSS profile over one cardiac c ycle. Instantaneous WSS measurements were extracted at five different time points in the cardiac cycle: C1, acceleration phase of systole past the time ave raged WSS magnitude (TA); C2, Peak systolic; C3, First notch after peak systo lic deceleration; C4, Middiastolic approximately at 60% of the cardiac cycle and C5, End-diastolic. (B) Instantaneous WSS measurements extracted at five di fferent time points in the cardiac cycle were reduced by half in TIA compared to HC (all p < 0.05). Instantaneous WSS measurements extracted at five ch aracteristic time points in the cardiac cycle (Figure 2A) were also lower in th e TIA cohort (C1: 13.4 8 vs 22.9 8, p = 0.003; C2: 25.0 13 vs 42.3 13, p = 0.001; C3: 8.18 5 vs 15.6 8, p = 0.002; C4: 6.73 6 vs 12.2 6, p = 0.02; a nd C5: 3.80 4 vs 7.68 5, p =

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98 0.01; Figure 2B). The Grubbs test on the log transf ormed data revealed no significant outliers. Temporal and Spatial Characteristics of WSS Instantaneous WSS measurements were spatial and pha se averaged to qualitatively and quantitatively evaluate the timevarying patterns of WSS waveforms in the TIA and healthy control cohorts (F igure 7.3). The ensemble of averaged WSS profiles revealed some variation betwe en individuals among the Figure 7. 3. Temporal distribution of spatial and phase averaged WSS in the TIA cohort. (A) Instantaneous WSS measurements were phase avera ged (over 3-4 cardiac cycles) spatially along the vessel length within th e field of view. The WSS scale for subjects 2, 9, 10 and 12 were adjusted for thei r smaller peak systolic magnitudes as denoted by the two parallel bars on t he y-axis. (B) A representative WSS waveform from the health control s (Gurung et al. 2014a). TIA cohort. Some variability in WSS profiles was al so observed among the healthy individuals (Gurung et al 2014, submitted t o J Physiol). Qualitatively, the temporal shear distributions of some TIA individual s resembled the waveform of

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99 Figure 7. 4. Differences in temporal waveforms of W SS in TIA and HC. (A) Peak temporal shear gradient was calculated by taking the maximum gradient value. (B) The decay constant was estimated by fitting an exponential decay curve to the data points originating from the immediate peak prior to the descend and ending at the first notch. (C) The systolic pulse duration was calculat ed from the time difference between the initial systolic upstroke and the arrival time of the late-systolic notch. Asterisk denotes statistical significance at p<0.05.

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100 HC, except the maximum systolic shear was reduced a nd extended over a longer duration of the cardiac cycle compared to HC. Furth er quantification of WSS waveforms yield three temporal metrics, including t he peak systolic WSS gradient, the systolic decay constant (l), and the systolic time duration (see Methods). The peak temporal WSS gradient (Figure 7. 4A) was significantly lower in the TIA cohort compared to the healthy controls (938.6 792 for TIA and 1682 752 dyn/cm2/s for HC, p = 0.03) but the peak systolic decay ra tes were similar among both cohorts (for 11 7.5 s-1for TIA and 9.9 6.2 s-1 for HC, p = 0.6; Figure 7.4B). Interestingly, the systolic pulse dur ation was significantly longer in the TIA cohort (0.22 0.08 s and 0.14 0.06 s for TIA vs HC respectively at p = 0.007; Figure 7.4C). The ensembles of all temporal and spatial averaged waveforms from TIA and HC subjects were compiled into phenotypical rep resentations for each group (Figure 7.5). The WSS waveform representative of a healthy population group exhibited three phases with three prominent peaks w ith decreasing magnitudes towards diastole. In contrast, the WSS waveform ens emble averaged from the TIA cohort revealed multiple, less prominent peaks diffused over a longer time period in the normalized cardiac cycle. Similar to the instantaneous WSS distributions shown quantitatively in Figure 7.2, t he TIA phenotypical WSS waveform showed reduced shear stress magnitude thro ughout the cardiac cycle compared to the healthy phenotype.

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101 Figure 7. 5. Ensemble averaged WSS waveforms. Individual spatial and phase averaged WSS distribut ion over 3-4 cardiac cycles were ensemble averaged for both the TIA and healthy study groups. Spatial averaging along with the phase averaging operation acts as a low pass filter removing high frequency components and results in l ower WSS magnitudes compared to the spatially local instantaneous measu rements. A review of, temporal WSS profiles from TIA subject (Figure 7.3) suggested different trends that either more closely resembled HC profiles or displayed a broad and smaller elevation of WSS over the cardiac cycle. To better illustrate the spatial and temporal patterns of WSS the spatial and temporal distributions of WSS gradients in the right CCA wer e summarized in twodimensional contour plots that displayed the spatia l distribution of WSS along the vessel length (the horizontal axis) and its tempora l distribution along the vertical axis (Figure 7.6). The spatial-temporal WSS patter ns in the right CCA of healthy

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102 individual were uniform along the vessel segment, t herefore, the highest intensity band observed during systole across the imaged vess el length (Figure 7.6A), corresponds to the peaks in the instantaneous curve s during the systolic acceleration phases C2, after C3 and preceding C4 i n the cardiac cycle, as shown in Figure 3. At least two spatio-temporal pa tterns of WSS could be observed in the TIA contour plots. The WSS contour s in some TIA individuals (pattern A) more closely resembled that of healthy individuals because it displayed a prominent band of higher WSS gradients at the accelerating (C1) or peak-systolic (C2) cardiac phases; however, the dur ation of the WSS gradient band appeared to last longer in the cardiac cycle c ompared to the healthy group. In contrast, the spatio-temporal distributions of s ystolic WSS gradients by other TIA subjects exhibited multiple bands of systolic W SS gradients diffused over a prolonged period of time, as shown in the represent ative contour plot for pattern B. Similar to HC contours, TIA contours also displa yed a uniform WSS along the vessel length but the higher intensity WSS band dur ing systolic acceleration did not reach as high of a magnitude and a series of sy stolic shear gradients were diffused over a longer time duration.

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103 Figure 7. 6. Differences in spatio-temporal WSS pat terns between TIA and HC. Two-dimensional contour plots of spatial and tempor al distribution of WSS in the representative TIA and healthy individuals reveal d istinct WSS spatio-temporal patterns between the two groups. All the three patt erns revealed sharp temporal gradients during systole. In the healthy control, a single band of peak temporal gradient was present during early systole (accelera ting phase) which was uniform across the vessel length and two lesser int ensity shear gradients were noted at time points corresponding to the late syst olic and early diastolic waves. Within the TIA cohort, two distinct patterns were n oted. The first pattern (Pattern A) consisted of a spatio-temporal pattern similar t o the healthy individual with a single band of temporal gradient localized during e arly systole and uniform along the streamwise direction. In contrast, the second pattern (Pattern B) exhibited a more diffused systolic shear over a longer time dur ation. Discussion The present study characterized the time varying pa tterns of carotid WSS using ultrasound echo particle image velocimetry in two s tudy groups of TIA and healthy individuals. The TIA individuals showed sig nificant variations in both their magnitude and temporal distribution of WSS. In cont rast, conventional ultrasound parameters were not different between the two group s.

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104 Several studies have shown that the endothelial fu nction depends not only on the magnitudes of WSS but also on its spatial an d temporal variations introduced by the pulsatile nature of blood flow th at is also interdependent on the arterial geometry [7–10], [39]. A number of computa tional and in-vitro studies have analyzed the spatial [7], [8], [16], [40] and temporal [9], [10], [29], [39], [41] patterns of wall shear stresses in vitro in arteria l regions predisposed to atherosclerosis or with varying degrees of stenosis These studies have shown that the endothelial cells respond to both spatial and temporal shear gradients by differentially activating endothelial transcription factors and independent mechanotransduction pathways. While these detailed analyses of endothelial responses to fluid mechanics in atherosclerosis sus ceptible regions have advanced our understanding of the mechanisms by whi ch shear stresses regulate endothelial behavior, the exact role and t he spatio-temporal patterns of WSS involved in the pathogenesis of atherosclerosis remain poorly defined. This is primarily due to the difficulty and complexity a ssociated with measuring WSS in vivo [7], [10], [16]. In this study, we measured carotid WSS in individuals with a recent transient ischemic event and the healthy con trols using a previously validated [34] ultrasound based measurement techniq ue called echo PIV. Our findings extend the observations obtained from the computational and biological studies by clinically demonstrating that individual s with a recent history of a transient ischemic event exhibit a significantly lo wer carotid WSS across the cardiac cycle and have significantly different temp oral WSS patterns compared to the healthy controls.

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105 Compared to the healthy controls, the time average d WSS in the carotid artery was reduced by 50% in the TIA cohort. It is well established that atherosclerosis occurs preferentially in the arteri al segments where WSS is low due to altered flow field such as flow stagnation o r flow reversal [2], [12]. Atherosclerosis is a highly focal arterial disease with plaques localized within regions of complex flow and geometry such as bifurc ations and curvatures [2]. Such localized distribution of atherosclerotic lesi ons gave rise to the prevailing hypothesis that certain patterns of blood flow coul d either be atheroprotective or atherosclerotic [2], [8], [11], [16], [42], [92–94] Undisturbed laminar flow in regions with straight arterial walls are known to i nduce physiologically high shear stress which are atheroprotective, for example by d ecreasing the endothelial cell mitosis [16] or by reducing transjunctional permeab ility [56]. Disturbed or turbulent flow patterns often observed in regions w ith branching or curvatures are known to induce low and oscillatory shear stress an d are atherogenic primarily because of the compromised blood-wall mass transpor t [2], [12], [92]. In this study, we measured in vivo WSS in the common carotid artery (CCA) of the healthy and TIA population samples using ultrasound echo PIV. The CCA is a typically straight conduit vessel supplying blood f low to the cerebral vasculature. We evaluated the carotid flow field using the Reyno lds number and the Womersley number and did not find any difference be tween the two groups. Proximal aortic stiffness as well as downstream res istance from the cerebral vasculature are known to affect the pulsatility of carotid blood flow and vice versa [47], [87], [95]. In our study groups, we did not f ind any differences in the flow

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106 pulsatility as quantified by the pulsatility index and the resistivity index measured using the flow velocity waveform. Regardless, the t ime averaged WSS in the CCA was significantly lower in the TIA group compar ed to the healthy controls. Following the well-established theory that arterial walls exposed to low WSS are predisposed to atherosclerosis, the TIA cohort pres ents as a group susceptible to atherosclerosis [2], [6], [12]. Instantaneous WSS measurements at five different ti me points in the cardiac cycle were also significantly reduced in th e TIA cohort compared to the healthy controls. Different flow patterns are known to exist during different phases of the cardiac cycle which will affect the t emporal distribution of the resulting shear forces [4], [87], [96]. Compared to the acceleration phase of systole, the flow patterns tend to be more turbulen t during systolic deceleration because it takes time for turbulence to develop and because of a strong temporal gradient present during the systolic upstroke and a s reported in this study, the accelerating flow does not allow enough time for tu rbulence to develop [4]. Once the flow has reached its peak systolic magnitude, i t starts to decelerate allowing enough time for turbulence to develop which causes the post-systolic flow to be less stable [4]. As the kinetic flow energy dissipa tes towards diastole, the diastolic flow becomes more stable. Compared to the diastolic WSS distribution, we found that the instantaneous WSS measurements du ring the systolic phase had higher sensitivity. The peak systolic WSS diffe rence was the most sensitive (TIA vs HC p = 0.001) followed by the decelerating systolic (TIA vs HC p = 0.002) and the accelerating systolic WSS difference betwee n the two groups (p =

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107 0.003). This suggests that the highly time varying patterns of WSS may produce a more sensitive set of flow markers containing inf ormation about the hemodynamic milieu of the endothelial cells. The rate at which the WSS varies with time was also different between the two study groups. Temporal shear gradient is the ch ange in WSS over a small period of time at a fixed spatial point on the arte rial segment [10]. In vitro studies have shown that sharp temporal gradients enhance en dothelial cell proliferation that may increase the permeability of the endotheli al cells to plasma components such as low-density lipoproteins that are atherogen ic [9–11], [56]. However, White et al. (2001) also showed that the proliferative effect of the temporal shear gradient was suppressed in the presence of a unifor m steady shear stress (i.e. in the absence of a pulsatile flow) [10]. Since arteri al blood flow is pulsatile in nature, a uniform steady shear stress could be deri ved from the average of the dynamic shear components across the cardiac cycle. It can thus be speculated that the magnitude of the time averaged WSS could a lter the effect of the temporal shear gradient on endothelial cell prolife ration akin to the steady shear stress. We have already shown that both the time av eraged and the pulsatile components of WSS were reduced by a factor of 2 in the TIA cohort compared to the healthy controls. Based on the in vitro findings of White et al. and our in vivo results reported here, we hypothesize that the time averaged magnitude of the shear stresses would play a similar role in inhibit ing the atherogenic effect of strong temporal shear gradients and that temporal g radients in the presence of low mean shear stress could promote atherogenesis. However, the exact

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108 mechanism by which a steady shear stress suppresses the proliferative effect of the temporal shear gradient is not known. Dynamic, pulsatile components of shear stress form a periodic waveform which differed between our two study groups. A typi cal velocity waveform in a healthy individual consists of three pulses with de creasing magnitudes for subsequent peaks [87]. In our study, the healthy WS S waveform was indeed triphasic with its first systolic peak larger in magni tude compared to both the second systolic peak and the diastolic peak. In con trast, this tri-phasic feature of the shear waveform was distorted or absent in the T IA shear waveforms. The TIA representative waveforms differed significantly fro m the healthy phenotype; the systolic shear stress was distributed over a longer time period across multiple peaks in the TIA cohort. This sustained systolic sh ear force and the increased number of systolic peaks might be indicative of inc reased flow pulsatility. The carotid arteries are the direct supplier of blood f low to a normally high flow, low resistance cerebral vasculature [97]. Several studi es have shown that increased flow pulsatility perturbs the cerebral microcircula tion and increases the risk of cerebrovascular disease by inducing microvascular i schemia, white-matter damage and dementia [95], [97], [98]. In addition, several studies have linked endothelial dysfunction to ischemic cerebrovascular events [38]. Our findings that the carotid arteries in the TIA cohort were exposed to reduced but highly pulsatile WSS suggest that individuals with a history of TIA are at a higher risk for future ischemic cerebrovascular events.

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109 In summary, we have shown that temporal patterns o f wall shear stresses are complex, dynamic and more sensitive than the co nventional flow markers. Our study is limited by its small sample size (12 s ubjects with a history of TIA and 27 apparently healthy individuals) and besides bein g a retrospective observational study, it has nonetheless identified new features of in vivo carotid wall shear stress distribution in two different pop ulation groups. A larger, possibly blinded and longitudinal, clinical study is needed to further validate and refine these WSS characteristics and to fully exploit thei r utility. With the present study, we have provided a basis for such a study by identi fying detailed markers of WSS that may serve as important biomechanical stimu li for atherogenesis.

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110 8. Summary and Future Work Echo PIV is a novel ultrasound based particle image velocimetry technique capable of measuring detailed markers of physiological and pathological wall shear stress in vivo This is an important feat because the role of WSS in vascular biology and vessel disease is kn own to be increasingly complex and highly dynamic as more information abou t the underlying mechanisms are revealed through computational and b iological studies. Through our clinical study, we showed that spatial and temp oral flow patterns of carotid WSS are indeed complex and dynamic, do not fit well with traditional assumptions about blood flow in arteries and differ significantly between physiological versus pathological conditions. We found that echo PIV measured WSS information ex tends far beyond the absolute magnitude of this mechanical force. Th e time evolution of WSS in a cardiac cycle revealed significant information with regards to its sensitivity and measurement reliability. For example, the measureme nt accuracy of echo PIV is dependent on the microbubble concentration or the p article image density. During end diastole, reduced flow tends to be very low in particle image density which led echo PIV to underestimate WSS. Whereas, d uring the clinical study involving the TIA cohort and the healthy controls, it was shown that the systolic WSS measurements had the highest sensitivity. This could be due to several factors such as enhanced particle image density wit h increased systolic flow and increased velocity vector to noise ratio which also improves WSS estimation. Other temporal metrics such as temporal WSS gradien t, peak systolic decay and

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111 time duration of the systolic shear force all appea r to interact dynamically with not just the vessel wall and the endothelial cells but amongst one another in almost a compensatory fashion. For example, the decay consta nt was similar between the TIA and healthy groups though the peak temporal WSS gradient in the healthy controls was significantly stronger. The time diffe rence between the first notch in systole and the upstroke was significantly longer i n the TIA cohort compared to the healthy controls. Given that our study is limit ed by its small sample size, a larger clinical study is needed to validate these f indings and refine these WSS characteristics that might be useful both clinicall y and physiologically. Extending this study for measuring hemodynamic variables in d ifferent population groups such as those with type 2 diabetes mellitus, for ex ample via a flow mediated dilation (FMD) study, could provide useful informat ion regarding the stimulus role of WSS in the synthesis of endothelial based nitric oxide synthase (eNOS), a key regulator of vascular health. The ability and accur acy of echo PIV for quantifying complex flow patterns such as turbulence is of spec ial interest because the ability to quantify complex flow behavior would further our understanding of the spatiotemporal patterns of WSS at different cardiac phase s (decelerating systolic phases known to exhibit a more turbulent flow), com plex vessel geometry (such as the carotid bifurcations) and different hemodyna mic conditions (post-stenotic flow reattachment sites, etc.). In our study, we measured hemodynamic WSS in the ri ght carotid artery of both the healthy and TIA cohorts. A TIA event co uld be related to presence of an atherosclerotic plaque either on the right or th e left carotid artery or disease in

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112 the aortic arch. Could the reported WSS results at the right carotid artery relate to generalized endothelial dysfunction in the individu als and/or do the WSS variables in the right and left carotid arteries co rrespond in the same individual? Future studies should therefore focus on WSS measur ements on both the right and the left carotid arteries and the comparisons o f the results with context to the presence of ipsilateral or contralateral plaque bur den. Findings could help determine whether systemic variables like endotheli al dysfunction could be similar in the right and the left carotids and/or w hether the WSS values might relate to plaque burden that might be different bet ween both vessels. It should also be noted that clinical variables such as cardi ac output (not significantly different between the healthy and TIA cohorts in th is study) and presence of congestive heart failure (patients with a congestiv e heart failure were excluded) could affect the time-averaged WSS results. Future studies are needed to test for these effects. One could examine the echo PIV measu red WSS on the right carotid artery during a congestive heart failure ep isode and after recovery when cardiac output might have improved. Likewise, simil ar studies could be designed to investigate whether WSS measurements change in s ubject with hypertension, before and after correcting blood pressure or wheth er the use of statin medications (that improves endothelial function) co uld modify WSS magnitudes and patterns before and after the start of treatmen t. As such, measurements of carotid artery wall shear stress could be used as a clinical variable to monitor the role of WSS in pathogenesis of atherosclerosis and screening for clinical ischemic events.

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113 Future work will be dedicated to optimizing the ec ho PIV image acquisition procedure with the goal to overcome the limitations associated with spatial resolution, velocity vector density and particle im age density. As discussed in chapter 4, out of plane loss of particle image pair threatens the measurement accuracy of echo PIV. A key optimization step for r educing this risk is to increase the dynamic range of velocity that can be resolved. This focus is doubly important given our finding that the temporal evolu tion of WSS is highly dynamic. Additionally, spatial WSS gradients are also found known to affect the endothelial function which means that spatial resolution will p lay a more determinant role in the measurement accuracy. Therefore, an ultrasound imaging protocol optimized for flow velocimetry allowing quantification of hig hly time-varying hemodynamic variables would be valuable. Echo PIV benefits from the usability of ultrasound imaging but its spatial resolution is limited compa red to computed or acoustic tomography [99–101]. Schiffner et al. recently showed that with a regularized reconstruction scheme, the ultrasound image quality could be greatly enhanced [100–103]. Given that the current computing capacit y cannot allow real time reconstruction of these high resolution ultrasound images, modifications could be made such that a hybrid regularized scheme could be employed. For instance, a super resolution ultrasound particle image could be used as a template for subsequent particle image matching or cross-correla tion at specific time points of interest, e.g. during peakto latesystole or ear ly diastole where blood flow patterns are known to be highly time varying, e.g. due to increased turbulence or

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114 increased decay rate. This leads to the second fram ework of optimization which belongs to the domain of temporal resolution. Highe r temporal resolution would allow a more accurate measurement of highly transie nt WSS markers that are of clinical and physiological interest. Poelma et al. recently developed a novel image acquisition scheme called interleaved ultraso und imaging custom designed for enhancing the maximum resolvable dynam ic velocity range [82]. However, this new technique is associated with the well-known tradeoff of compromised spatial resolution. This could indeed b e circumvented if quantitative, theoretical acoustic based image reco nstruction scheme could be adapted to echo PIV. Furthermore, a regularization based motion estimation algorithms could improve the motion estimation accu racy compared to the conventional cross-correlation estimator. This summ arizes the notion that movement towards a velocimetry focused ultrasound i maging protocol might be necessary to bring significant advancement in the a ccuracy and utility of echo PIV for in vivo wall shear stress measurement. Future, collaborati ve effort must therefore be in place to collectively utilize the b enefits of quantitative ultrasound imaging and optimized velocimetry approaches to ful ly exploit the utility of echo PIV in providing physiologically important and clin ically relevant markers of hemodynamic wall shear stresses.

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