Review
Wall Shear Stress and Early Atherosclerosis: A Review
Akram M. Shaaban 1,2 and André J. Duerinckx 1,3,4
A
therosclerosis remains the leading
cause of morbidity and mortality in
the Western world [1, 2]. It is usually regarded as a systemic disease and several
well-identified risk factors (i.e., hypertension,
hyperlipidemia, diabetes mellitus, and cigarette smoking) have been implicated in its
pathogenesis. Noninvasive imaging of atherosclerosis, such as intimal wall thickening and
plaque formation, is routinely available using a
variety of imaging techniques. The causes of
atherosclerosis are multifactorial and knowing
them could allow earlier prevention and detection of the disease. The frequent occurrence of
atherosclerotic plaques in well-recognized arterial districts, together with the focal distribution
of these plaques in regions of curvature, bifurcation, and branching of the vessels, suggests
that fluid dynamics and vessel geometry may
play a localizing role in the cause of plaque formation [3]. In vitro and in vivo models have
been used to study the flow patterns in a variety
of arterial territories and to look for an association between areas of preferential atherosclerotic plaque formation and blood flow
hemodynamics [4–7]. The magnitude and rate
of change of blood flow close to a vessel wall,
which can be expressed using the concept of
wall shear stress, have been linked to the pathogenesis of atherosclerosis. Vessel segments
with low wall shear stress or highly oscillatory
wall shear stress appear to be at the highest risk
1
for development of atherosclerosis. The purpose of this review is to familiarize the imager
with the concepts and principles underlying
wall shear stress measurements. Wall shear
stress mapping may someday become part of
the multifactorial, multidisciplinary approach
to early atherosclerosis detection.
We first review this hypothesized association between atherosclerosis and wall shear
stress. We then review the use of phase-contrast velocity-encoded MR imaging and Doppler sonography to map velocity profiles in
vascular structures. These hemodynamic parameters can be used to calculate how quickly
the blood velocity increases when moving
from the vessel wall to the center of the vessel. Estimation of wall shear stress is now
possible with noninvasive imaging techniques such as MR imaging and Doppler
sonography. MR imaging can be used to confirm, in vivo, what is known from in vitro hemodynamic studies and observations made at
autopsy and in experimental models. Someday, this may help us better understand the
importance of flow hemodynamics in the
multifactorial etiology of atherosclerosis.
Wall Shear Stress
In nonpulsatile flow in a straight vessel, fluid
does not move at the same velocity at every
point in the vessel. Instead, fluid flow is fastest
at the center and slowest close to the wall. The
fluid velocities assume a parabolic profile referred to as the “laminar flow” profile [8] (Fig.
1). This pattern of flow is the result of friction
within the fluid and between the fluid and the
vessel wall, and is related to the fluid viscosity.
This friction creates a tangential force exerted
by the flowing fluid on the intimal surface of the
artery and is referred to as the “wall shear
stress” (Fig. 2). The magnitude of wall shear
Fig. 1.—Drawing shows paraboloid distribution of
blood velocity in a straight rigid vessel with constant
flow. Velocity increases gradually, starting with zero
at walls, to peak velocity when moving from vessel
wall to center of vessel. u (x,y) is velocity in x,y coordinate system. (Reprinted with permission from [9])
Radiology Service, Mail Rte. W114, MRI, Bldg. 507, VA Greater Los Angeles Healthcare Center, 11301 Wilshire Blvd., Los Angeles, CA 90073.
2
Present address: Department of Radiological Sciences, University of Utah Health Sciences Center, 50 N. Medical Dr., Salt Lake City, UT 84132.
3
Present address: Radiology Service, Mail Code 114, VA North Texas Healthcare System, 4500 S. Lancaster Rd., Dallas, TX 75216. Address correspondence to A. M. Duerinckx.
4
Present address: Department of Radiology, University of Texas Southwestern Medical Center, 5323 Harry Hines Blvd., Dallas, TX 75235-8896.
AJR 2000;174:1657–1665 0361–803X/00/1746–1657 © American Roentgen Ray Society
AJR:174, June 2000
1657
Shaaban and Duerinckx
Effect of Wall Shear Stress on the
Histology and Function of the
Endothelial Cells
Fig. 2.—Drawing shows forces acting on blood vessel
wall: pressure (P) acting normally to wall and wall
shear stress (W) acting tangentially to wall.
stress depends on how fast the fluid velocity increases when moving from the vessel wall toward the center of the vessel. This velocity
gradient near the wall is called the “wall shear
rate.” Wall shear stress is defined as:
δv
wall shear stress = µ ----- ,
δr
(1)
measured close to the vessel wall, where µ is
---- is the shear rate or the
fluid viscosity, µ δv
δr
velocity gradient at the wall (change in velocity unit per change in radial distance
unit), v is the velocity along the vessel axis,
and r is the distance perpendicular to and
away from the wall [9, 10].
The pattern of blood flow is much more
complex in vivo, where the flow is pulsatile
and any change in the shape or curvature of a
vessel alters the flow dynamics—for example, when a vessel curves, blood velocity is
greater along the outside wall of the curvature than along the inside wall [8]. Also,
when a vessel bifurcates, blood flow is slowest close to the outer wall and fastest near the
flow divider [3]. These complex changes in
blood velocity can create significant changes
in wall shear stress both along the length and
around the circumference of the blood vessel. The wall shear stress also varies with the
cardiac cycle because of the pulsatile
changes in the velocity and direction of
blood flow. This cardiac cycle variation is referred to as the oscillatory pattern of wall
shear stress.
1658
Evidence from in vitro and in vivo studies
suggests that both low wall shear stress and
high oscillatory patterns of wall shear stress
cause intimal wall thickening [4–7, 11].
Some studies also suggest that these local
hemodynamic factors act independently of
other known risk factors for atherosclerosis.
For example, in a prospective study by Gibson et al. [12] of 26 patients with 74 lesions,
low local shear stress was significantly correlated with an increased rate of atherosclerosis progression in human coronary arteries
independently of circulating lipoprotein values and systemic hemodynamics.
It has long been hypothesized that low wall
shear stress and the resultant stagnation of
blood permit increased uptake of atherogenic
blood particles as a result of increased residence time [13]. More recent research has provided us with a better understanding of the
mechanisms underlying this. It has been shown
that wall shear stress can change the morphology and orientation of the endothelial cell layer.
Endothelial cells subjected to elevated levels of
wall shear stress tend to elongate and align in
the direction of flow, whereas those experiencing low or oscillatory wall shear stress remain
more rounded and have no preferred alignment
pattern [14, 15]. Moreover, exposure of the arterial wall to a relatively low wall shear stress
may increase intercellular permeability and
consequently increase the vulnerability of these
regions of the vessel to atherosclerosis [16].
Levels of the vasoactive substances released by
endothelial cells (prostacyclin, nitric oxide, and
endothelin-1) are strongly influenced by shear
stress. An acute increase in wall shear stress in
vitro elicits rapid cytoskeletal remodeling and
activates a signaling cascade in endothelial
cells, with the consequent acute release of the
vasodilators nitric oxide and prostacyclin [17].
Nitric oxide in particular appears to be a key
mediator in the atheroprotective effect of high
wall shear stress [18]. High laminar shear stress
sharply reduces endothelial cell levels of precursor preproendothelin mRNA. This decreases the level of endothelin-1 peptide, which
exerts a constricting and mitogenic effect on
vascular smooth muscle cells [19]. Finally, prolonged oscillatory shear stress induces expression of endothelial leukocyte adhesion
molecules, which are important in mediating
leukocyte localization in the arterial wall [20].
The overall picture is that nonpulsatile high
shear stress promotes release of factors from
endothelial cells that inhibit coagulation, migration of leukocytes, and smooth muscle proliferation, while simultaneously promoting
endothelial cell survival. Conversely, low shear
stress and flow reversal shift the profile of secreted factors and expressed surface molecules
to one that favors the opposite effects, thereby
contributing to the development of atherosclerosis [16]. This complex endothelial cell response to shear stress may also provide a
mechanism by which known risk factors act to
promote atherosclerosis [18].
Clinical Applications
The relation between wall shear stress and
the development of atherosclerosis has been
studied using wall shear stress values derived
in vivo from phase-contrast MR imaging,
pulsed Doppler sonography, or quantitative
arteriography. The relationship between wall
shear stress and other known risk factors for
atherosclerosis has also been investigated.
Wall shear stress inversely relates to age, systolic blood pressure, and body mass index,
factors directly implicated in the pathogenesis of atherosclerosis [21].
The theory of low shear stress and cyclic
variations in shear stress is one that is gaining popularity. What is clinically relevant is
the location of atherosclerotic lesions. This
knowledge was available long before wall
shear stress was being measured. Whether
the knowledge of wall shear stress will have
any clinical relevance is subject to discussion
and is still hotly debated. However, wall
shear stress mapping may become one of
several screening tests for a multifactorial
approach to atherosclerosis prediction in the
future, and as such is receiving much attention from agencies that fund research in the
early detection of atherosclerosis.
We will review the available preclinical
applications of wall shear stress measurement in important vascular territories often
affected by atherosclerosis.
Abdominal Aorta
The distribution and severity of atherosclerosis in the abdominal aorta is not uniform: it preferentially involves the posterior wall of the
infrarenal abdominal aorta. Several investigators
have measured wall shear stress in the abdominal aorta to look for an explanation. Oshinski et
al. [22] calculated wall shear stress in the suprarenal and infrarenal abdominal aorta in eight
healthy volunteers as summarized in Table 1.
The mean and peak wall shear stress were higher
AJR:174, June 2000
Wall Shear Stress and Early Atherosclerosis
TABLE 1
Wall Shear Stress Values in Human Abdominal Aorta as Measured by
Oshinski et al. [22]
Suprarenal Aorta (dynes/cm2)
Infrarenal Aorta (dynes/cm2)
Wall Shear Stress
Minimal
Peak
Mean
Anterior Wall
Posterior Wall
Anterior Wall
Posterior Wall
–4.3 (4.5)
48.0 (6.0)
8.6 (3.2)
–2.3 (2.3)
54.0 (11.0)
10.4 (2.9)
–6.9 (4.0)
33.0 (2.6)
6.1 (2.6)
–7.5 (2.9)
30.0 (7.0)
4.7 (2.6)
Note.—Measurements are mean (SD). 1 dyne/cm 2 = 0.1 Pa = 0.1 N/m2.
in the suprarenal aorta than in the infrarenal
aorta, with the lowest wall shear stress measured
along the infrarenal posterior wall. Furthermore,
a correlation was seen between the oscillatory
component of wall shear stress and the development of atherosclerosis. Similar results were obtained by Oyre et al. [23] in six healthy
volunteers, as summarized in Table 2.
Moore et al. [24] studied blood flow patterns
in the abdominal aorta. They showed that in the
suprarenal aorta the velocity profiles were
mostly forward and axisymmetric, whereas in
the infrarenal aorta extensive flow reversal was
noted throughout diastole near the posterior wall
(Fig. 3). This persistent diastolic flow was not
seen in the suprarenal aorta. This localized dias-
TABLE 2
Wall Shear
Stress
Minimal
Peak
Mean
Wall Shear Stress Values in
Human Abdominal Aorta as
Measured by Oyre et al. [23]
Suprarenal
Aorta
(dynes/cm2)
Infrarenal Aorta
(dynes/cm2)
–7.1
40.7
6.3
–10.0
27.2
2.8
Note.—1 dyne/cm2 = 0.1 Pa = 0.1 N/m2.
tolic reversal of flow is the result of the curvature
of the aorta and the high percentage of flow
taken away by major anterior aortic branches
distal to the diaphragm [25]. Moore et al. postulated that the aortic curvature causes the velocity
profile to be skewed toward the outer wall of the
curvature, with the fluid near the inner wall moving at relatively low velocities. This velocity pat-
Fig. 3.—Graphs show velocity profiles measured in infrarenal aorta in vivo (top row ) and in vitro (middle row ) using MR imaging at five points (A, B, C, D, and E) during
cardiac cycle. Horizontal axes are in millimeters (anterior to posterior, right to left), and points in time when each image was taken are on volume flow rate waveforms
(bottom row ). Vertical axes are velocity (cm/sec) for the top and middle rows, and in vitro flow (ml/sec) for the bottom row. Note that most extensive flow reversal was
located along posterior wall. (Reprinted with permission from [24])
AJR:174, June 2000
1659
Shaaban and Duerinckx
tern is caused by centrifugal forces moving the
fluid around the curve. The branches along the
anterior wall of the aorta pull a significant
amount of fluid away from the posterior wall,
also creating a region of relatively low flow in
that location. At the aortic bifurcation, two peaks
of flow reversal were also noted near the lateral
posterior walls, and the lowest velocities were
located near the lateral wall. These flow patterns
help explain the influence of wall shear stress on
the progression of atherosclerosis in the abdominal aorta. The strongest flow reversal (the posterior wall of the infrarenal aorta and the lateral
posterior walls of the aortic bifurcation) corresponds to the locations with the most atherosclerotic lesions and intimal thickening [24].
In addition, Moore et al. [26] documented
that the near-wall diastolic flow reversal seen
in the infrarenal aorta and aortic bifurcation
during rest was nearly eliminated during simulated exercise. They assumed that the changes
in wall shear stress during exercise might account for some of the reduction in atherosclerosis progression seen clinically in association
with exercise. It is unknown how patient positioning (erect versus supine during an MR
study) might affect these flow patterns.
dominal aorta. Helical flow and extensive flow
reversal are consistent features of aortic flow in
healthy subjects that result, at least in part, from
the curvature of the arch and the strong pulsatility of flow [27–29]. Bogren et al. [28] studied 24
healthy subjects using MR velocity mapping.
Systolic velocity maps were similar in the proximal aorta and the mid ascending aorta, with
maximum early systolic flow along the left posterior wall. Toward the end of systole and
throughout diastole, a channel of reverse flow
developed in the same region in the mid ascending aorta, but in the proximal aorta it split to enter the sinuses of Valsalva, predominantly the left
and right coronary sinuses. Mean percentage ratio of retrograde-to-antegrade flow was 6.3%,
with most retrograde flow occurring in early diastole. Bogren et al. suggested that retrograde
aortic flow assists coronary flow. Even though
the flow reversal in the ascending aorta is expected to result in low wall shear stress, the ascending aorta is known to be less affected by
atherosclerosis than the abdominal aorta. The
reason for this contradictory observation is not
known but may point to the presence of other
factors besides low wall shear stress responsible
for the development of atherosclerosis.
Ascending Thoracic Aorta
Carotid Bifurcation
The pattern of flow in the ascending thoracic
aorta is more complex than in the descending ab-
Atherosclerosis in the carotid artery bifurcation has been extensively studied because of its
A
great clinical importance. An inverse relationship
exists between the in vivo measured wall shear
stress and the arterial wall thickness in the carotid arteries [21, 30]. Gnasso et al. [30] measured the peak and mean wall shear stresses in
the carotid arteries of 23 patients with evidence
of stenosis and found that wall shear stress is
lower in the arteries in which plaques are present
than in plaque-free arteries. Because of the vital
importance of blood flow in patients with stroke,
great efforts have also been made to develop
complex computer modeling of blood flow in
the carotid bulb. Milner et al. [31] used such an
approach to get a detailed map of variations in
wall shear stress in the carotid bulb. They reconstructed three-dimensional (3D) models of the
carotid bifurcation lumen from serial black
blood MR images of two healthy volunteers.
Common and internal carotid artery flow rate
waveforms were determined from MR imaging
phase-contrast velocity imaging in the same subjects and were used for the computational
model. Subject-specific velocities and wall shear
stresses were computed with a finite elementbased model, yielding maps of a variety of wall
shear stress indexes. Maps of the average wall
shear stress magnitude in the carotid bifurcation
of two healthy volunteers were included in this
study (Figs. 4A and 4B). Hoeks et al. [32] calculated the wall shear rate in the common carotid
arteries in volunteers presumed to be healthy, in
B
Fig. 4.—Drawings show time-averaged wall shear stress for carotid bifurcation geometry.
A and B, Drawings are derived from in vivo MR imaging data from 28-year-old volunteer (A) and 32-year-old volunteer (B). Anterior and posterior views are provided to
identify asymmetry of patterns. Notice contour levels. Scale of wall shear stress values is shown on bottom right side. Darker shades correspond to higher time-averaged
wall shear stress, indicative of lower probability for atherosclerotic change. Comparison of A and B illustrates individual variability in wall shear stress patterns and carotid
artery geometry. (Reprinted with permission from [31])
1660
AJR:174, June 2000
Wall Shear Stress and Early Atherosclerosis
two categories: young age group (20–30 years
old; n = 8) and old age group (60–70 years old;
n = 6). These researchers found that although the
peak shear rate decreases with age, the mean
shear rate averaged over the cardiac cycle is the
same for both age groups. They assumed that the
reduced relative change in diameter, associated
with a reduced elasticity of the arterial wall at
older age, does not result in a higher mean wall
shear rate because of the increase in diameter.
This assumption corroborates earlier observations about the possible interaction between
mean wall shear rate and the caliber of the artery.
Coronary Arteries
The coronary arteries are also commonly affected by atherosclerosis. The coronary arteries
are unique in the body because blood flow is intermittent and shows wide phasic variations as a
result of systolic contraction of the heart. Coronary systole and diastole are out of phase with
systemic systole and diastole. Approximately
50% of the total coronary blood flow occurs in
early diastole, 25% in late diastole, and only 25%
in systole [33]. The anatomic curvatures inherent
in the coronary circulation add to the complexity
of the flow pattern because major epicardial arteries curve gently around the border of the heart
[3]. Pathologic examination of coronary arteries
reveals that the atherosclerotic plaques are located mainly along the inner side of the curved
coronary arteries [3, 34–36]. The composite effects of these hydraulic factors seem to be significant in the predisposition of the coronary arteries
to atherosclerotic changes and in the selection of
the site of involvement [3]. Krams et al. [37]
evaluated wall shear stress and vessel 3D geometry as factors determining the development of
atherosclerosis in curved coronary artery segments in which atherosclerotic plaques are
mainly localized on the inner curvature. They
found that areas of maximum shear stress were
close to the outer wall and areas of minimum
shear stress were close to the inner curve.
Wall Shear Stress Measurement:
Techniques and Challenges
As discussed, multiple experimental studies
confirm the association between wall shear
stress and early atherosclerosis. Simplistic measurements of wall shear stress seem to be adequate to help predict areas at risk. However, the
precise role played by hemodynamics and wall
shear stress in the development and progression
of vascular disease remains unclear, in large part
because of lack of in vivo studies with humans.
The inability to conclusively identify the hemo-
AJR:174, June 2000
dynamic quantities that influence atherosclerosis may be attributed in part to the fact that flow
studies are typically carried out in idealized
models with averaged flow parameters, whereas
sites predisposed to atherosclerosis are identified from averaged postmortem measurements
[31]. The flow pattern in a blood vessel can be
complex and can vary with time, as seen in the
pulsatile flow pattern in the infrarenal abdominal aorta (Fig. 3). We will provide a review of
how to use the velocity profiles to estimate the
wall shear rate. We will then review some of the
methods used to obtain blood velocity data noninvasively in vivo and discuss the limitations of
the methods and how to overcome them. The
methods considered will be phase-contrast MR
imaging and Doppler sonography. Older approaches using quantitative arteriography will
not be discussed.
Estimation of Wall Shear Rate: The Need to
Interpolate from Discrete Velocity Measurements
The first step in estimating wall shear stress
requires velocity measurements derived from
duplex Doppler sonography, velocity-encoded
cine MR imaging, or quantitative angiography.
These velocity measurements are made at a discrete number of points and must be interpolated
or extrapolated to obtain the velocity profile
[38]. Velocity is a vector quantity, and the appropriate component of the vector must be used to
calculate wall shear stress. The vector is zero at
the vessel wall. The wall shear rate calculation
requires an estimate of the slope of a velocity
profile from at least two, preferably three, velocity values obtained near the vessel wall [22]. The
accuracy of wall shear stress is a function of the
spatial resolution of the velocity estimates [39]
and the interpolation algorithm used. A review
of several interpolation techniques for wall shear
stress calculation was made by Lou et al. [38].
They compared the techniques used to estimate
wall shear rate based on one, two, or three velocity measurements near the vessel wall.
The interpolation methods used can be classified according to the degree of polynomial
curve fitting of the velocity profiles [38]. The
simplest interpolation, called the linear method,
assumes a linear velocity distribution and measures the velocity component in a single point
away from the wall. If v is the component of velocity parallel to the wall measured at a distance
dr from the wall, then the wall shear rate can be
approximated with the following equation:
ν
wall shear rate = ----(2)
dr
The second method, called the quadratic
method, is based on a quadratic fit between two
velocity measurements, v1 and v2 , at distances
dr1 and dr2 from the wall [38]. In another
method, a third velocity is measured at a point
between the two points used in the quadratic
method. A least-squares fit method is adopted to
accommodate all three points, or four points if
the point at the wall is included, in a parabolic
velocity profile. The benefit of the extra point is
doubtful because it forces the velocity profiles
to comply more with the data in the region farther away from the wall than with the data
closer to the wall. A higher order polynomial,
however, is generally less robust. As the order of
the curve fitting increases, the result becomes
sensitive to small amplitude, more or less randomly distributed errors in the data [38].
Pulsed Doppler Sonography
Pulsed Doppler sonography is noninvasive
and is routinely used to determine the velocity
distribution in the human arterial system in vivo.
The Doppler technique measures the velocity
component along the direction of insonation. A
correction is then made to determine the velocity
component along the axis of the vessel. This approach is subject to error that will propagate to
the wall shear stress calculation. Pulsed Doppler
sonography measures average velocities in the
sensitive volume of the focused acoustic wave.
This averaging is referred to as the “sample volume sensitivity function.” Velocity profiles
determined from Doppler measurements are
generally not known with sufficient accuracy as
a result of numerous errors affecting both spatial
and velocity measurements: errors in the positioning of the sonographic probe and its sample
volume, alteration of the signal-to-noise ratio,
echoes of the distal wall, and inadequate spatial
resolution that interferes with the accuracy of velocity profile determination, particularly near the
wall in which the velocity gradient is often high
and has to be determined accurately [40]. We
will review several of the proposed solutions to
overcome these limitations.
The wall shear rate can be calculated using
one central velocity and vessel diameter measurements. This simple approach was used by
Gnasso et al. [21, 30] to calculate the peak and
mean wall shear rates using an assumed parabolic model of velocity distribution across the
arterial lumen. Some of these measurements
thus represent temporal and spatial averages.
Echo Doppler sonography examination to measure arterial diameter, intima–media thickness,
and blood flow velocity was performed using
ECG-triggered high-resolution sonography. The
researchers found that Doppler sonography
measurement of wall shear stresses in the com-
1661
Shaaban and Duerinckx
mon carotid arteries in vivo was reproducible
[21]. The major drawback of their approach is
the assumption of a linear velocity distribution
and the fact that only the central peak velocity is
used to measure the wall shear rate.
More complex signal processing can be used
to obtain more realistic velocity profiles, as done
by Brands et al. [10], who described a method to
estimate noninvasively the time-dependent wall
shear rate in vivo. They evaluated the velocity
distribution using off-line signal processing of
the sonographic signal. The off-line processing
was performed in the radiofrequency (RF) domain and consisted of an RF domain velocity estimator preceded by an adaptive vessel wall
filter. The latter was adopted to get an optimal
discrimination between the slowly moving structures, like vessel walls, and the slowly moving
blood near the vessel wall. This in vivo estimate
of the time-dependent wall shear rate was reproducible, but only in relatively straight blood vessels, because in curved vessels the peak velocity
shifts toward the outer wall of the vessel, thus
making the wall shear stress estimate more complex. Hoeks et al. [32] used a similar approach
for the measurement of wall shear stress in the
carotid arteries.
Several other methods have been proposed
to improve the accuracy of pulsed Doppler
sonographic measurements of velocity profiles. Spatial resolution can be improved by
applying a deconvolution process. Corrected
deconvoluted velocity profiles have allowed
noticeable improvement in the estimation of
wall shear rate when compared with the uncorrected Doppler profiles [40, 41].
Even more complex approaches using 3D reformatting, mainly from Doppler and sonographic measurements, have been tested.
Chandran et al. [42] performed computer simulation of 3D velocity profiles and wall shear stress
distribution in a morphologically realistic 3D reconstruction of an arterial segment. They used
intravascular sonography with a constant pullback technique in the abdominal aorta of dogs to
obtain the velocity profiles [42]. Similarly,
Krams et al. [37] combined 3D reconstruction
from angiography and intravascular sonography
with computational fluid dynamics and were
able to measure wall shear stress and wall thickness in the right coronary artery in vivo [37].
MR Imaging
MR velocity measurements typically provide less temporal resolution than pulsed
Doppler sonographic measurements, but MR
imaging can be used to examine almost any
vessel in the body without regard to overly-
1662
ing bone or bowel gas. Furthermore, the velocity data can be precisely matched with
anatomic pictures, providing an integrated
anatomic and functional examination [8].
Velocity-encoded phase-contrast MR imaging relies on the phase shift of spins moving
along the direction of a bipolar velocity-encoding gradient. Phase-contrast MR imaging
allows direct measurement of flow velocity,
and volume flow rate can be obtained [43].
MR imaging velocity measurement represents an average value of the velocity over the
entire pixel, including both moving and stationary structures. One important source of error
when using MR velocity measurements for the
calculation of wall shear stress is that the position of the vessel wall within the edge pixel (the
pixel that is partially covered with moving
blood and partially with stationary tissues) is
not known because of limited spatial resolution.
If the wall position in the edge pixel is not correctly estimated, an error of 34% in wall shear
stress measurement can be made [22]. Another
lesser source of error is the limited temporal resolution of the velocity measurements, which is
more a limitation of MR imaging than of sonography. Sonographic measurements are made
about every 1 msec, whereas MR imaging measurements are made every 30 msec or more [8].
Several methods have been proposed to overcome the problem of inadequate spatial resolu-
tion in the evaluation of wall shear stress by MR
imaging. Strang et al. [44] suggested ignoring
the edge pixel when determining the slope of
the velocity profile from a polynomial fit to the
velocity points. Frayne and Rutt [45] attempted
to overcome extrapolation-based techniques using Fourier velocity encoding to determine the
velocity distribution in a voxel that straddles the
blood–vessel wall interface. These researchers
found, by appropriate processing, that the velocity distribution could both determine the location of the interface in the voxel and estimate
the velocity profile across the spatial extent of
the voxel. From this information, estimates
of shear rate were obtained with a mean error
of 15% compared with 73% obtained by extrapolation of the velocity profile over multiple voxels. However, the total image acquisition times
were lengthy (approximately 2 hr), which probably excludes the in vivo application of the technique to humans [45].
Oshinski et al. [22] proposed an attractive
method for estimating the position of the
vessel wall in the edge pixel that then allows
the estimation of shear rate in the aorta in humans using MR phase velocity mapping
(Fig. 5). In their method, the flow volume
through a pixel is measured by multiplying
the MR imaging–measured velocity through
the pixel by the pixel surface area (d2 for a
square pixel), even if the entire pixel is not
Fig. 5.—Drawing shows simplified
representation of velocity interpolation method for estimating wall shear
stress proposed by Oshinski et al.
[22]. Vertical axis represents velocity.
Horizontal axis represents one axis in
cross-section of vessel. v1 and v2 are
average velocities measured by MR
imaging in edge pixel and first interior
pixel, respectively; vh is calculated
velocity at inner side of edge pixel; x
is estimate of position of vessel wall
within edge pixel.
AJR:174, June 2000
Wall Shear Stress and Early Atherosclerosis
occupied by flowing material. The volume
flow (Q ) through the edge pixel thus can be
measured as:
Q = ν1 d
2
(3)
where Q is the flow rate (ml/sec) through
the edge pixel, v1 is the average velocity (cm/
sec) in the edge pixel measured with MR
phase mapping, and d is the pixel dimension
(cm) for a square pixel. Next the velocity (vh)
at the inner side of the edge pixel is estimated. The assumption is made that the velocity profile near the vessel wall is linear,
and therefore vh is the average value of v1
and v2 (v2 is the velocity [cm/sec] measured
with MR imaging in the first interior pixel).
ν1 + ν2
(4)
ν h = ----------------2
Using the estimate of vh and the fact that the
velocity is zero at the wall, the expression for
the flow in the edge pixel can be rewritten as:
1
(5)
Q = --- ν h xd
2
Next the distance x between the vessel wall
and the inner side of the edge pixel is estimated (Fig. 5). By combining equation 3 with
equation 5, the location of the vessel wall in
the edge pixel can be determined as:
2 ν1 d
x = ----------νh
(6)
Using this estimate of the position of the
vessel wall in the edge pixel, the wall shear
rate can be determined with high accuracy.
An important assumption in the theory is that
the radius of the artery is large enough that a
straight line, instead of a curved line, can represent the edge of the vessel in the edge pixel,
and consequently this method is not applicable to medium- and small-sized vessels. The
principal advantage of the technique proposed by Oshinski et al. [22] is its speed. A
major drawback is that shear rate is calculated using linear interpolation and velocity
measurements from adjacent voxels and,
thus, the accuracy of the technique is still intrinsically coupled to the voxel size [45].
Moore et al. [26] calculated the wall shear
stress from MR velocity measurements of pulsatile flow in an anatomically accurate model of
the human abdominal aorta. Fluid velocities
were measured with a phase velocity-encoding
gradient-echo sequence. In another study by
Moore et al. [24], a variant of phase-contrast
MR angiography called “free induction decay
acquired echoes” (FAcE) sequence was used for
velocity quantification based on the phase of the
AJR:174, June 2000
MR imaging sequence. This variant is a sequence with separate sampling of the left and
right K-space half-planes that allows very short
TEs with inherent motion compensation of the
frequency-encoding gradient. Thus, both motion-related dislocation artifacts and signal
voids caused by coherence loss in regions with
irregular flow are minimal [46]. Oyre et al. [23]
used the same FAcE sequence for the measurement of wall shear stress in the abdominal aorta.
In both studies, measurement of wall shear
stress was based on simple edge detection.
In 1998, Oyre et al. [9] described a new
method for determination of wall shear stress
based on circumferential subpixel edge detection. These researchers applied a priori knowledge of the parabolic blood velocity
distribution in the thin boundary layer of the
vessel wall to velocity data from the whole circumference of the vessel. A standard ECG
gradient-echo pulse sequence with bipolar velocity-encoding gradients was used to obtain
the velocity data. By this technique, a 3D paraboloid model could be fitted to the large
number of velocity data obtained in the parabolic boundary layer. Position of the lumen
vessel wall, wall shear stress, and volume
blood flow were then determined at a subpixel
level from the 3D paraboloid model. To assess
the validity of their concept, in vitro lumen
area was measured in a glass tube using MR
velocimetry with a mean error of 0.6%. These
researchers then measured the wall shear stress
in the common carotid artery in seven healthy
volunteers, the first attempt of MR imaging
measurement of wall shear stress in a mediumsized artery.
The methods we have mentioned were
successfully applied for measurement of
wall shear stress in a two-dimensional configuration. A 3D approach for the measurement of wall shear stress in areas where the
blood flow is more complicated, as in the ascending aorta, was described in 1998 by Suzuki et al. [47]. They measured axial and
nonaxial wall shear rates using MR velocity
mapping and were able to successfully do
vector analysis of the wall shear rate.
TABLE 3
Most of the in vivo measurements of wall
shear stress show qualitative agreement. However, differences exist in absolute values for
the measured wall shear stress among different investigators. To illustrate this point, we
compared published wall shear stress measurements in the common carotid arteries (Table 3). The variation in measured wall shear
stress can be attributed to many factors. First,
different techniques were used to obtain the
blood velocity data. Second, the interpolation
algorithms used to estimate wall shear stress
differed. Gnasso et al. [21, 30] assumed a linear velocity distribution and estimated wall
shear stress in the common carotid arteries
from one central velocity measurement and a
vessel diameter measurement. However, both
Oyre et al. [9] and Hoeks et al. [32] found that
blood flow in the common carotid artery was
blunt (i.e., velocity profile was flat-topped) in
peak systole and does not assume the full paraboloid pattern presumed by Gnasso et al.
[21, 30]. When data of Oyre et al. [9] were analyzed in the same way as the studies by
Gnasso et al., the peak wall shear stress is underestimated by 50% and the mean wall shear
stress is underestimated by 22%. Third, the
sites of wall shear stress measurement were
inconsistent. Gnasso et al. measured wall
shear stress in the common carotid artery 1–2
cm proximal to the bulb, whereas Hoeks et al.
measured it 2–3 cm proximal to the tip of the
flow divider. Wide quantitative variation in the
measured wall shear stress along the same
vessel was reported by several investigators;
thus, the measured wall shear stress values
should be regarded as site-specific [22, 31].
Fourth, individual variations existed because
wide variation in the measured wall shear
stress among different individuals was reported [22, 31]. This fact may partly explain
why some individuals are more prone to atherosclerosis, because the etiology is multifactorial. Fifth, age-related changes exist in wall
compliance. Also, wall excursion changes
during the cardiac cycle, and the effects of
Summary of Wall Shear Stress Measurements in Common Carotid Arteries
by Four Investigators
Wall Shear Stress
Method used
Peak
Mean
Differences in the Measured Wall Shear
Stress
Gnasso et al. [21]
Gnasso et al. [30]
Hoeks et al. [32]
Oyre et al. [9]
Sonography
29.5 (8.2)
12.1 (3.1)
Sonography
18.7 (4.1)
15.3 (4.0)
Sonography
22.4 a
7.0 a
MR imaging
25.6
9.5
Note.—Measurements are mean (SD) and are expressed as dynes per square centimeter. 1 dyne/cm 2 = 0.1 Pa = 0.1 N/m2.
a Calculated from the wall shear rate values in young age group assuming blood viscosity of 3.5 mPa.
1663
Shaaban and Duerinckx
wall excursion changes on wall shear stress
variations have not been studied. For example,
the coronary wall diameter can change by
10% as a result of pulsatile flow.
Conclusion
The relation between wall shear stress and
the development and progression of atherosclerosis has been well established. The noninvasive in vivo measurement of wall shear
stress using MR imaging is feasible. Despite
the differences in the measured values of
wall shear stress, most available methods
show qualitative agreement, and some valuable clinical observations have been derived
from these in vivo measurements of wall
shear stress. Low and oscillating wall shear
stress seems to favor the development of atherosclerosis as determined by the inverse relation between wall shear stress and arterial
wall thickness. Wall shear stress also seems
to depend on age, blood pressure, and body
mass index. The value of wall shear stress is
subject-specific and vessel-specific. Wall
shear stress varies along the same vessel and
around the vessel circumference. More studies are needed to document variations in wall
shear stress in different vascular beds both at
rest and during exercise to better understand
the early atherosclerotic process. These studies may provide more insight about the effect
of known risk factors for atherosclerosis on
wall shear stress and how changes in these
risk factors affect wall shear stress.
Atherosclerosis has a complex multifactor
etiology. Wall shear stress mapping may someday become a factor in the screening of patients
predisposed to the development of atherosclerosis because of anatomic variations in the
blood vessel resulting in localized areas of low
or oscillatory wall shear stress. Many more
clinical studies in larger patient groups are
needed to validate this theory and to establish
reproducibility of the technique in vivo.
References
1. Singh GK, Mathews TJ, Clarke SC, Yannicos T,
Smith BL. Annual summary of births, marriages,
divorces, and deaths: United States, 1994. Mon
Vital Stat Rep 1995;43:1–37
2. Wissler RW. Pathobiological determination of
atherosclerosis in youth collaborating investigators: new insights into the pathogenesis of atherosclerosis as revealed by PDA. Atherosclerosis
1994;108[suppl]:S3–S20
3. Taxon M. Hemodynamic basis of atherosclerosis
with critique of the cholesterol-heart disease hypoth-
1664
esis. Wallingford, U.K.: Begell House, 1995:48–49
4. Caro CG, Fitz-Gerald JM, Schroter RC. Arterial
wall shear stress and distribution of early atheroma in man. Nature 1969;223:1159–1161
5. Friedman MH, Hutchins GM, Bargeron CB, Deters OJ, Mark FF. Correlation between intimal
thickness and fluid shear in human arteries. Atherosclerosis 1981;39:425–436
6. Ku DN, Giddens DP, Zarins CK, Glagov S. Pulsatile flow and atherosclerosis in the human carotid
bifurcation: positive correlation between plaque
location and low and oscillating shear stress. Arteriosclerosis 1985;5:293–302
7. Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai
VS, Mabon RF, Glagov S. Carotid bifurcation
atherosclerosis: quantitative correlation of plaque
localization with flow velocity profiles and wall
shear stress. Circ Res 1983;53:502–514
8. Anderson CM, Turski PA, Edelman RR. Flow
quantification. In: Anderson CM, Edelman RR,
Turski PA, eds. Clinical magnetic resonance angiography. New York: Raven, 1993:127–128
9. Oyre S, Ringgaard S, Kozerke S, et al. Accurate
noninvasive quantitation of blood flow, cross-sectional lumen vessel area and wall shear stress by
three-dimensional paraboloid modeling of magnetic resonance imaging velocity data. J Am Coll
Cardiol 1998;32:128–134
10. Brands PJ, Hoeks AP, Hofstra L, Reneman RS. A
noninvasive method to estimate wall shear rate
using ultrasound. Ultrasound Med Biol 1995;21:
171–185
11. Pedersen EM, Agerbaek M, Kristensen IB, Yoganathan AP. Wall shear stress and early atherosclerotic lesions in the abdominal aorta in young adults.
Eur J Vasc Endovasc Surg 1997;13:443–451
12. Gibson CM, Diaz L, Kandarpa K, et al. Relationship of vessel wall shear stress to atherosclerosis
progression in human coronary arteries. Arterioscler Thromb 1993;13:310–315
13. Glagov S, Zarins C, Giddens DP, Ku DN. Hemodynamics and atherosclerosis: insights and perspectives gained from studies of human arteries.
Arch Pathol Lab Med 1988;112:1018–1031
14. Levesque MJ, Nerem RM. The elongation and
orientation of cultured endothelial cells in response to shear stress. J Biomech Eng 1985;107:
341–347
15. Levesque MJ, Liepsch D, Moravec S, Nerem
RM. Correlation of endothelial cell shape and
wall shear stress in a stenosed dog aorta. Arteriosclerosis 1986;6:220–229
16. Okano M, Yoshida Y. Junction complexes of endothelial cells in atherosclerosis-prone and atherosclerosis-resistant regions on flow dividers of
brachiocephalic bifurcations in the rabbit aorta.
Biorheology 1994;31:155–161
17. Ballermann BJ, Dardik A, Eng E, Liu A. Shear
stress and the endothelium. Kidney Int Suppl
1998;67:S100–S108
18. Traub O, Berk BC. Laminar shear stress: mechanisms by which endothelial cells transduce an
atheroprotective force. Arterioscler Thromb Vasc
Biol 1998;18:677–685
19. Sharefkin JB, Diamond SL, Eskin SG, McIntire
LV, Dieffenbach CW. Fluid flow decreases preproendothelin mRNA and suppresses endothelin-1
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
peptide release in cultured human endothelial
cells. J Vasc Surg 1991;14:1–9
Chappell DC, Varner SE, Nerem RM, Medford
RM, Alexander RW. Oscillatory shear stress stimulates adhesion molecule expression in cultured
human endothelium. Circ Res 1998;82:532–539
Gnasso A, Carallo C, Irace C, et al. Association
between intima-media thickness and wall shear
stress in common carotid arteries in healthy male
subjects. Circulation 1996;94:3257–3262
Oshinski JN, Ku DN, Mukundan S Jr, Loth F, Pettigrew RI. Determination of wall shear stress in the
aorta with the use of MR phase velocity mapping. J
Magn Reson Imaging 1995;5:640–647
Oyre S, Pedersen EM, Ringgaard S, Boesiger P,
Paaske WP. In vivo wall shear stress measured by
magnetic resonance velocity mapping in the normal human abdominal aorta. Eur J Vasc Endovasc Surg 1997;13:263–271
Moore JE Jr, Maier SE, Ku DN, Boesiger P. Hemodynamics in the abdominal aorta: a comparison of in vitro and in vivo measurements. J Appl
Physiol 1994;76:1520–1527
Moore JE Jr, Ku DN. Pulsatile velocity measurements in a model of the human abdominal aorta
under resting conditions. J Biomech Eng 1994;
116:337–346
Moore JE Jr, Xu C, Glagov S, Zarins CK, Ku DN.
Fluid wall shear stress measurements in a model
of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 1994;110:225–240
Bogren HG, Mohiaddin RH, Kilner PJ, JimenezBorreguero LJ, Yang GZ, Firmin DN. Blood flow
patterns in the thoracic aorta studied with threedirectional MR velocity mapping: the effects of
age and coronary artery disease. J Magn Reson
Imaging 1997;7:784–793
Bogren HG, Klipstein RH, Firmin DN, et al. Quantitation of antegrade and retrograde blood flow in
the human aorta by magnetic resonance velocity
mapping. Am Heart J 1989;117:1214–1222
Kilner PJ, Yang GZ, Mohiaddin RH, Firmin DN,
Longmore DB. Helical and retrograde secondary
flow patterns in the aortic arch studied by threedirectional magnetic resonance velocity mapping.
Circulation 1993;88:2235–2247
Gnasso A, Irace C, Carallo C, et al. In vivo association between low wall shear stress and plaque
in subjects with asymmetrical carotid atherosclerosis. Stroke 1997;28:993–998
Milner JS, Moore JA, Rutt BK, Steinman DA.
Hemodynamics of human carotid artery bifurcations: computational studies with models reconstructed from magnetic resonance imaging of
normal subjects. J Vasc Surg 1998;27:143–156
Hoeks APG, Samijo SK, Brands PJ, Reneman
RS. Noninvasive determination of shear-rate distribution across the arterial lumen. Hypertension
1995;26:26–33
Neuhaus KL, Sauer G, Krause H, Tebbe U. Video
densitometric measurement of coronary flow. In:
Just H, Heintzen PH, eds. Angiocardiography:
current status and future developments. New
York: Springer Verlag, 1986:383–385
Sabbah HN, Khaja F, Brymer JF, Hawkins ET,
Stein PD. Blood velocity in the right coronary ar-
AJR:174, June 2000
Wall Shear Stress and Early Atherosclerosis
35.
36.
37.
38.
tery: relation to distribution of atherosclerotic lesions. Am J Cardiol 1984;53:1008–1012
Fox B, James K, Morgan B, Seed A. Distribution
of fatty and fibrous plaques in young human coronary arteries. Atherosclerosis 1982;41:337–347
Grottum P, Svinland A, Walloe L. Localization of
atherosclerotic lesions in the bifurcation of the main
left coronary artery. Atherosclerosis 1983;47:55–62
Krams R, Wentzel JJ, Oomen JAF, et al. Evaluation of endothelial shear stress and 3D geometry
as factors determining the development of atherosclerosis and remodeling in human coronary arteries in vivo: combining 3D reconstruction from
angiography and IVUS (ANGUS) with computational fluid dynamics. Arterioscler Thromb Vasc
Biol 1997;17:2061–2065
Lou Z, Yang W-J, Stein PD. Errors in the estimation of arterial wall shear rates that result from
AJR:174, June 2000
39.
40.
41.
42.
curve fitting of velocity profiles. J Biomech 1993;
26:383–390
Guo Z, Moreau M, Rickey DW, Picot PA, Fenster
A. Quantitative investigation of in vitro flow using three-dimensional colour Doppler ultrasound.
Ultrasound Med Biol 1995;21:807–816
Flaud P, Bensalah A, Peronneau P. Deconvolution
process in measurement of arterial velocity profiles via an ultrasound pulsed Doppler velocimeter for evaluation of the wall shear rate.
Ultrasound Med Biol 1997;23:425–436
Hughes PE, How TV. Quantitative measurement
of wall shear rate by pulsed Doppler ultrasound.
J Med Eng Technol 1993;17:58–64
Chandran KB, Vonesh MJ, Roy A, et al. Computation of vascular flow dynamics from intravascular ultrasound images. Med Eng Phys 1996;18:
295–304
43. Dumoulin CL, Souza SP, Walker MF, Wagle W.
Three dimensional phase contrast angiography.
Magn Reson Med 1989;9:139–149
44. Strang JG, Herfkens RJ, Pelc NJ. Voxel size effects
on vascular shear measurement (abstr). In: Proceedings of the second meeting of the Society of Magnetic
Resonance, vol. 2. Berkeley, CA: International Society of Magnetic Resonance in Medicine, 1994:1002
45. Frayne R, Rutt BK. Measurement of fluid shear
rate by Fourier encoded velocity imaging. Magn
Reson Med 1995;34:378–387
46. Maier SE, Scheidegger MB, Liu K, Boesiger P.
Accurate velocity mapping with FAcE. Magn Reson Imaging 1996;14:163–171
47. Suzuki J, Shimamoto R, Nishikawa J, et al. Vector analysis of the hemodynamics of atherogenesis in the human thoracic aorta using MR velocity
mapping. AJR 1998;171:1285–1290
1665
Shaaban and Duerinckx
1666
AJR:174, June 2000