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1
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.
4
Present address: Department of Radiology, University of Texas Southwestern
Medical Center, 5323 Harry Hines Blvd., Dallas, TX 75235-8896.
Address correspondence to A. M. Duerinckx
Introduction
 Top Introduction Wall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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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.
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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 | (1) |
is the
shear rate or the velocity gradient at the wall (change in velocity unit per
change in radial distance unit), 
is the velocity along the vessel axis,
and r is the distance perpendicular to and away from the wall
[9,
10].
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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.
Effect of Wall Shear Stress on the Histology and Function of the
Endothelial Cells
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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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].
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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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 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.
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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 diastolic 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 pattern 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].
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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.
Ascending Thoracic Aorta
The pattern of flow in the ascending thoracic aorta is more complex than in
the descending abdominal 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
[27,28,29].
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.
Carotid Bifurcation
Atherosclerosis in the carotid artery bifurcation has been extensively
studied because of its 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 element-based 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
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.
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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,
34,35,36].
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
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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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 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:
 | (2) |
The second method, called the quadratic method, is based on a quadratic fit
between two velocity measurements, 1 and
2, 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 common 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 pull-back 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 overlying 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 resolution 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 occupied by flowing
material. The volume flow (Q) through the edge pixel thus can be
measured as:
 | (3) |
1 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 (h) 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 h is the average value of
1 and 2 (2 is the velocity
[cm/sec] measured with MR imaging in the first interior pixel).
 | (4) |
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Using the estimate of h and the fact that the velocity is
zero at the wall, the expression for the flow in the edge pixel can be
rewritten as:
 | (5) |
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:
 | (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 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 medium-sized 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.
Differences in the Measured Wall Shear Stress
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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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.
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TopIntroductionWall Shear StressEffect of Wall Shear...Clinical ApplicationsWall Shear Stress Measurement:...Differences in the Measured...ConclusionReferences |
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