AJR 2002; 178:995-999
© American Roentgen Ray Society
Vector Analysis of the Wall Shear Rate at the Human Aortoiliac Bifurcation Using Cine MR Velocity Mapping
Taeko Tsuji1,
Jun-ichi Suzuki2,3,
Ryoichi Shimamoto1,
Tadashi Yamazaki1,
Toshiaki Nakajima1,
Ryozo Nagai1,
Shuhei Komatsu4,
Kuni Ohtomo4,
Teruhiko Toyo-oka2 and
Masao Omata5
1
Department of Cardiovascular Medicine, Faculty of Medicine, University of
Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 1138655, Japan.
2
Health Service Center, Faculty of Medicine, University of Tokyo, 1138655,
Japan.
3
Department of Internal Medicine, Laboratory-213, Faculty of Medicine,
University of Tokyo, 1138655, Japan.
4
Department of Radiology, Faculty of Medicine, University of Tokyo, 1138655,
Japan.
5
Department of Gastroenterology, Faculty of Medicine, University of Tokyo,
1138655, Japan.
Received July 12, 2001;
accepted after revision October 1, 2001.
Address correspondence to J.-i. Suzuki.
Abstract
OBJECTIVE. Small or oscillatory wall shear stress accelerates
atherosclerosis. MR velocity mapping is feasible for vector analysis of wall
shear rate (a spatial gradient of blood flow velocity at the vessel wall) in
humans. A relationship between anatomic variations at the aortoiliac
bifurcation and characteristics of wall shear rate was evaluated.
SUBJECTS AND METHODS. To obtain two components of wall shear rate
vectors, an axial component along the vessel axis and a nonaxial component
perpendicular to the former at the inner and outer walls of the common iliac
arteries just distal to the aortoiliac bifurcation, we performed cine MR
velocity mapping with three orthogonal velocity-encoded directions in seven
volunteers.
RESULTS. The peak axial component at the outer wall (120.6 ±
37.2 sec-1) was smaller than that at the inner wall (196.0 ±
53.7 sec-1) (p < 0.01). Oscillation described by a time
integral of the axial component in recessive blood flow direction over
integrals in dominant and recessive directions at the outer wall was greater
(0.24 ± 0.11) than that at the inner wall (0.15 ± 0.08)
(p < 0.01). The intersecting angle between the extrapolation of
the aortic axis and the direction of the axis of the common iliac artery
correlated positively with the peak axial component (r = 0.577,
p < 0.05) and inversely with oscillation (r = 0.603,
p < 0.05).
CONCLUSION. Three-dimensional vector analysis with MR velocity
mapping revealed that the outer wall at the aortoiliac bifurcation showed low
and oscillatory shear rate, and this inclination was increased when the
takeoff angle of the iliac artery was small.
Introduction
Wall shear stress hemodynamically regulates the atherosclerotic process
[1,2,3,4].
Low wall shear stress increases the atherogenic endothelin-1 peptide level,
and oscillatory prolongation induces expression of endothelial adhesion
molecules for monocytic emigration. High wall shear stress releases
atheroprotective nitric oxide and vasodilatory prostacyclin from the
endothelial cells
[5,6,7,8].
Wall shear stress is the product of the blood viscosity coefficient and wall
shear rate, a near-wall spatial gradient of velocity of blood flow paralleling
the vessel wall. Precise analysis of wall shear rate at the vessel wall
exposed to a complicated blood flow, such as at bifurcation, requires a
three-dimensional description of the velocity vector of blood flow
[9,
10]. MR velocity mapping can
noninvasively describe any velocity vector by obtaining three scans with three
orthogonal velocity-encoded directions in the common imaging plane. This
technique also can analyze wall shear rate induced by near-wall blood flow;
therefore, the current study was undertaken using MR velocity mapping to
elucidate focal characteristics at the aortoiliac bifurcation and to reveal
the correlation of characteristics of wall shear rate with individual
variations in the anatomic structure.
Subjects and Methods
Subjects and MR Imaging Technique
The study population consisted of seven healthy volunteers (seven men; mean
age, 28.4 ± 10.0 years) who all gave informed consent. They were
asymptomatic and normotensive. They had neither history of cardiovascular
disease nor abnormal ECG findings.
To obtain a magnitude cine loop and velocity-encoded cine frames, we used
an MR imager (Magnetom Vision; Siemens, Erlangen, Germany) with a 1.5-T
superconducting magnet. The imaging sequence was a fast low-angle shot (TR/TE,
6/80; flip angle, 30°). Three orthogonal velocity-encoded directions,
including a perpendicular direction to the imaging plane (through-plane
mapping) and two directions perpendicular to each other in the imaging plane
(right-to-left in-plane mapping and head-to-caudal in-plane mapping), were
chosen to obtain digital information of blood flow velocity in each direction
for each pixel in a single imaging plane. A field of view of 280-350 x
320-350 mm with an acquisition matrix of 224-256 x 256 was used,
yielding a pixel size of 1.3-1.4 x 1.3-1.4 mm. The velocity-encoded
value was chosen so that a phase shift of 180° corresponded to a velocity
of 75 cm/sec for through-plane mapping and right-to-left in-plane mapping and
150 cm/sec for head-to-caudal in-plane mapping so that no aliasing might
appear. The imaging plane was set to include the aortoailiac bifurcation,
which is the axis of the lower abdominal aorta and the course of right and
left common iliac arteries. Angle A (<90°) was defined as an
intersecting angle between the extrapolated axis of the abdominal aorta and
the course of the common iliac artery (Fig.
1A,1B).
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Fig. 1A. —Diagrams of vector analysis of blood flow velocity. Angle A
is intersecting angle between axis of abdominal aorta and course of common
iliac artery and is less than 90° for both right and left iliac arteries.
Diagram shows how to calculate blood flow velocity parallel to vessel wall
(axial component of vector of blood flow velocity) (cosA x
Vhead-caudal - sinA x Vright-left), which
constitutes axial component of wall shear rate for right common iliac
artery.
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Fig. 1B. —Diagrams of vector analysis of blood flow velocity. Angle A
is intersecting angle between axis of abdominal aorta and course of common
iliac artery and is less than 90° for both right and left iliac arteries.
Diagram shows how to calculate axial component of vector of blood flow
velocity (cosA x Vhead-caudal + sinA x
Vright-left) for left common iliac artery.
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Wall Shear Rate Measurement
Wall shear rate was measured at the inner and outer wall just distal to the
bifurcation (Fig.
1A,1B).
By setting a common cursor on the three velocity mappings at a single anatomic
location to intersect perpendicularly to the vessel wall of interest, three
kinds of velocity profile curves are automatically delineated on the display
by a software (Profile; Siemens) installed in the imager (Fig.
2A,2B,2C).
The horizontal axis, representing distance from the vessel wall, is common to
the three velocity profile curves. The vertical axis indicates blood flow
velocity in the right-to-left direction on the right-to-left in-plane mapping
(Fig. 2A), velocity in the
head-to-caudal direction on the head-to-caudal in-plane mapping
(Fig. 2B), and velocity
perpendicular to the imaging plane on through-plane mapping
(Fig. 2C). The cursor on each
velocity mapping has an indicator for identifying the anatomic location with a
vertical line on the velocity profile curve. When the indicator is set at the
edge of the vessel wall on each velocity mapping, the vertical line indicates
the edge of the vessel wall on the velocity profile curve (Fig.
2A,2B,2C).
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Fig. 2A. —Velocity profile curve (velocity distance relationship
superimposed on MR velocity mapping). Right—left in-plane (A),
head—caudal in-plane (B), and through-plane (C) MR
velocity mapping is obtained cinematically with temporal resolution of 80
msec, in common imaging plane including aortoiliac bifurcation. Superimposed
graph represents velocity profile for each encoded direction across common
iliac artery just distal to bifurcation. Vertical line (two
arrowheads) indicates anatomic position of edge of vessel wall and
corresponds to site of indicator (one arrowhead) on MR velocity
mapping. Horizontal and vertical axes of graph represent distance across
common iliac artery from edge of vessel wall and blood flow velocity in each
direction.
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Fig. 2B. —Velocity profile curve (velocity distance relationship
superimposed on MR velocity mapping). Right—left in-plane (A),
head—caudal in-plane (B), and through-plane (C) MR
velocity mapping is obtained cinematically with temporal resolution of 80
msec, in common imaging plane including aortoiliac bifurcation. Superimposed
graph represents velocity profile for each encoded direction across common
iliac artery just distal to bifurcation. Vertical line (two
arrowheads) indicates anatomic position of edge of vessel wall and
corresponds to site of indicator (one arrowhead) on MR velocity
mapping. Horizontal and vertical axes of graph represent distance across
common iliac artery from edge of vessel wall and blood flow velocity in each
direction.
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Fig. 2C. —Velocity profile curve (velocity distance relationship
superimposed on MR velocity mapping). Right—left in-plane (A),
head—caudal in-plane (B), and through-plane (C) MR
velocity mapping is obtained cinematically with temporal resolution of 80
msec, incommon imaging plane including aortoiliac bifurcation. Superimposed
graph represents velocity profile for each encoded direction across common
iliac artery just distal to bifurcation. Vertical line (two
arrowheads) indicates anatomic position of edge of vessel wall and
corresponds to site of indicator (one arrowhead) on MR velocity
mapping. Horizontal and vertical axes of graph represent distance across
common iliac artery from edge of vessel wall and blood flow velocity in each
direction.
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Wall shear rate vector at the vessel wall of interest consists of two
components of the velocity vector including a vector component along the axis
of the vessel lumen (an axial component) and a vector component perpendicular
to the axis and tangential to the vessel wall (a nonaxial component)
(Fig. 3). The spatial gradient
of velocity in three velocity-encoded directions at the common vessel wall of
interest is calculated from measuring the difference between the velocity
(intensity) at the first interior pixel and that at the second interior pixel
on each graph of the three kinds of blood flow velocity profile curves (Fig.
2A,2B,2C).
Of the three spatial gradients of blood flow velocity in the three directions,
the head-to-caudal velocity gradient and the right-to-left velocity gradent
constitute the axial component, and the through-plane velocity gradient
contributes to the nonaxial component of the wall shear rate. Accordingly, the
wall shear rate can be calculated as follows:
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Fig. 3. —Diagram of three-dimensional analysis of blood flow velocity
vector at vessel wall. Diagram shows how to decompose vector of blood flow
velocity into three orthogonal directions including axial direction
paralleling vessel axis, nonaxial direction perpendicular to axis and parallel
to vessel wall, and normal direction perpendicular to vessel wall. Of three
components, former two induce wall shear rate. Normal component does not
contribute to wall shear stress, but to normal stress.
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(wall shear rate)axial = 1/D x {(cosA x
V2head-caudal - sinA x
V2right-left) - (cosA x V1head-caudal - sinA x
V1right-left)}
= 1/D x {cosA x (V2 - V1)head-caudal
- sinA x (V2 - V1)right-left}
= 4,096/D x {150 x cosA x (I2 - I1)head-caudal
- 75 x sinA x (I2 - I1)right-left},
for the right common iliac artery, and
(wall shear rate)axial = 1/D x {(cosA x V2head-caudal + sinA x V2right-left) - (cosA x V1head-caudal + sinA x V1right-left)}
= 1/D x {cosA x (V2 -V1)head-caudal + sinA
x (V2-V1)right-left}
= 4,096/D x {150 x cosA x (I2 - I1)head-caudal
+ 75 x sinA x (I2 - I1)right-left}
for the left common iliac artery.
The wall shear ratenonaxial is calculated as follows:
(wall shear rate)nonaxial
= (V2 - V1)perpendicular/D
= 75/4,096/D x (I2 - I1)perpendicular,
where A is again the intersecting angle between the axis of the abdominal
aorta and that of the course of the common iliac artery, V1 is the velocity at
the first intraluminal pixel on the velocity profile chart, V2 is the velocity
at the second interior pixel on the chart, and D is the pixel size. I1 is the
intensity correlating with phase shift at the first interior pixel, and I2 is
that at the second interior pixel. The relative intensity corresponding to the
phase shift of 180° is 4,096.
It was difficult to calculate wall shear rate from flow velocity near zero
(flow velocity < 3 cm/sec in each direction), and therefore, the wall shear
rate caused by flow velocity of less than 3 cm/sec was considered to be zero
in mid-to-late diastole in our study.
Reproducibility of Wall Shear Rate Measurements
To evaluate measurement reproducibility of wall shear rate, we performed
the second measurements at the inner and outer walls of the right common iliac
artery at four cardiac phases in five randomly selected subjects.
Wall Shear Rate Analysis and Statistics
The peak wall shear rate was defined as the maximal absolute value of the
wall shear rate obtained at each time point in systole and early diastole. The
peak wall shear rate was calculated for the axial component and for the
nonaxial component.
For a description of the degree of the oscillation of the wall shear rate,
an oscillatory shear index was introduced:
where IAdominantI is an absolute value of the area with dominant
flow direction under the time—wall shear rate curve and
IArecessiveI is that of the area with recessive flow direction
under the curve (Fig. 4). In
our study, the terms of antegrade and retrograde were not used because the
antegrade flow was not always the dominant flow.
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Fig. 4. —Schematic graph represents time (cardiac phase)—wall
shear rate curve. Oscillatory shear index is defined as follows: (oscillatory
shear index) = IArecessiveI/(IAdominantI +
IArecessiveI), where IAdominantI is absolute value of
area with dominant flow direction under curve, and IArecessiveI is
that of area with recessive flow direction.
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There is a possible relationship between individual variations of the
anatomy of the aortoabdominal bifurcation and the degree of risk or
susceptibility to atherosclerosis. As a parameter of individuality, the
intersecting angle between the extrapolated axis of the abdominal aorta and
the axis of the running course of the common iliac artery was measured (angle
A mentioned previously) (Fig.
1A,1B),
and correlation of the angle A with the peak shear rate or oscillation was
evaluated.
The difference between two groups was analyzed by using Student's paired
t test. A statistical significance was indicated by a p
value of less than 0.05. All values were expressed as mean value ± 1
standard deviation (SD).
Reproducibility of measurements was tested by the absolute difference over
the mean of the paired measurements.
Results
Reproducibility of Measurements
The measurement reproducibility of wall shear rate was 10.4% ± 10.1%
for the inner wall and 10.1% ± 8.9% for the outer wall. The
reproducibility was 10.3% ± 9.5%.
Inner Wall Versus Outer Wall
The peak axial components and the peak nonaxial components of the wall
shear rate (sec-1) vector are 196.0±53.7 (significant
difference [p = 0.01] vs outer wall) at the inner wall and 120.6
± 37.2 at the outer wall and 27.8 ± 9.6 at the inner wall and
26.4 ± 16.2 at the outer wall, respectively (values are mean ±
SD). The peak axial component of the shear rate vector at the inner wall was
greater than that at the outer wall (p <0.01).
The oscillatory shear indexes of the axial and nonaxial components were
0.15 ± 0.08 (significant difference [p = 0.01] vs outer wall)
at the inner wall and 0.24±0.11 at the outer wall and 0.55±0.31
at the inner wall and 0.52±0.40 at the outer wall, respectively (values
are mean ± SD). The oscillation of the axial component at the inner
wall was smaller than that at the outer wall (p <0.01).
Anatomic Individuality and Wall Shear Rate Characteristics
The takeoff angle of the right iliac artery, the intersecting angle between
the aortic axis and the course of the right iliac artery (26.7° ±
9.5°), was greater than that of the left iliac artery (15.6° ±
8.1°). Figure
5A,5B
shows the correlation of the takeoff angle with the peak shear rate and that
with the oscillatory index at the outer wall at the common iliac artery. At
the outer wall, the takeoff angle significantly correlated with peak shear
rate (r = 0.577, p < 0.05) and correlated inversely with
the oscillatory index (r = 0.603, p < 0.05). At the inner
wall, however, there was no correlation.
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Fig. 5A. —Scattergrams of correlation between indexes of wall shear
rate and aortoiliac angle. Scattergram represents correlation of peak wall
shear rate with intersecting angle between abdominal aorta and common iliac
artery. One point of 13 points represents two data. Positive correlation is
shown (r = 0.577, p < 0.05).
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Fig. 5B. —Scattergrams of correlation between indexes of wall shear
rate and aortoiliac angle. Scattergram shows correlation between oscillation
of wall shear rate and takeoff angle. There is inverse correlation between
them (r = 0.603, p < 0.05).
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Discussion
Vector Analysis of Wall Shear Rate with MR Velocity Mapping
It has been difficult to evaluate the spatial gradient of velocity of
near-wall blood flow, which is the wall shear rate. The spatial resolution of
MR velocity mapping permits measuring near-wall blood flow velocity
[9]. Accordingly, many
researchers have consistently shown applicability of MR velocity mapping to
the evaluation of wall shear rate
[9,
11,12,13].
In our previous study, we showed that MR velocity mapping was feasible for
three-dimensional vector analysis of wall shear rate—induced complicated
blood flow in the thoracic aorta
[10]. Any blood flow can be
described using three orthogonal components of blood flow vector. The
information required for vector analysis can be acquired by obtaining three
kinds of scans with three orthogonal velocity-encoded directions. A set of the
right—left in-plane mapping, the head—caudal in-plane mapping, and
the through-plane mapping can describe any blood flow vector. At the vessel
wall of interest, the velocity vector described with the three vector
components of the blood flow was redecomposed into an axial component, a
nonaxial component, and a vector component perpendicular to the vessel wall (a
normal component (Fig. 3). Of
these three orthogonal components, the normal component does not contribute to
wall shear rate. Accordingly, the wall shear rate at the vessel wall can be
completely described with the axial and the nonaxial components.
Interpretation of the Current Observations
Lower or oscillatory wall shear stress is atherogenic
[14,15,16,17].
Accordingly, the current observation indicates that the outer wall is more
susceptible to atherosclerosis than the inner wall. Moreover, the correlation
between anatomic individuality and wall shear rate was evaluated in our study.
The intersecting angle between the extrapolation of the aortic axis and the
common iliac arterial axis may vary from subject to subject. The aortoiliac
angle was analyzed as a parameter representing individual variations. The
takeoff angle showed a positive correlation with wall shear rate and an
inverse relationship with oscillation at the outer wall. The observed
relationship suggests that the smaller the angle, the higher the risk to the
outer wall. Moreover, the smaller takeoff angle for the left iliac artery
indicates that atherosclerotic changes are more common at the left aortoiliac
bifurcation, and this speculation is supported by some surgical findings
[18,19,20].
In conclusion, characteristics of wall shear rate were three-dimensionally
analyzed with MR velocity mapping at the aortoiliac bifurcation. The outer
wall at the bifurcation showed a lower wall shear rate with greater
oscillations when compared with the inner wall. The outer wall may be at
increased risk for atherogenesis on the basis of this low shear rate.
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M. MATSUMOTO and S. HASHIMOTO
Edge Field Analysis
IEICE Trans D: Information,
January 1, 2007;
E90-D(1):
145 - 155.
[Abstract]
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Abstract
Introduction
