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A One-Dimensional Velocity Technique for NMR
Measurement of Aortic Distensibility
Christopher J. Hardy, Bradley D. Bolster, Elliot R. McVeigh, William J. Adams,
Elias A. Zerhouni
A technique is presented for rapidly and noninvasively determining aortic distensibility, by NMR measurement of wave
velocity in the aorta. A two-dimensional NMR selective-excitation pulse is used to repeatedly excite a cylinder of magnetization in the aorta, with magnetization read out along the
cylinder axis each time. A toggled bipolar flow-encoding pulse
is applied prior to readout, to produce a one-dimensional
phase-contrast flow image. Cardiac gating and data interleaving are employed to improve the effective time resolution to 2
ms. Wave velocities are determined from the slope of the leading edge of flow measured on the resulting M-mode velocity
image. The technique is sensitive over a range of distensibilities from 10“ to lo4 m s*/kg. The average value in the descending thoracic aorta in seven normal subjects was found
m s2/kg,with a significant inverse correlation
to be 4.8 x
with age.
Key words: aortic distensibility; wave speed; compliance;
blood velocity.
changes are instantaneously transmitted down the vessel, but for a vessel with compliant walls, the pressure
wave distends the vessel, and travels along it at a finite
velocity which can be determined from the flow image.
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THEORY
The distensibility, D, defined as the fractional change in
vessel cross-sectional arealunit change in pressure, may
alternatively be determined from the relation
D
=
l/pCz,
where p is the blood density and C is the wave speed in
the vessel (7, 8). (The related parameter, compliance, is
the change in volumelunit change in pressure.) The
blood density is 1.057 I+_ 0.007 g cm-3in normal subjects
(9) and, even among patients, will vary much less than
the experimental error of the wave-velocity measurements, and thus is taken to be constant. Proper determination of the wave velocity requires lack of interference
from reflected waves, and also that the wave velocity be
much larger than the blood velocity vb (8). If the foot of
the flow wave is followed, directly at the onset of systolic
flow, both of these requirements are generally met.
The wave velocity is measured using a variant of an
NMR flow-sensitive M-mode sequence. In the basic sequence (lo), shown in Fig. 1, a cylinder or “pencil” of
magnetization typically 1.5 cm in diameter is excited
along the ascending or descending aorta, using a spiralscan cylindrical excitation pulse (11). This employs a
constant-gradient-slew-rate traversal of the spiral to
maximize bandwidth (12) and a correction factor for the
RF waveform to compensate for uneven coverage of k
space by the spiral near the origin (13). Following the
pencil excitation a toggled bipolar velocity-encoding gradient is applied in the direction of blood flow and then a
half-echo readout gradient is played out along the pencil
axis. Alternate acquisitions are subtracted, yielding a
time-dependent phase-contrast flow profile with a time
resolution on the order of 50 ms (10). Alternatively, the
phase may be calculated first and subtracted to produce
a phase-difference image, in which directional information is retained, but the signal from static tissue is no
longer suppressed. For oblique pencil orientations the
logical gradient axes GX, GY, and GZ in Fig. 1 are combined via rotation matrices to produce the physical gradient waveforms.
This basic pulse sequence lacks the time resolution
needed to follow propagating wavefronts to determine C.
To achieve this, the sequence is gated to the cardiac
cycle, with an incremented trigger delay, and the resulting data are interleaved into the proper time order. In this
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INTRODUCTION
Sudden aortic dissection or rupture in patients with aneurysmal dilatation secondary to atherosclerosis or connective tissue disease is common. Monitoring of aortic
diameter is currently used as a guideline for surgical
intervention because no practical noninvasive method
exists to measure aneurysmal distensibility. A rapid and
noninvasive technique for determining aortic distensibility could play an important clinical role in this context.
Aortic compliance, a closely related measure of stiffness,
has also been shown to influence left ventricular afterload, and is an important variable in the management of
ventricular disease (1-3). Aortic stiffness appears as well
to be a correlate (although nonspecific) of coronary artery
disease and fitness (4-6).
We present here a noninvasive technique for determining aortic distensibility by means of wave-velocity measurements. An NMR phase-contrast pulse sequence employing cylindrical NMR selective excitation pulses is
used to produce M-mode velocity images, in which
propagating flow wavefronts in the aorta may be viewed.
For an incompressible fluid in a stiff vessel, pressure
MRM 31:513-520 (1994)
From the GE Corporate Research and Development Center, Schenectady,
New York; and Johns Hopkins University School of Medicine, Baltimore,
Maryland (B.D.B., E.R.M., E.A.Z.).
Address correspondence to: Christopher J. Hardy, Ph.D., GE Corporate Research and Development, P.O. Box 8, Schenectady, NY 12301.
Received October 8, 1993; revised December 21, 1993; accepted January
13, 1994.
Presented in part at the 12th annual meeting of the SMRM.
0740-3194/94 $3.00
Copyright 0 1994 by Williams & Wilkins
All rights of reproduction in any form reserved.
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Hardy et al.
RF
Here the bipolar gradient is stepped through a range of
amplitudes and a Fourier transform is applied to generate
velocity distributions at various phases of the heart cycle.
GY
MATERIALS AND METHODS
GZ
GX
flow
SIG
FIG. 1. Basic one-dimensionalvelocity-profiling pulse sequence.
Spiral-scan pulse excites a pencil of magnetization,and half-echo
readout yields a profile along the pencil. The bipolar flow-encoding
pulse shown at right may be added along any gradient axis to
produce flow sensitivity in that direction, but is typically placed
along GX. The bipolar waveform is toggled on alternate acquisitions, and the raw signal subtracted before 1D Fourier transformation, to yield a phase-contrast M-mode image.
z
The GE Signa MRI scanner is controlled interactively
from a Sun SPARCserver with a Mercury MC860 array
processor (AP) linked through a data path and a scancontrol path (15). The data are reconstructed one line at
a time on the AP and displayed in a scrolling fashion on
the Sun monitor, under control of an Xview window
system (Fig. 2). New pencil orientations and offsets are
prescribed graphically on a scout image displayed on the
Sun, and sent over the scan-control link to redirect the
pulse sequence in real time. A convention has been
adopted in which the prescription angles range from
-45' to 135' relative to a horizontal axis. The right side of
the flow image corresponds to the right end of the pencil
in Fig. 2 (where the angle is -42"), and for all angles
between -45' and 45O. For angles between 45' and 135O,
the right side of the flow image corresponds to the top
end of the pencil.
To achieve sufficient temporal resolution to follow
typical wave-propagation velocities of several hundred
cmls, the sequence of Fig. 1 is gated to the heart cycle in
groups of 16 excitationslcycle, with the sequence delayed by an additional 2 ms relative to the R-wave trigger
on each successive pair of cycles, as shown in Fig. 3. The
data are then interleaved into the proper time order and
a lDFT is applied. This results in a flow image that has
distance along the cylinder as one axis, and time relative
to the R-wave as the other axis, with an effective time
resolution of 2 ms, and spatial resolution on the order of
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manner an effective time resolution of 2 ms can be obtained within 32 heart cycles.
It is useful to perform quantitation of the blood velocity
to help determine whether any abnormal flow is present
which would invalidate this wave-velocity technique.
This is done using a cardiac-gated Fourier-velocity-encoded version of the basic pulse sequence of Fig. 1 (14).
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FIG. 2. Sun display for interactive
cardiac imaging system. Lines
drawn on the scout image at left direct placement of the NMR pencil in
real time, and a scrolling display of
blood flow appears on the right.
Here a phase-contrast reconstruction has been used; faster moving
blood produces a brighter signal,
and static tissue is suppressed.
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NMR Measurement of Aortic Distensibility
flow-
- fl(even beats)
/L (odd beats)
trigger
delay
(16 excitations)
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Figure 5a shows an oblique view of the descending
aorta in a normal volunteer, acquired using a segmented
gradient-echo pulse sequence. The line drawn on the
image indicates the position of the pencil subsequently
excited in the flow-encoding pulse sequence. Figure 5b
shows a phase-contrast flow profile obtained using the
nongated I D velocity pulse sequence of Fig. 1. Here the
horizontal dimension is time, and the vertical dimension
is position along the cylinder axis. The long streaks correspond to systolic flow in that portion of the aorta intersecting the pencil. Roughly 11heart cycles are covered
in 256 lines.
In Fig. 5c, the gated, interleaved version of the pulse
sequence has been used to measure flow in the same
region with much higher effective time resolution. In this
image the horizontal time axis extends over roughly the
first half of one heart cycle (512 ms). The bright region
corresponds to one of the streaks in Fig. 5b. The propagating wave front can be seen as the sloped region
(marked with a line) in the leading edge of the systolic
flow. Measurement of the slope yields a value for the
velocity of propagation of the wave front. Figure 5d
shows several flow profiles obtained by taking sections
through the image of Fig. 5c. The delay-time of the foot of
the flow wave is determined by setting a constant threshold which is higher than the baseline by roughly three
times the noise level in the profiles, and finding the
threshold crossing at each position. A best fit is then
performed of this time versus position, as shown in Fig.
5e, to determine the wave velocity, which is in this case
340 cmls. The first 1 cm at either end of the flow region
is excluded from the fit, because the aorta is curving into
or out of the pencil in these areas, and so is not completely aligned with the flow-encoding gradients. This
also has the advantage of excluding blood which is first
entering the pencil and so has not yet achieved equilibrium with the 30" pencil-excitation pulses.
Wave velocities have been determined in similar fashion from the ascending aorta. Figure 6a shows a scout
image from a normal volunteer, with subsequent pencil
position indicated again with a line. The free-running
phase-contrast image is shown in Fig. 6b, with the corresponding interleaved, cardiac-gated image shown in
Fig. 6c. Here systolic outflow from the left ventricle into
the ascending aorta is evident as the long streak, followed
by filling of the left ventricle from the left atrium, visible
as the shorter streak in the left ventricle. This filling is in
essentially the opposite direction from the systolic flow,
as seen using a phase-difference reconstruction algorithm (15). The wave velocity in the ascending aorta from
this subject was 270 cm/s.
Wave velocity in the descending thoracic aorta was
measured in seven volunteers ranging in age from 24 to
63 years. Figures 7a and 7b show free-running and gated
flow images, respectively, from a 63-year-old subject. The
slope of the wavefront is markedly steeper than in the
33-year-old subject of Fig. 5c, and corresponds to a wave
velocity of 960 cm/s. Wave velocity is plotted versus age
in Fig. 8a for all of the subjects. The best linear fit to these
data yields vp = 9.3X + 90, where X is age, with a correlation coefficient of R = 0.90. The error bars on the
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k-+
2 rns
A A
2 ms
515
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FIG. 3. Cardiac gating scheme for interleaved flow-profiling sequence. Sixteen phases of the heart are acquired in each heartbeat, with the trigger delay incremented by 2 ms with each pair of
heartbeats,and the data interleaved into the proper time order after
32 heart cycles.
1 mm. The wave velocity is then determined by measuring the slope of the edge corresponding to the foot of the
flow wave in this time-versus-distance image. The field
of view was typically around 30 cm and the pencil diameter 1.5 cm. The pencil-excitation pulse was based on
an %cycle k-space spiral, and was typically 11 ms in
duration. Each lobe of the bipolar flow-encoding gradient
was 1ms long, with an amplitude of 0.5 G/cm.
The Fourier-flow-encoded pulse sequence used to determine blood velocities employed 32 velocity-encoding
steps, and was gated to the R-wave, with data acquired
over 16 phases of the heart separated by 36 ms each. The
sinusoidal bipolar gradient had a maximum amplitude of
1G/cm, and each lobe was 6 ms long, yielding a velocity
resolution of 5 cm/s. This resulted in aliasing for velocities greater than 80 cm/s, but since the flow direction was
known, and flow was followed over the heart cycle, any
ambiguity in the velocity profiles was removed. This
aliasing could be easily eliminated at the cost of increased imaging time by employing 64 velocity-encoding
steps.
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RESULTS
Figure 4a shows a scout image from a volunteer, with the
position prescribed for the pencil indicated as a line on
the image. The Fourier velocity-encoded version of the
sequence of Fig. 1 was applied, with the flow direction
running orthogonal to the pencil and along the aorta. The
resulting flow distribution, shown over 16 heart phases,
is illustrated in Fig. 4b. The 16 long horizontal lines
correspond to static tissue in the excited pencil, at each
cardiac phase. Vertical displacements relative to each
long line are proportional to velocity at that heart phase.
Where the pencil intersects the aorta, a short segment can
be seen in Fig. 4b rising and then falling over the heart
cycle, arising from systolic blood flow in the aorta. The
peak velocity for this volunteer was 70 crn/s, with essentially plug flow observed across the aorta.
5113
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Hardy et al.
FIG. 4. (a) Oblique scout image of
descending aorta of normal volunteer. Line indicates position of prescribed pencil for subsequent Fourier flow sequence. (b) Results of
Fourier velocity-encoded pulse sequence over 16 heart phases. Long
lines correspond to static tissue,
and short lines to flow in the aorta,
with velocity proportional to vertical
displacement relative to each long
line. Velocity in the aorta rises to 70
cm/s and then falls again to zero.
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individual points in Fig. 8a are based upon a 0.5' uncertainty in the slope of the wavefronts, as measured for
example on Fig. 5c. This uncertainty was determined by
making repeated (between 3 and 6) NMR measurements
on the same subject, for three different subjects, and calculating the standard deviation of the slope for each subject. Note that this yields a larger uncertainty as the wave
velocity increases, as seen in Fig. 8a.
Distensibilities calculated using Eq. [I]are plotted on a
logarithmic scale versus age in Fig. 8b. The best fit was
D =- -0.021X + 2.48 (on a log scale) and the correlation
was R = 0.91.Here blood density was assumed to be 1.06
g/cm3.
DISCUSSION
We have developed a noninvasive technique for measuring aortic distensibility within a total of 64 heartbeats.
NMR pencil excitation followed by Fourier flow encoding is used to determine aortic blood velocity to an accuracy of 5 cmls with a time resolution of 36 ms, within
32 heartbeats, in order to characterize the flow. Wave
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NMR Measurement of Aortic Distensibility
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FIG. 5. (ar Quasi-sagittalscout image of descending aorta of normal volunteer. Line indicates position of prescribed pencil for subsequent
flow sequence. (b) Phase-contrast flow profile obtained using the nongated 1D velocity pulse sequence of Fig. 1, and covering roughly 11
heart cycles. (c) Gated, interleaved flow profile obtained using the gating scheme of Fig. 3.Effective time resolution has been improved to
2 ms. Sloped line corresponds to foot of velocity wave. (d) Series of flow profiles obtained at 2-cm intervals along the image of part c). The
propagation of the leading edge of the flow is evident on the left side of the plot. Differences in wave speed of the higher frequency
components of the pulse cause the shape of the curve to change slightly as the pulse moves down the aorta. (e) Best fit to the foot of the
wavefront of part c). The end regions have been excluded from the fit. Slope of line yields wave velocity of 340 cm/s. I, inferior; S, superior.
velocity in the aorta is then measured within 32 heartbeats using a cardiac-gated phase-contrast pulse sequence with NMR pencil excitation, which yields an effective time resolution of 2 ms. These pulse sequences
are both directed in a highly interactive fashion via a
workstation interface to the MR scanner. The chief virtue
of this technique is its ability to acquire regional measurements in a quick, noninvasive manner, over any portion of the aorta, along lengths as short as approximately
3 cm. It is sensitive over a range of distensibilities from
approximately
to
m sz/kg,where the lower limit
is determined by the time resolution of the technique,
and the upper limit is reached as wave velocities approach the blood velocity.
Previous methods for directly or indirectly assessing
distensibility or compliance have suffered from a variety
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of drawbacks. Ting et al. measured foot to foot flow intervals using micromanometers on a catheter inserted in
the aorta via the femoral artery (16), a technique which is
somewhat invasive. Changes in cross-sectional area of
the aorta over the heart cycle have been determined using
echocardiography (6) or MR imaging (5,17) and the regional blood pressure estimated from sphygmomanometer measurements. Determining compliance from these
measurements requires assumptions about the relationship between local and measured blood pressures and, in
the case of echocardiography, is limited to accessible regions of the aorta, such as the aortic arch. Aortic wave
velocities have recently been determined using MR cine
velocity imaging in an oblique plane passing through the
ascending and descending aorta, with calculation of the
transit time of the foot of the flow wave between the two
518
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Hardy et al.
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FIG. 6. (a) Scout image of left ventricle and ascending aorta of
normal volunteer. Line indicates position of prescribed pencil for
subsequent flow sequence. (b) Nongated and (c) gated phasecontrast flow images showing systolic and diastolic flow.
points, and with the distance measured from an oblique
spin-echo image through the aortic arch (3, 18). This,
however, is relatively time consuming and measures average wave velocity over the entire region between the
two points. More recently a multi-planar excitation
scheme with Fourier flow encoding has been used to
measure distensibility of the femoral arteries (7). This
typically requires 15 to 30 min for data acquisition, and
is subject to interference from any vessels which may be
overlying the vessel of interest, since it acquires projections across each slice.
Our values of aortic wave velocity fall somewhat above
those determined previously by micromanometer measurements (IS), and below those determined by phasecontrast MRI (3, 18). Ting et d.(16) obtained a foot-tofoot wave velocity of 374 ? 25 cm/s (all errors SEM) in
the proximal descending aorta in eight normal subjects of
average age 42.3 ? 3.1 years. This is not significantly
different (P > 0.05) from the average value of 519 5 81
cm/s obtained in the present study, which had a population of similar average age but wider age range (42.7 ?
5.3 years). Mohiaddin (18) found a linear dependence of
wave velocity in the proximal aorta with age vp = 8X +
300 (converted to cm/s). This line is roughly 20% higher
on average than the curve of Fig. 8a, but has a similar
slope. The 2D MRI measurements of wave velocity (3,18)
are averages from the ascending aorta, around the aortic
arch, to a point opposite on the descending aorta, and so
are not entirely equivalent to our measurements in the
descending aorta. Wave velocity (16) and compliance (5)
both appear to vary with position along the aorta.
The distensibilities plotted in Fig. 8b are roughly a
factor of 2 higher on average than those derived from
excised human thoracic aorta. Learoyd et al. (19) obtained average values for the Young’s modulus E of approximately lo7 dyn cm-’ and for the ratio of wall thickness to diameter h / d of 0.04, in subjects between 10 and
50 years old. Using the relationship (8) between distensibility and these quantities, D = [E (h/d)]-’,one obtains
an average value of D = 25 pm sz kg-’. This variation may
be due in part to differences between excised and in vivo
aorta. Dart et QI. (6) found an in vivo value for the “beta
index” in the aortic arch of fl = 0.16X - 2.0, where X i s
age. They defined p as ln(P,/P,) D,/(D, - D,), where P,
and P, are systolic and diastolic arterial pressure, respectively, and D, and Dd are maximum aortic diameter during systole and aortic diameter at end diastole, respectively. lJsing their mean values of P, = 127.5 ? 2.5 mm
Hg, Pd = 79.4 5 1.2 mm Hg, and Dd = 24.4 ? 0.71 mm,
one can calculate resulting average values for the distensibility. This yields 150 pm sz kg-’ at age 20 years and 20
pm s2 kg-I at age 60 years, which are somewhat higher
than the values shown in Fig. 8b, and therefore even
higher relative to the data from excised aorta (19). Mohiaddin et al. (5), on the other hand, in 1-cm thick slices
through the ascending aorta, found average values of
1.79 (in
compliance of 10 raised to the power -0.01X
pl/mm Hg), and a cross-sectional area of 0.09X 2.1 (in
cm’), where X is age. Converting units and dividing by
area times thickness, yields an average value of 75 pm sz
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FIG. 7. (a) Nongated and (b)
gated phase-contrast 1D flow
image of descending aorta of
63-year-old normal subject.
Wave velocity is much higher
than in 33-year-old subject of
Fig. 5.
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ACKNOWLEDGMENTS
1
20
locities were determined using the leading edge, or foot,
of the velocity wave.
Equation [I] holds strictly only when v,lC << 1, because under these conditions convective accelerations in
the blood are small compared with local accelerations
(8). This condition generally is met in blood flow under
normal physiological conditions, even in major vessels,
and Eq. [I]has in fact been verified directly in dogs (8).
However, when turbulent flow or jets are present, as in
the case of valve disorders, the blood velocity may become comparable with or exceed the wave velocity, and
Eq. [I]becomes invalid. Indeed, in these situations there
is usually a loss of signal and the wave front cannot be
followed in any event. This may limit any wave-velocity
technique applied to aneurysms in the ascending aorta, if
dilatation of the aorta has resulted in aortic insufficiency.
We found our determination of wave velocity to be
adversely affected in some cases by breathing artifacts,
which took the form of spurious signals running along
the time axis of the flow profiles, notably in that portion
of the descending aorta at the level of the diaphragm.
Breath-holding was found to ameliorate this problem
considerably, but may not be practical for all patients.
The use of repeated short breath-holds would prove beneficial in these cases; data acquisition could be triggered
by real-time scout views, which monitored the start of
breath-holding.
Measurement of aortic distensibility typically requires
knowledge of developed aortic pressure. Our method, in
addition to being totally noninvasive, does not require in
situ pressure measurements and can thus easily be applied clinically under various pharmacologic interventions.
The authors thank Bob Darrow and Chuck Dumoulin for useful
discussions.
70
REFERENCES
b
FIG. 8. (a) Wave velocity in the descending thoracic aorta of
seven normal subjects as a function of age, with linear fit and 95%
confidence intervals. A best-fit line of Y = 9.3X + 90 was obtained,
with an R-value of 0.90. (b) Aortic distensibilityversus age for the
same subjects. R = 0.91.
kg-l for the distensibility at age 20 years, and 15 pm sz
kg-' at age 60 years. Their values in the descending thoracic aorta were, on average, roughly 60% of their values
in the ascending aorta.
This and other wave-velocity techniques ignore contributions from reflected waves, which have been found to
be present, for instance, in the ascending aorta and near
the renal arteries (16). If measurements are acquired immediately after a period of relatively constant or minimal
flow, however, reflected waves will be insignificant,
since pressure waves are not created during steady flow,
and tend to attenuate quickly. For this reason, wave ve-
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