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Magnetic Resonance Imaging 24 (2006) 727 – 737
A new strategy for respiration compensation, applied toward
3D free-breathing cardiac MRI
Bruno Madore4, Gunnar Farneb7ck, Carl-Fredrik Westin, Alejandra Durán-Mendicuti
Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA 02115, USA
Received 26 December 2005; accepted 17 January 2006
Abstract
In thorax and abdomen imaging, image quality may be affected by breathing motion. Cardiac MR images are typically obtained while the
patient holds his or her breath, to avoid respiration-related artifacts. Although useful, breath-holding imposes constraints on scan duration,
which in turn limits the achievable resolution and SNR. Longer scan times would be required to improve image quality, and effective
strategies are needed to compensate for respiratory motion. A novel approach at respiratory compensation, targeted toward 3D free-breathing
cardiac MRI, is presented here. The method aims at suppressing the negative effects of respiratory-induced cardiac motion while capturing
the heart’s beating motion. The method is designed so that the acquired data can be reconstructed in two different ways: First, a time series of
images is reconstructed to quantify and correct for respiratory motion. Then, the corrected data are reconstructed a final time into a cardiacphase series of images to capture the heart’s beating motion. The method was implemented, and initial results are presented. A cardiac-phase
series of 3D images, covering the entire heart, was obtained for two free-breathing volunteers. The present method may prove especially
useful in situations where breath-holding is not an option, for example, for very sick, mentally impaired or infant patients.
D 2006 Elsevier Inc. All rights reserved.
Keywords: 3D imaging; Cardiac imaging; Free breathing; Fast imaging; Parallel imaging
1. Introduction
In cardiac MR applications, the need to freeze or resolve
both cardiac and respiratory motion poses a difficult
challenge. Breath-holding is widely used to avoid artifacts
caused by respiration-induced motion. Although very
useful, breath-holding effectively limits scan time to a
dozen seconds or so, which in turn limits the achievable
SNR and resolution. Longer scan times can be obtained with
free breathing, provided that respiration-related motion can
be satisfactorily corrected for. Extending scan time through
free breathing can allow improvements in image parameters
such as spatial resolution, spatial coverage, SNR and/or
temporal resolution within the cardiac cycle.
This work presents a new approach toward respiratory
compensation, applied to 3D free-breathing cardiac imaging. The proposed method is named bTracking to Remove
Artifacts from Cardiac KineticsQ (TRACK) [1], and its
purpose is to compensate for the complex respirationinduced kinetics of the heart while capturing its beating
4 Corresponding author. Tel.: +1 617 278 0024; fax: +1 617 264 5275.
E-mail address: [email protected] (B. Madore).
0730-725X/$ – see front matter D 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.mri.2006.01.009
motion. The method gains quantitative, high temporal
resolution knowledge about respiration-induced cardiac
motion by merging quantitative information from the image
data itself, along with high temporal resolution information
from a conventional respiration-monitoring belt strapped
around the patient. A main feature of the approach consists
in reconstructing the same acquired data in two very different ways: First, a time series of 3D images is acquired and
reconstructed using our fast-imaging method UNFOLDSENSE [2,3], so that valuable information about respirationinduced cardiac motion can be obtained (e.g., translation
and linear stretching). After correcting for motion, the same
acquired data set is reconstructed again, in a different way,
into the final result: a cardiac-phase series of images where
the cardiac beating motion is displayed and where respiration-related motion has been suppressed.
A number of very good papers have been written on the
topic of free-breathing magnetic resonance imaging (MRI).
Respiration is typically monitored through the stretching of a
belt strapped around the patient or through 1D navigator
measurements [4]. This information can be used to direct
k-space data ordering [5– 7] to reject unsuitable data [8,9], to
make a number of breath-holds appear like a very long one
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B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
Fig. 1. Block diagram describing the proposed TRACK method. The shaded blocks represent information acquired during the scan, while the numbered blocks
represent steps in the image reconstruction. Black arrows show the flow of processing, while the gray arrows show where the input data are used. A
characteristic of the method comes from reconstructing the same data in two very different ways: In Step 1, a large number of time frames are generated to
resolve the respiratory cycle, and after analyzing/correcting the data for respiration-induced motion (Steps 2 through 4), a second reconstruction (Step 5)
produces a number of cardiac phases to resolve the cardiac cycle.
[10,11] or to apply data correction [4,12]. Very impressive
work has been done to achieve free-breathing cardiac
imaging, through the use of 1D navigator echoes placed on
the dome of the right hemidiaphragm to monitor respiration
[13–16]. Such navigator echoes measure the respirationinduced motion of the interface between the high-signal liver/
diaphragm and the low-signal right lung in the superior–
inferior (S/I) direction. Cardiac respiratory-induced motion
can be estimated by assuming a linear relationship between
cardiac and right hemidiaphragm motion [17]. A predetermined correlation coefficient of 0.6 is often used to translate
right hemidiaphragm S/I translation measurements into
cardiac S/I translation [13,14,17,18], and a correlation factor
about one order of magnitude smaller can be used to translate
the measurements into cardiac anterior–posterior (A/P)
translation [17–19]. However, the relationship between right
hemidiaphragm and cardiac translation is only roughly linear
[20] and has been shown to vary significantly among subjects
[19,21], among targeted cardiac structures [17,19] and also
over time in a given subject [22]. A calibration scan,
performed before the actual scan, can be used on a patientby-patient basis to alleviate some of these problems [23].
Bulk motion, breathing patterns (e.g., more abdominal
vs. more thoracic), intersubject variability and the nonrigid
nature of the heart combine to make respiration correction a
difficult problem, as respiration-induced changes in the
heart can be complex both geometrically and temporally
[20,22,24]. Because correcting for breathing motion is
difficult, most existing free-breathing methods function by
rejecting unsuitable data points, rather than correcting them.
In the process of building a self-consistent data set that is
mostly free of respiratory motion, only a few percentage of
the acquired data are typically kept for reconstruction, while
the rest is simply discarded. Even when existing datacorrection methods are used to help relax the acceptance
criteria, the amount of rejected data is still expected to
remain several-fold larger than that of preserved data. In
contrast, for the results shown here, every bit of acquired
data was used in the reconstruction of the final results. SNR
efficiency is a major rationale behind the proposed line of
approach, as SNR is expected to vary roughly as the square
root of the amount of data included into the reconstruction.
The present method is geared toward detecting and
suppressing the effects of breathing motion in a way general
enough to allow all acquired data points to participate in the
reconstruction, leading to optimum SNR.
Because SNR is directly proportional to the volume of
the imaged voxels, it can be seen as the main factor limiting
spatial resolution in MRI. If we consider computed
tomography (CT) imaging for a moment, an exquisite
spatial resolution of about 0.5 mm isotropic (0.125 mm3)
can be achieved nowadays with cardiac CT, while voxels in
cardiac MR are often as much as hundreds of times more
voluminous (around 20 to 30 mm3). Cardiac CT has
shortcomings of its own, like patient dose and low temporal
resolution in the cardiac cycle, but its superior spatial
resolution allows coronary arteries to be reliably imaged and
evaluated, a goal still elusive with MR. To markedly reduce
voxel size in cardiac MR, one would first need to secure the
necessary SNR. The present work can be seen as the
exploration of a possible avenue to enable higher-resolution
cardiac MRI, by providing some of the required extra SNR.
This is done by removing the need for breath-holding to
allow for longer scan times and by incorporating 100% of
the acquired data into the image reconstruction. Of course,
nominal SNR and spatial resolution may lose some of their
meaning in the presence of artifacts. The main challenge for
free-breathing imaging is to reduce as much as possible the
artifact level due to imperfect compensation of respirationinduced motion. We believe that the present approach,
B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
729
where respiration-related motion is measured directly on the
heart, using 3D images, has the potential to better
compensate for geometrically complicated motion than
existing methods that use right hemidiaphragm motion as
an indicator of cardiac motion. The present method may
prove especially useful in situations where breath-holding is
not an option, for example, when imaging very sick,
mentally impaired or infant patients.
2. Theory
A fast MRI approach we previously developed [2] is used
here to time resolve the respiratory cycle. A respirationmonitoring stretchable belt, a standard accessory for MRI
scanners, provides a high temporal resolution rendering of the
respiratory waveform. The wealth of spatial/geometrical
information provided by the 3D images is fused with the
high temporal resolution information from the respirationmonitoring belt to detect and correct for spatially and
temporally complicated respiration-induced motion and
deformation. The acquired data are then corrected for the
effect of respiration, and signal from noncardiac structures is
suppressed. Finally, the resulting respiration-compensated
cardiac signal is converted from a time series of images to a
cardiac-phase series of images, where the cardiac beating
motion can be seen. As a result, a respiratory-compensated
cardiac-phase series of 3D images of the heart is generated.
These steps are depicted in the block diagram shown in Fig. 1
and explained in more detail below.
2.1. Data acquisition strategy
The shaded blocks in Fig. 1 represent the information
gathered during the scan: the acquired k-space data, a record
of the respiratory waveform as detected by a stretchable belt
strapped around the patient and a record of the cardiac
waveform and R wave triggers. Black arrows in Fig. 1 show
the flow of the processing, while gray arrows indicate where
the input data are used. The cardiac and respiratory
waveforms are simply gathered and recorded during the
scan and do not influence the actual k-space data acquisition
process (i.e., no gating/triggering).
Fig. 2 depicts the k y and k z coordinates of the needed
k-space lines, with k x oriented through the plane of the paper.
As usual, in parallel imaging [25,26], not all k-space lines are
sampled: One line for every two lines along both k y and k z are
sampled here. A higher density of data is acquired near
k-space center to allow self-calibration [2,27,28]. As customary with our UNFOLD method [29], the lines acquired for
odd time frames (black dots in Fig. 2) are different from those
acquired for even time frames (gray dots). As a consequence
of using partial Fourier imaging [30 – 32], a whole section of
the k-space matrix (30% here) is not sampled.
Not depicted in Fig. 2, a drift in the sampling function is
added on top of the temporal changes required by UNFOLD
to further diversify the k-space locations visited during the
exam. In addition to the usual UNFOLD shift between odd
Fig. 2. The k-space sampling scheme for TRACK is depicted here. See text
for more details.
and even frames (Fig. 2), the whole sampling function is
further shifted by one line in the k y direction every 10 frames
(alternating between a +k y and a k y shift). As a consequence, the modulation imposed by UNFOLD onto aliased
signals is not a Fourier function but a multiplicative
combination of a Fourier and a Hadamard function. To the
best of our knowledge, this is the first application where
UNFOLD is used to generate non-Fourier modulations. As
usual, UNFOLD forces aliased signals to behave in a peculiar
way through time; hence, they become conspicuous and can
be filtered out. Unlike in previous applications, this bpeculiar
behaviorQ of the aliased signals is not a high-frequency
Fourier modulation but rather a hybrid Fourier–Hadamard
function. Details on the filtering process are presented elsewhere [33]. Without the drift, looking at Fig. 2, some k-space
locations in the outer k-space regions would never get
sampled. The effect of the discontinuous drift is to make sure
that all locations get sampled in several of the time frames.
2.2. UNFOLD-SENSE reconstruction (Fig. 1, Step 1)
Using our UNFOLD-SENSE method [2,3] supplemented
with partial Fourier imaging [30–32], data acquired over
several minutes (about 10 min here) are reconstructed into a
large number of time frames (200 here), using a relatively
high acceleration factor (4.6 here).
2.3. Measurement of the respiratory motion (Fig. 1, Step 2)
The present step has much in common with the adaptive
averaging ideas developed by Hardy et al. [34] and Sussman
et al. [35], as the acquired data are used to detect motion.
The whole time series of reconstructed 3D time frames is
analyzed to detect the respiration-induced motion of the
heart throughout the exam. The cardiac beating motion
tends to be blurred in these images, and the procedure aims
at evaluating the respiration-induced cardiac motion. For
this task, we used a polynomial expansion-based registration
algorithm that we developed [36], which was adjusted to
evaluate three parameters: S/I displacements (X i ), A/P
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B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
displacements ( Yi ) and S/I linear stretching (S i ), with
i representing the frame number from 1 to N T. The user is
asked (a) to select a location z c in the R/L direction, near the
center of the heart, to be used for registration; (b) to draw an
ROI that loosely surrounds the heart, in a sagittal plane, to
delimit the area used for registration; (c) to identify an S/I
location near the base of the heart, x base. These are the only
user interactions required in the present reconstruction, and
in the future, we hope to replace these steps with automated
algorithms. The registration is performed on a single sagittal
slice, located at z c in the R/L direction, and all other slices
are assumed to feature similar respiration-induced motion.
x base is the reference location that remains unaffected by S/I
stretching. While the S/I stretching measurements are
independent of the choice of x base, the S/I translations, on
the other hand, are not. While the actual choice of x base has
no influence on the reconstructed images, choosing a
location near the base of the heart allows the S/I translation
values to be directly interpreted in the context of the
anatomy, simplifying comparisons among volunteers and
with values reported in the literature.
2.4. Fusing respiration waveform and respiration
measurements (Fig. 1, Step 3)
Fig. 3 depicts how the time series of 3D images provides
quantitative but low temporal resolution data, while the
monitoring belt provides high temporal resolution data with
arbitrary and possibly nonlinear scaling. These two sources
of information are fused to give a quantitative, high
temporal resolution rendering of respiration-induced motion. With R i representing the reading from the respirationmonitoring belt as k-space center was acquired for the ith
time frame out of N T, the following model is assumed for
S/I translation:
0
10 1 0
1
1 R1
R21
R31
a0
X1
B 1 R2
B C B
C
R22
R32 C
B
CB a1 C ¼ B X2 C:
ð1Þ
@v
v
v
v A @ a2 A @ v A
2
3
1 R NT R NT R NT
XNT
a3
The system of equations is solved for a 0, a 1, a 2 and a 3,
which represent, respectively, the coefficients for the zeroth-,
first-, second- and third-order terms in the relationship
between the readings from the respiration-monitoring belt
and the S/I translation of the base of the heart. Similar
systems that relate the A/P displacements Yi to coefficients
b 0, b 1, b 2 and b 3, as well as S/I linear stretching measurements S i to coefficients c 0, c 1, c 2 and c 3, are solved. While
R i , X i , Yi and S i represent low temporal resolution
functions, with only one data point every few seconds,
r(t), x(t), y(t) and s(t) represent their high-resolution
counterparts, with hundreds of data points per second. Once
polynomial coefficients that translate the low-resolution
version of the respiratory-belt readings R i into desired
motion parameters (Eq. (1)) are found, the same coefficients
are used to translate the high-resolution version of the
Fig. 3. Respiration is monitored with a stretchable respiration-monitoring
belt (high temporal resolution, nonquantitative information) and by
analyzing the time series of acquired 3D images (lower temporal resolution,
quantitative information). Each point in PV(t) comes from a motion
measurement in a 3D time frame. In essence, the continuous function r(t)
provides the functional support to interpolate PV(t) and transform it into a
near-continuous, quantitative description of a given motion parameter
during the imaging study (e.g., respiration-induced S/I translation, A/P
translation or S/I linear stretching).
respiratory-belt readings, r(t), into high-resolution versions
of these motion parameters:
xðt Þ ¼ a0 þ a1 rðt Þ þ a2 rðt Þ2 þ a3 rðt Þ3
yðt Þ ¼ b0 þ b1 rðt Þ þ b2 rðt Þ2 þ b3 rðt Þ3
sðt Þ ¼ c0 þ c1 rðt Þ þ c2 rðt Þ2 þ c3 rðt Þ3 :
ð2Þ
In the future, we may experiment with piecewise fits
along the time axis, by feeding only a fraction of all the N T
data points into Eq. (1) and solving multiple times for
different subsets of time points. This would allow the a, b
and c fit coefficients to vary slowly in time to account for
changes in breathing patterns that might alter the relationship between belt stretching and heart motion (e.g.,
changing from a more thoracic to a more abdominal type
of breathing while the exam is underway).
2.5. Correcting for breathing motion and suppressing
noncardiac signal (Fig. 1, Step 4)
Every k-space point acquired in the entire series of 3D
images needs to be corrected for the S/I translation, A/P
translation and S/I stretching values calculated from Eq. (2).
Through the shift theorem of the Fourier transform, the
translations are corrected by applying phase ramps in the
k-space domain. The stretching is corrected by performing a
modified version of an inverse discrete Fourier transform
(DFT), instead of an inverse FFT, in the stretched direction
as one goes from Fourier to object domain. As part of the
modified inverse DFT, each Fourier basis function involved
in the transform is stretched appropriately to counteract the
effect of the stretch s(t), yielding a reconstructed object
where stretch has been corrected for. The Fourier basis
functions, which are linear phase functions, are stretched by
increasing/decreasing appropriately the phase slope. More
usual interpolation schemes (e.g., linear, cubic and spline)
applied to either the object or k-space domain have been
proven unreliable, due in part to the complex nature of the
data. On the other hand, the interpolation scheme described
B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
above based on stretched Fourier basis functions proved
very robust.
Note that correcting for the respiration-induced kinetics of
the heart tends to make all surrounding noncardiac features,
which do not move with the heart, appear more dynamic. It is
important to suppress as much as possible the noncardiac
signals before the final reconstruction to avoid having these
features broadcast artifacts onto the heart. Three approaches
to do so have been investigated in this work.
1.
ROI-based selection. After a sampling-density correction, the respiration-corrected data are brought to
the object domain. The ROI previously drawn by the
user (as described above) is reused to mask out
signals located away from the heart. Because only a
fraction of the k-space matrix is available at each
time frame, the motion-corrected data are corrupted
by aliasing. While this ROI-based approach suppresses signals away from the heart, noncardiac
signals that are aliased within the ROI remain.
2. Coil-based selection. In the present implementation,
aliasing artifacts come from three locations: half an
FOV away in the y direction, in the z direction and in
both directions at once. The coil-sensitivity values at
each one of these three locations are combined into a
Y
vector, uY
y , and uyz , respectively. These vectors are
normalized to a unit length, in a function space
featuring N c (complex) dimensions, where N c is the
number of coil elements. With Y
v the signal at the
pixel under consideration, the signal AY
yz is identified
as being an artifact and is removed to obtain Y
vp , the
signal after processing:
Y
Y ¼Y
A
uyz conj Y
uyz d v ;
yz
Y
vYp ¼ Y
v Ayz ;
ð3Þ
where conj() is a complex-conjugate operator and bd Q is
a dot-product operator. The process described by Eq. (3)
will be referred to as a yz-type projection. By replacing
the byzQ subscripts with byQ or bz,Q one gets a y-type or
z-type projection, respectively. These different-type
projections could be applied sequentially. Although these
projections are closely related to parallel-imaging reconstructions, they differ in that they do not amplify noise
and they leave unchanged the number of coil images.
Because the most intense noncardiac signal to be
eliminated comes from the thoracic cage, located along
y with respect to the heart, the z-type projection is expected
to be the least useful of the three. Because differences in
sensitivity tend to grow with distance, the zy-type projection is expected to be the most useful type, with the
lowest risk of removing desired signal along with artifacts.
3. Magnitude-based selection. Most intense pixels in
the FOV contain fat, and the aliased and nonaliased
signals from subcutaneous fat located near the
731
receiver coils appear especially bright. A magnitude
threshold can be applied whereby all pixel values
with a magnitude beyond the threshold are brought
back to the threshold, without affecting their phase.
Such thresholding operation tends to remove mostly
fat signal and not cardiac signal.
While the ROI-based selection should be performed after
the motion compensation, the coil-based selection should be
performed before, while object signal and sensitivity maps
are still well registered. The magnitude-based selection can
be performed either before or after.
2.6. Reconstruction of the final result (Fig. 1, Step 5)
For the final reconstruction, the k-space data from all
time frames are binned into a new series of k-space data
sets. This is a retrospectively gated reconstruction, where
data are binned based on cardiac phase, using the record of
cardiac waveform and trigger information gathered during
the acquisition. Because the number of cardiac phases
created is much smaller than the number of time frames
originally acquired, parallel imaging and UNFOLD are not
needed in this reconstruction. As a final step, the data from
all coils can be combined in an SNR-optimum way, as
described by Roemer et al. [37]. The final result is a cardiacphase series of 3D images, corrected for respiration-induced
motion, and these 3D images can be played in a movie loop
to display the beating motion of the imaged heart.
2.7. Resolution in cardiac phase
Depending on the number of cardiac phases being
reconstructed, some data may have to be interpolated from
neighboring cardiac phases as part of the final reconstruction described above. Consider a given k-space location,
sampled in one m th of the time frames during an N T- frame
TRACK acquisition. Each one of these N T/m different
measurements falls into one of the N p different cardiac
phases being reconstructed. With all cardiac phases being
equally probable, the odds of this k-space location being
sampled at least once at a given cardiac phase is 1((N p1)
/N p)N T/m . The lines near k-space center, which represent a
fraction f c of all sampled lines, are sampled more often than
the lines near the edge of the k-space matrix. With central
lines sampled N T/m c times while other lines are sampled
N T/m o times, the fraction of lines expected to be readily
available (without interpolation) in an N p-phase TRACK
reconstruction is:
NT
NT
Np 1 mc
Np 1 mo
F Np ¼ 1 fc
ð1 fc Þ
ð4Þ
Np
Np
It can be noted that Eq. (4) does not depend on the
patient’s heart rate but only on the number of time frames,
number of phases and details of the k-space acquisition
scheme. Once one decides on a target value for the amount
of noninterpolated data, for example, 80%, the curve
732
B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
Table 1
Full
matrix size
TR (ms) Voxel
size (mm)
NT
N p S/I displacement:
a 0, a 1, a 2, a 3
Volunteer 1 12812840 2.6
2.52.54.0 200 20
Volunteer 2 12812840 2.7
2.32.34.0 200 20
2.05e1, 8.93e1,
8.65e1, 6.11e1
5.04e1, 2.00e2,
3.48e2, 2.18e2
described by Eq. (4) gives the number of cardiac phases that
can be reconstructed.
3. Methods
TRACK was implemented on a 1.5-T MR imager (GE
Medical Systems, Milwaukee, WI; software version 11.0
M4) equipped with eight receiver channels, using a product
eight-element cardiac phased-array coil and a modified 3D
steady-state free precession (SSFP) pulse sequence. Eight
volunteers have been imaged so far but only two with the
latest version of the implementation. Results from these two
latest volunteers are presented here. During the scan, as
k-space data became available, a Perl script automatically
archived them onto a nearby PC. Once archived, the data
were automatically deleted from the host of the MR imager
to avoid taxing the storage capabilities of the system.
A/P displacement:
b 0, b 1, b 2, b 3
S/I linear stretching:
c 0, c 1, c 2, c 3
Cardiac Breathing
rate
rate
(min1) (min1)
5.03e1, 2.63e1,
1.01e0, 4.90e1
2.22e1, 9.21e1,
1.29e2, 6.03e1
4.53e2, 2.20e3, 76
1.91e1, 1.35e1
1.08e2, 6.48e2, 55
9.87e2, 1.95e1
16
11
Respiratory and cardiac waveforms were also recorded and
archived, along with information about the timing of R
wave occurrences. Initially, the physiological waveforms
were captured using a webcam placed in front of the
console, but a software patch developed at GE is now used
instead to automatically record these waveforms to files.
This patch will become a standard product in future
software releases. The image reconstruction was performed
off-line, using programs written in the Matlab programming
language (The MathWorks, Natick, MA).
4. Results
Two volunteers were imaged, with parameters listed in
Table 1. The sampling function was changed from frame to
frame as required by UNFOLD, with the addition of a
discontinuous drift, as described in Section 2.
Fig. 4. An important step of the algorithm is illustrated here, which involves suppressing signal from noncardiac features before the final reconstruction. Row A
shows 1 of the 200 time frames about to be converted into cardiac phases, and Row B shows signal identified as noncardiac and excluded from the images in
Row A. Row C shows one of the reconstructed cardiac phases, and Row D gives a zoomed version of the heart region. Column i represents a case where no
suppression is applied, leading to cardiac phases corrupted by aliasing (D(i)). Columns ii through iv show the effect of different suppression strategies (ROI
based, projection of type zy and magnitude based, respectively). Column v represents a combination of strategies (ROI-based approach with projections of
types zy and y). Upon comparing D(i) and D(v), notice the substantial improvement in image quality achieved by suppressing noncardiac signal before the final
reconstruction. See text for more details.
B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
Fig. 5. The number of cardiac phases reconstructed, N p, is a free parameter
set by the user. The amount of data readily available, without interpolation,
is plotted as a function of the number of cardiac phases. Notice the close
agreement between experimental data (circles and x marks) and the
theoretical prediction from Eq. (4) (solid line). The dashed lines show
predictions from Eq. (4) for cases where the number of time frames is either
reduced from 200 to 100 or increased to 300. The two dotted lines
originating from the vertical axis enclose the normal range of operation for
clinical protocols, where roughly one half to two thirds of the data are
readily present at the reconstructed resolution, and the remainder is
interpolated from neighboring cardiac phases. The vertical dotted lines
show that, in TRACK, this range of operation would allow somewhere
between 50 and 80 cardiac phases to be reconstructed, roughly twice the
temporal resolution of our clinical protocol.
A respiratory waveform, r(t), was obtained from a
respiration-monitoring belt during the scan. The acquired
3D images were analyzed to evaluate the coefficients
describing the respiration-induced motion parameters in
Eq. (2), and their values are listed in Table 1. As the
individual 3D images are corrected to make the heart appear
at a same location and size in all time frames, the role of a 0,
b 0 and c 0 is simply to determine what this common location
and size should be. The numerical values of the ba,Q bbQ and
bcQ coefficients that allow r(t) to be converted into S/I
displacement, A/P displacement and S/I stretching depend
on the arbitrary units used in the data obtained from the
respiration-monitoring belt. The action of breathing-in
displaces the heart in the inferior and anterior directions
and leads to a positive stretching (elongation).
Fig. 4 displays an important part of the processing, where
signals originating from outside the heart are suppressed
before the final reconstruction can be performed (Step 4 in
Fig. 1). Row a shows one of the 200 time frames, just before
these frames are reformatted into cardiac phases. Row b
shows signal that was identified as noncardiac and
subtracted to obtain the images in Row a. Rows c and d
display a full-FOV and a zoomed version, respectively, of
one of the reconstructed cardiac phases. Columns i through
v illustrate different strategies for suppressing the noncardiac signal. In Column i, there is no suppression, leading to
cardiac phases corrupted by artifacts (Fig. 4c(i) and d(i)).
Column ii shows the effect of the ROI-based suppression
733
strategy presented in Section 2. Comparing Fig. 4d(ii) with
Fig. 4d(i) indicates that this ROI-based approach is effective
in reducing the artifact level but may not be sufficient by
itself to reduce artifacts to an acceptable level. Similarly,
Column iii suggests that the coil-based approach is effective
but not necessarily sufficient. As seen from Column iv, the
magnitude-based approach proved to be mostly ineffective,
at least in its current form. Column v represents the
processing used to reconstruct the data from Volunteer 1,
where the ROI-based approach was combined with two
different projection-based approaches (zy type and y type) to
eliminate most of the artifacts, as can be seen upon
comparing Fig. 4d(v) with Fig. 4d(i). The data from
Volunteer 2 featured a lower artifact content, and an ROIbased approach combined with a single projection (zy type)
was used. At this stage of development, it would seem that
the ROI-based approach and the zy-type projection should
always be applied, the magnitude-based approach seems
mostly ineffective and should be left aside and the y-type
projection may be used if needed.
The circles and bxQ marks in Fig. 5 give the fraction of
data readily available as a function of the number of cardiac
phases reconstructed for Volunteers 1 and 2, respectively.
Missing data would be interpolated from neighboring
cardiac phases. The solid line in Fig. 5 represents Eq. (4),
for the current k-space sampling scheme (N T = 200,
f c =24.44% of sampled k-space locations, m c =2, m o =4).
Note the close agreement between experiment and theory.
Twenty cardiac phases were reconstructed in the results
shown here, and accordingly, about 90% of the data were
readily available, that is, 10% of the data were interpolated.
Figs. 6 and 7 display the reconstructed results. In Fig. 6,
only two cardiac phases are displayed: one during systole
and one during diastole. Data are shown for Volunteers 1
and 2, using a 3D representation (Column i) and three
different 2D cross sections (Columns ii to iv). Fig. 7 shows
all 20 cardiac phases reconstructed with the data from
Volunteer 2, using a 3D representation. The displayed
anatomy, from the right side of the heart, was selected for
display because it undergoes large changes in the course of
the cardiac cycle. Accordingly, Fig. 7 is meant to demonstrate that the proposed approach does indeed capture the
beating motion of the heart.
5. Discussion
As shown in Figs 6 and 7, the TRACK method allows
the entire heart to be imaged, in 3D, during free breathing.
Although breath-held 3D imaging of cardiac function has
been demonstrated to be feasible [38 –40], typically only
one or two 2D slices can be acquired during the time one
holds his or her breath. Compared with 2D breath-held
protocols, TRACK can lead, at least in principle, to sizeable
improvements in SNR and temporal resolution. The scan
time for our 3D acquisition is about 10 min, compared with
about 12 s for the breath-held acquisition of one 2D slice.
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B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
Fig. 6. Two of the cardiac phases reconstructed using data from Volunteer 1 (Rows A and B) and Volunteer 2 (Rows C and D) are displayed: one during diastole
(Rows A and C) and one during systole (Rows B and D). A (same) 3D image is represented in four different ways: a 3D representation (Column i) and three
different sagittal cross sections (Columns ii to iv).
This increase by about a factor of 50 in the time any given
spin is imaged
should allow SNR improvements by about
pffiffiffiffiffi
a factor of 50c7. Imperfections visible in the results
shown here are believed to be leftover artifacts, not noise.
The extra SNR could in principle be used to improve spatial resolution, although in the present implementation, a
voxel size similar to that of our 2D clinical protocol was
prescribed (2.52.54.0 =25 mm3 for Volunteer 1 and 2.3
2.34.0= 21 mm3 for Volunteer 2, as compared with
about 1.72.08.0 =27 mm3 for our 2D clinical protocol).
Various aspects of the results are discussed in more detail
below.
5.1. Temporal resolution
As a result of the first data reconstruction in TRACK,
time frames were generated to resolve the respiratory cycle.
The term bresolveQ should not be understood here in the
Nyquist sense. Even if less than two time frames were
acquired per respiratory cycle, no aliasing would occur,
thanks to the complementary, near-continuous temporal
knowledge provided by the respiration-monitoring belt.
Nevertheless, if time frames were acquired over too large
a time window, respiratory motion could prove too blurred
to be effectively detected and quantified. In the present
implementation, the data acquisition window for any given
time frame was about 3.1 s, which appeared to be sufficient
to avoid significant blurring. Respiration-related blurring
could be reduced further using a centric acquisition scheme
in the k y –k z plane, but such approach was rejected to avoid
the entire central k-space region from being acquired too
rapidly at a same cardiac phase.
5.2. Cardiac-phase resolution
As a result of the second reconstruction in TRACK,
cardiac phases are generated to resolve the cardiac cycle. It
is difficult to determine precisely the btrueQ cardiac-phase
resolution provided by TRACK. A comparison of the data
in Fig. 5 with parameters used in clinical scans can however
be helpful. 2D breath-held clinical protocols typically
provide about 15 to 20 independent true cardiac phases,
interpolated to 30 cardiac phases for display. Accordingly,
the images presented to clinicians are typically made of
about one half to two thirds of true information, the missing
information being interpolated from neighboring cardiac
phases. As shown by the dotted lines in Fig. 5, similar
proportions of true and interpolated information would be
obtained with TRACK if about 50 to 80 cardiac phases were
reconstructed (which are about twice higher than the 30
B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
735
5.3. Randomness versus periodicity
Fig. 7. Twenty distinct 3D cardiac phases are displayed here, obtained with
TRACK while Volunteer 2 was breathing freely. Middiastole happens near
the middle of this image series. The method was able to capture the beating
motion of the heart, as can be seen from the anatomical changes from
cardiac phase to cardiac phase. The imaging parameters for the 3D SSFP
sequence were as follows: TR = 2.7 ms, TE = 1.2 ms, matrix size = 128
12840, spatial resolution = 2.32.34.0 mm3, flip angle = 408. The
TRACK-related parameters are the following: acceleration in first reconstruction = 4.6, 70% partial Fourier, drift of 1 k y line every 10 time frames,
200 time frames generated by first reconstruction, 20 cardiac phases
(displayed here) generated by second reconstruction.
The theoretical curve in Fig. 5 slightly overestimates the
experimental data, by about 2%. This may be caused by the
assumption, made in Eq. (4), about the cardiac phase being
an evenly distributed random variable. As many time frames
are being acquired, any given k-space location gets sampled
many times, and the cardiac phase at which these samples
occur is randomly distributed over the whole cardiac cycle.
If given k-space locations were more likely to be sampled at
some cardiac phases than others, a higher-than-expected
number of cardiac phases would be left unsampled, causing
experimental measurements to appear below the theoretical
curve in Fig. 5. An extreme example of this behavior can be
created in simulations, by adjusting the heart rate so that the
acquisition time for one time frame is an exact multiple of
the R–R interval. In this particular case, any given k-space
location gets sampled always at precisely the same cardiac
phase, time frame after time frame. Such systematic
behavior is very different from the binomial distribution
expected for a random cardiac phase and would lead to great
reductions in efficiency, that is, to curves far below the
theoretical curve in Fig. 5. However, further simulations
show that changing the heart rate by as little as a few tenths
of a beat per minute or alternatively allowing the heart rate
to randomly fluctuate with a standard deviation as small as
half a beat per minute is sufficient to essentially destroy
such periodic behavior. While nonrealistic simulations
involving a perfectly steady heart rate set at a precise (and
unfortunate) value may feature great losses in efficiency as
compared with the theoretical curve in Fig. 5, such extreme
effect is not expected to be observable in vivo. Small
departures from a purely random scenario may, however,
help explain the subtle discrepancies between experimental
and theoretical results such as in Fig. 5. Note that, in
principle, one may exceed the performance of the theoretical
curve in Fig. 5 by changing prospectively the k-space
acquisition order, based on the timing of past frames with
respect to the cardiac waveform. The present implementation relies on randomness to diversify the cardiac phases
sampled. Strategies with on-the-fly modifications to the
phase-encoding order could in principle be developed to
increase TRACK’s data collection efficiency.
5.4. Total scan time
phases from clinical protocols). Although it is difficult to get
a single precise number for the cardiac-phase resolution, it
seems clear that TRACK is significantly superior to our
clinical 2D breath-held protocol in that respect, with the
imaging parameters used here. As seen from Eq. (4), the
main imaging parameter affecting the number of cardiac
phases (N p) that can be reconstructed is N T (the number of
time frames acquired). The dashed curves in Fig. 5 show
how the ability of the method to reconstruct cardiac phases
is improved by increasing the number of time frames from
200 to 300 or worsened by decreasing it to 100.
At about 3.1 s/frame, one should be able to acquire 200
time frames in about 10.5 min. With the current implementation, about 15 min is required instead. Our MR system
requires delays in-between time frames, which force the use
of dummy excitations to reestablish the steady-state magnetization before each time frame. Furthermore, a pause of
about 25 s is inserted between blocks of 20 frames to slow
down the acquisition rate roughly to the rate at which raw data
get written into files. In future implementations, we will aim
to reduce scan time by eliminating as much as possible these
idle periods where no image data are acquired.
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B. Madore et al. / Magnetic Resonance Imaging 24 (2006) 727 – 737
5.5. Future work
We will focus on improving the registration process, on
further reducing the artifact content and on eliminating user
interactions as much as possible. We will also consider
extending TRACK to other applications where imaged
organs move due to respiration, such as in liver imaging
[41,42]. The method might also prove useful in functional
MRI, where bulk motion (instead of respiratory motion) has
to be corrected and images that resolve the paradigm cycle
(instead of the cardiac cycle) are desirable.
6. Conclusion
TRACK is a novel respiratory motion correction scheme,
targeted toward free-breathing 3D cardiac MRI. The
approach may prove especially useful in patient populations
where breath-holding cannot be effectively performed, such
as with very sick, mentally impaired or infant patients.
Acknowledgments
This project was supported by the NIH grants R01
HL073319 and U41 RR019703-01A2. Its contents are solely
the responsibility of the authors.
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