Iterative Decomposition of Water and Fat With Echo
Asymmetry and Least-Squares Estimation (IDEAL):
Application With Fast Spin-Echo Imaging
Scott B. Reeder,1*Angel R. Pineda,1Zhifei Wen,1Ann Shimakawa,2Huanzhou Yu,1
Jean H. Brittain,2Garry E. Gold,1Christopher H. Beaulieu,1and Norbert J. Pelc1
Chemical shift based methods are often used to achieve uni-
form water–fat separation that is insensitive to Boinhomoge-
neities. Many spin-echo (SE) or fast SE (FSE) approaches ac-
quire three echoes shifted symmetrically about the SE, creating
time-dependent phase shifts caused by water–fat chemical
shift. This work demonstrates that symmetrically acquired ech-
oes cause artifacts that degrade image quality. According to
theory, the noise performance of any water–fat separation
method is dependent on the proportion of water and fat within
a voxel, and the position of echoes relative to the SE. To ad-
dress this problem, we propose a method termed “iterative
decomposition of water and fat with echo asymmetric and
least-squares estimation” (IDEAL). This technique combines
asymmetrically acquired echoes with an iterative least-squares
decomposition algorithm to maximize noise performance. The-
oretical calculations predict that the optimal echo combination
occurs when the relative phase of the echoes is separated by
2?/3, with the middle echo centered at ?/2??k (k ? any inte-
ger), i.e., (–?/6??k, ?/2??k, 7?/6??k). Only with these echo
combinations can noise performance reach the maximum pos-
sible and be independent of the proportion of water and fat.
Close agreement between theoretical and experimental results
obtained from an oil–water phantom was observed, demon-
strating that the iterative least-squares decomposition method
is an efficient estimator. Magn Reson Med 54:636–644, 2005.
© 2005 Wiley-Liss, Inc.
Key words: fat suppression; fast spin echo; magnetic reso-
nance imaging; water–fat separation; asymmetric echoes; bra-
Reliable and uniform fat suppression is essential for accu-
rate diagnoses in many areas of MRI. This is particularly
true for sequences such as fast spin-echo (FSE) imaging, in
which fat is bright and may obscure underlying pathology.
Although conventional fat saturation may be adequate for
areas of the body with a relatively homogeneous Bofield,
there are many applications in which fat saturation rou-
tinely fails. This is particularly true for extremity imaging,
off-isocenter imaging, large field of view (FOV) imaging,
and challenging areas such as the brachial plexus and
skull base, as well as many others. Short-TI inversion
recovery (STIR) imaging provides uniform fat suppression,
but at a cost of a reduced signal-to-noise ratio (SNR) and
mixed contrast that is dependent on T1(1). This latter
disadvantage limits STIR imaging to T2-weighted (T2W)
applications, and current T1-weighted (T1W) applications
rely solely on conventional fat-saturation methods. An-
other fat-suppression technique used with FSE is the ap-
plication of spectral-spatial pulses; however, this method
is also sensitive to field inhomogeneities (2,3).
“In and out of phase” imaging was first described by
Dixon (4) in 1984, and was used to exploit the difference in
chemical shifts between water and fat in order to separate
water and fat into separate images. Glover (5) and Glover
and Schneider (6) further refined this approach in 1991
with a three-point method that accounts for Bofield inho-
mogeneities. Hardy et al. (7) first applied this method to
FSE imaging by acquiring three images with the readout
centered at the SE for one image, and symmetrically before
and after the SE in the subsequent two images. These
water–fat separation methods have since been combined
with both SE and FSE imaging for many applications (8–
13). Several of these three-point approaches acquire one
image with the readout centered at the SE and the other
two acquired symmetrically on each side of the SE
(5,7,13). This approach has the advantage of minimizing
the time between refocusing pulses of the FSE train while
providing sufficient time between echoes for phase be-
tween water and fat to evolve. Initial descriptions of the
relationship between the echo spacing and the noise per-
formance of the water–fat decomposition have been re-
ported (5,8,13); however, these approaches do not fully
characterize the theoretical noise performance of water–fat
It was recently demonstrated that decomposition of wa-
ter from fat with symmetrically acquired echoes cannot be
achieved when the proportions of water and fat within a
voxel are approximately equal (14–16). A complete char-
acterization of the theoretical maximum noise perfor-
mance of water–fat decomposition, including the effects of
field inhomogeneity estimation, was reported by Pineda et
al. (15,16). This work showed that the theoretical ability of
all water–fat separation methods to decompose water from
fat in a voxel is dependent on the relative proportions of
water and fat, as well as the position of acquired echoes
relative to the SE. The dependence on the proportions of
water and fat is particularly true for echoes that are ac-
quired symmetrically about the SE.
In this work we show both qualitatively and quantita-
tively a strong dependence of the noise performance of
1Department of Radiology, Stanford University Medical Center, Stanford,
2Applied Science Lab-West, GE Healthcare, Menlo Park, California, USA.
Grant sponsor: NIH; Grant numbers: P41 RR09784; 1RO1-EB002524; Grant
sponsors: Lucas Foundation; GE Healthcare.
*Correspondence to: Scott B. Reeder, M.D., Ph.D., Department of Radiology,
E3/311CSC,600 Highland Avenue,
Received 28 July 2004; revised 11 April 2005; accepted 18 April 2005.
Published online 9 August 2005 in Wiley InterScience (www.interscience.
Madison, WI,53792. E-mail:
Magnetic Resonance in Medicine 54:636–644 (2005)
© 2005 Wiley-Liss, Inc.
water–fat decomposition using echoes acquired symmet-
rically about an SE on the fat : water ratio within a voxel
and the choice of echo position. We propose a method
termed “iterative decomposition of water and fat with
echo asymmetric and least-squares estimation” (IDEAL).
This technique combines the acquisition of echoes ac-
quired asymmetrically with respect to the SE, and a re-
cently described iterative least-squares water–fat separa-
tion decomposition algorithm in order to maximize the
noise performance of the water–fat decomposition. The
behavior of symmetric and asymmetric echoes is verified
with an oil–water phantom using an iterative least-squares
water–fat decomposition method that permits the use of
arbitrary and unequally spaced echoes (13). Examples ob-
tained in volunteers and patients are shown for various
applications, including T2W and T1W imaging.
The phase shift between water and fat as a result of chem-
ical shift is
? ? 2? ?f t
where ?f is the chemical shift (Hz) between water and fat,
and t is the time relative to the SE. It is preferable to
calculate echo shifts in terms of ?, rather than t, because ?
is independent of field strength and provides more phys-
The noise performance of a water–fat decomposition is
conveniently described with the effective number of signal
averages (NSA), which can be defined as
where ?2is the variance of the noise in a source image and
image. Equation  is a helpful measure of the noise per-
formance of a water–fat decomposition. For any three-
point water–fat decomposition method, the maximum
possible NSA is 3, which is equivalent to what would be
obtained if the object contained only water or only fat, and
the three source images were averaged (5).
Figure 1a shows a 2D plot of the theoretical maximum
NSA of a calculated water image from three source images
acquired with echoes ?1and ?3shifted with respect to the
SE, when ?2is held fixed at zero and the voxel contains
mostly water (15,16). For symmetrically acquired echoes
(dashed line), the NSA increases to a maximum of 3 when
?1? –2?/3 and ?3? 2?/3 (asterisk, Fig. 1a). This combi-
nation of echoes (–2?/3, 0, 2?/3) is the optimum choice for
this case, and is an intuitive result that reflects equal
sampling around the unit circle (6). Figure 1b plots the
theoretical NSA for equal proportions of water and fat.
From this plot it can be seen that NSA is zero for almost all
choices of ?1and ?3, reflecting the fact that no water–fat
decomposition method can resolve water from fat when
they are in equal proportions. The only echo combination
that produces a nonzero NSA is (–?, 0, ?). However, this is
a singular result and any small deviation from this echo
spacing (e.g., –0.99?, 0, 0.99?) results in NSA ? 0 at this
fat : water ratio. The overall behavior of Fig. 2 agrees with
the geometrical prediction made by Wen et al. (14).
2is the variance of the noise in a calculated water or fat
FIG. 1. Theoretical NSA calculated against
?1and ?3for a voxel with (a) all water and (b)
water?fat, when ?2is fixed at zero at the SE.
Symmetrically acquired echoes occur along
the dashed line. Phase is plotted in units of
?. The asterisk indicates the optimal spac-
ing (2?/3) for the case in which the voxel
contains all water.
FIG. 2. Theoretical maximum NSA of pixels
in a calculated water image as a function of
fat : water ratio for (a) symmetric echoes
(–2?/3, 0, 2?/3; black curve), and (b) asym-
metric echoes (–?/6, ?/2, 7?/6).
Iterative Decomposition of Water and Fat 637
This effect is better illustrated in Fig. 2a, which plots the
theoretical maximum NSA of a calculated water image
against the fat : water ratio for symmetrically spaced ech-
oes (–2?/3, 0, 2?/3). From this figure it can be seen that
NSA meets the theoretical maximum (3) when the voxel
contains mostly water, and there is a broad minimum
when water and fat are in similar proportions. It is also
interesting to note that the theoretical NSA recovers to
only ?1.4 when the voxel contains mostly fat.
We calculated the NSA over a wide range of echo shifts
(?1, ?2, ?3) and fat:water ratios to determine the combina-
tion that maximized noise performance. From this analysis
we found that the combination of three echoes that maxi-
mized the NSA were those separated by 2?/3, with the
middle echo centered at ?/2??k (k ? any integer), i.e.,
(–?/6??k, ?/2??k, 7?/6??k). For practical SE and FSE
applications, the optimum echo combinations that mini-
mize the time between refocusing pulses are (–?/6, ?/2,
7?/6) and (–7?/6, –?/2, ?/6), which are equivalent from
the perspective of refocusing pulse spacing. Figure 2b
plots the theoretical maximum NSA against the fat:water
ratio for asymmetric echoes (IDEAL). A tremendous im-
provement in NSA from asymmetric echoes is seen in
comparison with the symmetric echoes, since the NSA
reaches the upper limit of 3 and is independent of the
fat : water ratio within a voxel.
MATERIALS AND METHODS
Phantom experiments were performed to quantitatively
validate the theoretical noise behavior of the water–fat
decomposition. A spherical phantom consisting of peanut
oil floating on 0.9% normal saline doped with 5 mM NiCl2
was imaged at 1.5T with an FSE pulse sequence modified
to shift the readout gradient with respect to the SEs (13).
Figure 3 shows axial calculated water (b) and fat (c) im-
ages, as well as a recombined (a) image through the oil–
water phantom. From this plane an obliquely oriented
slice was prescribed through the oil–water interface to
create a continuum of fat:water ratios. An extremity coil
and the following image parameters were used: Nx? 256,
Ny? 256, averages ? 1, FOV ? 20 cm, slice ? 9 mm, echo
train length (ETL) ? 16, BW ? ?31.3 kHz, and TR/TE ?
700/13.1 ms. TR and TE were empirically chosen to pro-
duce similar signal intensities from both water and fat.
Various combinations of symmetric and asymmetric ech-
oes were used. Although the time between refocusing
pulses (echo spacing) will vary with different echo shifts,
it was fixed at 13.1 ms to ensure that the MR signals, as
well as potential blurring in the phase-encoding direction,
were identical for all cases. Product automated shim rou-
tines were used for all of the phantom imaging.
For each combination of echoes, the phantom image
acquisition was repeated 200 times (scan time ? 2 hr
5 min, for 200 acquisitions), and water and fat images were
reconstructed with an online algorithm based on an itera-
tive least-squares algorithm, which easily accommodates
arbitrary TEs (13). This algorithm uses a “robust” region-
growing reconstruction algorithm (17) to prevent the wa-
ter–fat ambiguities that are commonly seen with water–fat
decomposition algorithms (5,6,17). The region-growing al-
gorithm uses field map estimates from nearby pixels to
improve the initial guess of the field map, ensuring that the
iterative algorithm converges to the correct solutions for
the field map, water, and fat. Although field map informa-
tion from nearby pixels is used, it does not affect the noise
performance of the water–fat decomposition for a given
pixel. The reason for this is analogous to phase-unwrap-
ping algorithms used with other water–fat separation
methods, that use a binary algorithm to choose between
two possible solutions, leaving the noise performance of
the solutions themselves unaffected (8,18,19). Smoothing
of the field map estimate, followed by computation of fat
and water signals based on the locally smoothed field map,
can improve the SNR water–fat decomposition, and may
be useful. However, this can also introduce bias or deter-
ministic errors in regions where the actual field map may
not be smooth. The effect of field map smoothing on noise
performance is an additional complexity that is beyond
the scope of this work. The NSA was calculated on an
individual pixel basis as the quotient of the variance of
each pixel from the three source images and the variance
of the calculated water image (Eq. ). Pixels outside the
phantom were excluded using a threshold mask. For each
pixel, the fat:water ratio was calculated from the ratio of
the average fat signal (computed over all 200 images) di-
vided by the average water signal (computed over all 200
sets of three source images). In this way, scatter plots of
measured NSA vs. fat:water ratio were made. All NSA
calculations (theoretical and experimental) were per-
formed with the use of offline programs written in Matlab
6.0 (Mathworks, Natick, MA, USA).
All human scanning was performed at 1.5T (Signa Twin-
Speed; GE Healthcare, Milwaukee, WI, USA) and 3.0T
(Signa VH/i; GE Healthcare, Milwaukee, WI, USA). The
knees, abdomen, and brachial plexus of healthy volunteers
and patients were imaged after approval was obtained
from our institutional review board (IRB) and informed
consent was given by the subjects. We used a modified FSE
pulse sequence to acquire three images with different echo
FIG. 3. Axial IDEAL FSE images through the
trating the obliquely prescribed slice (a) re-
combined image, (b) calculated water image,
and (c) calculated fat image. This slice creates
a continuum of fat:water ratios across the
slice through partial-volume effects. Note that
there is a small amount of water signal with
the oil region (b). W ? water, F ? fat.
638Reeder et al.
shifts. Fat-saturated FSE images were acquired for compar-
ison in many cases. Abdominal and pelvic imaging was
performed using a torso phased-array coil, knee imaging
was performed with an extremity coil, and brachial plexus
imaging was performed with a phased-array neurovascular
coil. All water–fat decomposition calculations were per-
formed with an online reconstruction algorithm based on
the iterative least-squares algorithm, which is capable of
multicoil reconstruction (13).
Figure 4 shows recombined, water, and fat images ac-
quired obliquely through the water–oil interface of the
phantom described in Fig. 3, for both asymmetric (IDEAL)
(a–c) and symmetric echoes (d–f). The IDEAL water image
(g) and symmetric water image (h) are also shown with
windowing to better demonstrate the increased noise in
the region that is mostly fat signal. The small amount of
signal in this region most likely caused olefinic compo-
nents of the oil that have resonant peaks very close to that
of water, reflecting an inherent limitation of all fat-sup-
pression methods that rely on the chemical shift between
water and fat (including water–fat decomposition meth-
ods) (20). The apparent increase in noise in the symmetric
water image can be explained by the curves shown in Fig.
2a for the high fat : water ratio. Note that Fig. 4 also shows
very noisy signal in the calculated symmetric water and fat
images in which water and fat are in similar proportions
(arrows). Drift in the magnitude and phase of these images
due to possible system instability was not observed over
the acquisition of the 200 images.
Figure 5 plots experimental NSAs from the phantom
experiments as a function of the fat : water ratio for four
different echo combinations: (–2?/3, 0, 2?/3), (–?/2, 0,
?/2), (–?/6, ?/2, 7?/6), and (0, ?/2, ?). Theoretical predic-
tions are shown as solid curves, and very close agreement
with experimental measurements is seen. The data from
Fig. 5c were fit to the linear equation: NSA ? slope * log10
(fat:water ratio) ? intercept. The intercept and slope were
calculated to be 2.901 ? 0.002, and 0.066 ? 0.001, respec-
tively, indicating very good agreement between experi-
ment and theory. The apparent scatter of the experimen-
tally measured NSA decreases when NSA approaches zero
(Fig. 5a and b). This occurs because NSA is the quotient of
the source image variance, which remains constant over
all fat : water ratios, and the variance of the calculated
water images, which becomes very large when the fat :
water ratio approaches one.
The theoretical and experimental plots of NSA perfor-
mance are shown for the NSA of calculated water images
only. A similar analysis was performed for the NSA of the
calculated fat images, but for brevity the results are not
included here. The theoretical and experimental NSAs of
the calculated fat images demonstrate almost identical be-
havior. The main difference is that the horizontal axis (i.e.,
the fat:water ratio) is reversed. For example, the NSA of fat
for symmetric echoes (–2?/3, 0, 2?/3) is 3 when the voxel
contains all fat instead of all water.
Figure 6 shows calculated water images from a T2W
sagittal knee acquisition at 3.0T acquired with symmetric
echoes (phase shifts ? –2?/3, 0, 2?/3; time shifts ?
–0.8 ms, 0 ms, 0.8 ms). For comparison, images acquired
with the IDEAL method (phase shifts ? –?/6, ?/2, and
through the oil–water interface of the oil–
water phantom with the IDEAL method
(–?/6, ?/2, 7?/6; top row), and symmetric
echoes (–?/2, 0, ?/2; bottom row). Recom-
bined (a and d), calculated water (b and e),
and calculated fat (c and f) images show
irregular and noisy signal when water and
fat are in similar proportions (black arrows).
g and h: The same water images as in b and
e, but windowed to better demonstrate the
increased noise in the water image from the
symmetric acquisition (h) in a region that
contains a small amount of water but is
mostly fat (white arrow). W ? water, F ? fat.
4. Oblique FSEimages acquired
Iterative Decomposition of Water and Fat 639
7?/6; time shifts ? –0.2 ms, 0.6 ms, and 1.4 ms) and
conventional fat saturation are also shown, as well as
magnified views of all three. Close inspection of these
images reveals several artifacts in the symmetric acquisi-
tion. Pixels that occur at interfaces between muscle (water
signal) and subcutaneous fat are very irregular and non-
anatomic. In addition, the signal in the bone marrow and
subcutaneous fat appears mottled and noisy. These arti-
facts are not seen in the IDEAL images and fat-saturated
images. Image quality was notably improved for all images
acquired with the IDEAL method compared to the sym-
metric images (not shown).
Several clinical examples acquired with IDEAL imaging
are shown in Figs. 7–10. Figure 7 shows recombined,
water, and fat images in the pelvis of a female patient with
a right adnexal mass, obtained at 1.5T. Direct visualization
of fat within this mass in the calculated fat image is diag-
nostic of a mature ovarian teratoma (dermoid). Figure 8
shows T2W FSE recombined, and calculated water and fat
images of the knee of a patient with pre-patellar edema. A
comparison with fat-saturated T2W images shows an area
of failed fat saturation that would lead to erroneous over-
estimation of the extent of the edema. Figure 9 shows
examples of sagittal T1W and coronal T2W images of the
brachial plexus and cervical spine acquired at 1.5T using a
neurovascular coil. A comparison with fat-saturated im-
ages shows marked improvement in the uniformity of fat
suppression across the images. Figure 10 shows two con-
(dots) plotted against measured fat : water
ratio for a) symmetric echoes (–2?/3, 0, 2?/
3), b) symmetric echoes (–?/2, 0, ?/2), c)
asymmetric echoes (–?/6, ?/2, 7?/6), and d)
asymmetric echoes with shortened echo
spacing (0, ?/2, ?). Smooth black lines in-
dicate the theoretical maximum NSA for
pixels in the calculated water image. Excel-
lent agreement between experimental mea-
surements and theory is seen.
5. Experimentallymeasured NSA
FIG. 6. Sagittal T2W FSE images through
the knee of a normal volunteer at 3.0T using
(a) symmetric echoes (–2?/3, 0, 2?/3), (b)
(IDEAL), and (c) fat saturation. Images in the
second row (d–f) are closeup views of cor-
responding images in a–c. Note the irregu-
lar margins between muscle and fat in the
symmetric echo image (white arrows), as
well as increased noise in the bone marrow
and subcutaneous fat. Image parameters:
TR/TE ? 5000/48 ms, matrix ? 384 ? 192,
FOV ? 16 cm, slice/gap ? 3.0 mm/0.5 mm,
ETL ? 10, BW ? ?31.25 kHz, total scan
time for entire knee ? 5 min 5 s.
640Reeder et al.
secutive calculated water images from a T1W MR arthro-
gram, acquired at 1.5T with a torso phased-array coil after
intra-articular injection of dilute Gd-DTPA.
Echoes acquired symmetrically about an SE can lead to the
inability of estimation methods to resolve water from fat
when they are in similar proportions within a voxel. This
can lead to image artifacts, such as irregular interfaces, and
increased noise in certain regions of the image. One can
achieve the maximum NSA of 3 for all fat:water ratios by
setting the phase of the middle image at ?/2 ? ?k (k ? any
integer) and spacing the other two images 2?/3 before and
after the middle image. Theoretical predictions of the max-
imum NSA were verified experimentally with an oil–water
phantom, for several combinations of symmetrical and
asymmetrical echoes. The experimental noise perfor-
mance matched theoretical predictions closely for both
symmetric and asymmetric echoes, demonstrating that the
iterative method is an efficient estimator that achieves the
best possible NSA for a given echo combination (21). With
the use of the IDEAL method, the noise performance of
water–fat separation in pixels with varying proportions of
fat is maximized, the dependence of NSA on the fat:water
ratio is eliminated, and the image artifacts that arise with
symmetric echo acquisitions are avoided. Several clinical
examples acquired with the IDEAL method are shown at
both 1.5T and 3.0T, demonstrating the feasibility of both
T1W and T2W imaging to obtain high-quality, high-SNR,
multicoil images with uniform water–fat separation.
Three-point water–fat separation methods that position
the phase of the center at ?/2 were described by Xiang and
An (8), and used by Ma et al. (12) as part of a (0, ?/2, ?)
combination. Although this choice of echoes helps to re-
duce the dependence of NSA on the fat:water ratio (Fig.
5d), these implementations were not designed for this
purpose. This choice of echoes has the primary advantage
of simplifying the analytical solutions that decompose wa-
ter and fat (8).
Uniform noise performance across all fat:water ratios
may be particularly important for special imaging applica-
tions that require quantification of the relative amounts of
water and fat within tissues (e.g., fatty liver in nonalco-
holic steatohepatitis (22), adrenal masses (23), etc.).
One can intuitively understand symmetric echoes, as
well as the asymmetric echoes used in the IDEAL method,
by realizing that complex images acquired symmetrically
before or after an SE are Hermitian conjugates of one
another, and therefore contain the same information. In
addition, all phase information is lost in echoes that are
acquired at the SE when chemical shift and field inhomo-
geneities are fully refocused. In general, at least three
unique images acquired at different TEs are required to
resolve water from fat (5,13). If an image is acquired when
the phases of water and fat are orthogonal, (i.e., the phase
shift between water and fat is ?/2??k (k ? any integer)),
and there are no additional phase shifts from field inho-
mogeneities or other sources (e.g., coil, receivers, flow,
etc.), water and fat could, in theory, be resolved simply
from the real and imaginary components of this image,
respectively (24,25). However, two additional images are
needed to compensate for field inhomogeneities and con-
stant phase shifts. These additional echoes are ideally
positioned so that the phase shift from the water–fat chem-
ical shift is sampled equally around the unit circle, i.e.,
2?/3 before and after the middle image that is acquired at
Water–fat separation methods have several disadvan-
tages. First, the additional time needed to shift readout
gradients to acquire echoes at different TEs may reduce
sequence efficiency. For FSE, echo shifts will increase the
time between refocusing pulses (echo spacing) and
lengthen the overall echo train time, and may result in
increased blurring (26). This will be most problematic
with proton density FSE imaging, in which the central
FIG. 7. IDEAL recombined (a), calculated water (b), and calculated
fat (c) images through the pelvis of a woman with a mature ovarian
teratoma (long arrows) acquired using a torso phased-array coil at
1.5T. The fat image clearly shows the extensive fat content of this
mass, and the water image shows subtle amounts of free fluid (short
arrow). Image parameters: TR/TE ? 5000/60 ms, matrix ? 384 ?
192, FOV ? 40 cm, slice/gap ? 9 mm/5 mm, ETL ? 10, BW ?
?31.25 kHz, total scan time for pelvis ? 5 min 5 s.
Iterative Decomposition of Water and Fat641
FIG. 8. IDEAL recombined (a), calculated
water (b), calculated fat (c) sagittal T2W FSE
images acquired in the knee of a patient
volunteer at 1.5T. Pre-patellar edema (long
arrows) in the calculated water image is
more accurately depicted in the IDEAL wa-
ter image than in the fat-saturated T2W im-
age that is shown for comparison (d). Areas
of failed fat saturation (short arrow) may
have overestimated the extent of the pre-
patellar edema. The scan time for the entire
knee was 5 min 30 s for both IDEAL and fat
saturation methods. Image parameters: TR/
TE ? 4000/48 ms, matrix ? 384 ? 256,
FOV ? 16 cm, slice/gap ? 2.5 mm/0.5 mm,
ETL ? 10, BW ? ?31.25 kHz, total scan
time for knee ? 5 min 20 s.
FIG. 9. Sagittal T1W IDEAL water (a) and
fat-saturated T1W (b) images of the bra-
chial plexus acquired with a phased-array
neurovascular coil. Coronal T2W IDEAL
water (c) and fat-saturated (d) images are
also shown. Tremendous improvement in
the uniformity of fat suppression is seen in
both T1W and T2W IDEAL imaging. Note
the “pseudo-tumor” appearance of the
failed fat saturation just superior to the lung
apices (thin arrows) and other regions of
failed fat saturation (thick arrows). Image
parameters for T2W images: TR/TE ?
4325/55 ms, matrix ? 384 ? 192, FOV ?
24 cm, slice/gap ? 4.5 mm/0.5 mm, ETL ?
10, BW ? ?20 kHz, total scan time for
unilateral brachial plexus and cervical
spine ? 4 min 33 s. Image parameters for
T1W images: TR/TE ? 650/12 ms, 384 ?
192, FOV ? 24 cm, slice/gap ? 4.5 mm/
0.5 mm, ETL ? 2, BW ? ?20 kHz, total
scan time for unilateral brachial plexus and
cervical spine ? 6 min 20 s.
642Reeder et al.
lines of k-space are acquired first and the outer lines of
k-space have substantial T2weighting. Blurring should not
be problematic for T2W and T1W imaging because early
echoes are weighted to the edges of k-space in T2W imag-
ing, and echo trains are short for T1W imaging. We have
not experienced any subjective increase in blurring with
proton-density IDEAL imaging compared to conventional
proton-density imaging for typical clinical imaging param-
eters (ETL ? 8–12). The increase in echo spacing will be
greater for the IDEAL method than for other FSE water–fat
separation methods (7,12,13). For example, the echo spac-
ing for a (–?/6, ?/2, 7?/6) combination will increase by
5.5 ms at 1.5T and 2.8 ms at 3.0T. In comparison, the (0,
?/2, ?) combination (8,12) will increase the echo spacing
by 4.8 ms at 1.5T and 2.4 ms at 3.0T. The latter combina-
tion of echoes reduces the increase in echo spacing by only
14%, while the NSA is decreased from 3 to approximately
2 (Fig. 5). For low-bandwidth imaging (?16–32 kHz), the
increment in echo spacing required for water–fat separa-
tion is a small fraction of the total echo spacing, usually
less than 30%. In fact, the overall sequence efficiency of
FSE water–fat separation methods may actually improve
in comparison with fat-saturation techniques, because the
overhead required for the fat-saturation pulse and accom-
panying crusher gradients is no longer required. This is
particularly true for short echo train sequences, especially
in T1W imaging.
The major disadvantage of most water–fat separation
methods is the threefold increase in the minimum scan
time. With IDEAL imaging, the SNR efficiency is very high,
since all information from source images is used efficiently
in the water–fat decomposition. In comparison to a fat-
saturated acquisition with three averages, there is no time
or SNR penalty. In addition, fat and recombined images
are provided in addition to the water image, and are avail-
able for review by the radiologist. Finally, while oversam-
pling in the phase-encoding direction, which is commonly
used to prevent aliasing (“no phase wrap”), works well
with water–fat separation methods, it currently requires an
additional doubling of scan time, which is a sixfold in-
crease from the time required for a single source image.
Although these acquisitions are also very SNR-efficient, in
our experience this increase in scan time is often prohib-
itive for clinical applications.
Early attempts to reduce the minimum scan time fo-
cused on combining parallel imaging (27,28) with water–
fat separation methods. Early results have been very prom-
ising (29–31). Parallel imaging plays a complementary role
with these methods: increases in acquisition time from
water–fat separation methods are offset by parallel imag-
ing, and decreases in SNR from parallel imaging ap-
proaches are offset by gains in SNR from water–fat decom-
Reductions in scan time can also be achieved with par-
tial k-space acquisitions that reduce the number of phase-
or depth-encoding steps used (for 3D acquisitions). Partial
k-space acquisitions in the readout (frequency) direction
are commonly used for ultrashort TR sequences to help
reduce TR and first-moment velocity phase shifts from the
readout gradient. Such acquisitions depend on homodyne
(25) or related reconstruction algorithms (32) to obtain
full-resolution images. Unfortunately, these methods de-
modulate the phase information from the source images
that is needed by water–fat decomposition algorithms to
separate water from fat. Zero-filling the k-space matrix is
an effective alternative, but reconstructed water and fat
images will suffer from blurring in comparison with con-
ventional images reconstructed with partial k-space algo-
rithms (13). Early attempts to apply homodyne reconstruc-
tion to water–fat separation methods have been described
(12), but this method has only been applied to source
images that contain water and fat that are in phase (zero) or
out of phase (?), and has not been applied to phase shifts
other than zero or ?.
A similar analysis of echo optimization can be easily ex-
tended to other pulse sequences, including gradient-echo
(GRE) and steady-state free precession (SSFP) sequences. For
GRE sequences, water and fat are aligned when TE ? 0, and
all echo shifts are referenced to this time point. Because all
echo shifts must be positive, the echo shift for the middle
echo of a GRE water–fat separation acquisition that maxi-
mizes NSA performance is ?/2 ? ?k (k ? 1). For example, an
optimal echo combination for a three-point GRE acquisition
is (5?/6, 3?/2,13?/6) with corresponding time shifts of
1.98 ms, 3.57 ms, and 5.16 ms at 1.5T, or 0.99 ms, 1.79 ms
and 2.58 ms at 3.0T. For SSFP, water, and fat refocus at TE ?
TR/2 (33,34), and therefore phase shifts for water–fat separa-
tion should be referenced to zero at TR/2. At this time point,
water and fat will refocus in either an aligned or anti-aligned
orientation depending on the TR and the local field inhomo-
geneity (33,34). The difference between aligned and anti-
aligned voxels is equivalent to a ? phase shift created by a
water–fat chemical shift. Fortunately, a ? phase shift will
shift one group of optimally spaced echoes to another group
FIG. 10. Coronal T1W IDEAL water images from
two consecutive slices of an MR hip arthrogram
performed after intra-articular injection of dilute
Gd-DTPA. Excellent depiction of the transverse
ligament (long arrow) and labrum (short arrow) is
seen, with uniform suppression of fat across all
images. Image parameters: TR/TE ? 600/12 ms,
matrix ? 384 ? 192, FOV ? 20 cm, slice/gap ?
4 mm/0.5 mm, ETL ? 2, BW ? ?32 kHz, NEX ? 2
(“no-phase wrap” on), total scan time for hip ?
6 min 30 s.
Iterative Decomposition of Water and Fat 643
with an identical NSA performance. For example, a SSFP
acquisition with phase shifts of (–7?/6, –?/2, ?/6) with re-
spect to TE ? TR/2, has the same noise performance as
effective phase shifts of (–?/6, ?/2, 7?/6) or (–13?/6, –3?/2,
–5?/6), which both have NSA ? 3 for all fat:water ratios.
Algorithms that optimize echo shifts for SSFP are complex
because echo positions affect many sequence parameters that
determine TR, while TR determines the reference point
this optimization is beyond the scope of the current study.
Careful selection of the TE is essential for SE and FSE water–
fat separation applications in order to optimize the perfor-
mance of water–fat decomposition in voxels with varying
relative quantities of water and fat. Poor selection of echo
shifts may cause image artifacts in calculated water and fat
images resulting from variation in the maximum theoretical
noise performance for different fat:water ratios within a
voxel. Noise performance can be maximized, and its depen-
dence on the fat:water ratio can be eliminated using the
IDEAL method. The middle image is acquired with a water–
fat phase shift of ?/2??k (k ? any integer), and the other two
images are acquired with phase –2?/3 and 2?/3 with respect
to the middle image. For FSE and SE applications, a practical
combination of echo shifts is (–?/6, ?/2, 7?/6) or (–7?/6,
–?/2, ?/6) with respect to the center of the SE. In addition,
the noise performance of the iterative least-squares water–fat
estimation method used in this work matches the theoretical
maximum, demonstrating that it is an efficient estimation
method. IDEAL separation of fat and water in clinical imag-
proton density imaging with and without intravenous or
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