Dwight G. Nishimura

Krishna S. Nayak

English

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Automatic Field Map Generation and Off-Resonance
Correction for Projection Reconstruction Imaging
Krishna S. Nayak* and Dwight G. Nishimura
A new projection reconstruction technique utilizes the over-
sampling of low spatial frequencies to estimate and correct
for off-resonance effects. Interleaved spokes are acquired at
one of two different echo times. From separated early-TE and
late-TE raw data, two one-quarter resolution images are re-
constructed and a one-quarter resolution field map is com-
puted. Multifrequency reconstruction with all the data is then
used to simultaneously correct for off-resonance and compen-
sate for the difference in echo times. Resulting images obtained
on phantoms and in vivo demonstrate significantly reduced
off-resonance artifact without the acquisition of a separate field
map. Magn Reson Med 43:151–154, 2000. r 2000 Wiley-Liss,
Inc.
Key words: projection reconstruction; off-resonance; pulse
sequences; reconstruction
Projection reconstruction (PR) is a popular MR imaging
technique. PR is gaining increasing popularity because of
its ability to achieve short echo times and to produce
images with minimal motion or flow artifacts. Short echo
times are particularly important in the imaging of short
T2 species (1) and in rapid imaging (2). Reduced mo-
tion artifacts (3) are important again for dynamic im-
aging, and particularly for angiography (4) and functional
MRI (5).
Inherent in PR imaging is the oversampling near the
k-space origin. This is considered to be a strong advantage
because it is well known that the low spatial frequencies
contain most of the energy in images. This oversampling
can however be exploited to improve imaging in other
ways. For example, image field of view (FOV) is often
calculated based on an inner area of k-space, tolerating
spoke artifacts from insufficiently sampling the outer
regions (6–9).
One drawback of PR is that off-resonant spins cause
blurring. The most common way to compensate for this
blurring involves acquiring a field map with an additional
scan and using a frequency-sensitive reconstruction to
compensate for off-resonance (10,11).
We present a technique that corrects for off-resonance
without a separate field-map acquisition. This technique
incorporates a field map acquisition within PR imaging by
interleaving spokes with two different echo times (TEs).
The acquired data is then used both to generate a low-
resolution field map, and to reconstruct the final image
with off-resonance correction. Results from phantom stud-
ies and in vivo studies are presented.
THEORY
In MR imaging, the Fourier relationship between image
domain and k-space, yields the following signal equa-
tion
S(t) 5 e
x,y
M(x, y)e22pi(kx(t)x1ky(t)y) dx dy [1]
where M(x, y) is the imaging slice and kx(t) and ky(t) are the
k-space trajectories determined by the linear gradients
fields; that is, kx(t) 5 g/2p e0
t
Gx(t) dt and ky(t) 5 g/2p e0
t
Gy(t) dt. In the presence of field inhomogeneity or off-
resonance the signal equation translates into the relation-
ship shown in Eq. [2].
S(t) 5 e
x,y
[M(x, y)e22piDf(x,y)t]e22pi(kx(t)x1ky(t)y) dx dy [2]
where Df(x, y) is the shift in the precession frequency at
point (x, y) in object space. If all of k-space were acquired at
the same instant (at the same time t), off-resonance would
not affect a reconstructed magnitude image. However,
acquisition windows have durations on the order of 2 to 8
msec, which introduces off-resonance artifacts. Note that
techniques that use longer readouts experience increased
artifact.
One way to compensate for off-resonance is to acquire a
field map to estimate Df(x, y) and to use this information to
better reconstruct the final image. The field map or off-
resonance map Dfm(x, y), can be computed by acquiring
two images at different echo times and comparing the
phase images at each location. These complex images
would represent M(x, y)e22piDf(x,y)TE1 and M(x, y)e22piDf(x,y)TE2.
The off-resonance term Df(x, y) is then simply found by
computing the phase difference between these two images
divided by the difference in echo times (TE2 2 TE1).
METHOD
Pulse Sequence
Figure 1 illustrates the pulse sequence. Flow-compensated
excitations are followed by radial spoke readouts and
dephasing pulses in the slice-select direction. Every alter-
nate spoke acquisition is delayed by a small amount
labeled DTE. For convenience, delayed spokes are labeled
‘‘late-TE’’ spokes, and non-delayed ones are labeled ‘‘early-
TE’’ spokes. Notice that this pulse sequence is identical to
conventional PR except for the echo delay between early-TE
and late-TE acquisitions.
Magnetic Resonance Systems Research Laboratory, Department of Electrical
Engineering, Stanford University, Stanford, California.
Grant sponsors: National Institutes of Health; GE Medical Systems; Fannie and
John Hertz Foundation.
*Correspondence to: Krishna S. Nayak, Packard 211, ISL, 350 Serra Mall,
Stanford University, Stanford, CA 94305-9510. E-mail: nayak@lad.stanford.edu
Received 9 July 1999; revised 1 September 1999; accepted 13 September
1999.
Magnetic Resonance in Medicine 43:151–154 (2000)
151r 2000 Wiley-Liss, Inc.
Field Map Computation
The central portion of k-space is then used to generate two
lower resolution images with different echo times–one
from the early-TE spokes and one from the late-TE spokes
(see Fig. 2). These images are formed from k-space data
within a disk of half the radius of the total extent covered
in k-space. Each of these images are therefore of one-
quarter resolution (i.e., half resolution in both the x and
y directions). Since image FOV is related to the maxi-
mum spacing of k-space samples, both low-resolution
images also have the same FOV as the final full-resolution
image.
A field map Dfm(x, y) is then computed in a standard
way, using the phase difference between the two low-
resolution images, Ilate-TE and Iearly-TE:
Dfm(x, y) 5
arg (Ilate-TEI*early-TE)
22pDTE
[3]
The measurable range of this field map (in Hz) is notably
limited by the off-resonance that will cause a phase shift of
6p after DTE:
0Dfm(x, y) 0 ,
1
2DTE
[4]
Since field map estimates are reliable in areas of suffi-
cient signal, a smooth polynomial approximation Dfp(x, y)
(12) is computed for use during reconstruction. This
polynomial field map Dfp(x, y) is found using a weighted
least-squares algorithm which minimizes:
o
i,j
wij[Dfp(xi, yj) 2 Dfm(xi, yj)]2 [5]
where wij measures the importance of minimizing the error
at that voxel. The weighting used is proportional to the
square magnitude of the voxel signal. In the final reconstruc-
tion step, we use this polynomial fit as our field map.
Image Reconstruction
Multifrequency image reconstruction is used to compen-
sate for off-resonance in the image while simultaneously
correcting for the different echo times (11,13). In multifre-
quency reconstruction, a finite set of frequency samples 5fn6
are selected such that they span the full range of off-
resonance frequencies. For each fn an image is recon-
structed based on that frequency of precession. This is
done by modulating the raw data of each readout by e12pifnt.
In order to use both the early-TE and late-TE measurements
for each fn image, the sets are phase-aligned by multiplying
the raw data from late-TE acquisitions by e12pifnDTE. An
image is then generated via gridding reconstruction (14)
with both early-TE and late-TE data. For the final image,
each voxel is estimated by interpolating between the
images based on the closest 5fn6 frequency samples to
Df(x, y).
In summary, early-TE and late-TE spokes are acquired at
different echo times. A low-resolution field map is com-
puted using the oversampled central region of k-space.
Finally, multifrequency reconstruction is used to correct
for off-resonance. This off-resonance correction is imple-
mented with no additional scan time and a modest in-
crease in reconstruction time.
RESULTS
Images shown here were acquired on a GE Signa 1.5 T
system. PR acquisitions consisting of 512 radial spokes
were used to achieve an image resolution of 163 3 163
pixels (0.98 mm resolution over a 16 cm circular FOV, or
0.74 mm resolution over a 12 cm circular FOV). Unless
specified, each spoke readout lasted 8.192 ms, providing
256 samples. Off-resonance corrected PR images used a 1
msec DTE, 12th order polynomial fit (including cross
terms) for the field map, and 10 frequency samples during
FIG. 1. Off-resonance corrected PR-pulse sequence: A small-tip
excitation (flow-compensated excitation is shown) is followed by a
refocused readout that acquires one radial spoke, and a crusher to
dephase remaining signal. Late-TE acquisitions have a delayed
readout and echo, as shown.
FIG. 2. k-space coverage. Of the full
coverage (left), solid lines represent
early-TE acquisitions and dotted lines
represent late-TE acquisitions. Early-TE
and late-TE low resolution images (middle
and right) are each computed from half of
the data in the central portion of k-space.
These images have the same FOV as
the final image, and have one-quarter the
resolution—one-half in both x and y.
152 Nayak and Nishimura
multifrequency reconstruction. A 1 msec DTE yields an
off-resonance range of 6500 Hz.
Results of this technique applied to a resolution phan-
tom are shown in Fig. 3. These images were acquired
using a head coil, 16 cm FOV, 3 mm slice thickness, 300
msec TR, 4.5 msec TE, and 90° flip angle. Figure 3a is the
result of a conventional PR scan (without DTE or off-
resonance correction). Figure 3b–d show corresponding
segments of the estimated field map, polynomial fit field
map, and the corrected image using our new scan and
reconstruction technique. The measured off-resonance was
entirely within the range of [238.3 to 19.4] Hz. The
corrected image shows improved definition in the comb
structure which is visible in cropped images (see Fig. 3e–f).
This improvement is greater for sequences with long
readouts, but is apparent even when imaging with shorter
readouts.
To demonstrate this method in vivo, we applied it to
peripheral angiography using 2D time of flight (TOF).
Images were acquired using an extremity coil, 12 cm FOV,
3 mm slice thickness, 33 msec TR, 4.5 msec TE, and 60° flip
angle. In this application, the presence of lipids and their
chemical-shift causes sharp discontinuities in the acquired
field map. To correct for smooth off-resonance variations
(main field inhomogeneity), lipid voxels are excluded from
the polynomial fitting. These lipid voxels are excluded by
masking voxels with a measured Dfm of at least 110 Hz
below the center frequency of water. Figure 4 illustrates a
conventional PR slice and the equivalent slice using our
new acquisition and reconstruction scheme. When recon-
structing these datasets, the field map estimate can be
customized to the application. When using a polynomial
fitted field map, with fat excluded from the fitting, slice
images show improved vessel definition (see Fig. 4b–c).
When using a hybrid field map consisting of the measured
off-resonance in areas of high signal, and the smooth
estimate elsewhere, resulting slice images show improved
definition in vessels and areas of fat, while introducing
some edge enhancement due to field map discontinuity
(see Fig. 4d–e).
Figure 5 illustrates targeted maximum intensity projec-
tions (MIPs) of peripheral vasculature imaged with and
without our technique. These images were acquired using
an echo time of 6.3 msec, which places water and fat
out-of-phase, and using a saturation pulse to suppress
FIG. 3. Resolution phantom images using 8.192 msec readouts.
Imaged with (a) conventional PR, and with off-resonance correcting
PR resulting in images of the (b) acquired field map, (c) smooth
polynomial fit field map, and (d) final reconstruction. The range of the
field map images is 238.3 to 19.4 Hz. Close-ups of the comb
structure in a and d are shown in e and f.
FIG. 4. In vivo example: An axial slice of the lower leg imaged with
(a) conventional PR and (b–e) PR with off-resonance correction. For
imaging vasculature, fat is ignored during field map approximation
Dfp (b) and the resulting corrected image (c) shows improved vessel
definition. Alternatively, the computed field map Dfm (d) can be used
directly during reconstruction, resulting in (e) improved definition in
areas of fat with added edge enhancement due to field map
discontinuity.
PR Off-Resonance Correction 153
signal from veins. The MIPs constructed with off-reso-
nance correction show improved vessel definition through-
out the popliteal trifurcation and decreased blurring.
DISCUSSION
In summary, PR can be modified by interleaving delayed
acquisitions with non-delayed acquisitions. This allows a
low resolution field map to be computed with no addi-
tional scan time and only a slight increase in reconstruc-
tion time. Multifrequency reconstruction can then be used
to compensate for off-resonance artifacts. Phantom and in
vivo studies indicate this is a practical method for reducing
off-resonance induced blurring. This technique is demon-
strated with radial spoke acquisitions, but works for full
projections as well.
This technique is a general one that is applicable to many
different k-space trajectories that oversample the low spa-
tial frequencies. It can be easily adapted for use with 3DPR,
twisting radial lines (TwiRL), and variable density spiral
(VDS) acquisitions. Ideal applications for this PR-based
technique are applications that require short echo times,
good flow and motion properties, and that suffer from
off-resonance artifacts.
For imaging ultra short T2 species, there is the added
consideration of mixed contrast. Since images are formed
from acquisitions at two echo times, differences in contrast
between those two echoes will produce streaking artifacts.
This streaking is similar to what is seen in angularly
undersampled PR because both echo images are angularly
undersampled during the final image reconstruction. In
general, this off-resonance correcting technique is in-
tended for areas where a small DTE does not significantly
alter image contrast.
ACKNOWLEDGMENTS
This work was supported by the National Institutes of
Health, GE Medical Systems, and by a Fannie and John
Hertz Foundation Graduate Fellowship to Krishna S. Nayak.
The authors thank Gerard Luk-Pat, Brian Hargreaves, Hat-
sumi Nielsen, and John Pauly for useful explanations and
assistance.
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FIG. 5. Targeted maximum intensity projections of the popliteal
trifurcation using multislice 2D TOF and venous saturation. Imaged
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154 Nayak and Nishimura


Automatic field map generation and off-resonance correction for projection reconstruction imaging

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Automatic field map generation and off-resonance correction for projection reconstruction imaging

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