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2002 ARRS President's Award |
1 Department of Radiology, Stanford University Medical Center, 300 Pasteur Ave.,
Rm. H1306, Stanford, CA 94304.
2 Department of Radiology, Veterans Affairs Palo Alto Health Care System, 3801
Miranda Ave., Palo Alto, CA 94304.
Received April 5, 2002;
accepted after revision July 17, 2002.
Supported by grants from the Department of Veterans Affairs Rehabilitation
Research and Development Service, the Whitaker Foundation, and the Lucas
Foundation and by grants P41-RR09784 and R01-AR46904 from the National
Institutes of Health.
Abstract
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SUBJECTS AND METHODS. The cartilage of 10 knees in five healthy volunteers was imaged with 3D SSFP imaging and a multipoint fat—water separation method capable of separating fat and water with short TE increments. Fat-saturated 3D spoiled gradient-echo (SPGR) images were obtained for comparison.
RESULTS. High-quality images of the knee with excellent fat—water separation were obtained with 3D SSFP imaging. Total imaging time required was 58% less than that required for 3D SPGR imaging with a comparable cartilage signal-to-noise ratio and spatial resolution. Unlike 3D SPGR images, 3D SSFP images exhibited bright synovial fluid, providing a potential arthrographic effect.
CONCLUSION. High-quality high-resolution images of articular cartilage with improved fat—water separation, bright synovial fluid, and markedly reduced acquisition times can be obtained with 3D SSFP imaging combined with a fat—water separation technique.
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An ideal technique for imaging articular cartilage is one that produces high resolution and good contrast relative to the adjacent tissues; these factors can be markedly improved with the use of fat-suppression techniques [4]. In addition, a technique that produces a bright appearance in synovial fluid is advantageous because the arthrographic effect "fills in" defects in articular cartilage, increasing the conspicuity of cartilage irregularities. Finally, an ideal sequence for imaging articular cartilage is one in which scanning times are short, so that little additional time is required to perform standard joint protocols.
Because of the widespread availability of high-speed gradient MR imaging systems, interest has recently been renewed in steady-state free precession (SSFP), a rapid gradient-echo MR imaging technique [5,6,7]. SSFP has a superior signal-to-noise ratio (SNR) compared with other gradient-echo techniques and has excellent contrast behavior with varying dependence on T1 and T2. Synovial fluid appears bright on SSFP images because of its long T2. The major limitation of SSFP is severe image degradation caused by local magnetic field inhomogeneties if the TR is long [7].
In this article, we present a generalized mathematic formulation for multiecho fat—water separation that allows the use of small TE increments; we applied this formula to three-dimensional (3D) SSFP imaging of articular cartilage in the knees of healthy volunteers. For comparison, we also obtained 3D spoiled gradient-echo (SPGR) images with fat saturation.
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, and 2
when the frequency difference between fat and water at 1.5 T is approximately
-220 Hz. These TE values lengthen the minimal TR and cause severe image
degradation with SSFP imaging in the presence of typical magnetic field
inhomogeneities. Figure
1A,1B
shows two sagittal SSFP images of a knee. The image acquired with a longer TR
exhibits substantial signal dropout throughout the bone marrow of the tibia
and femur, whereas the image acquired with a reduced TR shows substantially
reduced signal dropout in the bone marrow.
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Generalized Multipoint Fat—Water Separation
To address this problem, a generalized formula for fat—water
separation was developed to allow use of lower TE increments than those used
in standard three-point techniques. The signal from a voxel composed of water
(
w) and fat
(f) acquired at TE
tn in the presence of a resonance offset
(Hz), due to field in homogeneity can be written as follows:
 | (1) |
f is the
difference in resonance frequency between fat and water (Hz). If N
images, sn (n = 1,..., N) are
acquired with TE tn, then an estimate of the
water and fat images can be made using the linear least squares approach
described in Appendix 1 if the resonance offset, , can be
estimated. Although images acquired at any tn can
be used, optimal sampling to maximize SNR performance is achieved when points
are evenly spaced with TE increments of 1 / (N f)
[9]. This increment ensures
uniform phase sampling of the fat—water phase shift at intervals of
2 / N. For example, the optimal sampling at 1.5 T for a
three-point technique occurs when the TE increments are 0, 1.52, and 3.03
msec, leading to a fat—water phase difference at 0, 2 / 3,
and 4 / 3, respectively. Typical three-point schemes often use TE
increments of 0, 2.27, and 4.54 msec to achieve sampling at 0, , and 2
because the mathematics for this special case are greatly simplified and
postprocessing calculations are faster
[9].
Off-Resonance Map Estimation and Sorting
Several methods are available to determine the off-resonance map,
, including the standard three-point techniques
[9] and the modified two-point
techniques [10].
Unfortunately, these methods are not suited for short TE increments. A
convenient three-point method suitable for short TE increments has been
described by Xiang and An [11]
but only determines solutions for w and
f. Expanding on this work, we can calculate
two solutions of the off-resonance map for each pixel, as described in
Appendix 2. In regions containing only fat or only water, the two solutions
reflect the natural ambiguity that results from the fact that the on-resonance
water is indistinguishable from fat that is off-resonance by 220 Hz. This
factor causes abrupt transitions in the calculated off-resonance map that
results in some pixels from the water image being incorrectly assigned to the
fat image and vice versa when inserted into equation 3 of Appendix 1. We have
found that the "local orientation filter" described by Xiang and
An is an effective means of filtering the two solutions of the off-resonance
map, removing ambiguities in fat—water assignment. Like most
phase-sorting algorithms, the local orientation filter is based on the
supposition that the off-resonance map varies slowly with position, which is
generally a good assumption. Details of the local orientation filter are
outlined in Appendix 2. Insertion of the two filtered solutions of
into equation 3 in Appendix 1 yields both the water image and
fat image.
Optimal SSFP Tip Angle
The tip angle (
) that maximizes the signal of an SSFP image for a
material with a given T1, T2, and TR is given by the equation
[7,
12]
 | (2) |
Human Subjects
A 1.5-T scanner (40 mT/m maximum gradient strength, 150 mT/m per
millisecond slew rate; Signa, General Electric Medical Systems, Milwaukee, WI)
was used to acquire sagittal and axial images of the 10 knees of five
volunteers (three men, two women; age range, 28-39 years; mean age, 33.6
years) using an extremity coil. The left knee of one volunteer had had a
previous anterior cruciate ligament repair with titanium orthopedic fixation
devices in the distal femur and proximal tibia. The study was approved by our
institutional review board for human subjects. Before imaging, informed
consent was obtained from all volunteers.
Pulse Sequences
A 3D SSFP imaging sequence was used with the following imaging parameters:
Nx, 256; Ny, 192;
Nz, 64; field of view, 16 cm; and slice
thickness, 1.5 mm for voxel dimensions of 0.63 x 0.83 x 1.5
mm3. Other parameters included number of signal averages, 1;
bandwidth, ± 125 kHz; and TR/TE, 6.14/1.16, 2.08, 3.00, and 3.92. A
fractional echo was used to reduce TR and the minimum TE. Separate sequential
scans were obtained for each TE, and total scanning time for all four TE
parameters was 5 min 2 sec. Linear autoshimming was used. Using equation 2, we
chose 27° as the tip angle on the basis of published relaxation properties
of hyaline cartilage (T1, 674 msec and T2, 40 msec at 1.5 T
[13] and TR, 6.14 msec).
For comparison, 3D SPGR images with fat saturation were acquired at the same slice locations and same image resolution as the SSFP images. For this sequence, the parameters were TR/TE, 50/5 (full echo) and tip angle, 40°; the bandwidth was decreased to ± 16 kHz. These parameters are based on established reports using fat-saturated SPGR imaging of articular cartilage [4, 14]. Total SPGR time for a complete set of sagittal images was 12 min 4 sec for one knee.
Image Reconstruction
An off-line reconstruction program written in Matlab 6.0 (Mathworks,
Mountain View, CA) was used to perform fast Fourier transformation
reconstruction of all images. After the reconstruction of complex (magnitude
and phase) images, calculations based on equation 3 in Appendix 1 were
performed on SSFP water and fat images after the calculated off-resonance maps
had been sorted using a search algorithm that incorporated the local
orientation filter discussed previously.
SNR Measurements
Measurements of SNR from articular cartilage were used to calculate SNR
efficiency (
), which we defined as SNR2 /
T, where T is the total scanning time of the acquisition.
This metric allows equal comparisons of the SNR performance of pulse sequences
with different acquisition times. Using this definition, we compared the SNR
efficiency of 3D SSFP relative to 3D SPGR through the ratio of for SSFP
and SPGR imaging as follows:
 | (3) |
For both SSFP and SPGR imaging acquisitions, SNR for cartilage was measured from sagittal images through the lateral femoral condyle in all knees, and the ratio of SNR efficiency was calculated with equation 3 (Fig. 2A,2B,2C,2D).
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Figure 3A is an axial SSFP water image obtained through the patellofemoral joint of one volunteer with known cartilage abnormalities that shows bright synovial fluid intercalated between the femoral and patellar cartilage. In the SPGR image obtained at the same location (Fig. 3B), joint fluid has low to intermediate signal intensity because of the long T1, and a chemical shift artifact is also visible at fat—water interfaces perpendicular to the readout direction.
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Metallic implants often cause susceptibility artifacts that result in areas of focal signal dropout and distortion. In the one knee of one volunteer with titanium fixation screws, both SSFP and SPGR images showed comparable focal signal deficits in the vicinity of the fixation hardware, although the adjacent articular cartilage was largely unaffected (Fig. 4A,4B,4C).
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Because signal intensities of SSFP and SPGR imaging have different dependence on relaxation times, the comparison of SNR and SNR efficiency depends on which tissue is used in the comparison. We chose cartilage for our comparison because it generally has a low SNR, making increases or decreases quite noticeable. A logical alternative would have been to measure the contrast-to-noise ratio between cartilage and synovial fluid. This comparison would have greatly favored SSFP because the signal from fluid is much higher on SSFP imaging.
The tip angle used in this study was selected to provide the maximal signal intensity in the cartilage and was chosen on the basis of the known values of T1 and T2. Although optimizing the tip angle to maximize contrast between synovial fluid and cartilage may be interesting, the contrast between synovial fluid and cartilage appeared adequate even with a 27° tip angle chosen to maximize signal intensity in cartilage.
Visualization of cartilage is markedly improved if the lipid signal from adjacent tissues can be suppressed. SSFP fat-suppression techniques such as fluctuating equilibrium magnetic resonance [4] and fat saturation [5] are effective but are relatively sensitive to magnetic field inhomogeneities. Previous applications of the combination of modified three-point fat—water separation techniques with fast spin-echo techniques have been in low-field musculoskeletal imaging [15] and pediatric imaging [16], where the combination was found to provide excellent separation of fat and water. T2-weighted fast spin-echo MR images have bright synovial fluid that contrasts with osteochondral defects. However, the signal in cartilage is inherently low, and fast spin-echo techniques are slow and often have limited resolution due to spatial blurring from T2 decay [17, 18]. The proton density fast spin-echo technique also suffers from spatial blurring and has poor cartilage-to-fluid contrast. Three-dimensional SPGR imaging with fat saturation offers high-resolution images, but the contrast between cartilage and synovial fluid is suboptimal because of low SPGR fluid signal intensity [4, 14, 19, 20].
SSFP is a rapid gradient-echo technique that produces relatively high signal compared with other gradient-echo techniques such as SPGR imaging. Short TRs are required to prevent signal dropout artifacts caused by local magnetic field inhomogeneities. In our experience, a TR of approximately 6.1 msec provides a balance between signal dropout and the longest possible TE increments to maximize SNR in calculated water images. Optimal increments in TE to maximize the SNR of the water and fat images for a four-point scheme would be 0, 1.14, 2.27, and 3.41 msec. However, these increments in TE would have increased the TR of the SSFP pulse sequence to 6.6 msec, at which point signal dropout artifacts would have become troublesome. A compromise of 0, 0.92, 1.84, and 2.7 TE increments was chosen, yielding a TR of 6.14 msec, good SNR, and significantly fewer artifacts related to field inhomogeneity.
In our study, a bandwidth of ± 125 kHz was required for SSFP to maintain a TR that was short enough to prevent significant dephasing artifacts, compared with a bandwidth of ± 16 kHz used for the SPGR imaging. One advantage of a high receiver bandwidth is the reduction of distortion artifacts in areas of high susceptibility, such as metallic implants, and a reduction of fat—water chemical shift displacement artifacts. An important disadvantage of high bandwidth is the reduction in SNR of SSFP imaging relative to SPGR imaging by a factor of 2.8 (the square root of 125/16).
In addition, the time needed for the SSFP acquisition was shorter than the
time needed for the SPGR acquisition by a factor of approximately 2.4, which
reduces the relative SNR of SSFP by a factor of about 1.5 (the square root of
SSFP / SPGR, which equals the square
root of 2.4). Despite the differences in scanning time and bandwidth, the SNR
of articular cartilage in both sequences was comparable, reflecting the
inherently high SNR efficiency of SSFP. Here, the high SNR efficiency of SSFP
was used to achieve shorter scanning times. Alternatively, the SNR efficiency
of the technique could have been used to improve image resolution.
An additional advantage of SSFP fat—water separation is the availability of the initial source images, which can be averaged together, as well as the fat images and off-resonance maps that are available at little additional computational cost. Although the source images as well as the fat and water images may have diagnostic value, the off-resonance maps are less likely to contribute helpful information.
An inherent assumption of most phase-sorting algorithms used for multipoint fat—water separation methods is that the magnetic field inhomogeneities vary smoothly across the image [9]. Transitions greater than 220 Hz between two adjacent pixels may make un-wrapping algorithms difficult; fortunately, steep gradients such as these are seldom encountered. In addition, the smooth variation of the field inhomogeneity has been exploited with other fat—water separation techniques to reduce imaging time through acquisition of low-resolution images used to calculate off-resonance maps [16].
In summary, 3D SSFP imaging combined with a generalized multipoint fat—water separation technique is a novel and effective method of producing high-quality images of cartilage with improved fat—water separation. In addition, synovial fluid appears bright on 3D SSFP, and SNR is comparable to 3D SPGR fat-saturated MR imaging, despite the fact that 3D SSFP requires 58% less total imaging time. Future work includes identifying the optimal pulse sequence acquisition and detailed analysis of noise behavior to improve reconstruction and acquisition strategies.
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Acknowledgments
We thank Kim Butts and Howard Zebker for their helpful discussions.
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