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Keywords:

  • FLADE;
  • FLASE;
  • trabecular bone;
  • double spin echo;
  • high resolution imaging

Abstract

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES

Mechanical strength and fracture resistance of trabecular bone (TB) are largely determined by the structural arrangement of individual trabeculae. Fast 3D spin-echo approaches are preferable to gradient echoes in that they are less sensitive to local induced gradients at the bone/marrow interface caused by magnetic susceptibility difference between the two tissues. FLASE is a 3D pulse sequence that serves this purpose. Here, we present a new pulse sequence dubbed FLADE (fast low-angle dual spin-echo) that overcomes some of the limitations inherent to FLASE, such as sensitivity to artifactual stimulated echoes. The double-echo sequence features a flip angle <90 degrees allowing for TR ≪ T1. The second phase-reversal pulse has the dual function of creating a second echo and restoring inverted longitudinal magnetization. The prolonged TR, made possible by sampling only half of kz-space, is used to collect navigator echoes in adjacent slabs for sensing subpixel translational displacements. FLADE is shown to provide SNR comparable to FLASE while having narrower point-spread function and being more robust to imperfections in the nonselective 180 degree pulses. Structural parameters derived from the in vivo images with the two pulse sequences are highly correlated, therefore suggesting that clinical data obtained with either pulse sequence can be merged. Magn Reson Med, 2006. © 2006 Wiley-Liss, Inc.

The recognition of the role of trabecular bone (TB) architecture as a determinant of mechanical competence and fracture resistance (1–3) independent of apparent density has given substantial impetus to the development of noninvasive techniques for measuring TB structural parameters (see, for example, (4–6)). The clinical utility of imaging TB along with extraction of structural parameters has recently been demonstrated in a number of articles showing that fracture susceptibility is associated with the degree of integrity of the TB network (7, 8). The technique has also proven to be applicable to the evaluation of treatment efficacy (9, 10). However, obtaining images in a resolution regime on the order of 100–150 μm pixel size poses unique challenges not only in terms of SNR requirements (6).

Bone is more diamagnetic than fatty marrow (the type of marrow prevailing in the distal extremities of the adult skeleton) by about 2.5–3 ppm (11). The induced inhomogeneous fields in the boundary region between bone and marrow cause intra-voxel phase dispersion, which, in turn, leads to artifactual broadening of the trabeculae (12). Further, since the marrow is spectrally heterogeneous, the various spectral components are not in phase at k-space center, leading to significant SNR loss in gradient-echo images (13). These problems are largely overcome with fast 3D spin-echo imaging techniques such as FLASE (Fast Large-Angle Spin-Echo) (13). The FLASE pulse sequence provides significant advantages over other fast spin-echo sequences, such as RASEE (12), for high resolution TB imaging. However, there are several aspects of FLASE that can lead to difficulties. First, the large flip angle (>90°) of the selective excitation pulse can be problematic in terms of the uniformity of the slice profile. Second, the short repetition time (much shorter than T1 of the protons in fatty marrow) can cause stimulated echoes that are difficult to eliminate using crusher gradients (14). Third, the low receiver bandwidth required for good SNR performance causes broadening of the point spread function in the readout direction.

In this article, a new pulse sequence, dubbed FLADE (Fast Low-Angle Dual Spin-Echo), is proposed for TB imaging. The sequence features a flip angle <90°; it allows for a longer repetition time and a higher receiver bandwidth than FLASE, thus considerably alleviating the difficulties mentioned above. There are other advantages of FLADE, including the increased time between imaging acquisitions, which can be used for sensing patient motion with increased precision by means of navigator echoes. The new sequence was implemented on a 1.5T Siemens scanner and its performance compared with 3D FLASE.

METHODS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES

Pulse Sequence and Reconstruction

The FLADE sequence, depicted in Fig. 1, is a double spin-echo with a selective excitation pulse and two non-selective refocusing pulses. For an excitation RF pulse <90°, the residual longitudinal magnetization is negative after having been subjected to the first phase-reversal RF pulse. Hence, the second 180° pulse has the dual function of phase-reversal and restoration of longitudinal magnetization. The signals from the two echoes are combined as part of the reconstruction process detailed below. A high receiver bandwidth and partial coverage of kx-space (75%) during the first readout (Fig. 2) minimize the time between the two refocusing pulses. This is important for SNR efficiency because the (inverted) longitudinal magnetization experiences T1 decay rather than re-growth during this critical period.

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Figure 1. Pulse sequence diagrams for FLASE and FLADE. For details, see text.

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Figure 2. Portions of 3D k-space acquired by the first and second echoes of FLADE. Each echo acquires 50% of k-space in the Z direction. The first echo acquires 75% in the X direction.

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The sampling strategy is illustrated in Fig. 2. The YZ phase encoding occurs before the first refocusing pulse. Only one half of kz space is sampled in each echo, and the missing half is filled in by conjugation after phase correction. Various approaches for correcting the phase are described in (15). We found that the field was sufficiently homogeneous throughout the relatively small region of interest; hence, each dataset was simply multiplied by a global phase constant before correction. The two 3D datasets are then reconstructed using an FFT. The first echo is a partial readout, and is missing one fourth of the full data. To obtain the full resolution, the two datasets are combined, producing a single image. There are a number of options for combining the data sets. Here, the reconstructed magnitude images were combined via a simple linear combination, with the second echo weighted 30% lower than the first. A factor of 30% was chosen empirically to maximize the SNR of the combined image (note that the second image will be noisier than the first due to T2 relaxation). By sampling only half of kz-space, the same resolution and field of view can be obtained in half as many repetitions as compared to FLASE. This, in turn, allows doubling of the repetition time. It is noted that this sampling scheme is not possible in FLASE, where a fractional echo is sampled and thus conjugation is required to fill in the missing kx samples.

Pulse Sequence Implementation and Evaluation

The FLADE pulse sequence (Fig. 1) was implemented on a 1.5T Siemens Sonata with the following parameters: TR = 150 ms, TE1 = 11.1 ms, TE2 = 28.9 ms, Tref1 = 5.55 ms, Tref2 = 20 ms. The acquired data sets had dimensions 384 × 288 × 31 for the first echo and 512 × 288 × 31 for the second echo. The resolution was 137 × 137 × 410 μm3 in a scan time of 11.5 min and a field of view of approximately 70 × 40 × 13 mm3. The acquisition dwell time of 30 μs yielded a receiver bandwidth of 65 Hz/pixel. The excitation pulse was a 60 degree truncated sinc.

To minimize artifacts arising from imperfect 180 degree refocusing pulses, crusher gradients were placed around each of the two non-selective pulses. The moments of these gradients were chosen to prevent stimulated echoes in the second readout. After consideration of the coherence pathways, each gradient pair was chosen to crush in the Z direction, with the moment of the first set of crushers equal to twice that of the second set. A simple analysis shows that there are eight transverse components that could potentially cause a stimulated echo in the second readout. These correspond to the following linear combinations of the first (c1) and second (c2) crusher moments: c2, −c1, −2c1, 2c2, c1 + c2, −c1 + c2, c1 + 2c2, 2c1 + 2c2. For example, the −c1 +c2 term comes from pathways that are first stored as longitudinal magnetization by the first 180 degree pulse, and then refocused by the second 180 degree pulse (see Fig. 3). By choosing c1 = 2c2, such artifactual echoes are avoided. These intra-repetition stimulated echoes can similarly be avoided in FLASE. However, the FLASE artifacts that are the most difficult to eliminate are those that arise from residual longitudinal magnetization encoded in previous repetitions. For T1 = 300 ms, increasing the repetition time from 80 ms to 150 ms theoretically decreases the magnitude of such artifacts by approximately 20%, 40%, and 50% for encoded magnetization from one, two, and three prior pulse sequence cycles (50% ≈ exp(−150*3/300)/exp(−80*3/300)). In our data, we have so far not found evidence of the presence of such undesired echoes.

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Figure 3. Coherence pathway diagram predicting a spurious echo in FLADE if the two sets of crusher gradients are equal. This problem is resolved by setting the moment of the second set of crushers equal to half that of the first set. The longitudinal and transverse components are marked by “L” and “T,” and the bold line represents the pathway of the spurious echo. For simplicity, only the pathways coming from initial transverse magnetization are displayed.

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The wrist of two volunteers was scanned using a custom-made elliptical birdcage coil. Before Fourier reconstruction, the corners of k-space were zeroed, resulting in an ellipsoidal data volume. For comparison purposes, the same two volunteers were scanned using FLASE at the same resolution and scan time of 12 min.

For quantitative comparison, the FLADE and FLASE data in one volunteer were, after registering the images, subjected to virtual bone biopsy processing (6). This process yielded bone volume fraction, trabecular thickness, and the topological network parameters surface-to-curve ratio and erosion index (16) from 10 ROIs representing visually different trabecular densities.

Point Spread Function Analysis

To assess differences in the point spread function along the readout direction between FLADE and FLASE, the local FID was measured in a voxel of the bone specimen. This was achieved using spectroscopic imaging sequences that were exactly timed to correspond to FLADE and FLASE (equal TR, TE, RF pulses, readout windows, etc.) Specifically, the readout gradients were removed from the imaging sequences, and phase encoding was applied in the X and Y directions producing a low-resolution spectroscopic data set with two spatial directions. A 2D FFT was applied to the raw data to generate a FID in each voxel. These local FIDs represent the k-space modulation transfer function in the region of interest for FLADE and FLASE. The voxel size was varied to determine the resolution dependence of the signal decay. A voxel in the center of the region of interest was chosen, and the data subjected to FFT to yield the corresponding point spread functions in the readout direction. For comparison, a homogeneous phantom filled with peanut oil to mimic fatty bone marrow was used as well.

Motion Correction

Although no motion correction was applied in the in vivo validation experiments, the potential for correction of translational displacement during the scan was examined. As stated above, the increased TR provides additional time for inserting navigators. Therefore, XY translational motion was measured using one-dimensional projections. Within each repetition, two navigator slabs, inferior and superior to the high-resolution slab, were excited (see Fig. 4), and a linear projection was acquired in each slab. The projection direction was alternated between X and Y. The accuracy of the navigators was evaluated by comparing the predicted motion in the two independent slabs.

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Figure 4. To measure XY translational motion, two navigator slabs are excited during each repetition of FLADE.

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SNR Analysis

SNR was analyzed on the basis of the solutions to the Bloch equations for the steady-state magnetization for the two spin-echo sequences. For given values of T1 and T2, the relative SNR performance of double and single spin-echo sequences (i.e., FLADE and FLASE) in terms of the repetition time, the refocusing times, and the echo time can be predicted in this manner. For a single spin-echo, the theoretical steady-state signal immediately after the excitation pulse is proportional to

  • equation image(1)

where φ is the flip angle, TR is the repetition time, and τ1 is the refocusing time. Eq. [1] is a special case of the general formula derived in the Appendix. This computation ignores T2 decay, and assumes that no residual transverse magnetization remains at the end of each pulse sequence period. For a double spin-echo, the formula is similar:

  • equation image(2)

where τ1 and τ2 are the times of the first and second refocusing pulses, respectively.

For the optimal flip angle, these equations become

  • equation image(3)

and

  • equation image(4)

For more details, see the Appendix.

RESULTS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES

Assuming the imaging parameters specified previously and T1 = 300 ms (T1 of fatty bone marrow), Eqs [1]–[4] predict that the relative transverse magnetization available immediately after the excitation pulse is 0.42 for FLADE and 0.32 for FLASE. After normalizing to compensate for the difference in repetition times (and assuming equal echo times), we predict that the normalized signal at the first echo time of FLADE is approximately 94% that of FLASE. Of course, the SNR is also affected by receiver bandwidth. The higher receiver bandwidth of FLADE is largely compensated by sampling two echoes, emphasizing the point made by Macovski (17) that it is not the receiver bandwidth but rather the total sampling time that determines SNR. In principle, doubling of the bandwidth can be exactly compensated by acquiring two echoes. It should be noted, however, that the second echo will contribute less due to signal attenuation from T2 relaxation.

Figure 5 shows in vivo FLADE images of the wrist in two subjects. Image quality is comparable to the FLASE images shown in Fig. 6. Notice the banding artifact (vertical streaking) in Fig. 6c, caused by stimulated echoes (14) resulting from imperfections in the nonselective phase-reversal pulses. As mentioned above, the longer repetition time of FLADE diminishes this kind of artifact. Figures 5b and 6b show 3D shaded surface images from a virtual core obtained after registration of the FLASE and FLADE datasets, illustrating the high degree of similarity of the FLADE and FLASE data. The projections were generated from a cylindrical data volume after subjecting the data to subvoxel processing (18) and binarization.

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Figure 5. (a) and (c): One slice out of 31 contiguous in vivo 3D FLADE images obtained in two different subjects. (b): A 3D core taken from the series of images in (a). Scan time was 11.5 min, voxel size of 137 × 137 × 410 μm3.

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Figure 6. In vivo FLASE images in the same subjects in whom the images in Fig. 5 were obtained. Scan time was 12 min, voxel size 137 × 137 × 410 μm3, TR/TE = 80/10 ms, and a receiver bandwidth of 32 Hz/pixel. The images of data set (a) have been registered through rotations and translations to those represented by the corresponding FLADE data (Fig. 5a). (b) Structural features including individual trabecular elements seen in Fig. 5b are clearly reproduced in the corresponding 3D core derived from data set a. (c) One slice from a second patient showing banding artifacts due to stimulated echoes caused by imperfections in the nonselective 180° pulse.

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Figure 7 shows FIDs obtained with the spectroscopic imaging version of FLASE as a means to derive the modulation transfer function. One could argue that the relaxation in such a large voxel does not necessarily reflect the T2* decay in a high-resolution image. For example, this attenuation could be caused by local field inhomogeneities that could have less of an effect at higher resolution (19, 20). However, the similarity of the three FIDs (particularly between the marrow-intact bone specimen and the homogeneous oil phantom) indicates that these plots do indeed reflect the modulation due to chemical shift and, to some extent, T2* relaxation. At the microstructural level (i.e., for voxel sizes comparable to trabecular thickness), the point-spread function is location dependent, being wider in the vicinity of a trabecula due to the local gradients of the induced magnetic field, than for a voxel in a relatively large marrow cavity (21).

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Figure 7. Measured magnitude of the local FID for FLASE in a marrow-intact TB specimen (a and b) and a homogeneous oil phantom (c) at 1.5T. The voxel size for (a) and (c) was 2.2 × 2.2 × 10 mm3, and the voxel size for (b) was 0.8 × 0.8 × 10 mm3. The consistency of these plots suggests that the FID measured in a large voxel accurately reflects temporal signal evolution.

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The local FID for FLADE is plotted in Fig. 8. Note that as a result of the higher receiver bandwidth, the magnetization does not decay as much within the readout window as it does for FLASE. The effect of this reduction in high spatial-frequency attenuation is reflected in the narrowing of the point-spread function (see Figs. 8c and 8d), which needs be taken into consideration along with SNR when comparing the two imaging sequences. Notice that the FIDs are normalized to be equal to one at echo time, which is equivalent to normalizing the total area under the point spread function. Therefore, the higher peak value in the FLADE point spread function indicates that a higher proportion of the total signal in the FLADE reconstructed image arises from nearby pixels. In other words, although FLASE may produce images with a higher signal-to-noise ratio, the contrast-to-noise ratio may be lower, because the bone/marrow contrast depends on the contributions from the high spatial frequencies.

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Figure 8. The measured magnitude of the local FIDs for FLADE (a) and FLASE (b) representing the signal decay of fatty marrow in trabecular bone at 1.5T. The missing data were filled in by symmetry. The resulting point spread functions in the readout direction (c and d) were calculated from these data using an FFT.

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The measured displacement due to subject motion during the scan is plotted in Fig. 9. For the computation, the time-dependent translation was chosen to maximize the correlation between the navigator projections. The consistency between the two independent navigator slabs implies that sub-pixel accuracy can be achieved for tracking translational motion. In fact, the data suggest that the accuracy is on the order of a quarter of a pixel. The minor inconsistencies between the two displacement curves are attributed to slight through-plane rotation.

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Figure 9. In-plane translational motion measured with FLADE by the two independent out-of-slab navigators.

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Figure 10 illustrates the agreement between the two pulse sequences with respect to four structural parameters measured in 10 ROIs showing that the data are highly correlated. Further, for bone volume fraction and erosion index, the slopes are close to unity and the regression lines intercept near the origin. These results, therefore, suggest that patient data collected with one or the other of the two pulse sequences could be combined without incurring significant errors.

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Figure 10. Agreement among VBB parameters between FLADE and FLASE image data sets of Figs. 5a and 6a by comparing ten ROIs, five of which are shown in (a).

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DISCUSSION AND CONCLUSIONS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES

The resolution achievable in high-resolution imaging of trabecular bone is largely determined by SNR. However, there are other criteria that determine the choice of pulse sequence. Chief among these is the sensitivity to off-resonance effects. In this respect TB poses unique problems caused by locally induced gradients at the bone-bone marrow interface but also resulting from the presence of multiple chemically shifted species in bone marrow. Neither spin-echo nor gradient-echo-based pulse sequences are immune to off-resonance effects. In gradient-echo imaging, the phase dispersion from off-resonant spins (and concomitant signal attenuation near the interface between bone and bone marrow) is somewhat mitigated at very short echo times. Recently, 3D steady-state free precession pulse sequences, which have greater SNR efficiency than their spoiled counterparts, have been investigated for TB imaging (22, 23). While these pulse sequences have shown promise, FLASE was found to be superior in SNR efficiency (23).

While FLASE has proven its potential in several clinical studies (7, 10, 24), the pulse sequence has limitations and its robustness is suboptimal. Relative to FLASE, FLADE offers several advantages for fast imaging of TB. First, the two closely spaced refocusing pulses provide an optimal flip angle of less than 90 degrees, which avoids the difficulties associated with a large-angle selective pulse (13) while reducing SAR (recall that FLADE has the same number of large-angle pulses as FLASE, while TR is doubled). Second, the use of two short acquisition windows enables a more complete sampling of k-space in the readout direction, as compared to the single partial echo of FLASE. Thus, only half of kz-space (z = slice direction) is required by exploiting the conjugate symmetry of kz space, allowing a repetition time of twice that of FLASE (for the same resolution and scan time). Third, the longer repetition time reduces stimulated echo artifacts, which can be difficult to completely suppress using crusher gradients (14). Fourth, the increased time between acquisitions can be used to more effectively sense patient motion by means of out-of-slab gradient-echo navigators. In FLASE, patient motion is also measured, albeit with less precision, using the residual magnetization from the imaging slab. The non-selective refocusing pulse of FLASE saturates the spins outside of the imaging slab, making the use of adjacent navigator slabs ineffective (25). By contrast, in FLADE, these spins experience two closely spaced 180° pulses, which jointly have a much smaller saturation effect than a single 180° pulse (since the second pulse acts as a longitudinal magnetization restoration pulse). Finally, the shortened readout windows reduce the adverse effects of chemical shift dispersion and T2* relaxation as exemplified with the point-spread function analysis.

The preliminary in vivo images demonstrate image quality that is comparable to that of 3D FLASE. Future work will focus on experiments that quantitatively compare the relative performance of FLADE and other 3D imaging techniques with respect to SNR and point spread function behavior, along with an assessment of accuracy and reproducibility of the derived structural parameters. In the initial evaluation of the pulse sequence, FLADE was found to be a robust alternative for high-resolution imaging of trabecular bone. Lastly, the pulse sequence may have applications for high-resolution structural imaging of other spectrally and magnetically heterogeneous materials.

Acknowledgements

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES

The authors wish to acknowledge the assistance of Aranee Techawiboonwong in acquiring images.

APPENDIX

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES

Steady-State Formulae for Multiple Spin-Echo Sequences

Consider a multiple spin-echo sequence where each repetition consists of a single excitation pulse followed by n refocusing pulses occurring at times τ1, τ2, …, τn after excitation. According to the Bloch equation, the residual longitudinal magnetization at the end of a repetition is given by

  • equation image(5)

where ML(0) is the longitudinal magnetization directly before excitation. Indeed, this formula can be verified by induction on n, noting that the n = 0 case is the formula for a gradient echo. In steady state, we have ML(0) = ML(TR) and, therefore,

  • equation image(6)

Assuming no residual transverse magnetization at the end of the repetition, the steady-state signal after excitation is

  • equation image(7)

Elementary calculus shows that the general expression equation image is maximized by setting φ = cos−1 (B) yielding a maximum value of equation image. Therefore, the optimal flip angle is

  • equation image(8)

producing the following transverse magnetization immediately after excitation:

  • equation image(9)

A consequence of Eq. [8] is that the optimal flip angle depends on the ratio TR/T1 as well as the parity of the number of refocusing pulses. Thus, the optimal flip angle for a double (or quadruple) spin-echo is the same as for a gradient echo, namely, the Ernst angle.

REFERENCES

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION AND CONCLUSIONS
  6. Acknowledgements
  7. APPENDIX
  8. REFERENCES