This effect of readout bandwidth on SNR efficiency is sometimes overlooked in the literature. For example, in Ref.7, the authors state that for b-SSFP, the signal magnitude is largely independent of TR (when TR << T2), and therefore the shortest possible TR should be used. However, it is to be noted that when the acquisition time per repetition is constrained by TR, true SNR efficiency does not increase with decreased TR since the bandwidth must be increased proportional to the decrease in TR.
Most osteoporotic fractures occur at anatomic sites that contain a significant portion of trabecular bone (TB). Key among these skeletal locations are the vertebrae and the ends of the long bones near the joints where stresses are multidirectional (distal and proximal femur, distal radius and ulna). Even though osteoporosis is always associated with a loss of bone mass, there has been increasing evidence of the role of structure as independent predictors of the mechanical competence of TB (1). This situation has spurred the development of noninvasive imaging techniques for regional quantification of TB architecture (2). MRI has been shown to be particularly useful and both spin-echo (SE) and gradient-echo-(GRE) type pulse sequences are currently in use for this task (3).
Gradient-echo based steady-state free precession (SSFP) techniques, although used widely for TB imaging (4), suffer from signal loss and artifactual broadening of trabeculae due to susceptibility-induced gradient fields at the bone/bone marrow interface (5). The more recently implemented balanced SSFP (b-SSFP) is also sensitive to off-resonance effects (6, 7). Although b-SSFP has been shown to produce images with spin-echo type qualities at short repetition times (on the order of 10 ms) (7), this sequence has comparatively low signal-to-noise ratio (SNR) efficiency at the target resolution (∼150 μm) due to the necessarily high receiver bandwidth. Indeed, with TR = 10 ms, readout time per repetition cannot be much longer than 5 ms (considering the excitation pulse, phase encode, and rewinder gradients), compared with a fast large-angle spin-echo (FLASE) readout time of 18 ms per repetition (TR = 80 ms). These constraints result in an approximate SNR penalty factor of for b-SSFP that must be considered when comparing the relative efficiency of the two types of pulse sequences.* Of course, some of the signal loss is recovered in b-SSFP by the refocused transverse magnetization carried over from one repetition to the next. However, since the steady-state signal level is heavily T2-dependent, the relative performance of b-SSFP and FLASE is not straightforward to predict from simulation due to the complex relaxation behavior of fatty marrow protons. In prior work some of the present authors found FLASE to outperform the alternatives in terms of overall image quality and depiction of the trabecular network (8).
In the original formulation of FLASE (5) (hereafter referred to as steady-state FLASE or ss-FLASE), all phase-encoding gradients are rewound, and a consistent spoiler gradient is applied at the end of each repetition. Analogous to SSFP, there are two other variants of this sequence: fully-balanced FLASE (here denoted b-FLASE), and RF-spoiled FLASE (sp-FLASE). In b-FLASE, all gradients are fully rewound at the end of each repetition, so that residual transverse magnetization is utilized in subsequent repetitions. The two steady-state variants (ss-FLASE and b-FLASE) have a higher theoretical SNR efficiency than sp-FLASE, but are prone to ghosting artifacts caused by stimulated echoes resulting from imperfections in the nonselective refocusing pulse. While techniques exist to suppress such artifacts (see for example Ref.9), it is difficult if not impossible to handle all such ghosting problems, due to the large number of coherence pathways involved (TR = 80 is only around one-fourth the duration of the principal T1 component of the lipid resonance in fatty marrow). Furthermore, due to variations in shape and composition of the anatomy and the nature of the spatial B1 profile, the severity of such artifacts can vary from subject to subject, and even scan to scan, hampering quantitative studies, both cross-sectional and longitudinal. It should be noted that the implementation of b-FLASE (referred to as bSSSE in Ref.10), organizes the gradients in a manner so as to avoid these ghosting artifacts, at the cost of lost SNR, as will be discussed in detail further below.
Important criteria in the choice of the particular embodiment of the three-dimensional (3D) spin-echo pulse sequence (ss-FLASE, b-FLASE, or sp-FLASE) are SNR efficiency and robustness to artifacts. It is therefore essential to accurately predict the relative SNR performance of the three sequences. The SNR gain of b-FLASE over sp-FLASE depends on TR, TE, T1, and most significantly, T2 of fatty marrow. In Ref.10, this comparison was made assuming T2 = 130 ms (11). However, the difficulty is that the protons in fatty acid triglycerides do not have a well-defined T2 relaxation time that can be assumed for all pulse sequences and the range of sequence parameters. Allerhand et al. (12) first showed that in scalar coupled systems J-coupling leads to variation in the effective T2 relaxation rate (measured by Carr-Purcell-Meiboom-Gill [CPMG]) depending on the interecho spacing. Henkelman et al. (13) more recently showed that the anomalously high signal of fat in fast SE sequences was due to partial suppression of J-modulation dephasing causing interecho-time–dependent lengthening of the effective T2.
Several adaptations have previously been made to the original ss-FLASE pulse sequence, including addition of navigator echoes for motion detection (14) and rearrangement of gradients for artifact suppression (9). In this work, we present a substantially enhanced sp-FLASE pulse sequence, disclosed in abstract form in Ref.15. We provide a detailed rationale for the redesigned sequence for imaging of TB architecture at the distal extremities, including an analysis of the theoretical SNR gain of b-FLASE vs. sp-FLASE, taking into consideration an appropriate T2 relaxation time for fatty marrow. We further demonstrate the quality of the depiction of trabecular architecture with images along with 3D bone skeletons for comparison between baseline and 6-month follow-up. Finally, we report on the SNR gain achievable at 3T with the improved pulse sequence, and show how this gain can be used to obtain isotropic (160-μm) resolution images within clinically tolerable scan times as a means to provide what is likely a more accurate representation of TB network architecture.
MATERIALS AND METHODS
Effective Spin-Spin Relaxation Rate
Accurate estimation of T2 for fatty marrow is essential for the optimal selection of the pulse sequence. Estimation of T2 is complicated by the multiple chemically-shifted components involving homonuclear scalar coupling between protons in fatty acid chains of the triglyceride molecules of which fatty marrow is composed. Therefore, as pointed out earlier, spin-spin relaxation is not a simple monoexponential process; rather, when measured using a CPMG sequence, for example, the relaxation rate depends on the interecho spacing of the refocusing pulses (13). To estimate the effective T2 relaxation time, and hence evaluate the relative SNR performance between b-FLASE and sp-FLASE, a collection of CPMG readouts were acquired on a sample of peanut oil, which, as all edible oils, has chemical makeup close to that of adipose fat. Interecho spacing ranged between 4 and 120 ms (in increments of 1 ms), with eight SE readouts per repetition. A repetition time (TR) of 3 s was used to ensure sufficient restoration to equilibrium magnetization between acquisitions. An effective T2 relaxation rate was computed from these measurements as a function of echo number and echo time using the formula:
where Sj(TE) is the magnitude of the signal of the jth echo (j = 1 … 8) at echo time TE, and TEj,min = 4j ms is the minimum acquired echo time (TE). Note that in the case where transverse magnetization decays monoexponentially, Eq.  yields the actual decay rate. The estimated effective T2 was then used to predict the expected SNR gain of b-FLASE over sp-FLASE according to the formulae of Appendix A.
A modification of the FLASE pulse sequence was implemented (Fig. 1). Hereafter, this new sequence is termed sp-FLASE, noting that there are further differences between this sequence and the original ss-FLASE besides merely the application of RF spoiling. The modified sequence incorporates a number of improvements relating to artifact suppression and motion correction.
As in the original sequence, a nonselective 180 degree refocusing pulse was used to minimize echo time (a selective pulse with sufficiently sharp transition bands would have a prohibitively long duration). As a result, even modest B1 field inhomogeneity can cause spurious echoes leading to image artifacts. Within a single repetition, this problem is addressed by the use of crusher gradients around the refocusing pulse, as well as phase alternation to push direct current (DC) artifacts to the edge of the phase-encode field-of-view (5). A more serious problem occurs when phase-encoded signal is stored as longitudinal magnetization, reappearing as transverse magnetization in a subsequent repetition. While reorganization of gradients can reduce the severity of such stimulated echoes (9), the relatively short repetition time (TR = 80 ms < T1 ∼ 300 ms) and the presence of two large-flip-angle pulses per repetition create a vast number of coherence pathways (9, 16). These types of artifacts are therefore difficult to predict or correct because artifact severity is subject dependent.
To overcome these difficulties, two critical modifications were applied. The dephasing lobe of the readout gradient is placed after (rather than before) the refocusing pulse (at the expense of a small increase in echo time), as suggested (9). This ensures that any stimulated echo aligns with the main echo in the kx direction, eliminating the possibility of banding (see Fig. 2). Second, RF spoiling was implemented by applying a random offset to the large-angle excitation pulse. Such phase randomization ensures that any stimulated echoes are phase-incoherent, preventing systematic artifacts in the reconstructed image.
The sequence also includes improved navigator motion detection. Rather than using residual magnetization after sampling of the imaging signal (14), a separate excitation pulse is used for navigator acquisition. To avoid loss of imaging signal, the navigator pulse excites a slice adjacent to the imaging slab (16). In this manner, navigator SNR is enhanced, improving overall sensitivity in motion detection. Finally, to reduce the occurrence of aliasing artifacts caused by insufficient field-of-view in the phase encode direction (Fig. 2), the four corners of kY/kZ space are not acquired, i.e., a cylindrical k-space volume is sampled. The time saved is used to increase the field-of-view in the in-plane phase-encoding direction. To minimize echo time, the phase-encoding gradients (in the y direction) were split, with 70% of the moment occurring before the refocusing pulse and 30% after.
To demonstrate the sensitivity to ghosting artifacts of b-FLASE, images of a phantom were acquired using both b-FLASE and sp-FLASE. The phantom, designed to mimic the chemical composition and relaxation properties of muscle and yellow bone marrow, consisted of a cylindrical plastic container (∼7 cm diameter) filled with agarose gelatin and containing two smaller plastic containers of corn oil (∼3 cm and ∼4 cm diameter). The size of the oil-filled containers placed within the larger container was chosen to mimic the relative sizes and locations of the tibia and fibula in the distal ankle. Agarose was doped with GdCl3 and NaCl according to the formula in Ref.17 to reflect the relaxivity and conductivity of knee muscle. Plastic tubes of varying sizes with a wall thickness comparable to that of bone trabeculae were inserted into one of the oil containers.
In Vivo Imaging
The performance of the pulse sequence is illustrated with data drawn from ongoing clinical research studies at the authors' institution. So far, sp-FLASE has been used in approximately 150 patient examinations on a 1.5T Siemens Sonata scanner with the following scan parameters: TE = 10.5 ms, TR = 80 ms, flip angle = 140°, readout bandwidth = 32 Hz/pixel, in-plane resolution = 137 × 137 μm2, slice thickness = 410 μm, and total scan time = 15.5 minutes. The in-plane matrix size was 512 × 460 for a field-of-view of 70 × 63 mm2. A custom-built two-element surface coil was used. In one pilot study, 30 patients with end-stage renal disease were examined at baseline and again 6 months later. Half of the study subjects were subjected to low-magnitude mechanical stimulation (18). Preliminary data of this study showing a treatment effect on trabecular structural parameters have been reported in abstract form (19) and will be published elsewhere.
The sequence was also implemented at 3T (Siemens TIM Trio) as part of a reproducibility evaluation in view of a forthcoming drug intervention study. In brief: sp-FLASE images were collected with a custom-built four-element receive coil array (Insight MRI, Worcester, MA, USA) at the distal tibia. In addition to the standard imaging protocol used at 1.5T (resolution = 137 × 137 × 410 μm3 with same parameters as at 1.5T except TE = 11.8 ms), images were also acquired at isotropic 160-μm resolution (matrix size = 512 × 400 for a field-of-view = 70 × 64 mm2). Since structure analysis requires acquisition of a sufficient volume along z (typically the major loading direction), reduction in slice thickness (by more than a factor of 2) requires at least a doubling of the number of slice encodings that, in turn, would double the scan time. We have therefore implemented the sequence for parallel imaging along with multiline, multicolumn generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction (20) with a kernel size of 3 and 4 points in the readout and phase-encode directions, respectively. The calibration region consisted of 60 phase-encode lines (out of a total of 400). In this manner, total scan time was maintained at 16 min.
The relatively low receiver bandwidth of 32 Hz/pixel was chosen to maximize SNR (the gain from lowering bandwidth must be weighed against the loss from lengthening echo time). Even though the resulting chemical shift effect between fat and muscle is relatively large (∼7 pixels or 1 mm at 1.5T, and 14 pixels or 2 mm at 3T) this is not problematic since the signal-producing tissue of the TB marrow in the distal extremities is purely fatty, and this region is separated from muscle by the cortex. Further, the signal from fatty-acid triglyceride (fat) has a single dominant peak with minor chemically-shifted signals of much lower intensity. Last, as compared to fat, muscle produces a relatively weak signal for FLASE due to a significantly longer T1.
Comparing SNRs of images acquired with different numbers of receive coils can be more difficult than one might expect. A typical approach (and the method used here) is to measure the mean signal within the region of interest and divide by the mean signal level in a region of pure noise. However, depending on the method of combining images from separate receive channels, an appropriate adjustment needs to be made. In the present case, channels were combined using a square-root sum-of-squares formula
where Sj is the signal of the combined image at the jth pixel, and S is the signal for the cth receive channel (L = 2 or 4). In the case of multiple receive coils the measured noise level (mean signal in a region of pure noise) is actually higher than the true noise level within the region of interest. This leads to an artificially low SNR measurement for four coils as compared to two. To compensate, SNR measurements were adjusted by the following factor:
as found in Ref.21, where L is the number of coils. Equation  was derived with the assumption that the noise is Gaussian distributed and uncorrelated between channels, and that it has equal standard deviation (SD) between channels. Note that in the case of a single receive coil (L = 1), this adjustment corresponds to the expression found in Ref.22.
RESULTS AND DISCUSSION
The results of the CPMG experiments performed on the peanut oil sample are shown in Fig. 3. It is noted that the overall functional dependence of the effective T2 is very similar at the two field strengths. Estimated T2 values are on the order of 60 ms for echo times in the range of 0–200 ms. By Eq. , the calculation of the effective T2 is more reliable for larger values of TE (until of course the noise floor is reached), so the data for TE < 20 ms were omitted from the plot. As suggested by the data in Fig. 3, the effective spin-spin relaxation is not a simple monoexponential process in that the effective T2 depends on various factors, in particular interecho spacing. This functional behavior is contrasted with the flat plot for water. Although effective T2 for oil increases to over 100 ms for echo times exceeding 600 ms, such values are not relevant for SNR predictions in our situation, in which repetition time is 80 ms.
Although the results of the CPMG experiment cannot be used to directly predict the relative SNR performance of the various implementations of FLASE, the data allow selection of an approximate effective T2 time to be inserted into the signal equations. Note that the echo time for FLASE (around 11 ms) is not the relevant quantity in this analysis, since the signal loss due to echo time is exactly the same between b-FLASE, ss-FLASE, and sp-FLASE. Because the signal gain in b-FLASE and ss-FLASE is caused by magnetization refocused from previous repetitions, the relevant echo times are multiples of TR, i.e., 80 ms, 160 ms, 240 ms, etc. Furthermore, of these echo times, the echo at 80 ms contributes the greatest amount to the signal.
Figure 4 shows the predicted gain of b-FLASE over sp-FLASE as a function of T2, at various repetition times. Note that the relatively simple expression for the gain, derived in Appendix A, has no T1 dependence and, interestingly, is equal to the relative gain from balancing in gradient-echo sequences. If T2 = 60 ms is used in the formula, as suggested by the CPMG experiments, then the expected gain at TR = 80 ms is a mere 3.7%, as compared to a value as high as 19% if a value of 130 ms were chosen for T2 as in Ref.10. This discrepancy illustrates the importance of selecting an appropriate value of T2 when estimating the gain. In the present situation (TR = 80 ms), the expected gain could be considered insignificant relative to the benefits of spoiling (i.e., artifact reduction).
The plot in Fig. 4 suggests that decreasing TR to 60 ms would result in a more significant gain from balancing (7.5% for TR = 60 ms compared to 3.7% for TR = 80 ms). However, there are also significant tradeoffs to consider. First, a decrease in TR leaves less time for motion detection navigators and increases the magnitude of interrepetition spurious encoded longitudinal magnetization. Second, according to Eq. [A11], the SNR efficiency (signal at echo time divided by square root of TR) of b-FLASE would decrease by around 6% (assuming TE = 12, T1 = 300 ms, and TR decrease from 80 to 60 ms), virtually eliminating the expected 7.5% gain from balancing in this case.
The images acquired in the phantom experiment, comparing b-FLASE to sp-FLASE, are shown in Fig. 5. The b-FLASE image shows significant ghosting artifacts, resulting from encoded signal stored between repetitions as longitudinal magnetization. It should be noted that such artifacts do not occur in all scans, and can be managed to some extent by arranging crusher gradients appropriately. Further, their presence may be masked by noise at typical SNR values of 10–15 in TB imaging. However, the vast number of coherence pathways created by the two large-flip-angle pulses greatly complicates the situation, making it virtually impossible to consistently eliminate these subject-dependent (and hardware-dependent) artifacts.
Additional complicating factors arise when scanning at 3D isotropic resolution. For example, crusher gradients (surrounding the refocusing pulse) are only effective if they wind up the magnetization to at least one full cycle within an imaging voxel. At increased resolution (e.g., 160 μm compared to 410 μm slice thickness), this requires significantly longer duration crushers, therefore prolonging achievable echo time. A second factor relates to the use of parallel imaging. As mentioned above, one method for dealing with DC artifacts is to push them to the edge of the field-of-view by alternating the phase of the refocusing pulse (5). However, this technique will fail in the reduction direction of parallel imaging (with R = 2) because the artifact will be aliased back into the center of the image. In summary, suppression of stimulated echo artifacts to which b-FLASE is prone, is nontrivial. These difficulties must be weighed against the modest SNR gains expected from balancing.
As mentioned in the introduction, for the implementation of b-FLASE found in Ref.10, termed fully-balanced steady-state spin-echo (bSSSE), the gradients are arranged in a manner so as to avoid stimulated echo-induced ghosting artifacts. Specifically, this is achieved by placing the phase-encode gradients in their entirety after the refocusing pulse. However, as compared with the scheme presented here (where 70% phase encoding occurs before the refocusing pulse), this results in increased echo time, and hence lost SNR. In fact, because the refocusing pulse is constrained to occur at time TE/2 after excitation, a lengthening of the postrefocusing phase-encode gradients will result in a two-fold increase in TE. Therefore, the necessary increase in echo time would be
For example, with gradient amplitude of G = 24 mT/m (used in this work) and resolution of 137 μm, the echo time increase would be 5 ms, corresponding to a signal loss (according to Eq. [A11]) of 14% (for TR = 80 ms and T2 = 60 ms). Even in the case where G = 40 mT/m (a stretch for clinical scanners considering peripheral nerve-stimulation restrictions), echo time would increase by 3 ms, resulting in a predicted signal loss of 9%. In either case, this loss exceeds the expected gain from balancing, as predicted above.
Figure 6 shows pairs of sp-FLASE images of the distal tibia acquired for three of the low-magnitude mechanical stimulation subjects at two time points. The registered cross-sectional images and the 3D cores of the skeletonized images visually highlight the reproducibility achievable with the pulse sequence. Details of the processing procedure are given in Ref.23.
For the anisotropic protocol, the SNR (obtained in the manner described above, including adjustment by Eq. ) derived from five randomly selected images was 18.6 ± 2.4 at 1.5T and 36.8 ± 3.9 at 3T for five randomly selected images at each field strength. The data suggest an approximate two-fold increase in SNR by doubling the field strength.
In none of the approximately 150 sp-FLASE examinations were there noticeable ghosting or banding artifacts common with the prior version of ss-FLASE, although some of the images suffered from motion corruption. Because the navigators only detect in-plane translational motion, rotational or through-plane motion cannot be corrected. We are currently investigating further techniques that have the potential to correct for these other types of motion, including a recently published version of the autofocusing method (24) that can retrospectively correct for in-plane rotational as well as translational motion. Another possibility is to acquire navigator echoes along more than just two projection directions.
Figure 7 illustrates the performance achievable at 3T in the isotropic resolution regime (160 × 160 × 160 μm3) in conjunction with parallel imaging (R ≈ 2) as described previously. This voxel volume is 53% of 137 × 137 × 410 μm3 (the voxel size of our standard 1.5T clinical protocol). Thus, in order to maintain SNR in the same 16-min scan time an increase in intrinsic SNR by a factor of 2 was needed, which was achieved by a combination of increased field strength (1.5T to 3T) and more efficient receive coil (recall that a four-element coil was used at 3T instead of a two-element coil at 1.5T). Of note in the images of Fig. 7 is the virtual absence of artifacts and the recovery of the plate-like trabecular architecture expected in this young individual, clearly evident in the 3D surface-rendered core.
A new RF-spoiled variant of the basic 3D FLASE pulse sequence, dubbed sp-FLASE, for high-resolution imaging of TB, has been introduced. A theoretical T2 analysis suggests that the benefit, in terms of artifact reduction, outweighs the modest SNR loss relative to alternative embodiments such as ss-FLASE and b-FLASE. The robustness of the new protocol is supported by consistent performance over the course of clinical studies involving human subjects.
We are indebted to Catherine Jones for acquiring the images in Fig. 6.
Here we derive a formula for the relative gain in SNR efficiency of balanced vs. spoiled FLASE (i.e., b-FLASE vs. sp-FLASE). The spoiled case mirrors the derivation (for the same quantity) found in Chapter 14 of Ref.25. For simplicity we normalize the equilibrium magnetization vector to (0,0,1)T. Let MY,0 and MZ,0 be the steady-state transverse and longitudinal magnetization levels immediately before excitation. Immediately after excitation (by a pulse of flip angle φ) we have
Immediately after the refocusing pulse (occurring at one-half the echo time), we have
and at the end of the repetition period:
In the case of sp-FLASE, we assume the initial transverse magnetization is zero (MY,0 = 0), and upon setting MZ,3 = MZ,0, we obtain:
yielding a signal strength at echo time of
This expression is maximized by setting cosφ = − e to yield an optimized signal of
For b-FLASE, the transverse magnetization carries over, and we set MY,3 = MY,0 and MZ,3 = MZ,0 to obtain the following matrix equation:
Solving this system gives:
and a signal at echo time of:
The optimal flip angle is obtained by setting
for the following optimal signal:
Comparing Eq. [A3] with Eq. [A8], we therefore see that switch from spoiled to balanced FLASE results in a signal gain of
Note that this expression depends only on TR/T2 (and not on TE and T1), and that this is precisely the same gain factor obtained from switching between the spoiled and balanced gradient echo (see Ref.25).