Magnetic Resonance in Medicine 62:1185–1194 (2009)
Improved Signal Spoiling in Fast Radial Gradient-Echo Imaging: Applied to Accurate T1 Mapping and Flip Angle Correction Wei Lin1* and Hee Kwon Song2 In conventional spoiled gradient echo imaging utilizing quadratic radio frequency (RF) spoiling, nonideal signal intensities are often generated, particularly when repetition time is short and/or excitation flip angle (FA) becomes larger. This translates to significant errors in various quantitative applications based on T1-weighted image intensities. In this work, a novel spoiling scheme is proposed, based on random gradient moments and RF phases. This scheme results in a non-steady-state condition, but achieves ideal mean signal intensity. In order to suppress artifacts created by the inter-TR signal variations and at the same time attain the ideal signal intensity, radial data acquisition is utilized. The proposed method achieves ideal spoiling for a wide range of T1, T2, TR, and FAs. Phantom and in vivo experiments demonstrate improved performance for T1 mapping and FA correction when compared with conventional RF spoiling methods. Magn Reson Med 62:1185–1194, 2009. © 2009 Wiley-Liss, Inc. Key words: RF spoiling; random spoiling; T1 mapping; B1 mapping; radial imaging
Spoiled gradient-echo imaging is widely used in many clinical MR applications due to its high signal-to-noise ratio (SNR) efficiency through the use of short repetition times (TR), combined with low flip angles (FAs) to limit the spin system saturation. In the ideal spoiling condition, transverse magnetization at the end of each TR is effectively nulled, leading to a purely T1-weighted signal behavior. In addition to general qualitative imaging that requires T1-weighted image contrast, spoiled gradient-echo imaging is often used in applications when quantitative analysis is required, such as dynamic contrast-enhanced imaging of tumors (1). Currently, radio frequency (RF) spoiling is the only established spoiling method widely accepted for gradientecho imaging. It is typically based on a quadratic variation of RF (and receiver) phase angles in successive TRs, coupled with a constant gradient moment at the end of each TR period to create a range of resonance offset angles within each imaging voxel (2). However, it was recently recognized that RF spoiling yields nonideal steady-state signal intensities at larger FAs and T1/TR ratios, leading to significant quantification errors (3,4).
1Invivo
Corporation, Philips Healthcare, Gainesville, Florida, USA. of Radiology, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania, USA. *Correspondence to: Wei Lin, PhD, Invivo Corporation, Philips Healthcare, 3545 SW 47th Ave, Gainesville, FL 32608. E-mail:
[email protected] Received 9 October 2008; revised 7 April 2009; accepted 29 April 2009. DOI 10.1002/mrm.22089 Published online 24 September 2009 in Wiley InterScience (www.interscience. wiley.com). 2Department
© 2009 Wiley-Liss, Inc.
Among many quantitative MR methods that could benefit from improved gradient-echo signal spoiling are T1 and B1 mappings. T1 mapping based on variable FA (VFA) three-dimensional (3D) spoiled gradient-echo imaging has been proposed (5,6) as a faster and more precise alternative to the conventional method based on inversion or saturation recovery. However, a recent VFA study reported systematic T1 measurement errors of 20% to 50% due to nonideal signal spoiling as implemented by major MR scanner manufacturers (4). Furthermore, it was shown that accurate T1 measurements are difficult to achieve with conventional RF spoiling, since the optimal RF phase increment value varies for tissues with different T2 values (4). A second application for which an improved spoiling mechanism may be significant is the mapping of transmitted RF field B1, which is important for the accuracy in various quantitative methods, as well as in validating theoretical models for field calculations and ensuring quality control of RF coils. Recently, a novel 3D actual FA imaging (AFI) technique has been proposed (7) based on large FA gradient-echo imaging with two interleaved acquisitions with different TRs, where the signal ratio can be used to derive the FA map. The advantage of AFI technique over conventional 2D slice-based B1 mapping methods is its speed advantage and the ability to account for nonuniform excitation across the slice profile. Critical to the success of this technique is the complete spoiling of residual transverse magnetization at the end of each TR, which is made more challenging considering that TR is typically much shorter than T1 and T2, and the optimal FA for AFI sequences is large (40 – 80°). More recently, applying a very large spoiling gradient moment (⬃350 mT 䡠 ms/m, 150 cycles/1 cm voxel) at the end of each TR has been proposed as a remedy to produce nearly ideally spoiled signal with conventional RF spoiling (8,9). On most commercial whole-body MR scanners, however, this translates to a minimum TR of 20 to 30 ms, which is undesirable in many fast imaging applications. In addition, such a method relies on assumptions about a sufficiently large diffusion coefficient (equivalent to that of free water) for the tissue being imaged, which may not be valid in all tissues of interest. In recent years, there has been a steady increase of interest in radial (projection reconstruction) MRI due to its potential for significant acceleration in dynamic imaging applications (10,11), advantage for motion artifacts reduction (12,13), and ability to achieve ultrashort echo times (14). It is demonstrated in this work that radial gradientecho acquisition has the additional advantage of generating images with ideally-spoiled signal intensity at very short TRs (⬍5 ms) and a wide range of FAs (up to 90°),
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when a spoiling scheme with random RF phase and gradient moments is applied. Unlike conventional RF spoiling in which a steady state is achieved (albeit potentially at a nonideal amplitude), the proposed random spoiling scheme leads to a non-steady-state condition but with a mean signal intensity equal to that of an ideally-spoiled condition. Comparisons with conventional (quadratic) RF spoiling in simulation, phantom, and in vivo experiments demonstrate the advantage of the proposed method in achieving more ideally-spoiled signal. Our results also demonstrate the effectiveness of the technique in achieving fast and accurate 3D T1 mapping and FA correction in the presence of inhomogeneous B1 transmit field. Theory Conventional RF spoiling is usually based on a quadratic variation of RF (and receiver) phase values n ⫽ n共n ⫹ 1), where is a constant and n is the absolute RF phase value at the nth TR. This is equivalent to an additional phase of n ⫽ n,
[1]
that the transverse magnetization obtains at the end of the nth TR (2). It was shown that Eq. [1] leads to a pseudosteady-state Mpss() for an isochromat with a resonance offset angle (3,15): lim M⫹ n 共兲 ⫽ Mpss 共 ⫹ n兲.
[2]
n3⬁
Here, Mn⫹ indicates the transverse magnetization after the nth RF excitation, and Mpss() is a fixed periodic function of the resonance offset angle . Equation [2] shows that the transverse magnetization is a periodic function of the resonance offset angle with a period of 2, which simply shifts by between successive TRs for a given isochromat. As a result, a constant spoiling gradient moment applied at the end of each TR will generate a steadystate voxel signal if it creates a 2 (or an integer multiple of 2) distribution of resonance offset angles within each imaging voxel: 2N
S voxel ⫽
1 N
冕
M pss共兲d ⫽ constant.
[3]
0
However, at large FAs, this steady-state value may differ significantly from the ideal spoiled signal Sspoiled, as determined by the well known Ernst formula. This is demonstrated with a Bloch equation simulation (Fig. 1), where the steady-state voxel signals with different RF phase angle offsets are computed, assuming an off-resonance distribution of 2 within each voxel. At a small FA of ␣ ⫽ 10°, RF spoiling generates a signal intensity profile nearly uniformly identical to the ideal spoiling condition for all phase increment values . At a larger FA of ␣ ⫽ 60°, however, RF spoiled signal becomes a rapid varying function of the phase increment , and generally differs signif-
FIG. 1. RF vs. ideal spoiled voxel signal intensities derived from the simulation of the Bloch equation. T1/TR ⫽ 60, T2/TR ⫽ 40. Signal for flip angle ␣ ⫽ 60° and RF phase angle ⫽ 117° is indicated by the arrow.
icantly from the ideal spoiled signal. These observations are consistent with those reported previously (2,3,16). For example, at ⫽ 117°, which was originally proposed for ideal RF spoiling (2), conventional RF spoiled signal intensity is 30% higher than the ideal. These errors could translate into significant errors in T1 and B1 mapping procedures. As pointed out in Ref. 3, local sharp peaks (more significant in the lower curve, ␣ ⫽ 60°) shown in Fig. 1 are due to effects of the various coherence pathways, or summation of signals from previous TRs. The peaks occur at ⫽ N/M, where both N and M are integers. It has been shown that at a small FA ␣, the deviation from the ideal signal is approximately proportional to ␣2. Since the magnitude of the ideal signal (as determined by the Ernst formula) is approximately proportional to ␣ at small angles, RF spoiling introduces relatively little error. At larger FAs, however, higher-order terms become more significant, leading to larger deviation from ideal signal intensity. A possible means to effectively destroy any residual coherence and therefore achieve the ideal spoiling condition is the introduction of a sufficient amount of true randomness into the spin dynamic. Darrasse et al. (17) first proposed to use random gradient moments to suppress residual transverse magnetization and to achieve better image contrast. Zur et al. (2) showed that random RF phase alone, which was first proposed by Freeman and Hill (18), is unsuitable for general purpose gradient-echo imaging due to the failure to achieve a steady state (2). In this work, by simultaneously applying both random RF and random gradients, we show that an ideal mean signal intensity level can be achieved, while the non-steady-state nature of the signal can be accommodated by an acquisition method such as radial imaging. Here we examine two possible random spoiling schemes, one applying a random RF phase and the other applying a random gradient moment in addition to the random RF phase within each TR. (It is shown later that the random gradient spoiling scheme alone is insufficient.) Figure 2 compares these two spoiling schemes with the conventional quadratic RF spoiling, by simulating Bloch equation for different isochromats along the direction of
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FIG. 2. Bloch equation simulation results comparing different spoiling schemes. T1/TR ⫽ 60, T2/TR ⫽ 40, flip angle ␣ ⫽ 60°. a–d: Transverse magnetization at the end of TR, showing both magnitude (solid) and phase (dashed). a: Conventional quadratic RF spoiling with the phase increment value ⫽ 117°. b: Random RF spoiling. c,d: Random RF and gradient spoiling, with a maximal gradient moment of 1 cycle/pixel (c) and 20 cycles/pixel (d). The horizontal line in each plot indicates the net voxel signal magnitude resulting from the vector sum of all isochromats in the voxel. e,f: Transverse magnetization after each RF excitation for conventional RF spoiling (e) and random spoiling (f), showing both magnitude (lower curves) and phase (upper curves).
the applied spoiling gradient. With conventional quadratic RF spoiling (Fig. 2a), the spatial profile of transverse magnetization at the end of TR, Mt⫺, has a fixed shape for a given combination of T1, T2, TR, and FA (other than a horizontal shift of after each TR, similar to Eq. [2]), and generally does not vectorally add to zero. Notice that isochromat signal is a periodic function of its position; i.e., f(x) ⫽ f(x ⫹ 1). Therefore, the overall voxel signal will remain at the same nonzero steady-state value even if the spoiling gradient moment is increased to create a multiple of 2 intravoxel phase dispersion. When a random RF phase is applied at each TR (Fig. 2b), although the signal varies more rapidly throughout the voxel, the overall voxel signal remains nonzero. Due to the application of a constant gradient moment, isochromat at a certain spatial location undergoes the same amount of precession in different TRs. Therefore, the coherence pathways are generally preserved, although each coherence term is modulated by a random factor at each TR, which results in a non-steady-state voxel signal. Moreover, since the signal is still a periodic function of its spatial location (as in conventional RF spoiling), increasing the gradient moment does not improve the spoiling but merely compresses the function shown in the figures. In addition to random RF phase, we also propose a random gradient spoiling scheme, in order to achieve the desired spoiled condition. In the proposed method, a uniformly distributed random gradient moment is applied at the end of each TR, in addition to applying a random RF phase. Since spins at different spatial locations accumulate different and random precession angles at different
TRs, spatial profile of the signal within each voxel becomes a nonperiodic function. As shown in Fig. 2c and d, isochromat signal f(x) ⫽ f(x ⫹ 1). When the range of the applied random gradient moment is small (Fig. 2c, with intravoxel phase dispersion in the range of [0, 2]), the overall voxel signal can still be nonzero due to the slow varying nature of both signal magnitude and phase. However, when a larger random gradient moment is applied (Fig. 2d, with intravoxel precession angles in the range of [20, 40]; the reason to avoid smaller gradients will be provided later), the isochromat signal magnitude and phase becomes a much more rapidly varying function of its position. As a result, the total transverse magnetization of each voxel becomes very close to zero. An important difference between conventional RF spoiling and random spoiling scheme is that the intravoxel signal profile achieves a steady-state with conventional spoiling (apart from the shifting according to Eq. [2]), while steady-state does not occur with random spoiling. Although the conventional quadratic RF spoiling results in a steady-state voxel signal (as determined by Eq. [3]), this value is generally different from the ideally-spoiled signal, as shown in Fig. 2e. In contrast, the proposed random spoiling scheme (with both random RF phase and gradient moments) results in a transverse signal, which slightly oscillates randomly around the ideally-spoiled signal, as shown in Fig. 2f. The dependence of this signal fluctuation on the gradient moment is further investigated below. Although the proposed random spoiling scheme introduces signal variations among different TRs, which can lead to image artifacts, radial imaging is more immune to
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FIG. 3. The point spread function (PSF) and errors caused by inter-TR signal variation for Cartesian and radial acquisition schemes, both on a 256 (readout) ⫻ 256 (view) matrix. For both schemes, each readout line is modulated by a uniformly distributed random factor with a mean of 1. a,b: PSF for Cartesian sampling (a) and radial sampling (b), when the random factor has a standard deviation of 0.5. Only the central 50 ⫻ 50 pixels of the entire FOV are shown. c: The corresponding intensity profile along the x ⫽ 0 line. The peak PSF signals at y ⫽ 0 are near 1.0. d: The dependence of the mean pixelwise error as a fraction of peak signal, on the standard deviation of the random factor. To assess the artifact level, pixels along the x ⫽ 0 line were evaluated for Cartesian data, while the central 50 ⫻ 50 pixels were evaluated for radial data.
such view-to-view signal intensity variations than conventional Cartesian imaging, not unlike the well-known robustness to motion artifacts (12). Due to the oversampling in the central k-space region and the effective signal averaging during the image reconstruction process, view-toview signal variations only result in relatively minor artifacts for radial imaging. Figure 3 compares the point spread function (PSF) and the artifact level generated by both Cartesian and radial sampling. Note that the term PSF is used here to examine the artifact level caused by the modulation in k-space due to the non-steady-state nature of the signal, as opposed to describing the appearance of a strictly point-like object. Previously, Leupold et al. (19) showed that additional signal oscillation could occur during the readout process, due to changes in the amount of intravoxel phase dispersion. For simplicity, only inter-TR signal oscillations are considered in this simulation. In this simulation, all k-space points were first set to 1, followed by modulating each readout line by a uniformlydistributed complex random factor and subsequent image reconstruction to derive the PSF. The random magnitude factors have a mean of 1 and standard deviation ranging from 0 to 0.5, which corresponds to TR-to-TR signal variations of 0 to ⫾50%. Such a large range is realistic for the proposed random spoiling scheme, as will be demonstrated in the results section. The random phase factors have an angle range of ⫾15°. For Cartesian sampling, artifacts are limited to the phase-encoding direction and therefore may be relatively high (Fig. 3a). In contrast, artifacts in radial imaging are spread out in all directions throughout the field-of-view (FOV) and therefore are attenuated (Fig. 3b). The comparison of signal profile of the PSF along the x ⫽ 0 line (Fig. 3c) shows that artifact level in the radial sampling is much lower than that of Cartesian sampling. For radial sampling, although there is some local broadening near the y ⫽ 0 line, the full-width half-maximum of PSF is still on the order of 1 pixel. Further evaluation of mean pixelwise error (Fig. 3d) shows that while error steadily increases
with the signal variation (up to 3% of the peak signal when ⫽ 0.5) in Cartesian sampling, it remains small (⬍0.4% of the peak signal) and does not increase with the amount of signal variation in radial sampling. The nonzero error for ⫽ 0 in radial sampling is likely due to the slightly broadening of PSF at its base, resulting from the imperfect interpolation during the regridding process. It is quite remarkable that inter-TR signal variation as high as 50% only introduce a negligible level of artifact for the radial sampling, due to effective signal averaging at k-space center and the “distribution of artifacts” throughout the FOV.
MATERIALS AND METHODS Simulation Bloch equation simulations were performed to further compare three different random spoiling schemes: random RF spoiling, random gradient spoiling, and the combination of random RF and gradient spoiling. Voxel signal intensities after the RF excitation were computed as the modulus of the transverse magnetization after vector summation of 360 isochromats within each voxel located linearly along the direction of applied spoiling gradient. For each isochromat, Bloch equation was iteratively solved for a total repetition number N ⫽ 4*T1/TR ⫹ 400. Both signal mean and standard deviation were evaluated using the last 400 TRs and compared with the ideal spoiled condition as determined by T1, TR, and FA ␣. To investigate the impact of the gradient moment amplitude, moments were generated according to M ⫽ rMmax, where r is a uniformly distributed number in the range of [a,1] (0 ⬍ a ⬍ 1), and the maximal random gradient moments Mmax were varied to generate 2, 4, 10, 20, 50, and 100 cycles within each voxel. As previously shown in the Theory section and further demonstrated in the Results section, spoiling is best achieved with both random RF phase and gradient moments. Therefore, the deviation from the ideally-spoiled signal intensity is compared between this random spoiling
Random Spoiling in Fast Gradient Echo Imaging
scheme and the conventional quadratic RF spoiling, at various T1/TR and T2/TR ratios in the range of [1, 200] and FAs in the range of [0, 90°]. Pulse Sequence A standard RF-spoiled 3D gradient-echo (fast low-angle shot [FLASH]) sequence was modified to allow the investigation of different spoiling schemes. A uniformly distributed random number is generated using the pseudorandom number generating function rand() provided by the Microsoft Visual C⫹⫹ 6.0 library, and used to modify the RF phase angle, the spoiling gradient moments, or both, in each TR. A second modification allows the selection of a slab-selective or a nonselective RF pulse. The latter option avoids possible complications from a nonideal slab-select profile, therefore ensuring the prescribed FAs in the computation of the ideally-spoiled signal intensity and in the T1 mapping experiments. In addition, the original Cartesian sequence was modified into a hybrid 3D radial sequence, in which the inner slice-encoding loop is phaseencoded, while in-plane a radial acquisition scheme is used. A golden angle view-angle order (20) was used to advance successive views throughout the entire scan. Phantom Experiments All phantom experiments were conducted on a 1.5T Siemens Sonata MR scanner with maximum gradient amplitude of 26 mT/m. Parameters for 3D gradient echo imaging were as follows: volume ⫽ 380 ⫻ 380 ⫻ 150 mm3, matrix size ⫽ 192 (readout) ⫻ 192 (view) ⫻ 10 (slice), scan time ⫽ 10 to 30 s. To compare the artifact levels with different acquisition and spoiling methods, Cartesian and radial phantom images were acquired with both the conventional RF spoiling and the proposed random spoiling, using the same FA, TR, and maximal spoiling gradient moments. In addition to visual inspection, the background noise levels in the images were evaluated in a region with no imaging object. To compare the effectiveness of spoiling with the proposed method with conventional RF spoiling, a phantom imaging experiment was carried out. The phantom contained 1.25 g NiSO4 䡠 (H2O)6 and 5g NaCl per 1000 g H2O, and its T1 value was measured with a standard 2D inversion-recovery spin-echo sequence. 3D gradient-echo radial images with standard RF spoiling and the proposed random spoiling were acquired with FAs ␣ ⫽ 10° to 90° in 10-degree increments at both TR ⫽ 15 ms and TR ⫽ 4.3 ms. The system transmitter gain was calibrated manually while using nonselective RF to ensure the prescribed FAs. For the random spoiling, a spoiling gradient moment along the slice direction was applied at the end of each TR, with a uniformly-distributed random value in the range of [11.8, 23.6] mT 䡠 ms/m, corresponding to a resonance offset angle range of [10, 20] within a slice thickness of 10 mm. For conventional RF spoiling, a fixed phase increment value of ⫽ 117° was used, while a fixed gradient moment of 23.6 mT 䡠 ms/m (10 cycles/voxel) was applied at the end of each TR. Since both spoiling mechanisms generate nearly ideal signal at ␣ ⫽ 10° (as shown in Fig. 1), one can derive the ideal spoiling signal at larger FA, with the knowledge of T1
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value determined from the inversion-recovery experiment. The mean signal intensities from the same region of interest near the isocenter (to reduce the potential influence of B1 inhomogeneity) were compared for the two spoiling schemes. T1 Mapping and FA Correction Suboptimal spoiling with conventional techniques is especially problematic when quantitative parameters, such as T1 and FA, are measured. A phantom experiment was carried out to compare the accuracy of T1 mapping with the proposed technique and conventional RF spoiling, on a 1.5T Siemens Sonata MR scanner. The phantom consists of six tubes with the following concentrations of gadolinium solutions: 3.0, 1.5, 1.0, 0.5, and 0.3 mM, in order to achieve a T1 range of ⬃80 ms to 800 ms. Radial images were acquired at following FAs: ␣ ⫽ 3°, 10°, 20°, and 40°. The signal intensity S was then fitted to the following equation to determine the T1s (6): S S ⫽ E1 ⫹ M0 共1 ⫺ E1 兲. sin␣ tan␣
[4]
Here, M0 is the equilibrium magnetization and the slope E1 ⫽ exp (–TR/T1). The true T1 values were determined with a separate set of inversion-recovery measurements. To compare the accuracy of FA correction with the proposed method with conventional RF spoiling, T1 mapping and FA correction experiments were also carried out on a large (⬃36 cm in length) homogeneous phantom which contained 1.24 g NiSO4 䡠 (H2O)6 and 2.62g NaCl per 1000 g H2O. The T1 mapping procedure was the same as the previous experiment, while the FA mapping procedure was carried out using the AFI technique proposed recently (7). AFI uses gradient-echo imaging with two interleaved TRs (TR1 and TR2) with different lengths and the same FA to establish an alternating steady state. It was shown that when TR1 ⬍ TR2 Ⰶ T1, the signal ratio of two interleaved acquisitions, r ⫽ S2 /S1, becomes independent of T1. Rather, the actual FA can be then determined from this ratio as: ␣ ⫽ arccos
rn ⫺ 1 . n⫺r
[5]
Here n ⫽ TR2/TR1. In our experiment, n ⫽ 4 and FA ␣ ⫽ 60°. A calibration factor was then computed as the ratio of the true FA ␣ computed from Eq. [5] to the prescribed FA. This calibration factor was subsequently used to adjust the FA ␣ used in the fitting shown in Eq. [4]. To further demonstrate the utility of the proposed method, brain T1 mapping and FA correction experiments were also carried out in a healthy volunteer on a 3.0T Philips Achieva MR scanner, using a body transmit coil and an eight-channel receive-only head coil. Both the T1 mapping and AFI experiment used the same imaging volume and similar scan parameters: 3D sagittal imaging volume ⫽ 230 ⫻ 230 ⫻ 210 mm3, matrix size ⫽ 256 (readout) ⫻ 256 (total view number) ⫻ 35 (slice encodes), scan times ⫽ 1.5 min for each FA for T1 mapping and 7.5 min
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FIG. 4. a,b: Bloch equation simulation results of the voxel signal for two different random spoiling schemes, with solid and dashed lines showing the normalized mean and standard deviation, respectively. T2/TR ⫽ 40, flip angle ␣ ⫽ 60°. a: A random gradient moment in the form of M ⫽ r Mmax is applied, where r is a uniformly distributed random number in the range of [0.5, 1]. b: A combination of random gradient moment (same as in (a)) and a random RF phase (in the range of [0, 360°]) was applied. c: The dependence of the voxel signal standard deviations on flip angles at different maximal spoiling gradient moments for the scheme shown in (b). T1/TR ⫽ 60, T2/TR ⫽ 40. The legend indicates the maximal gradient moments per voxel.
for AFI scan. For the two T1 mapping scans, TR ⫽ 10 ms and FA ␣ ⫽ 5° and 20°. For AFI, TR1/TR2 ⫽ 10 ms/40 ms and FA ␣ ⫽ 60°. To reduce the interference from noise, a fourth-order 2D polynomial function was used to fit the FA calibration factor determined from the AFI scan.
RESULTS Figure 4 shows the simulation results comparing the voxel signal for different random spoiling schemes. A relatively large FA ␣ ⫽ 60° was selected, and two T1/TR ratios of 60 and 200 were studied. When applying random gradient moments, it was found that avoiding small gradient moments generate closer to ideal signal levels. This can be understood as follows: if the applied gradient moment is too small, intravoxel phase dispersion is also small, resulting in the preservation of some coherence and negating the purpose of applying random gradient moments. Therefore, the random gradient moment was applied according to M ⫽ rMmax, where r is a uniformly distributed number in the range of [0.5, 1]. Figure 4a and b compares random gradient spoiling without and with additional random RF phase. When random gradient moments were used alone (Fig. 4a), nearly ideal spoiled signals (mean close to 1) were only achieved when a large gradient moments (⬃100 cycles/voxel) were applied. When random gradient moments were applied in combination with a random RF phase (Fig. 4b), ideal signal levels were achieved with much lower maximal gradient moments. With a maximal gradient moment of 20 cycles per voxel, mean signal magnitude deviates from ideal value by ⬍1%, and the inter-TR signal standard deviation is less than 40%. In comparison, spoiling with only the random RF phase generated signals (mean ⫾ standard deviation) of 0.87 ⫾ 0.76 and 0.88 ⫾ 1.16, for T1/TR ⫽ 60 and 200, respectively.
Figure 4c shows the dependence of the normalized standard deviation of the voxel signal on FAs at different maximal gradient spoiling moments. In general, increasing the maximal spoiling gradient moment reduces the amount of signal variation, consistent with results shown in Fig. 4a and b. Furthermore, for any fixed maximal gradient moment, the relative amount of signal variation (as expressed by normalized standard deviations) increase as FAs increase and the ideal spoiled signal level goes down. These results demonstrate that optimal random spoiling is achieved with simultaneous application of random RF phase and gradient moment (10 –20 cycles/voxel). Images from phantom experiments demonstrate the advantage of radial vs. Cartesian acquisition in suppressing artifacts caused by inter-TR signal variation (Fig. 5). In conventional RF spoiling, a steady state is reached, therefore resulting in an artifact-free image with the Cartesian acquisition (Fig. 5a), although its signal intensity is incorrect due to nonideal spoiling. In contrast, Cartesian images acquired with the proposed spoiling method show significant ghosts due to the residual signal variation occurring between different readout lines (Fig. 5b). However, when radial acquisition is used in conjunction with the proposed random spoiling, imaging artifact due to signal variation is substantially reduced (Fig. 5c). Further evaluation of noise levels at background regions shows that additional noise (streaks) introduced by random spoiling scheme is negligible (⬍1%), in agreement with results from Fig. 3. This indicates that the non-steady-state nature of the proposed random spoiling does not introduce significant streaking artifacts. Figure 6 shows the simulation results comparing signal intensities at different T1/TR, T2/TR ratios, and FAs for conventional RF spoiling and the proposed random spoiling schemes. In conventional RF spoiling, the signal level
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FIG. 5. Images from a phantom experiment. a: Cartesian acquisition with conventional quadratic RF spoiling. b: Cartesian acquisition with the proposed random spoiling. c: Radial acquisition with the proposed random spoiling. For random spoiling, maximal gradient moments is 20 cycles/voxel. T1 ⫽ 300 ms, T2 ⫽ 260 ms, ␣ ⫽ 60°, TR ⫽ 4.3 ms. All three datasets use 192 views.
begins to deviate significantly (up to 30 – 60%) from the ideal spoiling condition when T1,2/TR ⬎ 50 or FA ␣ ⬎ 20°. In contrast, with the proposed random spoiling, voxel signal level never deviate from the ideal spoiling condition by more than 7% in the entire range of T1/TR, T2/TR ratios (1–200) and FAs (0 –90°). Figure 7 shows results from the phantom experiment, comparing the performance of two spoiling schemes. At TR ⫽ 15 ms (Fig. 7a), RF spoiled image intensity starts to deviate from ideal when ␣ ⬎ 20°, with a largest error of 29% at ␣ ⫽ 50°. For random spoiling, measured signal
deviates from ideal value less than 4% throughout the entire range of FA from 10° to 90°. The mean absolute error of random spoiled signal is 2%, compared with 14% for RF spoiling for the nine FA values where data were acquired. At TR ⫽ 4.3 ms (Fig. 7b), again random spoiling produced more ideal signal, with a mean absolute error of 5.0% compared with a 16.7% error for conventional RF spoiling, for the range of FA from 10° to 90°. The experimental measurements (Fig. 7, markers) are consistent with Bloch simulation results (Fig. 7, dashed lines).
FIG. 6. Bloch simulation results of conventional RF spoiling (a,c) and the proposed random spoiling (b,d). a,b: Signal dependence on T1/TR ratio at different flip angles, assuming a fixed T1/T2 ratio of 2. c,d: Signal dependence on T2/TR ratio at different flip angles, assuming a fixed T1/TR ratio of 200. Both plots contain data from five flip angles: ␣ ⫽ 5, 10, 20, 40, and 60. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
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FIG. 7. The image intensity ratio to the ideal spoiling condition, for conventional RF spoiling and the proposed random spoiling schemes, measured in a phantom experiment. The phantom T1 ⫽ 300 ms, T2 ⫽ 260 ms. a: TR ⫽ 15 ms. b: TR ⫽ 4.3 ms. Dashed lines are from Bloch equation simulation, while markers are experimental measurements.
The T1 mapping results from the gadolinium phantom experiment is shown in Fig. 8. The errors in the computed T1 values were consistently ⬍3% with random spoiling, while it increases to 15.7% for the phantom with a small T1 (⬃80 ms) with quadratic RF spoiling. These results underscore the advantage of the proposed random spoiling scheme in achieving accurate T1 measurements. The reason that short-T1 species are more sensitive to imperfect spoiling will be discussed further below. The importance of proper spoiling is further demonstrated in another T1 mapping phantom experiment when inhomogeneous transmitted B1 field (and thus FA) is accounted for with the AFI technique (Fig. 9). It can be seen that due to the large size of the phantom (⬃36 cm in length), inhomogeneous B1 fields near both ends of the phantom cause large T1 errors when no FA correction is performed (Fig. 9a). When FA correction was performed with the conventional RF spoiling, there is still significant residual T1 variation within the homogeneous phantom
due to suboptimal spoiling (Fig. 9b). In particular, the edge of the phantom shows significantly underestimated T1 values. When AFI correction was performed with random spoiling (Fig. 9c), the resulting T1 map becomes homogeneous throughout the phantom, including the edges. Comparison of the T1 profile (Fig. 9d) confirmed the superior performance of the random spoiling over conventional RF spoiling, in achieving FA correction and accurate T1 mapping. Brain T1 mapping and FA correction results are shown in Fig. 10. It can be seen that at 3.0T, the transmit B1 field falls off quickly from the center of the object (Fig. 10b). Without FA correction, T1 values are underestimated and inhomogeneous, particularly near the superior regions of the brain (Fig. 10c and d). When conventional RF spoiling method was used for FA correction, T1 values at the frontal lobe and posterior regions of the brain are still underestimated (Fig. 10e). When the proposed random spoiling method was used, the T1 values are more consistent for the each tissue type throughout the image (Fig. 10f). The T1 value derived from the map is consistent with previous reported T1 values (21) for brain tissue at 3T (white matter [corpus callosum] ⬃1000 ms, gray matter ⬃1800 ms, cerebrospinal fluid [CSF] ⬎3000 ms). These results underscore the importance of an appropriate spoiling method in achieving accurate quantitative measurements with gradient-echo sequences and reveal the weakness of currently used protocols.
DISCUSSION AND CONCLUSIONS
FIG. 8. Comparison of T1 measurement errors in a gadolinium phantom experiment. Six phantom tubes were filled with doped water with gadolinium concentrations of 3.0, 1.5, 1.0, 0.75, 0.5, and 0.3 mM, respectively. 3D radial gradient-echo images, acquired with TR ⫽ 5 ms and flip angles ␣ ⫽ 5, 10, 20, and 40, with either conventional RF spoiling or the proposed random spoiling schemes, were used to determine T1 values according to Eq. [4]. Actual T1 values were determined from a separate inversion-recovery experiment.
Interestingly, the results of the T1 mapping experiment plotted in Fig. 8 show that short-T1 species are more sensitive to nonideal spoiling. This can be understood as follows: As previously shown by Deoni et al. (22), T1 fitting with Eq. [4] is most sensitive to signal errors occurring at two FAs ␣1 and ␣2, which lie at either sides of Ernst angles ␣E (S␣1 ⫽ S␣2 ⫽ 0.71S␣E, where S␣ is the signal intensity at the FA ␣). As shown in Fig. 7, conventional RF spoiling contains more error at larger FAs (e.g., 40°), which is closer to the Ernst angle of the shorter T1 phantom (e.g., ␣E ⫽ 20°
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FIG. 9. T1 mapping and AFI correction phantom experiment. a: T1 map (in ms) before AFI correction. b,c: T1 maps after AFI correction with conventional RF spoiling (b) and the proposed random spoiling (c). d: T1 profiles along the dashed line shown in (a). The horizontal dashed line is the T1 value determined from a separate inversionrecovery experiment.
for T1/TR ⫽ 80/5 ms) than that of the longer T1 phantom (e.g., ␣E ⫽ 6° for T1/TR ⫽ 800/5 ms). In other words, the T1 fitting procedure we have used in this work is less sensitive to imperfect spoiling for longer T1 species.
In general, quadratic RF spoiling begins to deviate significantly from the ideal spoiling condition at either larger FAs (␣ ⬎ 20°) or shorter repetition times (T1/TR ⬎ 50 or T2/TR ⬎ 50) due to the contributions from refocused coherence path-
FIG. 10. In vivo brain T1 mapping and flip angle correction results. a: T1-weighted image acquired with the proposed random spoiling scheme. b: Flip angle correction factor determined from the AFI scan with random spoiling. c,d: T1 map (in ms) without flip angle correction, using conventional RF spoiling (c) and the proposed random spoiling (d). e,f: Corrected T1 map with conventional RF spoiling (e) and the proposed random spoiling method (f).
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ways, or residual magnetization from earlier TRs (see Fig. 6). As a result, the conventional RF spoiling strategy could generate significant quantitative errors at imaging conditions commonly prescribed. For T1 and B1 mapping applications where larger FAs are necessary, the relative errors further increase. This is consistent with results from an earlier study (3), showing that quadratic RF spoiling becomes nonideal when T1/TR or T2/TR becomes large. It was first demonstrated in this work that a combination of random RF phase and gradient moments effectively achieve nearly ideally-spoiled voxel signal for a wide range of T1/TR and T2/TR ratios (1–200) and FAs (0 –90°). While random gradient moments destroy the voxel coherence pathways, application of an additional random RF phase was shown to further reduce the maximal gradient moment requirement to 10 to 20 cycles per voxel, therefore allowing short repetition times. When the proposed random spoiling scheme is applied to radial MRI, artifact introduced by inter-TR signal variation is attenuated, producing ideal T1-weighted images. In our experiments, spoiling gradients were applied along the slice direction. Since the slice thickness is typically larger than the in-plane pixel size, this choice reduces the minimum TR length required to achieve the desired level of intravoxel phase dispersion. It has been shown previously that diffusion could further reduce the residual transverse magnetization and result in an improved spoiling behavior (8,9). Therefore, it is possible that a smaller spoiling gradient moment may be sufficient for ideal spoiling when diffusion is considered, further reducing the minimum TR. It should be noted that the random gradient moments, in addition to creating an intravoxel dephasing, will also introduce a voxel-dependent random phase, which is proportional to the product of the spoiler gradient moment and the distance of the voxel from the isocenter, along the direction of the spoiler gradient. This phase term is analogous to a randomized RF phase for all the slices with some distance from the isocenter. For the central slice passing through the isocenter, however, simulation shows that random gradients alone result in mean signal intensities 40% to 100% different from the ideal spoiled condition. Thus, random RF phase is needed in addition to random spoiler gradients. A by-product of applying random RF phase and gradient moments is that the signal no longer reaches a true steadystate. As demonstrated in simulations and phantom experiments, this results in negligible errors for radial acquisitions due to the “distribution of artifacts” throughout the entire FOV. Due to the random nature of view-to-view signal variation, it is expected that artifact will remain negligible for any other radial view-angle ordering schemes. For Cartesian acquisitions, however, inter-TR signal variation may introduce significant image ghosting in high-SNR applications. One possible means to reduce such signal variation is to apply a larger random gradient moment, as demonstrated in Fig. 4c, at a cost of longer TR. In conclusion, an improved spoiling method has been proposed for fast radial gradient-echo imaging, based on a combination of random RF phase and random gradient moments. When compared with conventional RF spoiling, the new schemes provide more ideal T1-weighted signal at
Lin and Song
shorter TRs and larger FAs. Phantom and in vivo experiments demonstrate the capability of the proposed method to achieve accurate 3D T1 mapping and FA correction. It is anticipated that the proposed technique will be particularly useful in dynamic contrast-enhanced imaging applications where T1 maps are required to compute tissue perfusion while the use of undersampled radial imaging may be beneficial to enhance temporal resolution. REFERENCES 1. Tofts PS, Kermode AG. Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging. 1. Fundamental concepts. Magn Reson Med 1991;17:357–367. 2. Zur Y, Wood ML, Neuringer LJ. Spoiling of transverse magnetization in steady-state sequences. Magn Reson Med 1991;21:251–263. 3. Denolin V, Azizieh C, Metens T. New insights into the mechanisms of signal formation in RF-spoiled gradient echo sequences. Magn Reson Med 2005;54:937–954. 4. Yarnykh VL. Effect of phase increment on the accuracy of T1 measurements by the variable flip angle method using a fast RF spoiled gradient echo sequence. In: Proceedings of the 15th Annual Meeting of ISMRM, Berlin, Germany, 2007 (Abstract 1796). 5. Deoni SC, Rutt BK, Peters TM. Rapid combined T1 and T2 mapping using gradient recalled acquisition in the steady state. Magn Reson Med 2003;49:515–526. 6. Cheng HM, Wright GA. Rapid high-resolution T1 mapping by variable flip angles: accurate and precise measurements in the presence of radiofrequency field inhomogeneity. Magn Reson Med 2006;55:566 –574. 7. Yarnyth VL. Actual flip-angle imaging in the pulsed steady state: a method for rapid three-dimensional mapping of the transmitted radiofrequency field. Magn Reson Med 2007;57:192–200. 8. Yarnykh VL. Improved accuracy of variable flip angle T1 measurements using optimal radiofrequency and gradient spoiling. In: Proceedings of the 16th Annual Meeting of ISMRM, Toronto, Ontario, Canada, 2008 (Abstract 234). 9. Yarnykh VL. Optimal spoiling of the transverse magnetization in the actual flip-angle (AFI) sequence for fast B1 mapping. In: Proceedings of the 16th Annual Meeting of ISMRM, Toronto, Ontario, Canada, 2008 (Abstract 3090). 10. Peters DC, Grist TM, Korosec FR, Holden JE, Block WF, Wedding KL, Carroll TJ, Mistretta CA. Undersampled projection reconstruction applied to MR angiography. Magn Reson Med 2000;43:91–101. 11. Mistretta CA, Wieben O, Velikina J, Block W, Perry J, Wu Y, Johnson K, Wu Y. Highly constrained backprojection for time-resolved MRI. Magn Reson Med 2006;55:30 – 40. 12. Glover GH, Noll DC. Consistent projection reconstruction (CPR) techniques for MRI. Magn Reson Med 1993;29:345–351. 13. Larson AC, White RD, Laub G, McVeigh ER, Li D, Simonetti OP. Self-gated cardiac cine MRI. Magn Reson Med 2004;51:93–102. 14. Rahmer J, Boernert P, Groen J, Bos C. Three-dimensional radial ultrashort echo-time imaging with T2 adapted sampling. Magn Reson Med 2006;55:1075–1082. 15. Crawley AP, Wood ML, Henkelman RM. Elimination of transverse coherences in FLASH MRI. Magn Reson Med 1988;8:248 –260. 16. Duyn JH. Steady state effects in fast gradient echo magnetic resonance imaging. Magn Reson Med 1997;37:559 –568. 17. Darrasse L, Mao L, Saint-Jalmes H. Steady-state management in fast low-angle imaging. In: SMRM Book of Abstracts, Montreal, Quebec, Canada; 1986. pp. 944 –945. 18. Freeman R, Hill HDW. Phase and intensity anomalies in Fourier transform NMR. J Magn Reson (1969) 1971;4:366 –383. 19. Leupold J, Hennig J, Scheffler K. Moment and direction of the spoiler gradient for effective artifact suppression in RF-spoiled gradient echo imaging. Magn Reson Med 2008;60:119 –127. 20. Winkelmann S, Schaeffter T, Koehler T, Eggers H, Doessel O. An optimal radial profile order based on the golden ratio for time-resolved MRI. IEEE Trans Med Imaging 2007;26: 68 –76. 21. Stanisz GJ, Odrobina EE, Pun J, Escaravage M, Graham SJ, Bronskill MJ, Henkelman RM. T1, T1 relaxation and magnetization transfer in tissue at 3T. Magn Reson Med 2005;54:507–512. 22. Deoni SC, Peters TM, Rutt BK. High-resolution T1 and T2 mapping of the brain in a clinically acceptable time with DESPOT1 and DESPOT2. Magn Reson Med 2005;53:237–241.
