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A fast 3D Look-Locker method for volumetric T1 mapping
Magnetic Resonance Imaging, Vol. 17, No. 8, pp. 1163–1171, 1999 © 1999 Elsevier Science Inc. All rights reserved. Printed in the USA. 0730-725X/99 $–see front matter
PII S0730-725X(99)00025-9
● Original Contribution
A FAST 3D LOOK-LOCKER METHOD FOR VOLUMETRIC T1 MAPPING ELIZABETH HENDERSON,* GRAEME MCKINNON,§ TING-YIM LEE ,*†‡
AND
BRIAN K. RUTT*†
*Imaging Research Laboratories, The John P. Robarts Research Institute; †Department of Diagnostic Radiology, London Health Sciences Center, University Campus; ‡Department of Radiology and Lawson Research Institute, St. Joseph’s Health Center, London, Ontario, Canada; and §Applied Science Laboratory, GE Medical Systems, Milwaukee, WI, USA We introduce a fast technique, based on the principles of the 2D Look-Locker T1 measurement scheme, to rapidly acquire the data for accurate maps of T1 in three dimensions. The acquisition time has been shortened considerably by segmenting the acquisition of the ky phase encode lines. Using this technique, the data for a 256 ⴛ 128 ⴛ 32 volumetric T1 measurement can be acquired in 7.6 min. T1 measurements made in phantoms with T1s between 200 and 1200 ms had an accuracy of 4% and a reproducibility of 3.5%. Measurements of T1 made in normal brain using the fast 3D sequence corresponded well with inversion-recovery fast spin-echo measurements. © 1999 Elsevier Science Inc. Keywords: Longitudinal relaxation time; T1; 3D; Look-Locker.
INTRODUCTION
therapy have led to increasingly complex target volumes being prescribed, generating a need for practical 3D radiation dosimetry techniques for quality control. Gel dosimeters have potential for 3D radiation dosimetry, since the dose of ionizing radiation absorbed is inversely proportional to the T1 of the irradiated gels.7 As a result, gel T1 has been studied extensively as a measure of the radiation dose absorbed by dosimetric gels.8 –13 A volumetric measurement of gel T1 would enable accurate 3D radiation dosimetry with greater through-plane spatial resolution than is achievable with single slice measurements. One of the major problems encountered in making accurate maps of T1 is the long imaging time required. For good accuracy over a wide range of T1 values, multiple points of the T1 recovery curve must be sampled. If a conventional two-dimensional (2D) inversionrecovery spin-echo sequence is used, data acquisition for each slice can take hours. Several schemes have been developed for the rapid imaging of T1 in 2D in which multiple points on the recovery curve are sampled.14 These techniques include methods based on Look-Locker,15–22 snapshot-fast low-angle shot (snapshot–
Several new magnetic resonance (MR) applications require quantitative measurements of the spin-lattice relaxation time (T1) in three dimensions (3D) in relatively short time frames (under 10 min). For example, quantitative tracer kinetic studies, in which vascular parameters such as blood volume and capillary permeability are calculated from dynamic contrast-enhanced MR data, require an accurate measurement of pre-contrast tissue T1. Before application of a tracer kinetic model, tissue enhancement following contrast agent administration must be converted into contrast agent concentration, and it can be shown that this calibration is strongly dependent on the pre-contrast tissue T1.1– 6 Ideally, tracer kinetic studies should be done in 3D for complete characterization of a lesion, for locating small lesions not apparent in pre-contrast scans, or for examining multiple lesions in one study. Furthermore, the pre-contrast T1 measurement should be made in less than 10 min for the study to fit into a reasonable time frame. Another application requiring a measurement of volumetric T1 is radiation dosimetry. Advances in radiation RECEIVED 11/22/98; ACCEPTED 3/20/99. Address correspondence to Dr. Brian K. Rutt, Imaging Research Laboratories, The John P. Robarts Research Institute,
P.O. Box 5015, 100 Perth Drive, London, Ontario, Canada, N6A 5K8. E-mail: [email protected] 1163
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FLASH),23–26 inversion-prepared echo planar imaging (EPI),27–30 and stimulated echo imaging.31–33 There are two approaches to snapshot-FLASH based T1 measurement. In the first, an inversion pulse is followed by a train of snapshot-FLASH images with which the T1 relaxation curve is sampled.23 This is a very rapid and easily implemented method for T1 measurement. It would also be very simple to alter this technique for 3D volume acquisition. One problem with this approach, however, is that the time taken to acquire a high spatial resolution image is too long to properly sample the T1 relaxation curve. For volumetric imaging in particular, this problem would severely limit the accuracy of the T1 map. Nekolla et al.24 have circumvented this problem in 2D imaging by acquiring only phase encode lines covering the center quarter of k-space. Another difficulty with this T1 measurement scheme is that T1 relaxation is modulated by the sampling process, limiting the accuracy of the T1 measurements. For the case in which there is no delay between successive snapshot-FLASH image acquisitions, however, this modulation of the T1 relaxation is described by Look-Locker theory,15 and very accurate measurements of T1 can be obtained.25 The second snapshot-FLASH based approach to T1 imaging is to repeat an inversion-pulse/single snapshotFLASH image combination for various delay times (TI) between the inversion pulse and the snapshot-FLASH acquisition.23,26 This approach could also be easily modified for 3D T1 mapping. In this case, if centric k-space acquisition is used, errors due to improper sampling of the relaxation curve and modulation of the relaxation by the snapshot-FLASH imaging are avoided.26 This second approach, however, suffers from a relatively longer imaging time. The EPI technique for T1 measurement consists of an inversion pulse followed by multiple EPI acquisitions.27 The major advantages of this technique are that the data required for EPI-based T1 maps can be acquired extremely rapidly, that multiple slices can be acquired, and that the EPI acquisition does not interfere with the T1 relaxation. Recently, a technique (LL-EPI) has been proposed in which EPI is combined with Look-Locker readout so that the data needed to sample the entire T1 relaxation curve for a 2D T1 map is acquired in under 3s.28,29 The accuracy and repeatability that have been reported for LL-EPI technique, however, are not as good as those reported for the more time-consuming LookLocker technique with spin-warp imaging.21,28 Other characteristics of EPI, including the need for high-performance gradient coils, sensitivity to magnetic field inhomogeneities, chemical shift artifacts, and low signal to noise, limit the applicability of EPI techniques. Stimulated echo techniques for T1 measurement con-
sist of a STEAM acquisition in which the third saturation pulse is broken up into a series of variable tip angle read pulses, which are used to sample the T1 relaxation of the stored longitudinal magnetization.31–33 The major advantage of these techniques is that they are insensitive to magnetic field heterogeneity.33 If only stimulated echoes are used for the T1 measurement,31,32 the very low dynamic range limits the effectiveness of the T1 map generation.16 If, however, a spin echo is acquired and included in the fit in combination with the stimulated echoes, the dynamic range of the technique is increased. T1 measurements made with this technique are very accurate, although precision is lower than that obtained using Look-Locker techniques.33 The major advantages to Look-Locker based T1 measurement techniques are that the acquisition time is short, and that the T1 relaxation behavior has been well-characterized.15 It has been shown in a theoretical analysis that if the Look-Locker technique is used, rather than the more time-consuming conventional inversion recovery method, T1 can be measured quickly with no penalty to the signal-to-noise ratio of the calculated T1 image.16 Other authors have demonstrated the high degree of accuracy and precision achievable with this technique experimentally.17–21 In this paper, we introduce a fast 3D technique, based on the principles of the 2D Look-Locker T1 measurement scheme, to rapidly acquire the data for accurate maps of T1 in 3D. The acquisition time needed for volumetric T1 mapping has been shortened considerably by segmenting the acquisition of the ky phase encode lines. This technique is similar to what might be obtained by modifying the snapshot-FLASH based T1 measurement schemes for 3D, however, since there is no delay between acquisition of successive volumes and since the T1 relaxation is governed by the principles introduced by Look and Locker, we refer to it as a fast 3D Look-Locker (f3DLL) technique. A preliminary version of this work has been presented previously.34
PULSE SEQUENCE The fast 3D pulse sequence for T1 measurement (f3DLL) is based on the spectroscopic method for T1 measurement developed in 1970 by Look and Locker15 and later adapted for 2D imaging applications.17–21 The basic principle is that following an inversion pulse (for optimal dynamic range), the recovery of longitudinal magnetization to a steady state is repeatedly sampled by a series of small flip-angle rf pulses (␣) separated by a small time . The recovery of the magnetization is modulated by the alpha pulses, and therefore the magnetiza-
A fast volumetric T1 measurement method ● E. HENDERSON
Fig. 1. Schematic diagram of a conventional 2D Look-Locker type pulse sequence.
tion is driven to steady state with the modified relaxation time T1*: T1* ⫽
T1 T1 1 ⫺ ln(cos(␣))
(1)
In a conventional (2D) Look-Locker imaging scheme (Fig. 1), the inversion-pulse/␣-pulse train is repeated for every ky phase encode step. For N ␣-pulses, a series of N images are formed corresponding to times TIn ⫽ td ⫹ (n⫺1), (n ⫽ 1,2, . . . N) after the inversion pulse, where td is the time between the inversion pulse and the first ␣ pulse. A T1 map can be produced by fitting the T1 recovery curve of each pixel to a theoretical signal equation. Adapting this conventional Look-Locker approach to 3D, however, would make the sequence time very long. For example, if 16 ␣-pulses spaced 75 ms apart, with no undisturbed recovery period, tr, were used to sample the recovery curve,19 then acquisition of a 256 ⫻ 128 ⫻ 32 matrix would take 1.4 h. Because of the above concern for scan time in the case of 3D T1 mapping, we introduce here an accelerated method for Look-Locker acquisition (Fig. 2). A slab selective inversion pulse is followed by a long train (N ⬎ 100) of low flip angle (␣) readout pulses with minimal (⬍10 ms). Transverse magnetization is completely spoiled before the application of each subsequent excitation pulse. At the end of the train of ␣-pulses, an undisturbed delay (tr) is optionally inserted to allow recovery of longitudinal magnetization prior to the next inversion pulse. The train of ␣-pulses is divided into several (e.g., M ⫽ 16) groups, and within each group,
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multiple phase encodes (ky lines) are acquired. Each group yields one “effective TI” volume. If the number of ky lines spanned by each group were equal to the total number of ky lines, Nky, the spins would be driven to steady state too rapidly, and the longitudinal recovery would be undersampled. This would lead to inaccurate determinations of T1. In order to ensure that the effective TI volumes are spaced close enough together to achieve adequate sampling of the recovery curve, the ky lines are acquired in an interleaved multi-shot fashion. The inversion-pulse/␣-train combination is repeated for the number of shots (Nshots) needed to cover the entire ky plane, (inner loop) and for all kz slices (Nkz) in the volume (outer loop). The number of ␣-pulses following the inversion pulse therefore is equal to (Nky/Nshots)*M. An alternative approach to implementing this sequence would be to have kz acquisition in the inner loop and ky acquisition in the outer loop. In this case, since Nkz is typically smaller than Nky, the acquisition of kz would not have to be divided into multiple shots. This strategy, however, may lack some flexibility in the choice of N/M. The behavior of the MR signal for a 2D Look-Locker imaging sequence has been derived by Brix et al.18 This theoretical signal equation assumes complete spoiling of transverse magnetization before each readout pulse and includes the effects of a non-zero time (td) between the inversion pulse and first ␣-pulse, and a waiting time (tr) at the end of the train of ␣-pulses. The relevant timings are shown in the schematic pulse sequence diagram for the 2D imaging implementation in Fig. 1. The longitudinal magnetization just before the nth read-out pulse, mn, is given by the equation:15,18 mn ⫽ meq关F⫹(cos(␣)E)n⫺1(Q ⫺ F)兴
(2)
Fig. 2. Schematic diagram of the f3DLL pulse sequence.
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where F ⫽ (1⫺E)/(1⫺cos(␣)E), Q⫽
⫺F cos(␣)ErEd关1 ⫺ (cos(␣)E)N⫺1兴 ⫺ 2Ed ⫹ Er ⫹ 1 , 1 ⫹ cos(␣)ErEd(cos(␣)E)N⫺1 E ⫽ exp(⫺/T1), Er ⫽ exp(⫺tr/T1), Ed ⫽ exp(⫺td/T1),
meq is the equilibrium magnetization, and N is the total number of read-out pulses (and hence the total number of 2D images). The image intensity of pixel (i,j) in the nth gradient-echo image produced by this sequence is therefore: Sn(i,j) ⫽ 兩sin(␣)(i,j)mn(i,j)exp共⫺TE/T2*(i,j)兲兩
(3)
Equation 3 may be used to fit to the data from the fast 3D Look-Locker sequence, except in this case, ‘n’ must be reinterpreted as the number of the ␣-pulse at which the center of k-space is collected. For example, if a 256 ⫻ 128 ⫻ 32 matrix is acquired with linear ky phase encoding in four shots, then 32 ky lines are collected in each shot or group, and the center of ky is acquired after 16(2 m ⫺1) ␣-pulses, for m ⫽ 1,2,3. . . M, where M is the number of volumes (effective TI’s) acquired. A volumetric measurement of T1 can be made by fitting Eq. 3 to the data from each voxel acquired using the pulse sequence illustrated in Fig. 2. There are several things to consider when setting the timings for the 3D acquisition. In general, for optimal accuracy in T1 measurements, the first time point on the recovery curve should be as close to zero as possible.35 In the f3DLL case, this translates to minimizing the time between the inversion pulse and the acquisition of the center of k-space for the first effective TI volume. In our implementation, we minimize this time through a partial ky acquisition (i.e., from ⫺kymax/8 to kymax). Another solution would be to centrically acquire ky. In addition, since the train of ␣-pulses is very long for the 3D implementation, ␣ should be small (⬍15°) so that the magnetization is not driven to steady state too rapidly, and should be set to its minimum value (preferably ⬍ 5 ms). MATERIALS AND METHODS The 3D pulse sequence was implemented on a whole body 1.5T MR scanner equipped with 22 mT/m gradients (Signa Horizon EchoSpeed, GE Medical Systems, Mil-
waukee, WI, USA). The number of effective TI volumes acquired (M) was kept fixed at 16. The T1 maps were calculated by fitting Eq. 3 to the data from each voxel using the quasi-Newton bounded minimization routine E04JAF from the NAG Fortran Library (The Numerical Algorithms Group Ltd., Downers Grove, IL). Equation 3 was fit for two parameters only: T1 and the scaling constant A ⫽ meqsin(␣)exp(⫺TE/T2*). This approach assumes that the value of ␣ is known and constant over the volume. When fitting for A and T1 only, a 256 ⫻ 128 T1 map can be calculated in approximately 22 min on a Sun Sparc 10 (Sun Microsystems, Mountain View, CA, USA). However, computing time can be reduced significantly by only fitting the regions of the image that are of interest. The performance of the pulse sequence and fitting was evaluated using a set of 9 aqueous solutions of Gd-DTPA (Magnevist, Berlex Canada, Lachine, PQ) in 3 cm diameter tubes covering a range of T1’s between 100 ms and 1200 ms. The tubes were imaged in a transmit/receive head rf coil, inside a cylindrical loader shell filled with doped saline (GE Medical Systems, Milwaukee, WI, USA). Accuracy of the T1 measurements was assessed by comparison with T1 measurements made with a 2D inversion-recovery spin-echo (IRSE) sequence repeated for 12 inversion times. The 2D sequence had the following parameters: 256 ⫻ 128 matrix size, 36 ⫻ 18 cm field of view, 10 mm slice thickness, ⫾ 16 kHz bandwidth, TR ⫽ 5000 ms, TE ⫽ 14 ms, TI ⫽(50, 80, 180, 340, 600, 900, 1200, 1600, 2100, 2700, 3300, 4000 ms). T1 was calculated using a 3-parameter (T1, A, B) fit of the inversion-recovery signal equation SIR ⫽ A共1⫺B exp(⫺TI/T1)兲
(4)
to image intensity measurements made in regions of interest drawn over the tubes in the inversion-recovery images. The performance of the 3D sequence was evaluated by imaging the phantoms on four separate occasions using several values of ␣ (Nshots ⫽ 4, 5 mm slice thickness), and several numbers of shots for the ky acquisition (␣ ⫽ 5o, 5 mm slice thickness). The effect of varying the signal to noise ratio was examined by varying slice thickness (Nshots ⫽ 4, ␣ ⫽ 5o). The remaining pulse sequence timing parameters were as follows: 36 ⫻ 18 cm field-of-view (FOV), 256 ⫻ 128 ⫻ 32 matrix, 5/8 ky acquired, TE ⫽ 2.0 ms, ⫽ 5.5 ms, td ⫽ 4.3 ms, tr ⫽ 2000 ms, ⫾ 62.5 kHz bandwidth. Eighty ky phase encodes (128 ⫻ 5/8) were therefore collected for each effective TI volume. The total imaging time for a 4-shot acquisition was 8 min. Although the sequence was tested using a 36 cm FOV, the FOV can be reduced to 20 cm
A fast volumetric T1 measurement method ● E. HENDERSON
(0.8 mm in-plane spatial resolution) with the same timing parameters. Gradient performance limits on the MR system employed for this study caused an increase in scan time for a further reduction in FOV. For example, for a 12 cm FOV (0.5 mm in-plane spatial resolution), total imaging time would increase to 9.5 min ( ⫽ 8 ms). T1 maps were calculated over the center slice of the volume, and the mean and standard deviation of T1 were calculated in a 69 pixel region of interest placed over each tube. The accuracy of the f3DLL T1 measurement was assessed by calculating mean error in the T1 measurement, defined as the average over all tubes and all repeated measures of the absolute percentage error in mean T1 (compared to the 2D IR-SE T1 measurements). The precision of the f3DLL T1 measurement was evaluated in terms of its reproducibility and of the mean noise in the T1 measurement. The reproducibility of the measurement was defined as the percentage standard deviation of the 4 repeated T1 measurements made in each tube, averaged over all tubes. The mean noise in the T1 maps was determined by taking the average over all tubes and all repeated measures of the percentage standard deviation of T1 in each region of interest. Finally, T1 maps of the brain were acquired in a normal volunteer using two T1 mapping methods: the f3DLL sequence and a 12-point 2D inversion-recovery fast spin-echo (IR-FSE) sequence. The 2D IR-FSE image was aligned to the center slice of the f3DLL volume. The imaging parameters used for the f3DLL sequence were the same as for the phantom experiments, with ␣ ⫽ 5o, slice thickness ⫽ 5 mm and Nshots ⫽ 4. The IR-FSE sequence had an echo train length of 4, an effective TE of 15 ms, a 5 mm slice thickness, and was otherwise identical to the IR-SE sequence used for the phantom measurements. Acquisition time for the single-slice IRFSE image was 30 min, compared to 8 min for the f3DLL volume. T1 maps were calculated using a 2-parameter fit to Eq. 3 (f3DLL) or a 3-parameter fit to Eq. 4 (IR-FSE). The mean and standard deviation of T1 in homogeneous-appearing regions of white matter, gray matter and cerebrospinal fluid (CSF) were calculated over identical regions of interest in the two T1 maps.
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RESULTS
Fig. 3. Representative T1 recovery curves for (a) the 2D inversion-recovery spin-echo sequence, (b) the fast 3D LookLocker (f3DLL) sequence with ␣ ⫽ 5°, Nshots ⫽ 4, and 5-mm slice thickness, (c) the f3DLL sequence with ␣ ⫽ 14°, Nshots ⫽ 4, and 5 mm slice thickness. Data from one pixel in the T1 ⫽ 206 ms phantom (open circles) and one pixel in the T1 ⫽ 1,260 ms phantom (filled circles) are shown. Solid curves indicate the fits to the data.
Phantoms Figure 3 shows representative data and fits from pixels in the 200 ms and 1260 ms phantoms for 2D IRSE and for f3DLL with ␣ ⫽ 5° and 14°. The fits to the ␣ ⫽ 5° data (Fig. 3b) were qualitatively very good, stable with respect to the starting point of the fit, and the data points were well spaced along the relaxation curves. When ␣ is large (Fig. 3c), magnetization is driven to
steady state too rapidly and most data points sample the steady state part of the relaxation curve. In this case, the fits were poor, particularly for long T1s (where there is the added problem of noise bias), and the fits were unstable as indicated by their sensitivity to the initial conditions given.
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Fig. 4. Comparison between T1 measurements made with 2D inversion-recovery spin-echo sequence (IR-SE) and with the 3D Look-Locker (f3DLL) sequence (36 ⫻ 18 cm FOV, 256 ⫻ 128 ⫻ 32, 5/8 ky acquisition, Nshots ⫽ 4, TE ⫽ 2.0 ms, ⫽ 4.9 ms, td ⫽ 4.3 ms, tr ⫽ 2000 ms, ␣ ⫽ 5o). (a) Data points indicate the mean and standard deviation of four T1 measurements made in a region of interest in each phantom on the T1 map (center slice). The dashed line indicates the line of identity. (b) Mean and standard deviation of the absolute percentage error in the f3DLL T1 measurement.
Overall, the accuracy and precision of the f3DLL T1 measurements were very high. Figure 4 compares the mean and standard deviation of T1 values obtained using the f3DLL sequence with ␣ ⫽ 5o, Nshots ⫽ 4 and 5 mm slice thickness, to T1 measurements made using the inversion-recovery spin-echo sequence (IR-SE). Agreement between the two measurements is very close, although f3DLL tends to slightly over-estimate T1. The T1 measurements were accurate and precise (⬍10% error) for T1s above 200 ms, for the range of sequence parameters studied, and for ␣ less than 14o. In general, T1’s lower than 200 ms can not be estimated with any confidence for ␣ above 5o, or for Nshots less than 4. Figure 5 illustrates the mean error, reproducibility and mean noise of the T1 measurement as a function of ␣, of the number of shots in the ky acquisition, and of slice thickness (signal to noise) for T1 greater than 200 ms. The accu-
Fig. 5. Mean error (filled circles), reproducibility, (open circles) and mean noise (filled triangles) of the T1 measurement (%T1) as a function of (a) ␣ (with 4 shots and 5 mm slice thickness), (b) number of shots in the ky acquisition (␣ ⫽ 5o, 5 mm slice thickness), and (c) slice thickness (␣ ⫽ 5o, 4 shots), for T1 greater than 200 ms. Other parameters for the f3DLL sequence were: 36 ⫻ 18 cm FOV, 256 ⫻ 128 ⫻ 32 matrix, 5/8 ky acquisition, TE ⫽ 2.0 ms, ⫽ 4.9 ms, td ⫽ 4.3 ms, and tr ⫽ 2000 ms.
racy and precision of the measurement are optimal for Nshots ⫽ 4, and for ␣ between 5 and 8 degrees. Mean error, reproducibility, and mean noise decrease as a function of slice thickness, although there is not much gain in accuracy and precision for greater than 5 mm slice thickness.
A fast volumetric T1 measurement method ● E. HENDERSON
Fig. 6. T1 map of a normal brain (center slice) acquired using f3DLL.
In vivo A T1 map of a normal brain, acquired using f3DLL, is shown in Fig. 6. T1 measurements made using the f3DLL sequence and the inversion-recovery fast spin-echo (IRFSE) sequence are compared in Table 1 for regions of interest in white matter, gray matter, and CSF. There is a close correspondence between the in vivo T1 measurements made with the two sequences, although the standard deviation of the IR-FSE measurements is smaller in all tissue regions. DISCUSSION The pulse sequence described permits a measurement of T1 in a 3D volume in under 8 min with less than 10% error, for T1 values between 200 and 1200 ms. We have found the performance of the sequence to be relatively insensitive to pulse sequence parameters. For scan pa-
Table 1. Comparison of T1 measurements made using the 3DLL sequence and a conventional 2D Inversion-Recovery Fast-Spin-Echo (IR-FSE) sequence in normal human brain tissue
Tissue
T1 (IR-FSE) (ms) (right side)
T1 (f3DLL) (ms) (right side)
T1 (f3DLL) (ms) (left side)
White matter Gray matter CSF
633 ⫾ 8 1148 ⫾ 24 5127 ⫾ 350
591 ⫾ 13 1260 ⫾ 45 5242 ⫾ 791
613 ⫾ 26 1226 ⫾ 69 5077 ⫾ 658
Note: Values are mean ⫾ standard deviation of T1 in a homogeneous region of interest.
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rameters similar to those we have used in this study, we recommend using minimum , ␣ ⫽ 5o, Nshots ⫽ 4, and a slice thickness of 5 mm or greater. In fitting Eq. (3), we have fit for two parameters only: T1 and the scaling constant A ⫽ meqsin(␣)exp(-TE/T2*). The goodness of the fit therefore is highly dependent on the accuracy with which ␣ is known. Errors in ␣ arise from three sources: slice profile errors, B1 inhomogeneities, and resonance offset effects. One of the advantages of using a 3D sequence for a T1 measurement is that a 3D sequence is generally less sensitive to slice profile errors than is a 2D sequence, within the flat portion of the 3D slab profile. On the other hand, B1 inhomogeneities and resonance offset errors will limit the accuracy of the 2-parameter fit. We have found the sequence to be somewhat sensitive to coil non-uniformities. The effect of coil non-uniformities could be eliminated by doing a 3-parameter fit (A, T1, and ␣). In this case, however, the accuracy of the T1 estimate becomes highly dependent on the initial guess for T1, A and ␣, and reconstruction time increases considerably. The sensitivity to initial guess is due to the fact that longitudinal magnetization recovers according to T1* (see Eq. 1) in which T1 and ␣ are coupled. It is an inherent problem with the LookLocker technique that uncertainty in ␣ propagates into estimate of T1.16 Initial guesses can be estimated from the data, as suggested by Brix et al.,18 or B1 can be mapped by repeating the sequence for 2 flip angles, as suggested by Parker et al.36 Both of these methods increase the reconstruction time. Another approach would be to use B1-insensitive pulses, such as composite pulses or adiabatic fast passage pulses,14 although there will be a penalty in sequence time. Gowland and Leach21 obtained a significant improvement in accuracy of the 2D Look-Locker technique by using a hyperbolic secant inversion pulse, which is less sensitive to B1 inhomogeneities. If coil uniformity is good, for example if a head coil is used, then it is best to do a 2-parameter fit for T1 and the scaling factor A. Otherwise, some method must be used to either map ␣ or otherwise eliminate effects of magnetic field inhomogeneities. In our 3D implementation of the Look-Locker scheme, we have significantly reduced the acquisition time by acquiring multiple lines of ky in each shot. Because each effective TI volume is not collected instantaneously, but is acquired while the magnetization is changing, there will be a point spread function distortion introduced in the phase encode direction. This effect can be lessened by increasing the number of shots with which ky is acquired, with the necessary trade-off that imaging time will increase. Another technique for the 3D measurement of T1 has been demonstrated by Brookes et al.37 This technique is
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based on the variable flip angle method38 – 40 in which T1 is calculated from two spoiled gradient echo volumes acquired at two different flip angles. The advantages of the variable flip angle method are that it is easier to implement than the f3DLL method, and that maps can be calculated more rapidly, as a linear regression can be used for the fit. On the other hand, for the small TR necessary for short 3D acquisition times, it is impossible to properly optimize the choice of the two flip angles to allow accurate T1 measurement over a wide range of T1’s. When applied to 3D data, using short TR, the variable flip angle method suffers from poor accuracy and precision. Brookes et al.37 found that they could only measure T1 accurately for T1 ⬍ 900 ms. In general, the sensitivity to pulse sequence settings, such as flip angle or TI, is a weakness of any 2-point T1 measurement technique. CONCLUSION The fast 3D Look-Locker based technique for T1 measurement provides a rapid and accurate method for measuring the spin-lattice relaxation time in 3D. A 256 ⫻ 128 ⫻ 32 matrix can be acquired in 8 min with a mean error in T1 of 4%, and a reproducibility of 3.5% for T1 between 200 and 1200 ms. Acknowledgments—This work was supported by the Canadian Breast Cancer Research Initiative of the National Cancer Institute of Canada, and by General Electric Medical Systems. The authors thank Dr. Kenneth C. Chu for his assistance in pulse sequence testing.
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contrast agent uptake kinetics. J. Magn. Reson. Imaging 7:564 –574; 1997. den Boer, J.A.; Hoenderop, R.K.; Smink, J.; Dornseiffen, G.; Koch, P.W.; Mulder, J.H.; Slump, C.H.; Volker, E.D.; de Vos, R.A. Pharmacokinetic analysis of Gd-DTPA enhancement in dynamic three-dimensional MRI of breast lesions. J. Magn. Reson. Imaging 7:702–715; 1997. Gore, J.C.; Kang, Y.S.; Schulz, R.J. Measurement of radiation dose distributions by nuclear magnetic resonance (NMR) imaging. Phys. Med. Biol. 29:1189 –1197; 1984. Olsson, L.E.; Fransson, A.; Ericsson, A.; Mattsson, S. MR imaging of absorbed dose distributions for radiotherapy using ferrous sulphate gels. Phys. Med. Biol. 35:1623– 1631; 1990. Hazle, J.D.; Hefner, L.; Nyerick, C.E.; Wilson, L.; Boyer, A.L. Dose-response characteristics of a ferrous-sulphatedoped gelatin system for determining radiation absorbed dose distributions by magnetic resonance imaging (Fe MRI). Phys. Med. Biol. 36:1117–1125; 1991. Podgorsak, M.B.; Schreiner, L.J. Nuclear magnetic relaxation characterization of irradiated Fricke solution. Med. Phys. 19:87–95; 1992. Kron, T.; Pope, J.M. Dose distribution measurements in superficial x-ray beams using NMR dosimetry. Phys. Med. Biol. 39:1337–1349; 1994. Olsen, D.R.; Hellesnes, J. Absorbed dose distribution measurements in brachytherapy using ferrous sulphate gel and magnetic resonance imaging. Br. J. Radiol. 67:1121–1126; 1994. Johansson, B.S.; Magnusson, P.; Fransson, A.; Olsson, L.E.; Montelius, A.; Holmberg, O.; Andreo, P.; Mattsson, S. Improvements in absorbed dose measurements for external radiation therapy using ferrous dosimeter gel and MR imaging (FeMRI). Phys. Med. Biol. 43:261–276; 1998. Kaldoudi, E.; Williams, S.C.R. Relaxation time measurements in NMR imaging. Part I: Longitudinal relaxation time. Concepts Magn. Reson. 5:217–242; 1993. Look, D.C.; Locker, D.R. Time saving in measurement of NMR and EPR relaxation times. Rev. Sci. Instrum. 41: 250 –251; 1970. Crawley, A.P.; Henkelman, R.M. A comparison of oneshot and recovery methods in T1 imaging. Magn. Reson. Med. 7:23–34; 1988. Hinson, W.H.; Sobol, W.T. A new method of computing spin-lattice relaxation maps in magnetic resonance imaging using fast scanning protocols. Med. Phys. 15:551–561; 1988. Brix, G.; Schad, L.R.; Deimling, M.; Lorenz, W.J. Fast and precise T1 imaging using a TOMROP sequence. Magn Reson Imaging 8:351–356; 1990. Kay, I.; Henkelman, R.M. Practical implementation and optimization of one-shot T1 imaging. Magn. Reson. Med. 22:414 – 424; 1991. Zhang, Y.T.; Yeung, H.N.; Carson, P.L.; Ellis, J.H. Experimental analysis of T1 imaging with a single-scan, multiple-point, inversion-recovery technique. Magn. Reson. Med. 25:337–343; 1992.
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21. Gowland, P.A.; Leach, M.O. Fast and accurate measurements of T1 using a multi-readout single inversion-recovery sequence. Magn. Reson. Med. 26:79 – 88; 1992. 22. Tong, C.Y.; Prato, F.S. A novel fast T1-mapping method. J. Magn. Reson. Imaging 4:701–708; 1994. 23. Haase, A. Snapshot FLASH MRI. Applications to T1, T2.; and chemical-shift imaging. Magn. Reson. Med. 13:77– 89; 1990. 24. Nekolla, S.; Gneiting, T.; Syha, J.; Deichmann, R.; Haase, A. T1 maps by K-space reduced snapshot-FLASH MRI. J. Comput. Assist. Tomogr. 16:327–332; 1992. 25. Deichmann, R.; Haase, A. Quantification of T1 values by SNAPSHOT-FLASH NMR imaging. J. Magn. Reson. 96: 608 – 612; 1992. 26. Bluml, S.; Schad, L.R.; Stepanow, B.; Lorenz, W.J. Spinlattice relaxation time measurement by means of a TurboFLASH technique. Magn. Reson. Med. 30:289 –295; 1993. 27. Ordidge, R.J.; Gibbs, P.; Chapman, B.; Stehling, M.K.; Mansfield, P. High-speed multislice T1 mapping using inversion-recovery echo-planar imaging. Magn. Reson. Med. 16:238 –245; 1990. 28. Gowland, P.; Mansfield, P. Accurate measurement of T1 in vivo in less than 3 s using echo-planar imaging. Magn. Reson. Med. 30:351–354; 1993. 29. Freeman, A.J.; Gowland, P.A.; Mansfield, P. Optimization of the ultrafast Look-Locker echo-planar imaging T1 sequence. Magn. Reson. Imaging 16:765–772; 1998. 30. Rozijn, T.H.; van der Sanden, B.P.J.; Heerschap, A.; Creyghton, J.H.N.; Bovee, W.M.M.J. Influence of the pharmacokinetic model on the quantification of the GdDTPA uptake rate in brain tumours using direct T1 measurements. Magn. Reson. Materials Biol. Phys. Med. 6:37– 43; 1998. 31. Haase, A.; Frahm, J. NMR imaging of spin-lattice relaxation using stimulated echoes. J. Magn. Reson. 65:481– 490; 1985.
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32. Mareci, T.H.; Sattin, W.; Scott, K.N. Tip-angle-reduced T1 imaging. J. Magn. Reson. 67:55– 65; 1986. 33. Franconi, F.; Seguin, F.; Sonier, C.B.; Le Pape, A.; Akoka, S. T1 mapping from spin echo and stimulated echoes. Med. Phys. 22:1763–1769; 1995. 34. Rutt, B.K.; Henderson, E.; Lee, T.Y. Quantitative tracer kinetic studies of breast cancer: accurate and rapid 3D initial T1 mapping (abstract). In: Book of abstracts: Fifth annual meeting of the International Society for Magnetic Resonance in Medicine. Vol. 3. Berkeley CA:ISMRM; 1997: p. 2081. 35. Weiss, G.H.; Ferretti, J.A. The choice of optimal parameters for measurement of spin-lattice relaxation times. IV. Effects of nonideal pulses. J. Magn. Reson. 61:499 –515; 1985. 36. Parker, D.L.; Christian, B.A.; Goodrich, K.C.; Alexander, A.L.; Buswell, H.R.; Yoon, C. Improved accuracy in T1 measurements (abstract). In: Book of abstracts: Sixth annual meeting of the International Society for Magnetic Resonance in Medicine. Vol. 3. Berkeley CA:ISMRM; 1998: p. 2171. 37. Brookes, J.A.; Redpath, T.W.; Gilbert, F.J.; Needham, G.; Murray, A.D. Measurement of spin-lattice relaxation times with FLASH for dynamic MRI of the breast. Br. J. Radiol. 69:206 –214; 1996. 38. Homer, J.; Beevers, M.S. Driven-equilibrium single-pulse observation of T1 relaxation. A re-evaluation of a rapid “new” method for determining NMR spin-lattice relaxation times. J. Magn. Reson. 63:287–297; 1985. 39. Fram, E.K.; Herfkens, R.J.; Johnson, G.A.; Glover, G.H.; Karis, J.P.; Shimakawa, A.; Perkins, T.G.; Pelc, N.J. Rapid calculation of T1 using variable flip angle gradient refocused imaging. Magn. Reson. Imaging 5:201–208; 1987. 40. Wang, H.Z.; Riederer, S.J.; Lee, J.N. Optimizing the precision in T1 relaxation estimation using limited flip angles. Magn. Reson. Med. 5:399 – 416; 1987.
PII S0730-725X(99)00025-9
● Original Contribution
A FAST 3D LOOK-LOCKER METHOD FOR VOLUMETRIC T1 MAPPING ELIZABETH HENDERSON,* GRAEME MCKINNON,§ TING-YIM LEE ,*†‡
AND
BRIAN K. RUTT*†
*Imaging Research Laboratories, The John P. Robarts Research Institute; †Department of Diagnostic Radiology, London Health Sciences Center, University Campus; ‡Department of Radiology and Lawson Research Institute, St. Joseph’s Health Center, London, Ontario, Canada; and §Applied Science Laboratory, GE Medical Systems, Milwaukee, WI, USA We introduce a fast technique, based on the principles of the 2D Look-Locker T1 measurement scheme, to rapidly acquire the data for accurate maps of T1 in three dimensions. The acquisition time has been shortened considerably by segmenting the acquisition of the ky phase encode lines. Using this technique, the data for a 256 ⴛ 128 ⴛ 32 volumetric T1 measurement can be acquired in 7.6 min. T1 measurements made in phantoms with T1s between 200 and 1200 ms had an accuracy of 4% and a reproducibility of 3.5%. Measurements of T1 made in normal brain using the fast 3D sequence corresponded well with inversion-recovery fast spin-echo measurements. © 1999 Elsevier Science Inc. Keywords: Longitudinal relaxation time; T1; 3D; Look-Locker.
INTRODUCTION
therapy have led to increasingly complex target volumes being prescribed, generating a need for practical 3D radiation dosimetry techniques for quality control. Gel dosimeters have potential for 3D radiation dosimetry, since the dose of ionizing radiation absorbed is inversely proportional to the T1 of the irradiated gels.7 As a result, gel T1 has been studied extensively as a measure of the radiation dose absorbed by dosimetric gels.8 –13 A volumetric measurement of gel T1 would enable accurate 3D radiation dosimetry with greater through-plane spatial resolution than is achievable with single slice measurements. One of the major problems encountered in making accurate maps of T1 is the long imaging time required. For good accuracy over a wide range of T1 values, multiple points of the T1 recovery curve must be sampled. If a conventional two-dimensional (2D) inversionrecovery spin-echo sequence is used, data acquisition for each slice can take hours. Several schemes have been developed for the rapid imaging of T1 in 2D in which multiple points on the recovery curve are sampled.14 These techniques include methods based on Look-Locker,15–22 snapshot-fast low-angle shot (snapshot–
Several new magnetic resonance (MR) applications require quantitative measurements of the spin-lattice relaxation time (T1) in three dimensions (3D) in relatively short time frames (under 10 min). For example, quantitative tracer kinetic studies, in which vascular parameters such as blood volume and capillary permeability are calculated from dynamic contrast-enhanced MR data, require an accurate measurement of pre-contrast tissue T1. Before application of a tracer kinetic model, tissue enhancement following contrast agent administration must be converted into contrast agent concentration, and it can be shown that this calibration is strongly dependent on the pre-contrast tissue T1.1– 6 Ideally, tracer kinetic studies should be done in 3D for complete characterization of a lesion, for locating small lesions not apparent in pre-contrast scans, or for examining multiple lesions in one study. Furthermore, the pre-contrast T1 measurement should be made in less than 10 min for the study to fit into a reasonable time frame. Another application requiring a measurement of volumetric T1 is radiation dosimetry. Advances in radiation RECEIVED 11/22/98; ACCEPTED 3/20/99. Address correspondence to Dr. Brian K. Rutt, Imaging Research Laboratories, The John P. Robarts Research Institute,
P.O. Box 5015, 100 Perth Drive, London, Ontario, Canada, N6A 5K8. E-mail: [email protected] 1163
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FLASH),23–26 inversion-prepared echo planar imaging (EPI),27–30 and stimulated echo imaging.31–33 There are two approaches to snapshot-FLASH based T1 measurement. In the first, an inversion pulse is followed by a train of snapshot-FLASH images with which the T1 relaxation curve is sampled.23 This is a very rapid and easily implemented method for T1 measurement. It would also be very simple to alter this technique for 3D volume acquisition. One problem with this approach, however, is that the time taken to acquire a high spatial resolution image is too long to properly sample the T1 relaxation curve. For volumetric imaging in particular, this problem would severely limit the accuracy of the T1 map. Nekolla et al.24 have circumvented this problem in 2D imaging by acquiring only phase encode lines covering the center quarter of k-space. Another difficulty with this T1 measurement scheme is that T1 relaxation is modulated by the sampling process, limiting the accuracy of the T1 measurements. For the case in which there is no delay between successive snapshot-FLASH image acquisitions, however, this modulation of the T1 relaxation is described by Look-Locker theory,15 and very accurate measurements of T1 can be obtained.25 The second snapshot-FLASH based approach to T1 imaging is to repeat an inversion-pulse/single snapshotFLASH image combination for various delay times (TI) between the inversion pulse and the snapshot-FLASH acquisition.23,26 This approach could also be easily modified for 3D T1 mapping. In this case, if centric k-space acquisition is used, errors due to improper sampling of the relaxation curve and modulation of the relaxation by the snapshot-FLASH imaging are avoided.26 This second approach, however, suffers from a relatively longer imaging time. The EPI technique for T1 measurement consists of an inversion pulse followed by multiple EPI acquisitions.27 The major advantages of this technique are that the data required for EPI-based T1 maps can be acquired extremely rapidly, that multiple slices can be acquired, and that the EPI acquisition does not interfere with the T1 relaxation. Recently, a technique (LL-EPI) has been proposed in which EPI is combined with Look-Locker readout so that the data needed to sample the entire T1 relaxation curve for a 2D T1 map is acquired in under 3s.28,29 The accuracy and repeatability that have been reported for LL-EPI technique, however, are not as good as those reported for the more time-consuming LookLocker technique with spin-warp imaging.21,28 Other characteristics of EPI, including the need for high-performance gradient coils, sensitivity to magnetic field inhomogeneities, chemical shift artifacts, and low signal to noise, limit the applicability of EPI techniques. Stimulated echo techniques for T1 measurement con-
sist of a STEAM acquisition in which the third saturation pulse is broken up into a series of variable tip angle read pulses, which are used to sample the T1 relaxation of the stored longitudinal magnetization.31–33 The major advantage of these techniques is that they are insensitive to magnetic field heterogeneity.33 If only stimulated echoes are used for the T1 measurement,31,32 the very low dynamic range limits the effectiveness of the T1 map generation.16 If, however, a spin echo is acquired and included in the fit in combination with the stimulated echoes, the dynamic range of the technique is increased. T1 measurements made with this technique are very accurate, although precision is lower than that obtained using Look-Locker techniques.33 The major advantages to Look-Locker based T1 measurement techniques are that the acquisition time is short, and that the T1 relaxation behavior has been well-characterized.15 It has been shown in a theoretical analysis that if the Look-Locker technique is used, rather than the more time-consuming conventional inversion recovery method, T1 can be measured quickly with no penalty to the signal-to-noise ratio of the calculated T1 image.16 Other authors have demonstrated the high degree of accuracy and precision achievable with this technique experimentally.17–21 In this paper, we introduce a fast 3D technique, based on the principles of the 2D Look-Locker T1 measurement scheme, to rapidly acquire the data for accurate maps of T1 in 3D. The acquisition time needed for volumetric T1 mapping has been shortened considerably by segmenting the acquisition of the ky phase encode lines. This technique is similar to what might be obtained by modifying the snapshot-FLASH based T1 measurement schemes for 3D, however, since there is no delay between acquisition of successive volumes and since the T1 relaxation is governed by the principles introduced by Look and Locker, we refer to it as a fast 3D Look-Locker (f3DLL) technique. A preliminary version of this work has been presented previously.34
PULSE SEQUENCE The fast 3D pulse sequence for T1 measurement (f3DLL) is based on the spectroscopic method for T1 measurement developed in 1970 by Look and Locker15 and later adapted for 2D imaging applications.17–21 The basic principle is that following an inversion pulse (for optimal dynamic range), the recovery of longitudinal magnetization to a steady state is repeatedly sampled by a series of small flip-angle rf pulses (␣) separated by a small time . The recovery of the magnetization is modulated by the alpha pulses, and therefore the magnetiza-
A fast volumetric T1 measurement method ● E. HENDERSON
Fig. 1. Schematic diagram of a conventional 2D Look-Locker type pulse sequence.
tion is driven to steady state with the modified relaxation time T1*: T1* ⫽
T1 T1 1 ⫺ ln(cos(␣))
(1)
In a conventional (2D) Look-Locker imaging scheme (Fig. 1), the inversion-pulse/␣-pulse train is repeated for every ky phase encode step. For N ␣-pulses, a series of N images are formed corresponding to times TIn ⫽ td ⫹ (n⫺1), (n ⫽ 1,2, . . . N) after the inversion pulse, where td is the time between the inversion pulse and the first ␣ pulse. A T1 map can be produced by fitting the T1 recovery curve of each pixel to a theoretical signal equation. Adapting this conventional Look-Locker approach to 3D, however, would make the sequence time very long. For example, if 16 ␣-pulses spaced 75 ms apart, with no undisturbed recovery period, tr, were used to sample the recovery curve,19 then acquisition of a 256 ⫻ 128 ⫻ 32 matrix would take 1.4 h. Because of the above concern for scan time in the case of 3D T1 mapping, we introduce here an accelerated method for Look-Locker acquisition (Fig. 2). A slab selective inversion pulse is followed by a long train (N ⬎ 100) of low flip angle (␣) readout pulses with minimal (⬍10 ms). Transverse magnetization is completely spoiled before the application of each subsequent excitation pulse. At the end of the train of ␣-pulses, an undisturbed delay (tr) is optionally inserted to allow recovery of longitudinal magnetization prior to the next inversion pulse. The train of ␣-pulses is divided into several (e.g., M ⫽ 16) groups, and within each group,
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multiple phase encodes (ky lines) are acquired. Each group yields one “effective TI” volume. If the number of ky lines spanned by each group were equal to the total number of ky lines, Nky, the spins would be driven to steady state too rapidly, and the longitudinal recovery would be undersampled. This would lead to inaccurate determinations of T1. In order to ensure that the effective TI volumes are spaced close enough together to achieve adequate sampling of the recovery curve, the ky lines are acquired in an interleaved multi-shot fashion. The inversion-pulse/␣-train combination is repeated for the number of shots (Nshots) needed to cover the entire ky plane, (inner loop) and for all kz slices (Nkz) in the volume (outer loop). The number of ␣-pulses following the inversion pulse therefore is equal to (Nky/Nshots)*M. An alternative approach to implementing this sequence would be to have kz acquisition in the inner loop and ky acquisition in the outer loop. In this case, since Nkz is typically smaller than Nky, the acquisition of kz would not have to be divided into multiple shots. This strategy, however, may lack some flexibility in the choice of N/M. The behavior of the MR signal for a 2D Look-Locker imaging sequence has been derived by Brix et al.18 This theoretical signal equation assumes complete spoiling of transverse magnetization before each readout pulse and includes the effects of a non-zero time (td) between the inversion pulse and first ␣-pulse, and a waiting time (tr) at the end of the train of ␣-pulses. The relevant timings are shown in the schematic pulse sequence diagram for the 2D imaging implementation in Fig. 1. The longitudinal magnetization just before the nth read-out pulse, mn, is given by the equation:15,18 mn ⫽ meq关F⫹(cos(␣)E)n⫺1(Q ⫺ F)兴
(2)
Fig. 2. Schematic diagram of the f3DLL pulse sequence.
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where F ⫽ (1⫺E)/(1⫺cos(␣)E), Q⫽
⫺F cos(␣)ErEd关1 ⫺ (cos(␣)E)N⫺1兴 ⫺ 2Ed ⫹ Er ⫹ 1 , 1 ⫹ cos(␣)ErEd(cos(␣)E)N⫺1 E ⫽ exp(⫺/T1), Er ⫽ exp(⫺tr/T1), Ed ⫽ exp(⫺td/T1),
meq is the equilibrium magnetization, and N is the total number of read-out pulses (and hence the total number of 2D images). The image intensity of pixel (i,j) in the nth gradient-echo image produced by this sequence is therefore: Sn(i,j) ⫽ 兩sin(␣)(i,j)mn(i,j)exp共⫺TE/T2*(i,j)兲兩
(3)
Equation 3 may be used to fit to the data from the fast 3D Look-Locker sequence, except in this case, ‘n’ must be reinterpreted as the number of the ␣-pulse at which the center of k-space is collected. For example, if a 256 ⫻ 128 ⫻ 32 matrix is acquired with linear ky phase encoding in four shots, then 32 ky lines are collected in each shot or group, and the center of ky is acquired after 16(2 m ⫺1) ␣-pulses, for m ⫽ 1,2,3. . . M, where M is the number of volumes (effective TI’s) acquired. A volumetric measurement of T1 can be made by fitting Eq. 3 to the data from each voxel acquired using the pulse sequence illustrated in Fig. 2. There are several things to consider when setting the timings for the 3D acquisition. In general, for optimal accuracy in T1 measurements, the first time point on the recovery curve should be as close to zero as possible.35 In the f3DLL case, this translates to minimizing the time between the inversion pulse and the acquisition of the center of k-space for the first effective TI volume. In our implementation, we minimize this time through a partial ky acquisition (i.e., from ⫺kymax/8 to kymax). Another solution would be to centrically acquire ky. In addition, since the train of ␣-pulses is very long for the 3D implementation, ␣ should be small (⬍15°) so that the magnetization is not driven to steady state too rapidly, and should be set to its minimum value (preferably ⬍ 5 ms). MATERIALS AND METHODS The 3D pulse sequence was implemented on a whole body 1.5T MR scanner equipped with 22 mT/m gradients (Signa Horizon EchoSpeed, GE Medical Systems, Mil-
waukee, WI, USA). The number of effective TI volumes acquired (M) was kept fixed at 16. The T1 maps were calculated by fitting Eq. 3 to the data from each voxel using the quasi-Newton bounded minimization routine E04JAF from the NAG Fortran Library (The Numerical Algorithms Group Ltd., Downers Grove, IL). Equation 3 was fit for two parameters only: T1 and the scaling constant A ⫽ meqsin(␣)exp(⫺TE/T2*). This approach assumes that the value of ␣ is known and constant over the volume. When fitting for A and T1 only, a 256 ⫻ 128 T1 map can be calculated in approximately 22 min on a Sun Sparc 10 (Sun Microsystems, Mountain View, CA, USA). However, computing time can be reduced significantly by only fitting the regions of the image that are of interest. The performance of the pulse sequence and fitting was evaluated using a set of 9 aqueous solutions of Gd-DTPA (Magnevist, Berlex Canada, Lachine, PQ) in 3 cm diameter tubes covering a range of T1’s between 100 ms and 1200 ms. The tubes were imaged in a transmit/receive head rf coil, inside a cylindrical loader shell filled with doped saline (GE Medical Systems, Milwaukee, WI, USA). Accuracy of the T1 measurements was assessed by comparison with T1 measurements made with a 2D inversion-recovery spin-echo (IRSE) sequence repeated for 12 inversion times. The 2D sequence had the following parameters: 256 ⫻ 128 matrix size, 36 ⫻ 18 cm field of view, 10 mm slice thickness, ⫾ 16 kHz bandwidth, TR ⫽ 5000 ms, TE ⫽ 14 ms, TI ⫽(50, 80, 180, 340, 600, 900, 1200, 1600, 2100, 2700, 3300, 4000 ms). T1 was calculated using a 3-parameter (T1, A, B) fit of the inversion-recovery signal equation SIR ⫽ A共1⫺B exp(⫺TI/T1)兲
(4)
to image intensity measurements made in regions of interest drawn over the tubes in the inversion-recovery images. The performance of the 3D sequence was evaluated by imaging the phantoms on four separate occasions using several values of ␣ (Nshots ⫽ 4, 5 mm slice thickness), and several numbers of shots for the ky acquisition (␣ ⫽ 5o, 5 mm slice thickness). The effect of varying the signal to noise ratio was examined by varying slice thickness (Nshots ⫽ 4, ␣ ⫽ 5o). The remaining pulse sequence timing parameters were as follows: 36 ⫻ 18 cm field-of-view (FOV), 256 ⫻ 128 ⫻ 32 matrix, 5/8 ky acquired, TE ⫽ 2.0 ms, ⫽ 5.5 ms, td ⫽ 4.3 ms, tr ⫽ 2000 ms, ⫾ 62.5 kHz bandwidth. Eighty ky phase encodes (128 ⫻ 5/8) were therefore collected for each effective TI volume. The total imaging time for a 4-shot acquisition was 8 min. Although the sequence was tested using a 36 cm FOV, the FOV can be reduced to 20 cm
A fast volumetric T1 measurement method ● E. HENDERSON
(0.8 mm in-plane spatial resolution) with the same timing parameters. Gradient performance limits on the MR system employed for this study caused an increase in scan time for a further reduction in FOV. For example, for a 12 cm FOV (0.5 mm in-plane spatial resolution), total imaging time would increase to 9.5 min ( ⫽ 8 ms). T1 maps were calculated over the center slice of the volume, and the mean and standard deviation of T1 were calculated in a 69 pixel region of interest placed over each tube. The accuracy of the f3DLL T1 measurement was assessed by calculating mean error in the T1 measurement, defined as the average over all tubes and all repeated measures of the absolute percentage error in mean T1 (compared to the 2D IR-SE T1 measurements). The precision of the f3DLL T1 measurement was evaluated in terms of its reproducibility and of the mean noise in the T1 measurement. The reproducibility of the measurement was defined as the percentage standard deviation of the 4 repeated T1 measurements made in each tube, averaged over all tubes. The mean noise in the T1 maps was determined by taking the average over all tubes and all repeated measures of the percentage standard deviation of T1 in each region of interest. Finally, T1 maps of the brain were acquired in a normal volunteer using two T1 mapping methods: the f3DLL sequence and a 12-point 2D inversion-recovery fast spin-echo (IR-FSE) sequence. The 2D IR-FSE image was aligned to the center slice of the f3DLL volume. The imaging parameters used for the f3DLL sequence were the same as for the phantom experiments, with ␣ ⫽ 5o, slice thickness ⫽ 5 mm and Nshots ⫽ 4. The IR-FSE sequence had an echo train length of 4, an effective TE of 15 ms, a 5 mm slice thickness, and was otherwise identical to the IR-SE sequence used for the phantom measurements. Acquisition time for the single-slice IRFSE image was 30 min, compared to 8 min for the f3DLL volume. T1 maps were calculated using a 2-parameter fit to Eq. 3 (f3DLL) or a 3-parameter fit to Eq. 4 (IR-FSE). The mean and standard deviation of T1 in homogeneous-appearing regions of white matter, gray matter and cerebrospinal fluid (CSF) were calculated over identical regions of interest in the two T1 maps.
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RESULTS
Fig. 3. Representative T1 recovery curves for (a) the 2D inversion-recovery spin-echo sequence, (b) the fast 3D LookLocker (f3DLL) sequence with ␣ ⫽ 5°, Nshots ⫽ 4, and 5-mm slice thickness, (c) the f3DLL sequence with ␣ ⫽ 14°, Nshots ⫽ 4, and 5 mm slice thickness. Data from one pixel in the T1 ⫽ 206 ms phantom (open circles) and one pixel in the T1 ⫽ 1,260 ms phantom (filled circles) are shown. Solid curves indicate the fits to the data.
Phantoms Figure 3 shows representative data and fits from pixels in the 200 ms and 1260 ms phantoms for 2D IRSE and for f3DLL with ␣ ⫽ 5° and 14°. The fits to the ␣ ⫽ 5° data (Fig. 3b) were qualitatively very good, stable with respect to the starting point of the fit, and the data points were well spaced along the relaxation curves. When ␣ is large (Fig. 3c), magnetization is driven to
steady state too rapidly and most data points sample the steady state part of the relaxation curve. In this case, the fits were poor, particularly for long T1s (where there is the added problem of noise bias), and the fits were unstable as indicated by their sensitivity to the initial conditions given.
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Fig. 4. Comparison between T1 measurements made with 2D inversion-recovery spin-echo sequence (IR-SE) and with the 3D Look-Locker (f3DLL) sequence (36 ⫻ 18 cm FOV, 256 ⫻ 128 ⫻ 32, 5/8 ky acquisition, Nshots ⫽ 4, TE ⫽ 2.0 ms, ⫽ 4.9 ms, td ⫽ 4.3 ms, tr ⫽ 2000 ms, ␣ ⫽ 5o). (a) Data points indicate the mean and standard deviation of four T1 measurements made in a region of interest in each phantom on the T1 map (center slice). The dashed line indicates the line of identity. (b) Mean and standard deviation of the absolute percentage error in the f3DLL T1 measurement.
Overall, the accuracy and precision of the f3DLL T1 measurements were very high. Figure 4 compares the mean and standard deviation of T1 values obtained using the f3DLL sequence with ␣ ⫽ 5o, Nshots ⫽ 4 and 5 mm slice thickness, to T1 measurements made using the inversion-recovery spin-echo sequence (IR-SE). Agreement between the two measurements is very close, although f3DLL tends to slightly over-estimate T1. The T1 measurements were accurate and precise (⬍10% error) for T1s above 200 ms, for the range of sequence parameters studied, and for ␣ less than 14o. In general, T1’s lower than 200 ms can not be estimated with any confidence for ␣ above 5o, or for Nshots less than 4. Figure 5 illustrates the mean error, reproducibility and mean noise of the T1 measurement as a function of ␣, of the number of shots in the ky acquisition, and of slice thickness (signal to noise) for T1 greater than 200 ms. The accu-
Fig. 5. Mean error (filled circles), reproducibility, (open circles) and mean noise (filled triangles) of the T1 measurement (%T1) as a function of (a) ␣ (with 4 shots and 5 mm slice thickness), (b) number of shots in the ky acquisition (␣ ⫽ 5o, 5 mm slice thickness), and (c) slice thickness (␣ ⫽ 5o, 4 shots), for T1 greater than 200 ms. Other parameters for the f3DLL sequence were: 36 ⫻ 18 cm FOV, 256 ⫻ 128 ⫻ 32 matrix, 5/8 ky acquisition, TE ⫽ 2.0 ms, ⫽ 4.9 ms, td ⫽ 4.3 ms, and tr ⫽ 2000 ms.
racy and precision of the measurement are optimal for Nshots ⫽ 4, and for ␣ between 5 and 8 degrees. Mean error, reproducibility, and mean noise decrease as a function of slice thickness, although there is not much gain in accuracy and precision for greater than 5 mm slice thickness.
A fast volumetric T1 measurement method ● E. HENDERSON
Fig. 6. T1 map of a normal brain (center slice) acquired using f3DLL.
In vivo A T1 map of a normal brain, acquired using f3DLL, is shown in Fig. 6. T1 measurements made using the f3DLL sequence and the inversion-recovery fast spin-echo (IRFSE) sequence are compared in Table 1 for regions of interest in white matter, gray matter, and CSF. There is a close correspondence between the in vivo T1 measurements made with the two sequences, although the standard deviation of the IR-FSE measurements is smaller in all tissue regions. DISCUSSION The pulse sequence described permits a measurement of T1 in a 3D volume in under 8 min with less than 10% error, for T1 values between 200 and 1200 ms. We have found the performance of the sequence to be relatively insensitive to pulse sequence parameters. For scan pa-
Table 1. Comparison of T1 measurements made using the 3DLL sequence and a conventional 2D Inversion-Recovery Fast-Spin-Echo (IR-FSE) sequence in normal human brain tissue
Tissue
T1 (IR-FSE) (ms) (right side)
T1 (f3DLL) (ms) (right side)
T1 (f3DLL) (ms) (left side)
White matter Gray matter CSF
633 ⫾ 8 1148 ⫾ 24 5127 ⫾ 350
591 ⫾ 13 1260 ⫾ 45 5242 ⫾ 791
613 ⫾ 26 1226 ⫾ 69 5077 ⫾ 658
Note: Values are mean ⫾ standard deviation of T1 in a homogeneous region of interest.
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rameters similar to those we have used in this study, we recommend using minimum , ␣ ⫽ 5o, Nshots ⫽ 4, and a slice thickness of 5 mm or greater. In fitting Eq. (3), we have fit for two parameters only: T1 and the scaling constant A ⫽ meqsin(␣)exp(-TE/T2*). The goodness of the fit therefore is highly dependent on the accuracy with which ␣ is known. Errors in ␣ arise from three sources: slice profile errors, B1 inhomogeneities, and resonance offset effects. One of the advantages of using a 3D sequence for a T1 measurement is that a 3D sequence is generally less sensitive to slice profile errors than is a 2D sequence, within the flat portion of the 3D slab profile. On the other hand, B1 inhomogeneities and resonance offset errors will limit the accuracy of the 2-parameter fit. We have found the sequence to be somewhat sensitive to coil non-uniformities. The effect of coil non-uniformities could be eliminated by doing a 3-parameter fit (A, T1, and ␣). In this case, however, the accuracy of the T1 estimate becomes highly dependent on the initial guess for T1, A and ␣, and reconstruction time increases considerably. The sensitivity to initial guess is due to the fact that longitudinal magnetization recovers according to T1* (see Eq. 1) in which T1 and ␣ are coupled. It is an inherent problem with the LookLocker technique that uncertainty in ␣ propagates into estimate of T1.16 Initial guesses can be estimated from the data, as suggested by Brix et al.,18 or B1 can be mapped by repeating the sequence for 2 flip angles, as suggested by Parker et al.36 Both of these methods increase the reconstruction time. Another approach would be to use B1-insensitive pulses, such as composite pulses or adiabatic fast passage pulses,14 although there will be a penalty in sequence time. Gowland and Leach21 obtained a significant improvement in accuracy of the 2D Look-Locker technique by using a hyperbolic secant inversion pulse, which is less sensitive to B1 inhomogeneities. If coil uniformity is good, for example if a head coil is used, then it is best to do a 2-parameter fit for T1 and the scaling factor A. Otherwise, some method must be used to either map ␣ or otherwise eliminate effects of magnetic field inhomogeneities. In our 3D implementation of the Look-Locker scheme, we have significantly reduced the acquisition time by acquiring multiple lines of ky in each shot. Because each effective TI volume is not collected instantaneously, but is acquired while the magnetization is changing, there will be a point spread function distortion introduced in the phase encode direction. This effect can be lessened by increasing the number of shots with which ky is acquired, with the necessary trade-off that imaging time will increase. Another technique for the 3D measurement of T1 has been demonstrated by Brookes et al.37 This technique is
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Magnetic Resonance Imaging ● Volume 17, Number 8, 1999
based on the variable flip angle method38 – 40 in which T1 is calculated from two spoiled gradient echo volumes acquired at two different flip angles. The advantages of the variable flip angle method are that it is easier to implement than the f3DLL method, and that maps can be calculated more rapidly, as a linear regression can be used for the fit. On the other hand, for the small TR necessary for short 3D acquisition times, it is impossible to properly optimize the choice of the two flip angles to allow accurate T1 measurement over a wide range of T1’s. When applied to 3D data, using short TR, the variable flip angle method suffers from poor accuracy and precision. Brookes et al.37 found that they could only measure T1 accurately for T1 ⬍ 900 ms. In general, the sensitivity to pulse sequence settings, such as flip angle or TI, is a weakness of any 2-point T1 measurement technique. CONCLUSION The fast 3D Look-Locker based technique for T1 measurement provides a rapid and accurate method for measuring the spin-lattice relaxation time in 3D. A 256 ⫻ 128 ⫻ 32 matrix can be acquired in 8 min with a mean error in T1 of 4%, and a reproducibility of 3.5% for T1 between 200 and 1200 ms. Acknowledgments—This work was supported by the Canadian Breast Cancer Research Initiative of the National Cancer Institute of Canada, and by General Electric Medical Systems. The authors thank Dr. Kenneth C. Chu for his assistance in pulse sequence testing.
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A fast volumetric T1 measurement method ● E. HENDERSON
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