- Email: [email protected]
RASEE: A rapid spin-echo pulse sequence
Magnetic Resonance Imaging. Vol. 8, pp. 13-19, 1990 Printed in the USA. All rights reserved.
Copyright
0730-725x/90 $3.00 + .oo 0 1990 Pergamon Press plc
l Original Contribution
RASEE: A RAPID SPIN-ECHO ANDREW R. BOGDAN Department
of Radiology,
University
AND
PULSE SEQUENCE PETER
of Pennsylvania,
M.
JOSEPH
Philadelphia,
PA, 19104-6086, USA
Most fast-imaging sequences use gradient echoes and a low flip-angle excitation. The low flip angle is used because it gives increased signal when TR < TI. However, spin-echo sequences are less productive of certain artifacts, among them flow and magnetic susceptibility artifacts. We present a modification of the spin-echo pulse sequence designed to optimize the signal-to-noise ratio for repetition times (TR) less than 100 mSec while preserving good image quality. Our implementation performs a 128 x 128 image in under 7 set (TR = 50 msec) and has been used to follow the dynamics of Cd-DTPA in the rat kidneys.
Keywords: Fast imaging; Gradient echo; Kidney contrast; Artifacts.
make good large angle slice-selective pulses.2 Hence, the need for a cleanly defined excitation over a slice is one reason gradient-echo sequences are used. The loss of signal with SE1 with reduced flip angles can be understood as stemming from the effect of the 180-degree pulse on the z component of the magnetization vector, M. After a small flip angle the 180-degree pulse will invert the remaining M,. One solution to this problem, called FATE3-’ (depicted in Fig. l), ap-
INTRODUCTION Fast-imaging sequences are often based on a gradient echo (GE), rather than a spin echo, because of ease of implementation and the shorter echo times achievable. However, spin-echo sequences, which use a 180-degree radio frequency (RF) pulse for refocussing, are less productive of certain artifacts, among them flow and magnetic susceptibility artifacts. We present a modification of the spin-echo pulse sequence, called RASEE (rapid spin-echo excitation, pronounced “racey”). It is designed to optimize the signal to noise ratio for repetition times (TR) less than 100 msec while preserving good image quality. Our implementation of RASEE performs a 128 x 128 image in under 7 seconds and has been used to follow the dynamics of GdDTPA in rat kidneys. Fast imaging is commonly done using GE with repetition times (TR) much less than the relaxation time T,. To obtain maximum signal strength one must operate with flip angles substantially less than 90 degrees. This is true regardless of which GE pulse sequence is chosen.’ Spin-echo imaging (SEI), on the other hand, produces the strongest signals with flip angles greater than 90 degrees, and the optimum angle approaches 180 degrees as the TR interval is decreased. Unfortunately, it is notoriously difficult to
RECEIVED 4/19/89; ACCEPTED
. -Tel2
.
TR
TI’-
-TI
RF
l-l
VW
n
JL
Pw
S1ice ? Read
A
1 M-s-
I
Phase v “FATE” Fig. 1. The FATE pulse sequence.
9/4/89.
Address correspondence to Peter M. Joseph, Ph.D., University of Pennsylvania, 308 Medical Education Building, 36th and Hamilton Walk, Philadelphia, PA 19104-6086, USA.
Acknowledgment-This
work was supported in part by grants l-ROl-CA44580 and T-32-CA09524 from U.S. National Institutes of Health. 13
14
Magnetic
Resonance
Imaging
plies a second 180-degree pulse after the spin echo in an attempt to restore M, to its initial value. The pulse sequence discussed in this paper, RASEE, is shown in Fig. 2. Note the nonselective 180degree pulse just before the selective-excitation pulse. This combination is equivalent to a spatially selective pulse whose flip angle is close to 180 degrees but without the problems of nonlinearity and spatial definition of large-angle selective pulses. In this way we can combine the good signal to noise ratio (SNR) of a GE sequence such as FLASH6 with the image quality of SEI. In the theory section we present theoretical aspects of the RASEE pulse sequence and compare it with gradient echo and FATE. 3m5It is shown that under certain conditions RASEE can achieve a better SNR than FATE, In the Implementation and Phantom Experiments section, we discuss its implementation and present results obtained with phantoms. In section III we will present applications of this pulse sequence. THEORY Ernst and Anderson’ formulated the steady state response of a spin system to a series of equally spaced RF pulses. They showed that the transverse magnetization is given by M = M,sin(a!)
,
(1 - E, (TR))/( 1 - cos(a)E,(TR))
(1) where E, = exp(-TR/T, ), assuming remaining transverse magnetization
. _Tl’--
“*
__
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1, 1990
pulse. Equation (1) implies that the maximum signal is obtained when the flip angle, 01, is equal to the Ernst angle CY,,given by COS(CX~)= E,(TR)
.
(2)
For a spin-echo pulse sequence the sign of the COS(CY)term in the denominator of Eq. (1) is reversed, the corresponding optimal flip angle is a-a,, so the use of a small flip angle will give much less signal. This can be understood as due to an increase in the time necessary for recovery of A4, after the refocussing 180” pulse inverts the existing longitudinal magnetization, which leads to decreased magnetization in the steady state. Ideally, one should use a large flip angle near 180 degrees to obtain the optimal SNR. With the FATE pulse sequence, for a given TE the signal intensity is less than the gradient-echo pulse sequence due to recovery of longitudinal magnetization during the inter-180-pulse interval, TI. (Our use of the abbreviation TI is consistent with that of Tkach and Haacke,3*4 and should not be confused with that defined for inversion recovery pulse sequences.) However, this sequence retains the advantages of SE1 with relative freedom from flow and susceptibility artifacts. By contrast, our modification of this pulse sequence places one of the 180” pulses just before the slice-selective CYpulse (Fig. 2). This pulse sequence can be thought of in two ways: (i) as a composite pulse of a-CYradians; or (ii) as a limiting case of the FATE sequence, in which the value of TI has been increased to its maximum value, while keeping TR constant. We have derived an expression for the transverse magnetization of the FATE sequence, as a function of T,, T2, TE, TR, and TI, which does not assume that the transverse component is zero before the next RF pulse:
.
TR
-Tel2
RF
that there is no prior to each
0 Volume
A4, = A4, sina! exp(-TE/T*)
*
TI
n
x ( 1 - Er(TR)
+ 2E,(TR
- 2E, (TR - TE/2 x
n
- TE/2) - TI))f(8,ol)
a
where f(0,ol) Read
2
Phase
s
= (1 - &cose)/[(l -
n “RASEE” Fig. 2. The RASEE pulse sequence.
(E, - cosa)(E,
- E,cosa)(l - cosB)Ez]
- &cosB) (3)
where E, = E,(TR) = exp(-TR/T;) and 0 is the net phase rotation experienced by a spin due to the applied gradients during the interval TR. (The angle 0 is sometimes called “the resonant offset angle.“4) This
RASEE: A rapid spin-echo pulse sequence 0 A.R.
expression for MX,, is identical to that for a gradientecho pulse sequence if the term in curly brackets is replaced by (1 - E, ). Thus, any results derived for gradient-echo pulse sequences need only be modified by this substitution. In the limit of TR << T, Eq. (3) reduces to MX,, = M,sincr
exp(-TE/T,)f(B,a)(TR
.
- 2TI)/T,
(4) A gradient-echo sequence would have TI = 0, and the FATE signal would be smaller by a factor (1 2TI/TR). Evidently, one way to maximize the signal is to make TI as small as possible. However, consider what happens if TI is increased as TR remains constant. As the second 180” pulse approaches the first 180” pulse of the next excitation the transverse magnetization passes through zero, then reemerges with the opposite sign (which is not apparent in a magnitude image), as shown in Fig. 3. Increasing TI towards TR, and noting that TR = TI + TI’, creates the RASEE pulse sequence, as shown in Fig. 2. The resulting transverse magnetization is MYYa 1 - E,(TR)
+ 2Ei (TR - TE/2)
- 2E, (TI’ - TE/2)
(9
In the limit TR CC T, Eq. (5) becomes equivalent to the negative of the Eq. (4) with TI replaced by TI’: MXYa -(TR
- 2TI’)/T,
(6)
Hence, on comparing Eqs. (4) and (6), we see the close relationship between the FATE and RASEE sequences. In particular, optimal SNR with FATE requires reducing TI as much as possible, while for RASEE one needs to similarly reduce TI’ as much as possible.
BOGDANAND P.M.
JOSEPH
15
There are two considerations which are relevant to fast pulse sequences; namely, T2 may not be much less than TR, and there may be a net phase rotation, 0, of the remaining transverse magnetization between excitations. The latter effect could be due to the gradients or to other field inhomogeneities. These factors have been considered by several authors.‘,7-‘3 For T2 K TR, E2 = 0, all e-dependent terms drop out and f(13,c~) = l/( 1 - Eicoscu). However, if E2 # 0, &dependent terms must be considered and they lead to an optimum flip angle greater than the Ernst angle. Sekihara8 has considered three cases: (i) No rephasing gradients are applied. Thus, the phase-encoding gradient changes between views and the individual spins do not reach a steady state. However, the spins within a voxel may, as a group, reach a steady state. (ii) The phase-encoding gradient is rephased. In this case each spin reaches a steady state dependent on the 0 due to the slice-select and readout gradients. (iii) All gradients are rephased, giving 0 = 0. In this case the pulse sequence is quite sensitive to main field inhomogeneities. In (i) and (ii) the nonrephased gradients act as spoiler pulses which scramble the transverse magnetization and help prevent coherence effects. However, this is not the same as assuming E2 = 0, and leads to a different signal intensity as a function of flip angle. To determine the observed signal intensity one must integrate Eq. (3) spatially over the voxel. In our pulse sequence the phase-encoding gradient is rephased, corresponding to Sekihara’s case 2, so that each spin’s steady state depends on its value of 8. Assuming the phase rotation across one voxel during the interval between RF pulses is much greater than 2a there will be a uniform distribution of 8 within the voxel and the spatial integral can be replaced with an integral over 0 from 0 to 27r. The integral of f( 8, a) is given by’,s,9:
I=
fta,e)de
(112%)
= p2 - (B -A)E~J/AC
(7)
s where A = (Z32 - C2)“2 B = 1 - E,COSCY- E;(E1 - cow) C= E,(l - E,)(l + cosa). Hence, the average signal is given by Eq. (3) andf( 0) replaced by the above expression for I. Note that the integral Z is independent of TI (or TI’). DISCUSSION Fig. 3. Transverse magnetization as a function of the inter-180” pulse spacing TI, for different values of T, , with T, = TR = 50 msec, and a flip angle of 40”.
As we have seen, the dependence of RASEE on TI’ is similar to the dependence of FATE on TI. The question here is which time interval is more easily re-
Magnetic
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duced in MR imaging experiments. The minimum value of TI in the FATE pulse sequence is approximately TE/2 + SAMP/2 (where SAMP, the data sampling time, must be less than TE). For the RASEE pulse sequence the minimum value of TI’ is approximately TE/2 + T,,,, where T,,, is the separation between the cx and the preceding a pulses. (Additional terms related to gradient turn on and turn off delays have been left out as they affect both pulse sequences similarly.) Now one can see an advantage to the RASEE pulse sequence: if TE is increased, both TI(FATE) and TI’(RASEE) are increased by the same amount, but with RASEE one can then increase SAMP with no further increase in TI’ (Fig. 4). As shown in Eq. (4)-(6), any increase in either TI or TI’ reduces the signal strength. Thus, in RASEE the sampling bandwidth is reduced with a corresponding decrease in image noise by a factor of (SAMP)“‘, without the additional loss of signal which would come from increasing TI. In many cases, the loss of signal due to the increased echo time may be less than the decrease in noise due to the increased SAMP, resulting in an increase in SNR. For example, if TR = 50 msec, TE can be increased from 11.5 to 13.5 msec, and SAMP from 4 to 6 msec, with a concomitant gain in SNR as long as T2 is greater than 10 msec.
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tation inverted for the second. Before reconstruction, the second excitation is subtracted from the first to eliminate any DC offset which may be present in the receiver electronics. This technique, called “chopping,” increases the SNR and prevents an artifact which looks like a star in the center of the image. However, in these experiments a factor of 2 reduction in imaging time was obtained by eliminating the chopping step. Special care was taken to adjust the DC offset of the amplifiers to minimize the center dot artifact in the images. Since in RASEE there is only one LYpulse per phase encoding step there is no possibility to alternate its sign, so we decided to look at the effect of alternating the sign of the two 180” pulses as the phase-encoding gradient is advanced. All imaging experiments were performed at 1.9 T on a 20 mM CuS04 phantom which has T, = T2 =I 60 msec. The images corresponding to the four possible sequences are presented in Fig. 5. The upper left image has no alternation, the upper right alternates the second 180” pulse, the bottom left alternates the first 180” pulse, and the bottom right shows alternation of both 180” pulses. Clearly, alternating both 180” pulses is the preferred mode of operation. Three types of artifacts are apparent in these phan-
IMPLEMENTATION AND PHANTOM EXPERIMENTS In our experiments we were concerned to reduce the overall scan time as much as possible so that rapid physiologic phenomena could be accurately imaged. In our standard pulse sequences we use two excitations per phase-encoding step with the sign of the RF exci-
-Te/2
-TI-
RQ+J-Jn
*
x
rH-
Read A Gradient -Te/z -
Read A Gradient
“FATE”
-
TI’-
Y
4YXM-
l-4
Fig. 4. Comparison of FATE and RASEE. Note that the noise in RASEE can be reduced by increasing SAMP with no loss in signal strength.
Fig. 5. Images of a 20 mM CuS04 phantom taken under the following conditions: (upper left) no alternation of the 180” pulses; (upper right) alternate the second 180” pulse; (bottom left) alternate the first 180” pulse; (bottom right) alternation of both 180” pulses. The image in the lower right has no artifacts within the phantom. The DC artifact is present to the left of the phantom in all images.
RASEE:
A
rapid spin-echo pulse sequence 0
tom images. The first is the DC artifact described above. It appears to the left of the phantom because the phantom has been positioned off-center. The two other artifacts shown are due to out-of-plane transverse magnetization, due to imperfections in the nonselective 180” pulses, which is not sufficiently spoiled by the gradients. The artifacts are not due to coherence effects because they remain after increasing TR to much greater than T,.The horizontal artifact, present in the two left hand images, is due to the nonalternation of the second 180” pulse, which occurs after the phase-encoding gradient. Because its effect is the same as the phase-encoding gradient is incremented, the artifact appears at zero frequency in the phase-encoding direction. The ring artifact is due to nonalternation of the first 180” pulse, which precedes the phase-encoding gradient, and hence, is not the same from one value of the phase-encoding gradient to the next. Because of the sign alternation of their transverse components as the phase-encoding gradient is incremented, both of these artifacts move to the top and bottom of the image space. Thus, with this simple technique a major class of artifacts is mitigated. The quantitative validity of the analysis was tested in a phantom experiment. The flip-angle dependence of the signal from 0 to 90 degrees was also compared to the theory. The experimental values agreed with theory to better than 2.5%. Finally, the SNRs were compared for one RASEE pulse sequence with TE = 11.5 msec and SAMP = 4 msec, and a second with TE = 13.5 msec and SAMP = 6 msec. The SNR was calculated as mean phantom intensity divided by mean background intensity. The SNR was 1.20 times greater in the second case. The theory predicts an increase of 1.18 times assuming that T2 = 60 msec. This illustrates the increase in SNR achievable without the increase in TI’ with RASEE. APPLICATIONS
In our laboratory this pulse sequence has been applied to the study of dynamic phenomena using GdDTPA as a contrast agent. Both kidney functioning under various pathological conditions and tumor uptake of Gd-DTPA are being studied. The desired effect of Gd-DTPA is due to the shortening of T,, which leads to increased local signal intensity. Shortening Tlmonotonically increases the signal for a fast pulse sequence. Images obtained with GE and RASEE are shown in Figs. 6 and 7, respectively. The GE sequence had TE = 11.5 and SAMP = 4 msec, while the RASEE sequence had TE = 13.5 msec, SAMP = 6 msec. The
A.R.
BOGDAN AND P.M.
JOSEPH
17
Fig. 6. Comparison of gradient-echo (top) and RASEE (bottom) images of rat kidneys enhanced by Gd-DTPA for TE = 11.5 msec, TR = 50 msec, SAMP = 4 msec, and an cr pulse of 40”.
GE pulse sequence is obtained from RASEE by turning off the 180” pulses and changing the sign of the prephasing and phase-encoding gradients. In all cases the flow artifacts and the chemical shift artifacts at the fat-muscle boundaries are more apparent in the GE images. Changing the echo time by 2 msec drastically worsens the appearance of the gradient-echo image while having a negligible effect on the RASEE image. Figure 8 shows the dark ring pattern in the renal cortex sometimes seen in gradient-echo images of kidneys using Gd-DTPA.14 This has not been seen in RASEE images, indicating that it is a susceptibility effect. The absence of susceptibility effects in RASEE images gives a more uniform enhancement of the kidney. CONCLUSIONS
We have presented a new pulse sequence, RASEE, designed to optimize the SNR for fast spin-echo imaging. It is a modification of the FATE pulse sequence using a slice-selective composite exciting pulse with an effective flip angle of ?T-(Y degrees. For some range of
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Fig. 8. Gradient echo images showing the dark ring pattern due to T;” effects. The bottom image was taken 7.4 set after the top one.
7. Comparison of gradient-echo (top) and RASEE (bottom) images of rat kidneys enhanced by Gd-DTPA for TE = 13.5 msec, TR = 50 msec, SAMP = 6 msec, and an (Ypulse of 40”. Note the many artifacts in the gradient-echo image. Fig.
tion per phase encoding step artifacts due to out-ofplane transverse magnetization are eliminated by alternating the sign of the r pulses on sequential RF excitations. In such imaging sequences one trades the signal loss relative to a gradient-echo image for the reduced susceptibility to artifacts of the spin-echo image. This is particularly useful in eliminating the susceptibility effects which may be observed when imaging with contrast agents. The RASEE sequence was primarily designed for studying the dynamics of Gd-DTPA enhancement of normal and pathological kidney functioning, but may also be used for studying the dynamics of other physiological phenomena which may require a time resolution on the order of 5-10 sec. REFERENCES
TE and TI values, because of the different placement of the r pulses it is possible to increase the data sampling time for RASEE relative to FATE and thereby
increase
the SNR. When imaging
with one RF excita-
1. Van der Meulen, P.; Groen, J.P.; Tinus, A.M.C.; Bruntink, G. Fast field echo imaging: An overview and contrast calculations. Magn. Reson. Imaging 6:355-368; 1988. 2. Joseph, P.M.; Axel, L.; O’Donnell, M. Potential prob-
RASEE:
3. 4.
5.
6.
7.
8.
A
rapid spin-echo pulse sequence 0
lems with selective pulses in NMR imaging systems. Med. Phys. 11:772-777; 1984. Tkach, J.A.; Haacke, E.M. Fast low angle spin-echo (FATE) imaging. SMRM 557; 1987. Tkach, J.A.; Haacke, E.M. A comparison of fast spin echo and gradient field echo sequences. Magn. Reson. Imaging 6:373-389; 1988. Axel, L.; Dougherty, L. Small excitation flip angles and double 180” echoes for T,-weighted imaging with relatively short repetition times. RSNA 30; 1987. Haase, A.; Frahm, J.; Matthaei, D.; Hanicke, W.; Merboldt, K.-D. FLASH imaging. Rapid NMR imaging using low flip-angle pulses. J. Magn. Reson. 67:258-266; 1986. Ernst, R.R.; Anderson, W.A. Application of Fourier transform spectroscopy to magnetic resonance. Rev. Sci. Znstr. 37:93-102; 1966. Sekihara, K. Steady-state magnetizations in rapid NMR imaging using small flip angles and short repetition intervals, IEEE Trans. Med. Imaging MI-6:157-164; 1987.
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9. Buxton, R.B.; Fisel, C.R.; Edelman, R.R.; Rosen, B.R.; Brady, T.J. Signal intensity in rapid MR imaging. SMRM 457; 1987. 10. Lee, S.Y.; Cho, Z.H. Full utilization of the echo and FID signal in SSFP fast NMR imaging. SMRM 460; 1987. 11. Joseph, P.M.; Bogdan, A.R. LEAPS: A Large Ernst angle pulse sequence for fast imaging. SMRM (Worksin-Progress):99; 1988. 12. Ackerman, J.L.; Raleigh, D.P.; Hoch, J.; Conneily, P.; Garrido, L. A fast Ernst angle spin each technique for rapid spectroscopy and imaging. SMRM 608; 1988. 13. Freeman, R.; Hill, H.D.W. Phase and intensity anomalies in Fourier transform NMR. J. Magn. Reson. 4: 366-383; 1971. 14. Carvlin, M.J.; Arger, P.H.; Kundel, H.L.; Axe], L.; Dougherty, L.; Kassab, E.A.; Moore, B. Acute tubular necrosis: Use of Gadolinium-DTPA and fast MR imaging to evaluate renal function in the rabbit. J. Comput. Assist. Tomogr. 11(3):488-495; 1987.
Copyright
0730-725x/90 $3.00 + .oo 0 1990 Pergamon Press plc
l Original Contribution
RASEE: A RAPID SPIN-ECHO ANDREW R. BOGDAN Department
of Radiology,
University
AND
PULSE SEQUENCE PETER
of Pennsylvania,
M.
JOSEPH
Philadelphia,
PA, 19104-6086, USA
Most fast-imaging sequences use gradient echoes and a low flip-angle excitation. The low flip angle is used because it gives increased signal when TR < TI. However, spin-echo sequences are less productive of certain artifacts, among them flow and magnetic susceptibility artifacts. We present a modification of the spin-echo pulse sequence designed to optimize the signal-to-noise ratio for repetition times (TR) less than 100 mSec while preserving good image quality. Our implementation performs a 128 x 128 image in under 7 set (TR = 50 msec) and has been used to follow the dynamics of Cd-DTPA in the rat kidneys.
Keywords: Fast imaging; Gradient echo; Kidney contrast; Artifacts.
make good large angle slice-selective pulses.2 Hence, the need for a cleanly defined excitation over a slice is one reason gradient-echo sequences are used. The loss of signal with SE1 with reduced flip angles can be understood as stemming from the effect of the 180-degree pulse on the z component of the magnetization vector, M. After a small flip angle the 180-degree pulse will invert the remaining M,. One solution to this problem, called FATE3-’ (depicted in Fig. l), ap-
INTRODUCTION Fast-imaging sequences are often based on a gradient echo (GE), rather than a spin echo, because of ease of implementation and the shorter echo times achievable. However, spin-echo sequences, which use a 180-degree radio frequency (RF) pulse for refocussing, are less productive of certain artifacts, among them flow and magnetic susceptibility artifacts. We present a modification of the spin-echo pulse sequence, called RASEE (rapid spin-echo excitation, pronounced “racey”). It is designed to optimize the signal to noise ratio for repetition times (TR) less than 100 msec while preserving good image quality. Our implementation of RASEE performs a 128 x 128 image in under 7 seconds and has been used to follow the dynamics of GdDTPA in rat kidneys. Fast imaging is commonly done using GE with repetition times (TR) much less than the relaxation time T,. To obtain maximum signal strength one must operate with flip angles substantially less than 90 degrees. This is true regardless of which GE pulse sequence is chosen.’ Spin-echo imaging (SEI), on the other hand, produces the strongest signals with flip angles greater than 90 degrees, and the optimum angle approaches 180 degrees as the TR interval is decreased. Unfortunately, it is notoriously difficult to
RECEIVED 4/19/89; ACCEPTED
. -Tel2
.
TR
TI’-
-TI
RF
l-l
VW
n
JL
Pw
S1ice ? Read
A
1 M-s-
I
Phase v “FATE” Fig. 1. The FATE pulse sequence.
9/4/89.
Address correspondence to Peter M. Joseph, Ph.D., University of Pennsylvania, 308 Medical Education Building, 36th and Hamilton Walk, Philadelphia, PA 19104-6086, USA.
Acknowledgment-This
work was supported in part by grants l-ROl-CA44580 and T-32-CA09524 from U.S. National Institutes of Health. 13
14
Magnetic
Resonance
Imaging
plies a second 180-degree pulse after the spin echo in an attempt to restore M, to its initial value. The pulse sequence discussed in this paper, RASEE, is shown in Fig. 2. Note the nonselective 180degree pulse just before the selective-excitation pulse. This combination is equivalent to a spatially selective pulse whose flip angle is close to 180 degrees but without the problems of nonlinearity and spatial definition of large-angle selective pulses. In this way we can combine the good signal to noise ratio (SNR) of a GE sequence such as FLASH6 with the image quality of SEI. In the theory section we present theoretical aspects of the RASEE pulse sequence and compare it with gradient echo and FATE. 3m5It is shown that under certain conditions RASEE can achieve a better SNR than FATE, In the Implementation and Phantom Experiments section, we discuss its implementation and present results obtained with phantoms. In section III we will present applications of this pulse sequence. THEORY Ernst and Anderson’ formulated the steady state response of a spin system to a series of equally spaced RF pulses. They showed that the transverse magnetization is given by M = M,sin(a!)
,
(1 - E, (TR))/( 1 - cos(a)E,(TR))
(1) where E, = exp(-TR/T, ), assuming remaining transverse magnetization
. _Tl’--
“*
__
8, Number
1, 1990
pulse. Equation (1) implies that the maximum signal is obtained when the flip angle, 01, is equal to the Ernst angle CY,,given by COS(CX~)= E,(TR)
.
(2)
For a spin-echo pulse sequence the sign of the COS(CY)term in the denominator of Eq. (1) is reversed, the corresponding optimal flip angle is a-a,, so the use of a small flip angle will give much less signal. This can be understood as due to an increase in the time necessary for recovery of A4, after the refocussing 180” pulse inverts the existing longitudinal magnetization, which leads to decreased magnetization in the steady state. Ideally, one should use a large flip angle near 180 degrees to obtain the optimal SNR. With the FATE pulse sequence, for a given TE the signal intensity is less than the gradient-echo pulse sequence due to recovery of longitudinal magnetization during the inter-180-pulse interval, TI. (Our use of the abbreviation TI is consistent with that of Tkach and Haacke,3*4 and should not be confused with that defined for inversion recovery pulse sequences.) However, this sequence retains the advantages of SE1 with relative freedom from flow and susceptibility artifacts. By contrast, our modification of this pulse sequence places one of the 180” pulses just before the slice-selective CYpulse (Fig. 2). This pulse sequence can be thought of in two ways: (i) as a composite pulse of a-CYradians; or (ii) as a limiting case of the FATE sequence, in which the value of TI has been increased to its maximum value, while keeping TR constant. We have derived an expression for the transverse magnetization of the FATE sequence, as a function of T,, T2, TE, TR, and TI, which does not assume that the transverse component is zero before the next RF pulse:
.
TR
-Tel2
RF
that there is no prior to each
0 Volume
A4, = A4, sina! exp(-TE/T*)
*
TI
n
x ( 1 - Er(TR)
+ 2E,(TR
- 2E, (TR - TE/2 x
n
- TE/2) - TI))f(8,ol)
a
where f(0,ol) Read
2
Phase
s
= (1 - &cose)/[(l -
n “RASEE” Fig. 2. The RASEE pulse sequence.
(E, - cosa)(E,
- E,cosa)(l - cosB)Ez]
- &cosB) (3)
where E, = E,(TR) = exp(-TR/T;) and 0 is the net phase rotation experienced by a spin due to the applied gradients during the interval TR. (The angle 0 is sometimes called “the resonant offset angle.“4) This
RASEE: A rapid spin-echo pulse sequence 0 A.R.
expression for MX,, is identical to that for a gradientecho pulse sequence if the term in curly brackets is replaced by (1 - E, ). Thus, any results derived for gradient-echo pulse sequences need only be modified by this substitution. In the limit of TR << T, Eq. (3) reduces to MX,, = M,sincr
exp(-TE/T,)f(B,a)(TR
.
- 2TI)/T,
(4) A gradient-echo sequence would have TI = 0, and the FATE signal would be smaller by a factor (1 2TI/TR). Evidently, one way to maximize the signal is to make TI as small as possible. However, consider what happens if TI is increased as TR remains constant. As the second 180” pulse approaches the first 180” pulse of the next excitation the transverse magnetization passes through zero, then reemerges with the opposite sign (which is not apparent in a magnitude image), as shown in Fig. 3. Increasing TI towards TR, and noting that TR = TI + TI’, creates the RASEE pulse sequence, as shown in Fig. 2. The resulting transverse magnetization is MYYa 1 - E,(TR)
+ 2Ei (TR - TE/2)
- 2E, (TI’ - TE/2)
(9
In the limit TR CC T, Eq. (5) becomes equivalent to the negative of the Eq. (4) with TI replaced by TI’: MXYa -(TR
- 2TI’)/T,
(6)
Hence, on comparing Eqs. (4) and (6), we see the close relationship between the FATE and RASEE sequences. In particular, optimal SNR with FATE requires reducing TI as much as possible, while for RASEE one needs to similarly reduce TI’ as much as possible.
BOGDANAND P.M.
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There are two considerations which are relevant to fast pulse sequences; namely, T2 may not be much less than TR, and there may be a net phase rotation, 0, of the remaining transverse magnetization between excitations. The latter effect could be due to the gradients or to other field inhomogeneities. These factors have been considered by several authors.‘,7-‘3 For T2 K TR, E2 = 0, all e-dependent terms drop out and f(13,c~) = l/( 1 - Eicoscu). However, if E2 # 0, &dependent terms must be considered and they lead to an optimum flip angle greater than the Ernst angle. Sekihara8 has considered three cases: (i) No rephasing gradients are applied. Thus, the phase-encoding gradient changes between views and the individual spins do not reach a steady state. However, the spins within a voxel may, as a group, reach a steady state. (ii) The phase-encoding gradient is rephased. In this case each spin reaches a steady state dependent on the 0 due to the slice-select and readout gradients. (iii) All gradients are rephased, giving 0 = 0. In this case the pulse sequence is quite sensitive to main field inhomogeneities. In (i) and (ii) the nonrephased gradients act as spoiler pulses which scramble the transverse magnetization and help prevent coherence effects. However, this is not the same as assuming E2 = 0, and leads to a different signal intensity as a function of flip angle. To determine the observed signal intensity one must integrate Eq. (3) spatially over the voxel. In our pulse sequence the phase-encoding gradient is rephased, corresponding to Sekihara’s case 2, so that each spin’s steady state depends on its value of 8. Assuming the phase rotation across one voxel during the interval between RF pulses is much greater than 2a there will be a uniform distribution of 8 within the voxel and the spatial integral can be replaced with an integral over 0 from 0 to 27r. The integral of f( 8, a) is given by’,s,9:
I=
fta,e)de
(112%)
= p2 - (B -A)E~J/AC
(7)
s where A = (Z32 - C2)“2 B = 1 - E,COSCY- E;(E1 - cow) C= E,(l - E,)(l + cosa). Hence, the average signal is given by Eq. (3) andf( 0) replaced by the above expression for I. Note that the integral Z is independent of TI (or TI’). DISCUSSION Fig. 3. Transverse magnetization as a function of the inter-180” pulse spacing TI, for different values of T, , with T, = TR = 50 msec, and a flip angle of 40”.
As we have seen, the dependence of RASEE on TI’ is similar to the dependence of FATE on TI. The question here is which time interval is more easily re-
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duced in MR imaging experiments. The minimum value of TI in the FATE pulse sequence is approximately TE/2 + SAMP/2 (where SAMP, the data sampling time, must be less than TE). For the RASEE pulse sequence the minimum value of TI’ is approximately TE/2 + T,,,, where T,,, is the separation between the cx and the preceding a pulses. (Additional terms related to gradient turn on and turn off delays have been left out as they affect both pulse sequences similarly.) Now one can see an advantage to the RASEE pulse sequence: if TE is increased, both TI(FATE) and TI’(RASEE) are increased by the same amount, but with RASEE one can then increase SAMP with no further increase in TI’ (Fig. 4). As shown in Eq. (4)-(6), any increase in either TI or TI’ reduces the signal strength. Thus, in RASEE the sampling bandwidth is reduced with a corresponding decrease in image noise by a factor of (SAMP)“‘, without the additional loss of signal which would come from increasing TI. In many cases, the loss of signal due to the increased echo time may be less than the decrease in noise due to the increased SAMP, resulting in an increase in SNR. For example, if TR = 50 msec, TE can be increased from 11.5 to 13.5 msec, and SAMP from 4 to 6 msec, with a concomitant gain in SNR as long as T2 is greater than 10 msec.
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tation inverted for the second. Before reconstruction, the second excitation is subtracted from the first to eliminate any DC offset which may be present in the receiver electronics. This technique, called “chopping,” increases the SNR and prevents an artifact which looks like a star in the center of the image. However, in these experiments a factor of 2 reduction in imaging time was obtained by eliminating the chopping step. Special care was taken to adjust the DC offset of the amplifiers to minimize the center dot artifact in the images. Since in RASEE there is only one LYpulse per phase encoding step there is no possibility to alternate its sign, so we decided to look at the effect of alternating the sign of the two 180” pulses as the phase-encoding gradient is advanced. All imaging experiments were performed at 1.9 T on a 20 mM CuS04 phantom which has T, = T2 =I 60 msec. The images corresponding to the four possible sequences are presented in Fig. 5. The upper left image has no alternation, the upper right alternates the second 180” pulse, the bottom left alternates the first 180” pulse, and the bottom right shows alternation of both 180” pulses. Clearly, alternating both 180” pulses is the preferred mode of operation. Three types of artifacts are apparent in these phan-
IMPLEMENTATION AND PHANTOM EXPERIMENTS In our experiments we were concerned to reduce the overall scan time as much as possible so that rapid physiologic phenomena could be accurately imaged. In our standard pulse sequences we use two excitations per phase-encoding step with the sign of the RF exci-
-Te/2
-TI-
RQ+J-Jn
*
x
rH-
Read A Gradient -Te/z -
Read A Gradient
“FATE”
-
TI’-
Y
4YXM-
l-4
Fig. 4. Comparison of FATE and RASEE. Note that the noise in RASEE can be reduced by increasing SAMP with no loss in signal strength.
Fig. 5. Images of a 20 mM CuS04 phantom taken under the following conditions: (upper left) no alternation of the 180” pulses; (upper right) alternate the second 180” pulse; (bottom left) alternate the first 180” pulse; (bottom right) alternation of both 180” pulses. The image in the lower right has no artifacts within the phantom. The DC artifact is present to the left of the phantom in all images.
RASEE:
A
rapid spin-echo pulse sequence 0
tom images. The first is the DC artifact described above. It appears to the left of the phantom because the phantom has been positioned off-center. The two other artifacts shown are due to out-of-plane transverse magnetization, due to imperfections in the nonselective 180” pulses, which is not sufficiently spoiled by the gradients. The artifacts are not due to coherence effects because they remain after increasing TR to much greater than T,.The horizontal artifact, present in the two left hand images, is due to the nonalternation of the second 180” pulse, which occurs after the phase-encoding gradient. Because its effect is the same as the phase-encoding gradient is incremented, the artifact appears at zero frequency in the phase-encoding direction. The ring artifact is due to nonalternation of the first 180” pulse, which precedes the phase-encoding gradient, and hence, is not the same from one value of the phase-encoding gradient to the next. Because of the sign alternation of their transverse components as the phase-encoding gradient is incremented, both of these artifacts move to the top and bottom of the image space. Thus, with this simple technique a major class of artifacts is mitigated. The quantitative validity of the analysis was tested in a phantom experiment. The flip-angle dependence of the signal from 0 to 90 degrees was also compared to the theory. The experimental values agreed with theory to better than 2.5%. Finally, the SNRs were compared for one RASEE pulse sequence with TE = 11.5 msec and SAMP = 4 msec, and a second with TE = 13.5 msec and SAMP = 6 msec. The SNR was calculated as mean phantom intensity divided by mean background intensity. The SNR was 1.20 times greater in the second case. The theory predicts an increase of 1.18 times assuming that T2 = 60 msec. This illustrates the increase in SNR achievable without the increase in TI’ with RASEE. APPLICATIONS
In our laboratory this pulse sequence has been applied to the study of dynamic phenomena using GdDTPA as a contrast agent. Both kidney functioning under various pathological conditions and tumor uptake of Gd-DTPA are being studied. The desired effect of Gd-DTPA is due to the shortening of T,, which leads to increased local signal intensity. Shortening Tlmonotonically increases the signal for a fast pulse sequence. Images obtained with GE and RASEE are shown in Figs. 6 and 7, respectively. The GE sequence had TE = 11.5 and SAMP = 4 msec, while the RASEE sequence had TE = 13.5 msec, SAMP = 6 msec. The
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Fig. 6. Comparison of gradient-echo (top) and RASEE (bottom) images of rat kidneys enhanced by Gd-DTPA for TE = 11.5 msec, TR = 50 msec, SAMP = 4 msec, and an cr pulse of 40”.
GE pulse sequence is obtained from RASEE by turning off the 180” pulses and changing the sign of the prephasing and phase-encoding gradients. In all cases the flow artifacts and the chemical shift artifacts at the fat-muscle boundaries are more apparent in the GE images. Changing the echo time by 2 msec drastically worsens the appearance of the gradient-echo image while having a negligible effect on the RASEE image. Figure 8 shows the dark ring pattern in the renal cortex sometimes seen in gradient-echo images of kidneys using Gd-DTPA.14 This has not been seen in RASEE images, indicating that it is a susceptibility effect. The absence of susceptibility effects in RASEE images gives a more uniform enhancement of the kidney. CONCLUSIONS
We have presented a new pulse sequence, RASEE, designed to optimize the SNR for fast spin-echo imaging. It is a modification of the FATE pulse sequence using a slice-selective composite exciting pulse with an effective flip angle of ?T-(Y degrees. For some range of
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Fig. 8. Gradient echo images showing the dark ring pattern due to T;” effects. The bottom image was taken 7.4 set after the top one.
7. Comparison of gradient-echo (top) and RASEE (bottom) images of rat kidneys enhanced by Gd-DTPA for TE = 13.5 msec, TR = 50 msec, SAMP = 6 msec, and an (Ypulse of 40”. Note the many artifacts in the gradient-echo image. Fig.
tion per phase encoding step artifacts due to out-ofplane transverse magnetization are eliminated by alternating the sign of the r pulses on sequential RF excitations. In such imaging sequences one trades the signal loss relative to a gradient-echo image for the reduced susceptibility to artifacts of the spin-echo image. This is particularly useful in eliminating the susceptibility effects which may be observed when imaging with contrast agents. The RASEE sequence was primarily designed for studying the dynamics of Gd-DTPA enhancement of normal and pathological kidney functioning, but may also be used for studying the dynamics of other physiological phenomena which may require a time resolution on the order of 5-10 sec. REFERENCES
TE and TI values, because of the different placement of the r pulses it is possible to increase the data sampling time for RASEE relative to FATE and thereby
increase
the SNR. When imaging
with one RF excita-
1. Van der Meulen, P.; Groen, J.P.; Tinus, A.M.C.; Bruntink, G. Fast field echo imaging: An overview and contrast calculations. Magn. Reson. Imaging 6:355-368; 1988. 2. Joseph, P.M.; Axel, L.; O’Donnell, M. Potential prob-
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3. 4.
5.
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7.
8.
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lems with selective pulses in NMR imaging systems. Med. Phys. 11:772-777; 1984. Tkach, J.A.; Haacke, E.M. Fast low angle spin-echo (FATE) imaging. SMRM 557; 1987. Tkach, J.A.; Haacke, E.M. A comparison of fast spin echo and gradient field echo sequences. Magn. Reson. Imaging 6:373-389; 1988. Axel, L.; Dougherty, L. Small excitation flip angles and double 180” echoes for T,-weighted imaging with relatively short repetition times. RSNA 30; 1987. Haase, A.; Frahm, J.; Matthaei, D.; Hanicke, W.; Merboldt, K.-D. FLASH imaging. Rapid NMR imaging using low flip-angle pulses. J. Magn. Reson. 67:258-266; 1986. Ernst, R.R.; Anderson, W.A. Application of Fourier transform spectroscopy to magnetic resonance. Rev. Sci. Znstr. 37:93-102; 1966. Sekihara, K. Steady-state magnetizations in rapid NMR imaging using small flip angles and short repetition intervals, IEEE Trans. Med. Imaging MI-6:157-164; 1987.
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9. Buxton, R.B.; Fisel, C.R.; Edelman, R.R.; Rosen, B.R.; Brady, T.J. Signal intensity in rapid MR imaging. SMRM 457; 1987. 10. Lee, S.Y.; Cho, Z.H. Full utilization of the echo and FID signal in SSFP fast NMR imaging. SMRM 460; 1987. 11. Joseph, P.M.; Bogdan, A.R. LEAPS: A Large Ernst angle pulse sequence for fast imaging. SMRM (Worksin-Progress):99; 1988. 12. Ackerman, J.L.; Raleigh, D.P.; Hoch, J.; Conneily, P.; Garrido, L. A fast Ernst angle spin each technique for rapid spectroscopy and imaging. SMRM 608; 1988. 13. Freeman, R.; Hill, H.D.W. Phase and intensity anomalies in Fourier transform NMR. J. Magn. Reson. 4: 366-383; 1971. 14. Carvlin, M.J.; Arger, P.H.; Kundel, H.L.; Axe], L.; Dougherty, L.; Kassab, E.A.; Moore, B. Acute tubular necrosis: Use of Gadolinium-DTPA and fast MR imaging to evaluate renal function in the rabbit. J. Comput. Assist. Tomogr. 11(3):488-495; 1987.