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Spatially selective pulse sequences: Elimination of harmonic responses
JOURNAL
OF MAGNETIC
RESONANCE
62, 340-345 (1985)
Spatially Selective Pulse Sequences: Elimination of Harmonic Responses A.J. SHAKAANDRAYFREEMAN Physical Chemistry Laboratory, Oxford University, Oxford, England Received December 18, 1984
It is clear that one of the most exciting applications of NMR is in the field of biochemistry and medicine. These experiments all hinge on the possibility of relating the observed NMR signal to the spatial coordinates within the sample, usually a living animal. The two main areas of application are NMR imaging and highresolution spectroscopy from some restricted “active volume” within the sample. Recent developments focus on the idea of using gradients of the radiofrequency field B, to label the coordinates, rather than gradients of the static field B,,, partly on the grounds that the former are unlikely to have any deleterious physiological effects. These B, gradients may either be deliberately engineered or emerge as a byproduct of the use of a “surface coil.” One convenient approach is to discover a sequence of radiofrequency pulses which excites an NMR response from a restricted volume of the sample; this might then be scanned in order to obtain a two- or three-dimensional image, or used simply to obtain a high-resolution spectrum of a particular chosen region. Spatially selective pulse sequences have been described by Rendall et al. (I, 2), Shaka et al. (3, 4) and Tycko et al. (5, 6) and it seems clear that many other families of pulse sequences remain to be discovered. Since geometrical considerations normally preclude using the most intense region of the Bi field to define the excitation volume, there is the possibility of artifacts due to “harmonics” of the frequency yBr/27r where By is the nominal intensity .at the chosen region of space. For example, if BP is set for a simple 90” excitation pulse, spurious NMR signals will also be excited from sample regions where the flip angle is around 270”, 450” . . . etc. We propose a family of preparation schemes which may be prefixed to any type of spatially selective pulse sequence in order to suppress or greatly attenuate these unwanted harmonic responses. Take the simplest case where the selective pulse sequence is just a 90” read pulse, generating spurious responses at the third, fifth, seventh . . . harmonics (Fig. la). Appreciable attenuation of the third harmonic may be achieved by a 30” prepulse applied with opposite phases in two successive experiments (Fig. lb): 3o”(+x)
9o”(+x)
Acquire
30”( -X)
9o”(+x)
Acquire
0022-2364185 $3.00 Copyri@ 0 1985 by Academic Ress. Inc. All rights of reprcdunicn in any form reserved.
340
341
COMMUNICATIONS
I 0123456789 Harmonic RG. 1. Computer-simulated excitation profiles in a perfectly homogeneous radiofrequency field as a fimction of flip angle. Resonance offset effects are neglected. Trace (a) shows the expected Y magnetization after a simple 90”(X) read pulse. In the lower traces the read pulse is preceded by the prepulse sequences (b) 307+X), (c) lP(kX) 3O’(fl), (d) 12.9”(S) 18”(H) 3O”(ti). The flip angles correspond to the nominal condition (first harmonic). All intensities are on the same absolute scale.
The 30” prepulse excites Mxv components which are equal and opposite in these two acquisitions, so the net effect is to reduce the Mz component by a factor approximately equal to cos(?~B&@), the small discrepancy which arises off resonance being attributable to the slight tilting of the effective field. To all intents and purposes, at the end of the cycle the prepulse merely attenuates the 2 component im.mediately prior to the read pulse and transverse magnetization may be neglected. Alternatively, a similar result may be achieved in a single experiment if the transverse magnetization excited by the 30” prepulse is dispersed by applying a strong static field gradient pulse before the read pulse. At the third-harmonic condition, that is to say, sample regions where B, = 3BP, the Z component is reduced to zero by the prepulse. Since the prepulse may be regarded as acting purely to reduce Z magnetization, it is clear that any number of such sequences may be cascaded (in any order). Consequently the fifth harmonic (B, = 5BT) may be strongly attenuated along with the third harmonic by the scheme: Acquire 18=(+X) 3o"(+x) 9o"(+x) 18”(-X)
3o"(+x)
9o"(+x)
Acquire
1sO(+x)
30"(-X)
9o"(+x)
Acquire
18’(-X)
30"(-X)
9o"(+x)
Acquire
Figure lc shows the predicted degree of suppression.
342
COMMUNICATIONS
In situations where the seventh harmonic might be excited, the prepulse sequence 12.9’(+X)
lV(kX)
3O”(LY)
may be used, cycled through all eight sign combinations. If a single-shot experiment is required, then the three pulsed B,, gradients should have different widths (or
a
e 11
0123456789
*
3
‘1.
’
11
Harmonic
FIG. 2. Experimental verification of the prepulse scheme for eliminating harmonic responses. The sequences were applied on resonance. The traces show the observed Y magnetization excited by a 90”(X) read pulse preceded by (a) no prepulse, (b) 30”(H), (c) 3O”(kX) 307*X), (d) 18”(G) 30°(kX), (e) 12.9’(G) 18’(M) 30’(S). The flip angles correspond to the nominal condition (first harmonic). All intensities are on the same absolute scale.
COMMUNICATIONS
343
intensities) to avoid the possibility of echo formation. Figure Id shows the quality of suppression predicted for the third, fifth, seventh, and ninth harmonics, for a loss of only 20% at the first maximum. These simulations assume complete elimination of transverse magnetization after the prepulses and neglect off-resonance effects. These predictions were tested by experiments on a Varian XL-200 spectrometer with a sample of 10% Hz0 in DzO (to avoid any effects of radiation damping). Spatial inhomogeneity of the B, field was simulated by incrementing all pulse durations in the same proportion. The actual spatial inhomogeneity was quite mild, as; seen from the envelope of the signal response in Fig. 2a, the well-known damped sine wave with the first maximum at rBPtp = a/2 rad. The attenuation of the third (and ninth) harmonics by a single 30” prepulse is illustrated in Fig. 2b; the same absolute intensity scale is employed. Transverse magnetization after the prepulse was cancelled by adding the signals acquired in two consecutive runs, one with 3O”(+X), the other with 30”(-X). Better suppression in the region of the third harmonic was achieved by cascading two prepulses, 3O”(+X) 3O”(+X), resulting in a cycle of four separate signal acquisitions (Fig. 2~). It is possible to broaden the range over which this suppression is effective by slightly missetting the prepulse conditions (30” + t and 30” - c) at the expense of the absolute attenuation at the exact third-harmonic condition. Fifth-harmonic suppression was tested with the prepulse sequence 18”(+X) 30”(+-X) in a cycle of four signal acquisitions. Since the third and ninth harmonics are also attenuated, the only significant spurious response is at the seventh-harmonic condition (Fig. 2d). Finally a sequence of three prepulses 12.9”(fX) 18”(-tX) 3O”(+X) in an eightfold cycle eliminates all the unwanted harmonics in this range (Fig. 2e). These prepulse schemes naturally invite comparison with an earlier method of suppressing the third-harmonic response-the use of a 60” read pulse, which behaves like a 180” pulse when B1 = 3Bp (2, 4, 5). Unfortunately this very simple scheme is not as attractive when resonance offset behavior is taken into account because a 180” pulse excites appreciable transverse magnetization when the effective field is tilted away from the X axis of the rotating frame. The prepulse schemes proposed above fare rather better since pulses of small flip angle are particularly tolerant of resonance offset effects (7). Calculations of the off-resonance behavior of thie cascaded 3O”(?X) 3O”(+X) prepulse sequence are shown in Fig. 3. The lefthand diagram shows Z magnetization remaining after the first 30” pulse, while the central diagram shows Z magnetization after two cascaded pulses (assuming that all transverse magnetization has been cancelled). Note that there is no negative Z component after two such pulses. Clearly there is only a very mild dependence on re:sonance offset. For spatially selective NMR experiments, this Z magnetization must be excited by some kind of read pulse. Although this could be a nominal 90” pulse, better suppression of higher harmonics off-resonance is achieved by suitable composite read pulses. One example is 30’(--X) 1200(+X). Note that in this context, 30”(--X) is not a prepulse; transverse magnetization is conserved at this point. Contours of XY magnetization are shown in the right-hand diagram of Fig. 3 for this case. Near the nominal intensity (B, = BP) the contour lines are almost
344
4 4 ---__ -----10
COMMUNICATIONS M2
4
4
-----------3o----------30
--
--_-
-----10
3-
3 l-I
;I::
IO -
3
IO -
22-p
IO -
50 -
i=l -
10 -
-90
so -
IO
2
30-
El 30 50 70
50 m-
90
so -
Bl
-0 Bl
I
so
SO
i-1 Oi -I
,4
‘IO
-
30 -
B, -6 Bl
MXY
“-k--T-+
0
ABIB;
i +I
+I
I -i-I
i,0
As/B;
+i +I
-I
0
0
+I
ABIB:
RG. 3. Calculated contour plots, over a 128 X 128 matrix, showing the Z or XY magnetization as a function of resonance offset AB and radiofrequency intensity B, . The diagrams show (from left to right) the Z component remaining after the prepulse 30”(G), the Z component remaining after the prepulse sequence 30”(H) 3O”(+x), and the XY magnetization excited by the sequence 30”(H) 30“(+4 300(-X) 12O”(+X). Contours in each case are shown as a percentage of the maximum value in the matrix. The absolute intensities in the last plot are in fact a factor of 0.75 smaller.
horizontal, indicating that resonance offset effects are unimportant. Over a wide area between the second- and fourth-harmonic conditions the relative excitation is negligibly small (less than 10%) and remains so over a considerable range of offsets. A 30” prepulse suppresses the third-harmonic response very effectively over a wide range of resonance offsets because it becomes a self-compensated 90” pulse (7). Similar considerations apply to 18” and 12.9” pulses at the fifth and seventh harmonics, respectively. Even better effectiveness with respect to offset may be achieved with composite 30” prepulses-for example 7.5”(-X) 37S”(+X) which becomes the composite pulse 22.5”(-x) 112.5’(+X) at the third-harmonic condition (8). Bendall (2) has suggested suppressing the third-harmonic response by combining signals after 60” and 120” read pulses, in the ratio 2: 1. Although this gives a very flat null around the condition B1 = 3Bi’ on resonance, unwanted breakthrough occurs off-resonance. Furthermore, at the nominal pulse condition B1 = BP, the signals to be combined have different phase errors, except at exact resonance. There is an entirely different aspect of prepulse excitation. Prepulses may be used to narrow the excitation as a function of B, rather than suppress harmonic responses. For example, a 180” prepulse gives nulls at 0.5 BP and at 1.5 BP providing the basis for some selectivity in the B, domain (I). Rather better is the composite prepulse 360”(X) 180”(Y) which has nulls at 0.25 BP, 0.5 BP, and 0.75 BP etc., generating a quite high sensitivity to B1. These and related spatially selective composite pulses will be described in a future publication.
COMMUNICATIONS
345
ACKNOWLEDGMENTS Thii work was made possible by an equipment grant from the Science and Engineering Research Council. The authors would like to thank Dr. J. Keeler for advice and assistance. REFERENCES 1. M. R. BENDALLANDR. E.G~RDoN,J. Magn. Reson. 53, 365 (1983). .?. M. R. BENDALL, J. Mup. Reson. 59, 406 (1984). 3. A. J. SHAKA AND R. FREEMAN, J. Magn. Reson. 59, 169 (1984). .1. A.J. SHAKA,J. KEELER, M. B. SMITH, ANDR. FREEMAN, J. Magn. Reson. 61, 175 (1985). 5. R. TYCKO AND A. PINES, J. Magn. Reson. 60, 156 (1984). 15. R. TYCKO AND A. PINES, Chem. Phys. Lett. 111, 462 (1984). 7. R.FREEMAN ANDH. D. W. HILL,J. Chem. Phys. 54, 3367 (1971). 8. A. J. SHAKA, J. KEELER, ANDR. FREEMAN, J. Magn. Reson. 53, 313 (1983).
OF MAGNETIC
RESONANCE
62, 340-345 (1985)
Spatially Selective Pulse Sequences: Elimination of Harmonic Responses A.J. SHAKAANDRAYFREEMAN Physical Chemistry Laboratory, Oxford University, Oxford, England Received December 18, 1984
It is clear that one of the most exciting applications of NMR is in the field of biochemistry and medicine. These experiments all hinge on the possibility of relating the observed NMR signal to the spatial coordinates within the sample, usually a living animal. The two main areas of application are NMR imaging and highresolution spectroscopy from some restricted “active volume” within the sample. Recent developments focus on the idea of using gradients of the radiofrequency field B, to label the coordinates, rather than gradients of the static field B,,, partly on the grounds that the former are unlikely to have any deleterious physiological effects. These B, gradients may either be deliberately engineered or emerge as a byproduct of the use of a “surface coil.” One convenient approach is to discover a sequence of radiofrequency pulses which excites an NMR response from a restricted volume of the sample; this might then be scanned in order to obtain a two- or three-dimensional image, or used simply to obtain a high-resolution spectrum of a particular chosen region. Spatially selective pulse sequences have been described by Rendall et al. (I, 2), Shaka et al. (3, 4) and Tycko et al. (5, 6) and it seems clear that many other families of pulse sequences remain to be discovered. Since geometrical considerations normally preclude using the most intense region of the Bi field to define the excitation volume, there is the possibility of artifacts due to “harmonics” of the frequency yBr/27r where By is the nominal intensity .at the chosen region of space. For example, if BP is set for a simple 90” excitation pulse, spurious NMR signals will also be excited from sample regions where the flip angle is around 270”, 450” . . . etc. We propose a family of preparation schemes which may be prefixed to any type of spatially selective pulse sequence in order to suppress or greatly attenuate these unwanted harmonic responses. Take the simplest case where the selective pulse sequence is just a 90” read pulse, generating spurious responses at the third, fifth, seventh . . . harmonics (Fig. la). Appreciable attenuation of the third harmonic may be achieved by a 30” prepulse applied with opposite phases in two successive experiments (Fig. lb): 3o”(+x)
9o”(+x)
Acquire
30”( -X)
9o”(+x)
Acquire
0022-2364185 $3.00 Copyri@ 0 1985 by Academic Ress. Inc. All rights of reprcdunicn in any form reserved.
340
341
COMMUNICATIONS
I 0123456789 Harmonic RG. 1. Computer-simulated excitation profiles in a perfectly homogeneous radiofrequency field as a fimction of flip angle. Resonance offset effects are neglected. Trace (a) shows the expected Y magnetization after a simple 90”(X) read pulse. In the lower traces the read pulse is preceded by the prepulse sequences (b) 307+X), (c) lP(kX) 3O’(fl), (d) 12.9”(S) 18”(H) 3O”(ti). The flip angles correspond to the nominal condition (first harmonic). All intensities are on the same absolute scale.
The 30” prepulse excites Mxv components which are equal and opposite in these two acquisitions, so the net effect is to reduce the Mz component by a factor approximately equal to cos(?~B&@), the small discrepancy which arises off resonance being attributable to the slight tilting of the effective field. To all intents and purposes, at the end of the cycle the prepulse merely attenuates the 2 component im.mediately prior to the read pulse and transverse magnetization may be neglected. Alternatively, a similar result may be achieved in a single experiment if the transverse magnetization excited by the 30” prepulse is dispersed by applying a strong static field gradient pulse before the read pulse. At the third-harmonic condition, that is to say, sample regions where B, = 3BP, the Z component is reduced to zero by the prepulse. Since the prepulse may be regarded as acting purely to reduce Z magnetization, it is clear that any number of such sequences may be cascaded (in any order). Consequently the fifth harmonic (B, = 5BT) may be strongly attenuated along with the third harmonic by the scheme: Acquire 18=(+X) 3o"(+x) 9o"(+x) 18”(-X)
3o"(+x)
9o"(+x)
Acquire
1sO(+x)
30"(-X)
9o"(+x)
Acquire
18’(-X)
30"(-X)
9o"(+x)
Acquire
Figure lc shows the predicted degree of suppression.
342
COMMUNICATIONS
In situations where the seventh harmonic might be excited, the prepulse sequence 12.9’(+X)
lV(kX)
3O”(LY)
may be used, cycled through all eight sign combinations. If a single-shot experiment is required, then the three pulsed B,, gradients should have different widths (or
a
e 11
0123456789
*
3
‘1.
’
11
Harmonic
FIG. 2. Experimental verification of the prepulse scheme for eliminating harmonic responses. The sequences were applied on resonance. The traces show the observed Y magnetization excited by a 90”(X) read pulse preceded by (a) no prepulse, (b) 30”(H), (c) 3O”(kX) 307*X), (d) 18”(G) 30°(kX), (e) 12.9’(G) 18’(M) 30’(S). The flip angles correspond to the nominal condition (first harmonic). All intensities are on the same absolute scale.
COMMUNICATIONS
343
intensities) to avoid the possibility of echo formation. Figure Id shows the quality of suppression predicted for the third, fifth, seventh, and ninth harmonics, for a loss of only 20% at the first maximum. These simulations assume complete elimination of transverse magnetization after the prepulses and neglect off-resonance effects. These predictions were tested by experiments on a Varian XL-200 spectrometer with a sample of 10% Hz0 in DzO (to avoid any effects of radiation damping). Spatial inhomogeneity of the B, field was simulated by incrementing all pulse durations in the same proportion. The actual spatial inhomogeneity was quite mild, as; seen from the envelope of the signal response in Fig. 2a, the well-known damped sine wave with the first maximum at rBPtp = a/2 rad. The attenuation of the third (and ninth) harmonics by a single 30” prepulse is illustrated in Fig. 2b; the same absolute intensity scale is employed. Transverse magnetization after the prepulse was cancelled by adding the signals acquired in two consecutive runs, one with 3O”(+X), the other with 30”(-X). Better suppression in the region of the third harmonic was achieved by cascading two prepulses, 3O”(+X) 3O”(+X), resulting in a cycle of four separate signal acquisitions (Fig. 2~). It is possible to broaden the range over which this suppression is effective by slightly missetting the prepulse conditions (30” + t and 30” - c) at the expense of the absolute attenuation at the exact third-harmonic condition. Fifth-harmonic suppression was tested with the prepulse sequence 18”(+X) 30”(+-X) in a cycle of four signal acquisitions. Since the third and ninth harmonics are also attenuated, the only significant spurious response is at the seventh-harmonic condition (Fig. 2d). Finally a sequence of three prepulses 12.9”(fX) 18”(-tX) 3O”(+X) in an eightfold cycle eliminates all the unwanted harmonics in this range (Fig. 2e). These prepulse schemes naturally invite comparison with an earlier method of suppressing the third-harmonic response-the use of a 60” read pulse, which behaves like a 180” pulse when B1 = 3Bp (2, 4, 5). Unfortunately this very simple scheme is not as attractive when resonance offset behavior is taken into account because a 180” pulse excites appreciable transverse magnetization when the effective field is tilted away from the X axis of the rotating frame. The prepulse schemes proposed above fare rather better since pulses of small flip angle are particularly tolerant of resonance offset effects (7). Calculations of the off-resonance behavior of thie cascaded 3O”(?X) 3O”(+X) prepulse sequence are shown in Fig. 3. The lefthand diagram shows Z magnetization remaining after the first 30” pulse, while the central diagram shows Z magnetization after two cascaded pulses (assuming that all transverse magnetization has been cancelled). Note that there is no negative Z component after two such pulses. Clearly there is only a very mild dependence on re:sonance offset. For spatially selective NMR experiments, this Z magnetization must be excited by some kind of read pulse. Although this could be a nominal 90” pulse, better suppression of higher harmonics off-resonance is achieved by suitable composite read pulses. One example is 30’(--X) 1200(+X). Note that in this context, 30”(--X) is not a prepulse; transverse magnetization is conserved at this point. Contours of XY magnetization are shown in the right-hand diagram of Fig. 3 for this case. Near the nominal intensity (B, = BP) the contour lines are almost
344
4 4 ---__ -----10
COMMUNICATIONS M2
4
4
-----------3o----------30
--
--_-
-----10
3-
3 l-I
;I::
IO -
3
IO -
22-p
IO -
50 -
i=l -
10 -
-90
so -
IO
2
30-
El 30 50 70
50 m-
90
so -
Bl
-0 Bl
I
so
SO
i-1 Oi -I
,4
‘IO
-
30 -
B, -6 Bl
MXY
“-k--T-+
0
ABIB;
i +I
+I
I -i-I
i,0
As/B;
+i +I
-I
0
0
+I
ABIB:
RG. 3. Calculated contour plots, over a 128 X 128 matrix, showing the Z or XY magnetization as a function of resonance offset AB and radiofrequency intensity B, . The diagrams show (from left to right) the Z component remaining after the prepulse 30”(G), the Z component remaining after the prepulse sequence 30”(H) 3O”(+x), and the XY magnetization excited by the sequence 30”(H) 30“(+4 300(-X) 12O”(+X). Contours in each case are shown as a percentage of the maximum value in the matrix. The absolute intensities in the last plot are in fact a factor of 0.75 smaller.
horizontal, indicating that resonance offset effects are unimportant. Over a wide area between the second- and fourth-harmonic conditions the relative excitation is negligibly small (less than 10%) and remains so over a considerable range of offsets. A 30” prepulse suppresses the third-harmonic response very effectively over a wide range of resonance offsets because it becomes a self-compensated 90” pulse (7). Similar considerations apply to 18” and 12.9” pulses at the fifth and seventh harmonics, respectively. Even better effectiveness with respect to offset may be achieved with composite 30” prepulses-for example 7.5”(-X) 37S”(+X) which becomes the composite pulse 22.5”(-x) 112.5’(+X) at the third-harmonic condition (8). Bendall (2) has suggested suppressing the third-harmonic response by combining signals after 60” and 120” read pulses, in the ratio 2: 1. Although this gives a very flat null around the condition B1 = 3Bi’ on resonance, unwanted breakthrough occurs off-resonance. Furthermore, at the nominal pulse condition B1 = BP, the signals to be combined have different phase errors, except at exact resonance. There is an entirely different aspect of prepulse excitation. Prepulses may be used to narrow the excitation as a function of B, rather than suppress harmonic responses. For example, a 180” prepulse gives nulls at 0.5 BP and at 1.5 BP providing the basis for some selectivity in the B, domain (I). Rather better is the composite prepulse 360”(X) 180”(Y) which has nulls at 0.25 BP, 0.5 BP, and 0.75 BP etc., generating a quite high sensitivity to B1. These and related spatially selective composite pulses will be described in a future publication.
COMMUNICATIONS
345
ACKNOWLEDGMENTS Thii work was made possible by an equipment grant from the Science and Engineering Research Council. The authors would like to thank Dr. J. Keeler for advice and assistance. REFERENCES 1. M. R. BENDALLANDR. E.G~RDoN,J. Magn. Reson. 53, 365 (1983). .?. M. R. BENDALL, J. Mup. Reson. 59, 406 (1984). 3. A. J. SHAKA AND R. FREEMAN, J. Magn. Reson. 59, 169 (1984). .1. A.J. SHAKA,J. KEELER, M. B. SMITH, ANDR. FREEMAN, J. Magn. Reson. 61, 175 (1985). 5. R. TYCKO AND A. PINES, J. Magn. Reson. 60, 156 (1984). 15. R. TYCKO AND A. PINES, Chem. Phys. Lett. 111, 462 (1984). 7. R.FREEMAN ANDH. D. W. HILL,J. Chem. Phys. 54, 3367 (1971). 8. A. J. SHAKA, J. KEELER, ANDR. FREEMAN, J. Magn. Reson. 53, 313 (1983).