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Generation of coupled spin-only images using multiple-echo acquisition
JOURNALOFMAGNETIC
RESONANCE84,
159-165 ( 1989)
Generation of Coupled Spin-Only Images Using Multiple-Echo Acquisition A. G. WEBB, S. C. R. WILLIAMS,
AND L. D. HALL
Laboratory for MedicinaI Chemistry, Level 4 R. T.C., Addenbrookes Hospital, Hills Road, Cambridge CB2 2QQP United Kingdom Received September 22, 1988; revised November 28, 1988
The development of imaging techniques to distinguish between the two components of a binary system has previously been achieved by a variety of methods using one, or a combination, of the differences in chemical shift ( 1-6), selective saturation ( 7-13), differential relaxation times (Id), and the effects of scalar coupling (1.5-19). If noncoupled and coupled resonances overlap, due either to magnetic field inhomogeneity or to insufficient chemical-shift dispersion, the last method of discrimination is the most appropriate to implement. However, the method is limited by the long preparation times necessary for J evolution to occur, and may typically be as long as 150 ms which leads to low signal intensity from components with short spin-spin relaxation times ( T2). In this Note we apply a property of multiple-echo techniques that was developed in an earlier paper (20) to produce an experiment in which a coupled spin-only image can be obtained, even in poor magnetic field homogeneity, from a single excitation per phase-encode step, and with improved signal-to-noise ratio when compared with existing techniques. The pulse sequence used is shown in Fig. 1. A second phase-encoding gradient with opposite polarity was applied after each data acquisition in order to reverse the effect of the former. The 180” refocusing pulses used were a previously documented (21) and recently elaborated composite type (22), which exhibit low-phase distortion caused by B, inhomogeneity. In order to illustrate the way in which coupled spin images may be obtained, we consider the case of an AX system with a coupling constant J, plus a single-component noncoupled spin system. If the coupling constant between the two spins is much smaller than their difference in chemical shift, then the system can be treated as first order. Assuming that the AX doublet is on resonance, the echo intensity, I( T), of the coupled spins is a function of the spin-echo time (7) (23,24) given by
[II
I(T) = cos(rJ7)exp(-7/T2).
In order to produce a coupled spin-only image, we use the Taylor series expansion for exp(x) = 1 + x + x2/2! + x3/3! + x4/4! + . . . . If we denote the signal intensity from the noncoupled spins (A) immediately after the 90” pulse as &A, that from the coupled spins (B) as IOB, and the intensity of the noncoupled spins from the n th echo 159
0022-2364/89$3.00 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.
160
NOTES ---T
R.F.
_.. ----
r --.._
180~
180~
90x
n
&
n
.r
~~~~...
180~ "$!j/j$
n
180~ #p/J-+
SAMPLE
G-READ n
I
1
G-SLICE
u G-PHASE aa
a
FIG. 1. Pulse/gradient
aa
a
sequence used for acquisition of multiple-echo data.
then, when we consider the noncoupled spin system, using only the first two =&A, terms of the Taylor expansion, it can be shown that the sum of the intensities of the first and fourth echoes (ZrA + ZdA) is the same as that for the sum of the second and third echoes (12A + ZjA); i.e., for T < TZA
[21 hA+~~A=4Aexp(-~)+z~Aexp(-~)
$=: 2&A-&.
[3]
The case for the coupled spins is, however, complicated by a cosinusoidal modulation of each echo intensity caused by scalar coupling. The mathematical expressions for the signal intensity of each echo derived from both a noncoupled and a model two-spin coupled system are given in Table 1. Hence, if the echoes (En), where n corresponds to the echo number, are now combined as (E,+&-(E,+&)=&
[41
then the resultant signal intensity ( ER) comprises signals derived, in the main, from coupled spins. For a simple two-spin system it can be shown that this corresponds to TABLE 1 Signal Intensities of Noncoupled and Coupled Spin Echoes Echo no.
Noncoupled
I
Uw-~lTd
2 3
IoAexH-2dT2A) hmp(371 T2, 1
Zo~coti~J~kxP(-~/T2~)
bw-47IT2~)
(1 +4)!(2+3)
Coupled
0
I~~os(2?rJr)exp(-2~/T,,) ~,,coS(~?~JT)~XP(-~T/T,,) Z~,,cos(47rJ~)e.xp(-4~/T~~) r,,cos(~JT)exp(-4T/T2s)
161
NOTES
0
0.3
0.4
FIG. 2. Residual signal intensity of noncoupled
0.6
0.8
spins (A) as a function of 7/T,,,
1
as derived from
Eq. [51.
a value for ER of ZO,cos( a Jr )( -47/ TzB). The error, \k, in this first-order approximation of the Taylor expansion, which will result in a contribution of signal from noncoupled spins, can be calculated from
9 = Led-r/T&
+ exp(-4~/Tdl- [ew(-27/Td + ew(-37/Tdl [ew(-~/Td + exp(-4~/TdI
Figure 2 shows this error plotted as a function of the value of 7 / T2*. It can be seen that the residual error is less than 5% for 7/ T2A values of less than 0.25; for example, a typical in vivo T2 of 100 ms would require a T value of 25 ms. Hence, having measured the T2 values of the noncoupled and coupled spin systems, a value of 7 is calculated in order to maximize the ratio of the signal intensity from the coupled spins against that from the noncoupled spins. Preliminary measurements were made using methanol and ethanol which have comparable diffusion coefficients (which is known to cause signal attenuation (25)) and whose chemical shifts overlap at low magnetic field strengths. All experiments were undertaken at 2.0 T in a 3 1 cm bore Oxford Instruments horizontal cryomagnet controlled by a Biospec (Oxford Research Systems, Bruker) console. Figure 3 shows the series of magnitude image data obtained from the four echoes using the pulse/ gradient sequence given in Fig. 1, and also the resulting coupled spin image derived using the data manipulation technique documented above. The weighted-mean T2
162
NOTES
FIG. 3. (A) Four echo data setsacquired using the pulse sequence shown in Fig. 1. T = 25 ms, TR = 1 s, and a slice thickness of 1 cm was used to acquire a 128 X 128 data matrix of a phantom consisting of one vial (i.d. 0.5 cm) each of methanol (left) and ethanol with a read gradient of 0.75 G cm- ‘. (B) Image and corresponding profile taken from a row of the first echo data. (C) Resultant image and profile of coupled spins only derived from a row of the data after manipulation as described in Eq. [4].
NOTES
value measured from all the proton resonances for methanol was 1.03 s, and for ethanol 60 ms, giving an optimum value for TE of 24 ms. The methanol signal was suppressed by a factor of 400 when compared to the signal observed from the first echo, whereas approximately 70% of the coupled spin signal remains. It must be emphasized that this order of suppression is only obtained for a noncoupled spin system with a long spin-spin relaxation time, and will thus find greater use in nonmedical applications, such as the study of solvent diffusion through certain porous media. The signal intensity of the ethanol image was found to be three times greater than that obtained using techniques in which only one echo is acquired at a time 1/Jafter the initial 90” pulse. This method may be applied to biological systems in order to produce images from mobile, coupled spins such as lipids and, in particular, for the differentiation between noncoupled and coupled spin components of similar T2. In general, the condition that J is much less than the chemical-shift difference is no longer the case; therefore, there will be a degree of second-order effects causing a more complex modulation pattern. However, as mentioned by previous authors (26)) the proton signal from fat has a short T2 value and hence inhibits quantification of both chemical-shift and coupling constants from discrete resonances. Hence we have chosen to adopt the course of previous studies and have optimized 7 for one value of J. In order to mimic physiological conditions, we used a phantom that consisted of two vials of water doped to different extents with manganese( II) chloride ( MnC12) plus one vial of undoped corn oil. The T, values were tailored in order to lie within a range of typical in vivo values, i.e., 60- 120 ms (27). Figure 4B shows the oil-only image obtained assuming a scalar-coupling value of 7.5 Hz. The 7 value used was 22 ms and the T2 values for the two water samples and the oil were 97, 120, 107 ms, respectively. In comparing the resultant signal-to-noise ratios shown in Fig. 4, it should be noted that corn oil contains both coupled and noncoupled spin systems which contribute to the signal intensity of the image derived from the first echo, whereas only the noncoupled spin component will contribute to the signal intensity of the resultant image. Therefore the apparent suppression ratio of 5: 1 visible in Fig. 4B represents the lowest value, which would only be correct if all the spins in the corn oil were coupled. In this Note we have presented a pulse sequence for producing images from coupled spins only. It may be used for both chemical and biological applications where the coupled spin systems have relatively long spin-spin relaxation times. In common with existing techniques which use J modulation to differentiate between coupled and noncoupled spins, it can be used in cases where &, homogeneity is low, and selective presaturation techniques cannot be used. The gain in signal-to-noise with respect to existing techniques, where only one echo is collected at TE = 1/J (approximately 150 ms), arises from the fact that the short values of T2 will cause the image to be heavily weighted by the first echo which occurs at TE = 24 ms. Postprocessing requirements are minimal and the technique is robust since direct manipulation of magnitude data is feasible. We envisage that this technique will be most applicable to clinical imaging at lower field strengths, where the chemical-shift dispersion between water and fat will not be sufficient for some other techniques, and where the signal-to-noise ratio is intrinsically lower.
NOTES
164
FIG. 4. (A) First echo image and profile from a three-tube phantom (i.d. 0.5 cm) containing water. corn oil, and water, respectively. T = 22 ms; all other imaging parameters were identical to those used for Fig. 3. (B) Resultant image showing the coupled spins present in corn oil: the level of water suppression for both spin-spin relaxation times is highlighted by the trace shown. ACKNOWLEDGMENTS We thank Dr. Herchel Smith for an endowment (L.D.H.) and for Research Studentships ( A.G.W. and S.C.R.W.). We are also very grateful to M. A. Horsfield for general discussions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16.
L. PYKETT AND B. R. ROSEN, Radiology 149, 197 ( 1975 ). W. T. DIXON, Radiology153,189 ( 1984). L. D. HALLAND S. SUKUMAR, J. Magn. Reson. 56,314 ( 1984). A. HAASE AND J. FRAHM, J. Magn. Reson. 64,84 ( 1985). I.
L. D. P. A. C. S. D. D. P. R. N. C.
AXEL, G. GLOVER, AND N. PELC, Magn. Reson. Med. 2,428 ( 1985). GUILFOYLE AND P. MANSFIELD, Magn. Reson. Med. 2,419 ( 1985). A. BOTTOMLEY, T. H. FOSTER, AND W. M. LEUE, Proc. Natl. Acad. Sci. USA 81,6856 ( 1984). HAASE AND J. FRAHM, J. Magn. Reson. 64,94 ( 1985). DUMOULIN, Magn. Reson. Med. 2,583 ( 1985). AXELAND L. DOUGHERTY, J. Magn. Reson. 66,194 ( 1985). KUNZ, Magn. Reson. Med. 3,639 ( 1986). MA~HEI, A. HAASE, J. FRAHM, H. BOMSDORF, AND W. VOLLMANN, Radiology 160,79 1 ( 1986). KELLER, W. HUNTER, AND P. S~HMALBROCK, Radiology 64,539 ( 1987). J. ORDIDGE AND F. L. VAN DE VYVER, Radiology 157,55 1 ( 1985). M. SZEVERENVI AND E. M. HAAKE, J. Comput. Assist. Tomogr. 8,484 ( 1986). L. DUMOULIN, Magn. Reson. Med. 3,90 ( 1986).
NOTES
165
17. C. L. DUMOULIN AND D. VATIS, Magn. Reson. Med. 3,282 ( 1986). 18. C. J. HARDY AND C. L. DUMOULIN, Magn. Reson. Med. 5,58 ( 1987). 19. L. D. HALL, T. J. NORWOOD, AND S. C. R. WILLIAMS, J. Magn. Reson. 79,363 (1988). 20. S. C. R. WILLIAMS, M. A. HORSFIELD, AND L. D. HALL, Radiology, in press. 21. D. P. BURUM, M. LINDER, AND R. R. ERNST, J. Magn. Reson. 44,173 ( 1981). 22. A. E. DEROME, J. Magn. Reson. 78,113 ( 1988). 23. A. ABRAGAM, “The Principles of Nuclear Magnetism,” p. 500. Oxford Univ. Press, London/New York, 196 1. 24. E. L. HAHN AND D. E. MAXWELL, Phys. Rev. 88,107O ( 1952). 25. E. L. HAHN, Phys. Rev. 80,580( 1950). 26. D. W. KORMOS, Y-L. FENG, J. B. MURDOCH, AND H. N. YEUNG, “Fifth Annual Meeting of the Society of Magnetic Resonance in Medicine, 1986,” p. 836. 27. R. M. DE-VRE, Brit. J. Radiol. 57,955 ( 1984).
RESONANCE84,
159-165 ( 1989)
Generation of Coupled Spin-Only Images Using Multiple-Echo Acquisition A. G. WEBB, S. C. R. WILLIAMS,
AND L. D. HALL
Laboratory for MedicinaI Chemistry, Level 4 R. T.C., Addenbrookes Hospital, Hills Road, Cambridge CB2 2QQP United Kingdom Received September 22, 1988; revised November 28, 1988
The development of imaging techniques to distinguish between the two components of a binary system has previously been achieved by a variety of methods using one, or a combination, of the differences in chemical shift ( 1-6), selective saturation ( 7-13), differential relaxation times (Id), and the effects of scalar coupling (1.5-19). If noncoupled and coupled resonances overlap, due either to magnetic field inhomogeneity or to insufficient chemical-shift dispersion, the last method of discrimination is the most appropriate to implement. However, the method is limited by the long preparation times necessary for J evolution to occur, and may typically be as long as 150 ms which leads to low signal intensity from components with short spin-spin relaxation times ( T2). In this Note we apply a property of multiple-echo techniques that was developed in an earlier paper (20) to produce an experiment in which a coupled spin-only image can be obtained, even in poor magnetic field homogeneity, from a single excitation per phase-encode step, and with improved signal-to-noise ratio when compared with existing techniques. The pulse sequence used is shown in Fig. 1. A second phase-encoding gradient with opposite polarity was applied after each data acquisition in order to reverse the effect of the former. The 180” refocusing pulses used were a previously documented (21) and recently elaborated composite type (22), which exhibit low-phase distortion caused by B, inhomogeneity. In order to illustrate the way in which coupled spin images may be obtained, we consider the case of an AX system with a coupling constant J, plus a single-component noncoupled spin system. If the coupling constant between the two spins is much smaller than their difference in chemical shift, then the system can be treated as first order. Assuming that the AX doublet is on resonance, the echo intensity, I( T), of the coupled spins is a function of the spin-echo time (7) (23,24) given by
[II
I(T) = cos(rJ7)exp(-7/T2).
In order to produce a coupled spin-only image, we use the Taylor series expansion for exp(x) = 1 + x + x2/2! + x3/3! + x4/4! + . . . . If we denote the signal intensity from the noncoupled spins (A) immediately after the 90” pulse as &A, that from the coupled spins (B) as IOB, and the intensity of the noncoupled spins from the n th echo 159
0022-2364/89$3.00 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.
160
NOTES ---T
R.F.
_.. ----
r --.._
180~
180~
90x
n
&
n
.r
~~~~...
180~ "$!j/j$
n
180~ #p/J-+
SAMPLE
G-READ n
I
1
G-SLICE
u G-PHASE aa
a
FIG. 1. Pulse/gradient
aa
a
sequence used for acquisition of multiple-echo data.
then, when we consider the noncoupled spin system, using only the first two =&A, terms of the Taylor expansion, it can be shown that the sum of the intensities of the first and fourth echoes (ZrA + ZdA) is the same as that for the sum of the second and third echoes (12A + ZjA); i.e., for T < TZA
[21 hA+~~A=4Aexp(-~)+z~Aexp(-~)
$=: 2&A-&.
[3]
The case for the coupled spins is, however, complicated by a cosinusoidal modulation of each echo intensity caused by scalar coupling. The mathematical expressions for the signal intensity of each echo derived from both a noncoupled and a model two-spin coupled system are given in Table 1. Hence, if the echoes (En), where n corresponds to the echo number, are now combined as (E,+&-(E,+&)=&
[41
then the resultant signal intensity ( ER) comprises signals derived, in the main, from coupled spins. For a simple two-spin system it can be shown that this corresponds to TABLE 1 Signal Intensities of Noncoupled and Coupled Spin Echoes Echo no.
Noncoupled
I
Uw-~lTd
2 3
IoAexH-2dT2A) hmp(371 T2, 1
Zo~coti~J~kxP(-~/T2~)
bw-47IT2~)
(1 +4)!(2+3)
Coupled
0
I~~os(2?rJr)exp(-2~/T,,) ~,,coS(~?~JT)~XP(-~T/T,,) Z~,,cos(47rJ~)e.xp(-4~/T~~) r,,cos(~JT)exp(-4T/T2s)
161
NOTES
0
0.3
0.4
FIG. 2. Residual signal intensity of noncoupled
0.6
0.8
spins (A) as a function of 7/T,,,
1
as derived from
Eq. [51.
a value for ER of ZO,cos( a Jr )( -47/ TzB). The error, \k, in this first-order approximation of the Taylor expansion, which will result in a contribution of signal from noncoupled spins, can be calculated from
9 = Led-r/T&
+ exp(-4~/Tdl- [ew(-27/Td + ew(-37/Tdl [ew(-~/Td + exp(-4~/TdI
Figure 2 shows this error plotted as a function of the value of 7 / T2*. It can be seen that the residual error is less than 5% for 7/ T2A values of less than 0.25; for example, a typical in vivo T2 of 100 ms would require a T value of 25 ms. Hence, having measured the T2 values of the noncoupled and coupled spin systems, a value of 7 is calculated in order to maximize the ratio of the signal intensity from the coupled spins against that from the noncoupled spins. Preliminary measurements were made using methanol and ethanol which have comparable diffusion coefficients (which is known to cause signal attenuation (25)) and whose chemical shifts overlap at low magnetic field strengths. All experiments were undertaken at 2.0 T in a 3 1 cm bore Oxford Instruments horizontal cryomagnet controlled by a Biospec (Oxford Research Systems, Bruker) console. Figure 3 shows the series of magnitude image data obtained from the four echoes using the pulse/ gradient sequence given in Fig. 1, and also the resulting coupled spin image derived using the data manipulation technique documented above. The weighted-mean T2
162
NOTES
FIG. 3. (A) Four echo data setsacquired using the pulse sequence shown in Fig. 1. T = 25 ms, TR = 1 s, and a slice thickness of 1 cm was used to acquire a 128 X 128 data matrix of a phantom consisting of one vial (i.d. 0.5 cm) each of methanol (left) and ethanol with a read gradient of 0.75 G cm- ‘. (B) Image and corresponding profile taken from a row of the first echo data. (C) Resultant image and profile of coupled spins only derived from a row of the data after manipulation as described in Eq. [4].
NOTES
value measured from all the proton resonances for methanol was 1.03 s, and for ethanol 60 ms, giving an optimum value for TE of 24 ms. The methanol signal was suppressed by a factor of 400 when compared to the signal observed from the first echo, whereas approximately 70% of the coupled spin signal remains. It must be emphasized that this order of suppression is only obtained for a noncoupled spin system with a long spin-spin relaxation time, and will thus find greater use in nonmedical applications, such as the study of solvent diffusion through certain porous media. The signal intensity of the ethanol image was found to be three times greater than that obtained using techniques in which only one echo is acquired at a time 1/Jafter the initial 90” pulse. This method may be applied to biological systems in order to produce images from mobile, coupled spins such as lipids and, in particular, for the differentiation between noncoupled and coupled spin components of similar T2. In general, the condition that J is much less than the chemical-shift difference is no longer the case; therefore, there will be a degree of second-order effects causing a more complex modulation pattern. However, as mentioned by previous authors (26)) the proton signal from fat has a short T2 value and hence inhibits quantification of both chemical-shift and coupling constants from discrete resonances. Hence we have chosen to adopt the course of previous studies and have optimized 7 for one value of J. In order to mimic physiological conditions, we used a phantom that consisted of two vials of water doped to different extents with manganese( II) chloride ( MnC12) plus one vial of undoped corn oil. The T, values were tailored in order to lie within a range of typical in vivo values, i.e., 60- 120 ms (27). Figure 4B shows the oil-only image obtained assuming a scalar-coupling value of 7.5 Hz. The 7 value used was 22 ms and the T2 values for the two water samples and the oil were 97, 120, 107 ms, respectively. In comparing the resultant signal-to-noise ratios shown in Fig. 4, it should be noted that corn oil contains both coupled and noncoupled spin systems which contribute to the signal intensity of the image derived from the first echo, whereas only the noncoupled spin component will contribute to the signal intensity of the resultant image. Therefore the apparent suppression ratio of 5: 1 visible in Fig. 4B represents the lowest value, which would only be correct if all the spins in the corn oil were coupled. In this Note we have presented a pulse sequence for producing images from coupled spins only. It may be used for both chemical and biological applications where the coupled spin systems have relatively long spin-spin relaxation times. In common with existing techniques which use J modulation to differentiate between coupled and noncoupled spins, it can be used in cases where &, homogeneity is low, and selective presaturation techniques cannot be used. The gain in signal-to-noise with respect to existing techniques, where only one echo is collected at TE = 1/J (approximately 150 ms), arises from the fact that the short values of T2 will cause the image to be heavily weighted by the first echo which occurs at TE = 24 ms. Postprocessing requirements are minimal and the technique is robust since direct manipulation of magnitude data is feasible. We envisage that this technique will be most applicable to clinical imaging at lower field strengths, where the chemical-shift dispersion between water and fat will not be sufficient for some other techniques, and where the signal-to-noise ratio is intrinsically lower.
NOTES
164
FIG. 4. (A) First echo image and profile from a three-tube phantom (i.d. 0.5 cm) containing water. corn oil, and water, respectively. T = 22 ms; all other imaging parameters were identical to those used for Fig. 3. (B) Resultant image showing the coupled spins present in corn oil: the level of water suppression for both spin-spin relaxation times is highlighted by the trace shown. ACKNOWLEDGMENTS We thank Dr. Herchel Smith for an endowment (L.D.H.) and for Research Studentships ( A.G.W. and S.C.R.W.). We are also very grateful to M. A. Horsfield for general discussions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16.
L. PYKETT AND B. R. ROSEN, Radiology 149, 197 ( 1975 ). W. T. DIXON, Radiology153,189 ( 1984). L. D. HALLAND S. SUKUMAR, J. Magn. Reson. 56,314 ( 1984). A. HAASE AND J. FRAHM, J. Magn. Reson. 64,84 ( 1985). I.
L. D. P. A. C. S. D. D. P. R. N. C.
AXEL, G. GLOVER, AND N. PELC, Magn. Reson. Med. 2,428 ( 1985). GUILFOYLE AND P. MANSFIELD, Magn. Reson. Med. 2,419 ( 1985). A. BOTTOMLEY, T. H. FOSTER, AND W. M. LEUE, Proc. Natl. Acad. Sci. USA 81,6856 ( 1984). HAASE AND J. FRAHM, J. Magn. Reson. 64,94 ( 1985). DUMOULIN, Magn. Reson. Med. 2,583 ( 1985). AXELAND L. DOUGHERTY, J. Magn. Reson. 66,194 ( 1985). KUNZ, Magn. Reson. Med. 3,639 ( 1986). MA~HEI, A. HAASE, J. FRAHM, H. BOMSDORF, AND W. VOLLMANN, Radiology 160,79 1 ( 1986). KELLER, W. HUNTER, AND P. S~HMALBROCK, Radiology 64,539 ( 1987). J. ORDIDGE AND F. L. VAN DE VYVER, Radiology 157,55 1 ( 1985). M. SZEVERENVI AND E. M. HAAKE, J. Comput. Assist. Tomogr. 8,484 ( 1986). L. DUMOULIN, Magn. Reson. Med. 3,90 ( 1986).
NOTES
165
17. C. L. DUMOULIN AND D. VATIS, Magn. Reson. Med. 3,282 ( 1986). 18. C. J. HARDY AND C. L. DUMOULIN, Magn. Reson. Med. 5,58 ( 1987). 19. L. D. HALL, T. J. NORWOOD, AND S. C. R. WILLIAMS, J. Magn. Reson. 79,363 (1988). 20. S. C. R. WILLIAMS, M. A. HORSFIELD, AND L. D. HALL, Radiology, in press. 21. D. P. BURUM, M. LINDER, AND R. R. ERNST, J. Magn. Reson. 44,173 ( 1981). 22. A. E. DEROME, J. Magn. Reson. 78,113 ( 1988). 23. A. ABRAGAM, “The Principles of Nuclear Magnetism,” p. 500. Oxford Univ. Press, London/New York, 196 1. 24. E. L. HAHN AND D. E. MAXWELL, Phys. Rev. 88,107O ( 1952). 25. E. L. HAHN, Phys. Rev. 80,580( 1950). 26. D. W. KORMOS, Y-L. FENG, J. B. MURDOCH, AND H. N. YEUNG, “Fifth Annual Meeting of the Society of Magnetic Resonance in Medicine, 1986,” p. 836. 27. R. M. DE-VRE, Brit. J. Radiol. 57,955 ( 1984).