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Solvent signal suppression without phase distortion in high-resolution NMR
JOURNAL
OF MAGNETIC
RESONANCE
71, 576-581
(1987)
Solvent Signal Suppressionwithout PhaseDistortion in High-Resolution NMR MALCOLM H. LEVITT
AND
MARY
F. ROBERTS
Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received
November
13, 1986
We report a new pulse sequence, NERO-l, for the suppression of resonances over a narrow band of frequencies in a high-resolution NMR spectrum. The sequence is expected to be useful for suppressing strong solvent peaks which otherwise create difficult dynamic range problems. In common with previously known methods (IZO), the new frequency-selective sequence is short enough to avoid chemical exchange or relaxation effects. In addition, it combines for the first time a flat null near the carrier frequency with a wide band of maximal excitation almost free of phase variations. The wide null allows the suppression of broad solvent peaks while the good phase behavior makes strong spectral phase corrections after Fourier transformation unnecessary. The introduction of a “rolling” baseline may be avoided and overlapping or inhomogeneously broadened signals may be obtained with high fidelity. The suppression of the strong solvent signal is essential for proton NMR studies of biomolecules in aqueous solution to circumvent degradation of the spectrum quality caused by the finite dynamic range of the receiver, digitizer, and computer electronics. Although hardware modifications may reduce this problem (II), the present method of choice is to exploit particular NMR properties of the solvent, such as its relaxation behavior or distinct resonance frequency, in order to avoid exciting its signal. Rapid selective excitation methods such as those suggested by Redfield and others (Z-10) employ a sequence of pulses having the property of not exciting magnetization resonating at one frequency while exciting signals over a band of other frequencies. The most recent implementations favor sequences which produce zero excitation on-resonance with the carrier, as these are expected to be less sensitive to instrumental defects (3-10). The sequence to be described is also used by placing the carrier at the same frequency as the solvent resonance. It is well known that for small perturbations, the frequency response of a pulse sequence is proportional to the Fourier transform of the time-domain excitation. Therefore, an irradiation scheme providing zero excitation on-resonance and exciting a band on either side may be based on the inverse Fourier transform of this desirable frequency response, with small corrections for nonlinearity as necessary. The great majority of previous “band reject” schemes have been constructed on this prin0022-2364187
$3.00
Copyright Q 1987 by Academic FYes, Inc.
576
577
COMMUNICATIONS
ciple, including both “hard” pulse (1-8) and continuously shaped irradiation field techniques (9). Although the Fourier transform is useful for predicting sequences with a flat region of vanishing response near the carrier, it inevitably leads to serious phase problems for strongly excited resonances offset in frequency from the carrier. In most cases these resonances behave as if excited by a single strong pulse placed at the center of the selective sequence. The strong spectral phase gradient arises because signal may only be acquired after waiting until the end of the excitation sequence, which must have an appreciable duration in order to achieve frequency selectivity. For example, the commonly used “1 3 3 1” sequence (4-6), applied with delays between the pulses of 500 ps, produces a spectrum having a phase gradient of approximately 360” between A
1.0
V-----I / /
0.8
\ \ \
/
\ \
0.6
signal intensity
\ \ \
0.4
\ \
0.2
\
\
0.0 0.5
0.0
B
I
I
1.0
1.5
\
180.
90.
phase
0.
-90. ’ I/
-180. 0.0
I I
/’ (
I
0.5
1.0
resonance
’
1.5
offset
RG. I. Performance of the pulse sequences NERO-l (solid line) and 1 3 3 1 (dashed line) as a function of offset frequency Aw/~A, predicted by numerical simulation of the Bloch equations in the absence of relaxation. The intensity (A) and phase (B) of excited transverse magnetization are shown. The frequency units are Ao/Aw,,, where the center frequency of the excitation band Aw,J2rr is defined by the delays between the pulses, according to Eq. [2] in the case of NERO-l. For the 1 3 3 1 sequence, the pulse flip angles were 11.25 and 33.75” with the four pulses separated by three delays, all of duration OS/(AwJ27r). In both casesa radiofrequency nutation frequency of lOAw,J2a was assumed, and the pulses were given phases k90”. For either sequence the intensity of transverse magnetization is unaffected by change of sign of offset, while the phase is inverted in sign.
578
COMMUNICATIONS
points 2.7 ppm apart in a 500 MHz spectrum (see Fig. 1B). If broadening the excitation band by employing a longer sequence (7-9) is attempted, the phase problem becomes proportionally worse. It is important to realize that even though this phase gradient is nearly linear with respect to frequency, it is too large to be corrected cleanly by conventional frequency-dependent complex multiplication of the transformed spectrum without introducing artifacts such as baseline “roll” and degradation of broad or overlapping signals. The same applies to resolution enhancement or calculation of the absolute value. On the basis of Fourier transform arguments, frequency selectivity and good phase behavior seem mutually incompatible. In fact, both may be produced simultaneously if adherence to linear response solutions (small tlip angles) is abandoned. A simple example is the “jump and return” sequence of two 90” pulses demonstrated by Plateau and G&on (10). This has good phase behavior but its frequency response is less than optimal: The signal is strongly dependent on offset around the carrier and the excited signal band is sinusoidal rather than flat. Another possibility is to follow a binomial or similar pulse sequence by a strong, ideal, 180” pulse in order to refocus the phase dispersion. However, pulse imperfections would probably make it impossible to achieve good solvent suppression this way, even allowing for the use of a composite 180” pulse (12). More suitable nonlinear solutions are difficult to locate because there is an enormous number of candidate pulse sequences, very few of which are effective, and the only general way of predicting the complete frequency response of a given sequence outside the linear regime is by time-consuming numerical integration of the Bloch equations. Our approach was to greatly reduce the number of candidate pulse sequences by using coherent averaging theory (13) to treat the frequency response in the neighborhood of zero offset, as will be described fully elsewhere. Briefly, we formulated constraints on the possible combinations of pulses and delays which ensure that (a) the signal is zero exactly on-resonance, independent of the radiofrequency field strength; (b) the signal has at least a cubic dependence on offset from resonance-this ensures a broad “null” in the frequency response at the carrier frequency; and (c) the offset dependence near the carrier is not degraded by small errors in the radiofrequency field strength. These constraints were used as the basis for an unintelligent computer search over sequences of a small number of pulses and delays. The valid sequences were compared on the basis of their performance off-resonance, as simulated by numerical integration of the Bloch equations ignoring relaxation. Those displaying the best behavior (wide bandwidth with small phase distortions) were chosen and optimized further by fine tuning of the pulse sequence intervals. We refer to this new class of pulse sequences by the acronym NERO (nonlinear excitation with rejection on-resonance). A promising example, NERO- 1, may be written as 120°-r,-1150-~2-1 15’-2~~-1 15°-~2-1150-r,-1200-7,, 111 where ri are interpulse delays, pulses 180” out of phase having an overbar. (Note that the pulses do not simply alternate in phase.) The delays between the pulses must be calculated according to the resonance offset of the center of the desired spectral region to be excited. If this offset is A~~,,,4217(in Hz), the delays are given by
COMMUNICATIONS
579
T1 = 0.139/( AweXJ27r)
r2=0.625/(Aw,,/2?r) 2r3=0.428/(AoexJ2n).
PI
As is shown in Fig. lA, this sequence excites to better than 90% efficiency signals having offsets between 0.5 and 1.7 times AU,, J2a (and the same at negative offsets). If a refocusing delay
~,=0.222/(Apo,J2u)
131
is inserted, the phase variations over the excited signal band between OSAo,J27r and lSAhw,, J21r are only f 10” (Fig. 1B). These phase errors are barely detectable in the experimental spectrum but are small enough to be corrected if necessary without introducing severe distortions. The phase at negative offsets (not shown) differs from that at positive offsets by approximately 45”, simply requiring a separate phase adjustment of the two halves of the spectrum. The above sequence was actually optimized for use with slightly “soft” pulses having an rf nutation frequency of only ten times AU,, J2r, but its performance is rather insensitive to this setting. Adjustments to the pulse lengths for different radiofrequency intensities will be given elsewhere. Depending on the spectrometer, it may be advisable to add a short “trim” pulse, 90” out of phase, in order to correct the solvent response for small instrumental phase or amplitude errors. This is also common usage with other suppression methods (2 8).
NERO-l is superficially similar to the earlier binomial sequences, being an antisymmetric set of short pulses alternating with delays. However, the presence of large hip angles (115 and 120”) betrays its radically different construction and properties. Some preliminary experimental results demonstrating the potential of NERO- 1 for phasedistortionless solvent suppression are given in Fig. 2. The sample was a 3 mM solution of the 36-amino acid protein ELH, an egg-laying hormone from the marine mollusk Aplysiu culifornicu (14), in 5% Hz0 and 95% 40 at pH 6.5. The proton NMR spectra are Fourier transforms of single transients acquired at 500 MHz on a home-built spectrometer of the Francis Bitter Magnet Laboratory, with 1 Hz line broadening. Figure 2A shows the result of a single 90” pulse of duration 15.5 I.IS.Figure 2B was obtained by placing the carrier on the Hz0 peak and applying a 1 3 3 1 sequence with interpulse delays of 0.3 ms. The spectrum shows good suppression of the solvent resonance but displays distorted intensities reflecting the restricted excitation bandwidth of Fig. IA. Furthermore, the rolling baseline and attenuation of broad peaks brought about by the strong linear phase correction are very evident. Figure 2C was obtained using NERO-I, with an additional 0.7 PS trim pulse at the end of the sequence, determined empirically. The degree of solvent suppression was in this case comparable to that obtained with the binomial sequence (about 400: 1) but the phase and intensity distortions were much smaller: The intensities of the indicated excited band are comparable to those in Fig. 2A. Excitation closer to the solvent resonance may of course be achieved by lengthening the delays between the pulses, just as for the binomial sequences. This is naturally at the expense of the signals furthest removed in frequency from the solvent.
COMMUNICATIONS
580
I
6.0
I
6.0 Chemical
I
I
4.0 Shift
2.0
I
0.0
(ppm)
FIG. 2. Experimental 500 MHz proton NMR spectra of ELH (8 mg./ml) in 5% Hz0 and 95% DaO. (A) Single 90” pulse excitation; (B) solvent peak suppression by I 3 3 1 displaying spectral distortions; and (C) solvent peak suppression by NERO-1 showing an almost undistorted excited frequency band around (AwJ 27r) = 1.67 kI-Iz, as indicated by the bar.
Attempts at using NERO- 1 to suppress the solvent resonance for solutions of higher Hz0 content have so far proven to be rather disappointing. A tentative explanation is that NERO- 1, which momentarily creates large transverse magnetization components, is sensitive to distortions of the magnetization vector trajectories by radiation damping (15), which we observed to be noticeable for aqueous solutions at 500 MHz. Whether or not this is always a significant problem will depend on the resonance frequency and the radiofrequency coil characteristics. In summary, we have demonstrated that selective excitation and good phase behavior are not incompatible, providing a nonlinear excitation method is used. The new pulse sequence, NERO-l, is potentially useful in cases where broad or overlapping lines make the strong phase distortions associated with most previous methods undesirable. ACKNOWLEDGMENTS This research was supported by grants from the National Institutes of Health (GM-26762 (M.F.R.), GM36920-01, and RR-00995 (M.H.L.)) and from the National Science Foundation DMR-8211416 (M.H.L.). The authors thank Dr. Felix Strumwasser of the Physiology Department, Boston University Medical Center, for the sample of ELH, Dave Ruben for help in implementing the pulse sequences, and R. G. Griffin for computer time.
COMMUNICATIONS REFERENCES I. 2. 3. 4.
A. J. V. D.
G. REDFIELD, S. D. Ku~z, AND E. K. RALPH, J. Mugs. Reson. 19, 114 ( 1975). M. WRIGHT, J. FEIGON, W. LEUPIN, AND D. R. KEARNS, J. II&P. Reson. 45,5 14 ( 198 1). SKLENAR AND Z. STAR&K, J. Magn. Reson. 50,495 (1982). L. TURNER, J. Magn. Reson. 54, 146 (1983).
5. P. J. HORE, J. Magn. Reson. 54,539 (1983). 6. P. J. HORE, J. Mugn. Reson. 55,283 (1983). 7. Z. STAR&JK AND V. SKLENAR, J. Magn. Reson. 66,39 1 (1986). 8. G. A. MORRIS, K. I. SMITH, AND J. C. WATERTON, J. Mum. Reson. 68, 526 (1986). 9. J. H. C&TOW, M. MCCOY, F. SPANO, AND W. S. WARREN, Phys. Rev. Lett. 55, 1090 (1985). 10. P. PLATEAU AND M. GUBRON, J. Am. Chem. Sot. 104,731O (1982). 11. S. DAVIES, C. BAUER, P. BARKER, AND R. FREEMAN, J. Mugn. Reson. 64, 155 (1985). 12. M. H. LEVITT, Prog. NMR Spectrosc. 18,61 (1986). 13. U. HAEBERLEN AND J. S. WAUGH, Phys. Rev. 175,453 (1968). 14. A. Y.CHIUANDF. STRUMWASSER, J. Neurosci. 1,812(1981). 15. A. ABRAGAM, “Principles of Nuclear Magnetism,” Oxford Univ. Press, Oxford, 196 1.
581
OF MAGNETIC
RESONANCE
71, 576-581
(1987)
Solvent Signal Suppressionwithout PhaseDistortion in High-Resolution NMR MALCOLM H. LEVITT
AND
MARY
F. ROBERTS
Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received
November
13, 1986
We report a new pulse sequence, NERO-l, for the suppression of resonances over a narrow band of frequencies in a high-resolution NMR spectrum. The sequence is expected to be useful for suppressing strong solvent peaks which otherwise create difficult dynamic range problems. In common with previously known methods (IZO), the new frequency-selective sequence is short enough to avoid chemical exchange or relaxation effects. In addition, it combines for the first time a flat null near the carrier frequency with a wide band of maximal excitation almost free of phase variations. The wide null allows the suppression of broad solvent peaks while the good phase behavior makes strong spectral phase corrections after Fourier transformation unnecessary. The introduction of a “rolling” baseline may be avoided and overlapping or inhomogeneously broadened signals may be obtained with high fidelity. The suppression of the strong solvent signal is essential for proton NMR studies of biomolecules in aqueous solution to circumvent degradation of the spectrum quality caused by the finite dynamic range of the receiver, digitizer, and computer electronics. Although hardware modifications may reduce this problem (II), the present method of choice is to exploit particular NMR properties of the solvent, such as its relaxation behavior or distinct resonance frequency, in order to avoid exciting its signal. Rapid selective excitation methods such as those suggested by Redfield and others (Z-10) employ a sequence of pulses having the property of not exciting magnetization resonating at one frequency while exciting signals over a band of other frequencies. The most recent implementations favor sequences which produce zero excitation on-resonance with the carrier, as these are expected to be less sensitive to instrumental defects (3-10). The sequence to be described is also used by placing the carrier at the same frequency as the solvent resonance. It is well known that for small perturbations, the frequency response of a pulse sequence is proportional to the Fourier transform of the time-domain excitation. Therefore, an irradiation scheme providing zero excitation on-resonance and exciting a band on either side may be based on the inverse Fourier transform of this desirable frequency response, with small corrections for nonlinearity as necessary. The great majority of previous “band reject” schemes have been constructed on this prin0022-2364187
$3.00
Copyright Q 1987 by Academic FYes, Inc.
576
577
COMMUNICATIONS
ciple, including both “hard” pulse (1-8) and continuously shaped irradiation field techniques (9). Although the Fourier transform is useful for predicting sequences with a flat region of vanishing response near the carrier, it inevitably leads to serious phase problems for strongly excited resonances offset in frequency from the carrier. In most cases these resonances behave as if excited by a single strong pulse placed at the center of the selective sequence. The strong spectral phase gradient arises because signal may only be acquired after waiting until the end of the excitation sequence, which must have an appreciable duration in order to achieve frequency selectivity. For example, the commonly used “1 3 3 1” sequence (4-6), applied with delays between the pulses of 500 ps, produces a spectrum having a phase gradient of approximately 360” between A
1.0
V-----I / /
0.8
\ \ \
/
\ \
0.6
signal intensity
\ \ \
0.4
\ \
0.2
\
\
0.0 0.5
0.0
B
I
I
1.0
1.5
\
180.
90.
phase
0.
-90. ’ I/
-180. 0.0
I I
/’ (
I
0.5
1.0
resonance
’
1.5
offset
RG. I. Performance of the pulse sequences NERO-l (solid line) and 1 3 3 1 (dashed line) as a function of offset frequency Aw/~A, predicted by numerical simulation of the Bloch equations in the absence of relaxation. The intensity (A) and phase (B) of excited transverse magnetization are shown. The frequency units are Ao/Aw,,, where the center frequency of the excitation band Aw,J2rr is defined by the delays between the pulses, according to Eq. [2] in the case of NERO-l. For the 1 3 3 1 sequence, the pulse flip angles were 11.25 and 33.75” with the four pulses separated by three delays, all of duration OS/(AwJ27r). In both casesa radiofrequency nutation frequency of lOAw,J2a was assumed, and the pulses were given phases k90”. For either sequence the intensity of transverse magnetization is unaffected by change of sign of offset, while the phase is inverted in sign.
578
COMMUNICATIONS
points 2.7 ppm apart in a 500 MHz spectrum (see Fig. 1B). If broadening the excitation band by employing a longer sequence (7-9) is attempted, the phase problem becomes proportionally worse. It is important to realize that even though this phase gradient is nearly linear with respect to frequency, it is too large to be corrected cleanly by conventional frequency-dependent complex multiplication of the transformed spectrum without introducing artifacts such as baseline “roll” and degradation of broad or overlapping signals. The same applies to resolution enhancement or calculation of the absolute value. On the basis of Fourier transform arguments, frequency selectivity and good phase behavior seem mutually incompatible. In fact, both may be produced simultaneously if adherence to linear response solutions (small tlip angles) is abandoned. A simple example is the “jump and return” sequence of two 90” pulses demonstrated by Plateau and G&on (10). This has good phase behavior but its frequency response is less than optimal: The signal is strongly dependent on offset around the carrier and the excited signal band is sinusoidal rather than flat. Another possibility is to follow a binomial or similar pulse sequence by a strong, ideal, 180” pulse in order to refocus the phase dispersion. However, pulse imperfections would probably make it impossible to achieve good solvent suppression this way, even allowing for the use of a composite 180” pulse (12). More suitable nonlinear solutions are difficult to locate because there is an enormous number of candidate pulse sequences, very few of which are effective, and the only general way of predicting the complete frequency response of a given sequence outside the linear regime is by time-consuming numerical integration of the Bloch equations. Our approach was to greatly reduce the number of candidate pulse sequences by using coherent averaging theory (13) to treat the frequency response in the neighborhood of zero offset, as will be described fully elsewhere. Briefly, we formulated constraints on the possible combinations of pulses and delays which ensure that (a) the signal is zero exactly on-resonance, independent of the radiofrequency field strength; (b) the signal has at least a cubic dependence on offset from resonance-this ensures a broad “null” in the frequency response at the carrier frequency; and (c) the offset dependence near the carrier is not degraded by small errors in the radiofrequency field strength. These constraints were used as the basis for an unintelligent computer search over sequences of a small number of pulses and delays. The valid sequences were compared on the basis of their performance off-resonance, as simulated by numerical integration of the Bloch equations ignoring relaxation. Those displaying the best behavior (wide bandwidth with small phase distortions) were chosen and optimized further by fine tuning of the pulse sequence intervals. We refer to this new class of pulse sequences by the acronym NERO (nonlinear excitation with rejection on-resonance). A promising example, NERO- 1, may be written as 120°-r,-1150-~2-1 15’-2~~-1 15°-~2-1150-r,-1200-7,, 111 where ri are interpulse delays, pulses 180” out of phase having an overbar. (Note that the pulses do not simply alternate in phase.) The delays between the pulses must be calculated according to the resonance offset of the center of the desired spectral region to be excited. If this offset is A~~,,,4217(in Hz), the delays are given by
COMMUNICATIONS
579
T1 = 0.139/( AweXJ27r)
r2=0.625/(Aw,,/2?r) 2r3=0.428/(AoexJ2n).
PI
As is shown in Fig. lA, this sequence excites to better than 90% efficiency signals having offsets between 0.5 and 1.7 times AU,, J2a (and the same at negative offsets). If a refocusing delay
~,=0.222/(Apo,J2u)
131
is inserted, the phase variations over the excited signal band between OSAo,J27r and lSAhw,, J21r are only f 10” (Fig. 1B). These phase errors are barely detectable in the experimental spectrum but are small enough to be corrected if necessary without introducing severe distortions. The phase at negative offsets (not shown) differs from that at positive offsets by approximately 45”, simply requiring a separate phase adjustment of the two halves of the spectrum. The above sequence was actually optimized for use with slightly “soft” pulses having an rf nutation frequency of only ten times AU,, J2r, but its performance is rather insensitive to this setting. Adjustments to the pulse lengths for different radiofrequency intensities will be given elsewhere. Depending on the spectrometer, it may be advisable to add a short “trim” pulse, 90” out of phase, in order to correct the solvent response for small instrumental phase or amplitude errors. This is also common usage with other suppression methods (2 8).
NERO-l is superficially similar to the earlier binomial sequences, being an antisymmetric set of short pulses alternating with delays. However, the presence of large hip angles (115 and 120”) betrays its radically different construction and properties. Some preliminary experimental results demonstrating the potential of NERO- 1 for phasedistortionless solvent suppression are given in Fig. 2. The sample was a 3 mM solution of the 36-amino acid protein ELH, an egg-laying hormone from the marine mollusk Aplysiu culifornicu (14), in 5% Hz0 and 95% 40 at pH 6.5. The proton NMR spectra are Fourier transforms of single transients acquired at 500 MHz on a home-built spectrometer of the Francis Bitter Magnet Laboratory, with 1 Hz line broadening. Figure 2A shows the result of a single 90” pulse of duration 15.5 I.IS.Figure 2B was obtained by placing the carrier on the Hz0 peak and applying a 1 3 3 1 sequence with interpulse delays of 0.3 ms. The spectrum shows good suppression of the solvent resonance but displays distorted intensities reflecting the restricted excitation bandwidth of Fig. IA. Furthermore, the rolling baseline and attenuation of broad peaks brought about by the strong linear phase correction are very evident. Figure 2C was obtained using NERO-I, with an additional 0.7 PS trim pulse at the end of the sequence, determined empirically. The degree of solvent suppression was in this case comparable to that obtained with the binomial sequence (about 400: 1) but the phase and intensity distortions were much smaller: The intensities of the indicated excited band are comparable to those in Fig. 2A. Excitation closer to the solvent resonance may of course be achieved by lengthening the delays between the pulses, just as for the binomial sequences. This is naturally at the expense of the signals furthest removed in frequency from the solvent.
COMMUNICATIONS
580
I
6.0
I
6.0 Chemical
I
I
4.0 Shift
2.0
I
0.0
(ppm)
FIG. 2. Experimental 500 MHz proton NMR spectra of ELH (8 mg./ml) in 5% Hz0 and 95% DaO. (A) Single 90” pulse excitation; (B) solvent peak suppression by I 3 3 1 displaying spectral distortions; and (C) solvent peak suppression by NERO-1 showing an almost undistorted excited frequency band around (AwJ 27r) = 1.67 kI-Iz, as indicated by the bar.
Attempts at using NERO- 1 to suppress the solvent resonance for solutions of higher Hz0 content have so far proven to be rather disappointing. A tentative explanation is that NERO- 1, which momentarily creates large transverse magnetization components, is sensitive to distortions of the magnetization vector trajectories by radiation damping (15), which we observed to be noticeable for aqueous solutions at 500 MHz. Whether or not this is always a significant problem will depend on the resonance frequency and the radiofrequency coil characteristics. In summary, we have demonstrated that selective excitation and good phase behavior are not incompatible, providing a nonlinear excitation method is used. The new pulse sequence, NERO-l, is potentially useful in cases where broad or overlapping lines make the strong phase distortions associated with most previous methods undesirable. ACKNOWLEDGMENTS This research was supported by grants from the National Institutes of Health (GM-26762 (M.F.R.), GM36920-01, and RR-00995 (M.H.L.)) and from the National Science Foundation DMR-8211416 (M.H.L.). The authors thank Dr. Felix Strumwasser of the Physiology Department, Boston University Medical Center, for the sample of ELH, Dave Ruben for help in implementing the pulse sequences, and R. G. Griffin for computer time.
COMMUNICATIONS REFERENCES I. 2. 3. 4.
A. J. V. D.
G. REDFIELD, S. D. Ku~z, AND E. K. RALPH, J. Mugs. Reson. 19, 114 ( 1975). M. WRIGHT, J. FEIGON, W. LEUPIN, AND D. R. KEARNS, J. II&P. Reson. 45,5 14 ( 198 1). SKLENAR AND Z. STAR&K, J. Magn. Reson. 50,495 (1982). L. TURNER, J. Magn. Reson. 54, 146 (1983).
5. P. J. HORE, J. Magn. Reson. 54,539 (1983). 6. P. J. HORE, J. Mugn. Reson. 55,283 (1983). 7. Z. STAR&JK AND V. SKLENAR, J. Magn. Reson. 66,39 1 (1986). 8. G. A. MORRIS, K. I. SMITH, AND J. C. WATERTON, J. Mum. Reson. 68, 526 (1986). 9. J. H. C&TOW, M. MCCOY, F. SPANO, AND W. S. WARREN, Phys. Rev. Lett. 55, 1090 (1985). 10. P. PLATEAU AND M. GUBRON, J. Am. Chem. Sot. 104,731O (1982). 11. S. DAVIES, C. BAUER, P. BARKER, AND R. FREEMAN, J. Mugn. Reson. 64, 155 (1985). 12. M. H. LEVITT, Prog. NMR Spectrosc. 18,61 (1986). 13. U. HAEBERLEN AND J. S. WAUGH, Phys. Rev. 175,453 (1968). 14. A. Y.CHIUANDF. STRUMWASSER, J. Neurosci. 1,812(1981). 15. A. ABRAGAM, “Principles of Nuclear Magnetism,” Oxford Univ. Press, Oxford, 196 1.
581