Hadamard-encoded localized high-resolution NMR spectroscopy via intermolecular double-quantum coherences

Chemical Physics Letters 622 (2015) 63–68

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Hadamard-encoded localized high-resolution NMR spectroscopy via intermolecular double-quantum coherences Hanping Ke, Honghao Cai, Yanqin Lin ∗ , Liangjie Lin, Shuhui Cai ∗ , Zhong Chen Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen 361005, China

a r t i c l e

i n f o

Article history: Received 5 December 2014 In final form 13 January 2015 Available online 17 January 2015

a b s t r a c t A scheme based on Hadamard encoding and intermolecular double-quantum coherences is designed to obtain localized one-dimensional high-resolution NMR spectra in inhomogeneous fields. Brief theoretical derivation was performed to illuminate its principle. Experiments were carried out on phantom solution and biological tissues to verify its effectiveness in yielding useful spectral information and efficiency in suppressing solvent signal even when the field inhomogeneity is sufficiently severe to erase almost all spectral information. This sequence may provide a promising way for analyzing heterogeneous biological tissues and chemical systems. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Localized magnetic resonance spectroscopy (MRS) is a nondestructive experimental technique [1–3] that can detect the signals from a portion of the sample with the aid of threedimensional (3D) gradients. Its application ranges from chemistry, materials science to life science [4–7]. Most applications rely on homogeneous magnetic fields with spatial variations below 10−9 . However, there are many circumstances where magnetic field homogeneity is degraded because of external field inhomogeneity or internal sample heterogeneity, such as heterogeneous biological tissues. Spectral line broadening due to inhomogeneous fields causes loss of fine spectral features or severe peak overlap, hindering the interpretation of NMR spectra. A number of techniques have been proposed to acquire high-resolution NMR spectra under conditions where shimming technique [8,9] cannot perfectly remove magnetic field inhomogeneity. The spin-echo module can refocus the dephasing induced by the inhomogeneous B0 field, demonstrating scalar coupling information but eliminating chemical shift information [10]. It is known that the evolution of intramolecular zero-quantum coherence (ZQC) is insensitive to magnetic field inhomogeneity [11,12]. However, the ZQC method only provides information of chemical shift differences among scalar-coupled resonances. The influence of the field inhomogeneity accumulates with the sample size. The long-range dipolar interactions typically range

∗ Corresponding authors. E-mail addresses: [email protected] (Y. Lin), [email protected] (S. Cai). http://dx.doi.org/10.1016/j.cplett.2015.01.025 0009-2614/© 2015 Elsevier B.V. All rights reserved.

from 5 to 500 ␮m, far smaller than the sample size along any dimension. Therefore, the intermolecular multiple-quantum coherences (iMQCs) have been utilized to retrieve high-resolution NMR spectral information under inhomogeneous fields [13–15]. Warren and co-workers proposed some sequences based on intermolecular zero-quantum coherences (iZQC), including HOMOGENIZED (HOMOGeneity Enhancement by Intermolecular ZEro-quantum Detection) [16], composite CPMG-HOMOGENIZED [17], and fast iZQC two-dimensional (2D) spectroscopy [18]. Chen et al. proposed intermolecular Double-Quantum Filter (iDQF)-HOMOGENIZED [19] based on iZQCs, IDEAL (Intermolecular Dipolar-interaction Enhanced All Lines) (also referred to as IDEAL-I) [20] and IDEAL-II [21] based on intermolecular double-quantum coherences (iDQC), and IDEAL-III based on intermolecular single-quantum coherences (iSQC) [13]. However, these methods share the same principle of exhibiting n-dimensional high-resolution information via (n + 1)dimensional acquisitions. The spectral resolution in the additional dimension is strictly requested and the time cost is increased by orders of magnitude. Meanwhile, the long evolution time in the indirect dimension will introduce transversal relaxation decay of the signal, especially in disposal of systems with short transversal relaxation time. The Hadamard encoding technique proposed by Kupce and coworkers has already been utilized to accelerate multidimensional NMR experiments without penalty in sensitivity per unit time [22–26]. Recently, the Hadamard encoding technique was integrated with iMQCs to offer 1D high-resolution NMR spectra in inhomogeneous magnetic fields [27,28]. The idea is to excite the solvent peak with soft polychromatic pulse encoded by reference to an N-order Hadamard matrix. The conventional t1 evolution

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with progressive delay is replaced by a constant duration  and the numerous repetitions are reduced to a small number N [29]. This technique greatly shortens the scan time and avoids the long evolution time in the indirect dimension. In this study, a scheme named Hadamard-encoding Localized IDEAL (HL-IDEAL) was proposed to obtain fast localized 1D high-resolution spectra in moderate inhomogeneous fields by integrating iDQC technique, Hadamard encoding technique and localization technique. Experiments on phantom solutions and biological tissues were carried out to demonstrate the feasibility and effectiveness of the proposed scheme.

2. Theory Point-resolved spectroscopy (PRESS) is the preferred method for localized 1D spectroscopic acquisition. It has been adopted to localize the iDQC signal on a 3 T whole-body scanner [32]. In this study, the PRESS localization module was adapted to be comprised of three 180◦ selective pulses in unison with slice selection gradient and flanked by a pair of spoiling gradients. The IDEAL sequence was updated with this module to construct localized IDEAL sequence. To implement the Hadamard encoding, we made two adjustments to the localized IDEAL sequence. Firstly, at the very beginning of the sequence, a 180◦ soft polychromatic pulse was used to selectively excite different segments of the solvent resonance by reference to an N-order Hadamard matrix. Secondly, a constant duration  was used to replace original incremental delay. The solvent-suppression module composed of two WATERGATE-5 modules [30,31] was utilized narrowly prior to the acquisition period instead of at the beginning of the sequence because the solvent magnetization was needed to produce the dipolar field. Since the theoretical deduction of the signal evolution under the IDEAL sequence was detailed in previous report [20,27], in this study, we only give a brief interpretation. Without loss of generality, a two-component sample with spin species S and I is considered. S is an AX spin-1/2 system (including Sk and Sl spins with a scalar coupling constant Jkl ) and I is a single spin-1/2 system. It is assumed that I (corresponding to solvent) is abundant and S (corresponding to solutes) is either abundant or dilute. In the following, the distant-dipolar field (DDF) treatment combined with product operator formalism is employed for theoretical deduction. For simplification, the effects of radiation damping, diffusion, relaxation, and intermolecular nuclear Overhauser effects are ignored [33]. The line width of the solvent peak will increase with the field inhomogeneity and can be divided into N segments (N is the order

I =

4  j=1

S =

4 

−

Figure 1. Schematic diagram of Hadamard-encoding Localized IDEAL (HL-IDEAL) sequence. The module, composed of three sinc-shaped pulses in unison with slice selection gradient and flanked by a pair of spoiling gradients, is for volume localization. The first RF pulse is a soft polychromatic 180◦ pulse, and the Gaussian pulse is a 90◦ pulse selectively exciting the solvent spins. The dash rectangles represent coherence selection gradients. The rectangle labeled ‘WS’ represents two W5 water suppression modules [30,31].

Figure 2. Encoding diagram of 4-order Hadamard matrix.

For example, an encoding diagram (N = 4) is shown in Figure 2. The solvent peak is divided into four segments, and the four center frequencies are ωI1 , ωI2 , ωI3 and ωI4 , respectively. These frequencies are encoded according to every row of the Hadamard matrix, and four soft polychromatic pulses can be produced correspondingly for four scans. The linear sign operator Pj (j = 1–4), which is ‘+’ or ‘−’ in every row of Hadamard matrix represents the effect of Hadamard encoding. The ‘+’ represents that the magnetization remains unchanged, while ‘−’ represents that the magnetization is reversed in the corresponding frequency offset band of solvent spin. In the acquisition period, the reduced density operators for all the spins in the four segments can be deduced to be

2 J2 (Pj 1 )ei(ωIj +Bj )t2 e−2i(ωIj +Bj ) 1 (1)

1 − (ei2Jkl  ei(ωS +Bj +Jkl )t2 e−i(ωS −Jkl ) + e−i2Jkl  ei(ωS +Bj −Jkl )t2 e−i(ωS +Jkl ) )Pj J1 (5 )e−i(ωIj +2Bj ) 2

j=1

of the Hadamard matrix). The center frequencies of these segments are encoded according to the Hadamard matrix to generate a soft polychromatic pulse [26]. After N scans, the corresponding N composite responses are decoded by reference to the same Hadamard matrix. By encoding the sign of the DDF from the solvent spins inside different frequency offset band, we encode the iDQC signals accordingly. After Hadamard decoded, the iDQC signals suffering from different inhomogeneous fields will be separated. As the field inside each frequency offset band of solvent spins is relatively homogeneous, solute signals with high resolution can be achieved with the aid of iDQCs (Figure 1).

where S represents Sk or Sl , which are similar to each other in an AX spin-1/2 system.  I and  S are reduced density operators for I and S spins. Bj is the frequency offset band of the j-th component in the polychromatic pulse. Jn ( j ) is the Bessel function with integer order n,  1 =  3 = − (2/3 d )(2 + ) and  5 = (2/3 d )( − 2) −1

are arguments for the Bessel functions. d = ( 0 M0I ) is the dipolar demagnetizing time of the I spin, in which 0 is the vacuum magnetic permeability,  is the gyromagnetic ratio, and M0I is the equilibrium magnetization per unit volume. The integer-order Bessel function has the following property: Jn (− ) = (− 1)n Jn (). It indicates that J2 (− ) = J2 (), and thus no matter how Pj changes, Scan1 = Scan2 = Scan3 = Scan4 for solvent signal. The recovery of the

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individual signals involves the combination of the four scan results according to the appropriate columns of the Hadamard matrix. For example, Scan1 − Scan2 + Scan3 − Scan4 gives four times of the signals produced due to the DDF of ωI3 in segment 3, and other signals, including the solvent signal, are canceled. The ‘all plus’ column in the matrix is not used, because it is more sensitive to scanner imperfection than other columns with equal numbers of plus and minus signs. Four 1D high-resolution spectra can be obtained after Hadamard decoding and the solvent signal will be entirely eliminated. The signal peak shifts with a certain frequency offset as a result of different solvent excitation frequency in each different decoded spectrum. These different decoded spectra are aligned and summed to enhance the signal-to-noise ratio (SNR). The decoded results can be expressed as follows:

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1.8, 7.5, 1.0, and 5.0 mM, respectively. In the inhomogeneous field with a line width of 150 Hz, spectral data were acquired with the PRESS and HL-IDEAL methods. For comparison, the PRESS was also performed under a well-shimmed magnetic field. The duration of ␲/2 RF pulse was 11.5 ␮s, with a RF power of 17 W. The voxel size was 4 mm × 4 mm × 16 mm. The other parameters were:  = 5.5 ms,

= 50 ms, TR = 4.0 s, and nt = 16. The width of the selective ␲/2 Gaussian pulse for solvent spins was 9.8 ms. The parameters for the CSGs were G = 0.1 T/m and ı = 1.2 ms. The acquisition lasted 0.15 s and the total experimental time was about 17 min. A sample of intact pig brain tissue and cucumber was used to demonstrate the performance of HL-IDEAL for biological tissues with intense water and intrinsic macroscopic susceptibility gradients. All experiments were performed without field locking

P

S 1 = −2J1 (5 )(ei2Jkl  ei(ωS +B1 +Jkl )t2 e−i(ωS −Jkl ) + e−i2Jkl  ei(ωS +B1 −Jkl )t2 e−i(ωS +Jkl ) )e−i(ωI1 +2B1 ) P

S 2 = −2J1 (5 )(ei2Jkl  ei(ωS +B2 +Jkl )t2 e−i(ωS −Jkl ) + e−i2Jkl  ei(ωS +B2 −Jkl )t2 e−i(ωS +Jkl ) )e−i(ωI2 +2B2 ) P

S 3 = −2J1 (5 )(ei2Jkl  ei(ωS +B3 +Jkl )t2 e−i(ωS −Jkl ) + e−i2Jkl  ei(ωS +B3 −Jkl )t2 e−i(ωS +Jkl ) )e−i(ωI3 +2B3 )

(2)

P

S 4 = −2J1 (5 )(ei2Jkl  ei(ωS +B4 +Jkl )t2 e−i(ωS −Jkl ) + e−i2Jkl  ei(ωS +B4 −Jkl )t2 e−i(ωS +Jkl ) )e−i(ωI4 +2B4 ) From the expression, the best possible spectral line width equals to the excitation frequency interval of adjacent segments. The spectral resolution may be insufficient to exhibit fine scalar-coupling splitting. 3. Materials and methods All experiments were performed at 298 K using a 500 MHz NMR System (Agilent Technologies, Santa Clara, CA, USA), equipped with a 1.6 cm indirect detection probe with 3D gradient coils. The spectral widths were 10 ppm for all experiments. For the PRESS experiments, the repetition time (TR) was 4.0 s and the average number was 32. The water signal was suppressed by the method of variable power and optimized relaxation delays (VAPOR). For all HL-IDEAL experiments, a 16-order Hadamard encoding was implemented and a four-step phase cycling was utilized; the phases for the first selective 90◦ RF pulse and the receiver were (x, y, −x, −y) and (x, x, −x, −x); the polychromatic pulse duration was 200 ms with an excitation frequency interval of 20 Hz. To investigate the localization property of the HL-IDEAL sequence, a sample containing two NMR tubes of different diameters was tested under an inhomogeneous field (150 Hz line width) generated by intentionally de-shimming the X1, Y1 and Z1 shimming coils. The inner tube contained a 1 M threonine aqueous solution and the outer one contained a 1 M ␥-aminobutyric acid (GABA) aqueous solution. One voxel of 1 mm × 1 mm × 8 mm was positioned in the inner tube marked by I, another of 4 mm × 4 mm × 9 mm was positioned in the outer tube marked by II. A voxel of 4 mm × 4 mm × 16 mm was used to localize the whole sample. The duration of ␲/2 RF pulse was 10.8 ␮s, with a RF power of 17 W. It should be noted that the entire excitation range covered the range of the solvent peak. A fixed delay  = 4 ms was used after the polychromatic pulse. The width of the selective ␲/2 Gaussian pulse for solvent spins was 10.1 ms. The parameters for the coherence selection gradients (CSGs) were G = 0.1 T/m and ı = 1.2 ms. The number of transient (denoted as nt) was 4. The other parameters were: TR = 4.0 s and = 32.5 ms. The acquisition lasted 0.1 s and the total experimental time was about 4.8 min. A brain phantom was used to testify the feasibility of the pulse sequence for complicated spin systems with low concentrations. The concentrations of creatine hydrate, N-acetyl-dl-aspartic acid, phosphocreatine sodium salt, choline chloride, l-glutamine, l-glutamic acid, glutathione, ␥-aminobutyric acid, myo-inositol, taurine and Lac in this phantom were 10.0, 12.5, 4, 3, 1.5, 12.5, 1.25,

and shimming. The probe was well tuned to preserve high sensitivity. The duration of ␲/2 RF pulse was 11.1 ␮s, with a RF power of 17 W. The width of the selective ␲/2 Gaussian pulse for solvent spins was 9.7 ms. The parameters for CSGs were G = 0.1 T/m and ı = 1.2 ms. The localized regions of the pig brain tissue and the cucumber were marked by I and II, respectively. The voxels in the pig brain tissue and the cumber were both 4 mm × 4 mm × 5 mm. The experiments on voxels I and II shared a same nt of 64 with the total experimental duration of about 1 h. Another voxel of 4 mm × 4 mm × 16 mm was used to localize the whole stratified sample. The corresponding nt equals to 32 and the total experimental time was about 34 min. The other parameters were:  = 4 ms,

= 33 ms, and TR = 4 s with the acquisition lasting 0.10 s.

4. Results and discussion Figure 3 shows the results of the two-compartment phantom experiments aiming at demonstrating the localization effect of the HL-IDEAL in inhomogeneous fields. Figure 3d shows the signal of GABA only, and Figure 3e shows the signal of threonine only, indicating that the HL-IDEAL has excellent localization capability. Solvent signals are completely suppressed in Figure 3d–f, consistent with the theoretical prediction. From rough comparison between the spectra of Figure 3c and f, it can be found that the HL-IDEAL spectrum exhibits higher resolution. The experimental results of the brain phantom are shown in Figure 4. The average line width of conventional PRESS spectrum (Figure 4a) is 3.0 Hz under the homogeneous field. Little useful spectral information is available from Figure 4b. The spectral line width is reduced from 150 Hz to 20.5 Hz (Figure 4c) with the utilization of HL-IDEAL. The resolution of 20.5 Hz is very close to the excitation frequency interval (20 Hz), in good agreement with the theoretical predication. The HL-IDEAL spectrum (Figure 4c) acquired in the inhomogeneous field shows good consistency with the PRESS spectrum under the homogeneous field (Figure 4a). This suggests that the HL-IDEAL can serve as a complement to the PRESS method under inhomogeneous fields. According to the theoretical analysis, the solvent signal can be completely removed due to the use of Hadamard technique, together with two WATERGATE-5 modules. However, as shown in Figure 4c, residual solvent peak exists. The residual may result from imperfect experimental conditions, such as inaccurate flip angle of the sinc-shaped ␲ RF pulses, which lead to residual single-quantum coherence (SQC) signals. Since the

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Figure 3. 1 H NMR spectra of GABA and threonine solution acquired in an inhomogeneous field with a line width of 150 Hz. (a) Molecular structure of GABA; (b) molecular structure of threonine; (c) PRESS spectrum acquired from voxel III; (d) HL-IDEAL spectrum acquired from voxel I, together with spin echo image of the sample; (e) HL-IDEAL spectrum acquired from voxel II; (f) HL-IDEAL spectrum acquired from voxel III.

Figure 4. 1 H NMR spectra of brain phantom. (a) 1D PRESS spectrum under a well-shimmed field; (b) 1D PRESS spectrum under the inhomogeneous field; (c) 1D HL-IDEAL spectrum obtained under the same inhomogeneous field. The full names of the abbreviations are listed in the right side.

solvent concentration is much larger than the solute concentration in this sample, the residual solvent SQC signal is obvious and the residual solute SQC signals are negligible. Moreover, the SQC signal is much stronger than the iDQC signals, so the solvent SQC signal is still detected. The experimental results of HL-IDEAL on biological tissues are presented in Figure 5. Little spectral information can be obtained with the PRESS method due to the presence of intense water signal and line broadening caused by magnetic susceptibility

gradients among various structural components (Figure 5d–f). In Figure 5a–c, the water signal is effectively suppressed and the weak metabolite signals are observable. The spectral resolution is improved from 165.0 to 25.0 Hz by the HL-IDEAL. The resolution of the biological tissues spectra is not as good as that in the brain phantom experiment due to the short relaxation times of metabolites in tissues. As in the brain phantom experiment, residual solvent peak exists. The metabolites were assigned according to literature [34].

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Figure 5. 1 H NMR spectra of a sample packed with pig brain tissue and cucumber acquired in a magnetic field without shimming. (a–c) 1D HL-IDEAL spectra acquired from voxels III, I and II, respectively; (d–f) 1D PRESS spectra acquired from voxels III, I and II, respectively. Spin echo image of the sample is shown on the top right panel.

Due to the employment of IDEAL technique, the prerequisite to implement HL-IDEAL is that the broad solvent peak should not overlap with solute peaks. The maximum allowed field inhomogeneity is related to the chemical shift difference between the solvent peak and its nearest solute peak. Therefore, the HL-IDEAL is more proper for disposing systems under small or moderate magnetic field inhomogeneity. Regarding the HL-IDEAL, the achievable best spectral resolution depends on the excitation bandwidth of the individual selective encoding pulses. The duration of the polychromatic pulse can be extended to reduce the excitation frequency interval, thus improving the resolution. However, extending the pulse duration may introduce larger T1 modulation and may impose extra influences on systems with spins having great difference in longitudinal relaxation times. In addition, with the reduction of the excitation frequency interval, the order of Hadamard matrix should be increased, thus the experimental time will increase. On the other hand, the methods, e.g. the dynamic

nuclear polarization technique [31,32], focusing on improving the sensitivity of NMR experiments may be helpful in promoting the application of HL-IDEAL. 5. Conclusion In this work, the IDEAL pulse sequence was developed to HL-IDEAL based on the Hadamard encoding technique and the localization technique. It can be executed to obtain high-resolution localized 1D NMR spectra under inhomogeneous fields. Experiments were carried out to verify its practical feasibility and performance. The experimental results prove the ability of HLIDEAL in recovering high-resolution spectral information under inhomogeneous fields and effectively suppressing the solvent peak. The results are in good agreement with theoretical predictions. This sequence may be useful for in vivo and in situ high-resolution magnetic resonance spectroscopy.

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Acknowledgments This work was supported by the NNSF of China under Grants 11474236, U1232212 and 11105114, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 20130121110014. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

R.A. de Graaf, D.L. Rothman, K.L. Behar, J. Magn. Reson. 187 (2007) 320. Z. Wu, S. Ding, Solid State Nucl. Magn. Reson. 35 (2009) 214. G. Di Pietro, M. Palombo, S. Capuani, Appl. Magn. Reson. 45 (2014) 771. K.-H. Chiu, S. Ding, Y.-W. Chen, C.-H. Lee, H.-K. Mok, Fish Physiol. Biochem. 37 (2011) 701. S. Capuani, E. Piccirilli, G. Di Pietro, M. Celi, U. Tarantino, Aging Clin. Exp. Res. 25 (2013) S51. Z.L. Wei, L.J. Lin, Y.Q. Lin, S.H. Cai, Z. Chen, Chem. Phys. Lett. 581 (2013) 96. P. Porcari, S. Capuani, R. Campanella, A. La Bella, L.M. Migneco, B. Maraviglia, Phys. Med. Biol. 51 (2006) 3141. K.M. Koch, L.I. Sacolick, T.W. Nixon, S. McIntyre, D.L. Rothman, R.A. de Graaf, Magn. Reson. Med. 57 (2007) 587. K.M. Koch, S. McIntyre, T.W. Nixon, D.L. Rothman, R.A. De Graaf, J. Magn. Reson. 180 (2006) 286. M.D. Hurlimann, J. Magn. Reson. 184 (2007) 114. H.-P. Ke, H. Chen, Y.-Q. Lin, Z.-L. Wei, S.-H. Cai, Z.-Y. Zhang, Z. Chen, Chin. Phys. B 23 (2014) 063201. R.A. de Graaf, D.W.J. Klomp, P.R. Luijten, V.O. Boer, Magn. Reson. Med. 71 (2014) 451.

[13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34]

Y. Huang, S. Cai, X. Chen, Z. Chen, J. Magn. Reson. 203 (2010) 100. Y. Huang, X. Chen, S. Cai, C. Cai, Z. Chen, J. Chem. Phys. 132 (2010) 134507. B. Jiang, H. Liu, M. Liu, C. Ye, X.A. Mao, J. Chem. Phys. 126 (2007) 054502. S. Vathyam, S. Lee, W.S. Warren, Science 272 (1996) 92. Y.Y. Lin, S. Ahn, N. Murali, W. Brey, C.R. Bowers, W.S. Warren, Phys. Rev. Lett. 85 (2000) 3732. G. Galiana, R.T. Branca, W.S. Warren, J. Am. Chem. Soc. 127 (2005) 17574. X. Chen, M.J. Lin, Z. Chen, S.H. Cai, J.H. Zhong, Phys. Chem. Chem. Phys. 9 (2007) 6231. Z. Chen, Z.W. Chen, J.H. Zhong, J. Am. Chem. Soc. 126 (2004) 446. Z. Chen, S.H. Cai, Z.W. Chen, J.H. Zhong, J. Chem. Phys. 130 (2009) 084504. A. Tal, B. Shapira, L. Frydman, Angew. Chem. Int. Ed. 48 (2009) 2732. E. Kupce, R. Freeman, J. Magn. Reson. 206 (2010) 147. E.A. Mellon, et al., Magn. Reson. Med. 62 (2009) 1404. L. Fleysher, R. Fleysher, S.T. Liu, O. Gonen, Magn. Reson. Med. 60 (2008) 524. E. Kupce, T. Nishida, R. Freeman, Prog. Nucl. Magn. Reson. Spectrosc. 42 (2003) 95. Y. Chen, S. Cai, C. Cai, X. Cui, Z. Chen, NMR Biomed. 25 (2012) 1088. Z. Zhang, S. Cai, K. Wang, H. Chen, Y. Chen, Z. Chen, Chem. Phys. Lett. 582 (2013) 148. E. Kupce, R. Freeman, J. Magn. Reson. 162 (2003) 158. M.L. Liu, X.A. Mao, C.H. Ye, H. Huang, J.K. Nicholson, J.C. Lindon, J. Magn. Reson. 132 (1998) 125. G. Zheng, W.S. Price, Prog. Nucl. Magn. Reson. Spectrosc. 56 (2010) 267. Y. Lin, T. Gu, Z. Chen, S. Kennedy, M. Jacob, J. Zhong, Magn. Reson. Med. 63 (2010) 303. S. Lee, W. Richter, S. Vathyam, W.S. Warren, J. Chem. Phys. 105 (1996) 874. V. Govindaraju, K. Young, A.A. Maudsley, NMR Biomed. 13 (2000) 129.