spectroscopic techniques

An Intermolecular Single-Quantum Coherence Detection Schemefor High-Resolution Two-Dimensional J-resolved Spectroscopy inInhomogeneous Fields

YUQING HUANG, SHUHUI CAI, YANQIN LIN, and ZHONG CHEN*Department of Physics, Fujian Key Laboratory of Plasma and Magnetic Resonance, State Key Laboratory of Physical Chemistry of Solid

Surfaces, Xiamen University, Xiamen 361005, PR China

A new pulse sequence based on intermolecular single-quantum coherences

(iSQCs) is proposed to achieve high-resolution two-dimensional (2D) J-

resolved spectra in inhomogeneous fields via three-dimensional (3D)

acquisition. Since the iSQC evolution period and spin echo evolution

period in this sequence are intrinsically insensitive to magnetic field

inhomogeneities, high-resolution 2D J-resolved spectra can be recovered

from nuclei in inhomogeneous fields by projecting the 3D data onto the 2D

plane. Analytical expressions of the resulting signals were derived

assuming the secular dipole–dipole interaction. Analyses of a solution

sample placed in a deliberately unshimmed magnetic field and of a

biological sample with intrinsic field inhomogeneities were performed.

The results show that this sequence provides an attractive and efficient

way to eliminate the influence of field inhomogeneities on 2D J-resolved

spectra, which is potentially useful for characterizing complex chemical

materials and studying biological metabolites in inhomogeneous fields.

Index Headings: Nuclear magnetic resonance; NMR; J-resolved spectros-

copy; High resolution; Intermolecular single-quantum coherences;

Inhomogeneous fields.

INTRODUCTION

High-resolution two-dimensional (2D) nuclear magneticresonance (NMR) spectroscopy with information on chemicalshifts, J-coupling constants, and spin concentrations is anextremely powerful tool in many fields, such as chemistry,materials science, and life science.1–3 2D J-resolved spectros-copy4 is one of the first 2D NMR techniques developed. It is animportant tool for the analysis of complex chemical andbiological materials.5–9 The J-resolved pulse sequence, f(p/2)� t1/2� (p)� t1/2� t2g, allows one to achieve a 2D spectrumthat separates chemical shift and J-coupling information alongtwo different axes. The J-coupling information is distributedalong the F1 axis. A completely decoupled spectrum can beobtained when the 2D spectrum is clockwise rotated by 458 andprojected along the F2 axis.

Many modified versions have been developed to enhance theability of 2D J-resolved spectroscopy. For example, multiple-quantum J-resolved spectroscopy (MQ-JRES) has been putforward to measure multiple-quantum relaxation rates and

relative J-coupling constants.10 Spin-selective double quantumJ-resolved (SSDQ-J-resolved) and triple quantum J-resolved(SS3Q-J-resolved) have been proposed to aid the determinationof remote J couplings.11,12 An ultrafast technique can beutilized to allow acquisition of a 2D J-resolved spectrum in asingle scan.13,14 However, the quality of 2D J-resolved spectraare generally affected by magnetic field inhomogeneity. Theinhomogeneous line broadening would hamper the spectralresolution of 2D J-resolved spectra. Although spin echo in theJ-resolved pulse sequence can remove the inhomogeneous linebroadening in the F1 dimension, the influence of inhomoge-neous fields remains in the F2 dimension, which results in theloss of exact chemical shift and J-coupling information andeven overlapping of spectral peaks. Various shimmingtechniques have been developed to remove field inhomogene-ities.15,16 However, there are many circumstances in which themagnetic field homogeneities are degraded due to variations inmagnetic susceptibilities among various tissues and cellularstructures, and these inhomogeneities usually cannot becompletely eliminated by conventional shimming methods.

Intermolecular multiple-quantum coherences (iMQCs)caused by long-range dipolar interactions among spins indifferent molecules have many useful features.17–20 It has beenshown that iMQCs can be utilized to achieve high-resolutionspectra in inhomogeneous fields.21 The main advantage ofiMQC methods lies in its ability to detect identical interactionsfor different spin groups in a molecule, therefore simulta-neously retaining all desired spectral features such as chemicalshifts, scalar coupling, multiplet patterns, and relative peakareas. Several iMQC pulse sequences have been designed toachieve high-resolution 1D NMR spectra under inhomoge-neous fields based on 2D acquisition.21–26 Since the directacquisition results from conventional single-quantum coher-ence (SQC) evolution and suffers from inhomogeneousbroadening, another dimension must be examined to producea high-resolution spectrum. That means, if all the indirectdimensions are preserved, (nþ 1)D acquisition is required foran nD spectrum. Therefore, an intuitive way to apply iMQCsfor high-resolution 2D J-resolved spectra in inhomogeneousfields is 3D acquisition.27

It has been reported that the apparent diffusion rates ofintermolecular zero-quantum coherences (iZQCs) and inter-

Received 15 September 2009; accepted 9 November 2009.* Author to whom correspondence should be sent. E-mail: chenz@xmu.edu.cn.

Volume 64, Number 2, 2010 APPLIED SPECTROSCOPY 2350003-7028/10/6402-0235$2.00/0

� 2010 Society for Applied Spectroscopy

molecular double-quantum coherences (iDQCs) during theevolution time are larger than that of conventional SQCs, whilethe transverse relaxation times of iZQCs and iDQCs during theevolution time are shorter than that of SQCs.28 On the otherhand, intermolecular single-quantum coherences (iSQCs) havesimilar diffusion and relaxation behavior to the conventionalSQCs during the evolution time,29 thus providing a differentmethod for high-resolution NMR spectroscopy. In this paper, apulse sequence, iSQC-JRES, is proposed based on iSQCs toobtain high-resolution 2D J-resolved spectra in inhomogeneousfields via 3D acquisition. This sequence is a new application ofiSQCs in inhomogeneous fields. In comparison with conven-tional 2D J-resolved techniques, the fundamental requirementof the iSQC-JRES approach is that one component of thesample (e.g., the solvent) should contain a concentrated protondensity in order to create a distant dipolar field (DDF) for iSQCsignals. Solution state chemical or biological samples usuallycontain concentrated solvent, which provides the natural DDFsource for the application of the new sequence.

THEORY

The pulse sequence is shown schematically in Fig. 1. Thefirst and third RF pulses are solvent selective, while the secondRF pulse is solute selective. To select the coherence-transferpathway 0 !þ1 !þ2 !þ1 !�1, three linear coherence-selection gradients (CSGs) with an area ratio of 1:0.7:�2.4 areapplied. In this way, the desired solvent–solute iSQCs areselected and conventional SQCs and other orders of iMQCs arefiltered out. The excitation sculpting scheme30 before acquisi-tion is used as a water-suppression (WS) module to furthersuppress the residual solvent signals. Compared to the direct-detection period t3, both the indirect-detection period t1 (iSQCevolution) and t2 (spin echo evolution) are insensitive to fieldinhomogeneity. In addition, a constant-time (CT) scheme31 isutilized to achieve J decoupling during t1 period, in which theminimum value for the echo time D is �0:5tmax

1 . To achieve ahigh-resolution 2D J-resolved spectrum, the direct-acquisitiondimension (F3) is discarded and the two indirect dimensions(F1 and F2) are preserved by projecting the 3D spectrum ontothe F1–F2 plane. The projection is an accumulation projectionparallel to the F3 axis. Since the DDF has an equal effect on allsolute spins with the same spatial distribution and does notinterfere with the J coupling, the conventional 2D J-resolvedspectral information is preserved in the projection spectrum.

In the present work, the analytical expressions of the signalsresulting from the pulse sequence were derived according tothe DDF theory.32,33 Without loss of generality, a homoge-neous liquid mixture consisting of S and I components is takenas an example. S is an AX spin-1/2 system (including Sk and Sl

spins with a scalar coupling constant Jkl) and I is an isolatedspin-1/2 system. It is assumed that I (corresponding to solvent)is abundant and S (corresponding to solute) is either abundantor dilute. Assume that xm is the frequency offset of spin m (m¼I, Sk, Sl) in the rotating frame in the absence of fieldinhomogeneity. For simplification, the effects of radiationdamping, diffusion, relaxation, and intermolecular NOE areignored. The magnetic field is assumed to be only inhomoge-neous along the Z axis, and DB(z) is the field inhomogeneity atposition z. If the magnetization is fully modulated and variesonly in one direction, the dipolar field is localized and an exacttheoretical expression for the iSQC signal can be obtained. Theanalytical expression for the signals from the Sk spin is:

MþSkðt1 þ t2 þ t3; zÞ

¼ iMS0

2½eipJklðt2þt3þ2DÞ þ e�ipJklðt2þt3þ2DÞ�

X‘

m¼�‘

imJmðnÞ

3 ei½1:7ðmþ1ÞcGdzþxSkt1þmxI t1þðmþ1ÞcDBðzÞt1þxSk

t3þcDBðzÞt3�

ð1Þ

where Jm(n) is the Bessel function of integer order m; n ¼ (2/3)cl0MI

0(2D þ t2þ t3) is the argument of the Bessel function;cGdz is the dephasing angle at position z due to the first CSG,in which c is the gyromagnetic ratio, l0 is permeability of freespace, and G and d are the strength and duration of the CSG,respectively; and MS

0 and MI0 are the equilibrium magnetization

densities of S and I spins, respectively. Since the analyticalexpression of signal from the Sk spin is similar to that of signalfrom the Sl spin in an AX spin-1/2 system, only the signal fromthe Sk spin is discussed.

To evaluate the detected signals from the whole sample, anaverage of the complex magnetization over all z positions istaken. If the sample size is much larger than the dipolarcorrelation distance dc¼ p/(cGd), the spatial averaging acrossthe sample causes the terms to vanish unless mþ 1¼ 0, whichis independent of the absolute position in the sample.34 Whenm¼�1, the observable signal from the Sk spin at the detectionperiod can be expressed as

MþSkðt1 þ t2 þ t3; zÞ

¼ �MS0

2J1

2

3cl0MI

0ð2Dþ t2 þ t3Þ� �

3�

ei ðxSk�xIÞt1þpJklt2þ½xSk

þpJklþcDBðzÞ�t3f gei2pJklD

þei ðxSk�xIÞt1�pJklt2þ½xSk

�pJklþcDBðzÞ�t3f ge�i2pJklD�ð2Þ

The F3 dimension suffers from the field inhomogeneityDB(z) due to conventional SQC evolution in the t3 period(expfi[xSk

6 pJkl þ cDB(z)]t3g). However, the F1 and F2dimensions (indirect dimension) are free of the field inhomo-geneity DB(z) since the signal evolves as iSQC and spin echoduring the t1 and t2 periods, respectively. In addition, J-coupling information is eliminated in the F1 dimension due tothe CT scheme but it is preserved in the F2 dimension(exp[i(xSk

� xI)t1 6 ipJklt2]). To obtain a 2D J-resolvedspectrum free of inhomogeneous broadening, the F3 dimensionis discarded and the F1 and F2 dimensions are preserved by

FIG. 1. The iSQC-JRES sequence for high-resolution 2D J-resolved spectra ininhomogeneous fields via 3D acquisition. Full vertical bars stand fornonselective RF pulse. Gaussian pulses are selective RF pulses. Dashedrectangles represent coherence-selection gradients, ‘‘WS’’ is the spare modulefor solvent suppression.

236 Volume 64, Number 2, 2010

projecting the 3D spectrum onto the F1–F2 plane. Afterprojection, the analytical expression for the signal from the Sk

spin in the F1–F2 plane is

MþSkt1 þ t2ð Þ ¼ �p

MS0

2J1

2

3cl0MI

0ð2Dþ t2 þ t3Þ� �

3 ei½ðxSk�xIÞt1þpJklt2�ei2pJklD

�

þei½ðxSk�xIÞt1�pJklt2�e�i2pJklDg ð3Þ

where p is a factor related to the projection. Equation 3provides a quantitative description for the signal in the iSQC-JRES 2D projection spectrum. The signal in the resulting 2Dspectrum is located at (xSk

� xI, pJkl) and (xSk� xI, �pJkl),

respectively, due to J splitting. If the frequency offset of the Ispin is set to zero, i.e., xI¼ 0, the signal is located at (xSk

, pJkl)and (xSk

,�pJkl). Hence, the 2D spectrum from the iSQC-JRESsequence separates chemical shift and J-coupling informationalong the F1 and F2 dimensions, respectively, i.e., the 2Dspectrum is a J-resolved spectrum. Although in the conven-tional J-resolved spectrum, information on the chemical shiftand information on the J coupling are distributed along the F2and F1 dimensions, respectively, this difference is only relatedto the display mode. The spectral pattern of the 2D iSQC-JRESspectrum acquired in an inhomogeneous field is the same asthat of a conventional 2D J-resolved spectrum with a clockwiserotation of 458 obtained in a homogeneous field.

EXPERIMENTS

All experiments were performed at 298 K using a VarianNMR Systems 500 MHz NMR spectrometer (Varian, PaloAlto, CA), equipped with a 5 mm 1Hf15N–31Pg XYZ indirect-detection probe with 3D gradient coils. A solution of butylmethacrylate (C8H14O2) in methanol (CH3OH) was used to

demonstrate the implementation of the sequence shown in Fig.1. The molar ratio of C8H14O2 and CH3OH was 1:9.8. Tosimulate an inhomogeneous field, the magnetic field wasintentionally deshimmed by randomly altering the currents inthe shimming coils to produce broad peaks (the full width athalf-maximum (FWHM) of the broad peak at 3.41 ppm was200 Hz in absolute-valued mode). In this inhomogeneous field,the spectra were acquired using our sequence and with theconventional 2D J-resolved sequence. A conventional 2D J-resolved spectrum was also acquired under the sameacquisition conditions except that the magnetic field was wellshimmed. The conventional 2D J-resolved experiments wereperformed with 16 transients. The pulse repetition time andacquisition time were 3.0 s and 1.5 s, respectively. 80 3 9024points were acquired with spectral widths of 50 3 3000 Hz (F13 F2) in 1.6 h. For our sequence in inhomogeneous field, thesolute-selective pulse was a p/2 hard RF pulse following asolvent-selective p/2 Gaussian pulse having the opposite phase.The width of the p/2 hard RF pulses was extended to 60 ls bydeliberately detuning the probe to suppress the effect ofradiation damping during the evolution and detection periods.The width and power of the solvent-selective p/2 Gaussianpulses were 5.5 ms and 26 dB. The CSGs with strength G¼0.1T/m and duration d ¼ 1.2 ms were applied. No phase cyclingwas applied in the iSQC-JRES experiment. The WS modulewas not applied for this solution sample. The pulse repetitiontime was 1.0 s, the echo time (D) was 60 ms, and theacquisition time t3 was 50 ms. 299 3 30 3 300 points wereacquired with spectral widths of 3000 3 50 3 3000 Hz (F1 3F2 3 F3) in 2.6 h.

To test the feasibility of our sequence for enhancing thespectral resolution in samples with intrinsic macroscopicsusceptibility gradients, a sample of in vitro pig brain tissuefitted in a 5 mm NMR tube was studied. All experiments wereperformed without locking and shimming. The probe was well

FIG. 2. 2D J-resolved spectra of a solution of butyl methacrylate in methanol. (A) Conventional spectrum with a clockwise rotation of 458 in a well-shimmed fieldand its projection along the F2 axis, (B) conventional spectrum of spins in an inhomogeneous field with the FWHM of solvent peak of 200 Hz (absolute-valuedmode), (C) iSQC-JRES projection spectrum under the same inhomogeneous field and its projection along the F1 axis. The structure of butyl methacrylate is shownon the top left of the frame, together with proton labels.

APPLIED SPECTROSCOPY 237

tuned to preserve high sensitivity. The pulse repetition timewas 1.0 s and the echo time (D) was 40 ms. The CSGs withstrength G ¼ 0.1 T/m and duration d ¼ 1.2 ms were applied.The WS module was utilized to suppress the intense solventsignals further. The W3 binomial p pulse35 was used as asolvent-exclusive p pulse in the WS module, while theparameters of the gradient pulses were G1 ¼ 0.07 T/m, G2 ¼0.18 T/m, and d0 ¼ 1.0 ms. The acquisition time t2 was 30 ms.180 3 18 3 150 points were acquired with spectral widths of4500 3 80 3 4500 Hz (F1 3 F2 3 F3) in 58 min. Aconventional 2D water-presaturated J-resolved experiment wasalso performed for comparison. To confirm the results of iSQC-JRES, a 1D water-presaturated spin echo experiment of pigbrain tissue was also performed using a 1Hf15N–31Pg 4 mmPFG indirect-detection NanoProbe (VT, 500 NB). The samplewas spun along the magic angle (54.78) direction at a rate of 2kHz. For this 1D experiment, a T2-edited Carr-Purcell-Meiboom-Gill (CPMG) segment, with total echo time 360ms, was incorporated into the pulse sequence to selectively

record the signals of small metabolites in the brain tissue. Thepulse repetition time was 4.0 s and the scan number was 64.

RESULTS AND DISCUSSION

The experimental results of butyl methacrylate in methanolare presented in Figs. 2 and 3. The molecular structure of butylmethacrylate is given on the top left of Fig. 2, with the sevendifferent kinds of protons marked by ‘‘a’’ through ‘‘g’’. Theconventional 2D J-resolved spectrum of the sample in ahomogeneous magnetic field is shown in Fig. 2A. The 1Dcompletely decoupled spectrum is obtained by rotating the 2Dspectrum clockwise by 458 and then projecting onto the F2dimension. The FWHM of the peak at 4.15 ppm in theprojection spectrum is 5.5 Hz. The signals marked by ‘‘a’’through ‘‘g’’ originate from the corresponding protons of butylmethacrylate. The peak at 3.41 ppm is from protons of the CH3

group in methanol and the peak at 4.84 ppm is from the protonsof the OH group in methanol and residual water in the sample.

FIG. 3. The expanded regions and their projections of Figs. 2A and 2C. (A–D) The expanded regions and the corresponding projections for the signals in Fig. 2A;(A0–D0) for the signals in Fig. 2C.

238 Volume 64, Number 2, 2010

All the J-coupling information can be obtained from the F1dimension. The 2D J-resolved spectrum obtained in theinhomogeneous field using the conventional method is shownin Fig. 2B. The high-resolution information is lost. The signalsstretch along the F2 axis because, during t2, the system issubject to inhomogeneous broadening. The chemical informa-tion can hardly be obtained from the J-decoupled spectrumprojected along the F2 dimension. Although the inhomoge-neous broadening in the F1 dimension can be refocused by thespin echo, the overlap of neighboring signals makes it difficultto obtain exact J-coupling information from the F1 dimension.

The iSQC-JRES spectrum was acquired in the sameinhomogeneous field. The projection of the 3D iSQC-JRESspectrum onto the F1–F2 plane is presented in Fig. 2C.Compared to the conventional J-resolved spectrum in Fig. 2B,the influence of field inhomogeneity is eliminated in the iSQC-JRES projection spectrum (Fig. 2C). The FWHM of the peak at3.41 ppm in the J-decoupled projection spectrum is reducedfrom 200 to 7.5 Hz. Clearly, all the spectral informationprovided in this spectrum is the same as that in theconventional high-resolution J-resolved spectrum (Fig. 2A).The chemical shift information is along the F2 dimension andthe J-coupling information is along the F1 dimension in theiSQC-JRES projection spectrum, in agreement with thetheoretical analysis.

To show the ability of the iSQC-JRES sequence in removingthe influence of field inhomogeneity, the regions remarked byb, c, e and f in Figs. 2A and 2C are expanded and shown in Fig.3. Figures 3A through 3D show the expanded regions andcorresponding projections for the conventional J-resolvedspectrum in a homogeneous field (Fig. 2A) and Figs. 3A 0

through 3D0 for the iSQC-JRES projection spectrum in aninhomogeneous field (Fig. 2C). Except for the line width, allthe information provided in Figs. 3A 0 through 3D 0 is similar tothat in Figs. 3A through 3D. The FWHMs of peaks in the

projection spectra of Figs. 3A0 through 3D0 are larger thanthose of Figs. 3A through 3D. Taking Figs. 3B and 3B0 forcomparison, the FWHM of the peak in the J-couplingprojection spectrum of Fig. 3B is 2.1 Hz, whereas thecorresponding one in Fig. 3B0 is 4.1 Hz. On the other hand,the FWHM of the peak in the J-decoupling projection spectrumof Fig. 3B is 5.5 Hz, whereas the corresponding one in Fig. 3B0

is 7.5 Hz. The larger line width in the iSQC-JRES projectionspectrum is mainly due to the residual field inhomogeneitywithin the dipolar correlation distance, which cannot becompletely eliminated by the present iSQC detection scheme.Since the solvent signal should be selected solely for the DDF,the ability of the iSQC-JRES sequence in removing fieldinhomogeneities is mainly limited by the separation betweenthe solvent peak and the nearest solute peak. For this sample,when the magnetic field was deliberately unshimmed toproduce a field inhomogeneity of more than 500 Hz, it isimpossible for the solvent-selective pulse to excite the solventspins solely; thus, a high-resolution J-resolved spectrum cannot be obtained. In previous studies, accurate measurement ofJ-coupling constants was achieved through apparently magni-fying J-coupling constants,25,36 which would deteriorate theoverlap of spectral peaks. In this study, this issue is overcomethrough separating chemical shift and J coupling onto differentaxes.

The experimental results of the sample of in vitro pig braintissue fitted in a 5 mm NMR tube are shown in Fig. 4. TheFWHM of the water resonance at 4.81 ppm is 60.3 Hz in theconventional 1D 1H NMR spectrum (Fig. 4A). Hardly anyspectral information can be obtained from this spectrum due tothe intense water signal and line broadening caused bymagnetic susceptibility gradients among various structuralcomponents. The 1D water-presaturated MAS spin echospectrum acquired using the PFG indirect-detection NanoProbeis shown in Fig. 4B. The metabolites in the pig brain tissue

FIG. 4. NMR spectra of pig brain tissues. (A) Conventional 1D SQC spectrum and the expanded regions for the metabolites, (B) 1D water-presaturated MAS spinecho spectrum acquired with the PFG indirect-detection NanoProbe, (C) conventional 2D water-presaturated J-resolved spectrum after a clockwise rotation of 458and its projection along the F2 axis, and (D) iSQC-JRES projection spectrum and its projection along the F1 axis.

APPLIED SPECTROSCOPY 239

were assigned according to the literature.37 The conventional2D water-presaturated J-resolved spectrum after a clockwiserotation of 458 and its J-decoupling spectrum along the F2dimension are shown in Fig. 4C. Since the spectral resolution islimited by the intrinsic macroscopic susceptibility gradients, itis difficult to obtain spectral information from this spectrum.The 2D projection spectrum acquired from the iSQC-JRESsequence is presented in Fig. 4D. The metabolites in the tissueare also assigned according to the literature.37 The mainmetabolites detected in the MAS spin echo spectrum (Fig. 4B)can be observed in the iSQC-JRES spectrum (Fig. 4D).Compared to Fig. 4C, the J-decoupling projection spectrum ofFig. 4D along the F1 dimension has a much higher resolution.Most J-coupling information on metabolites such as lactate(Lac, 1.31 ppm), alanine (Ala, 1.47 ppm), and glutamate (Glx,3.75 ppm) can be obtained. Spectral resolution enhancementand solvent suppression in this measurement of pig brain tissuesuggest potential applications of our sequence in in vivostudies.38,39 However, the FWHMs of the peaks in theprojection spectrum are still larger (e.g., the FWHM of thepeak at 1.31 ppm is 18 Hz) due to the intrinsically shortrelaxation times of the metabolites, which may hinder thedifferentiation of some peaks.

CONCLUSION

A new pulse sequence, iSQC-JRES, has been designed toobtain high-resolution 2D J-resolved spectra in inhomogeneousfields via 3D acquisition. The field inhomogeneity may becaused by the external magnetic field or by intrinsicmacroscopic susceptibility gradients in the sample. The DDFtreatment was used to derive an analytical expression for theresulting signals. Our theoretical expression and experimentalobservations show that a high-resolution 2D J-resolvedspectrum can be recovered from samples in inhomogeneousfields after the 3D iSQC-JRES spectrum is projected onto theF1–F2 plane, in which the spectral information are the same asa conventional 2D J-resolved spectrum obtained in well-shimmed fields. In addition, the new sequence is insensitive tothe imperfections of the RF pulse flip angles. This sequencemay provide an attractive way to characterize complexchemical materials and study biological metabolites ininhomogeneous fields. Improvement of the acquisition effi-ciency of the pulse sequence may be achieved by combinationwith certain fast strategies for multidimensional data, such asfold-over correction27,40 and the ultrafast single-scan NMRtechnique.41

ACKNOWLEDGMENTS

This work was partially supported by the NNSF of China under Grants10774125 and 10875101, and the Key Project of Chinese Ministry ofEducation under Grant 109092.

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