Acquisition strategy to obtain quantitative diffusion NMR data

Journal of Magnetic Resonance 216 (2012) 201–208

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Communication

Acquisition strategy to obtain quantitative diffusion NMR data Caroline Barrère, Pierre Thureau, André Thévand, Stéphane Viel ⇑ Aix-Marseille Univ & CNRS, UMR 7273: Institut de Chimie Radicalaire, Spectrométries Appliquées à la Chimie Structurale, F-13397 Marseille, France

a r t i c l e

i n f o

Article history: Received 9 December 2011 Available online 8 January 2012 Keywords: PGSE Quantitative data qDECRA Relaxation times Mixture analyzis

a b s t r a c t Pulsed Gradient Spin Echo (PGSE) diffusion NMR experiments constitute a powerful tool for analyzing complex mixtures because they can in principle separate the NMR spectra of each mixture component. However, because these experiments intrinsically rely on spin echoes, they are traditionally regarded as non-quantitative, due to the signal attenuation caused by longitudinal (T1) and transverse (T2) nuclear magnetic relaxation during the rather long delays of the pulse sequence. Alternatively to the quantitative Direct Exponential Curve Resolution Algorithm (qDECRA) approach proposed by Antalek (J. Am. Chem. Soc. 128 (2006) 8402–8403), this work presents an acquisition strategy that renormalizes this relaxation attenuation using estimates of the T1 and T2 relaxation times for all the nuclei in the mixture, as obtained directly with the pulse sequence used to record the PGSE experiment. More specifically, it is shown that only three distinct PGSE experiments need to be recorded, each with a specific set of acquisition parameters. For small- and medium-sized molecules, only T1 is required for obtaining accurate quantification. For larger molecular weight species, which typically exhibit short T2 values, estimates of T2 must also be included but only a rough estimation is required. This appears fortunate because these data are especially hard to obtain with good accuracy when analyzing homonuclear scalar-coupled systems. Overall, the proposed methodology is shown to yield a quantification accuracy of ±5%, both in the absence and in the presence of spectral overlap, giving rise – at least, in our hands – to results that superseded those achieved by qDECRA, while requiring substantially less experimental time. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Pulsed Gradient Spin Echo (PGSE) [1] and, more recently, Diffusion Ordered SpectroscopY (DOSY) [2], currently constitute major tools for characterizing the structure and dynamics of complex mixtures [3,4]. Combined with proper data processing schemes, these experiments allow the NMR spectra of the compounds of a mixture to be extracted, at least in favorable cases [5]. Indeed, spectral overlapping seriously complicates the analyzis, which may fail yielding the correct NMR spectra. While this probably remains the most challenging limitation of the technique, many solutions have already been proposed to reduce its impact by playing upon either the acquisition or processing of the data [6–18]. Enhanced resolution can also be achieved by adding to the investigated solution a component (e.g. complexing agent [19], stationary phase [20]), which interacts specifically with some of the compounds of the mixture, hereby leading to significant differences in diffusion coefficient values (and hence resolution).

⇑ Corresponding author. Address: Campus Scientifique de St. Jérôme, case 512, Av. Escadrille Normandie Niémen, 13397 Marseille cedex 20, France. Fax: +33 491 282 897. E-mail address: [email protected] (S. Viel). 1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jmr.2011.12.022

However, diffusion NMR also suffers from another severe limitation. Because it intrinsically relies on spin echoes, magnetic relaxation phenomena lead to non-quantitative results. This does not only concern the nuclei of different molecules but also different nuclei within the same molecule, which gives rise overall to signal integrals that cannot be compared. Thus, diffusion NMR is usually regarded as a non-quantitative technique. Recently, Antalek has introduced a clever method to achieve quantitative PGSE data for mixtures of small- to medium-sized molecules [21,22]. The idea is to record a series of PGSE experiments by keeping constant the ratio between the times s1 and s2 during which the magnetization in the pulse sequence appears longitudinal and transverse, respectively. Each PGSE experiment is subsequently analyzed using the Direct Exponential Curve Resolution Algorithm (DECRA) scheme [10], so as to extract the NMR spectrum of each mixture component. The relative intensity of a selected resonance in these DECRA-extracted NMR spectra is then plotted semi-logarithmically as a function of one of the previous two time variables (usually s1), and the data are linearly extrapolated to zero in order to estimate the corresponding signal intensity in the absence of magnetic relaxation. In this way, the signal intensities become comparable and quantitative data can be obtained. An implicit requirement of this procedure is obviously the successful separation of the NMR spectra of each mixture component by DECRA.

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Overall, the so-called quantitative-DECRA (or qDECRA) methodology was shown to work by recording 5 distinct PGSE experiments, hereby resulting in a 5-fold increase in experimental time without any sensitivity improvement. In other words, quantification comes at the expense of experimental time. Although it is likely that reliable results could have also been achieved using fewer PGSE experiments, this possibility was not discussed by the author. Moreover, Antalek pointed out that the artifacts arising from homonuclear scalar couplings evolution (the so-called J-modulation) during the rather long s2 values used in the data extrapolation (required to keep the s1/s2 ratio constant) hampered the analyzis. Overall, an average quantification accuracy between ±10% and ±15% was reported. Here, we propose an alternative strategy to achieve the same quantification information, by renormalizing PGSE data using estimates of the relaxation times for each NMR resonance. The idea is to obtain these estimates using the same pulse sequence as that used to record the PGSE experiment. The success of this method relies on analyzing the precision on T1 and T2 that is required to achieve a quantification accuracy that lies within a given threshold. Because signal quantification also relies on integral precision, which in turn depends on the spectrum signal-to-noise ratio (S/ N), high accuracy may intrinsically demand a high level of signal averaging and hence long experimental times. As a realistic compromise, we chose an accuracy threshold of ±5%, which supersedes the global accuracy reported in previous works [21,22]. In addition, because the present investigation focuses on the quantitative aspects of the PGSE experiment, an implicit prerequisite assumed in the subsequent part of this work is the ability of PGSE experiments to resolve the NMR spectra of the mixture components (for there would be no need in quantifying components that have not been resolved). In this context, the first part of the Results and Discussion section of this article highlights the non-quantitative aspect of diffusion NMR data, and shows that relaxation time estimates obtained using conventional NMR experiments (such as inversion recovery and CPMG) can be used to renormalize PGSE data properly. The second part shows that a specific PGSE pulse sequence can be applied not only to determine the diffusion coefficient of the various mixture components, but also to obtain accurate relaxation time estimates for all the nuclei. A third part describes the herein proposed methodology, providing experimental evidence that illustrates how it can yield reliable quantifications both in the absence and in the presence of overlapping resonances. Finally, a fourth part discusses the accuracy of the method and the impact of J-modulation. 2. Experimental section 2.1. Chemicals Three poly(ethylene glycol) (PEG) standards: PEG-43k (Mw = 42,700 g mol1; polydispersity index Ip = 1.26), PEG-10k (Mw = 10,000 g mol1; Ip = 1.12), and PEG-6k (Mw = 6550 g mol1; Ip = 1.18), as well as one poly(propylene glycol) (PPG) standard, PPG-1k (Mw = 790 g mol1; Ip = 1.03), were supplied by Polymer Standards Service (Mainz, Germany). L-Phenylalanine (Phe) Ultra (P99%) and methanol were from Sigma Aldrich (St. Louis, MO). The deuterated solvent used in NMR is D2O (P99.9%) from Eurisotop (Gif-sur-Yvette, France). 2.2. NMR model mixtures In this investigation, several model mixtures were prepared. A first model mixture (hereafter referred to as MM-1) consisted of: PEG-6k (5.1  105 mol L1), L-phenylalanine (1.0  102 mol L1)

and methanol (7.6  103 mol L1) in D2O. A second mixture (MM-2) contained PEG-43k (2.4  105 mol L1) and L-phenylalanine (3.34  102 mol L1) in D2O. A third mixture (MM-3) consisted of: phenylalanine (5 mg mL1), PPG-1k (4 mg mL1) and PEG-10k (0.7 mg mL1) in D2O. Note that, in all cases, the concentrations of the various compounds were chosen to yield NMR resonances of comparable intensity (hereby avoiding dynamic range problems). 2.3. NMR experiments All NMR experiments were performed on a BRUKER AVANCE spectrometer operating at 500 MHz for the 1H Larmor frequency, using a 5-mm triple resonance inverse cryoprobe optimized for 1 H detection and equipped with an actively shielded z-gradient coil. The gradient coil was calibrated by measuring the diffusion coefficient of the residual proton in D2O [23], and was found to be 55 G cm1. The temperature was set to 300 K and controlled with an air flow of 535 L h1 to avoid temperature fluctuations due to sample heating during the gradient pulses. The PGSE pulse sequence used in this study (Fig. 1a) was based on the BPP-LED pulse sequence described in Ref. [24]. It contained bipolar gradients and a longitudinal eddy current delay (LED) to minimize spectral artifacts resulting from eddy currents. Additional spoiler gradients were also included to reduce phase cycling. In this case, the amplitude of an NMR resonance observed at the echo is given by Eq. (1):

I¼

I0 Ts1 Ts2 DðcdgÞ2 ðDdsÞ 4 2 e 1 2e 2

ð1Þ

where I0 is the equilibrium magnetization, s1 and s2 the times during which the magnetization is longitudinal and transverse, respectively (while T1 and T2 are the respective relaxation times), c is the magnetogyric ratio of the observed nucleus, g and d are the strength and the duration of the half-sine shaped gradient pulses, respectively, D is the diffusion time (i.e. the time during which the diffusion is monitored), and s the gradient pulse recovery time. All these delays are illustrated in Fig. 1a. As can be seen from Eq. (1), the resonance intensity of the NMR spectrum obtained with this pulse sequence for a single gradient value becomes a function of several parameters, including diffusion and relaxation variables. For simplicity, such NMR spectrum will be hereafter referred to as a diffusion-filtered spectrum. In contrast, in a PGSE experiment, several gradient values are used. Usually, all delays are kept constant to avoid any complication arising from magnetic relaxation, and only the gradient strength is varied. Specifically, the gradient strength was quadratically incremented in 16 steps from 6% to 95% of its maximum value. The gradient pulse recovery time and the longitudinal eddy current delay were set to 0.1 and 25 ms, respectively. Generally, 32 scans were recorded for each gradient value. After Fourier transformation and phase correction, the baseline of the spectra was carefully adjusted. The data were analyzed with the DECRA module (version 1.10) implemented on Topspin 2.1 (BRUKER operating software). Reference values for longitudinal and transverse relaxation times were measured with the Inversion-Recovery (IR) and Carr–Purcell–Meiboom–Gill (CPMG) pulse sequences, respectively. Importantly, all NMR experiments were recorded with a relaxation delay that was about five times larger than the longest T1 in the sample. This ensured, on the one hand, that the 1H spectrum recorded with a simple pulse-acquire pulse sequence was quantitative (hereafter referred to as quantitative 1H NMR spectrum) and, on the other hand, that the signal attenuation due to relaxation in the PGSE experiment was simply related to the relaxation during the s1 and s2 time periods. This clearly requires knowledge on the longest T1 value of a given mixture, which is a typical prerequisite

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Fig. 1. Pulse sequences used in this work. (a) BPP-LED proposed by Wu et al. [24]. (b) Modified BPP-LED used in this work (see Ref. [26]), which simply consists in adding a CPMG pulse train at the beginning of the BPP-LED pulse sequence in order to allow T2 to be measured. In both pulse sequences, the time periods during which the magnetization is longitudinal (s1) and transverse (s2) are evidenced in dark and light gray, respectively.

when recording PGSE experiments. To this purpose, a rough estimation is usually sufficient and can be provided by recording a single point IR experiment (i.e. using a single delay between the inversion and excitation RF pulses), hereby avoiding the complete time-consuming IR experiment. 3. Results and discussion 3.1. Quantitative aspects of PGSE experiments First of all, in order to illustrate the non-quantitative aspect of PGSE experiments, a 1H diffusion-filtered spectrum (6% gradient strength) was recorded on sample MM-1. This model mixture was chosen because it did not show any spectral overlap and yielded diffusion coefficient values spanning the range (109– 1011 m2 s1) that is typically accessible with common NMR hardware (i.e. high-resolution NMR probe heads equipped with a gradient coil dedicated to coherence selection). The integrals are compared in Table 1 with those of the corresponding quantitative 1 H NMR spectrum (shown in Fig. 2). Table 1 also displays the reference T1 and T2 relaxation times obtained for all nuclei using the IR and CPMG pulse sequences, respectively. Data reported in Table 1 indicate that attenuation due to relaxation in PGSE experiments can be significant, leading to large differences in the relative integrals (deviations as high as 40% were observed in this case). However, renormalizing the data using the estimates of relaxation times achieved by IR and CPMG is shown to solve this problem. Second of all, the question arises as how much precision is required on the relaxation time estimates for achieving a quantification accuracy that lies within the targeted ±5% threshold. Using Eq.

Table 1 Comparison of the MM-1 signals integrals measured on the quantitative 1H spectrum (IQ) with those measured on the diffusion-filtered experiment (recorded with g = 2 G cm1, D = 400 ms and d = 3.5 ms). These latter integrals were successively renormalized by accounting for the attenuation due to diffusion only (ID), and then for the attenuation due both to diffusion and relaxation (ID,T1/T2).

a

#

IQ (a.u.)

ID (a.u.)a

Deviation (%)b

T ref 1 (s)c

T ref 2 (s)d

ID,T1/T2 (a.u.)

Deviation (%)e

1 2 3 4 5 6

0.99 1.00 2.09 2.87 0.99 5f

0.63 0.62 1.95 1.62 0.83 4.38

36.2 37.4 6.4 43.5 15.6 12.4

0.96 0.95 9.65 0.75 3.05 3.25

0.84 0.83 5.10 0.56 1.90 2.47

0.94 0.98 2.04 2.88 0.96 5f

+0.0 1.4 2.1 +0.5 2.7 +0.0

The self-diffusion coefficients (as expressed in 1010 m2 s1) were measured in separate PGSE experiments and were found to be: 0.1 (PEG), 6.5 (Phe) and 11.2 (methanol). b Relative deviation between ID and IQ. c As measured by IR. d As measured by CPMG. e Relative deviation between ID,T1/T2 and IQ. f The integral of the signals due to the aromatic protons was used to calibrate all the other integrals.

(1), the influence of T1 accuracy onto the renormalization reliability can be roughly modeled according to:

ðDI%ÞT 1 ¼

s1 T1

DT 1 %

ð2Þ

with (DI%)T1 the relative error on the signal integral due to the T1 measurement accuracy (DT1%). As expected, higher accuracy on T1 is required for large s1/T1 ratios. In addition, inspection of Eq. (1) shows that the impact of T2 relaxation will be greatest whenever s2 is maximum. On most high-resolution liquid-state NMR probe heads, the duration of a bipolar gradient pulse is limited to 2.5 ms, yielding a maximum accessible s2 value of the order of 10 ms. This implies from Eq. (1) that T2 values higher than 0.4 s will only contribute to a 2.5% signal loss at most (i.e. when s2 equals 10 ms). Therefore, depending upon the overall quantification accuracy that is needed, accounting for T2 relaxation for those 1H nuclei that exhibit T2’s higher than this cut-off value (0.4 s), could actually reveal unnecessary. Still, it might be interesting to analyze how the accuracy of the T2 estimation impacts the quantification accuracy. Similarly, Eq. (1) can again be used to express (DI%)T2, which is the relative error on the signal integral due to the T2 measurement accuracy (DT2%), such as:

ðDI%ÞT 2 ¼

s2 T2

DT 2 %

ð3Þ

The overall quantification accuracy can then be estimated by combining Eqs. (2) and (3). Typically, when using a pulse sequence based on the stimulated echo, s1 can be (much) more than one order of magnitude larger than s2, whereas T1 and T2 relaxation times for 1H nuclei in liquids of normal viscosity are roughly comparable (except for high molecular weight species). This implies that, for small- to medium-sized molecules, the accuracy of the T2 estimation will only have a negligible impact on the overall quantification accuracy with respect to that of T1. For instance, Eq. (3) shows that, even with a very large relative error on the T2 measurement (30%), it is still possible to obtain a quantification accuracy of 2.5% as long as T2 P 0.12 s. Just as an illustration, the order of magnitude for the 1H T2 values of a high molecular weight (1.8  106 g mol1) polystyrene polymer of low polydispersity is 0.10 s (for a dilute CDCl3 solution at 25 °C and 7.05 T). 3.2. Proposed quantification methodology of PGSE experiments The previous section has illustrated the quantitative aspects of PGSE experiments, showing that estimates of relaxation times could be used to properly renormalize the relaxation attenuation in PGSE data. We now need to investigate whether these estimates can be obtained using the same pulse sequence as the one used for recording the PGSE experiment, with an accuracy that matches the requirements listed in the previous section. Another model mixture was considered in this case (MM-2), containing PEG-43k and Phe in D2O, but without methanol (the slowest relaxing species),

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Fig. 2. 1H 500 MHz quantitative spectrum of sample MM-1 containing poly(ethylene glycol) (PEG-6k), phenylalanine (Phe) and methanol (MeOH) recorded at 300 K in D2O. The molecular structures of the corresponding compounds are shown in the inset, together with the NMR assignment (shown as Arabic numbers ranging from 1 to 6). No attempt was made to distinguish the various aromatic NMR signals. The exchangeable protons were not observable in this solvent. The intensity of the residual 1H signal of deuterated water (HOD) at about 4.7 ppm as well as the intensity of signals S3 and S4 have been truncated. Signals {S1, S2, S5, S6}, S3, and S4, are due to Phe, MeOH and PEG, respectively.

so as to decrease the experimental time. Several PGSE experiments with different diffusion times D – hence, different s1 values – were recorded using the BPP-LED pulse sequence, and processed with DECRA to extract the 1H NMR spectrum of each component (Fig. 3). We used DECRA for processing the PGSE experiments in order to compare our results with those reported by Antalek, but other processing schemes could have been used as well [6–8,18]. Then, for all the mixture components, the signal integrals measured on the DECRA-extracted NMR spectra were plotted on a semi-logarithmic graph as a function of s1 (Fig. 4), and the data were subsequently adjusted to yield the T1 values of each signal from the slope of the curves. Moreover, the excellent linearity evidenced in Fig. 4 suggested that T1 values could also be obtained with only 2 data points (Dmin and Dmax), in agreement with previous works [25]. Longitudinal relaxation values measured in this way are compared to reference values measured with InversionRecovery experiments in Table 2. As can be seen, a very good agreement was obtained between both methods. In parallel, T2 relaxation times can be evaluated by recording several PGSE experiments with different values of s2. In the BPPLED pulse sequence shown in Fig. 1a, this would normally require to increase the spin echo diffusion-encoding delay (namely, the gradient pulse duration and/or the gradient recovery time). However, as previously mentioned, this strategy leads to J-modulation that may potentially cause important signal distortions for homonuclear scalar-coupled spin systems, hereby reducing the quantification accuracy [22]. To tentatively reduce this difficulty, the BPPLED pulse sequence was modified by adding an initial CPMG pulse train (Fig. 1b). In this way, increasing the s2 value now implies increasing the number of CPMG cycles (nCPMG) while keeping constant the spin echo diffusion-encoding delay. A similar pulse sequence has already been used by other authors when recording PGSE experiments in order to remove broad NMR signals due to fast relaxing species [26]. We note that alternative pulse sequences could have been used as well, which use other ways of reducing Jmodulation artifacts [27]. Similarly to the T1 measurements, several PGSE experiments were recorded on sample MM-2 and processed with DECRA to extract the NMR spectra of the different mixture components. The signal integrals of all nuclei could then be measured for each experiment. Fig. 5 shows on a semi-logarithmic plot the evolution of each signal integral as a function of s2 (or, equivalently, as a function of the total number of CPMG loops). The data could then be linearly fitted and the slope of the curves yielded the corre-

Fig. 3. Series of 1H 500 MHz NMR spectra recorded on MM-2 at 300 K: (a) quantitative 1H spectrum, and (b–d) 1H spectra of each mixture component obtained by processing the PGSE experiment with DECRA, showing PEG-43k (b), Phe (c), and HOD (d).

sponding T2 values (Table 2). Despite the use of the CPMG pulse train, the decay curves observed in Fig 5 appeared strictly linear only for the PEG singlet. Decay curves associated with coupled signals showed a residual oscillation behavior, suggesting that the observed deviations in T2 measurements (up to 30%) could be due to residual J-modulation artifacts. In this case, however, low precision on the T2 values is not a major problem, because the previous section has shown that its impact on quantification accuracy could be neglected whenever T2’s were higher than 0.4 ms. Thus, T2 measurements will become a difficulty for very large molecules (with small T2 values) having coupled signals. Note that, as a first approximation and to keep the experiment as simple as possible, the 180°

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Fig. 4. Logarithm of the signal integrals of the component spectra obtained with DECRA for the MM-2 mixture plotted as a function of the diffusion time (D) for several PGSE experiments. The data points correspond to signals: S1 (j), S2 (s), S4 (), S5 ( ), and S6 (h). These signals have been defined in Fig. 2. For each signal, the signal intensities were normalized to the value measured for the shortest diffusion time value (0.1 ms). The corresponding linear fits are shown as short dashed lines (either black or gray).

Fig. 5. Logarithm of the signal integrals of the component spectra obtained with DECRA for the MM-2 mixture plotted as a function of s2 for several PGSE experiments. The data points correspond to signals: S1 (j), S2 (s), S4 (), S5 ( ), and S6 (h). These signals have been defined in Fig. 2. For each signal, the signal intensities were normalized to the value measured for the shortest s2 value (2.8 ms). The corresponding linear fits are shown as short dashed lines (either black or gray).

Table 2 Reference T1 and T2 relaxation times obtained for the MM-2 sample using traditional NMR experiments (IR and CMPG, respectively). These values are compared to those obtained with the pulse sequence reported in Fig. 1a: T1’s were measured with only two distinct PGSE experiments (recorded with D = 100 and 1100 ms) while T2’s were obtained with 2 PGSE experiments with different CPMG loops number (n = 35 and 100 with sCPMG = 0.7 ms).

3.3. Testing the methodology on an overlapped spectrum

a b c d e f

#

T ref 1 (s)a

T PGSE 1 (s)b

Deviation (%)c

T ref 2 (s)d

T PGSE 2 (s)e

Deviation (%)f

1 2 4 5 6

0.99 0.97 0.73 3.13 3.34

0.96 0.93 0.71 3.28 3.21

3.0 4.3 3.1 +4.6 3.7

0.89 0.89 0.58 2.03 3.06

0.86 0.80 0.58 1.59 2.91

3.3 10.4 1.2 21.6 +4.7

As measured by IR. As measured with the BPP-LED pulse sequence (Fig 1a). PGSE Relative difference between T ref . 1 and T 1 As measured by CPMG. As measured with the pulse sequence reported in Fig. 1b. PGSE Relative difference between T ref . 2 and T 2

RF pulses of the CPMG train were not phase cycled. Improvement can thus be anticipated once the phase cycle of the pulse sequence reported in Fig. 1b is optimized. Moreover, T1 estimates obtained with this modified pulse sequence were shown to be equivalent to those reported in Table 2, which were achieved with the BPPLED pulse sequence. At this point, it may be useful to define an intensity threshold in order to decide a priori whether or not T2 estimates should be included in the PGSE data renormalization. More specifically, considering a maximum s2 value of 10 ms (see Section 3.1) and the echo time of the CPMG pulse train chosen here (sCPMG  0.7 ms), a limiting number of 600 CPMG loops (nCPMG) was chosen. In other words, two PGSE experiments could be recorded, each one having the same diffusion time (Dmin) but distinct nCPMG values (1 and 600, respectively). If, for a given mixture component, the residual intensity of a selected NMR resonance between the two corresponding DECRA-extracted spectra appears to be larger than 12% (calculated for a T2 cut-off value of 0.4 s and a total evolution time of 0.84 s), then T2 relaxation can be neglected in the renormalization. Otherwise, the corresponding T2 estimates must be included.

The proposed methodology then consists in recording three distinct PGSE experiments (using the pulse sequence shown in Fig. 1b), each with a given set of experimental parameters, in order to extract the information (D, T1, T2) that is required to renormalize the PGSE data and obtain quantitative results. Indeed, the previous section has shown that T1 and T2 could be measured with a total of 3 distinct PGSE experiments, combining different values of diffusion times (Dmin and Dmax) and CPMG cycles (1 and 600), while keeping constant the spin echo diffusion-encoding delay (gradient pulse duration d and gradient recovery time). More specifically, these parameters are chosen such as: (Dmin; nCPMG = 1; d), (Dmax; nCPMG = 1; d) and (Dmin; nCPMG = 600; d) for the first, second and third experiments, respectively. The objective of this section is thus to test this methodology on a slightly more complex system which NMR spectrum displays signal overlap. Results are compared to the qDECRA approach, which currently represents the only available method to achieve quantification in PGSE experiments. At this point, a third model mixture was tested (MM-3), consisting of Phe, PPG-1k, and PEG-10k in D2O. The spectral region between 3.35 and 4.05 ppm shows partial signal overlapping between these three compounds. The protocol first consists in optimizing the diffusion parameters (D and d) in order to achieve a clear separation of the NMR spectra of the various components with DECRA (Fig. 6). As outlined above, a total of three PGSE experiments were recorded using the pulse sequence reported in Fig. 1b, and the integrals were measured for each signal on the 1H spectra extracted by DECRA from the PGSE experiments. These integrals were then used to estimate the T1 and T2 values of the various signals. The so-obtained data are compared in Table 3 to those obtained by IR and CPMG, respectively. Note in this case that, because of signal overlap, the reference values were obtained by analyzing a D2O solution containing only one component at a time, at the same concentration and with the same experimental conditions. Table 3 shows a good estimation of longitudinal and transverse relaxation times, except for some of the phenylalanine signals. Quantification was then achieved by using these relaxation time estimates, considering the PGSE experiment recorded with the lowest values of diffusion time and CPMG cycles (Dmin;

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Communication / Journal of Magnetic Resonance 216 (2012) 201–208 Table 4 Comparison of various integrals obtained on the MM-3 sample from the quantitative NMR spectrum (IQ) as well as from quantitative PGSE experiments based either on the herein proposed methodology (ID,T1/T2,) or the qDECRA approach (IqDECRA). Signal (d ppm)

IQ (a.u.)

ID,T1/T2 (a.u.)

Deviation (%)

IqDECRA (a.u.)

Deviation (%)

PPG(1.1) Phe(3.2) Phe(3.3) PPG(3.3) PEG(3.7) Phe(4.1) Phe(7.4)

5.84 0.99 0.99a 5.84a 2.14a 0.99a 5b

5.86 0.98 0.98 5.73 2.11 1.01 5b

+0.4 1.2 0.6 2.0 1.2 +2.0 +0.0

5.89 1.05 1.01 5.41 2.44 0.97 5b

+0.9 +6.3 +2.3 7.3 +13.9 2.3 +0.0

a Because of spectral overlapping, these integrals values were estimated using non-overlapped signal integrals (knowing the respective number of protons for each NMR resonance). b The integral of the signals due to the aromatic protons was used to calibrate all the other integrals.

Fig. 6. Series of 1H 500 MHz NMR spectra recorded on MM-3 at 300 K: (a) quantitative 1H spectrum, and (b–e) 1H spectra of each mixture component obtained by processing the PGSE experiment with DECRA, showing PEG-10k (b), PPG-1k (c), Phe (d), and HOD (e).

Table 3 T1 and T2 measurements obtained for MM-2, resulting from 3 PGSE experiments (pulse sequence of Fig. 1b) recorded with (Dmin = 400 ms; Dmax = 500 ms, nCPMG max = 700). These values are compared to the reference values as measured by IR and CPMG., respectively. Signal (d ppm)

T IR 1 (s)

T PGSE 1 (s)

Deviation (%)

T CPMG 1 (s)

T PGSE 2 (s)

Deviation (%)

PPG(1.1) Phe(3.2) Phe(3.3) PPG(3.3) PEG(3.7) Phe(4.1) Phe(7.4)

0.72 1.00 0.98 0.67 0.76 3.24 3.36

0.75 0.99 0.97 0.67 0.79 3.01 3.68

+4.3 0.3 0.4 +1.0 +4.1 7.0 +9.4

0.53 0.93 0.93 0.42 0.60 2.14 2.72

0.57 0.88 0.89 0.53 0.55 2.61 2.95

+8.3 4.9 4.2 +26.6 9.1 +22.0 +8.3

nCPMG = 1) in order to minimize quantification errors, as suggested by Eqs. (2) and (3). For comparison, the qDECRA methodology was also applied on the same mixture by recording 5 distinct PGSE experiments with s1 = 347, 374, 480, 613 and 745 ms and taking s1/s2 = 133, with the same PGSE pulse sequence as the one described in Ref. [22] (which is basically the BPP-LED pulse sequence shown in Fig. 1a without the LED and the purge gradients). The results reported in Table 4 show that the herein proposed methodology gave overall very good quantification accuracy. This can be evaluated somehow by considering a global error function defined as the sum of the absolute values of all relative errors, giving a total error of 7%. In this specific example, the results were shown to be superior to those achieved with the qDECRA methodology (with a total error of 33%). The observed differences in terms of quantification accuracy are specifically discussed in the next section. 3.4. Methods accuracy and impact of J-modulation Quantification accuracy in qDECRA merely depends on three factors: cross-relaxation, chemical exchange, and J-modulation [21,22]. Considering the systems used in this study, only J-modula-

tion must be considered here. In other words, discussing differences in accuracy between qDECRA and our method is equivalent to discussing how these methods are affected by J-modulation. To investigate this issue, we first repeated the qDECRA experiments using the pulse sequence shown in Fig. 1b (with nCPMG set to 1), and the accuracy of the results improved (with a total error of 14%). This is in agreement with the fact that, contrary to the BPP pulse sequence used in [22], the pulse sequence shown in Fig. 1b has a LED during which a purge gradient is applied. This is known to reduce artifacts arising from J-modulation because only zero quantum coherences survive this so-called z filter [27]. In other words, quantification accuracy is improved because fewer spectral distortions due to J-modulation are present. However, the achieved accuracy is still lower than that obtained with our methodology (total error of 14% instead of 7% in our case). As will be shown below, the impact of J-modulation artifacts on the accuracy of qDECRA and our method is intrinsically different. In qDECRA, the quantitative integrals are determined through a linear regression of data points arising from PGSE experiments recorded for increasing values of s2. Only this variable is important for the discussion here, as it represents the total time during which the magnetization is transverse (and hence subjected to J-modulation in the case of homonuclear scalar-coupled spin systems). The critical point is that, for the linear regression to be accurate, there must be some significant attenuation in terms of signal intensity between the first and the last experiments, recorded with the lowest and largest s2 values, respectively. However, for large s2 values, the data points become more and more affected by J-modulation, because transverse magnetization is allowed to evolve freely during longer and longer times as the spin echo diffusion-encoding delay is increased. Hence, the accuracy of the data points decreases, which jeopardizes the fitting quality and hence the reliability of the intercept (i.e. the quantitative integral). In our strategy, J-modulation only impacts the accuracy of the T2 estimation, which is obtained by using a CPMG pulse train. Measuring T2 accurately is known to be intrinsically difficult in homonuclear scalar-coupled spin systems because the scalar coupling interaction leads to modulation of the echoes envelope. The CPMG pulse sequence has been shown to cancel these modulations provided that the delay between two consecutive 180° pulses is sufficiently short with respect to 1/J, where J is the scalar coupling constant involved. However, the observed cancellation is never perfect and residual modulations are typically seen for short evolution times. For larger evolution times, i.e. when a large number of 180° refocusing pulses have been applied, the oscillations usually smoothen and practically cancel out, resulting in an envelope decay that looks exponential. This is typically attributed to the cumulative effect of the 180° pulses imperfections. However, the

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T2 values obtained in this case are apparent values that usually differ from the real ones. In other words, the accuracy is reduced. The key point to grasp here is that this reduced accuracy is actually sufficient in our case for renormalizing the data with enough precision. Indeed, Section 3.1 has shown that accounting for T2 relaxation may either prove unnecessary (whenever T2’s are larger than a cut-off value of 0.4 s) or does not require highly accurate T2 estimates for achieving suitable quantification accuracy (a 30% error on the estimation being tolerable as long as T2’s are larger than 0.12 s). Most importantly, one of the most significant advantages of our strategy with respect to qDECRA is that the above-mentioned cutoff values for T2 (0.4 s and 0.12 s) are strictly hardware-dependent. Recall, indeed, that our strategy renormalizes the DECRA-extracted NMR spectrum associated with the PGSE experiment recorded with the lowest diffusion time. Therefore, if signal attenuation due to diffusion is to be significant enough for the DECRA analyzis to be successful in discriminating the mixture components, the gradient pulse duration has to be sufficiently large. This was the reasoning behind the use of a maximum s2 value of 10 ms in Section 3.1, from which the cut-off T2 values were derived. Clearly, increasing the maximum gradient strength would allow other cut-off values to be envisioned. For instance, a factor-10 increase in gradient strength, from 50 G cm1 (a typical value on commercially available high resolution NMR probe heads) to 500 G cm1 (currently not unrealistic) would allow a same PGSE experiment to be conducted with a 10-times lower gradient pulse duration. As such, accounting for T2 relaxation in this case would become unnecessary whenever T2’s were larger than 0.04 s. Alternatively, keeping a maximum s2 value of 10 ms with such gradient strength would extend the range of T2’s (T2 P 0.012 s) that can be measured with a 30% accuracy without compromising the targeted 2.5% quantification accuracy. This is a striking difference with respect to qDECRA, for which increasing the gradient strength does not bring any improvement in terms of J-modulation artifacts because it will always be necessary to increase the evolution delays in order to sample properly the attenuation due to relaxation.

4. Conclusion Alternatively to the qDECRA approach, this study has presented an acquisition strategy based on a modified BBP-LED pulse sequence incorporating an initial CPMG pulse train, which allows quantitative PGSE data to be obtained. Only three PGSE experiments need to be recorded, involving two distinct values of diffusion times (Dmin and Dmax) and CPMG loop cycles (nCPMG = 1 and 600), but keeping the spin echo diffusion-encoding delay constant. These PGSE experiments were analyzed by DECRA in order to extract the 1H spectra of the mixture components. Comparing the relative intensity of the NMR resonances between these spectra then allowed T1 and T2 to be estimated for all nuclei. In all cases, a very good accuracy was achieved for the T1 estimations. In contrast, the T2 estimation accuracy was found to be much lower because of Jmodulation artifacts. Still, the overall quantification accuracy obtained with our method was shown to be better than that obtained with qDECRA, while requiring substantially less experimental time. Reasons for this were provided, considering the different intrinsic dependence that both methods have with respect to J-modulation artifacts. In qDECRA, these artifacts directly jeopardize the reliability of the data regression that is used to obtain the quantitative integrals, hereby reducing the quantification accuracy. In our method, these artifacts only perturb the accuracy of the T2 estimations, which is not intrinsically critical to obtain good quantification accuracy. Indeed, for small- to medium-sized molecules, accounting for T2 relaxation is not systematically required. In

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contrast, for larger molecular weight species, T2 estimates must be included. However, large relative errors on T2 can be tolerated without compromising drastically the quantification accuracy. Interestingly, the proposed methodology is expected to work better with NMR probe heads equipped with magnetic field gradient coil of higher strength. Finally, it could prove useful to investigate the quality of the results obtained when applying our strategy with other pulse sequences, such as those described in Ref. [27]. Acknowledgments The authors acknowledge the support from Spectropole, the analytical facility of the Aix-Marseille University, for privileged access to the NMR instruments. References [1] P. Stilbs, Fourier transform pulsed-gradient spin-echo studies of molecular diffusion, Progress in Nuclear Magnetic Resonance Spectroscopy 19 (1987) 1– 45. [2] C.S. Johnson Jr., Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications, Progress in Nuclear Magnetic Resonance Spectroscopy 34 (1999) 203–256. [3] W.S. Price, NMR studies of translational motion, Cambridge University Press, 2009. [4] P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, New York, 1991. [5] G.A. Morris, Diffusion-ordered spectroscopy, in: D.M. Grant, R.K. Harris (Eds.), Encyclopedia of Magnetic Resonance, vol. 9, John Wiley and Sons, Ltd., Chichester, 2002, pp. 35–44. [6] M.-A. Delsuc, T.E. Malliavin, Maximum entropy processing of DOSY NMR spectra, Analytical Chemistry 70 (1998) 2146–2148. [7] R. Huo, C. Geurts, J. Brands, R. Wehrens, L.M.C. Buydens, Real-life applications of the MULVADO software package for processing DOSY NMR data, Magnetic Resonance in Chemistry 44 (2006) 110–117. [8] G.S. Armstrong, N.M. Loening, J.E. Curtis, A.J. Shaka, V.A. Mandelshtam, Processing DOSY spectra using the regularized resolvent transform, Journal of Magnetic Resonance 163 (2003) 139–148. [9] C. Mouro, P. Mutzenhardt, D. Canet, HR-DOSY experiments with radiofrequency field gradients (RFG) and their processing according to the HD method, Magnetic Resonance in Chemistry 40 (2002) S133–S138. [10] B. Antalek, W. Windig, Generalized rank annihilation method applied to a single multicomponent pulsed gradient spin echo NMR data set, Journal of the American Chemical Society 118 (1996) 10331–10332. [11] W. Windig, B. Antalek, Direct exponential curve resolution algorithm (DECRA): a novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles, Chemometrics and Intelligent Laboratory Systems 37 (1997) 241–254. [12] L.C.M. Van Gorkom, T.M. Hancewicz, Analysis of DOSY and GPC-NMR experiments on polymers by multivariate curve resolution, Journal of Magnetic Resonance 130 (1998) 125–130. [13] L. Nilsson, G.A. Morris, Pure shift proton DOSY: diffusion-ordered 1H spectra without multiplet structure, Chemical Communications (2007) 933–935. [14] M. Nilsson, A. Botana, G.A. Morris, T-1-Diffusion-ordered spectroscopy: nuclear magnetic resonance mixture analysis using parallel factor analysis, Analytical Chemistry 81 (2009) 8119–8125. [15] M. Nilsson, G.A. Morris, Speedy component resolution: an improved tool for processing diffusion-ordered spectroscopy data, Analytical Chemistry 80 (2008) 3777–3782. [16] A.A. Juan, F. Stephen, N. Mathias, A.M. Gareth pure shift 1H NMR: a resolution of the resolution problem? Angewandte Chemie International Edition, vol. 49, 2010, pp. 3901–3903. [17] S. Viel, S. Caldarelli, Improved 3D DOSY-TOCSY experiment for mixture analysis, Chemical Communications (2008) 2013–2015. [18] P. Stilbs, K. Paulsen, P.C. Griffiths, Global least-squares analysis of large, correlated spectral data sets: application to component-resolved FT-PGSE NMR spectroscopy, Journal of Physical Chemistry 100 (1996) 8180–8189. [19] A.K. Rogerson, J.A. Aguilar, M. Nilsson, G.A. Morris, Simultaneous enhancement of chemical shift dispersion and diffusion resolution in mixture analysis by diffusion-ordered NMR spectroscopy, Chemical Communications 47 (2011) 7063–7064. [20] S. Viel, F. Ziarelli, S. Caldarelli, Enhanced diffusion-edited NMR spectroscopy of mixtures using chromatographic stationary phases, Proceedings of the National Academy of Sciences of the United States of America 100 (2003) 9696–9698. [21] B. Antalek, Accounting for spin relaxation in quantitative pulse gradient spin echo NMR mixture analysis, Journal of the American Chemical Society 128 (2006) 8402–8403. [22] B. Antalek, Using PGSE NMR for chemical mixture analysis: quantitative aspects, Concepts in Magnetic Resonance Part A 30A (2007) 219–235.

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