CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201301117
Ultrafast Two-Dimensional NMR Relaxometry for Investigating Molecular Processes in Real Time Susanna Ahola and Ville-Veikko Telkki*[a] Nuclear spin–lattice (T1) and spin–spin (T2) relaxation times provide versatile information about the dynamics and structure of substances, such as proteins, polymers, porous media, and so forth. Multidimensional experiments increase the information content and resolution of NMR relaxometry, but they also multiply the measurement time. To overcome this issue, we present an efficient strategy for a single-scan measurement of a 2D T1–T2 correlation map. The method shortens the experimental time by one to three orders of magnitude as compared to the
conventional method, offering an unprecedented opportunity to study molecular processes in real-time. We demonstrate that, despite the tremendous speed-up, the T1–T2 correlation maps determined by the single-scan method are in good agreement with the maps measured by the conventional method. The concept of the single-scan T1–T2 correlation experiment is applicable to a broad range of other multidimensional relaxation and diffusion experiments.
1. Introduction The power of traditional nuclear magnetic resonance (NMR) spectroscopy in chemical analysis relies on the versatile chemical information conveyed by chemical shifts and couplings.[1, 2] Multidimensional experiments[3, 4] greatly enhance the chemical resolution and information content, but they also multiply the experimental time, restricting the investigations of fast processes. Frydman et al.[5] introduced the single-scan (ultrafast) multidimensional NMR approach as a solution to this issue. This finding has been widely considered as one of the brightest recent innovations in NMR spectroscopy. As described in recent reviews,[6, 7] since its invention the ultrafast method has been shown to be capable of delivering any type of multidimensional spectrum in a single transient. It has been used, for example, for real-time identification of analytes undergoing chromatographic separation,[8] chemical transformations,[9] and H/D exchange processes in proteins,[10] as well as recording NMR spectra of hyperpolarized substances.[11, 12] In addition, the principles of continuous spatial encoding[13] of ultrafast NMR have also been applied to magnetic resonance imaging (MRI)[7, 14] and to measure so-called Z-spectra in chemical exchange saturation transfer experiments.[15] Typically, the NMR spectrum of fluids absorbed on another material contains little information; it may even consist of a single broad peak, as, for example, in the case of moisture in wood.[16] However, the relaxation time distributions, reflecting different rates of decay and recovery of the initially perturbed magnetization to the thermal equilibrium, may reveal the existence of differing environments of the fluid molecules. Consequently, detailed information about the structure of the materi[a] Dr. S. Ahola, Dr. V.-V. Telkki Department of Physics, NMR Research Group University of Oulu, P.O.Box 3000 FIN-90014 (Finland) E-mail: [email protected]
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
al may be provided.[16, 17] Relaxometry is also used to investigate the dynamics of protein backbones, water/protein interfaces, liquid crystals, polymers, solutions, networks, and so forth.[18] One-dimensional (1D) spin–lattice relaxation time (T1) distributions are usually measured either by inversion recovery (IR)[19] or saturation recovery (SR)[20] sequences, while spin–spin relaxation (T2) is probed by the spin-echo[21] or the Carr–Purcell–Meiboom–Gill (CPMG)[22] methods. In analogy to traditional NMR spectroscopy, the resolution and information content of relaxometry can be increased by a multidimensional approach such as the 2D T1–T2 correlation experiment.[23, 24] The approach has become in routine use only in recent years, after a sufficiently reliable and robust 2D Laplace inversion algorithm has been developed for extracting a relaxation time map from the experimental data.[25, 26] The 2D T1–T2 correlation method has been used, for example, to investigate brine-saturated rock samples,[24] surface relaxation and chemical exchange in hydrating cement pastes,[27] magnetic environments in porous media,[28] quantitative analysis of food products,[29] and water exchange in wood.[30] However, similarly as in traditional multidimensional NMR, long experimental times restrict the applicability of multidimensional relaxometry in the study of fast processes. A wait time of about T1 is necessary before repeating the experiment with a different time in the evolution dimension. Therefore, the acquisition of full 2D data may take from minutes to hours. Inspired by Frydman’s single-scan multidimensional NMR, we introduce in the present work a novel approach for a single-scan measurement of the T1–T2 relaxation correlation. While the method consists of successive IR and CPMG blocks, as in the conventional experiment, in the present case all the different evolution times undergo a multiplexing process within layers of the sample perpendicular to the axis of a sample tube. The magnetization profile along the axis direcChemPhysChem 2014, 15, 1687 – 1692
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tion is imaged at each value of the CPMG echo time similarly as in 1D multiple-echo MRI. The IR block corresponds to the singlescan IR approach published by Loening et al.[31] (note that the IR measurement of a 1D T1 distribution is already a 2D experiment). A similar IR block has also been present in a recently published UF-IR experiment, in which chemical shift information is collected using echo planar spectroscopic imaging (EPSI) type detection.[32] Our method shortens the experimental time by one to three orders of magnitude as compared to the traditional method; the typical experiment time of a single-scan experiment without accumulation is only about a few seconds. Consequently, the method proposed here offers an unforeseen opportunity for studying dynamic processes by multidimensional relaxometry in real-time. As in single-scan spectroscopy, the multiplexing decreases the signal-to-noise ratio (SNR) of the experiment. However, this is not Figure 1. A) Conventional IR-CPMG pulse sequence. B) SS-IR-CPMG pulse sequence (top), evolution of magnetizaa limiting factor as long as high- tion vectors at different z positions during T1 encoding (bottom left), and the magnetization profiles correspondconcentration samples are inves- ing to different CPMG echoes (bottom right). tigated using a modern and sensitive, high-field NMR apparatus. In fact, a too strong signal may even disturb the conventional 2. Method relaxation experiments. This may happen because of radiation damping occurring due to a coupling between the detection The pulse sequences of the conventional T1–T2 relaxation excoil and strong transverse magnetization.[33] In contrast, in the periment, referred to as IR-CPMG, and the herein proposed single-scan version, dubbed SS-IR-CPMG, are shown in single-scan experiment, the effect of radiation damping is supFigure 1. Both sequences include an IR-type T1 relaxation enpressed due to the fact that there is no coherent transverse coding part followed by a CPMG-type T2 encoding. In the magnetization during the IR part because of the continuously varying phase of the frequency sweep pulse and the use of single-scan T1 encoding, the Larmor frequency of the nuclei is a sweep gradient. Furthermore, the magnitude of the coherent rendered linearly dependent on the position (z) along the axis transverse magnetization during the CPMG loop is, on average, of the sample tube by the gradient Gsweep. At the same time, smaller than in the conventional experiment because of the the spins are inverted by the adiabatic frequency sweep p use of a read gradient. Another common feature of the singlepulse, called a chirped pulse, the frequency of which increases scan spectroscopy and relaxometry methods is that the linearly with time.[34, 35] Consequently, the magnetization at the sample has to be homogeneous along the axis direction. bottom of the tube is inverted first and that at the top is inIn this article, we introduce the 2D single-scan T1–T2 relaxaverted last. One can imagine the sample to be divided into layers corresponding to different IR times, with a linear relation correlation method, demonstrate its significant speed-up tionship prevailing between the z position and time. The T2 enas compared to the conventional method, and show that the 2D relaxation correlation maps determined by the method are coding part comprises a CPMG loop, and the magnetization nevertheless in good agreement with those of the latter. profile along the z direction is imaged at each CPMG echo time similarly as in a 1D multiple-echo MRI experiment. The Fourier transform of the measured data, M(k,t2), in the spatial 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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frequency (k) dimension conveys the magnetization profiles along the z direction. The first magnetization profile is in fact a 1D IR curve, provided that the z axis is converted into the IR time (t1) dimension by using the linear dependence between z and t1. The profiles corresponding to the subsequent CPMG echoes decay due to T2 relaxation, as illustrated in Figure 1 B. The Fourier transformed data, M(t1,t2), is described by the same equation as data obtained in a conventional IR-CPMG experiment [Eq. (1)]: Mðt1 ; t2 Þ ¼
Z Z
1 2 exp
t1 T1
exp
mersed in excess of water. The concentration of H2O in water was decreased to 1–5 % in all the samples to avoid radiation damping in the reference methods; the rest was D2O. The data of the SS-IR-CPMG experiment on the double-tube sample after Fourier transform of M(k,t2) into M(t1,t2), are shown in Figure 2. The sharp minima at t1 = 0 and tchirp (tchirp is the length of the chirped pulse) are artifacts originating from
t2 F ðT1 ; T2 ÞdT1 dT2 T2 ð1Þ
where F(T1,T2) is the probability density of molecules with relaxation times T1 and T2, that is, the relaxation correlation map. A 2D Laplace inversion is used to extract F(T1,T2) from the experimental data.[25, 26] If the sample contains nuclei with significantly differing resonance frequencies, the magnetization profiles (and hence the T1 profiles) become blurred by a phenomenon known as the fat shift artifact from MRI.[35] To avoid this problem and to facilitate chemically selective SS-IR-CPMG, a frequency selective p/2 pulse (illustrated in gray in Figure 1 B), which excites only the desired resonance, may be applied instead of a hard p/2 pulse after the T1 encoding. To make a realistic comparison between the efficiency of the conventional IR-CPMG and the proposed SS-IR-CPMG methods, let us assume that in the SS-IR-CPMG experiment the chirp pulse duration is 2 s and the CPMG train length is 0.5 s, and in the IR-CPMG experiment t1 is increased from 0 to 2 s with equal steps, the CPMG train length is the same as in the SS-IRCPMG experiment, and the relaxation delay is 2 s. If the number of t1 increments is either 16 or 1024, the experiment time of the IR-CPMG method is either 1 or 60 min, respectively, without accumulation. In contrast, the experiment time of the SS-IR-CPMG measurement is only 2.5 s regardless of the number of t1 values (which is defined by the resolution in the 1D image). Therefore it is justified to conclude that SS-IRCPMG is one to three orders of magnitude faster than the conventional IR-CPMG method.
3. Results In order to test the new approach, 2D T1–T2 correlation maps of three samples were measured both by SS-IR-CPMG and conventional IR-CPMG methods. In addition, 1D T1 and T2 relaxation time distributions were acquired by IR and CPMG methods, respectively. The doped-water sample contained water, in which the relaxation times were shortened by a contrast agent, in a 10 mm sample tube. The double-tube sample consisted of two concentric, 5 and 10 mm, sample tubes, with the relaxation times of water in the compartments made different by the contrast agent. Finally, the silica 60 sample contained silica gel 60, a porous, powder-like material with an average pore diameter of 6 nm and a particle size of 63–200 mm, im 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 2. SS-IR-CPMG experiment on the double-tube sample (see text) after Fourier transform of M(k, t2) into M(t1, t2), in absolute value. The profile corresponding to the first CPMG echo (black solid line) is shown at the top of the data, along with the excitation-detection profile of the coil (gray dashed line). The region of the data used in 2D Laplace inversion is indicated by the white dashed line.
the beginning and the end of the frequency sweep. Some Gibbs ringing[36] can be seen in the vicinity of the dips (see the profile of the first echo on top of the data). True magnetization profiles occur between t1 = 0 and tchirp ; folding of these profiles, weighted by the excitation-detection profile of the coil, is visible outside that region. The processing involved division of the data first by the coil excitation-detection profile in order to compensate the influence of the latter effect. Next, the region between t1 = 0 and tchirp containing correct, good-quality data was extracted and the data on the right of the profile minimum was flipped to the negative side in order to make the data correspond to the correct IR curve. The sign change may, however, be problematic in case of a complex sample because the profile may include several minima corresponding to many zero crossings. Therefore, it may be advantageous to measure phase-sensitive imaging data, if possible. Alternatively, one could modify the kernel of the Laplace inversion integral fit to correspond to the absolute value data. A third option is to replace the IR block of the SS-IR-CPMG sequence by SR, by simply replacing the chirped p pulse with a chirped p/2 pulse. The modified SS-SR-CPMG experiment returns only positive data points, and a change of the sign of the absolute value data is no longer necessary. In the current proof-of-principle experiments the sign of the relevant data points was changed as described above, and the T1–T2 relaxation correlation maps were extracted from the data by 2D Laplace inversion. ChemPhysChem 2014, 15, 1687 – 1692
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Figure 3. 1D T1 and T2 distributions as well as 2D single-scan (SS-IR-CPMG) and reference (IR-CPMG) T1–T2 correlation maps of water in the three test samples.
The results of the relaxometry experiments are shown in Figure 3. Whereas the SS-IR-CPMG measurements of the doped-water and double-tube samples represent true singlescan experiments, 64 scans were accumulated from the silica 60 sample to improve the SNR. Qualitatively, the singlescan and reference maps are in good agreement; the same main peaks are seen in the maps. Only one peak is observed from the doped-water sample, expectedly, because the relaxation of water is known to be single-exponential. On the other hand, two peaks are visible in the double-tube maps; the one with shorter relaxation time arising from water in the outer tube, and the other with longer relaxation time from the inner tube. Three dominant peaks can be found in the maps of the silica 60 sample: Most likely the shortest relaxation-time peak originates from water in the 6 nm pores, while the longest relaxation-time peak arises from “free water” in between the particles of the porous material. The third, intermediate relaxation-time peak may be a consequence of exchange between these two sites. Some additional small-amplitude peaks are visible in the single-scan map; they are most likely artifacts due to Gibbs ringing and/or lowered SNR. We note that, although the SNR is a complex function of several factors, including receiver bandwidth,[7, 37] we measured that, with our 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
experimental parameters, the SNR per unit time was comparable with the conventional IR-CPMG, because SS-IR-CPMG can be repeated about one hundred times in the time of an IRCPMG measurement. Quantitatively, T1 times in the single-scan and reference maps are identical, while the T2 values tend to be too short in the single-scan maps. The CPMG block of the SS-IR-CPMG experiment belongs to the class of multiple-echo MRI experiments, which are known to result in underestimated T2 values due to their sensitivity to B1 inhomogeneity.[38] More accurate values could be obtained by improving B1 homogeneity and/ or by using better refocusing pulses such as composite pulses.[39] On the other hand, in many cases relaxometry does not even aim at quantitative results. Therefore, the underestimated T2 values do not constitute major concerns provided that the peaks of the desired components are separable.
4. Conclusions We introduced a novel 2D single-scan T1–T2 relaxation correlation experiment (SS-IR-CPMG), which shortens the experimental time by one to three orders of magnitude as compared to the conventional method (IR-CPMG), allowing investigation of ChemPhysChem 2014, 15, 1687 – 1692
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CHEMPHYSCHEM ARTICLES fast processes, such as gel formation, phase changes in ionic liquids and protein folding, in real-time. We demonstrated that the relaxation maps measured by the single-scan method are in good agreement with the maps determined by the conventional method. The single-scan method requires homogeneous samples, and the price to pay for a dramatically shortened experimental time is the lowered signal-to-noise ratio, but this is not a problem if the samples have sufficiently high concentration. The SS-IR-CPMG method reduces also the effect of radiation damping. The sequence can be made chemically selective by replacing the hard p/2 pulse by a soft, frequency selective p/2 pulse. We note additionally that the concept of the singlescan T1–T2 correlation experiment is applicable to a broad range of other multidimensional relaxation and diffusion experiments, many of them also being suitable for the investigation of hyperpolarized substances, as we will show in future.
Experimental Section The experiments were carried out on a Bruker Avance III 300 MHz spectrometer equipped with a micro-imaging unit. The experimental parameters were the following:
1) Doped-water SS-IR-CPMG experiment: Relaxation delay 2 s,
2)
3)
4)
5)
6)
echo time 20 ms, acquisition matrix size 256 64, matrix size after processing 113 64 resulting in t1 list ranging from 0.02 s to 0.89 s, 113 values with equal steps, field of view in the z direction 3 cm, chirp pulse duration 1 s. Doped-water REF IR-CPMG experiment: Relaxation delay 2 s, echo time 20 ms, acquisition matrix size 64 113, matrix size after processing 113 64, t1 list ranging from 0.02 s to 0.89 s, 113 values with equal steps. Double-tube SS-IR-CPMG experiment: Relaxation delay 4 s, echo time 10 ms, acquisition matrix size 256 64, matrix size after processing 111 64 resulting in t1 list ranging from 0.02 s to 1.31 s, 111 values with equal steps, field of view in z direction 3 cm, chirp pulse width 1.5 s. Double-tube REF IR-CPMG experiment: Relaxation delay 4 s, echo time 20 ms, acquisition matrix size 64 111, matrix size after processing 111 64, t1 list ranging from 0.02 s to 1.31 s, 111 values with equal steps. Silica 60 SS-IR-CPMG experiment: Relaxation delay 4 s, echo time 7 ms, acquisition matrix size 256 64, matrix size after processing 71 64 resulting in t1 list ranging from 0.03 s to 1.69 s, 71 values with equal steps, field of view in z direction 3 cm, chirp pulse width 2 s. Silica 60 REF IR-CPMG experiment: Relaxation delay 4 s, echo time 7 ms, acquisition matrix size 64 83, matrix size after processing 71 64, t1 list ranging from 0.5 ms to 5 s, including a range of 0.03 s to 1.69 s, 71 values with equal steps.
In all the SS experiments (1, 3, and 5) the chirp pulse bandwidth was 10 kHz and the smoothing factor was 1 %. The strength of the gradient applied during the chirp pulse was 0.16 G mm1 for the doped-water and double-tube samples (experiments 1 and 3) and 0.24 G mm1 for the silica sample (5). The read and dephase gradient amplitude was 0.79 G mm1, and the acquisition bandwidth was 100 kHz. Laplace inversion program provided by P. Callaghan (Victoria University of Wellington, New Zealand) was used for de 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org termining the relaxation distributions.[40] The program is based on the method published by Venkataramanan et al.[24, 25]
Acknowledgements We thank late Prof. P. Callaghan for providing the Laplace inversion program, Dr. Anu Kantola for her assistance in experimental issues, and Prof. Juha Vaara and Dr. Perttu Lantto for their valuable comments on the manuscript. Keywords: nuclear magnetic resonance · relaxation correlation · single-scan measurements · spectroscopy · twodimensional
[1] R. R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford, 1987. [2] M. H. Levitt, Spin Dynamics: Basics of Nuclear Magnetic Resonance, Wiley, Chischester, 2005. [3] J. Jeener, International Ampere Summer School, Basko Polje, Yugoslavia, September 1971; lecture notes published in NMR and More in Honour of Anatole Abragam (Eds.: M. Goldman, M. Porneuf), Les Editions de Physique, Les Ulis, France, 1994. [4] W. P. Aue, E. Bartholdi, R. R. Ernst, J. Chem. Phys. 1976, 64, 2229 – 2246. [5] L. Frydman, T. Scherf, A. Lupulescu, Proc. Natl. Acad. Sci. USA 2002, 99, 15858 – 15862. [6] M. Mishkovsky, L. Frydman, Annu. Rev. Phys. Chem. 2009, 60, 429 – 448. [7] A. Tal, L. Frydman, Prog. Nucl. Magn. Reson. Spectrosc. 2010, 57, 241 – 292. [8] B. Shapira, A. Karton, D. Aronzon, L. Frydman, J. Am. Chem. Soc. 2004, 126, 1262 – 1265. [9] M. Gal, M. Mishkovsky, L. Frydman, J. Am. Chem. Soc. 2006, 128, 951 – 956. [10] M. Gal, P. Schanda, B. Brutsher, L. Frydman, J. Am. Chem. Soc. 2007, 129, 1372 – 1377. [11] B. Shapira, E. Morris, K. A. Muszkat, L. Frydman, J. Am. Chem. Soc. 2004, 126, 11756 – 11757. [12] L. Frydman, D. Blazina, Nat. Phys. 2007, 3, 415 – 419. [13] P. Pelupessy, J. Am. Chem. Soc. 2003, 125, 12345 – 12350. [14] Y. Shrot, L. Frydman, J. Magn. Reson. 2005, 172, 179 – 190. [15] X. Xu, J.-S. Lee, A. Jerschow, Angew. Chem. 2013, 125, 8439 – 8442; Angew. Chem. Int. Ed. 2013, 52, 8281 – 8284. [16] V.-V. Telkki, M. Yliniemi, J. Jokisaari, Holzforschung 2012, 67, 291 – 300. [17] Y.-Q. Song, J. Magn. Reson. 2013, 229, 12 – 24. [18] R. Kimmich, A. Esteban, Prog. Nucl. Magn. Reson. Spectrosc. 2004, 44, 257 – 320. [19] R. L. Vold, J. S. Waugh, M. P. Klein, D. E. Phelps, J. Chem. Phys. 1968, 48, 3831 – 3832. [20] J. L. Markley, W. J. Horsley, M. P. Klein, J. Chem. Phys. 1971, 55, 3604 – 3605. [21] E. L. Hahn, Phys. Rev. 1950, 80, 580 – 594. [22] S. Meiboom, D. Gill, Rev. Sci. Instrum. 1958, 29, 688 – 691. [23] H. Peemoeller, R. K. Shenoy, M. M. Pintar, J. Magn. Reson. 1981, 45, 193 – 204. [24] Y.-Q. Song, L. Venkataramanan, M. D. Hrlimann, M. Flaum, P. Frulla, C. Straley, J. Magn. Reson. 2002, 154, 261 – 268. [25] L. Venkataramanan, Y.-Q. Song, M. D. Hrlimann, IEEE Trans. Signal. Proc. 2002, 50, 1017 – 1026. [26] J. Granwehr, P. J. Roberts, J. Chem. Theory Comput. 2012, 8, 3473 – 3482. [27] P. J. McDonald, J.-P. Korb, J. Mitchell, L. Monteilhet, Phys. Rev. E 2005, 72, 011409. [28] C. Casieri, F. De Luca, L. Nodari, U. Russo, C. Terenzi, Chem. Phys. Lett. 2010, 496, 223 – 226. [29] M. Hrlimann, L. Burcaw, Y.-Q. Song, J. Colloid Interface Sci. 2006, 297, 303 – 311. [30] J. Cox, P. J. McDonald, B. A. Gardiner, Holzforschung 2010, 64, 259 – 266.
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CHEMPHYSCHEM ARTICLES [31] N. M. Loening, M. J. Thrippleton, J. Keeler, R. G. Griffin, J. Magn. Reson. 2003, 164, 321 – 328. [32] P. E. S. Smith, K. J. Donovan, O. Szekely, M. Baias, L. Frydman, ChemPhysChem 2013, 14, 3138 – 3145. [33] C. Szntay, Jr., A. Demeter, Concepts Magn. Reson. 1999, 11, 121 – 145. [34] B. Shapira, A. Lupulescu, Y. Shrot, L. Frydman, J. Magn. Reson. 2004, 166, 152 – 163. [35] M. Garwood, L. DelaBarre, J. Magn. Reson. 2001, 153, 155 – 177. [36] E. M. Haacke, R. W. Brown, M. R. Thompson, R. Venkatesan, Magnetic Resonance Imaging, Physical Principles and Sequence Design, Wiley, New York, 1999.
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www.chemphyschem.org [37] M. Pathan, S. Akoka, I. Tea, B. Charrier, P. Giraudeau, Analyst 2011, 136, 3157 – 3163. [38] S. Majumdar, S. C. Orphanoudakis, A. Gmitro, M. O’Donnell, J. C. Gore, Magn. Reson. Med. 1986, 3, 397 – 417. [39] M. H. Levitt, R. Freeman, J. Magn. Reson. 1981, 43, 65 – 80. [40] S. Godefroy, P. T. Callaghan, Magn. Reson. Imaging 2003, 21, 381 – 383.
Received: November 26, 2013 Published online on March 13, 2014
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Ultrafast Two-Dimensional NMR Relaxometry for Investigating Molecular Processes in Real Time Susanna Ahola and Ville-Veikko Telkki*[a] Nuclear spin–lattice (T1) and spin–spin (T2) relaxation times provide versatile information about the dynamics and structure of substances, such as proteins, polymers, porous media, and so forth. Multidimensional experiments increase the information content and resolution of NMR relaxometry, but they also multiply the measurement time. To overcome this issue, we present an efficient strategy for a single-scan measurement of a 2D T1–T2 correlation map. The method shortens the experimental time by one to three orders of magnitude as compared to the
conventional method, offering an unprecedented opportunity to study molecular processes in real-time. We demonstrate that, despite the tremendous speed-up, the T1–T2 correlation maps determined by the single-scan method are in good agreement with the maps measured by the conventional method. The concept of the single-scan T1–T2 correlation experiment is applicable to a broad range of other multidimensional relaxation and diffusion experiments.
1. Introduction The power of traditional nuclear magnetic resonance (NMR) spectroscopy in chemical analysis relies on the versatile chemical information conveyed by chemical shifts and couplings.[1, 2] Multidimensional experiments[3, 4] greatly enhance the chemical resolution and information content, but they also multiply the experimental time, restricting the investigations of fast processes. Frydman et al.[5] introduced the single-scan (ultrafast) multidimensional NMR approach as a solution to this issue. This finding has been widely considered as one of the brightest recent innovations in NMR spectroscopy. As described in recent reviews,[6, 7] since its invention the ultrafast method has been shown to be capable of delivering any type of multidimensional spectrum in a single transient. It has been used, for example, for real-time identification of analytes undergoing chromatographic separation,[8] chemical transformations,[9] and H/D exchange processes in proteins,[10] as well as recording NMR spectra of hyperpolarized substances.[11, 12] In addition, the principles of continuous spatial encoding[13] of ultrafast NMR have also been applied to magnetic resonance imaging (MRI)[7, 14] and to measure so-called Z-spectra in chemical exchange saturation transfer experiments.[15] Typically, the NMR spectrum of fluids absorbed on another material contains little information; it may even consist of a single broad peak, as, for example, in the case of moisture in wood.[16] However, the relaxation time distributions, reflecting different rates of decay and recovery of the initially perturbed magnetization to the thermal equilibrium, may reveal the existence of differing environments of the fluid molecules. Consequently, detailed information about the structure of the materi[a] Dr. S. Ahola, Dr. V.-V. Telkki Department of Physics, NMR Research Group University of Oulu, P.O.Box 3000 FIN-90014 (Finland) E-mail: [email protected]
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
al may be provided.[16, 17] Relaxometry is also used to investigate the dynamics of protein backbones, water/protein interfaces, liquid crystals, polymers, solutions, networks, and so forth.[18] One-dimensional (1D) spin–lattice relaxation time (T1) distributions are usually measured either by inversion recovery (IR)[19] or saturation recovery (SR)[20] sequences, while spin–spin relaxation (T2) is probed by the spin-echo[21] or the Carr–Purcell–Meiboom–Gill (CPMG)[22] methods. In analogy to traditional NMR spectroscopy, the resolution and information content of relaxometry can be increased by a multidimensional approach such as the 2D T1–T2 correlation experiment.[23, 24] The approach has become in routine use only in recent years, after a sufficiently reliable and robust 2D Laplace inversion algorithm has been developed for extracting a relaxation time map from the experimental data.[25, 26] The 2D T1–T2 correlation method has been used, for example, to investigate brine-saturated rock samples,[24] surface relaxation and chemical exchange in hydrating cement pastes,[27] magnetic environments in porous media,[28] quantitative analysis of food products,[29] and water exchange in wood.[30] However, similarly as in traditional multidimensional NMR, long experimental times restrict the applicability of multidimensional relaxometry in the study of fast processes. A wait time of about T1 is necessary before repeating the experiment with a different time in the evolution dimension. Therefore, the acquisition of full 2D data may take from minutes to hours. Inspired by Frydman’s single-scan multidimensional NMR, we introduce in the present work a novel approach for a single-scan measurement of the T1–T2 relaxation correlation. While the method consists of successive IR and CPMG blocks, as in the conventional experiment, in the present case all the different evolution times undergo a multiplexing process within layers of the sample perpendicular to the axis of a sample tube. The magnetization profile along the axis direcChemPhysChem 2014, 15, 1687 – 1692
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tion is imaged at each value of the CPMG echo time similarly as in 1D multiple-echo MRI. The IR block corresponds to the singlescan IR approach published by Loening et al.[31] (note that the IR measurement of a 1D T1 distribution is already a 2D experiment). A similar IR block has also been present in a recently published UF-IR experiment, in which chemical shift information is collected using echo planar spectroscopic imaging (EPSI) type detection.[32] Our method shortens the experimental time by one to three orders of magnitude as compared to the traditional method; the typical experiment time of a single-scan experiment without accumulation is only about a few seconds. Consequently, the method proposed here offers an unforeseen opportunity for studying dynamic processes by multidimensional relaxometry in real-time. As in single-scan spectroscopy, the multiplexing decreases the signal-to-noise ratio (SNR) of the experiment. However, this is not Figure 1. A) Conventional IR-CPMG pulse sequence. B) SS-IR-CPMG pulse sequence (top), evolution of magnetizaa limiting factor as long as high- tion vectors at different z positions during T1 encoding (bottom left), and the magnetization profiles correspondconcentration samples are inves- ing to different CPMG echoes (bottom right). tigated using a modern and sensitive, high-field NMR apparatus. In fact, a too strong signal may even disturb the conventional 2. Method relaxation experiments. This may happen because of radiation damping occurring due to a coupling between the detection The pulse sequences of the conventional T1–T2 relaxation excoil and strong transverse magnetization.[33] In contrast, in the periment, referred to as IR-CPMG, and the herein proposed single-scan version, dubbed SS-IR-CPMG, are shown in single-scan experiment, the effect of radiation damping is supFigure 1. Both sequences include an IR-type T1 relaxation enpressed due to the fact that there is no coherent transverse coding part followed by a CPMG-type T2 encoding. In the magnetization during the IR part because of the continuously varying phase of the frequency sweep pulse and the use of single-scan T1 encoding, the Larmor frequency of the nuclei is a sweep gradient. Furthermore, the magnitude of the coherent rendered linearly dependent on the position (z) along the axis transverse magnetization during the CPMG loop is, on average, of the sample tube by the gradient Gsweep. At the same time, smaller than in the conventional experiment because of the the spins are inverted by the adiabatic frequency sweep p use of a read gradient. Another common feature of the singlepulse, called a chirped pulse, the frequency of which increases scan spectroscopy and relaxometry methods is that the linearly with time.[34, 35] Consequently, the magnetization at the sample has to be homogeneous along the axis direction. bottom of the tube is inverted first and that at the top is inIn this article, we introduce the 2D single-scan T1–T2 relaxaverted last. One can imagine the sample to be divided into layers corresponding to different IR times, with a linear relation correlation method, demonstrate its significant speed-up tionship prevailing between the z position and time. The T2 enas compared to the conventional method, and show that the 2D relaxation correlation maps determined by the method are coding part comprises a CPMG loop, and the magnetization nevertheless in good agreement with those of the latter. profile along the z direction is imaged at each CPMG echo time similarly as in a 1D multiple-echo MRI experiment. The Fourier transform of the measured data, M(k,t2), in the spatial 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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frequency (k) dimension conveys the magnetization profiles along the z direction. The first magnetization profile is in fact a 1D IR curve, provided that the z axis is converted into the IR time (t1) dimension by using the linear dependence between z and t1. The profiles corresponding to the subsequent CPMG echoes decay due to T2 relaxation, as illustrated in Figure 1 B. The Fourier transformed data, M(t1,t2), is described by the same equation as data obtained in a conventional IR-CPMG experiment [Eq. (1)]: Mðt1 ; t2 Þ ¼
Z Z
1 2 exp
t1 T1
exp
mersed in excess of water. The concentration of H2O in water was decreased to 1–5 % in all the samples to avoid radiation damping in the reference methods; the rest was D2O. The data of the SS-IR-CPMG experiment on the double-tube sample after Fourier transform of M(k,t2) into M(t1,t2), are shown in Figure 2. The sharp minima at t1 = 0 and tchirp (tchirp is the length of the chirped pulse) are artifacts originating from
t2 F ðT1 ; T2 ÞdT1 dT2 T2 ð1Þ
where F(T1,T2) is the probability density of molecules with relaxation times T1 and T2, that is, the relaxation correlation map. A 2D Laplace inversion is used to extract F(T1,T2) from the experimental data.[25, 26] If the sample contains nuclei with significantly differing resonance frequencies, the magnetization profiles (and hence the T1 profiles) become blurred by a phenomenon known as the fat shift artifact from MRI.[35] To avoid this problem and to facilitate chemically selective SS-IR-CPMG, a frequency selective p/2 pulse (illustrated in gray in Figure 1 B), which excites only the desired resonance, may be applied instead of a hard p/2 pulse after the T1 encoding. To make a realistic comparison between the efficiency of the conventional IR-CPMG and the proposed SS-IR-CPMG methods, let us assume that in the SS-IR-CPMG experiment the chirp pulse duration is 2 s and the CPMG train length is 0.5 s, and in the IR-CPMG experiment t1 is increased from 0 to 2 s with equal steps, the CPMG train length is the same as in the SS-IRCPMG experiment, and the relaxation delay is 2 s. If the number of t1 increments is either 16 or 1024, the experiment time of the IR-CPMG method is either 1 or 60 min, respectively, without accumulation. In contrast, the experiment time of the SS-IR-CPMG measurement is only 2.5 s regardless of the number of t1 values (which is defined by the resolution in the 1D image). Therefore it is justified to conclude that SS-IRCPMG is one to three orders of magnitude faster than the conventional IR-CPMG method.
3. Results In order to test the new approach, 2D T1–T2 correlation maps of three samples were measured both by SS-IR-CPMG and conventional IR-CPMG methods. In addition, 1D T1 and T2 relaxation time distributions were acquired by IR and CPMG methods, respectively. The doped-water sample contained water, in which the relaxation times were shortened by a contrast agent, in a 10 mm sample tube. The double-tube sample consisted of two concentric, 5 and 10 mm, sample tubes, with the relaxation times of water in the compartments made different by the contrast agent. Finally, the silica 60 sample contained silica gel 60, a porous, powder-like material with an average pore diameter of 6 nm and a particle size of 63–200 mm, im 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 2. SS-IR-CPMG experiment on the double-tube sample (see text) after Fourier transform of M(k, t2) into M(t1, t2), in absolute value. The profile corresponding to the first CPMG echo (black solid line) is shown at the top of the data, along with the excitation-detection profile of the coil (gray dashed line). The region of the data used in 2D Laplace inversion is indicated by the white dashed line.
the beginning and the end of the frequency sweep. Some Gibbs ringing[36] can be seen in the vicinity of the dips (see the profile of the first echo on top of the data). True magnetization profiles occur between t1 = 0 and tchirp ; folding of these profiles, weighted by the excitation-detection profile of the coil, is visible outside that region. The processing involved division of the data first by the coil excitation-detection profile in order to compensate the influence of the latter effect. Next, the region between t1 = 0 and tchirp containing correct, good-quality data was extracted and the data on the right of the profile minimum was flipped to the negative side in order to make the data correspond to the correct IR curve. The sign change may, however, be problematic in case of a complex sample because the profile may include several minima corresponding to many zero crossings. Therefore, it may be advantageous to measure phase-sensitive imaging data, if possible. Alternatively, one could modify the kernel of the Laplace inversion integral fit to correspond to the absolute value data. A third option is to replace the IR block of the SS-IR-CPMG sequence by SR, by simply replacing the chirped p pulse with a chirped p/2 pulse. The modified SS-SR-CPMG experiment returns only positive data points, and a change of the sign of the absolute value data is no longer necessary. In the current proof-of-principle experiments the sign of the relevant data points was changed as described above, and the T1–T2 relaxation correlation maps were extracted from the data by 2D Laplace inversion. ChemPhysChem 2014, 15, 1687 – 1692
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Figure 3. 1D T1 and T2 distributions as well as 2D single-scan (SS-IR-CPMG) and reference (IR-CPMG) T1–T2 correlation maps of water in the three test samples.
The results of the relaxometry experiments are shown in Figure 3. Whereas the SS-IR-CPMG measurements of the doped-water and double-tube samples represent true singlescan experiments, 64 scans were accumulated from the silica 60 sample to improve the SNR. Qualitatively, the singlescan and reference maps are in good agreement; the same main peaks are seen in the maps. Only one peak is observed from the doped-water sample, expectedly, because the relaxation of water is known to be single-exponential. On the other hand, two peaks are visible in the double-tube maps; the one with shorter relaxation time arising from water in the outer tube, and the other with longer relaxation time from the inner tube. Three dominant peaks can be found in the maps of the silica 60 sample: Most likely the shortest relaxation-time peak originates from water in the 6 nm pores, while the longest relaxation-time peak arises from “free water” in between the particles of the porous material. The third, intermediate relaxation-time peak may be a consequence of exchange between these two sites. Some additional small-amplitude peaks are visible in the single-scan map; they are most likely artifacts due to Gibbs ringing and/or lowered SNR. We note that, although the SNR is a complex function of several factors, including receiver bandwidth,[7, 37] we measured that, with our 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
experimental parameters, the SNR per unit time was comparable with the conventional IR-CPMG, because SS-IR-CPMG can be repeated about one hundred times in the time of an IRCPMG measurement. Quantitatively, T1 times in the single-scan and reference maps are identical, while the T2 values tend to be too short in the single-scan maps. The CPMG block of the SS-IR-CPMG experiment belongs to the class of multiple-echo MRI experiments, which are known to result in underestimated T2 values due to their sensitivity to B1 inhomogeneity.[38] More accurate values could be obtained by improving B1 homogeneity and/ or by using better refocusing pulses such as composite pulses.[39] On the other hand, in many cases relaxometry does not even aim at quantitative results. Therefore, the underestimated T2 values do not constitute major concerns provided that the peaks of the desired components are separable.
4. Conclusions We introduced a novel 2D single-scan T1–T2 relaxation correlation experiment (SS-IR-CPMG), which shortens the experimental time by one to three orders of magnitude as compared to the conventional method (IR-CPMG), allowing investigation of ChemPhysChem 2014, 15, 1687 – 1692
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CHEMPHYSCHEM ARTICLES fast processes, such as gel formation, phase changes in ionic liquids and protein folding, in real-time. We demonstrated that the relaxation maps measured by the single-scan method are in good agreement with the maps determined by the conventional method. The single-scan method requires homogeneous samples, and the price to pay for a dramatically shortened experimental time is the lowered signal-to-noise ratio, but this is not a problem if the samples have sufficiently high concentration. The SS-IR-CPMG method reduces also the effect of radiation damping. The sequence can be made chemically selective by replacing the hard p/2 pulse by a soft, frequency selective p/2 pulse. We note additionally that the concept of the singlescan T1–T2 correlation experiment is applicable to a broad range of other multidimensional relaxation and diffusion experiments, many of them also being suitable for the investigation of hyperpolarized substances, as we will show in future.
Experimental Section The experiments were carried out on a Bruker Avance III 300 MHz spectrometer equipped with a micro-imaging unit. The experimental parameters were the following:
1) Doped-water SS-IR-CPMG experiment: Relaxation delay 2 s,
2)
3)
4)
5)
6)
echo time 20 ms, acquisition matrix size 256 64, matrix size after processing 113 64 resulting in t1 list ranging from 0.02 s to 0.89 s, 113 values with equal steps, field of view in the z direction 3 cm, chirp pulse duration 1 s. Doped-water REF IR-CPMG experiment: Relaxation delay 2 s, echo time 20 ms, acquisition matrix size 64 113, matrix size after processing 113 64, t1 list ranging from 0.02 s to 0.89 s, 113 values with equal steps. Double-tube SS-IR-CPMG experiment: Relaxation delay 4 s, echo time 10 ms, acquisition matrix size 256 64, matrix size after processing 111 64 resulting in t1 list ranging from 0.02 s to 1.31 s, 111 values with equal steps, field of view in z direction 3 cm, chirp pulse width 1.5 s. Double-tube REF IR-CPMG experiment: Relaxation delay 4 s, echo time 20 ms, acquisition matrix size 64 111, matrix size after processing 111 64, t1 list ranging from 0.02 s to 1.31 s, 111 values with equal steps. Silica 60 SS-IR-CPMG experiment: Relaxation delay 4 s, echo time 7 ms, acquisition matrix size 256 64, matrix size after processing 71 64 resulting in t1 list ranging from 0.03 s to 1.69 s, 71 values with equal steps, field of view in z direction 3 cm, chirp pulse width 2 s. Silica 60 REF IR-CPMG experiment: Relaxation delay 4 s, echo time 7 ms, acquisition matrix size 64 83, matrix size after processing 71 64, t1 list ranging from 0.5 ms to 5 s, including a range of 0.03 s to 1.69 s, 71 values with equal steps.
In all the SS experiments (1, 3, and 5) the chirp pulse bandwidth was 10 kHz and the smoothing factor was 1 %. The strength of the gradient applied during the chirp pulse was 0.16 G mm1 for the doped-water and double-tube samples (experiments 1 and 3) and 0.24 G mm1 for the silica sample (5). The read and dephase gradient amplitude was 0.79 G mm1, and the acquisition bandwidth was 100 kHz. Laplace inversion program provided by P. Callaghan (Victoria University of Wellington, New Zealand) was used for de 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org termining the relaxation distributions.[40] The program is based on the method published by Venkataramanan et al.[24, 25]
Acknowledgements We thank late Prof. P. Callaghan for providing the Laplace inversion program, Dr. Anu Kantola for her assistance in experimental issues, and Prof. Juha Vaara and Dr. Perttu Lantto for their valuable comments on the manuscript. Keywords: nuclear magnetic resonance · relaxation correlation · single-scan measurements · spectroscopy · twodimensional
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Received: November 26, 2013 Published online on March 13, 2014
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