Flip-back, an old trick to face highly contrasted relaxation times: application in the characterization of pharmaceutical mixtures by CPMAS NMR

The ¹³C–¹H CPMAS with flip-back pulse NMR experiment is revisited in view of applications to pharmaceutical mixtures. The analysis of the kinetics of relaxation and CP transfer with and without the flip-back pulse shows that a significant gain in ¹³C signal can be expected (thus in experimental time) from the flip-back pulse for protons with long T₁. The gain is of the order of T₁ of the protons expressed in seconds. The experiment is applied on samples with highly contrasted spin-lattice relaxation times T₁ for protons, situation encountered in pharmaceutical mixtures. The application of the flip-back increases significantly the relative signal intensity of the component with the longer T₁, making this component detectable even after using short recycle delays. Therefore, this CPMAS with flip-back experiment could be used routinely to get ¹³C CPMAS NMR spectra of mixtures in constant experimental time and signal-to-noise ratio without the need for optimization of the recycle delays, and for whatever may be the degree of crystallinity of the active principal ingredient (API) and/or excipients.     

T1 and T2 effects during radio-frequency pulses in spoiled gradient echo sequences

Finite pulse durations in diverse pulse schemes lead to the reduction of the magnitude of the magnetization vector due to T₁ and T₂ effects during the radio-frequency pulses. This paper presents an analysis of the steady state signal in the presence of relaxation effects during radio-frequency pulses in MRI spoiled gradient echo sequences. It is shown that minor attenuations of the magnetization vector can have dramatic consequences on the measured signal, and may thus entail a loss in SNR benefits at high static magnetic fields if a careful analysis is not performed. It is emphasized that it is the time-integrated magnetization vector trajectory that matters for these effects and not only the pulse duration. Some experimental results obtained on a phantom at 3 T verify this analysis.     

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (¹⁴N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T ₁ (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T ₂ (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.     

New pulse sequences for T1− and T1/T2−contrast enhancing in NMR imaging

Improved pulse sequences DIFN (abbreviation of the words: DIFferentiation by N pulses), 90° − τ₁ − 180° − τ₁ − … 180° − τ_n, with optimised time intervals τ₁ for T₁ measurement and contrast enhancing in NMR imaging are presented. The pulse sequences DIFN have a better sensitivity to T₁ than the well-known pulse sequence SR. In contrast to the IR pulse sequence, the information given by the DIFN pulse sequence is more reliable, because the NMR signal does not change its sign. For a given time interval τ₀ ≤ (0.1 − 0.3) T₁′ the DIFN pulse sequences serve as T₁-filters. They pass the signal components with relatively short T₁ < T₁′ and suppress the components with relatively long T₁ < T₁′. The effects of the radiofrequency field inhomogeneity and inaccurate adjusting of pulse lengths are also considered. It is also proposed in this work to use the joint T₁T₂-contrast in NMR imaging obtained as a result of applying the DIFN pulse sequences in combination with the well-known Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The region of interest, where the contrast should be especially enhanced, is specified by the two times at which measurements are performed, which allow the amplitudes of pixels to reach some defined levels by spin-lattice and spin-spin relaxation.     

The application of steady-state free precession in rapid 2DFT NMR imaging: FAST and CE-FAST sequences

In the classic spectroscopic steady-state free precession (SSFP) experiment, a regular sequence of phase-coherent radio frequency pulses is applied with constant flip angle and a repetition time shorter than the NMR relaxation times of the sample. As the steady state is reached, an NMR signal appears between pulses that consists of two distinct components: a free induction signal following the RF pulses and decaying during the repetition interval and a spin-echo-like signal forming at its end prior to the subsequent RF pulse. Both signals may be exploited for NMR imaging if the gradient schemes fulfill the phase coherence requirements of SSFP. This article describes two Fourier acquired steady-state sequences dubbed FAST and CE-FAST, which may be used for the rapid acquisition of NMR images from the SSFP signals.     

Emulation of petroleum well-logging D-T2 correlations on a standard benchtop spectrometer

An experimental protocol is described that allows two-dimensional (2D) nuclear magnetic resonance (NMR) correlations of apparent diffusion coefficient D_app and effective transverse relaxation time T_2,eff to be acquired on a bench-top spectrometer using pulsed field gradients (PFG) in such a manner as to emulate D_app − T_2,eff correlations acquired using a well-logging tool with a fixed field gradient (FFG). This technique allows laboratory-scale NMR measurements of liquid-saturated cored rock to be compared directly to logging data obtained from the well by virtue of providing a comparable acquisition protocol and data format, and hence consistent data processing. This direct comparison supports the interpretation of the well-logging data, including a quantitative determination of the oil/brine saturation. The D − T₂ pulse sequence described here uses two spin echoes (2SE) with a variable echo time to encode for diffusion. The diffusion and relaxation contributions to the signal decay are then deconvolved using a 2D numerical inversion. This measurement allows shorter relaxation time components to be probed than in conventional diffusion measurements. A brief discussion of the numerical inversion algorithms available for inverting these non-rectangular data is included. The PFG-2SE sequence described is well suited to laboratory-scale studies of porous media and short T₂ samples in general.     

Radiofrequency pulse sequences which compensate their own imperfections. 1980

Radiofrequency pulse sequences are described which have the same overall effect as a single 90° or 180° pulse but which compensate the undesirable effects of resonance offset and spatial inhomogeneity of the radiofrequency field H₁. These “composite” pulses are built up from a small number of conventional pulses which rotate the nuclear magnetization vectors about different axes in the rotating frame, while in the intervals between pulses a limited amount of free precession may be allowed to occur. Insight into the way in which pulse imperfections are compensated is obtained by computer simulation of trajectories of families of nuclear spin “isochromats” representing a distribution of H₁ intensity or resonance offset. Composite 90° pulses are suggested as a method of reducing systematic errors in spin-lattice relaxation times derived from progressive saturation or saturation-recovery experiments, and as the preparation pulse of a spin-locking experiment. A test of the effectiveness of the composite 180° pulse sequence has been made by using it for population inversion in a spin-lattice relaxation measurement, where T₁ is derived from the null point in the recovery curve, a technique known to be very sensitive to pulse imperfections.     

Generation of picosecond and subpicosecond light pulses with saturable absorbers

Single light pulses, generated by a mode-locked Nd-glass laser, were shortened with saturable absorbers of low initial transmissionT ₀. The pulse duration was reduced from 8 to 2.6 ps after a single pass through a dye cell ofT ₀=10^–7. Light pulses as short as 0.5 ps were observed after five transits through an absorberamplifier system. Detailed calculations of the stationary and the transient situation (with respect to the dye relaxation time) are presented to demonstrate optimum conditions for the pulse shortening.     

NMR and quantum chemistry study of mesoscopic structuring in 3-methylpyridine/water/NaBr mixture in the vicinity of the phase separation boundary

²³Na and ⁸¹Br NMR spin-lattice relaxation times and signal half widths (Δ_1/2) have been measured in 3-methylpyridine (3MP)/H₂O/NaBr mixture along T?=?294 and 301 K isotherms gradually increasing the mass fractions of salt (X) up to the phase separation boundary. The extreme narrowing condition and thus 1/T ₁?=?1/T ₂?=?πΔ _1/2 was found to be valid in all cases. Discontinuous changes in slope of 1/T _1,2?=?f(X) were detected, and then corresponding points on the phase diagram (X, T) were attributed to the borderline between the molecular-ionic solution and the area of enhanced mesoscopic structuring. A very strong relaxation effect was observed for ⁸¹Br nuclei reaching relaxation rates of 14,000 s^–1. ²³Na and ⁸¹Br NMR relaxation data together with calculations of quantum chemistry model of electrical field gradient tensor evidence the migration of 3-methylpyridinium at increasing X from the anions hydration shells towards cations. An interchange from migration to steady distribution regimes is observed for anions and vice versa for cations at the borderline of the structured phase.     

NMR Study of Water Distribution inside Tomato Cells: Effects of Water Stress

Tomato pericarp tissue was studied by low-field nuclear magnetic resonance (NMR) relaxometry. Two kinds of experiments were performed to investigate the correlation between multi-exponential NMR relaxation and the subcellular compartments. The longitudinal (T ₁) versus transverse (T ₂) relaxation times were first measured on fresh samples and then the transverse relaxation time was measured on samples exposed to water stress. Four signal components were found in all experiments. The results showed that all signal components corresponded to the water in different cell compartments, and that no signal from non-exchangeable protons was present. Moreover, we demonstrated that NMR relaxation is suitable for the continuous monitoring of water rebalancing between subcellular compartments of plant tissues.     

Fiber modification by steam-explosion: 13C NMR and dynamic mechanical analysis studies of co-refined wood and polypropylene

Wood-plastic material from a novel reactive processing method (co-refining by steam-explosion) was investigated by ¹³C solid state nuclear magnetic resonance (NMR) and dynamic mechanical analysis (DMA). NMR spectra indicated chemistry of the material changed as a result from co-steam-explosion. It was also observed from NMR analysis that the crystallinity of the cellulose increased in the presence of iPP during steam-explosion co-processing. By using variable contact time cross pulse experiments, the relaxation parameters (T _CH and T _1ρ ) for the constitutive components were evaluated to reveal the level of interactions. T _1ρ values for steam-exploded wood had values similar to those published in literature, which are independent relaxation values for lignin and cellulose. However, for co-steam-exploded wood and iPP, the independent value of lignin relative to the amorphous cellulose was absent. It is proposed that lignin adopts an alternate arrangement during co-steam-explosion processing. This arrangement is transient because the independent relaxation of lignin is recovered after the application of heat during compression molding. DMA demonstrated a mechanical reinforcing effect of the steam-exploded wood without influencing the glass transition of polypropylene for the compression molded co-steam-exploded sample. The paper concludes by describing a hypothetical scheme for a meta-stable interaction of wood bio-polymers and iPP.     

Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Flow propagators, used for the study of advective motion of brine solution in porous carbonate and sandstone rocks, have been obtained without the influence of Nuclear Magnetic Resonance (NMR) relaxation times, T₁ and T₂. These spin relaxation mechanisms normally result in a loss of signal that varies depending on the displacement ζ of the flowing spins, thereby preventing the acquisition of quantitative propagator data. The full relaxation behaviour of the system under flow needs to be characterised to enable the implementation of a true quantitative measurement. Two-dimensional NMR correlations of ζ − T₂ and T₁ − T₂ are used in combination to provide the flow propagators without relaxation weighting. T₁ − ζ correlations cannot be used due to the loss of T₁ information during the displacement observation time Δ. Here the moments of the propagators are extracted by statistical analysis of the full propagator shape. The measured displacements (first moments) are seen to correlate with the expected mean displacements for long observation times Δ. The higher order moments of the propagators determined by this method indicate those obtained previously using a correction were overestimated.     

A New Approach of Two-Dimensional the NMR Relaxation Measurement in Flowing Fluid

Driven-equilibrium fast saturation recovery (DEFSR), as a new method for two-dimensional (2-D) nuclear magnetic resonance (NMR) relaxation measurement based on pulse sequence in flowing fluid, is proposed. The two-dimensional functional relationship between the ratio of transverse relaxation time to longitudinal relaxation time of fluid (T ₁/T ₂) and T ₁ distribution is obtained by means of DEFSR with only two one-dimensional measurements. The rapid measurement of relaxation characteristics for flowing fluid is achieved. A set of the down-hole NMR fluid analysis system is independently designed and developed for the fluid measurement. The accuracy and practicability of DEFSR are demonstrated.     

Spectral estimation of NMR relaxation

In this paper, spectral estimation of NMR relaxation is constructed as an extension of Fourier Transform (FT) theory as it is practiced in NMR or MRI, where multidimensional FT theory is used. nD NMR strives to separate overlapping resonances, so the treatment given here deals primarily with monoexponential decay. In the domain of real error, it is shown how optimal estimation based on prior knowledge can be derived. Assuming small Gaussian error, the estimation variance and bias are derived. Minimum bias and minimum variance are shown to be contradictory experimental design objectives. The analytical continuation of spectral estimation is constructed in an optimal manner. An important property of spectral estimation is that it is phase invariant. Hence, hypercomplex data storage is unnecessary. It is shown that, under reasonable assumptions, spectral estimation is unbiased in the context of complex error and its variance is reduced because the modulus of the whole signal is used. Because of phase invariance, the labor of phasing and any error due to imperfect phase can be avoided. A comparison of spectral estimation with nonlinear least squares (NLS) estimation is made analytically and with numerical examples. Compared to conventional sampling for NLS estimation, spectral estimation would typically provide estimation values of comparable precision in one-quarter to one-tenth of the spectrometer time when S/N is high. When S/N is low, the time saved can be used for signal averaging at the sampled points to give better precision. NLS typically provides one estimate at a time, whereas spectral estimation is inherently parallel. The frequency dimensions of conventional nD FT NMR may be denoted D₁, D₂, etc. As an extension of nD FT NMR, one can view spectral estimation of NMR relaxation as an extension into the zeroth dimension. In nD NMR, the information content of a spectrum can be extracted as a set of n-tuples (ω₁, … ω_n), corresponding to the peak maxima. Spectral estimation of NMR relaxation allows this information content to be extended to a set of (n + 1)-tuples (λ, ω₁, … ω_n), where λ is the relaxation rate.     

In vivo NMR T2 relaxation of experimental brain tumors in the cat: A multiparameter tissue characterization

Experimental gliomas (F98) were inoculated in cat brain for the systematic study of their in vivo T₂ relaxation time behavior. With a CPMG multi-echo imaging sequence, a train of 16 echoes was evaluated to obtain the transverse relaxation time and the magnetization M(0) at time t = 0. The magnetization decay curves were analyzed for biexponentiality. All tissues showed monoexponential T₂, only that of the ventricular fluid and part of the vital tumor tissue were biexponential. Based on these NMR relaxation parameters the tissues were characterized, their correct assignment being assured by comparison with histological slices. T₂ of normal grey and white matter was 74 ± 6 and 72 ± 6 msec, respectively. These two tissue types were distinguished through M(0) which for white matter was only 0.88 of the intensity of grey matter in full agreement with water content, determined from tissue specimens. At the time of maximal tumor growth and edema spread a tissue differentiation was possible in NMR relaxation parameter images. Separation of the three tissue groups of normal tissue, tumor and edema was based on T₂ with T_2(normal) < T_2(tumor) < T_2(edema). Using M(0) as a second parameter the differentiation was supported, in particular between white matter and tumor or edema. Animals were studied at 1–4 wk after tumor implantation to study tumor development. The magnetization M(0) of both tumor and peritumoral edema went through a maximum between the second and third week of tumor growth. T₂ of edema was maximal at the same time with 133 ± 4 msec, while the relaxation time of tumor continued to increase during the whole growth period, reaching values of 114 ± 12 msec at the fourth week. Thus, a complete characterization of pathological tissues with NMR relaxometry must include a detailed study of the developmental changes of these tissues to assure correct experimental conditions for the goal of optimal contrast between normal and pathological regions in the NMR images.     

180° Pulse Imperfection Effects on Fitting of Relaxation Curves Obtained by Low Field NMR Spectroscopy

Low field NMR spectroscopy is well adapted to the study of heterogeneous media, such as those found in the food industry or in life sciences, because it does not require preparation of samples.

CPMG relaxation curves obtained with different pulse spacing times, on samples without exchange phenomenon, are not superimposable. We show that this phenomenon, due to pulse imperfections at 180°, is not a single drift; pulses reach a stationary regime towards the 80^th pulse; values of T₂ of the order of milliseconds, are then a bit perturbed. For the same reason, with a liquid sample, the total signal of a CPMG curve does not exactly correspond to the total signal obtained with a FID curve. With some fitting programs, by iterating on the value of the offset in order to minimise the standard deviation of the relaxation curve fitting, it is no longer necessary to know the value of the baseline of the CPMG relaxation curves; it enables one to better sample the first part of the curve.     

MSE-MRI sequence optimisation for measurement of bi- and tri-exponential T2 relaxation in a phantom and fruit

The transverse relaxation signal from vegetal cells can be described by multi-exponential behaviour, reflecting different water compartments. This multi-exponential relaxation is rarely measured by conventional MRI imaging protocols; mono-exponential relaxation times are measured instead, thus limiting information about of the microstructure and water status in vegetal cells. In this study, an optimised multiple spin echo (MSE) MRI sequence was evaluated for assessment of multi-exponential transverse relaxation in fruit tissues. The sequence was designed for the acquisition of a maximum of 512 echoes. Non-selective refocusing RF pulses were used in combination with balanced crusher gradients for elimination of spurious echoes. The study was performed on a bi-compartmental phantom with known T₂ values and on apple and tomato fruit. T₂ decays measured in the phantom and fruit were analysed using bi- and tri-exponential fits, respectively. The MRI results were compared with low field non-spatially resolved NMR measurements performed on the same samples.     

Magnetic Resonance Imaging of Gases: A Single-Point Ramped Imaging with T1 Enhancement (SPRITE) Study

A pure phase-encoding MRI technique, single-point ramped imaging withT₁enhancement, SPRITE, is introduced for the purpose of gas phase imaging. The technique utilizes broadband RF pulses and stepped phase encode gradients to produce images, substantially free of artifacts, which are sensitive to the gasT₁andT^*:₂relaxation times. Images may be acquired from gas phase species with transverse relaxation times substantially less than 1 ms. Methane gas images,¹H, were acquired in a phantom study. Sulfur hexafluoride,¹⁹F, images were acquired from a gas-filled porous coral sample. High porosity regions of the coral are observed in both the MRI image and an X-ray image. Sensitivity and resolution effects due to signal modulation during the time-efficient acquisition are discussed. A method to increase the image sensitivity is discussed, and the predicted improvement is shown through 1D images of the methane gas phantom.     

Time-shift quantum key distribution with decoy states

We suggest a protocol for quantum key distribution—a technology allowing two distant parties to create an unconditionally secure cryptographic key. For the creation of the key we suggest to use laser pulses weakened to the single-photon level of duration T, the pulse carrying the value “1” being shifted in time by T/2 compared to the pulse carrying the value “0”. The overlap of the pulses provides their non-orthogonality and, therefore, impossibility to discriminate between them with certainty. Besides the signal pulses the protocol uses coherent decoy pulses, having longer duration than the signal ones and providing a more effective protection from a wide class of attacks. Security of the protocol is based on interferometric control of the pulse coherence at the receiving station. We analyze the security of the protocol against a number of intercept-resend attacks and on the basis of this analysis substantiate the necessity of decoy state implementation.     

Electronic states of boron in superconducting MgB2 studied by11B NMR

Nuclear magnetic resonance (NMR) spectra and nuclear spin-lattice relaxation rateT ₁⁻¹ of¹¹B have been measured in superconducting polycrystalline MgB₂ with 7_c^ons = 39.5 K. It is shown that (T ₁T⁻¹ and the Knight shiftK _s are independent of temperature and nearly isotropic aboveT _c. Both of these quantities are decreased gradually in going to the superconducting state. According to NMR data the density of states near the Fermi level is flat at the scale of about 500 K. Some conclusions on the orbital content of the density of states at the Fermi level were drawn and compared with the results of the band structure calculations.