Study of proton spin echoes in the nematic liquid crystalline phase

We studied spin echoes formed in the nematic crystalline phase using 90°- τ-β pulse sequence, where τ is the time between pulses and β the rotation produced by the second pulse. The decay of the echoes as a function of 2τ is nearly exponentail with a time constant T_E. Both T_E and the echo amplitude at a fixed τ were studied as a function of β in two nematics.     

Optimal echo spacing for multi-echo imaging measurements of Bi-exponential T2 relaxation

Calculations, analytical solutions, and simulations were used to investigate the trade-off of echo spacing and receiver bandwidth for the characterization of bi-exponential transverse relaxation using a multi-echo imaging pulse sequence. The Cramer–Rao lower bound of the standard deviation of the four parameters of a two-pool model was computed for a wide range of component T₂ values and echo spacing. The results demonstrate that optimal echo spacing (TE_opt) is not generally the minimal available given other pulse sequence constraints. The TE_opt increases with increasing value of the short T₂ time constant and decreases as the ratio of the long and short time constant decreases. A simple model of TE_opt as a function of the two T₂ time constants and four empirically derived scalars is presented.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

14N pulsed nuclear quadrupole resonance. 3. Effect of a pulse train. Optimal conditions for data averaging

The calculations developed in this paper aim at determining the optimal conditions of a NQR experiment when a transition is monitored by means of a pulse train with pulses of identical duration and signal acquisition after each pulse; coherences are assumed to vanish by effective transverse relaxation prior to every new pulse. These calculations demonstrate that, as in NMR, a steady state is effectively reached for any value of the recycle time. However, by contrast with NMR, it is shown that, for optimal data averaging under steady state conditions, the recycle time T can be kept as low as possible (the only limitation is the acquisition time). Nutation curves (signal amplitude versus pulse length) calculated in the steady state case are shown to depend strongly on the ratio T/T ₁ (T ₁: longitudinal relaxation time). The signal growth as a function of T/T ₁under averaging of the first transients has been evaluated as well as the number of pulses necessary for reaching a steady state.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.     

Single-Pulse Echo and Its Secondary Signals in Two-Level Spin Systems

The dependences of the amplitudes of single- and two-pulse spin echoes and their secondary signals in NMR (protons of glycerin in an inhomogeneous magnetic field) in the exciting-pulse repetition period T _r have been compared. The difference in origin of the primary and secondary signals of a single-pulse echo in a two-level spin system has been confirmed. It is shown that only a primary single-pulse echo observed when T _r > T ₁ (T ₁ is the spin lattice relaxation time) results from single-pulse excitation. The secondary single-pulse echo signals are observed for T _r < T ₁ and are due to the multiphase formation mechanism. The results obtained for magnetically ordered substances are analyzed. Based on these data, it was inferred earlier that primary and secondary single-pulse echo signals were formed by one and the same multiphase mechanism.     

Quasi-spin locking and simultaneous averaging of signal and baseline in dipolar solids

An alternating train of solid echoes and zero signals obtained by a 90° pulse sequence could be prolonged for a time of the order of T_1?. This quasi-spin locking effect enables one to average simultaneously the signal of the transverse magnetization and the baseline at a high data rate.     

The proton relaxation of CH3OD in the presence of Co(II) ions,as studied by spin-echo techniques

By measurement of the proton relaxation times T ₁ and T ₂ of CH₃OD containing Co⁺⁺ ions in dilute solution and the dependence of the observed decay time (T ₂ ^?) on t _ep the separation between pulses in a Carr-Purcell sequence the coordination number is shown to be six. Since this result has previously been obtained by an independent method, the use of the dependence of T ₂ ^? on t _ep to determine coordination numbers is justified for solutions of paramagnetic ions. The validity of analytical expressions derived previously has been checked by numerical methods, and the analytical expression is shown to be valid even in the presence of H ₀ and H ₁ inhomogeneity and inaccurate pulses of finite duration, provided that the Meiboom-Gill method is used. In an Appendix insight derived from the results of the numerical solutions is used to give a brief derivation of the dependence of T ₂ ^? on H ₀, exchange rate and t _ep.     

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.     

Spin echo SPI methods for quantitative analysis of fluids in porous media

Fluid density imaging is highly desirable in a wide variety of porous media measurements. The SPRITE class of MRI methods has proven to be robust and general in their ability to generate density images in porous media, however the short encoding times required, with correspondingly high magnetic field gradient strengths and filter widths, and low flip angle RF pulses, yield sub-optimal S/N images, especially at low static field strength. This paper explores two implementations of pure phase encode spin echo 1D imaging, with application to a proposed new petroleum reservoir core analysis measurement.In the first implementation of the pulse sequence, we modify the spin echo single point imaging (SE-SPI) technique to acquire the k-space origin data point, with a near zero evolution time, from the free induction decay (FID) following a 90° excitation pulse. Subsequent k-space data points are acquired by separately phase encoding individual echoes in a multi-echo acquisition. T₂ attenuation of the echo train yields an image convolution which causes blurring. The T₂ blur effect is moderate for porous media with T₂ lifetime distributions longer than 5 ms. As a robust, high S/N, and fast 1D imaging method, this method will be highly complementary to SPRITE techniques for the quantitative analysis of fluid content in porous media.In the second implementation of the SE-SPI pulse sequence, modification of the basic measurement permits fast determination of spatially resolved T₂ distributions in porous media through separately phase encoding each echo in a multi-echo CPMG pulse train. An individual T₂ weighted image may be acquired from each echo. The echo time (TE) of each T₂ weighted image may be reduced to 500 μs or less. These profiles can be fit to extract a T₂ distribution from each pixel employing a variety of standard inverse Laplace transform methods. Fluid content 1D images are produced as an essential by product of determining the spatially resolved T₂ distribution. These 1D images do not suffer from a T₂ related blurring.The above SE-SPI measurements are combined to generate 1D images of the local saturation and T₂ distribution as a function of saturation, upon centrifugation of petroleum reservoir core samples. The logarithm mean T₂ is observed to shift linearly with water saturation. This new reservoir core analysis measurement may provide a valuable calibration of the Coates equation for irreducible water saturation, which has been widely implemented in NMR well logging measurements.     

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.     

Pattern recognition for rapid T2 mapping with stimulated echo compensation

Indirect echoes (such as stimulated echoes) are a source of signal contamination in multi-echo spin-echo T₂ quantification and can lead to T₂ overestimation if a conventional exponential T₂ decay model is assumed. Recently, nonlinear least square fitting of a slice-resolved extended phase graph (SEPG) signal model has been shown to provide accurate T₂ estimates with indirect echo compensation. However, the iterative nonlinear least square fitting is computationally expensive and the T₂ map generation time is long. In this work, we present a pattern recognition T₂ mapping technique based on the SEPG model that can be performed with a single pre-computed dictionary for any arbitrary echo spacing. Almost identical T₂ and B₁ maps were obtained from in vivo data using the proposed technique compared to conventional iterative nonlinear least square fitting, while the computation time was reduced by more than 14-fold.     

The influence of stimulated echoes on contrast in fast spin-echo imaging

Tissue contrast obtained using fast spin-echo (FSE) and conventional spin-echo (SE) sequences is not identical and a number of mechanisms are thought to contribute to these contrast differences. The effect of stimulated echoes has previously been apparently ruled out as a contributing mechanism. Signal-to-noise ratios of single-slice matched FSE and conventional SE sequences were compared in aqueous solutions of CuSO₄, Cr₂(SO₄)₃ and MnSO₄ with various T₁ and T₂ values. Enhancement of the FSE signal was observed in short T₂ solutions and the effect was greater in samples where the T₁ to T₂ ratio was high. Reducing the refocusing pulse flip angle to increase the contribution from stimulated echoes also resulted in slightly increased enhancement. Experimental results were verified by computer simulations. Our results show that stimulated echoes do contribute to the contrast differences between FSE and conventional SE images and may be significant in the imaging of brain hemorrhage.     

Anomalous pulse angle dependence of the single and double quantum echoes in a photoinduced spin-correlated coupled radical pair

In this work the response of a spin-correlated coupled radical pair to the sequence flash-t-P _ζ-τ-P _2ζ-T is investigated. For the theoretical analysis, the density operator formalism is used. Analytical expressions are derived for the electron spin single (SQ ESE) and double-quantum echoes (DQ ESE) as a function of pulse flip angle and singlet-triplet mixing angle. To illustrate the theoretical results, computer simulations are presented. In the limit of weak coupling, the “out-of-phase” SQ ESE is shown to be of a pure two-spin order having the maximal amplitude for the flip angle of 65.9°. The echo following the Hahn sequence vanishes in the same limit. This confirms the theoretical result already presented in the literature. However, the more general analysis shows that outside the weak coupling approximation the Hahn echo is of purely one-spin order, whereas the echo following the flash-t-P _ζ-τ-P _2ζ-t sequence has its maximal amplitude for the flip angle of 75° and the singlet-triplet mixing angle of 27°. The “in-phase” single- and double-quantum echoes are shown to vanish due to averaging out, within the electron spin resonance spectrometer deadtime, of contributions modulated with the sum and difference of the zero-quantum beat frequency and the frequency due to the spin-spin interaction within the pair. The calculated out-of-phase DQ ESE signal is inverted with respect to the out-of-phase SQ ESE and has only the half of its amplitude. The DQ ESE vanishes for the Hahn sequence. The echo has maximal amplitude in the weak-coupling limit for the flip angle of 65.9°. In contradiction to the analytical result previously published, the out-of-phase DQ ESE does not vanish for long τ and large zero-quantum-beat frequency.     

NMR relaxation study of avocado quality

Four nuclear magnetic resonance relaxation protocols are investigated as potential candidates for off-line and on-line determination of avocado maturity. Two-dimensionalT ₁-T ₂ andT ₂-D correlation spectroscopy provides the most information but is only suitable for off-line quality control. The CPMGT ₂ spectrum gives avocado oil content but requires intensive data processing. Suppression of the tissue water signal byT ₁-Null methods is shown to be unreliable but a new, single-shot pulse sequence which uses diffusive attenuation to suppress the tissue water is shown to give a good correlation with oil content and is suitable for both off-line and on-line implementation.     

Slow Dynamics Mapping of Large-Linewidth Solids by a MARF Spin-Lock Filter

A new method forT_1ρcontrast in solid-state imaging is presented. The method is based upon the addition of aT_1ρspin-lock pulse to the standard MARF pulse sequence and is able to provide relaxation contrast in dependence either on the lock time or on the intensity of the lock field, without having effects related to the line-narrowing procedure. The results on some large-linewidth solids show thatT_1ρvalues measured by the usual spin-lock pulse sequence agree with those measured on space-resolved lines.     

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.     

Sublevel echoes induced by resonant light pulses: Quantum beat echoes

We predict and observe a new class of echoes of atomic sublevel coherences induced by two impact excitations with resonant light pulses which may be either coherent or incoherent. The Zeeman-sublevel echoes in 3 ²S_{$\text{1}\text{2}$} of sodium were observed by using polarization selective detection technique under the excitation condition that the optical T₂ (5 × 10^-11 s) was much shorter than the pulse width (5 ns). Theoretical analysis also predicts the echoes involving coherence transfer between ground and excited states.     

Effect of excited state absorption on the transmissivity of organic-dye-based media under two-photon excitation

duration ranging from femtoseconds to nanoseconds has been simulated. The effect of the absorption from excited singlet and triplet states on the transmissivity of the medium under two-photon excitation has been investigated. It has been shown that in a medium excited by monopulses, the S ₁→ S _n and T ₁→ T _m absorption makes a considerable contribution to the total nonlinear absorption of the medium only for nanosecond pulse durations. When a medium is excited by a sequence of femtosecond pulses with a repetition frequency of some tens of megahertz, significant additional nonlinear absorption can arise only due to T ₁→T _m transitions that occur due to accumulation of molecules in triplet states. This effect should be taken into account in determining the cross-section for two-photon absorption in dyes and also in developing radiation intensity limiters for femtosecond lasers.     

Detection of glutamate and glutamine (Glx) by turbo spectroscopic imaging

Turbo spectroscopic imaging (TSI) is a spin echo spectroscopic imaging technique in which two or more echoes are acquired per excitation to reduce the acquisition time. The application of TSI has primarily been limited to the detection of uncoupled spins because the signal from coupled spins is modulated as a function of echo time. In this work we demonstrate how the TSI sequence can be modified to observe spins like the C₂ protons of Glx (≈3.75 ppm) which are involved solely in weak-coupling interactions. The technique exploits the chemical shift displacement effect by employing TSI refocusing pulses that have bandwidths which are less than the chemical shift difference between the target spins and the spins to which they are weakly coupled. The modified TSI sequence rewinds the J-evolution of the target protons in the slice of interest independently of the echo time or echo spacing, thereby removing any signal variation between successive echoes (apart from T₂ relaxation effects). In this study we tailored the narrow-bandwidth TSI sequence for observation of the C₂ Glx protons. The echo time was experimentally optimized to minimize signal contamination from myo-inositol, and the efficacy of the method was verified on phantom solutions of Glx and on brain in vivo.