Coherence Pathways Research Articles

Spectral Quantum Beating in Mixed Frequency/Time-Domain Coherent Multidimensional Spectroscopy

Coherent multidimensional spectroscopy performed in the mixed frequency/time domain exhibits both temporal and spectral quantum beating when two quantum states are simultaneously excited. The excitation of both quantum states can occur because either the spectral width of the states or the excitation pulse exceeds the frequency separation of the quantum states. The quantum beating appears as a line that broadens and splits into two peaks and then recombines as the time delay between excitation pulses increases. The splitting depends on the spectral width of the excitation pulses. We observe the spectral quantum beating between the two nearly degenerate asymmetric carbonyl stretch modes in a nickel tricarbonyl chelate using the nonrephasing, ground state bleaching coherence pathway in triply vibrationally enhanced four-wave mixing as the time delay between the first two excitation pulses changes.

Encoding of diffusion and T1 in the CPMG echo shape: single-shot D and T1 measurements in grossly inhomogeneous fields

Abstract We present a new approach of NMR measurements in the presence of grossly inhomogeneous fields where information is encoded in the echo shape of CPMG trains. The method is based on sequences that consist of an initial encoding sequence that generates echoes with contributions from at least two different coherence pathways that are then both refocused many times by a long string of closely spaced identical pulses. The generated echoes quickly assume an asymptotic shape that encodes the information of interest. High signal-to-noise ratios can be achieved by averaging the large number of echoes. We demonstrate this approach with different implementations of the measurements of longitudinal relaxation time, T 1 , and diffusion coefficient, D . It is shown that the method can be used for novel single-shot measurements.

Coherence pathway selection by cogwheel phase cycling in liquid‐state NMR

AbstractCoherence selection as an integral element of most multipulse NMR methods also represents a bottleneck to the efficiency of multidimensional NMR methods. In particular, phase cycling often requires total scan numbers in excess of signal‐to‐noise demands. M. H. Levitt and coworkers have recently introduced cogwheel phase cycling in solid‐state NMR, which improves on this problem. In this article we recapitulate the principles of coherence selection in multipulse and multidimensional NMR. The fundamental differences between various coherence selection strategies are discussed, and examples of implementing cogwheel phase cycling in liquid‐state NMR experiments commonly used for biopolymers are given. Design guidelines are suggested for incorporating cogwheel phase cycles into other pulsed NMR techniques. For experiments with multiple coherence transfer steps, cogwheel phase cycling is more efficient in spectrometer time usage than traditional nested phase cycling, as the scan numbers can be adjusted in smaller steps. Even compared with pulsed field gradient selection methods advantages exist, especially for fast relaxing resonances. © 2007 Wiley Periodicals, Inc. Concepts Magn Reson Part A 30A: 81–99, 2007.

Using error correction to determine the noise model

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterize noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of $c=0.5\ifmmode\pm\else\textpm\fi{}0.2$ using the error correction protocol, and $c=0.3\ifmmode\pm\else\textpm\fi{}0.2$ using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.

Encoding of diffusion and T1 in the CPMG echo shape: Single-shot D and T1 measurements in grossly inhomogeneous fields

We present a new approach of NMR measurements in the presence of grossly inhomogeneous fields where information is encoded in the echo shape of CPMG trains. The method is based on sequences that consist of an initial encoding sequence that generates echoes with contributions from at least two different coherence pathways that are then both refocused many times by a long string of closely spaced identical pulses. The generated echoes quickly assume an asymptotic shape that encodes the information of interest. High signal-to-noise ratios can be achieved by averaging the large number of echoes. We demonstrate this approach with different implementations of the measurements of longitudinal relaxation time, T 1, and diffusion coefficient, D. It is shown that the method can be used for novel single-shot measurements.

A nomenclature and data model to describe NMR experiments

Despite ongoing efforts in organising NMR information, there is no consistent and well-described generic standard for naming NMR experiments. The main reason for the absence of a universal naming system is that the information content of the coherence pathways is difficult to describe in full detail. We propose a system that describes the common and generic elements of the coherence pathways produced by pulse sequences. The system itself is formalised by an 'NMR experiment protocol' model, which is described in the Universal Modelling Language (UML) as part of the CCPN data model. Furthermore, normalized experiment names can be derived from this proposed model. We hope this article will stimulate discussion to organise the wealth of NMR experiments, and that by bringing this discussion into the public domain we can improve and expand our proposed system to include as much information and as many NMR experiments as possible.

Interferometric Coherence Transfer Modulations in Triply Vibrationally Enhanced Four-Wave Mixing

Triply vibrationally enhanced (TRIVE) four-wave mixing (FWM) spectroscopy in a mixed frequency/time domain experiment contains new output coherences that isolate nonlinear pathways that involve coherence transfer. Coherence transfer occurs when a thermal bath induces coupling between two states so a quantum mechanical entanglement of a pair of quantum states evolves to entangle a new pair of quantum states. The FWM includes several equivalent coherence pathways that interfere and create a temporal modulation of the output coherence that is a signature of coherence transfer. The transfer shifts the output coherence frequency and isolates coherence transfer pathways from the stronger FWM processes that form the basis of coherent multidimensional spectroscopy. The use of coherence transfer offers the opportunity for another form of coherent multidimensional spectroscopy where cross-peaks appear because of the coherence transfer between quantum states. Since this approach is based on frequency domain methods, it requires only short-term phase coherence during the excitation process so the method is not constrained to accessing the quantum states lying within the excitation pulse bandwidth.

Robust prescan calibration for multiple spin-echo sequences: application to FSE and b-SSFP

The collection of fast imaging techniques that use multiple spin-echo (MSE) sequences relies on a precise phase relationship between spin echoes and stimulated echoes that form along the radiofrequency refocusing pulse train. Failure to achieve this condition produces dark banding artifacts that result from destructive interference between signal coherence pathways. Satisfying this condition on the microsecond timescale required is technically challenging for conditions involving strong diffusion-weighted gradients, for arbitrary orientation acquisitions and at large field strengths with high-resolution acquisitions. Two clinically significant MSE sequences, fast spin echo (FSE) and balanced steady-state free precession (b-SSFP), are investigated in this work using a 4-T whole-body scanner. We developed a readout-projection-based prescan technique that ensures coherent signal formation by utilizing banding artifacts to automatically adjust gradient balance. Subsequent image acquisition using the results of this prescan permits the formation of coherent-echo images, which are robust under challenging imaging conditions. The robustness of this approach is demonstrated for FSE and b-SSFP images obtained from the knees of human volunteers. We believe that the use of this prescan calibration technique for the alignment of signal pools in MSE sequences is critical at high fields and will facilitate the implementation of high-quality clinically significant sequences such as FSE and b-SSFP.

Mixed Frequency/Time Domain Optical Analogues of Heteronuclear Multidimensional NMR

Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.

SPAM-MQ-HETCOR: an improved method for heteronuclear correlation spectroscopy between quadrupolar and spin-1/2 nuclei in solid-state NMR

The recently introduced concept of soft pulse added mixing (SPAM) is used in two-dimensional heteronuclear correlation (HETCOR) NMR experiments between half-integer quadrupolar and spin-1/2 nuclei. The experiments employ multiple quantum magic angle spinning (MQMAS) to remove the second order quadrupolar broadening and cross polarization (CP) or refocused INEPT for magnetization transfer. By using previously unexploited coherence pathways, the efficiency of SPAM-MQ-HETCOR NMR is increased by a factor of almost two without additional optimization. The sensitivity gain is demonstrated on a test sample, AlPO(4)-14, using CP and INEPT to correlate (27)Al and (31)P nuclei. SPAM-3Q-HETCOR is then applied to generate (27)Al-(31)P spectra of the devitrified 41Na(2)O-20.5Al(2)O(3)-38.5P(2)O(5) glass and the silicoaluminophosphate ECR-40. Finally, the method allowed the acquisition of the first high resolution solid-state correlation spectra between (27)Al and (29)Si.

Single scan TROSY and E.COSY suite of experiments for the measurement of residual dipolar couplings in proteins

Simple modifications of the gradient enhanced version of the TROSY experiment allow to obtain four different spectra containing each one of the components of the H–N doublet in 15N labelled proteins. By measuring the difference in peak position among these four spectra, residual dipolar coupling values can be obtained for medium sized proteins. This experiment, which exploits the use of pulse field gradients to select the 15N coherence pathway, produces excellent results in terms of water suppression. Moreover, tuning of a single delay in the sequence reduces notably the presence of artifacts. The performance of this suite of experiments, that we called TEC (Trosy–E.Cosy) experiment, is tested against a J‐modulation method, inherently more accurate but more time consuming, for the accuracy in the observed values of residual dipolar couplings. For larger proteins, the use of this strategy allows to select the most favourable combination of peaks giving the sharpest signals.

A phase rotation scheme for achieving very short echo times with localized stimulated echo spectroscopy

In a single-voxel stimulated echo localization sequence in magnetic resonance spectroscopy, magnetic field gradients are inserted within the echo time (TE) to filter signals generated through coherence pathways other than that leading to the stimulated echo. There is a significant penalty for these gradients as they increase the minimum TE, thereby leading to significant signal loss from spin-spin relaxation and phase distortions in coupled spin systems. Here, an RF phase rotation technique is described for a stimulated echo localization sequence that allows removal of the gradients in the TE intervals and, subsequently, reduction of the minimum TE to only 6 ms. Experiments carried out on six healthy volunteers on a 1.5-T whole-body MR system show a significant signal increase in the metabolite concentrations when measured with a 6-ms TE (N-acetyl-aspartate, 12%, P=.002; creatine, 15%, P=.04; and glutamate+glutamine, 92%, P=.02) compared to concentrations measured with data collected at TEs of 15 and 20 ms.

QTROSY – a novel scheme for recovery of the anti-TROSY magnetisation

In TROSY experiments, spin state selection (S3) retains only the single HSQC sub-spectrum with minimal T2 relaxation and maximal resolution, yet at the cost of eliminating half of the available polarisation as undesired anti-TROSY component. We here introduce queued TROSY (qTROSY) as a novel scheme to partially recover and exploit this anti-TROSY polarisation in two concatenated scans. After initial orthogonal spin state separation (oS3), anti-TROSY polarisation is explicitly stored while its TROSY counterpart follows the desired coherence pathway recorded in a first scan A. The immediately appended scan B then quantitatively converts the recovered anti-TROSY polarisation into a second TROSY spectrum, skipping the time-limiting long reequilibration delay. Both concatenated qTROSY scans thus ideally exploit the full initial polarisation within almost the same measurement time. In practice, T2 relaxation losses accruing during the coupling evolution delays reduced anti-TROSY polarisation recovery below 40%, obviating sensitivity enhancement through addition of both qTROSY scans; yet, scan B retained a complete scan A spectrum with up to 75% intensity. We therefore propose to employ qTROSY asymmetrically, compacting two separate conventional into one queued TROSY-type experiment with significantly reduced measurement time, implying primarily the concatenation of different three- or higher-dimensional experiments. Both anti-TROSY polarisation recoveries and possible time savings are largest for deuterated and smaller non-deuterated proteins, extending the rentability limit of the TROSY principle towards smaller molecular weights.

A band-selective composite gradient: Application to DQF-COSY

We describe a unique band-selective method that utilizes a selective composite gradient to simultaneously achieve band selection and coherence pathway selection. This element is similar to the composite gradient known as the CLUB sandwich except the original broadband pulses have been replaced with selective pulses and the strengths of the antipolar gradients have been unbalanced. In this way, only the signals within the inversion band will continue to dephase throughout the duration of the element and satisfy the proper encoding-to-decoding gradient ratio necessary for coherence selection. Apart from the inverted polarity and asymmetry of the gradients, the band-selective CLUB sandwich is identical to the DPFGSE sequence and provides many of its desirable characteristics. We have successfully incorporated the band-selective CLUB into the DQF-COSY pulse sequence to create a band-selective experiment that offers the selectivity desired for resolution enhancement while maintaining excellent phase behavior. This is demonstrated on the congested aliphatic region of the ionophorous antibiotic Lasalocid A.

A new approach for simultaneous measurement of ADC and T2 from echoes generated via multiple coherence transfer pathways

The study of rotational and translational diffusion requires the measurement of both T 2 and apparent diffusion coefficient (ADC), quantities that are typically measured in separate experiments. The exploitation of echoes generated via multiple coherence transfer pathways offers an opportunity for measuring T 2 and ADC values simultaneously in a single experiment. A series of RF pulses can generate multiple echoes via different coherence pathways with each one being uniquely encoded. Here, we demonstrate one pulse sequence that uses an initial θ RF pulse to generate three coherence orders ( C = 0, −1, +1). In the particular version of the method discussed here only two are used ( C = 0, +1). Each order is encoded with a different b value from which the ADC is derived. The coherence order echo C = 0 is refocused to quantify T 2. The performance of the method—dubbed simultaneous measurement of ADC and relaxation time (SMART)—is demonstrated on a set of samples differing in T 2 and ADC achieved by varying the relative volume fractions in mixtures of gadolinium-doped H 2O and D 2O. The regional SMART derived T 2 and ADC agree well with those obtained with conventional double-spin–echo and pulsed gradient spin–echo methods.

An NMR technique for rapid measurement of flow

We present a one-scan method for determining fluid flow velocity within a few milliseconds in the presence of a static field gradient, and without the need of multiple scans. A few RF-pulses populate a series of coherence pathways, each of which exhibits a phase shift that is proportional to fluid velocity. These coherence pathways produce spin echoes separated in the time domain, thus eliminating the need for phase cycling.

Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr–Purcell–Meiboom–Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing. The direct path, therefore, is well suited for probing shorter length scales than is possible with the conventional approach. In our experiments in a low-field static-gradient system, the direct CPMG pathway was found to be sensitive to structure an order of magnitude smaller than accessible with the stimulated-echo pathway.

Short-time restricted diffusion in a static gradient and the attenuation of individual coherence pathways

We experimentally explore some of the implications of a recent theoretical study [J. Magn. Reson. 64 (2003) 145] for the measurement of restricted diffusion in connected porous media in a static gradient. In particular, we examine how restriction affects the short-time attenuation of different coherence pathways, all excited with the same sequence of slice-selective radiofrequency (RF) pulses, and how the various pathways make the transition to the long-time or tortuosity regime. We confirm that every pathway contains equivalent diffusional information and, for short times, yields the surface-to-volume ratio ( S/ V) of the confining space. We find also, in agreement with the theoretical predictions, that different pathways are controlled by different time scales and, thus, exhibit different sensitivity to restriction. This property might be exploited when designing optimal sequences to study restricted motion.

Functional MRI Based on Intermolecular Double-Quantum Coherences (iDQC) at 3 Tesla

Contrast generated by intermolecular double-quantum coherences (iDQC) is a novel approach to fMRI, which is qualitatively and quantitatively different from the standard blood oxygen level dependent (BOLD) contrast. Specifically, it was suggested that the sensitivity of iDQC to local susceptibility gradients can be adjusted on a mesoscopic scale (between 10µm and 1mm) externally by the experimenter. A drawback of iDQC experiments, however, is their inherently poor signal-to-noise ratio leading to substantial signal fluctuations in previous pilot studies. In the current work, parameters of modified CRAZED sequences were carefully optimized to achieve high signal stability in iDQC experiments at 3 T with the standard birdcage headcoil. Initial phantom experiments were utilized to verify that the detected signal was due to iDQC by recording its angular dependence. A four-step phase-cycling scheme was used to filter out specific multiple-quantum coherences. Contributions from unwanted coherence pathways at the center of the k-space were of the noise level. In in vivo experiments (series of 60 repetitions) in healthy volunteers a systematic variation of the repetition time (TR) yielded sufficient signal stability (as compared to ordinary EPI time series) if a relatively long TR 3 5s was used. A two-step phase cycling scheme was used in these experiments. A reason for the suboptimal signal stability at shorter TRs are contributions from additional stimulated echoes, which are not suppressed by the crusher gradients after image acquisition. fMRI studies were performed in 6 subjects with a simple visual paradigm (blocked design). In all subjects, both gradient-recalled echo (GRE) and spin-echo type iDQC sequences were recorded. Additional GRE or SE BOLD measurements were also performed. While no functional contrast was observed with SE-iDQC, functional maps were reproducibly obtained with GRE-iDQC (Fig. 1). These maps showed less activated pixels compared to routine BOLD experiments, however, the averaged functional signal change was >10% (GRE-iDQC) as compared to only 2% in the BOLD experiments. The optimized sequences provide a basis for future experimental investigations into the origin of the functional iDQC contrast.

High-resolution fast spin echo imaging of the human brain at 4.7 T: implementation and sequence characteristics.

In this work, a number of important issues associated with fast spin echo (FSE) imaging of the human brain at 4.7 T are addressed. It is shown that FSE enables the acquisition of images with high resolution and good tissue contrast throughout the brain at high field strength. By employing an echo spacing (ES) of 22 ms, one can use large flip angle refocusing pulses (162 degrees ) and a low acquisition bandwidth (50 kHz) to maximize the signal-to-noise ratio (SNR). A new method of phase encode (PE) ordering (called "feathering") designed to reduce image artifacts is described, and the contributions of RF (B(1)) inhomogeneity, different echo coherence pathways, and magnetization transfer (MT) to FSE signal intensity and contrast are investigated. B(1) inhomogeneity is measured and its effect is shown to be relatively minor for high-field FSE, due to the self-compensating characteristics of the sequence. Thirty-four slice data sets (slice thickness = 2 mm; in-plane resolution = 0.469 mm; acquisition time = 11 min 20 s) from normal volunteers are presented, which allow visualization of brain anatomy in fine detail. This study demonstrates that high-field FSE produces images of the human brain with high spatial resolution, SNR, and tissue contrast, within currently prescribed power deposition guidelines.