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1.  Efficient Amplitude-Modulated Pulses for Triple- to Single-Quantum Coherence Conversion in MQMAS NMR 
The Journal of Physical Chemistry. a  2014;118(31):6018-6025.
The conversion between multiple- and single-quantum coherences is integral to many nuclear magnetic resonance (NMR) experiments of quadrupolar nuclei. This conversion is relatively inefficient when effected by a single pulse, and many composite pulse schemes have been developed to improve this efficiency. To provide the maximum improvement, such schemes typically require time-consuming experimental optimization. Here, we demonstrate an approach for generating amplitude-modulated pulses to enhance the efficiency of the triple- to single-quantum conversion. The optimization is performed using the SIMPSON and MATLAB packages and results in efficient pulses that can be used without experimental reoptimisation. Most significant signal enhancements are obtained when good estimates of the inherent radio-frequency nutation rate and the magnitude of the quadrupolar coupling are used as input to the optimization, but the pulses appear robust to reasonable variations in either parameter, producing significant enhancements compared to a single-pulse conversion, and also comparable or improved efficiency over other commonly used approaches. In all cases, the ease of implementation of our method is advantageous, particularly for cases with low sensitivity, where the improvement is most needed (e.g., low gyromagnetic ratio or high quadrupolar coupling). Our approach offers the potential to routinely improve the sensitivity of high-resolution NMR spectra of nuclei and systems that would, perhaps, otherwise be deemed “too challenging”.
doi:10.1021/jp505752c
PMCID: PMC4126738  PMID: 25047226
2.  Direct Simulation of Magnetic Resonance Relaxation Rates and Line Shapes from Molecular Trajectories 
The Journal of Physical Chemistry. B  2012;116(22):6233-6249.
We simulate spin relaxation processes, which may be measured by either continuous wave or pulsed magnetic resonance techniques, using trajectory-based simulation methodologies. The spin–lattice relaxation rates are extracted numerically from the relaxation simulations. The rates obtained from the numerical fitting of the relaxation curves are compared to those obtained by direct simulation from the relaxation Bloch–Wangsness–Abragam– Redfield theory (BWART). We have restricted our study to anisotropic rigid-body rotational processes, and to the chemical shift anisotropy (CSA) and a single spin–spin dipolar (END) coupling mechanisms. Examples using electron paramagnetic resonance (EPR) nitroxide and nuclear magnetic resonance (NMR) deuterium quadrupolar systems are provided. The objective is to compare those rates obtained by numerical simulations with the rates obtained by BWART. There is excellent agreement between the simulated and BWART rates for a Hamiltonian describing a single spin (an electron) interacting with the bath through the chemical shift anisotropy (CSA) mechanism undergoing anisotropic rotational diffusion. In contrast, when the Hamiltonian contains both the chemical shift anisotropy (CSA) and the spin–spin dipolar (END) mechanisms, the decay rate of a single exponential fit of the simulated spin–lattice relaxation rate is up to a factor of 0.2 smaller than that predicted by BWART. When the relaxation curves are fit to a double exponential, the slow and fast rates extracted from the decay curves bound the BWART prediction. An extended BWART theory, in the literature, includes the need for multiple relaxation rates and indicates that the multiexponential decay is due to the combined effects of direct and cross-relaxation mechanisms.
doi:10.1021/jp2062628
PMCID: PMC3398626  PMID: 22540276
3.  Symmetry-Amplified J Splittings for Quadrupolar Spin Pairs: A Solid-State NMR Probe of Homoatomic Covalent Bonds 
Journal of the American Chemical Society  2013;135(34):12596-12599.
Chemically informative J couplings between pairs of quadrupolar nuclei in dimetallic and dimetalloid coordination motifs are measured using J-resolved solid-state NMR experiments. It is shown that the application of a double-quantum filter is necessary to observe the J splittings and that, under these conditions, only a simple doublet is expected. Interestingly, the splitting is amplified if the spins are magnetically equivalent, making it possible to measure highly precise J couplings and unambiguously probe the symmetry of the molecule. This is demonstrated experimentally by chemically breaking the symmetry about a pair of boron spins by reaction with an N-heterocyclic carbene to form a β-borylation reagent. The results show that the J coupling is a sensitive probe of bonding in diboron compounds and that the J values quantify the weakening of the B–B bond which occurs when forming an sp2–sp3 diboron compound, which is relevant to their reactivity. Due to the prevalence of quadrupolar nuclei among transition metals, this work also provides a new approach to probe metal–metal bonding; results for Mn2(CO)10 are provided as an example.
doi:10.1021/ja407138b
PMCID: PMC3762131  PMID: 23919916
4.  Characterisation of different polymorphs of tris(8-hydroxyquinolinato)aluminium(III) using solid-state NMR and DFT calculations 
Background
Organic light emitting devices (OLED) are becoming important and characterisation of them, in terms of structure, charge distribution, and intermolecular interactions, is important. Tris(8-hydroxyquinolinato)-aluminium(III), known as Alq3, an organomettalic complex has become a reference material of great importance in OLED. It is important to elucidate the structural details of Alq3 in its various isomeric and solvated forms. Solid-state nuclear magnetic resonance (NMR) is a useful tool for this which can also complement the information obtained with X-ray diffraction studies.
Results
We report here 27Al one-dimensional (1D) and two-dimensional (2D) multiple-quantum magic-angle spinning (MQMAS) NMR studies of the meridional (α-phase) and the facial (δ-phase) isomeric forms of Alq3. Quadrupolar parameters are estimated from the 1D spectra under MAS and anisotropic slices of the 2D spectra and also calculated using DFT (density functional theory) quantum-chemical calculations. We have also studied solvated phase of Alq3 containing ethanol in its lattice. We show that both the XRD patterns and the quadrupolar parameters of the solvated phase are different from both the α-phase and the δ-phase, although the fluorescence emission shows no substantial difference between the α-phase and the solvated phase. Moreover, we have shown that after the removal of ethanol from the matrix the solvated Alq3 has similar XRD patterns and quadrupolar parameters to that of the α-phase.
Conclusion
The 2D MQMAS experiments have shown that all the different modifications of Alq3 have 27Al in single unique crystallographic site. The quadrupolar parameters predicted using the DFT calculation under the isodensity polarisable continuum model resemble closely the experimentally obtained values. The solvated phase of Alq3 containing ethanol has structural difference from the α-phase of Alq3 (containing meridional isomer) from the solid-state NMR studies. Solid-state NMR can hence be used as an effective complementary tool to XRD for characterisation and structural elucidation.
doi:10.1186/1752-153X-3-15
PMCID: PMC2777900  PMID: 19900275
5.  Effect of IL-1β-Induced Macromolecular Depletion on Residual Quadrupolar Interaction in Articular Cartilage 
Purpose
Sodium multiple-quantum filtered (MQF) NMR spectroscopy may potentially be used to measure proteoglycan (PG) depletion in cartilage caused by osteoarthritis (OA). The purpose of this work was to quantify the effect of interleukin-1 (IL-1β)-induced macromolecule depletion on the residual quadrupolar interaction (RQI) of sodium in bovine cartilage plugs.
Materials and Methods
Fifteen 8-mm-diameter cartilage plug specimens were cored from the articular surface of fresh bovine patellae. All plugs were kept in culture media and nine of the plugs were subjected to interleukin-1 (IL-1β)-induced degeneration of cartilage for 4, 6, and 7 days. Sodium NMR spectra were obtained from each sample with a 1-cm-diameter solenoid coil in a 2T whole-body magnet interfaced to a custom-built spectrometer. We employed a previously described theoretical model to analyze triple-quantum filtered (TQF) and double-quantum filtered magic angle (DQFMA) spectra obtained from normal cartilage and cartilage treated with IL-1β. The model assumes a static Gaussian distribution of the RQI frequency, ωQ, in the sample. TQF and DQFMA spectra from each sample were fitted with the appropriate signal expressions to determine σ (the root mean square (RMS) ωQ), T2f, and T2s. An inversion-recovery sequence was used to determine T1 of each plug. A spectrophotometric assay was used to determine the amount of PG depleted from each plug. Histology was performed to visualize the PG loss in cartilage plugs. We defined σ as the measure of changes in macroscopic order in the tissue.
Results
Simulated spectra from the theoretical model were in excellent agreement with the experimental data. We were able to determine the relaxation times as well as σ of each specimen from their corresponding fits. T2f ranged between 2.26–3.50 msec, decreasing with increased PG loss. Over the range of PG depletion investigated, T2s increased from 12.3 msec to 14.9 msec, and T1 increased from 16 msec to 21 msec, while σ decreased from 180 Hz to 120 Hz. The order of macromolecules in the cartilage tissue decreased substantially with PG loss. Histology sections clearly showed qualitative visualization of the PG loss in cartilage following treatment with IL-1β.
Conclusion
We demonstrated that IL-β-induced macromolecule depletion in cartilage not only changes the relaxation characteristics of sodium but also changes RQI of the tissue. Using MQF sodium spectroscopy we quantified the changes in σ and showed that loss of macromolecules reduces the degree of order in the tissue.
PMCID: PMC2875789  PMID: 11891977
sodium; NMR; multiple-quantum filter; cartilage; proteoglycans
6.  Characterization of Non-Innocent Metal Complexes Using Solid-State NMR Spectroscopy: o-Dioxolene Vanadium Complexes 
Inorganic Chemistry  2011;50(20):9794-9803.
51V solid-state NMR (SSNMR) studies of a series of non-innocent vanadium(V) catechol complexes have been conducted to evaluate the possibility that 51V NMR observables, quadrupolar and chemical shift anisotropies, and electronic structures of such compounds can be used to characterize these compounds. The vanadium(V) catechol complexes described in these studies have relatively small quadrupolar coupling constants, which cover a surprisingly small range from 3.4 to 4.2 MHz. On the other hand, isotropic 51V NMR chemical shifts cover a wide range from −200 ppm to 400 ppm in solution and from −219 to 530 ppm in the solid state. A linear correlation of 51V NMR isotropic solution and solid-state chemical shifts of complexes containing non-innocent ligands is observed. These experimental results provide the information needed for the application of 51V SSNMR spectroscopy in characterizing the electronic properties of a wide variety of vanadium-containing systems, and in particular those containing non-innocent ligands and that have chemical shifts outside the populated range of −300 ppm to −700 ppm. The studies presented in this report demonstrate that the small quadrupolar couplings covering a narrow range of values reflect the symmetric electronic charge distribution, which is also similar across these complexes. These quadrupolar interaction parameters alone are not sufficient to capture the rich electronic structure of these complexes. In contrast, the chemical shift anisotropy tensor elements accessible from 51V SSNMR experiments are a highly sensitive probe of subtle differences in electronic distribution and orbital occupancy in these compounds. Quantum chemical (DFT) calculations of NMR parameters for [VO(hshed)(Cat)] yield 51V CSA tensor in reasonable agreement with the experimental results, but surprisingly, the calculated quadrupolar coupling constant is significantly greater than the experimental value. The studies demonstrate that substitution of the catechol ligand with electron donating groups results in an increase in the HOMO-LUMO gap and can be directly followed by an upfield shift for the vanadium catechol complex. In contrast, substitution of the catechol ligand with electron withdrawing groups results in a decrease in the HOMO-LUMO gap and can directly be followed by a downfield shift for the complex. The vanadium catechol complexes were used in this work because the 51V is a half-integer quadrupolar nucleus whose NMR observables are highly sensitive to the local environment. However, the results are general and could be extended to other redox active complexes that exhibit similar coordination chemistry as the vanadium catechol complexes.
doi:10.1021/ic200046k
PMCID: PMC3386638  PMID: 21842875
7.  Sodium and T1ρ MRI for molecular and diagnostic imaging of articular cartilage† 
NMR in biomedicine  2006;19(7):781-821.
In this article, both sodium magnetic resonance (MR) and T1ρ relaxation mapping aimed at measuring molecular changes in cartilage for the diagnostic imaging of osteoarthritis are reviewed. First, an introduction to structure of cartilage, its degeneration in osteoarthritis (OA) and an outline of diagnostic imaging methods in quantifying molecular changes and early diagnostic aspects of cartilage degeneration are described. The sodium MRI section begins with a brief overview of the theory of sodium NMR of biological tissues and is followed by a section on multiple quantum filters that can be used to quantify both bi-exponential relaxation and residual quadrupolar interaction. Specifically, (i) the rationale behind the use of sodium MRI in quantifying proteoglycan (PG) changes, (ii) validation studies using biochemical assays, (iii) studies on human OA specimens, (iv) results on animal models and (v) clinical imaging protocols are reviewed. Results demonstrating the feasibility of quantifying PG in OA patients and comparison with that in healthy subjects are also presented. The section concludes with the discussion of advantages and potential issues with sodium MRI and the impact of new technological advancements (e.g. ultra-high field scanners and parallel imaging methods). In the theory section on T1ρ, a brief description of (i) principles of measuring T1ρ relaxation, (ii) pulse sequences for computing T1ρ relaxation maps, (iii) issues regarding radio frequency power deposition, (iv) mechanisms that contribute to T1ρ in biological tissues and (v) effects of exchange and dipolar interaction on T1ρ dispersion are discussed. Correlation of T1ρ relaxation rate with macromolecular content and biomechanical properties in cartilage specimens subjected to trypsin and cytokine-induced glycosaminoglycan depletion and validation against biochemical assay and histopathology are presented. Experimental T1ρ data from osteoarthritic specimens, animal models, healthy human subjects and as well from osteoarthritic patients are provided. The current status of T1ρ relaxation mapping of cartilage and future directions is also discussed.
doi:10.1002/nbm.1102
PMCID: PMC2896046  PMID: 17075961
cartilage; arthritis; spin-lock; T1rho; sodium; MRI
8.  Simulation studies of instrumental artifacts on spin I=1 double quantum filtered NMR spectroscopy 
We report on the results of a simulation based study of the effect of various experimental artifacts for spin I=1 double quantum filtered NMR. The simulation captures the effects of static field inhomogeneity, finite pulse widths, phase errors, transients and radio frequency inhomogeneity. We simulated the spectral distortions introduced under these errors for four, eight and sixteen step phase cycles that are well known in the NMR community. The dominating pulse errors are radio frequency field inhomogeneity and antisymmetric pulse transients. These errors result in the reduction of signal intensity as well as an introduction of distortions in the detected double quantum filtered spectrum. Using the simulation tool we studied the improvement one obtains when implementing a sixteen step phase cycle over a four step phase cycle. The results indicate that implementing a sixteen step phase cycle over an eight or four step phase cycle does not result in a significant reduction in the DQF intensity loss, or reduction in spectral distortions for antisymmetric transients.
doi:10.1016/j.jmr.2010.04.008
PMCID: PMC2976484  PMID: 20451432
9.  Calculation of Double-Quantum-Coherence Two-dimensional Spectra: Distance Measurements and Orientational Correlations 
Applied magnetic resonance  2009;36(2-4):237-258.
The double quantum coherence (DQC) echo signal for two coupled nitroxides separated by distances ≳10 Å, is calculated rigorously for the six-pulse sequence. Successive application of six pulses on the initial density matrix, with appropriate inter-pulse time evolution and coherence pathway selection leaves only the coherent pathways of interest. The amplitude of the echo signal following the last π pulse can be used to obtain a one-dimensional dipolar spectrum (Pake doublet), and the echo envelope can be used to construct the two-dimensional DQC spectrum. The calculations are carried out using the product space spanned by the two electron-spin magnetic quantum numbers m1, m2 and the two nuclear-spin magnetic quantum numbers M1, M2, describing e.g. two coupled nitroxides in bilabeled proteins. The density matrix is subjected to a cascade of unitary transformations taking into account dipolar and electron exchange interactions during each pulse and during the evolution in the absence of a pulse. The unitary transformations use the eigensystem of the effective spin-Hamiltonians obtained by numerical matrix diagonalization. Simulations are carried out for a range of dipolar interactions, D, and microwave magnetic field strength B for both fixed and random orientations of the two 14N (and 15N) nitroxides. Relaxation effects were not included. Several examples of one- and two-dimensional Fourier transforms of the time domain signals vs. dipolar evolution and spin-echo envelope time variables are shown for illustration. Comparisons are made between 1D rigorous simulations and analytical approximations. The rigorous simulations presented here provide insights into DQC ESR spectroscopy, they serve as a standard to evaluate the results of approximate theories, and they can be employed to plan future DQC experiments.
doi:10.1007/s00723-009-0023-5
PMCID: PMC2786184  PMID: 20161423
10.  Water proton spin saturation affects measured protein backbone 15N spin relaxation rates 
Journal of Magnetic Resonance  2011;213(1):151-157.
Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichia coli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (〈S2〉 = 0.81) than the non-saturated ones (〈S2〉 = 0.88), indicating such order parameters may be previously underestimated.
doi:10.1016/j.jmr.2011.09.042
PMCID: PMC3339441  PMID: 22015249
Spin relaxation; Dephase; Flip-back; Saturation; Recovery time; Order parameter
11.  All-atom molecular dynamics simulations using orientational constraints from anisotropic NMR samples 
Journal of Biomolecular Nmr  2007;38(1):23-39.
Orientational constraints obtained from solid state NMR experiments on anisotropic samples are used here in molecular dynamics (MD) simulations for determining the structure and dynamics of several different membrane-bound molecules. The new MD technique is based on the inclusion of orientation dependent pseudo-forces in the COSMOS-NMR force field. These forces drive molecular rotations and re-orientations in the simulation, such that the motional time-averages of the tensorial NMR properties approach the experimentally measured parameters. The orientational-constraint-driven MD simulations are universally applicable to all NMR interaction tensors, such as chemical shifts, dipolar couplings and quadrupolar interactions. The strategy does not depend on the initial choice of coordinates, and is in principle suitable for any flexible molecule. To test the method on three systems of increasing complexity, we used as constraints some deuterium quadrupolar couplings from the literature on pyrene, cholesterol and an antimicrobial peptide embedded in oriented lipid bilayers. The MD simulations were able to reproduce the NMR parameters within experimental error. The alignment of the three membrane-bound molecules and some aspects of their conformation were thus derived from the NMR data, in good agreement with previous analyses. Furthermore, the new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of all three systems.
doi:10.1007/s10858-007-9142-1
PMCID: PMC1892527  PMID: 17334824
Molecular dynamics simulations; Orientational NMR constraints; 2H-NMR; Oriented samples; Cholesterol; Pyrene; PGLa peptide; Order parameters; Force field calculations
12.  The Application of Sodium Triple-Quantum Coherence NMR Spectroscopy for the Study of Growth Dynamics in Cartilage Tissue Engineering 
NMR in biomedicine  2013;26(6):709-717.
We studied the tissue growth dynamics for tissue-engineered cartilage at the early growth stage after cell seeding for four weeks using sodium triple-quantum coherence NMR spectroscopy. The following tissue-engineering constructs were studied: 1. Bovine chondrocytes cultured in alginate beads, 2. Bovine chondrocytes cultured as pellets (scaffold-free chondrocyte pellets), 3. Human Marrow Stromal Cells (HMSC) seeded in Collagen/Chitosan based scaffolds of chondrogenic extracellular matrix environment expecting chondrogenic differentiation, named as biomimetic scaffolds. We found that the sodium triple quantum coherence spectroscopy can differentiate between different tissue-engineering constructs and the native tissues based on the fast and the slow relaxation rates as well as based on the average quadrupolar coupling. Both the fast (Tf) and the slow (Ts) relaxation times were found to be longer in the chondrocyte pellets and the biomimetic scaffolds as compared to the chondrocytes suspended in alginate beads and the human articular cartilage tissues. In all cases, it was found that the relaxation rates and the motion of sodium ions, as measured from correlation time, were dependent on the amount of macromolecules, high cell density and the anisotropy of the cartilage tissue engineering constructs. Average quadrupolar couplings were found to be lower in the engineered tissue as compared to the native tissues, presumably due to the lack of order in collagen accumulated in the engineered tissue. These results indicate the use of sodium triple quantum coherence spectroscopy as a tool to investigate anisotropy and growth dynamics of cartilage tissue engineered constructs in a simple and reliable way.
doi:10.1002/nbm.2916
PMCID: PMC3634872  PMID: 23378198
Cartilage; Cartilage Tissue engineering; Sodium NMR; Sodium MRI; Triple-quantum coherence spectroscopy; Biomimetic scaffolds; Chondrocyte pellets; alginate beads; collagen; proteoglycans
13.  Quantum Entanglement and Spin Control in Silicon Nanocrystal 
PLoS ONE  2012;7(9):e45254.
Selective coherence control and electrically mediated exchange coupling of single electron spin between triplet and singlet states using numerically derived optimal control of proton pulses is demonstrated. We obtained spatial confinement below size of the Bohr radius for proton spin chain FWHM. Precise manipulation of individual spins and polarization of electron spin states are analyzed via proton induced emission and controlled population of energy shells in pure 29Si nanocrystal. Entangled quantum states of channeled proton trajectories are mapped in transverse and angular phase space of 29Si axial channel alignment in order to avoid transversal excitations. Proton density and proton energy as impact parameter functions are characterized in single particle density matrix via discretization of diagonal and nearest off-diagonal elements. We combined high field and low densities (1 MeV/92 nm) to create inseparable quantum state by superimposing the hyperpolarizationed proton spin chain with electron spin of 29Si. Quantum discretization of density of states (DOS) was performed by the Monte Carlo simulation method using numerical solutions of proton equations of motion. Distribution of gaussian coherent states is obtained by continuous modulation of individual spin phase and amplitude. Obtained results allow precise engineering and faithful mapping of spin states. This would provide the effective quantum key distribution (QKD) and transmission of quantum information over remote distances between quantum memory centers for scalable quantum communication network. Furthermore, obtained results give insights in application of channeled protons subatomic microscopy as a complete versatile scanning-probe system capable of both quantum engineering of charged particle states and characterization of quantum states below diffraction limit linear and in-depth resolution.
PACS numbers: 03.65.Ud, 03.67.Bg, 61.85.+p, 67.30.hj
doi:10.1371/journal.pone.0045254
PMCID: PMC3454410  PMID: 23028884
14.  Two-dimensional Electronic Double-Quantum Coherence Spectroscopy 
Accounts of chemical research  2009;42(9):1375-1384.
CONSPECTUS
The theory of electronic structure of many-electron systems like molecules is extraordinarily complicated. A lot can be learned by considering how electron density is distributed, on average, in the average field of the other electrons in the system. That is, mean field theory. However, to describe quantitatively chemical bonds, reactions, and spectroscopy requires consideration of the way that electrons avoid each other by the way they move; this is called electron correlation (or in physics, the many-body problem for fermions). While great progress has been made in theory, there is a need for incisive experimental tests that can be undertaken for large molecular systems in the condensed phase.
Here we report a two-dimensional (2D) optical coherent spectroscopy that correlates the double excited electronic states to constituent single excited states. The technique, termed two-dimensional double-coherence spectroscopy (2D-DQCS), makes use of multiple, time-ordered ultrashort coherent optical pulses to create double- and single-quantum coherences over time intervals between the pulses. The resulting two-dimensional electronic spectrum maps the energy correlation between the first excited state and two-photon allowed double-quantum states. The principle of the experiment is that when the energy of the double-quantum state, viewed in simple models as a double HOMO to LUMO excitation, equals twice that of a single excitation, then no signal is radiated. However, electron-electron interactions—a combination of exchange interactions and electron correlation—in real systems generates a signal that reveals precisely how the energy of the double-quantum resonance differs from twice the single-quantum resonance. The energy shift measured in this experiment reveals how the second excitation is perturbed by both the presence of the first excitation and the way that the other electrons in the system have responded to the presence of that first excitation.
We compare a series of organic dye molecules and find that the energy offset for adding a second electronic excitation to the system relative to the first excitation is on the order of tens of milli-electronvolts, and it depends quite sensitively on molecular geometry. These results demonstrate the effectiveness of 2D-DQCS for elucidating quantitative information about electron-electron interactions, many-electron wavefunctions, and electron correlation in electronic excited states and excitons.
doi:10.1021/ar9000795
PMCID: PMC2775063  PMID: 19552412
15.  Further exploration of MRI techniques for liver T1rho quantification 
With biliary duct ligation and CCl4 induced rat liver fibrosis models, recent studies showed that MR T1rho imaging is able to detect liver fibrosis, and the degree of fibrosis is correlated with the degree of elevation of the T1rho measurements, suggesting liver T1rho quantification may play an important role for liver fibrosis early detection and grading. It has also been reported it is feasible to obtain consistent liver T1rho measurement for human subjects at 3 Tesla (3 T), and preliminary clinical data suggest liver T1rho is increased in patients with cirrhosis. In these previous studies, T1rho imaging was used with the rotary-echo spin-lock pulse for T1rho preparation, and number of signal averaging (NSA) was 2. Due to the presence of inhomogeneous B0 field, artifacts may occur in the acquired T1rho-weighted images. The method described by Dixon et al. (Magn Reson Med 1996;36:90-4), which is a hard RF pulse with 135° flip angle and same RF phase as the spin-locking RF pulse is inserted right before and after the spin-locking RF pulse, has been proposed to reduce sensitivity to B0 field inhomogeneity in T1rho imaging. In this study, we compared the images scanned by rotary-echo spin-lock pulse method (sequence 1) and the pulse modified according to Dixon method (sequence 2). When the artifacts occurred in T1rho images, we repeated the same scan until satisfactory. We accepted images if artifact in liver was less than 10% of liver area by visual estimation. When NSA =2, the breath-holding duration for data acquisition of one slice scanning was 8 sec due to a delay time of 6,000 ms for magnetization restoration. If NSA =1, the duration was shortened to be 2 sec. In previous studies, manual region of interest (ROI) analysis of T1rho map was used. In this current study, histogram analysis was also applied to evaluate liver T1rho value on T1rho maps. MRI data acquisition was performed on a 3 T clinical scanner. There were 29 subjects with 61 examinations obtained. Liver T1rho values obtained by sequence 1 (NSA =2) and sequence 2 (NSA =2) showed similar values, i.e., 43.1±2.1 ms (range: 38.6-48.0 ms, n=40 scans) vs. 43.5±2.5 ms (range: 39.0-47.7 ms, 
n=12 scans, P=0.74) respectively. For the six volunteers scanned with both sequences in one session, the intraclass correlation coefficient (ICC) was 0.939. Overall, the success rate of obtaining satisfactory images per acquisition was slightly over 50% for both sequence 1 and sequence 2. Satisfactory images can usually be obtained by asking the volunteer subjects to better hold their breath. However, sequence 2 did not increase the scan success rate. For the nine subjects scanned by sequence 2 with both NSA =2 and NSA =1 during one session, the ICC was 0.274, demonstrated poor agreement. T1rho measurement by ROI method and histogram had an ICC of 0.901 (P>0.05), demonstrated very good agreement. We conclude that by including 135° flip angle before and after the spin-locking RF pulse, the rate of artifacts occurring did not decrease. On the other hand, sequence 1 and sequence 2 measured similar T1rho value in healthy liver. While reducing the breath—holding duration significantly, NSA =1 did not offer satisfactory signal-to-noise ratio. Histogram measurement can be adopted for future studies.
doi:10.3978/j.issn.2223-4292.2013.12.10
PMCID: PMC3882805  PMID: 24404445
Magnetic resonance imaging; liver; T1rho; quantification
16.  An efficient NMR method for the characterisation of 14N sites through indirect 13C detection 
Physical Chemistry Chemical Physics  2013;15(20):7613-7620.
An efficient NMR methods for the characterisation of 14N sites has been developed with efficiencies suitable for the quantitative analysis of biomolecular and natural abundance systems.
Nitrogen is one of the most abundant elements and plays a key role in the chemistry of biological systems. Despite its widespread distribution, the study of the naturally occurring isotope of nitrogen, 14N (99.6%), has been relatively limited as it is a spin-1 nucleus that typically exhibits a large quadrupolar interaction. Accordingly, most studies of nitrogen sites in biomolecules have been performed on samples enriched with 15N, limiting the application of NMR to samples which can be isotopically enriched. This precludes the analysis of naturally occurring samples and results in the loss of the wealth of structural and dynamic information that the quadrupolar interaction can provide. Recently, several experimental approaches have been developed to characterize 14N sites through their interaction with neighboring ‘spy’ nuclei. Here we describe a novel version of these experiments whereby coherence between the 14N site and the spy nucleus is mediated by the application of a moderate rf field to the 14N. The resulting 13C/14N spectra show good sensitivity on natural abundance and labeled materials; whilst the 14N lineshapes permit the quantitative analysis of the quadrupolar interaction.
doi:10.1039/c3cp50787d
PMCID: PMC3695532  PMID: 23589073
17.  Double tuning a single input probe for heteronuclear NMR spectroscopy at low field 
Applications of PASADENA in biomedicine are continuing to emerge due to recent demonstrations that hyperpolarized metabolic substrates and the corresponding reaction products persist sufficiently long to be detected in vivo. Biomedical applications of PASADENA typically differ from their basic science counterparts in that the polarization endowed by addition of parahydrogen is usually transferred from nascent protons to coupled storage nuclei for subsequent detection on a higher field imaging instrument. These pre-imaging preparations usually take place at low field, but commercial spectrometers capable of heteronuclear pulsed NMR at frequencies in the range of 100 kHz to 1 MHz are scarce though, in comparison to single channel consoles in that field regime. Reported here is a probe circuit that can be used in conjunction with a phase and amplitude modulation scheme we have developed called PANORAMIC (Precession And Nutation for Observing Rotations At Multiple Intervals about the Carrier), that expands a single channel console capability to double or generally multiple resonance with minimal hardware modifications. The demands of this application are geared towards uniform preparation, and since the hyperpolarized molecules are being detected externally at high field, detection sensitivity is secondary to applied field uniformity over a large reaction volume to accommodate heterogeneous chemistry of gas molecules at a liquid interface. The probe circuit was therefore configured with a large (40 mL) Helmholtz sample coil for uniformity, and double-tuned to the Larmor precession frequencies of 13C/1H (128/510 kHz) within a custom solenoidal electromagnet at a static field of 12 mT. Traditional (on-resonant) as well as PANORAMIC NMR signals with signal to noise ratios of approximately 75 have been routinely acquired with this probe and spectrometer setup from 1024 repetitions on the high frequency channel. The proton excitation pulse width was 240 μs at 6.31 W, compared to a carbon-13 pulse width of 220 μs at 2.51 W. When PANORAMIC refocusing waveforms were transmitted at a carrier frequency of 319 kHz, integrated signal intensities from a spin-echo sequence at both proton (510 kHz) and carbon-13 (128 kHz) frequencies were within experimental error to block pulse analogs transmitted on resonance. We anticipate that this probe circuit design could be extended to higher and lower frequencies, and that when used in conjunction with PANORAMIC phase and amplitude modulated arrays, will enable low field imaging consoles to serve as multinuclear consoles.
doi:10.1016/j.jmr.2012.06.008
PMCID: PMC4118687  PMID: 22975236
Single channel spectrometer; Low field NMR; Parahydrogen induced polarization; Dual resonant probe circuit; Double tuned; Single input; PANORAMIC; Phase and amplitude modulation; PASADENA; Hyperpolarization
18.  Effect of neural connectivity on autocovariance and cross covariance estimates 
Background
Measurements of auto and cross covariance functions are frequently used to investigate neural systems. In interpreting this data, it is commonly assumed that the largest contribution to the recordings comes from sources near the electrode. However, the potential recorded at an electrode represents the superimposition of the potentials generated by large numbers of active neural structures. This creates situations under which the measured auto and cross covariance functions are dominated by the activity in structures far from the electrode and in which the distance dependence of the cross-covariance function differs significantly from that describing the activity in the actual neural structures.
Methods
Direct application of electrostatics to calculate the theoretical auto and cross covariance functions that would be recorded from electrodes immersed in a large volume filled with active neural structures with specific statistical properties.
Results
It is demonstrated that the potentials recorded from a monopolar electrode surrounded by dipole sources in a uniform medium are predominantly due to activity in neural structures far from the electrode when neuronal correlations drop more slowly than 1/r3 or when the size of the neural system is much smaller than a known correlation distance. Recordings from quadrupolar sources are strongly dependent on distant neurons when correlations drop more slowly than 1/r or the size of the system is much smaller than the correlation distance. Differences between bipolar and monopolar recordings are discussed. It is also demonstrated that the cross covariance of the recorded in two spatially separated electrodes declines as a power-law function of the distance between them even when the electrical activity from different neuronal structures is uncorrelated.
Conclusion
When extracellular electrophysiologic recordings are made from systems containing large numbers of neural structures, it is important to interpret measured auto and cross covariance functions cautiously in light of the long range nature of the electric fields. Using recording electrodes that are bipolar or quadrupolar minimizes or eliminates these effects and hence these electrodes are preferred when electrical recordings are made for the purpose of auto and cross correlation analysis of local electrical activity.
doi:10.1186/1475-925X-6-3
PMCID: PMC1802087  PMID: 17227577
19.  Deuterium Spin Probes of Backbone Order in Proteins: A 2H NMR Relaxation Study of Deuterated Carbon α Sites 
Journal of the American Chemical Society  2009;131(43):15853-15865.
2H spin relaxation NMR experiments to study the dynamics of deuterated backbone α-positions, Dα, are developed. To date, solution-state 2H relaxation measurements in proteins have been confined to side-chain deuterons - primarily 13CH2D or 13CHD2 methyl groups. It is shown that quantification of 2H relaxation rates at Dα backbone positions and the derivation of associated order parameters of Cα-Dα bond vector motions in small [U-15N,13C,2H]-labeled proteins is feasible with reasonable accuracy. The utility of the developed methodology is demonstrated on a pair of proteins - ubiquitin (8.5 kDa) at 10°C, 27°C, and 40°C, and a variant of GB1 (6.5 kDa) at 22°C. In both proteins, the Dα-derived parameters of the global rotational diffusion tensor are in good agreement with those obtained from 15N relaxation rates. Semi-quantitative solution state NMR measurements yield an average value of the quadrupolar coupling constant, QCC, for Dα sites in proteins equal to 174 kHz. Using the uniform value of QCC for all Dα sites, we show that Cα-Dα bond vectors are motionally distinct from the backbone amide N-H bond vectors, with 2H-derived squared order parameters of Cα-Dα bond vector motions, S2 CαDα, on average slightly higher than their N-H amides counterparts, S2 NH. For ubiquitin, the 2H-derived backbone mobility compares well with that found in a 1-μs molecular dynamics simulation.
doi:10.1021/ja9063958
PMCID: PMC2770885  PMID: 19821582
20.  Measuring T2 and T1, and Imaging T2 without Spin Echoes 
Journal of Magnetic Resonance  2011;214(1):273-280.
During adiabatic excitation, the nuclear magnetization in the transverse plane is subject to T2 (spin-spin) relaxation, depending on the pulse length τ. Here, this property is exploited in a method of measuring T2 using the ratio of NMR signals acquired with short and long-duration self-refocusing adiabatic pulses, without spin-echoes. This Dual-τ method is implemented with B1-insensitive rotation (BIR-4) pulses. It is validated theoretically with Bloch Equation simulations independent of flip-angle, and experimentally in phantoms. Dual-τ T2 measurements are most accurate at short T2 where results agree with standard spin-echo measures to within 10% for T2 ≤ 100ms. Dual-τ MRI performed with a long 0° BIR-4 pre-pulse provides quantitative T2 imaging of phantoms and the human foot while preserving desired contrast and functional properties of the rest of the MRI sequence. A single 0° BIR-4 pre-pulse can provide T2 contrast-weighted MRI and serve as a “T2-prep” sequence with a lower B1 requirement than prior approaches. Finally, a Tri-τ experiment is introduced in which both τ and flip-angle are varied, enabling measurement of T2, T1 and signal intensity in just three acquisitions if flip-angles are well-characterized. These new methods can potentially save time and simplify relaxation measurements and/or contrast-weighted NMR and MRI.
doi:10.1016/j.jmr.2011.11.016
PMCID: PMC3304500  PMID: 22197502
spin-spin relaxation; measurement; adiabatic pulses; spin-lattice relaxation; MRI; T1; T2
21.  Impact of Chlorine Substitution on Spin Lattice Relaxation of Triarylmethyl and 1,4-Benzosemiquinone Radicals in Glass-forming Solvents between 25 and 295 K 
Applied magnetic resonance  2009;37(1):649.
Spin-lattice relaxation rates measured by long-pulse saturation recovery in glassy solvents for chlorinated aromatic radicals: perchlorotriphenylmethyl radical, 2,5-dichloro-3,6-dihydroxy-1,4-benzosemiquinone, and tetrachloro-1,4-benzosemiquinone, were compared with relaxation rates for non-chlorinated analogs. The impact of the quadrupolar chlorines is small, and less than the effects of changing the rigidity of the glass. The temperature dependence of relaxation rates below the glass transition temperature could be modeled as the sum of contributions from the direct, Raman, and local mode processes.
doi:10.1007/s00723-009-0086-3
PMCID: PMC2814433  PMID: 20126423
22.  Optimization of magnetic flux density for fast MREIT conductivity imaging using multi-echo interleaved partial fourier acquisitions 
Background
Magnetic resonance electrical impedance tomography (MREIT) has been introduced as a non-invasive method for visualizing the internal conductivity and/or current density of an electrically conductive object by externally injected currents. The injected current through a pair of surface electrodes induces a magnetic flux density distribution inside the imaging object, which results in additional magnetic flux density. To measure the magnetic flux density signal in MREIT, the phase difference approach in an interleaved encoding scheme cancels out the systematic artifacts accumulated in phase signals and also reduces the random noise effect by doubling the measured magnetic flux density signal. For practical applications of in vivo MREIT, it is essential to reduce the scan duration maintaining spatial-resolution and sufficient contrast. In this paper, we optimize the magnetic flux density by using a fast gradient multi-echo MR pulse sequence. To recover the one component of magnetic flux density Bz, we use a coupled partial Fourier acquisitions in the interleaved sense.
Methods
To prove the proposed algorithm, we performed numerical simulations using a two-dimensional finite-element model. For a real experiment, we designed a phantom filled with a calibrated saline solution and located a rubber balloon inside the phantom. The rubber balloon was inflated by injecting the same saline solution during the MREIT imaging. We used the multi-echo fast low angle shot (FLASH) MR pulse sequence for MRI scan, which allows the reduction of measuring time without a substantial loss in image quality.
Results
Under the assumption of a priori phase artifact map from a reference scan, we rigorously investigated the convergence ratio of the proposed method, which was closely related with the number of measured phase encode set and the frequency range of the background field inhomogeneity. In the phantom experiment with a partial Fourier acquisition, the total scan time was less than 6 seconds to measure the magnetic flux density Bz data with 128×128 spacial matrix size, where it required 10.24 seconds to fill the complete k-space region.
Conclusion
Numerical simulation and experimental results demonstrated that the proposed method reduces the scanning time and provides the recovered Bz data comparable to what we obtained by measuring complete k-space data.
doi:10.1186/1475-925X-12-82
PMCID: PMC3766253  PMID: 23981409
MREIT; MRI; Interleaved partial fourier acquisition; Magnetic flux density; Current density
23.  Strategies for inner volume 3D fast spin echo magnetic resonance imaging using non-selective refocusing radio frequency pulses* 
Medical physics  2006;33(1):173-186.
Fast Spin Echo (FSE) trains elicited by non-selective “hard” refocusing radio frequency (RF) pulses have been proposed as a means to enable application of FSE methods for high resolution 3D magnetic resonance imaging (MRI). Hard-pulse FSE (HPFSE) trains offer short (3–4 ms) echo spacings, but are unfortunately limited to imaging the entire sample within the coil sensitivity thus requiring lengthy imaging times, consequently limiting clinical application. In this work we formulate and analyze two general purpose combinations of 3D HPFSE with Inner Volume (IV) MR imaging to circumvent this limitation. The first method employs a 2D selective RF excitation followed by the HPFSE train, and focuses on required properties of the spatial excitation profile with respect to limiting RF pulse duration in the 5–6 ms range. The second method employs two orthogonally selective 1D RF excitations (a 90x°– 180y° pair) to generate an echo from magnetization within the volume defined by their intersection. Subsequent echoes are formed via the HPFSE train, placing the focus of the method on (a) avoiding spurious echoes that may arise from transverse magnetization located outside the slab intersection when it is unavoidably affected by the non-selective refocusing pulses, and (b) avoiding signal losses due to the necessarily different spacing (in time) of the RF pulse applications. The performance of each method is experimentally measured using Carr-Purcell-Meiboom-Gill (CPMG) multi-echo imaging, enabling examination of the magnetization evolution throughout the echo train. The methods as implemented achieve 95% to 97% outer volume signal suppression, and higher suppression appears to be well within reach, by further refinement of the selective RF excitations. Example images of the human brain and spine are presented with each technique. We conclude that the SNR effciency of volume imaging in conjunction with the short echo spacing afforded by hard pulse trains enable high resolution 3D HPFSE MRI of a small field-of-view (FOV) with minimal aliasing artifact.
PMCID: PMC1414094  PMID: 16485424
3D MRI; Inner Volume MRI; Fast Spin Echo MRI; Multiple-Echo Pulse Sequence; Spatial Excitation; High Resolution Imaging
24.  The partial independence of bioelectric and biomagnetic fields and its implications for encephalography and cardiography 
In this article, we clearly demonstrate that the electric potential and the magnetic field can contain different information about current sources in three-dimensional conducting media. Expressions for the magnetic fields of electric dipole and quadrupole current sources immersed in an infinite conducting medium are derived, and it is shown that two different point dipole distributions that are electrically equivalent have different magnetic fields. Although measurements of the electric potential are not sufficient to determine uniquely the characteristics of a quadrupolar source, the radial component of the magnetic field can supply the additional information needed to resolve these ambiguities and to determine uniquely the configuration of dipoles required to specify the electric quadrupoles. We demonstrate how the process can be extended to even higher order terms in an electrically silent series of magnetic multipoles. In the context of a spherical brain source model, it has been mathematically demonstrated that the part of the neuronal current generating the electric potential lives in the orthogonal complement of the part of the current generating the magnetic potential. This implies a mathematical relationship of complementarity between electroencephalography (EEG) and magnetoencephalography (MEG), although the theoretical result in question does not apply to the non-spherical case (Dassios (2008), Math Med Biol, vol. 25, p. 133). Our results have important practical applications in cases where electrically silent sources that generate measurable magnetic fields are of interest. Moreover, electrically silent, magnetically active moments of higher order can be useful when cancellation due to superposition of fields can occur, since this situation leads to a substantial reduction in the measurable amplitude of the signal. In this context, information derived from magnetic recordings of electrically silent, magnetically active multipoles can supplement electrical recordings for the purpose of studying the physiology of the brain. Magnetic fields of the electric multipole sources in a conducting medium surrounded by an insulating spherical shell are also presented and the relevance of this calculation to cardiographic and encephalographic experimentation is discussed.
PMCID: PMC3818693  PMID: 19518481
25.  Modeling and Phantom Studies of Ultrasonic Wall Shear Rate Measurements Using Coded Pulse Excitation 
Wall shear rate (WSR) is the derivative of blood velocity with respect to vessel radius at the endothelial cell (EC) surface. The product of WSR and blood viscosity is the wall shear stress (WSS) that has been identified as an important factor for atherosclerosis development. High echo signal-to-noise ratio (eSNR) and high spatial resolution are crucial for minimizing the errors in WSR estimates. By transmitting coded pulses with time-bandwidth product greater than one, high eSNR from weak blood scatter can be achieved without increasing instantaneous power or sacrificing spatial resolution. This paper summarizes a series of measurements in a straight tube (5-mm diameter), constant velocity flow phantom using a 10 MHz transducer (60% bandwidth, f/1.5) imaged with a 72° Doppler angle, 125 MHz sampling frequency and 1 kHz pulse repetition frequency. Measurements were made using a frequency-modulated (FM) code, phase-modulated (PM) codes, and uncoded broadband and narrow band pulse transmissions. Both simulation and experimental results show that coded-pulse excitation increases accuracy and precision in WSR estimation for laminar flow over a broad range of peak velocity values when compared to standard pulsing techniques in noise-limited conditions (eSNR < 30 dB). The code sequence and its length are selected to balance range lobe suppression with eSNR and echo coherence enhancements to minimize WSR errors. In our study, the combination of an eight bit Optimal coded pulse with a Wiener compression filter yielded the highest WSR estimation performance.
PMCID: PMC2717631  PMID: 16615576

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