Quantifying uncertainty in NMR T2 spectra using Monte Carlo inversion

Relaxation and diffusion data are often analyzed using a Laplace inversion algorithm that incorporates regularization. Regularization is used because Laplace inversion with finite and noisy data is an ill-conditioned problem for which many solutions exist for a given data set. This paper reports a different approach. Instead of finding a "best" solution by some ad hoc criterion, we developed an efficient Monte Carlo algorithm that generates thousands of probable solutions from which the statistical properties of the solution can be analyzed. We find that although all of the individual solutions are spiky, the mean solution spectrum is smooth and similar to the regularized solution. From the Monte Carlo solutions we obtain probability distributions for quantities derived from the spectrum, such as porosity and bound fluid. This ability to characterize the uncertainty of such quantities is novel.     

T(1) fast acquisition relaxation mapping (T(1)-FARM): optimized data acquisition

A theoretical procedure for estimating the precision of the T(1) Fast Acquisition Relaxation Mapping sequence as a function of a number of acquisition parameters has been validated by both simulations and experimental results. These results have clarified the selection of sequence parameters to give optimal accuracy and precision in the R(1)* measurements. There is excellent agreement between theory, simulation, and experiment except for flip angles greater than 9 degrees, at which point slice profile imperfections significantly degrade the precision of the technique. The experimental results indicate that over a range of T(1)s that would be seen in a bolus tracking experiment (25-1200 ms), T(1) Fast Acquisition Relaxation Mapping can be used to obtain 64 x 128 R(1)* maps at a rate of 1 map/s, with a precision of 10% or better.     

Measurement of (1)J(NC') and (2)J(H(N))(C') couplings from spin-state-selective two-dimensional correlation spectrum.

A method for the measurement of (1)J(NC') and (2)J(H(N))(C') coupling constants from a simplified two-dimensional [(15)N, (1)H] correlation spectrum is presented. The multiplet components of the (1)J(NC') doublet in the indirect dimension and (2)J(H(N))(C') in the direct dimension are separated into two subspectra by spin-state-selective filters. Thus each subspectrum contains no more peaks than the conventional [(15)N, (1)H]-HSQC spectrum. Furthermore, the method for the measurement of (1)J(NC') and (2)J(H(N))(C') is designed to exploit destructive relaxation interference (TROSY). The results are verified against the measurements of (1)J(NC') from spin-state-selective [(13)C', (1)H] correlation spectra recorded with additional sequence described here.     

Measurement of longitudinal relaxation times in crowded 1H NMR spectra using one- and two-dimensional maximum quantum (MAXY) NMR spectroscopy

Methods for measuring longitudinal relaxation times of protons in heavily overlapped ¹H NMR spectra are introduced and exemplified using a solution of cholesteryl acetate. The methods are based on 1-dimensional and 2-dimensional maximum quantum NMR spectroscopy (MAXY), which makes possible the selective detection of CH, CH₂ and CH₃ ¹H NMR resonances. A modification of the BIRD pulse sequence to achieve selective inversion of protons bonded to either ¹²C or ¹³C is given. The approach should find application in studies of molecular dynamics where isotopic enrichment is not possible and the level of available sample dictates the use of ¹H NMR spectroscopy.     

Precision-optimized single protocol pre-/post-contrast modified-look locker inversion T1 mapping using composite inversion group fitting

BackgroundInvestigation of a simple, precision optimized, identical pre−/post-contrast modified look locker inversion recovery (MOLLI) protocol employing Composite inversion group (IG) fitting in a clinical cardiomyopathy population.MethodsCardiac magnetic resonance imaging (MRI) was performed at 3 Tesla in 36 patients (48.0 years [IQR: 35.7, 58.2 years]) with known/suspicion of hypertrophic cardiomyopathy. T1 mapping was performed pre−/post-contrast (0.15 mmol/kg Gadobutrol) using a standard 3-parameter fit (STANDARD) and an optimized (OPTIMAL) single-protocol Composite-IG fitting MOLLI approach. The OPTIMAL protocol was based on a simulation study (for 11hb acquisitions) with cost metric analysis across the range of expected T1 values (300-1400 ms) and heart rates (50-80 bpm).All maps were generated offline based on motion corrected source images. Based on region of interest analysis, the precision of both approaches was assessed using a previously validated propagation of errors technique for pre−/post-contrast T1 mapping as well as calculated ECV (based on point-of care hematocrit measurements. Furthermore, respective T1 and ECV values were calculated. Statistical methods included Wilcoxon Signed-Rank tests and Student's paired t-test.ResultsA total of ~9000 11hb inversion groupings were simulated with a 4(0)2(0)2(0)2(0)1 grouping providing the optimal precision across the specified T1/heart rate range. In comparison to standard pre-contrast 5(3)3 MOLLI, this OPTIMAL protocol demonstrated a significantly improved pre-contrast precision (9.1 [6.2, 9.9]ms vs. 9.4 [7.3, 10.8]ms; P < 0.001) while no significant differences were found for post-contrast T1 mapping (4.5 [2.6, 5.3]ms vs. 4.2 [2.8, 5.1]ms; P = 0.25) and EVC mapping (0.38 [0.28, 0.45]ms vs. 0.35 [0.25, 0.44]ms; P = 0.07) or reproducibility (0.16 [0.14, 0.19] vs. 0.19 [0.13, 0.23] P = 0.53).Direct comparison of resulting T1/ECV values demonstrated no significant differences between STANDARD and OPTIMAL techniques for pre-contrast T1 (1178 [1158, 1199]ms vs. 1173 [1143, 1195]ms; P = 0.46) and significant differences for post-contrast T1 (466 [446, 506]ms vs. 456 [433, 503]ms; P = 0.04) and ECV (23.1 [20.8, 25.1]% vs. 23.9 [22.3, 26.4]%; P = 0.001).ConclusionsA single optimized Composite-IG fitting protocol for pre−/post-contrast T1 mapping demonstrated improved precision over standard MOLLI techniques. It enables a simplified workflow with reduction of potential sources of error especially with respect to image data co-registration easing advanced post-processing for generation of patient specific ECV maps.     

Probe the 2s_(1/2) and 1d_(3/2) state level inversion with electron-nucleus scattering

The neutron-rich even-even nuclei26–40Mg,28–46Si,30–48S,and32–56Ar are calculated with the RMF model and the phase-shift electron scattering method.Results show that level inversion of the 2s1/2and 1d3/2proton states may occur for the magnesium,silicon,sulphur,and argon isotopes with more neutrons away from the stability line.Calculations show that the variation of the central charge densities for30–48S,and32–56Ar are very sensitive to the 2s1/2and 1d3/2proton state level inversion,and the level inversion can lead to a large measurable central charge depletion to the charge density distributions for the neutron-rich isotopes.Calculations also show that the charge density diferences between the isotopes with and without central charge depletion can reveal not only the level inversion of the 2s1/2and 1d3/2proton states but also the behavior of the proton wave functions of both states.The results can provide references for the possible study of the nuclear level inversion and nuclear bubble phenomenon with electron scattering of short-lived nuclei at RIKEN or/and GSI in the future.In addition,direct nuclear reaction44S(n,d)43P or44S(3H,α)43P might also be a possible way to study the 2s1/2and 1d3/2proton state level inversion.     

Measurement of homonuclear (2)J-couplings from spin-state selective double-/zero-quantum two-dimensional NMR spectra.

(1)H-detected two-dimensional double-/zero-quantum experiments are described for measurement of homonuclear (2)J(HH)-couplings of NH(2) or CH(2) groups in proteins. These experiments utilize multiple-quantum coherence for determination of the size and the absolute sign of the geminal scalar and dipolar couplings in the presence of broad lines. Spectra are simplified by gradient selection and spin-state selective filters.     

The (29)Si T(1) and T(2) NMR relaxation in porous paramagnetic material SiO(2)-MnO-Al(2)O(3)

The (29)Si spin-lattice relaxation in porous silica-based material 1, doped by ions Mn(2+) at a Si/Mn ratio of 3.5, is non-exponential, independent of magic-angle spinning (MAS) rates and governed by direct dipolar coupling between electron and nucleus where an electron relaxation time is estimated to be about 10(-8)s. In the absence of mutual energy-conserving spin flips (spin diffusion) in 1, the (29)Si T(2) time increases linearly with spinning rates. None was observed in diamagnetic porous system 2. The unexpected (29)Si T(2) dependence has been interpreted in terms of the large bulk magnetic susceptibility (BMS) effects. It has been shown that editing the (29)Si Hahn-echo MAS NMR spectra eliminates wide lines, belonging to (29)Si nuclei in the proximity of paramagnetic centers, and reduces the BMS broadenings in sideband patterns for nuclei remote from these centers.     

Knee osteochondral junction imaging using a fast 3D T1-weighted ultrashort echo time cones sequence at 3T

The osteochondral junction (OCJ) of the knee joint is comprised of multiple tissue components, including a portion of the deep layer cartilage, calcified cartilage, and subchondral bone. The OCJ is of increasing radiological interest as it may be relevant in the early pathogenesis of osteoarthritis (OA). Due to its short transverse relaxation, the OCJ is invisible to clinical MR sequences. The purpose of this study was to develop a fast 3D T₁-weighted ultrashort echo time cones sequence with fat saturation (FS-UTE-Cones) for high resolution and high contrast imaging of the OCJ on a clinical 3T scanner. First, numerical simulations were performed to investigate how the flip angle affected the signal intensities and contrasts of both short and long T₁ tissues. The results from these simulations demonstrated that higher short T₁ contrast could be achieved with higher flip angle. Next, T₁ relaxation was measured for the different layers of a human patellar cartilage sample, and the results showed that the deepest layer had a significantly shorter T₁ value than other layers. Finally, a healthy knee joint was scanned with different flip angles and the OCJ was highlighted in the T₁-weighted FS-UTE-Cones sequence using a flip angle greater than 20°. The clinical T₂-weighted and proton density-weighted FSE sequences were also included for comparison, revealing a dark OCJ region. Representative T₁-weighted FS-UTE-Cones images of the whole knee of a healthy volunteer showed high signal intensity bands in the OCJ regions of the patella, femur, and tibia. On the other hand, T₁-weighted FS-UTE-Cones imaging of the knee joints of OA patients revealed regions with reduction or loss of these high signal intensity bands in the OCJ regions, indicating abnormal OCJ tissue composition. The proposed 3D T₁-weighted FS-UTE-Cones sequence with a 3-min scan time may be very useful for demonstrating the involvement of the OCJ regions in early OA.     

Recoupled polarization-transfer methods for solid-state (1)H--(13)C heteronuclear correlation in the limit of fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for (1)H--(13)C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR pi-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized (1)H--(13)C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with (13)C in natural abundance, as well as simulations, confirm the very weak effect of (1)H--(1)H homonuclear couplings on the spectra recorded with spinning frequencies of 25--30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH(n) groups is discussed, and (13)C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Dual-echo breathhold T(2)-weighted fast spin echo MR imaging of liver lesions

The purpose of this study was to develop a multi-shot dual-echo breathhold fast spin echo technique (DFSE) and compare it with conventional spin echo (T2SE) for T(2)-weighted MR imaging of liver lesions. The DFSE acquisition (EffTE1/EffTE2/TR = 66/143/2100 ms) imaged 5 sections per 17 s breathhold. T2SE imaging (TE1/TE2/TR = 60/120/2500 ms) required 16:55 (min:s) for 14 sections. Both techniques used a receive-only phased-array abdominal multicoil and provided 192 x 256 effective resolution. The results showed first and second echo relative DFSE/T2SE contrast values for 27 representative lesions (15 consecutive patients) were 1.08 +/- 0.05 and 1.16 +/- 0.09 (mean +/- STD mean), respectively. Corresponding CNR values were 1.12 +/- 0.09 and 0.97 +/- 0.12. Overall DFSE was comparable-to-superior to T2SE for lesion sizing and image artifact. DFSE lesion detection was inferior to T2SE's in several patient studies because of decreased conspicuity of lesions located near multicoil edges and because of poor breathhold-to-breathhold reproducibility and lack of breathholding. However both DFSE (and T2SE) provided lesion detection rated to be of diagnostic quality for all patient studies. In conclusion, we found that DFSE provides diagnostically useful dual-echo T(2)-weighted MR liver images in a greatly decreased acquisition time.     

Two-dimensional chemical shift/heteronuclear dipolar coupling spectra obtained with polarization inversion spin exchange at the magic angle and magic-angle sample spinning (PISEMAMAS)

High-resolution two-dimensional ¹⁵N chemical shift/¹H-¹⁵N dipolar coupling polarization inversion spin exchange at the magic angle (PISEMA) spectra of a polycrystalline sample of ¹⁵N-acetylvaline were obtained with and without magic-angle sample spinning. These spectra demonstrate the advantages of the PISEMA experiment over conventional approaches to separated local-field spectroscopy, especially the high resolution in the dipolar dimension where the spinning sidebands have uniformly narrow linewidths.     

New localized structures of a (2+1)-dimensional system obtained by variable separation approach

Starting from a quite universal formula, which is obtained by variable separation approach and valid for many (2+1)-dimensional nonlinear physical models, a new general type of solitary wave, i.e., semifolded solitary waves (SFSWs) and semifoldons, is defined and studied. We investigate the behaviors of the interactions for the new semifolded localized structures both analytically and graphically. Some novel features or interesting behaviors are revealed.     

Synthesis and superconductivity of a new 1222-type T1-based layered cuprate (T1, Nb) Sr2(Nd,Ce)2Cu2O z

Synthesis and superconductivity of a new 1222-type layered cuprate (Tl_1–x Nb _x ) Sr₂(Nd_1–y Ce _y )₂Cu₂O _z have been studied. The structure of this cuprate is directly related to that of Nb-1222 NbSr₂(Nd, Ce)₂Cu₂O _z with tetragonal body-center lattice. Partial substitution of Tl for Nb in Nb-1222 phase improves its superconductivity. (Tl_1–x Nb _x ) Sr₂(Nd_0.75Ce_0.25)₂Cu₂O _z samples prepared by the typical procedure exhibit superconductivity withT _c of 30–40 K. Effects of Tl and Nb on superconductivity of this cuprate are briefly discussed.     

T 1−T 2 NMR correlation studies of high-pressure-processed starch and potato tissue

Two-dimensionalT ₁?T ₂ correlation spectroscopy is used to monitor the effect of high-pressure and microwave processing on the microscopic water distribution and starch chain dynamics in water-saturated packed beds of native A and B type starches. B type starches are shown to be more resistant to pressure treatment than A type starches. High-pressure-induced A type starch gels are also shown to be radically different from the corresponding thermally induced gel. Although the cell walls of raw potato are resistant to high-pressure damage, the tonoplast and plasmalemma membranes are disrupted by high pressure.     

Relaxation of the topological T1 process in a two-dimensional foam

The so-called topological T1 process, during which bubbles within a foam exchange neighbours is studied. The Durand and Stone model (Phys. Rev. Lett., 97, 226101 (2006)) describes the growth of a film that is newly created during the T1 process, and also the evolution of surfactant concentration on this newly created film. Here some characteristic features of the Durand and Stone model (not previously described by Durand and Stone) are elucidated. In particular it is shown that the surfactant concentration on the newly created film is predicted to undergo an extremely rapid initial evolution, which occurs long before the film itself approaches anywhere near its final equilibrium length. Associated with this, the predicted length of the newly created film tends to exhibit an extremely rapid acceleration early on in its growth. An intermediate asymptotic analysis is developed to explain the above model predictions, by focussing on the regime when the film is several times larger than its initial length, but still several times smaller than its final length. A physical explanation is offered for these predictions in terms of slippage between material points instantaneously at the end of the newly created film, and the evolving location of the film endpoint itself: this slippage implies surfactant being transferred onto the newly created film from neighbouring films, overwhelming the amount of surfactant initially present. The implications of these predictions for the likely observations in an experimental study of the T1 process are discussed.     

Effective spin susceptibility, electron mass and Landé factor in two-dimensional (2D) Si inversion layers

We have studied the silicon (Si) band-structure, electron–electron and electron-ionized donor interaction effects on our accurate and approximate results (AcR and ApR) for renormalized effective spin susceptibitity (RESS), electron mass (EEM), Landé factor and spin polarization in the impure 2D Si (electron system), showing that:(i) our ApR, being strongly deviated from our AcR, reproduces approximately all the data obtained recently by Pudalov et al. (Phys. Rev. Lett. 88 (2002) 196404) [in particular, RESS =4.7 at the critical value of Wigner–Seitz radius r_s: r_s=r_c≈8.5 at which occur the “apparent” metal–insulator transition (MIT)] and can also be compared with other ApRs found in the recent literature,(ii) both the RESS and EEM produce physical singularities at the same critical value: r_s=r_c11.05661 (weakly disordered samples) at which occurs the “true” MIT; the existence of such two “apparent and true” critical values in this impure system agrees with a recent discussion by Abrahams et al. (Rev. Mod. Phys. 73 (2001) 251), and(iii) at r_s=r_c=8.5, at which occurs the “apparent” MIT, our AcR for effective spin polarization and the corresponding result, obtained using a disordered Hubbard model and a determinant quantum Monte Carlo method by Denteneer and Scalettar (Phys. Rev. Lett. 90 (2003) 246401), both give the same result: ξ_eff.=ξ_c0.31 at B0.4 T, which is found to be lower than the critical parallel magnetic field for full spin polarization, B_c=1.29 T, supporting thus the existence of such an “apparent” MIT.