核磁共振弛豫时间测量数据处理方法的讨论

分析和讨论了在超小型核磁共振成像仪测量弛豫时间T1的数据处理方法中存在的问题,并提出了测量方法和数据拟合的改进方案.     

A new method for multi-exponential inversion of NMR relaxation measurements

The NMR technique has been widely applied to petroleum well logging and rock core analysis since the 1990s when NUMAR introduced a reliable NMR logging tool to the oil industry. It has been playing an important role for prospecting and exploiting resource of oil and gas for the last ten years. In an oil well, NMR can provide parameters of reservoir and fluid properties, such as porosity, pore size distribution, bound water volume, bulk volume of free water, permeability, in-situ fluid dif…     

Sensitivity quantification of remote detection NMR and MRI

A sensitivity analysis is presented of the remote detection NMR technique, which facilitates the spatial separation of encoding and detection of spin magnetization. Three different cases are considered: remote detection of a transient signal that must be encoded point-by-point like a free induction decay, remote detection of an experiment where the transient dimension is reduced to one data point like phase encoding in an imaging experiment, and time-of-flight (TOF) flow visualization. For all cases, the sensitivity enhancement is proportional to the relative sensitivity between the remote detector and the circuit that is used for encoding. It is shown for the case of an encoded transient signal that the sensitivity does not scale unfavorably with the number of encoded points compared to direct detection. Remote enhancement scales as the square root of the ratio of corresponding relaxation times in the two detection environments. Thus, remote detection especially increases the sensitivity of imaging experiments of porous materials with large susceptibility gradients, which cause a rapid dephasing of transverse spin magnetization. Finally, TOF remote detection, in which the detection volume is smaller than the encoded fluid volume, allows partial images corresponding to different time intervals between encoding and detection to be recorded. These partial images, which contain information about the fluid displacement, can be recorded, in an ideal case, with the same sensitivity as the full image detected in a single step with a larger coil.     

Efficient and accurate determination of the overall rotational diffusion tensor of a molecule from (15)N relaxation data using computer program ROTDIF

We present a computer program ROTDIF for efficient determination of a complete rotational diffusion tensor of a molecule from NMR relaxation data. The derivation of the rotational diffusion tensor in the case of a fully anisotropic model is based on a six-dimensional search, which could be very time consuming, particularly if a grid search in the Euler angle space is involved. Here, we use an efficient Levenberg-Marquardt algorithm combined with Monte Carlo generation of initial guesses. The result is a dramatic, up to 50-fold improvement in the computational efficiency over the previous approaches. This method is demonstrated on a computer-generated and real protein systems. We also address the issue of sensitivity of the diffusion tensor determination from (15)N relaxation measurements to experimental errors in the relaxation rates and discuss possible artifacts from applying higher-symmetry tensor model and how to recognize them.     

A direct method for numerical analysis of relaxation of the statistical characteristics of brownian motion

We propose a numerical method for analyzing the relaxation of coordinate moments of the Brownian motion of a system described by a stochastic Liouville equation of the 1st or 2nd order with moderate-order polynomial nonlinearity. Using exact or approximate recurrence relations for the stationary values, at a certain step, we break the chain of equations for the moments of the Brownian motion. The evolution of the model probability distribution of coordinates is found from the numerical solution of the differential equations of relaxation of moments. This method is used for analyzing the nonstationary probability characteristics of a system with nonlinear rigidity described by a third-degree polynomial. The relaxation of moments and of the model probability distribution is plotted and tabulated. The results obtained allow us to draw certain conclusions on the statistical dynamics of the Brownian motion of the systems studied. Nizhny Novgorod Architecture and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 922–930, September 1999     

Assigning uncertainties in the inversion of NMR relaxation data

Recovering the relaxation-time density function (or distribution) from NMR decay records requires inverting a Laplace transform based on noisy data, an ill-posed inverse problem. An important objective in the face of the consequent ambiguity in the solutions is to establish what reliable information is contained in the measurements. To this end we describe how upper and lower bounds on linear functionals of the density function, and ratios of linear functionals, can be calculated using optimization theory. Those bounded quantities cover most of those commonly used in the geophysical NMR, such as porosity, T(2) log-mean, and bound fluid volume fraction, and include averages over any finite interval of the density function itself. In the theory presented statistical considerations enter to account for the presence of significant noise in the signal, but not in a prior characterization of density models. Our characterization of the uncertainties is conservative and informative; it will have wide application in geophysical NMR and elsewhere.     

Protein dynamics using frequency-dependent order parameters from analysis of NMR relaxation data

A novel approach is described to analyze NMR relaxation data on proteins. This method introduces the frequency-dependent order parameter, S(2)(omega), in order to estimate contributions to the generalized order parameter S(2) from different motional frequencies occurring on the picosecond to nanosecond time scales. S(2)(omega) is defined as the sum of a specified set of weighting coefficients from the Lorentzian expansion of the spectral density function. 15N NMR relaxation data (500, 600, and 800 MHz) on protein GB1 exemplify the method. Using this approach provides information on motional restrictions over specific frequency or time scale ranges and provides a normalized comparison of motional restrictions between proteins having different overall tumbling correlation times.     

The DOSY Toolbox: A new tool for processing PFG NMR diffusion data

The DOSY Toolbox is a free programme for processing PFG NMR diffusion data (sometimes loosely referred to as DOSY data), distributed under the GNU General Public License. NMR data from three major manufacturers can be imported and all processing is done in a user-friendly graphical user interface. The Toolbox is completely free-standing in the sense that all necessary basic processing of NMR data (e.g., Fourier transformation and phasing) is catered for within the programme, as well as a number of methods specific to DOSY data (e.g., DOSY and SCORE). The programme is written in MATLAB^® and as such can be run on any platform, but can also run independent of MATLAB^® in a free-standing compiled version for Windows, Mac, and Linux.     

A method for detection of spectral spin diffusion from minor peaks, and its application to F MAS NMR of antimony(III)-doped fluorapatite

A new technique for detecting spectral spin diffusion in solids under MAS NMR conditions that is particularly well suited for accurately measuring cross-relaxation from minor spectral components is presented. The pulse sequence, SINK (Saturation Inter-Nuclear Kinetics), selectively saturates the magnetization of a minor spectral component with a series of rotor-synchronized DANTE pulse trains and monitors spin diffusion to other peaks with a non-selective 90° pulse. We have used SINK with ¹⁹F MAS NMR on samples of calcium fluorapatite doped with Sb³⁺ to measure spin diffusion between a weak peak at 68.6 ppm due to fluoride ions associated with Sb³⁺ and other peaks in the spectrum. The SINK experiment clearly demonstrates that spin diffusion from the former peak to the main resonance of fluorapatite at 64.0 ppm is faster than spin diffusion to a second antimony-related peak at 65.6 ppm. These results strengthen our previous conclusion that antimony(III) occupies a phosphate site in the apatite lattice, with an SbO₃³⁻ group replacing a PO₄³⁻ group. The SINK experiment also enables the detection of a “hidden” peak at approximately 62.9 ppm that is otherwise obscured by the intense main peak at 64.0 ppm.     

The effect of rotational angle and experimental parameters on the diffraction patterns and micro-structural information obtained from q-space diffusion NMR: implication for diffusion in white matter fibers

Diffusion NMR may provide, under certain experimental conditions, micro-structural information about confined compartments totally non-invasively. The influence of the rotational angle, the pulse gradient length and the diffusion time on the diffusion diffraction patterns and q-space displacement distribution profiles was evaluated for ensembles of long cylinders having a diameter of 9 and 20 microm. It was found that the diffraction patterns are sensitive to the rotational angle (alpha) and are observed only when diffusion is measured nearly perpendicular to the long axis of the cylinders i.e., when alpha= 90 degrees +/- 5 degrees under our experimental conditions. More importantly, we also found that the structural information extracted from the displacement distribution profiles and from the diffraction patterns are very similar and in good agreement with the experimental values for cylinders of 20 microm or even 9 microm, when data is acquired with parameters that satisfy the short gradient pulse (SGP) approximation (i.e., delta -->0) and the long diffusion time limit. Since these experimental conditions are hardly met in in vitro diffusion MRI of excised organs, and cannot be met in clinical MRI scanners, we evaluated the effect of the pulse gradient duration and the diffusion time on the structural information extracted from q-space diffusion MR experiments. Indeed it was found that, as expected, accurate structural information, and diffraction patterns are observed when Delta is large enough so that the spins reach the cylinders' boundaries. In addition, it was found that large delta results in extraction of a compartment size, which is smaller than the real one. The relevance of these results to q-space MRI of neuronal tissues and fiber tracking is discussed.     

A simulation based method to assess inversion algorithms for transverse relaxation data

NMR relaxometry is a very useful tool for understanding various chemical and physical phenomena in complex multiphase systems. A Carr-Purcell-Meiboom-Gill (CPMG) [P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1991] experiment is an easy and quick way to obtain transverse relaxation constant (T₂) in low field. Most of the samples usually have a distribution of T₂ values. Extraction of this distribution of T₂s from the noisy decay data is essentially an ill-posed inverse problem. Various inversion approaches have been used to solve this problem, to date. A major issue in using an inversion algorithm is determining how accurate the computed distribution is. A systematic analysis of an inversion algorithm, UPEN [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data, Journal of Magnetic Resonance 132 (1998) 65–77; G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data II. Data spacing, T₂ data, systematic data errors, and diagnostics, Journal of Magnetic Resonance 147 (2000) 273–285] was performed by means of simulated CPMG data generation. Through our simulation technique and statistical analyses, the effects of various experimental parameters on the computed distribution were evaluated. We converged to the true distribution by matching up the inversion results from a series of true decay data and a noisy simulated data. In addition to simulation studies, the same approach was also applied on real experimental data to support the simulation results.     

Processing of heteronuclear NMR relaxation data with the new software DASHA

The new program DASHA is an efficient implementation of common data processing steps for the protein internal dynamic analysis. The “model-free” parameters and their uncertainties (Lipari G., Szabo A.: J. Am. Chem. Soc.104, 4546–4559 (1982) can be calculated from an arbitrary combination of experimental data sets (i.e. heteronuclear¹H?¹⁵N or¹H?¹³C relaxation times and NOE values at different spectrometer frequencies). Anisotropy of the molecular rotational diffusion could be also taken into account without introduction of the new adjustable parameters into the spectral density functionJ(ω), provided the structure of the molecule is known. Parameters of chemical (conformational) exchange can be estimated from the CPMG spin-lock frequency dependences (Bloomet al.: J. Chem. Phys.42, 1615–1624 (1965); Orekhovet al.: Eur. J. Biochem.219, 887–896 (1994). The program can be used both in the interactive and batch modes. It has sophisticated PostScript plotting facilities.     

NMR studies of water diffusion and relaxation in hydrating slag-based construction materials.

The NMR relaxation properties of hydrating blast-furnace slag cements have recently been shown to be dominated by the effect of water self-diffusion in internal magnetic field gradients in the pastes. While this was suggested on the basis of NMR relaxometry and magnetic susceptibility data, we report here the results from first direct studies of the water self-diffusion in the hydrating paste using a specialized PFG sequence and very intensive magnetic field gradient pulses.     

A fast method for the quantification of fat fraction and relaxation times: Comparison of five sites of bone marrow

PurposeBone marrow is found either as red bone marrow, which mainly contains haematopoietic cells, or yellow bone marrow, which mainly contains adipocytes. In adults, red bone marrow is principally located in the axial skeleton. A recent study has introduced a method to simultaneously estimate the fat fraction (FF), the T1 and T2* relaxation times of water (T1w, T2*w) and fat (T1f and T2*f) in the vertebral bone marrow. The aim of the current study was to measure FF, T1w, T1f, T2*w and T2*f in five sites of bone marrow, and to assess the presence of regional variations.MethodsMRI experiments were performed at 1.5 T on five healthy volunteers (31.6 ± 15.6 years) using a prototype chemical-shift-encoded 3D multi-gradient-echo sequence (VIBE) acquired with two flip angles. Acquisitions were performed in the shoulders, lumbar spine and pelvis, with acquisition times of < 25 seconds per sequence. Signal intensities of magnitude images of the individual echoes were used to fit the signal and compute FF, T1w, T1f, T2*w and T2*f in the humerus, sternum, vertebra, ilium and femur.ResultsRegional variations of fat fraction and relaxation times were observed in these sites, with higher fat fraction and longer T1w in the epiphyses of long bones. A high correlation between FF and T1w was measured in these bones (R = 0.84 in the humerus and R = 0.84 in the femur). In most sites, there was a significant difference between water and fat relaxation times, attesting the relevance of measuring these parameters separately.ConclusionThe method proposed in the current study allowed for measurements of FF, T1w, T1f, T2*w and T2*f in five sites of bone marrow. Regional variations of these parameters were observed and a strong negative correlation between the T1 of water and the fat fraction in bones with high fat fractions was found.     

Unresolved correlation time spectra and interpretation of NMR relaxation time data for superionic conductors

Problems in relating the results of NMR relaxation time measurements to the results of bulk conductivity/diffusion studies for superionics have been discussed in a number of ways, such as their being a result of lack of knowledge of the appropriate motional correlation function. It is argued that, in the case of hydrated proton conductors at least, the problem is more fundamental. When previously unrecognized temperature-dependent correlation time spectra are present, these cannot be resolved in reduction of relaxation time data and information on any single contributory motion is not simply available.     

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.     

A statistical method for characterizing the noise in nonlinearly reconstructed images from undersampled MR data: The POCS example

The projection-onto-convex-sets (POCS) algorithm is a powerful tool for reconstructing high-resolution images from undersampled k-space data. It is a nonlinear iterative method that attempts to estimate values for missing data. The convergence of the algorithm and its other deterministic properties are well established, but relatively little is known about how noise in the source data influences noise in the final reconstructed image. In this paper, we present an experimental treatment of the statistical properties in POCS and investigate 12 stochastic models for its noise distribution beside its nonlinear point spread functions. Statistical results show that as the ratio of the missing k-space data increases, the noise distribution in POCS images is no longer Rayleigh as with conventional linear Fourier reconstruction. Instead, the probability density function for the noise is well approximated by a lognormal distribution. For small missing data ratios, however, the noise remains Rayleigh distributed. Preliminary results show that in the presence of noise, POCS images are often dominated by POCS-enhanced noise rather than POCS-induced artifacts. Implicit in this work is the presentation of a general statistical method that can be used to assess the noise properties in other nonlinear reconstruction algorithms.     

A statistical study of the defect crystal lattice relaxation

That the statistical method of conditional distributions was productively used to describe uniform and, subsequently, nonuniform systems is indicative of its efficiency, which allows more and more complicated physical effects to be investigated with respect adjustments of the basic idea of the method to every particular situation. So, in this paper the earlier developed statistical theory of nonuniform systems is extended to the case of irregular deformable crystalline media with the aim of concerted account of the contributions due to the real lattice deformation within the framework of the statistical conditional distribution method. Various kinds of defects resulting in the relaxation of the lattice parameters near the defects may be a source of the lattice regularity disturbances. The statistical expression obtained for crystal free energy depends parametrically on the deformation tensor of the medium.     

Quantum calculations of rotational and NMR relaxation,depolarized Rayleigh and rotational Raman line shapes for H2(HD)−He mixtures

The two ab initio vibrotor potentials of H₂?He previously published by Meyer, Hariharan, and Kutzelnigg have been composed in one potential grid. After using this potential in close coupled scattering calculations we have subsequently obtained rotational relaxation cross sections for para- and ortho-H₂, NMR relaxation times for ortho-H₂, depolarized Rayleigh line broadening cross sections for para-, ortho-, and normal-H₂, and rotational Raman line width and shift cross sections for S₀(0), S₀(2) transitions, at temperatures between 20 and 450 K. The agreement with previous and more recent measurements has been found completely satisfying, with the exception of the rotational relaxation cross sections of para-H₂. Throughout the paper previous results derived from the multiple property fit of Shafer and Gordon have been included for comparison. The new ab initio potential is obviously better, except for the rotational relaxation cross sections. The interaction potential of HD?He transformed from the new H₂?He potential is also presented in this paper. It has been used recently in a very successful application of the Waldmann-Snider kinetic theory describing transport, relaxation, and reorientation phenomena in magnetic fields. Therefore, only the rotational relaxation cross sections, converged up to about 400 K, have been presented in this paper.     

On a method for detection of subsurface objects from ultrabroadband GPR data

An approach is presented, which allows determination of size and shape of subsurface low-contrast objects from their dielectric properties and location of people and things present inside the buildings from the echo ultrabroadband electromagnetic signals. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 94–99, November, 2008.