Continuous distribution analysis of marrow 1H magnetic resonance relaxation in bone

Longitudinal and transverse NMR relaxation of 1H nuclei were studied in vitro on fresh animal femur samples. A large number of data points were taken, starting at 100 micros for T(1) by inversion-recovery, at 200 micros for T(2) by single-echo sequences, and at 600 micros for T(2) by CPMG echo-trains. Quasi-continuous distributions of relaxation times were computed, giving wide distributions for all samples. Bulk marrow removed from the medullary cavity showed T(2) distributions from about 20 ms to 600 ms and T(1) distributions from about 40 ms to 2 s. The 1H nuclei in trabecular bone samples, where marrow is confined, may show long tails for T(2) at relaxation times down to 250 micros, the origin of which is still not known. These tails are absent in bulk marrow from the medullary cavity. The differences observed in T(1) distributions among trabecular bone samples are in accordance with the different marrow compositions. Discrete exponential fits were computed also, and in most cases four discrete exponential components were required to fit the experimental data adequately. However, the discrete components do not seem to correspond to any physically distinguishable separate compartments.     

Characterisation of crosslinked elastomeric materials by 1H NMR relaxation time distributions.

One of the most critical structural parameters in elastomeric materials is the density of cross-linking between the polymeric chains. This chemical feature greatly affects chain motions and is determinant in controlling mechanical properties of the final product. NMR techniques are widely and efficiently applied to investigation of such materials. In this study we have measured both transverse and longitudinal 1H relaxation times of a series of polybutadiene rubber samples with increasing crosslink density induced by chemical treatment. This approach allowed the observation of T(1) and T(2) decrease with the increase of crosslink density in the samples examined. The data obtained have been analyzed and compared to theoretical models.     

R'2 measured in trabecular bone in vitro: relationship to trabecular separation.

Measurement of key parameters of the microstructure of trabecular bone is critical to the study of osteoporosis and bone strength. Density based methods cannot provide this information, and give only the total amount of bone present, and not its arrangement. Magnetic resonance imaging has shown the potential to provide information related to the microarchitecture of the trabecular bone matrix. Twelve samples (8 x 8 x 8 mm3 bone cubes) were cut from sheep vertebrae such that the trabeculae ran either parallel or perpendicular to each face. Detailed measurements of the structure of these bone cubes were made by histomorphometry, and compared to R'2 and R*2 measured with a spin and gradient-echo sequence, Partially Refocused Interleaved Multiple Echo, at 1.5 Tesla. The precision of the R'2 measurement (% coefficient of variation) was 8.7+/-5.1, and 7.7+/-4.3 for R*2. Uncorrected values of R'2 and R*2 were significantly correlated to density measured by quantitative computed tomography (r = 0.87, p = 0.0005, and r = 0.90, p = 0.0002, respectively), and trabecular bone area measured by histomorphometry (r = 0.80, p = 0.002, and r = 0.83, p = 0.0008, respectively). Density correction was effected by imaging the same slice of bone in two orientations (90 degrees and 0 degrees ) to the main magnetic field. For both R'2 and R*2 there was a significant difference between measurements in the 90 degrees and 0 degrees orientations (p < 0.01). The difference between the two values was used, and termed R'2net or R*2net. The net parameters were independent of bone mass. R'2net and R*2net were significantly correlated to trabecular separation (p < 0.05) with r = -0.58 and r = -0.62, respectively. These results demonstrate the ability of magnetic resonance imaging to characterize a key measure of the trabecular microstucture. An increase in trabecular separation has important biomechanical consequences in osteoporosis. This result also strengthens the hypothesis that the sensitivity of R'2 to osteoporosis-related bone changes is due to magnetic susceptibility effects in which rapid transitions between bone and marrow create local magnetic field inhomogeneities that result in an increase in R'2 values.     

Selective imaging of biofilms in porous media by NMR relaxation.

Nuclear magnetic resonance imaging (NMRI) techniques were employed to identify and selectively image biological films (biofilm) growing in aqueous systems. Biofilms are shown to affect both the longitudinal (T1) and transverse (T2) NMR relaxation time values of proximal water hydrogens. Results are shown for biofilm growth experiments performed in a transparent parallel-plate reactor. A comparison of biofilm distributions by both NMR and optical imaging yielded general agreement for both an open-flow system and an idealized porous system (the reactor without and with packed glass beads, respectively). The selective imaging of biofilm by relaxation NMRI is dependent upon the resolution of relaxation times for the fluid phases, dynamic range, and signal-to-noise ratio. For open-flow systems, the use of a rapid and quantitative T2-sorted NMRI technique was preferred. For porous systems where T2 values are generally more similar, a T1-weighted technique was preferred.     

Scattering by a fluid cylinder in a porous medium: application to trabecular bone

In a trabecular bone, considered as a nondissipative porous medium, the scattering of an incident wave by cylindrical pores larger than the wavelength is studied. The goal is to know if scattering alone may cause such a high attenuation as that observed in calcaneus. The porous medium is modelized via Biot's theory and the scattering by a single pore is characterized from the definition of a scattering matrix. An approximation of weakly disordered medium is then discussed to estimate the effective attenuation and dispersion as a function of frequency. These effective properties are shown to be different of those measured on calcaneus, due to the neglect of wave conversions during the scattering process.     

Determination of the spatial distribution of multiple fluid phases in porous media by ultra-small-angle neutron scattering

In the present work contrast-matching USANS (ultra-small-angle neutron scattering) was employed in order to determine the spatial distribution of immiscible fluids confined within a macroporous α-Al₂O₃ membrane. Water-air as well as water-hydrocarbon and hydrocarbon-air systems were examined and the analysis of the results, also on the basis of a complementary numerical study provided significant information on the behaviour of the multiphase ensemble as it has been demonstrated that the individual fluids occupy certain positions in the pore space, regardless of the actual values of the respective interfacial properties.     

Modeling and analysis of multiple scattering of acoustic waves in complex media: application to the trabecular bone

The integral equations that describe scattering in the media with step-rise changing parameters have been numerically solved for the trabecular bone model. The model consists of several hundred discrete randomly distributed elements. The spectral distribution of scattering coefficients in subsequent orders of scattering has been presented. Calculations were carried on for the ultrasonic frequency ranging from 0.5 to 3 MHz. Evaluation of the contribution of the first, second, and higher scattering orders to total scattering of the ultrasounds in trabecular bone was done. Contrary to the approaches that use the μCT images of trabecular structure to modeling of the ultrasonic wave propagation condition, the 3D numerical model consisting of cylindrical elements mimicking the spatial matrix of trabeculae, was applied. The scattering, due to interconnections between thick trabeculae, usually neglected in trabecular bone models, has been included in calculations when the structure backscatter was evaluated. Influence of the absorption in subsequent orders of scattering is also addressed. Results show that up to 1.5 MHz, the influence of higher scattering orders on the total scattered field characteristic can be neglected while for the higher frequencies, the relatively high amplitude interference peaks in higher scattering orders clearly occur.     

Analysis of 1H-NMR relaxation time distributions in L1 to L6 rat lumbar vertebrae

A better knowledge of the NMR relaxation behavior of bone tissue can improve the definition of imaging protocols to detect bone diseases like osteoporosis. The six rat lumbar vertebrae, from L1 to L6, were analyzed by means of both transverse (T(2)) and longitudinal (T(1)) relaxation of (1)H nuclei at 20 MHz and 30 degrees C. Distributions of relaxation times, computed using the multiexponential inversion software uniform penalty inversion, extend over decades for both T(2) and T(1) relaxation. In all samples, the free induction decay (FID) from an inversion-recovery (IR) T(1) measurement shows an approximately Gaussian (solid-like) component, exp[-1/2(t/T(GC))2], with T(GC) approximately 12 micros (GC for Gaussian component) and a liquid-like component (LLC) with initially simple-exponential decay. Averaging and smoothing procedures are adopted to obtain the ratio alpha between GC and LLC signals and to get separate T(1) distributions for GC and LLC. Distributions of T(1) for LLC show peaks centered at 300-500 ms and shoulders going down to 10 ms, whereas distributions of T(1) for GC are single broad peaks centered at roughly 100 ms. The T(2) distributions by Carr-Purcell-Meiboom-Gill at 600 micros echo spacing are very broad and extend from 1 ms to hundreds of ms. This long echo spacing does not allow one to see a peak in the region of hundreds of micros, which is better seen by single spin-echo T(2) measurements. Results of the relaxation analysis were then compared with densitometric data. From the study, a clear picture of the intratrabecular and intertrabecular (1)H signals emerges. In particular, the GC is presumed to be due to (1)H in collagen, LLC due to all the fluids in the bone including water and fat, and the very short T(2) peak due to the intratrabecular water. Overall, indications of some trends in composition and in pore-space distributions going from L1 to L6 appeared. Published results on rat vertebrae obtained by fitting the curves by discrete two-component models for both T(2) and T(1) are consistent with our results and can be better interpreted in light of the shown distributions of relaxation times.     

Quantitative measurement and imaging of transport processes in plants and porous media by 1H NMR.

NMR and MRI have been applied to transport processes, that is, net flow and diffusion/perfusion, of water in whole plants, cells, and porous materials. By choosing proper time windows and pulse sequences, magnetic resonance imaging can be made selective for each of the two transport processes. For porous media and plant cells the evolution of the spatial distribution of excited spins has been determined by q-space imaging, using a 20 MHz pulsed 1H NMR imager. The results of these experiments are explained by including spin-relaxation and exchange at boundaries. A 10 MHz portable 1H NMR spectrometer is described, particularly suitable to study the response of net flow in plants and canopies to changing external conditions.     

1H and 2H NMR studies of benzene confined in porous solids: melting point depression and pore size distribution

The pore size distributions of four controlled pore glasses and three silica gels with nominal diameters in the range 4-24 nm were determined by measuring the 1H and 2H NMR signals from the non-frozen fraction of confined benzene and perdeuterated benzene as a function of temperature, in steps of ca. 0.1-1 K. The liquid and solid components of the adsorbate were distinguished, on the basis of the spin-spin relaxation time T2, by employing a spin-echo sequence. The experimental intensity curves of the liquid component are well represented by a sum of two error functions. The mean melting point depression of benzene and perdeuterated benzene confined in the four controlled pore glasses, with pore radius R, follows the simplified Gibbs-Thompson equation DeltaT=kp/R with a kp value of 44 K nm. As expected, the kp value mainly determines the position of the pore size distribution curve, i.e., the mean pore radius, while the transition width determines the shape of the pore size distribution curve. The excellent agreement between the results from the 1H and 2H measurements shows that the effect of the background absorption from protons in physisorbed water and silanol groups is negligible under the experimental conditions used. The overall pore size distributions determined by NMR are in reasonable agreement with the results specified by the manufacturer, or measured by us using the N2 sorption technique. The NMR method, which is complementary to the conventional gas sorption method, is particularly appropriate for studying pore sizes in the mesoporous range.     

Investigation of metabolic changes in irradiated rat brain tissue by means of 1H NMR in vitro relaxation study

The effect of irradiation on concentrations and relaxation behaviour of brain metabolites was studied by means of high-resolution 1H NMR in vitro. The studies were performed on rat brains irradiated with the doses of 20 Gy applied in fractions of 2 Gy. Standard procedures were used to obtain HClO4 extracts of rat brains. The 1H NMR studies of the extracts solutions in D2O were performed using a Varian Inova-300 NMR spectrometer. The integral intensities of the metabolite signals were found to change during the irradiation cycle and after it. These changes are accompanied by the variations in the T1 relaxation times. N-acetylaspartate, glycerophosphocholine, phosphocholine, choline, creatine and phosphocreatine, myoinositol and taurine were analysed as potential markers of irradiation injury.     

Johnson's SB distribution function as applied in the mathematical representation of particle size distributions. Part 1: Theoretical background and numerical simulation

An investigation was carried out of the transformation between the number, length, surface and volume size distributions expressed by Johnson's S_B distribution function – the bounded log-normal distribution function. As is well known, if any of the number, length, surface and volume distributions is log-normal, all the others will also be log-normal. Theoretical analysis suggests that the S_B function may have a similar property. This was confirmed by a computer-aided numerical simulation, in which emphasis was given to the transformation between successive order size distributions, i.e. ?_i(x) → ?_{i + 1}(x) or ?_i(x) → ?_{i ? 1}(x). The numerical results can be applied to the particle size distribution transformation because this transformation can generally be made step by step, for example, ?_i → ?_i?1 (x) → ?_{i ? 2}(x) → … → ?_j(x) for ?_i(x) → ?_j(x) ( i > j).     

The solution conformation and dynamics of biomolecules in the presence of internal motions: The use of jump models for the1H NMR analysis of relaxation data

Summary A jump model has been used to obtain motional information from proton relaxation parameters in complex molecular systems in which multiple internal motions are present. The proposed analysis takes into account changes in orientation and magnitude of interproton vectors, due to overall and internal motions. Intrinsic relaxation contributions can be calculated if the probability for each spatial configuration is independently known. From these contributions jump frequencies may be evaluated, yielding information on local molecular mobility.

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Riassunto è stato usato un modello ?jump? per ottenere informazioni dinamiche da parametri di rilassamento protonico in sistemi macromolecolari con moti interni multipli. L’analisi proposta tiene conto delle variazioni di orientazione ed intensità dei vettori interprotonici causate dai moti interni e browniani. Possono quindi essere calcolati contributi intrinseci al rilassamento se sono note le probabilità relative a ciascuna configurazione spaziale. Da questi contributi intrinseci possono essere calcolate le frequenze dei ?jump? tra le varie configurazioni.

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Резюме Прыжковая модель используется для получения динамической информации из параметров релаксации протонов в сложных молекулярных системах, в которых присутствуют сложные внутренние движения. Предложенный анализ учитывает изменения в ориентациях и величинах векторов между протонами, обусловленные полным и внутренним движениями. Могут быть вычислены вклады внутренней релаксации, если вероятность для каждои пространственной конфигурации является известной. Из этих вкладов могут быть оценены частоты ?прыжков? между различными конфигурациями, т.е. получена информация о локальной молекулярной подвижности.

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To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Biochemical characterization of metastatic lymph nodes of breast cancer patients by in vitro 1H magnetic resonance spectroscopy: a pilot study

Using one-dimensional (1D) and two-dimensional (2D) proton nuclear magnetic resonance (NMR) methods, the perchloric acid extract of involved (n = 11) and noninvolved (n = 12) axillary lymph nodes (ALN) of breast cancer patients was investigated. Resonances from 40 metabolites such as lactate (Lac), glucose, several amino acids (alanine, lysine, glutamic acid, glutamine, etc.), nucleotides (adenosine triphosphate, guanosine triphosphate, uridine triphosphate, uridine monophosphate, etc.), membrane metabolites [glycerophosphocholine (GPC), phosphocoline (PC), phosphoethanolamine (PE), choline] were unambiguously assigned in both the involved and noninvolved ALN. The concentration of PC/GPC (p = 0.002) was significantly higher in the involved compared to noninvolved nodes. In addition, the concentration of glycolytic product Lac (p = 0.0001) was also found to be significantly higher in involved nodes. Increased concentration of membrane metabolites PC/GPC may be attributed to increased membrane synthesis in malignant cells and, therefore, suggests the presence of metastatic cells in lymph nodes. The higher concentration of Lac is indicative of the presence of malignant cells that derive energy via anaerobic glycolytic pathway. Present results demonstrate the potentials of in vitro proton NMR in detecting malignant cells in ALN and such studies may have an important bearing in determining the prognosis of breast cancer patients.     

Resolution enhancement in spectra of natural products dissolved in weakly orienting media with the help of 1H homonuclear dipolar decoupling during acquisition: application to 1H-13C dipolar couplings measurements

In weakly orienting media such as poly-gamma-benzyl-L-glutamate (PBLG) a polymer that forms a chiral liquid crystal in organic solvents, the spectral resolution for embedded molecules is usually poor because of numerous (1)H, (1)H dipolar couplings that generally broaden proton spectra. Therefore (1)H, (13)C dipolar couplings are difficult or impossible to measure. Here, we incorporate Flip-Flop decoupling during detection into an HSQC experiment. Flip-Flop removes the (1)H, (1)H dipolar couplings and scales the chemical shifts of the protons as well as the (1)H, (13)C dipolar couplings during detection. A resolution gain by a factor 1.5-4.2 and improved signal intensity by an average factor of 1.6-1.7 have been obtained. This technique is demonstrated on (+)-menthol dissolved in a PBLG/CDCl(3) phase.     

On the propagation of linear transverse acoustic waves in isotropic media with mechanical relaxation phenomena due to viscosity and a tensorial internal variable: II. Some cases of special interest (Poynting-Thomson,Jeffreys, Maxwell,Kelvin-Voigt,Hooke and Newton media)

The propagation of linear transverse acoustic waves in isotropic media in which mechanical relaxation phenomena occur was considered in a previous paper. In particular expressions for the velocity and attenuation of the waves were obtained and the limiting cases of waves with high and low frequencies were discussed. In the present paper we investigate the propagation of linear transverse acoustic waves in Poynting-Thomson, Jeffreys, Maxwell, Kelvin-Voigt, Hooke and Newton media. We show that the dispersion relations for these waves may be considered as degeneracies of the dispersion relation which we derived in the general case of a viscoanelastic medium with memory. In particular we investigate the explicit dependence of the dispersion relations on the thermodynamic parameters and the phenomenological coefficients.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 1. A phase transition concept to describe magnetic structures in crystals

On the basis of phase transition symmetry theory there has been developed an efficient method of calculating the possible magnetic structures liable to arise from the paramagnetic phase of the crystal. Every magnetic structure is described by the superposition of the basis functions of the irreducible representation incorporated in the magnetic representation of the crystal symmetry group. Convenient formulas are given to calculate the basis functions and composition of the magnetic representation. These formulas permit calculation by referring only to the tables of space group irreducible representations. The technique is illustrated on the example of magnetic structures in crystals with the symmetry group D⁶_3d.