Bone tissue and porous media: common features and differences studied by NMR relaxation

Despite significant differences between bone tissues and other porous media such as oilfield rocks, there are common features as well as differences in the response of NMR relaxation measurements to the internal structures of the materials. Internal surfaces contribute to both transverse (T2) and longitudinal (T1) relaxation of pore fluids, and in both cases the effects depend on, among other things, local surface-to-volume ratio (S/V). In both cases variations in local S/V can lead to distributions of relaxation times, sometimes over decades. As in rocks, it is useful to take bone data under different conditions of cleaning, saturation, and desaturation. T1 and T2 distributions are computed using UPEN. In trabecular bone it is easy to see differences in dimensions of intertrabecular spaces in samples that have been de-fatted and saturated with water, with longer T1 and T2 for larger pores. Both T1 and T2 distributions for these water-saturated samples are bimodal, separating or partly separating inter- and intratrabecular water. The T1 peak times have a ratio of from 10 to 30, depending on pore size, but for the smaller separations the distributions may not have deep minima. The T2 peak times have ratios of over 1000, with intratrabecular water represented by large peaks at a fraction of a ms, which we can observe only by single spin echoes. CPMG data show peaks at about a second, tapering down to small amplitudes by a ms. In all samples the free induction decay (FID) from an inversion-recovery (IR) T1 measurement shows an approximately Gaussian (solid-like) component, exp[-1/2 (T/TGC), with TGC approximately 11.7+/-0.7 micros (GC for "Gaussian Component"), and a liquid-like component (LLC) with initially simple-exponential decay at the rate-average time T(2-FID) for the first 100 micros. Averaging and smoothing procedures are adopted to derive T(2-FID) as a function of IR time and to get T1 distributions for both the GC and the LLC. It appears that contact with the GC, which is presumed to be 1H on collagen, leads to the T2 reduction of at least part of the LLC, which is presumed to be water. Progressive drying of the cleaned and water-saturated samples confirms that the long T1 and T2 components were in the large intertrabecular spaces, since the corresponding peaks are lost. Further drying leads to further shortening of T2 for the remaining water but eventually leads to lengthening of T1 for both the collagen and the water. After the intertrabecular water is lost by drying, T1 is the same for GC and LLC. T(2-FID) is found to be roughly 320/alpha micros, where alpha is the ratio of the extrapolated GC to LLC, appearing to indicate a time tau of about 320 micros for 1H transverse magnetization in GC to exchange with that of LLC. This holds for all samples and under all conditions investigated. The role of the collagen in relaxation is confirmed by treatment to remove the mineral component, observing that the GC remains and has the same TGC and has the same effect on the relaxation times of the associated water. Measurements on cortical bone show the same collagen-related effects but do not have the long T1 and T2 components.     

Nuclear magnetic resonance for cultural heritage

Nuclear magnetic resonance (NMR) portable devices are now being used for nondestructive in situ analysis of water content, pore space structure and protective treatment performance in porous media in the field of cultural heritage. It is a standard procedure to invert T(1) and T(2) relaxation data of fully water-saturated samples to get "pore size" distributions, but the use of T(2) requires great caution. It is well known that dephasing effects due to water molecule diffusion in a magnetic field gradient can affect transverse relaxation data, even if the smallest experimentally available half echo time tau is used in Carr-Purcell-Meiboom-Gill experiments. When a portable single-sided NMR apparatus is used, large field gradients due to the instrument, at the scale of the sample, are thought to be the dominant dephasing cause. In this paper, T(1) and T(2) (at different tau values) distributions were measured in natural (Lecce stone) and artificial (brick samples coming from the Greek-Roman Theatre of Taormina) porous media of interest for cultural heritage by a standard laboratory instrument and a portable device. While T(1) distributions do not show any appreciable effect from inhomogeneous fields, T(2) distributions can show strong effects, and a procedure is presented based on the dependence of 1/T(2) on tau to separate pore-scale gradient effects from sample-scale gradient effects. Unexpectedly, the gradient at the pore scale can be, in some cases, strong enough to make negligible the effects of gradients at the sample scale of the single-sided device.     

Characterization of Porous Materials by Magnetic Relaxometry in the Earth’s Field

In this paper, it is shown how free induction decay signals recorded in the Earth’s magnetic field from water protons confined in porous media can be used to derive transversal relaxation times (T ₂) and their distributions. After T ₂ determination of six sintered glass samples with various pore sizes, the common theoretical model can be fitted to the data set. The T ₂ distribution of water protons in a bimodal porous system is analyzed and compared to mercury porosimetry results. The implications for the calculation of pore sizes and pore size distributions of porous media by this method are discussed.     

Analysis of historical porous building materials by the NMR-MOUSE

Samples of sandstone with and without deposits of silicon oxide stone strengthener as well as samples of historical brick material were analyzed by transverse NMR relaxation and mercury intrusion porosimetry. Relaxation times and relaxation time distributions of the protons from the water saturated samples were measured by low-field NMR using homogeneous and inhomogeneous fields. The measurements in inhomogeneous fields were performed with two different NMR-MOUSE sensors, one with a field gradient of 2 T/m and the other with an average field gradient of about 20 T/m. In the sandstone samples the application of stone strengtheners was shown to result in a confinement of the large pores within the outer layer of a few millimeters depth. Depending on the ferromagnetic contamination of the brick samples, the relaxation time distributions can be affected. The agreement of T2 relaxation time distributions and pore size distributions from mercury intrusion porosimetry was found to be better for the NMR-MOUSE sensors than for the homogeneous field measurements. This is true even for different brick samples, unless the content in ferromagnetic particles is very strong.     

岩心孔隙介质中流体的核磁共振弛豫

弛豫时间是核磁共振研究中的一个重要参数,岩心孔隙介质流体的弛豫过程是自由流体弛豫机制、表面弛豫机制和流体的扩散弛豫机制共同作用的结果,它包含了丰富的孔隙和流体本身的信息. 弛豫时间和自扩散系数的测量及对弛豫时间的分析是核磁共振技术应用于岩心分析和石油勘测的重要内容.     

Spatial distribution of coke residues in porous catalyst pellets analyzed by field-cycling relaxometry and parameter imaging

The distribution of coke residues inside porous catalyst pellets was investigated on the molecular as well as the macroscopic scale. The presence of coke on the pore surface affects the relaxation properties of adsorbed liquid species; these were determined by field-cycling relaxometry for different polar and nonpolar liquids in metal-doped and metal-free catalyst carrier materials. The presence of metal in the Al2O3 matrix had only a minor influence on the dispersion behavior, while the interaction of the adsorbates with the coke layer leads to considerable changes in the relaxation times at low Larmor frequencies. Lowering the temperature to well below the bulk freezing point of dimethyl sulfoxide resulted in a slightly stronger frequency dependence of T1. Not only relaxation times but also the diffusion coefficient is affected by the presence of coke residues in the pores. For macroscopically heterogeneous samples, they offer the possibility to generate maps of the local coke concentration by introducing appropriate filters into NMR imaging sequences. High-temperature regeneration of coked catalysts leads to such heterogeneous distributions which is visualized by T1 parameter imaging.     

An NMR protocol for determining ice crystal size distributions during freezing and pore size distributions during freeze-drying

Nuclear magnetic resonance water proton relaxometry is widely used to investigate pore size distributions and pore connectivity in brine-saturated porous rocks and construction materials. In this paper we show that, by replacing water with acetone, a similar method can be used to probe the porous structure of freeze-dried starch gels and therefore the ice crystal size distribution in frozen starch gels. The method relies on the observation that the starch surface acts as a powerful relaxation sink for acetone proton transverse magnetization so that Brownstein-Tarr theory can be used to extract the pore size distribution from the relaxation data. In addition the relaxation time distribution is found to depend on the spectrometer frequency and the Carr-Purcell-Meiboom-Gill pulse spacing, consistent with the existence of large susceptibility-induced field gradients within the pores. The potential of this approach for noninvasively measuring ice crystal size distributions during freezing and pore size distributions during freeze-drying in other food systems is discussed.     

NMR Relaxation and Diffusion Measurements on Iron(III)-Doped Kaolin Clay

Kaolin clay samples were mixed with various amounts of Fe₂O₃ powder. The influence of this magnetic impurity on NMR relaxation and diffusion measurements on the water in this porous material was investigated. The NMR relaxation measurements showed a nearly mono-exponential decay, leading to the conclusion that the pore size distribution of the clay samples is either narrow and/or that the pores are interconnected very well. Both the longitudinal and the transverse relaxation rate depend linearly on the concentration of the Fe₂O₃ impurity. The NMR diffusion measurements revealed that the Fe₂O₃ causes internal magnetic field gradients that largely exceed the maximum external gradient that could be applied by our NMR apparatus (0.3 T/m). Additional SQUID measurements yielded the magnetization and magnetic susceptibility of the samples at the magnetic field strength used in the NMR measurements (0.8 T). A theoretical estimate of the internal magnetic field gradients leads to the conclusion that the water in the porous clay samples cannot be described by the commonly observed motional averaging regime. Probably an intermediate or a localization regime is induced by the large internal gradients, which are estimated to be on the order of 1 to 10 T/m in the pore volume and may exceed 1000 T/m at the pore surface.     

Combined MR-relaxation and MR-cryoporometry in the study of bone microstructure.

MR-Relaxation (MRR) of 1H nuclei and MR-Cryoporometry (MRC) are combined to assess their feasibility and their potential in the study of bone microstructure. In principle, both techniques are able to give information on the structure of the pore space confining the fluids. Cow femur samples were carefully cored and cleaned in order to remove the natural fluids inside. For MRR analysis quasi-continuous distributions of T(1) and T(2) were obtained on samples fully saturated with water. Cyclohexane was used as a saturating fluid for MRC analysis. All T(1) and T(2) quasi-continuous distributions of water confined in bone samples are more than three decades wide, showing sufficient details to differentiate the samples. Pore size distributions obtained by MRC also differentiate the samples showing different characteristics of the pore space structure in the range of the highest sensitivity of the method (typically 3 to 100 nm, mesopore range). In particular, in samples where MRR shows a large fraction of signal with relaxation times below 10(2) ms, MRC indicates a large fraction of pore volume with pore sizes in the mesopore range.     

Tracking pore to pore exchange using relaxation exchange spectroscopy

We observe the movement of water over time between pores of differing sizes in Castlegate sandstone. To achieve this, we perform an NMR transverse relaxation exchange experiment for several mixing times. The resulting data are converted to 2D T2 distributions using a 2D inverse Laplace transform (ILT). We show for the first time that quantitative analysis of ILT distributions enables one to extract characteristic times for different pores sizes. This information is potentially useful for permeability determination as well as better understanding of exchange between specific pore subpopulations.     

NMR study on the early stages of hydration of a porous carbonate stone

Nuclear Magnetic Resonance was employed to obtain information on the pore filling during the absorption process. A porous carbonate stone, largely employed for buildings and mainly outdoor decorations was studied during water absorption by capillary rise, and filled pores radii were evaluated by comparison between experimental and theoretical parametric magnetization decay curves. Non mono-exponential T2 allowed spin populations to be split among the associated different relaxation times.     

The modulation of coupled relaxation in porous media.

This work investigates the effects of modulation of the transverse and longitudinal relaxation of the surface-fluid/pore-fluid spin system in porous media. Important new NMR well logging applications identify pore fluids by varying the CPMG T(2) pulse spacing to discriminate on the basis of fluid diffusivities in applied and local static magnetic field gradients. However, anomalous laboratory CPMG T(2) results have been reported repeatedly over 25 years for various porous media filled with a single fluid. In relatively large pores, at near bulk conditions, the transverse relaxation of diffusing molecular spins should be proportional to the square of the CPMG pulse spacing tau, the susceptibility contrast at the pore wall and the applied gradient. Observed is a markedly linear tau dependence that saturates at a plateau for large tau. The effect is not quadratic in applied gradient or susceptibility. For large pores, the tau dependence and the saturation value are proportional to the surface-to-volume ratio of the pores. This is in distinct contrast to the behavior observed by Borgia, Brown and Fantazzini for systems with much smaller pores at higher magnetic fields. The large-pore anomalous behaviors can be explained as a modulation of the exchange between surface-fluid and pore-fluid spins, such as observed by Luz and Meiboom in 1963 for water enriched with quadrupolar 17O. Scalar coupling of the solid-surface spins to the fluid-surface spins was postulated by Kleinberg, Kenyon and Mitra as a dominant relaxation mechanism for the surface fluid. The CPMG tau effect can be described as the modulation of the exchange coupling by the CPMG pi pulses, which mix the magnetizations between the exchanging, strongly coupled spin systems of the pore-fluid and the surface-fluid, which is, in turn, weakly coupled by scalar or pseudo-scalar interactions to the fast-relaxing solid surface.     

Water 1H spin-lattice relaxation as a fingerprint of porous media

The 1H spin-lattice relaxation curves of water in samples of natural porous media can be thought of as "fingerprints" of the porous samples. Also the whole of traditional petrophysical properties (permeability, irreducible water saturation, etc.) can be thought of as "fingerprints" of the porous samples. The characteristics of the pore space determine on one hand the relaxation curve shape, and on the other the petrophysical properties. The understanding of this correspondence can contribute to a better definition of the concept of the architecture of a porous medium. At this purpose we have obtained 1H spin-lattice relaxation curves from a collection of standard sandstone cores of known petrophysical properties and characterized by the same surface properties. The results corroborate the idea that the structure of relaxation curves contains information on the distance scale and on the architecture of the pore space, even if it is difficult to extract it without ambiguities. Different methods of curve fitting were performed and compared with the aim of getting the maximum information from the relaxation curves. Several aspects of this kind of investigation indicate the analogies between 1H response of water confined in porous media and in biological tissues.     

Pore surface exploration by NMR

A carefully chosen set of experimental techniques applied to porous media characterization provides results that can be much greater than the sum of the individual parts. The inter-relation and complementarity of a number of techniques will be considered. NMR cryoporometry provides a valuable method of pore size measurement. An NMR method that is more widely used to assess pore dimensions relies on relaxation time analysis of a liquid that fills the pores and the enhanced relaxation that occurs in a liquid at the solid/liquid interface. Thermoporometry, a method based on the application of Differential Scanning Calorimetry (DSC), is closely related to cryoporometry, but employs a different set of assumptions to evaluate pore size distributions. Comparison of the results obtained on the same samples using all these methods together with gas adsorption serves to validate the methods and provide significantly more information about surface-fluid interaction and the behavior of nano-scale material within pores than each method employed in isolation. Technique developments will be discussed and applications of these methods to ideal silicas will be used to illustrate their power, particularly in combination.     

Pore-Size Distributions and Tortuosity in Heterogeneous Porous Media

The diffusion coefficient, measured at long observation times by pulsed-held-gradient NMR, can in principle be used to estimate the tortuosity of a porous medium. This method is useful for glass-sphere packs, but we find that it does not generally work for porous sedimentary rock. Natural sedimentary rocks are characterized by complex microgeometries and broad distributions of pore sizes, which cannot be adequately sampled by diffusing molecules in experimentally accessible observation times. The time-dependent diffusion coefficient D(t) can be distinctly irregular for rocks with very large pores. In heterogeneous porous media, determination of pore-size distribution by relaxation-time measurements and tortuosity by PFG diffusion measurements are mutually exclusive.     

In situ fluid typing and quantification with 1D and 2D NMR logging

In situ nuclear magnetic resonance (NMR) fluid typing has recently gained momentum due to data acquisition and inversion algorithm enhancement of NMR logging tools. T(2) distributions derived from NMR logging contain information on bulk fluids and pore size distributions. However, the accuracy of fluid typing is greatly overshadowed by the overlap between T(2) peaks arising from different fluids with similar apparent T(2) relaxation times. Nevertheless, the shapes of T(2) distributions from different fluid components are often different and can be predetermined. Inversion with predetermined T(2) distributions allows us to perform fluid component decomposition to yield individual fluid volume ratios. Another effective method for in situ fluid typing is two-dimensional (2D) NMR logging, which results in proton population distribution as a function of T(2) relaxation time and fluid diffusion coefficient (or T(1) relaxation time). Since diffusion coefficients (or T(1) relaxation time) for different fluid components can be very different, it is relatively easy to separate oil (especially heavy oil) from water signal in a 2D NMR map and to perform accurate fluid typing. Combining NMR logging with resistivity and/or neutron/density logs provides a third method for in situ fluid typing. We shall describe these techniques with field examples.     

Slowdown of atomic diffusion in liquid gallium–indium alloy under different nanoconfinements

NMR studies were carried out on three isotopes, ⁷¹Ga, ⁶⁹Ga, and ¹¹⁵In, in liquid gallium-indium (Ga–In) alloy embedded into porous glasses with 200 and 5 nm pore sizes at two magnetic fields, 9.4 and 17.6 T. Spin-lattice relaxation and the Knight shift were found to depend on pore size. For porous glass with 5 nm pores the relaxation rate was field-dependent which evidenced that the extreme narrowing limit was no longer valid. Magnetization recovery data were used to evaluate the correlation times of atomic mobility and the quadrupole constants under nanoconfinement.     

多孔材料内部结构的微CT扫描仪分析

本文介绍使用微CT扫描仪对样品进行扫描和图像重构的原理,以蛋糕为样品使用CT对多孔材料的内部结构进行研究,包括样品的孔隙率及其变化,水在大孔内的分布,空腔的三维重构图像和样品内部其它微细特征。结果表明, 浸水的样品在干燥后,骨架收缩,部分孔的尺寸明显增大,孔隙率增加,而没有浸水的蛋糕在干燥前后结构变化不大。文章表明,对于孔径大于几十微米的多孔性材料,使用文中的微CT扫描仪可以有效地对它们进行内部结构的研究。     

NMR 1D-imaging of water infiltration into mesoporous matrices

It is shown that coupling nuclear magnetic resonance (NMR) 1D-imaging with the measure of NMR relaxation times and self-diffusion coefficients can be a very powerful approach to investigate fluid infiltration into porous media. Such an experimental design was used to study the very slow seeping of pure water into hydrophobic materials. We consider here three model samples of nuclear waste conditioning matrices which consist in a dispersion of NaNO₃ (highly soluble) and/or BaSO₄ (poorly soluble) salt grains embedded in a bitumen matrix. Beyond studying the moisture progression according to the sample depth, we analyze the water NMR relaxation times and self-diffusion coefficients along its 1D-concentration profile to obtain spatially resolved information on the solution properties and on the porous structure at different scales. It is also shown that, when the relaxation or self-diffusion properties are multimodal, the 1D-profile of each water population is recovered. Three main levels of information were disclosed along the depth-profiles. They concern (i) the water uptake kinetics, (ii) the salinity and the molecular dynamics of the infiltrated solutions and (iii) the microstructure of the water-filled porosities: open networks coexisting with closed pores. All these findings were fully validated and enriched by NMR cryoporometry experiments and by performing environmental scanning electronic microscopy observations. Surprisingly, results clearly show that insoluble salts enhance the water progression and thereby increase the capability of the material to uptake water.     

气孔分布特性对含水多孔介质气体扩散的影响

本文基于多孔介质的气孔分布特性,计算了多孔介质在含水状态下的扩散性能,并且比较了采用两种方式计算相对渗透率时的相对扩散性能。其结果表明,基于气孔分布的计算结果低于与气孔分布无关的计算结果。另外,疏水性含水多孔介质的扩散性能低于亲水性含水多孔介质的扩散性能,基于气孔分布计算含水多孔介质的气体扩散性能时,Wyllie公式并不适用。