Trabecular bone score (TBS): available knowledge, clinical relevance, and future prospects

The diagnosis of osteoporosis rests on areal bone mineral density (BMD) measurement using DXA. Cancellous bone microarchitecture is a key determinant of bone strength but cannot be measured using DXA. To meet the need for a clinical tool capable of assessing bone microarchitecture, the TBS was developed. The TBS is a texture parameter that evaluates pixel gray-level variations in DXA images of the lumbar spine. The TBS variations may reflect bone microarchitecture. We explain the general principles used to compute the TBS, and we report the correlations between TBS and microarchitectural parameters. Several limitations of the TBS as it is used now are pointed out. We discuss data from currently available clinical studies on the ability of the TBS to identify patients with fractures and to evaluate the fracture risk. We conclude that this new index emphasizes the failure of the BMD T-score to fully capture the fragility fracture risk. However, although microarchitecture may influence the TBS, today, to the best of our understanding, there is no sufficient evidence that a TBS measurement provides reliable information on the status of the bone microarchitecture for a given patient. The TBS depends on gray-level variations and in a projectional image obtained in vivo, these variations can have many causes. Nevertheless, as clinical studies suggest that the TBS predicts the risk of fracture even after adjustment for BMD, we are encouraged to learn more about this score. Additional studies will have to be performed to assess the advantages and limitations of the TBS, in order to ensure that it is used appropriately in clinical practice.

Rheo-SAXS investigation of shear-thinning behaviour of very anisometric repulsive disc-like clay suspensions

Aqueous suspensions of swelling clay minerals exhibit a rich and complex rheological behaviour. In particular, these repulsive systems display strong shear-thinning at very low volume fractions in both the isotropic and gel states. In this paper, we investigate the evolution with shear of the orientational distribution of aqueous clay suspensions by synchrotron-based rheo-SAXS experiments using a Couette device. Measurements in radial and tangential configurations were carried out for two swelling clay minerals of similar morphology and size, Wyoming montmorillonite and Idaho beidellite. The shear evolution of the small angle x-ray scattering (SAXS) patterns displays significantly different features for these two minerals. The detailed analysis of the angular dependence of the SAXS patterns in both directions provides the average Euler angles of the statistical effective particle in the shear plane. We show that for both samples, the average orientation is fully controlled by the local shear stress around the particle. We then apply an effective approach to take into account multiple hydrodynamic interactions in the system. Using such an approach, it is possible to calculate the evolution of viscosity as a function of shear rate from the knowledge of the average orientation of the particles. The viscosity thus recalculated almost perfectly matches the measured values as long as collective effects are not too important in the system.

General Scaling Phenomena in Porous Silica Gels as Probed by Saxs and Molecular Adsorption (Tiling)

Using N2 adsorption (B.E.T.), small angle X-ray scattering and molecular adsorption (tiling) we attempt to describe the internal pore morphology and surface structure of three porous silica gels. The results are analyzed from both a classical euclidian and a fractal scaling viewpoint. The applicability of both viewpoints are shown to be limited but important in describing the structure of porous silicas.

Optimal reaction time for surface-mediated diffusion

We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which explicitly takes into account the combination of surface and bulk diffusion, shows the importance of correlations induced by the coupling of the switching dynamics to the geometry of the confinement, ignored so far. Our results show that, in the context of interfacial systems in confinement, the reaction time can be minimized as a function of the desorption rate from the surface, which puts forward a general mechanism of enhancement and regulation of chemical and biological reactivity.

Deviation from Archie's law in partially saturated porous media: Wetting film versus disconnectedness of the conducting phase

We experimentally study the electrical transport in partially water-saturated pore network. The porous medium under investigation is a Fontainebleau sandstone, characterized by x-ray tomography. We show the existence of two electrical conductivity regimes. At high water saturation, the electric resistivity follows a well-known Archie law. Below a water saturation S_{w} approximately 0.2 , a strong negative deviation from this Archie law is observed. We attribute this transition to the existence of "a thick liquid film," assuring the ionic conduction in the low saturation regime. A numerical simulation is proposed to confirm this scenario. Two possible protocols are used to distribute the brine phase in the pore network of a three-dimensional microtomography image. The first one is based on a minimization of the interfacial energy. The second takes into account a quasistatic capillary displacement. The classical random-walk algorithm is used to compute the electric conductivity at various water saturations. Without the "thick film," both of the two fluid-placing protocols show a disconnectedness transition of the brine phase when S_{w}<0.2 . Adding this "film" to solid surface, the electrical continuity is maintained. The bending down trend is correctly reproduced, showing that in this range, the electric response cannot be described by a power law as usual.

Intermittent Brownian dynamics over a rigid strand: heavily tailed relocation statistics in a simple geometry

We analyze the intermittent Brownian dynamics (a succession of adsorption and bulk relocation steps) of a test particle over a single strand. We propose an analytic expression of the relocation time distribution at all times. We show that this distribution has a nontrivial heavily tailed statistics at long time with a diverging average relocation time. In order to experimentally probe this first passage statistics, we follow the intermittent Brownian dynamics of water molecules over long and stiff imogolite mineral strands, using a field cycling NMR dispersion technique. Our analytic derivation is found to be in good agreement with experimental data on a large domain of observation. Implications for the efficiency of a search strategy on a single filament are then discussed and the importance of the confinement and/or the finite size effect is emphasized.

Changes in humic acid conformation during coagulation with ferric chloride: implications for drinking water treatment

Electrophoretic mobility, pyrene fluorescence, surface tension measurements, transmission electron microscopy on resin-embedded samples, and X-ray microscopy (XRM) were combined to characterize the aggregates formed from humic colloids and hydrolyzed-Fe species under various conditions of pH and mixing. We show that, at low coagulant concentration, the anionic humic network is reorganized upon association with cationic coagulant species to yield more compact structures. In particular, spheroids about 80nm in size are evidenced by XRM at pH 6 and 8 just below the optimal coagulant concentration. Such reorganization of humic colloids does not yield surface-active species, and maintains negative functional groups on the outside of humic/hydrolyzed-Fe complex. We also observe that the humic network remains unaffected by the association with coagulant species up to the restabilization concentration. Upon increasing the coagulant concentration, restructuration becomes limited: indeed, the aggregation of humic acid with hydrolyzed-Fe species can be ascribed to a competition between humic network reconformation rate and collision rate of destabilized colloids. A decrease in stirring favors the shrinkage of humic/hydrolyzed-Fe complexes, which then yields a lower sediment volume. Elemental analyses also reveal that the iron coagulant species are poorly hydrolyzed in the destabilization range. This suggests that destabilization mechanisms such as sweep flocculation or adsorption onto a hydroxyde precipitate are not relevant to our case. A neutralization/complexation destabilization mechanism accompanied by a restructuration of flexible humic network is then proposed to occur in the range of pHs investigated.

Irreversible shear-activated aggregation in non-Brownian suspensions

We have studied the effect of shear on the stability of suspensions made of non-Brownian solid particles. We demonstrate the existence of an irreversible transition where the solid particles aggregate at remarkably low volume fractions (phi approximately 0.1). This shear-induced aggregation is dramatic and exhibits a very sudden change in the viscosity, which increases sharply after a shear-dependent induction time. We show that this induction time is related exponentially to the shear rate, reflecting the importance of the hydrodynamic forces in reducing the repulsive energy barrier that prevents the particles from aggregating.

Brownian flights over a fractal nest and first-passage statistics on irregular surfaces

The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining interfacial systems involve a sequence of Brownian flights in the bulk, connecting successive hits with the interface (Brownian bridges). The statistics of times and displacements separating two interface encounters are then determinant in the overall transport. We present a theoretical and numerical analysis of this complex first-passage problem. We show that the bridge statistics is directly related to the Minkowski content of the surface within the usual diffusion length. In the case of self-similar or self-affine interfaces, we show and check numerically that the bridge statistics follows power laws with exponents depending directly on the surface fractal dimension.

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.

Slow dynamics of embedded fluid in mesoscopic confining systems as probed by NMR relaxometry

Mesoscopic media such as porous materials or colloidal dispersions strongly influence the dynamics of the embedded fluid. In the strong-adsorption regime, it was recently proposed that the effective surface diffusion on flat surface is anomalous and exhibits long-time pathology, enlarging the time domain of the embedded-fluid dynamics towards the low-frequency regime. An interesting way to probe such a slow interfacial process is to use the field-cycling NMR relaxometry. This technique is used here to probe the fluid dynamics in two types of interfacial systems: i) a colloidal glass made of thin and flat particles; ii) a fully saturated porous media, the Vycor glass. Experimental results are critically compared to either a simple theoretical model of NMR dispersion involving elementary steps of the fluid dynamics near an interface (loops, trains, tails) or Brownian-dynamics simulations performed inside 3D reconstructions of these confined systems.

Time domain analysis: an alternative way to interpret PGSE experiment

We report a theoretical development which aims at interpreting Pulsed Gradient Spin Echo data for diffusing fluids in saturated porous media. It consists in analyzing the time dependence of PGSE amplitudes for each single gradient strength, and introduces a new diffusion coefficient D(q) as being continuously dependent on the length scale in the material. Both experimental measurements on water saturated bead packings and simulated experiments in 2D and 3D model systems are interpreted with this approach. D(q) is shown to give a new insight in the micro-macro transition. Its evolution vs. the length scale is non trivial, and can be sensitive to local slow kinetic effects.

A new method for three-dimensional skeleton graph analysis of porous media: application to trabecular bone microarchitecture

This paper introduces a new three-dimensional analysis of complex disordered porous media. Skeleton graph analysis is described and applied to trabecular bone images obtained by high resolution magnetic resonance imaging. This technique was developed bearing in mind topological considerations. The correspondence between vertices and branches of the skeleton graph and trabeculae is used in order to get local information on trabecular bone microarchitecture. In addition to real topological parameters, local structural information about trabeculae, such as length and volume distributions, are obtained. This method is applied to two sets of samples: six osteoporosis and six osteoarthritis bone samples. We demonstrate that skeleton graph analysis is a powerful technique to describe trabecular bone microarchitecture.

Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture

The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

Adsorption of a Cationic Surfactant on Na-Montmorillonite: Inspection of Adsorption Layer by X-Ray and Fluorescence Spectroscopies

The adsorption of the cationic surfactant BDDAC on a hydrophilic smectite (montmorillonite) surface has been investigated, especially in the range of low coverage ratios where surfactant ions are adsorbed through cation-exchange with the counterions of the clay. The surfactant coions (Cl(-)) were found to be adsorbed simultaneously with the cationic part after a complete alkyl ammonium ion-exchange of montmorillonite (CEC). We observe that organoclay particles remain flocculated in aqueous medium in almost all the range of adsorption isotherms up to 1.38 CEC and afterward redisperse incompletely. The intercalation of surfactant in the interlamellar space was followed by X-ray measurements. Fluorescence spectroscopy was used to obtain information about the adsorption layer at the interface. A calculation from geometrical considerations and from adsorption isotherms shows that below 1.38 CEC, there is a flat double layer in the interlamellar space and after this amount of adsorbed surfactant, an interstratified clay-surfactant mixed system is formed. Copyright 1999 Academic Press.

Analysis of the Multilayer Thickness Relationship for Water Vapor and Nitrogen Adsorption

Six silica gels, where each gel had a characteristic calibrated pore size (40-4000 Å), have been characterized both by water vapor and nitrogen adsorption isotherms. From these results, it was concluded that two-thirds of the silica surface is hydrophobic. The selection of wide pores (>300 Å) has enabled the determination of both the water and nitrogen t-curves for porous silica. It was observed that the development of the multilayer was identical in the wide pores irrespective of their size between 300 and 4000 Å. The porous silica t-curve for water coincided exactly with the t-curve of nonporous adsorbents provided that their BET C constants were similar. For nitrogen t-curves, a matching BET C constant ensured similarity only in the monolayer region, above which divergence progressively increased, becoming important close to saturation. The effect of the t-curve choice on the pore size distribution was established. A t-curve displaying reduced adsorption had a tendency to shift the pore-size distribution to lower dimensions, toward the micropore region. As a consequence, the cumulated surface area obtained from the BJH model gave increasingly higher values than the BET nitrogen surface area. However, the pore-size distribution was shifted to higher pore sizes when the selected t-curve was above the natural t-curve. Errors as much as 25% were detected for the mean pore radius and cumulated surface area for certain literature t-curves. A comparison of the water and the nitrogen t-curves indicated a crossover point when the water multilayer thickness became greater than the nitrogen thickness. Such behavior lends support to the cooperative adsorption mechanism for water vapor once a fixed number of water molecules (two layers) are present on the surface. Copyright 1998 Academic Press.

A NMR investigation of adsorption/desorption hysteresis in porous silica gels

The purpose of this study is to investigate possible differences in geometry and connectivity of the liquid phase in a partially water-satured porous medium between the adsorption and the desorption branches, using a series of silica gels. This was done by comparing the T1 and T2 relaxation times (in 1H and 2H nuclear magnetic resonance (NMR) relaxation) as well as the water self-diffusion coefficient D (in 1H) along the two branches of the adsorption/desorption isotherms. The results show that the two relaxation times and the diffusion coefficient are strongly dependent on the water content (saturation level). When plotted in normalized coordinates, the T1 and T2 vs. P/Po curves fit closely the adsorption/desorption isotherms, which validates the two-population, fast-exchange model. Furthermore, because at equivalent saturation levels, there is no difference between the relaxation times and diffusion coefficients obtained along the adsorption branch and those obtained along the desorption branch, one is led to the conclusion that despite different equilibrium conditions, the geometry and connectivity of the liquid phase are statistically the same along the two branches.

Adsorption of Nonionic Surfactants on Kaolins

Adsorption of nonionic surfactant on kaolins of different origins was studied. The shape of the isotherm differs only slightly according to the origin of the kaolin, but the amount adsorbed is quite different. The relation between the morphology of the kaolin particles and the shape of the isotherm is not clear. Fluorescence studies show two different solubilization sites for adsorbed pyrene molecules. However, these two environments could not be correlated to the basal and lateral surfaces of the mineral particles.

129Xe NMR as a probe of the dynamics of gas confined in porous Vycor

We use 129Xe NMR to probe the diffusion of xenon gas in the porous network of Vycor glass, by monitoring its relaxation properties. When the mean free path of the diffusing gas is larger than the pore size (Knudsen conditions), both 129Xe chemical shifts and relaxation rates are sensitive to the confinement of xenon gas within a porous solid. The influence of both temperature and xenon pressure are recorded on the 129Xe chemical shifts and relaxation rates, in order to characterise the xenon/Vycor interactions. Monte Carlo (MC) and Molecular Dynamics (MD) simulations, using a numerical model of Vycor, are required to interpret the relaxation properties of xenon. MD simulations clearly establish the occurrence of confined diffusion of xenon within Vycor, related to the geometry of this porous media. This work shows the potentiality of NMR relaxation to obtain dynamical information on the diffusion within porous media.

Chemical and biological microstructures as probed by dynamic processes

The dynamic process of electronic energy transfer is shown to be an important tool for probing the microstructure of molecular systems, particularly those in which donors and acceptors occupy specifically labeled sites of spatially confining host matrices. Special attention is given to analyzing the temporal behavior of the direct energy transfer reaction for systems in which the dipolar coupling is between a donor and randomly distributed acceptors. This dynamic process is dependent on two competing lengths when the donor and acceptor distribution is determined by the microstructure of the confining system: Rp, the dominant length characterizing the size of the confinement, and R0, which scales the strength of the dipolar coupling. When energy transfer processes are viewed in the context of these two competing lengths, a picture emerges of the microstructure of the confinement that is consistent with and corroborated by other structural probes.