Anisotropy of spin relaxation of water protons in cartilage and tendon

Transverse spin relaxation rates of water protons in articular cartilage and tendon depend on the orientation of the tissue relative to the applied static magnetic field. This complicates the interpretation of magnetic resonance images of these tissues. At the same time, relaxation data can provide information about their organisation and microstructure. We present a theoretical analysis of the anisotropy of spin relaxation of water protons observed in fully hydrated cartilage. We demonstrate that the anisotropy of transverse relaxation is due almost entirely to intramolecular dipolar coupling modulated by a specific mode of slow molecular motion: the diffusion of water molecules in the hydration shell of a collagen fibre around the fibre, such that the molecular director remains perpendicular to the fibre. The theoretical anisotropy arising from this mechanism follows the “magic-angle” dependence observed in magnetic-resonance measurements of cartilage and tendon and is in good agreement with the available experimental results. We discuss the implications of the theoretical findings for MRI of ordered collagenous tissues.

Anisotropy of articular cartilage reflects the ECM gradient architecture : Hough-Radon Transform Analysis

Tissue-specific extracellular matrix (ECM) is known to be an ideal bioscaffold to inspire the future of regenerative medicine. It holds the secret of how nature has developed such an organization of molecules into a unique functional complexity. This work exploited an innovative image processing algorithm and high resolution microscopy associated with mechanical analysis to establish a correlation between the gradient organization of cartiligous ECM and its anisotropic biomechanical response. This was hypothesized to be a reliable determinant that can elucidate how microarchitecture interrelates with biomechanical properties. Hough-Radon transform of the ECM cross-section images revealed its conformational variation from tangential interface down to subchondral region. As the orientation varied layer by layer, the anisotropic mechanical response deviated relatively. Although, results were in good agreement (Kendall's tau-b > 90%), there were evidences proposing that alignment of the fibrous network, specifically in middle zone, is not as random as it was previously thought.

Effect of partial H2O-D2O replacement on the anisotropy of transverse proton spin relaxation in bovine articular cartilage

Anisotropy of transverse proton spin relaxation in collagen-rich tissues like cartilage and tendon is a well-known phenomenon that manifests itself as the "magic-angle" effect in magnetic resonance images of these tissues. It is usually attributed to the non-zero averaging of intra-molecular dipolar interactions in water molecules bound to oriented collagen fibers. One way to manipulate the contributions of these interactions to spin relaxation is by partially replacing the water in the cartilage sample with deuterium oxide. It is known that dipolar interactions in deuterated solutions are weaker, resulting in a decrease in proton relaxation rates. In this work, we investigate the effects of deuteration on the longitudinal and the isotropic and anisotropic contributions to transverse relaxation of water protons in bovine articular cartilage. We demonstrate that the anisotropy of transverse proton spin relaxation in articular cartilage is independent of the degree of deuteration, bringing into question some of the assumptions currently held over the origins of relaxation anisotropy in oriented tissues.

Genetics of anisotropy asymmetry: Registration and sample size effects

Brain asymmetry has been a topic of interest for neuroscientists for many years. The advent of diffusion tensor imaging (DTI) allows researchers to extend the study of asymmetry to a microscopic scale by examining fiber integrity differences across hemispheres rather than the macroscopic differences in shape or structure volumes. Even so, the power to detect these microarchitectural differences depends on the sample size and how the brain images are registered and how many subjects are studied. We fluidly registered 4 Tesla DTI scans from 180 healthy adult twins (45 identical and fraternal pairs) to a geometrically-centered population mean template. We computed voxelwise maps of significant asymmetries (left/right hemisphere differences) for common fiber anisotropy indices (FA, GA). Quantitative genetic models revealed that 47-62% of the variance in asymmetry was due to genetic differences in the population. We studied how these heritability estimates varied with the type of registration target (T1- or T2-weighted) and with sample size. All methods consistently found that genetic factors strongly determined the lateralization of fiber anisotropy, facilitating the quest for specific genes that might influence brain asymmetry and fiber integrity.

Multi-site study of additive genetic effects on fractional anisotropy of cerebral white matter: Comparing meta and megaanalytical approaches for data pooling

Combining datasets across independent studies can boost statistical power by increasing the numbers of observations and can achieve more accurate estimates of effect sizes. This is especially important for genetic studies where a large number of observations are required to obtain sufficient power to detect and replicate genetic effects. There is a need to develop and evaluate methods for joint-analytical analyses of rich datasets collected in imaging genetics studies. The ENIGMA-DTI consortium is developing and evaluating approaches for obtaining pooled estimates of heritability through meta-and mega-genetic analytical approaches, to estimate the general additive genetic contributions to the intersubject variance in fractional anisotropy (FA) measured from diffusion tensor imaging (DTI). We used the ENIGMA-DTI data harmonization protocol for uniform processing of DTI data from multiple sites. We evaluated this protocol in five family-based cohorts providing data from a total of 2248 children and adults (ages: 9-85) collected with various imaging protocols. We used the imaging genetics analysis tool, SOLAR-Eclipse, to combine twin and family data from Dutch, Australian and Mexican-American cohorts into one large "mega-family". We showed that heritability estimates may vary from one cohort to another. We used two meta-analytical (the sample-size and standard-error weighted) approaches and a mega-genetic analysis to calculate heritability estimates across-population. We performed leave-one-out analysis of the joint estimates of heritability, removing a different cohort each time to understand the estimate variability. Overall, meta- and mega-genetic analyses of heritability produced robust estimates of heritability.

Comparison of fractional and geodesic anisotropy in diffusion tensor images of 90 monozygotic and dizygotic twins

We used diffusion tensor magnetic resonance imaging (DTI) to reveal the extent of genetic effects on brain fiber microstructure, based on tensor-derived measures, in 22 pairs of monozygotic (MZ) twins and 23 pairs of dizygotic (DZ) twins (90 scans). After Log-Euclidean denoising to remove rank-deficient tensors, DTI volumes were fluidly registered by high-dimensional mapping of co-registered MP-RAGE scans to a geometrically-centered mean neuroanatomical template. After tensor reorientation using the strain of the 3D fluid transformation, we computed two widely used scalar measures of fiber integrity: fractional anisotropy (FA), and geodesic anisotropy (GA), which measures the geodesic distance between tensors in the symmetric positive-definite tensor manifold. Spatial maps of intraclass correlations (r) between MZ and DZ twins were compared to compute maps of Falconer's heritability statistics, i.e. the proportion of population variance explainable by genetic differences among individuals. Cumulative distribution plots (CDF) of effect sizes showed that the manifold measure, GA, comparably the Euclidean measure, FA, in detecting genetic correlations. While maps were relatively noisy, the CDFs showed promise for detecting genetic influences on brain fiber integrity as the current sample expands.

White matter integrity measured by fractional anisotropy correlates poorly with actual individual fiber anisotropy

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. High-angular resolution diffusion imaging (HARDI) can resolve more complex diffusion geometries than standard DTI, including fibers crossing or mixing. The tensor distribution function (TDF) can be used to reconstruct multiple underlying fibers per voxel, representing the diffusion profile as a probabilistic mixture of tensors. Here we found that DTIderived mean diffusivity (MD) correlates well with actual individual fiber MD, but DTI-derived FA correlates poorly with actual individual fiber anisotropy, and may be suboptimal when used to detect disease processes that affect myelination. Analysis of the TDFs revealed that almost 40% of voxels in the white matter had more than one dominant fiber present. To more accurately assess fiber integrity in these cases, we here propose the differential diffusivity (DD), which measures the average anisotropy based on all dominant directions in each voxel.

A novel measure of fractional anisotropy based on the tensor distribution function

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Diffusion tensor of water in model articular cartilage

We used Monte Carlo simulations of Brownian dynamics of water to study anisotropic water diffusion in an idealised model of articular cartilage. The main aim was to use the simulations as a tool for translation of the fractional anisotropy of the water diffusion tensor in cartilage into quantitative characteristics of its collagen fibre network. The key finding was a linear empirical relationship between the collagen volume fraction and the fractional anisotropy of the diffusion tensor. Fractional anisotropy of the diffusion tensor is potentially a robust indicator of the microstructure of the tissue because, in the first approximation, it is invariant to the inclusion of proteoglycans or chemical exchange between free and collagen-bound water in the model. We discuss potential applications of Monte Carlo diffusion-tensor simulations for quantitative biophysical interpretation of MRI diffusion-tensor images of cartilage. Extension of the model to include collagen fibre disorder is also discussed.

High-pressure Raman spectroscopic and other structural studies of hydrotalcites containing intercalated dicarboxylic acid anions

The results of pressure-tuning Raman spectroscopic, X-ray powder diffraction and solid-state 13C-NMR studies of selected dicarboxylate anions intercalated in a Mg-Al layered double hydroxide (talcite) lattice are reported. The pressure dependences of the vibrational modes are linear for pressures up to 4.6 GPa indicating that no phase transitions occur. The interlayer spacings show that the oxalate, malonate and succinate dianions are oriented perpendicular to the layers, but the glutarate and adipate are tilted. The solid-state 13C-NMR spectra of these materials show full chemical shift anisotropy and, therefore, the anions are not mobile at room temperature.

A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Turbulent velocity and suspended sediment concentration measurements in an urban environment of the Brisbane River Flood Plain at Gardens Point on 12-13 January 2011

The flood flow in urbanised areas constitutes a major hazard to the population and infrastructure as seen during the summer 2010-2011 floods in Queensland (Australia). Flood flows in urban environments have been studied relatively recently, although no study considered the impact of turbulence in the flow. During the 12-13 January 2011 flood of the Brisbane River, some turbulence measurements were conducted in an inundated urban environment in Gardens Point Road next to Brisbane's central business district (CBD) at relatively high frequency (50 Hz). The properties of the sediment flood deposits were characterised and the acoustic Doppler velocimeter unit was calibrated to obtain both instantaneous velocity components and suspended sediment concentration in the same sampling volume with the same temporal resolution. While the flow motion in Gardens Point Road was subcritical, the water elevations and velocities fluctuated with a distinctive period between 50 and 80 s. The low frequency fluctuations were linked with some local topographic effects: i.e, some local choke induced by an upstream constriction between stairwells caused some slow oscillations with a period close to the natural sloshing period of the car park. The instantaneous velocity data were analysed using a triple decomposition, and the same triple decomposition was applied to the water depth, velocity flux, suspended sediment concentration and suspended sediment flux data. The velocity fluctuation data showed a large energy component in the slow fluctuation range. For the first two tests at z = 0.35 m, the turbulence data suggested some isotropy. At z = 0.083 m, on the other hand, the findings indicated some flow anisotropy. The suspended sediment concentration (SSC) data presented a general trend with increasing SSC for decreasing water depth. During a test (T4), some long -period oscillations were observed with a period about 18 minutes. The cause of these oscillations remains unknown to the authors. The last test (T5) took place in very shallow waters and high suspended sediment concentrations. It is suggested that the flow in the car park was disconnected from the main channel. Overall the flow conditions at the sampling sites corresponded to a specific momentum between 0.2 to 0.4 m2 which would be near the upper end of the scale for safe evacuation of individuals in flooded areas. But the authors do not believe the evacuation of individuals in Gardens Point Road would have been safe because of the intense water surges and flow turbulence. More generally any criterion for safe evacuation solely based upon the flow velocity, water depth or specific momentum cannot account for the hazards caused by the flow turbulence, water depth fluctuations and water surges.