Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a Gradient Structure Tensor (GST) and a Sobel Structure Tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28°), and the error was inversely correlated to the degree of transverse isotropy (r=−0.34, p<0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p<0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p<0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone.

Seismic anisotropy in the Morcles nappe shear zone: Implications for seismic imaging of crustal scale shear zones

Microstructures and textures of calcite mylonites from the Morcles nappe large-scale shear zone in southwestern Switzerland develop principally as a function of 1) extrinsic physical parameters including temperature, stress, strain, strain rate and 2) intrinsic parameters, such as mineral composition. We collected rock samples at a single location from this shear zone, on which laboratory ultrasonic velocities, texture and microstructures were investigated and quantified. The samples had different concentration of secondary mineral phases (< 5 up to 40 vol.%). Measured seismic P wave anisotropy ranges from 6.5% for polyphase mylonites (~ 40 vol.%) to 18.4% in mylonites with < 5 vol.% secondary phases. Texture strength of calcite is the main factor governing the seismic P wave anisotropy. Measured S wave splitting is generally highest in the foliation plane, but its origin is more difficult to explain solely by calcite texture. Additional texture measurements were made on calcite mylonites with low concentration of secondary phases (≤ 10 vol.%) along the metamorphic gradient of the shear zone (15 km distance). A systematic increase in texture strength is observed moving from the frontal part of the shear zone (anchimetamorphism; 280 °C) to the higher temperature, basal part (greenschist facies; 350–400 °C). Calculated P wave velocities become increasingly anisotropic towards the high-strain part of the nappe, from an average of 5.8% in the frontal part to 13.2% in the root of the basal part. Secondary phases raise an additional complexity, and may act either to increase or decrease seismic anisotropy of shear zone mylonites. In light of our findings we reinterpret the origin of some seismically reflective layers in the Grône–Zweisimmen line in southwestern Switzerland (PNR20 Swiss National Research Program). We hypothesize that reflections originate in part from the lateral variation in textural and microstructural arrangement of calcite mylonites in shear zones.

Combined effect of heterogeneity, anisotropy and saturation on steady state flow and transport: Structure recognition and numerical simulation

1 Natural soil profiles may be interpreted as an arrangement of parts which are characterized by properties like hydraulic conductivity and water retention function. These parts form a complicated structure. Characterizing the soil structure is fundamental in subsurface hydrology because it has a crucial influence on flow and transport and defines the patterns of many ecological processes. We applied an image analysis method for recognition and classification of visual soil attributes in order to model flow and transport through a man-made soil profile. Modeled and measured saturation-dependent effective parameters were compared. We found that characterizing and describing conductivity patterns in soils with sharp conductivity contrasts is feasible. Differently, solving flow and transport on the basis of these conductivity maps is difficult and, in general, requires special care for representation of small-scale processes.

Combined effects of heterogeneity, anisotropy, and saturation on steady state flow and transport: A laboratory sand tank experiment

Field soils show rather different spreading behavior at different water saturations, frequently caused by layering of the soil material. We performed tracer experiments in a laboratory sand tank. Such experiments complement and help comprehension of field investigations. We estimated, by image analysis, the first two moments of small plumes traveling through a two-dimensional, heterogeneous medium with strongly anisotropic correlation structure. Three steady state regimes were analyzed. Two main conclusions were drawn. First, low saturation led to very large heterogeneity and to strong preferential flow. Thus the description of the flow paths and the prediction of the solute arrival times require, in this case, more accurate knowledge about the topological structure. Second, saturation-dependent macroscopic anisotropy is an essential element of transport in unsaturated media. For this reason, small structural soil features should be properly upscaled to give appropriate effective soil parameters to be input in transport models.

Upscaling of anisotropy in unsaturated Miller-similar porous media

Geological and pedological processes rarely form isotropic media as is usually assumed in transport studies. Anisotropy at the Darcy or field scale may be detected directly by measuring flow parameters or may become indirectly evident from movement and shape of solute plumes. Anisotropic behavior of a soil at one scale may, in many cases, be related to the presence of lower-scale directional structures. Miller similitude with different pore-scale geometries of the basic element is used to model macroscopic flow and transport behavior. Analytical expressions for the anisotropic conductivity tensor are derived based on the dynamic law that governs the flow problem at the pore scale. The effects of anisotropy on transport parameters are estimated by numerical modeling.

Nanometer-size anisotropy of injection-molded polymer micro-cantilever arrays

Understanding and controlling the structural anisotropies of injection-molded polymers is vital for designing products such as cantilever-based sensors. Such micro-cantilevers are considered as cost-effective alternatives to single-crystalline silicon-based sensors. In order to achieve similar sensing characteristics,structure and morphology have to be controlled by means of processing parameters including mold temperature and injection speed. Synchrotron radiation-based scanning small- (SAXS) and wide-angle x-ray scattering techniques were used to quantify crystallinity and anisotropy in polymer micro-cantilevers with micrometer resolution in real space. SAXS measurements confirmed the lamellar nature of the injection-molded semi-crystalline micro-cantilevers. The homogenous cantilever material exhibits a lamellar periodicity increasing with mold temperature but not with injection speed. We demonstrate that micro-cantilevers made of semi-crystalline polymers such as polyvinylidenefluoride, polyoxymethylene, and polypropylene show the expected strong degree of anisotropy along the injection direction.

Bone Volume Fraction and Fabric Anisotropy Are Better Determinants of Trabecular Bone Stiffness than Other Morphological Variables

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphologyelasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae and iliac crest were analysed. Their morphology was assessed via 25 variables and their stiffness tensor (inline image) was computed from six independent load cases using micro finite element analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multi-linear regression modelling the dependent variable inline image. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of inline image (inline image=0.889), especially in combination with fabric (inline image=0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (inline image=0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and post-elastic properties.

Nonequilibrium hysteresis and spin relaxation in the mixed-anisotropy dipolar-coupled spin-glass LiHo0.5Er0.5F4

We present a study of the model spin-glass LiHo0.5Er0.5F4 using simultaneous ac susceptibility, magnetization, and magnetocaloric effect measurements along with small angle neutron scattering (SANS) at sub-Kelvin temperatures. All measured bulk quantities reveal hysteretic behavior when the field is applied along the crystallographic c axis. Furthermore, avalanchelike relaxation is observed in a static field after ramping from the zero-field-cooled state up to 200–300 Oe. SANS measurements are employed to track the microscopic spin reconfiguration throughout both the hysteresis loop and the related relaxation. Comparing the SANS data to inhomogeneous mean-field calculations performed on a box of one million unit cells provides a real-space picture of the spin configuration. We discover that the avalanche is being driven by released Zeeman energy, which heats the sample and creates positive feedback, continuing the avalanche. The combination of SANS and mean-field simulations reveal that the conventional distribution of cluster sizes is replaced by one with a depletion of intermediate cluster sizes for much of the hysteresis loop.

Anisotropy of magnetic susceptibility in natural olivine single crystals

Mantle flow dynamics can cause preferential alignment of olivine crystals that results in anisotropy of physical properties. To interpret anisotropy in mantle rocks, it is necessary to understand the anisotropy of olivine single crystals. We determined anisotropy of magnetic susceptibility (AMS) for natural olivine crystals. High-field AMS allows for the isolation of the anisotropy due to olivine alone. The orientations of the principal susceptibility axes are related to the olivine’s crystallographic structure as soon as it contains >3 wt % FeO. The maximum susceptibility is parallel to the c axis both at room temperature (RT) and at 77 K. The orientation of the minimum axis at RT depends on iron content; it is generally parallel to the a axis in crystals with 3–5 wt % FeO, and along b in samples with 6–10 wt % FeO. The AMS ellipsoid is prolate and the standard deviatoric susceptibility, k0, is on the order of 8*10210 m3/kg for the samples with <1wt % FeO, and ranges from 3.1*1029 m3/kg to 5.7*1029 m3/kg for samples with 3–10 wt % FeO. At 77 K, the minimum susceptibility is along b, independent of iron content. The shape of the AMS ellipsoid is prolate for samples with <5 wt % FeO, but can be prolate or oblate for higher iron content. The degree of anisotropy increases at 77 K with p0 7757.160.5. The results from this study will allow AMS fabrics to be used as a proxy for olivine texture in ultramafic rocks with high olivine content.

Magnetic anisotropy in clinopyroxene and orthopyroxene single crystals

Pyroxenes constitute an important component in mafic igneous and metamorphic rocks. They often possess a prismatic habit, and their long axis, the crystallographic c axis, helps define a lineation in a textured rock. Anisotropy of magnetic susceptibility (AMS) serves as a fabric indicator in igneous and metamorphic rocks. If a rock’s AMS is carried by pyroxenes, it can be related to their crystallographic preferred orientation and degree of alignment. This requires knowing the intrinsic AMS of pyroxene single crystals. This study provides a comprehensive low-field and high-field AMS investigation of chemically diverse orthopyroxene and clinopyroxene crystals in relation to crystal structure, chemical composition, oxidation state of Fe, and the possible presence of ferromagnetic inclusions. The paramagnetic anisotropy, extracted from high-field data, shows clear relationships to crystallographic directions and Fe concentration both in clinopyroxene and orthopyroxene. In the diopside-augite series, the intermediate susceptibility is parallel to b, and the maximum is at 45° to the c axis. In aegirine, the intermediate axis remains parallel to b, while the maximum susceptibility is parallel to c. The AMS of spodumene depends on Fe concentration. In enstatite, the maximum susceptibility aligns with c and the minimum with b, and in the case of hypersthene, the maximum susceptibility is normal to the exsolution lamellae. Magnetite inclusions within augite possess a ferromagnetic anisotropy with consistent orientation of the principal susceptibilities, which dominates the low-field anisotropy. These results provide better understanding of magnetic anisotropy in pyroxenes and form a solid basis for interpretation of magnetic fabrics in pyroxene-bearing rocks.

Magnetic anisotropy in natural amphibole crystals

Anisotropy of magnetic susceptibility (AMS) is often used as a proxy for mineral fabric in deformed rocks. To do so quantitatively, it is necessary to quantify the intrinsic magnetic anisotropy of single crystals of rock-forming minerals. Amphiboles are common in mafic igneous and metamorphic rocks and often define rock texture due to their general prismatic crystal habits. Amphiboles may dominate the magnetic anisotropy in intermediate to felsic igneous rocks and in some metamorphic rock types, because they have a high Fe concentration and they can develop a strong crystallographic preferred orientation. In this study, the AMS is characterized in 28 single crystals and I crystal aggregate of compositionally diverse clino- and ortho-amphiboles. High-field methods were used to isolate the paramagnetic component of the anisotropy, which is unaffected by ferromagnetic inclusions that often occur in amphibole crystals. Laue imaging, laser ablation-inductively coupled plasma-mass spectrometry, and Mossbauer spectroscopy were performed to relate the magnetic anisotropy to crystal structure and Fe concentration. The minimum susceptibility is parallel to the crystallographic a*-axis and the maximum susceptibility is generally parallel to the crystallographic b-axis in tremolite, actinolite, and hornblende. Gedrite has its minimum susceptibility along the a-axis, and maximum susceptibility aligned with c. In richterite, however, the intermediate susceptibility is parallel to the b-axis and the minimum and maximum susceptibility directions are distributed in the a-c plane. The degree of anisotropy, k', increases generally with Fe concentration, following a linear trend: k' = 1.61 x 10(-9) Fe - 1.17 x 10(-9) m(3)/kg. Additionally, it may depend on the Fe2+/Fe3+ ratio. For most samples, the degree of anisotropy increases by a factor of approximately 8 upon cooling from room temperature to 77 K. Fen-oactinolite, one pargasite crystal and riebeckite show a larger increase, which is related to the onset of local ferromagnetic (s.l.) interactions below about 100 K. This comprehensive data set increases our understanding of the magnetic structure of amphiboles, and it is central to interpreting magnetic fabrics of rocks whose AMS is controlled by amphibole minerals.