Mean Intercept Length Research Articles

Comparison between experimental and numerical results for piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation

Abstract The bone formation is considered to be accompanied by the piezoelectric effects in bone. Therefore, the piezoelectric effect under ultrasound irradiation should be elucidated to realize the effective healing. Then, the piezoelectric properties in cancellous bone have been attempted to clarify by complementing experiments and simulations with each other. In this paper, the piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation were experimentally and numerically observed, and the effect of the trabecular orientation was investigated. The experimental observation was performed by the piezoelectric cell (PE-cell), which corresponds to an ultrasound receiver using the cancellous bone specimen as a piezoelectric element. The numerical observation was performed by the piezoelectric finite-difference time-domain (PE-FDTD) method, which is an elastic FDTD method with piezoelectric constitutive equations. In both the experimental and simulated results, the piezoelectric signal amplitude increased with the mean intercept lengths (MILs) of the trabecular elements and the pore spaces or the strength of the trabecular orientation. From the fact that the ultrasound propagation in water-saturated cancellous bone can depend on the trabecular orientation, it was considered that the ultrasound properties could be largely associated with the piezoelectric properties.

EFFECTS OF VOLUME OF INTEREST (VOI) SIZE ON TRABECULAR BONE QUANTIFICATION IN THE JUVENILE DISTAL FEMUR

Volumes of interest (VOI) are commonly assigned to image stacks generated from micro-computed tomography to specify areas for bone quantification. However, the size of the VOI can impact the values obtained for trabecular bone parameters. This study aims to investigate the effect of VOI size by applying VOIs of four different diameters (10%, 15%, 20% and 30% of the antero-posterior width). Ten juvenile right distal femora were included, aged from pre-natal to three years. Smaller VOIs were placed within the largest VOI, with multiple locations used for the same VOI size. The observed parameters included bone volume fraction (BV/TV), trabecular bone thickness (Tb.Th), separation (Tb.Sp), number (Tb.N), degree of anisotropy by mean intercept length (DA.MIL) and star volume distribution (DA.SVD). Statistically significant differences between VOI sizes were found for Tb.Sp, Tb.N, DA.MIL and DA.SVD. A possible effect of localized variation was found due to significantly different values for Tb.Th between VOI locations. The effect related to VOI geometry was reflected by DA.MIL and DA.SVD as no significant difference was found between locations. The minimum diametric strut quantity (DSQ, diameter multiplied by Tb.N) of 4 can be implied based on the zero DA.SVD value found in particular VOIs.

Quantitative correlation between rafting microstructure and anisotropic mechanical behavior in dual-phase materials

Continuum descriptions of the microstructure in dual-phase materials are introduced by fabric tensors computed from the mean intercept length (MIL) method. The fabric tensor can be decomposed into the isotropic and deviatoric components to represent the dilatation and orientation preferred properties, respectively. Systematic numerical simulations on micromechanics models and simplified microstructures are conducted. It is confirmed that the anisotropic elastic behavior can be quantitatively predicted with the help of deviatoric components. This component can be further implemented into the constitutive model to describe the time- and load-dependent evolution of the material state variable. Anisotropy induced by morphology and anisotropic constituents is discussed. The results match well with computational experiments, showing the promising application potential of the tensorial representation method and the microstructure-based mechanical property prediction model.

On the mechanical anisotropy of argillaceous Cobourg limestone: fabric tensor approach

The mechanical response of Cobourg limestone is anisotropic, which stems from heterogeneity of its fabric. In this work, a new fabric-dependent approach is developed for the description of strength and deformation characteristics of this rock. The quantification of fabric is carried out by employing the basic principles of stereology and the specific fabric descriptor used is the so-called mean intercept length. The results demonstrate that the material may be perceived as transversely isotropic and the mechanical response is affected by the volume fraction of argillaceous partings. The latter are spatially variable, so that the notion of Representative Elementary Volume (REV) is not, in general, applicable. A numerical study is included involving simulation of triaxial tests conducted on differently oriented samples of Cobourg limestone.

A fabric tensor based small strain constitutive law for the elastoplastic behavior of snow

The mechanical behavior of snow depends on its density and microstructure. The anisotropy in the microstructure is expressed in terms of fabric tensor that leads to an anisotropic stress-strain relation. Lately, fabric-based relations have successfully estimated the elastic properties of snow. Motivated by this, we propose a fabric-based macroscopic elasto-plastic constitutive law for snow, which can be used to study avalanche initiation. Mean Intercept Length tensor used as a measure of material fabric is determined by X-ray tomography. Fabric tensor and density-dependent yield surface with a provision for isotropic hardening/softening are used in this process. Beyond the initial yield, the yield function grows till the strength of the snow is reached and then softens. Since snow exhibits tension and compression behavior asymmetry, a piece-wise quadratic yield function is used. Stress-strain curves needed for determining the equation of the hardening/softening law and other parameters of the proposed macroscopic constitutive law are obtained through micro-Finite Element (μ-FE) simulations. The macroscopic constitutive law has been implemented as a user subroutine in a FE code and can predict the snow's multiaxial behavior.

Effect of captivity on the vertebral bone microstructure of xenarthran mammals.

Captive specimens in museum collections facilitate study of rare taxa, but the lifestyles, diets, and lifespans of captive animals differ from their wild counterparts. Trabecular bone architecture adapts to in vivo forces, and may reflect interspecific variation in ecology and behavior as well as intraspecific variation between captive and wild specimens. We compared trunk vertebrae bone microstructure in captive and wild xenarthran mammals to test the effects of ecology and captivity. We collected μCT scans of the last six presacral vertebrae in 13 fossorial, terrestrial, and suspensorial xenarthran species (body mass: 120 g to 35 kg). For each vertebra, we measured centrum length; bone volume fraction (BV.TV); trabecular number and mean thickness (Tb.Th); global compactness (GC); cross-sectional area; mean intercept length; star length distribution; and connectivity and connectivity density. Wild specimens have more robust trabeculae, but this varies with species, ecology, and pathology. Wild specimens of fossorial taxa (Dasypus) have more robust trabeculae than captives, but there is no clear difference in bone microstructure between wild and captive specimens of suspensorial taxa (Bradypus, Choloepus), suggesting that locomotor ecology influences the degree to which captivity affects bone microstructure. Captive Tamandua and Myrmecophaga have higher BV.TV, Tb.Th, and GC than their wild counterparts due to captivity-caused bone pathologies. Our results add to the understanding of variation in mammalian bone microstructure, suggest caution when including captive specimens in bone microstructure research, and indicate the need to better replicate the habitats, diets, and behavior of animals in captivity.

Domain coarsening in viscous sintering as a result of topological pore evolution

The microstructure evolution in 3D was studied by X-ray microtomography to reveal the relation between topology of pore networks and characteristic length in viscous sintering. The mean intercept length was defined from solid/pore interface for characterizing the length of solid phase and pore phase. The increase of the characteristic length with densification was termed as domain coarsening. The topological pore evolution was analyzed by using genus. The characteristic length increased with decreasing genus in the intermediate stage. The domain coarsening takes place as a natural consequence of pore evolution in viscous sintering, i.e., the decrease of total surface area concurrent with the topological transformations.

Anisotropic microstructural evolution and coarsening in free sintering and constrained sintering of metal film by using FIB-SEM tomography

The anisotropic microstructure develops during powder processing and constrained sintering. FIB-SEM tomography was used to investigate the microstructural evolutions of Au submicron particles during free sintering and constrained sintering. The decrease in total surface area and the coarsening, i.e. the increase of mean intercept length of solid phase, were observed during the densification process. The anisotropic packing structure of spherical particles induced by casting process was characterized by area weighted fabric tensor, which represented the bond orientation and the anisotropy of contact area. In free sintering, the initial anisotropy in packing structure decreased with densification. In constrained sintering, the initial anisotropy observed by the mean intercept length of pore was reversed in the later stage. The microstructure evolved so as to form the elongated pores along the thickness direction. An open pore structure model was presented to explain the microstructural evolution in the intermediate stage.

Anisotropy evolution of elastomeric foams during uniaxial compression measured via in-situ X-ray computed tomography

We have characterized the three-dimensional evolution of microstructural anisotropy of a family of elastomeric foams during uniaxial compression via in-situ X-ray computed tomography. Flexible polyurethane foam specimens with densities of 136, 160 and 240 kg/m3 were compressed in uniaxial stress tests both parallel and perpendicular to the foam rise direction, to engineering strains exceeding 70%. The uncompressed microstructures show slightly elongated ellipsoidal pores, with elongation aligned parallel to the foam rise direction. The evolution of this microstructural anisotropy during deformation is quantified based on the autocorrelation of the image intensity, and verified via the mean intercept length as well as the shape of individual pores. Trends are consistent across all three methods. In the rise direction, the material remains transversely anisotropic throughout compression. Anisotropy initially decreases with compression, reaches a minimum, then increases up to large strains, followed by a small decrease in anisotropy at the largest strains as pores collapse. Compression perpendicular to the foam rise direction induces secondary anisotropy with respect to the compression axis, in addition to primary anisotropy associated with the foam rise direction. In contrast to compression in the rise direction, primary anisotropy initially increases with compression, and shows a slight decrease at large strains. These surprising non-monotonic trends and qualitative differences in rise and transverse loading are explained based on the compression of initially ellipsoidal pores. Microstructural anisotropy trends reflect macroscopic stress-strain and lateral strain response. These findings provide novel quantitative connections between three-dimensional microstructure and anisotropy in moderate density polymer foams up to large deformation, with important implications for understanding complex three-dimensional states of deformation.

Anisotropic Microstructural Evolution and Coarsening in Free Sintering and Constrained Sintering of Metal Film by Using FIB-SEM Tomography

The anisotropic microstructure develops during powder processing and constrained sintering. In the present study, the microstructural evolutions of Au submicron particles during free sintering and constrained sintering were investigated by FIB-SEM tomography. The decrease in total surface area and the coarsening, i.e. the increase of mean intercept length of solid phase, were observed during the densification process. The anisotropic packing structure of spherical particles induced by casting process was characterized by area weighted fabric tensor, which represented the bond orientation and the anisotropy in contact area. In free sintering, the initial anisotropy in packing structure decreased with densification as indicated by the decrease in deviatoric component of surface energy tensor. In constrained sintering, the initial anisotropy observed by the mean intercept length of pore was reversed in the later stage. The microstructure evolved so as to form the elongated pores along the thickness direction.

An image-based approach for structure investigation and 3D numerical modelling of polymeric foams

Polymeric expanded materials are of great importance in many engineering applications. Despite this, as of today the development of models able to describe the mechanical behaviour of these material as a function of their microstructure is still an open challenge. In this study an image-based approach is proposed for both microstructure characterisation and 3D numerical mechanical simulations. Microstructure is investigated through different algorithms, such as Mean Intercept Length and Autocorrelation function, to determine synthetic parameters able to describe the internal structure. A novel algorithm has been developed to convert the images obtained from computed tomography into a finite element mesh with an optimized number of elements: this method preserves the original structure and can also be used to generate other fictitious structures that can be analysed. The investigation led to the identification of general relationships between foam microstructure and relevant macroscopic physical and mechanical properties. These relationships can serve as a tool to optimize foam morphology or product final properties for several different engineering applications.

Selective Voronoi tessellation as a method to design anisotropic and biomimetic implants

The geometry of a metallic scaffold is important for the success of bone implants, where the introduction of porosity can reduce stress shielding effects and allow for bone tissue integration. In this work, porous scaffolds were designed to closely mimic the natural structure of trabecular bone using selective Voronoi tessellation with preferential seeding. A workflow to generate these structures is introduced, where voided regions of seeds in the starting volume create preferential texture during polyhedral expansion, resulting in modified strut orientation in the implant. Anisotropy was digitally characterized by mean-intercept length and star volume distribution measurements to determine similarity to trabecular orientation. This work demonstrates that selective Voronoi tessellation is an effective method to generate biomimetic porous scaffolds with increased anisotropy and tunable strut architecture in three dimensions as a suitable alternative to patient-derived bone geometries.

Analysis of Sn-Bi Solders: X-ray Micro Computed Tomography Imaging and Microstructure Characterization in Relation to Properties and Liquid Phase Healing Potential.

This work provides an analysis of X-ray micro computed tomography data of Sn-xBi solders with x = 20, 30, 35, 47, 58 wt.% Bi. The eutectic thickness, fraction of eutectic and primary phase are analyzed. Furthermore, the 3D data is evaluated by means of morphology parameters, such as, shape complexity, flatness, elongation and mean intercept length tensor. The investigated alloys are categorized in three groups based on their morphology, which are described as “complex dominant”, “complex- equiaxed” and “mixed”. The mechanical behavior of Sn-Bi alloys in the semi-solid configuration and the correlation with microstructural parameters are discussed. A varying degree of geometric anisotropy of the investigated alloys is found through the mean intercept length tensor. Representative volume element models for finite element simulations (RVE-FEM) are created from tomography data of each alloy to analyze a correlation of geometric and elastic anisotropy. The simulations reveal an elastic isotropic behavior due to the small difference of elastic constants of primary and eutectic phase. A discussion of properties in the semi-solid state and liquid phase healing is provided.

Correlation between elastic properties and morphology in short fiber composites by X-ray computed micro-tomography

In this work the architectural anisotropy of short fiber reinforced polymers (SFRPs) has been characterized using X-ray computed micro-tomography (micro-CT) with four different morphometric methods: Mean Intercept Length (MIL), Volume Orientation (VO), Star Length Distribution (SLD) and Star Volume Distribution (SVD). The fabric tensor obtained from micro-CT analysis provided information on the fiber orientation, indicating that fibers were partially aligned in the injection direction. The fiber length and orientation obtained from optical microscopy and from the morphometric analysis in 3D, respectively, has been used to determine the mechanical properties of the composite sample, using a model based on micro and macromechanics. This approach leads to the prediction of the elastic constants of the component for any possible composite morphology resulting from injection, representing a key need for the design of SFRP components.

Numerical analysis of backscatter properties of fast and slow waves in cancellous bone

Fast and slow waves can propagate mainly in the trabecular and pore parts of cancellous bone, respectively. Their backscatter properties were numerically analyzed by finite-difference time-domain simulations. Numerical bone models, in which artificial absorbing layers were set at the back surfaces, were prepared, and an ultrasound pulse wave was transmitted from the front surface parallel to the main trabecular orientation. Only the backscattered waves were succeeded to isolate by differencing between two simulated waveforms obtained using the bone models with different thicknesses. The backscatter coefficients, which were the amplitude ratios of the backscattered waves to the incident waves, of the fast wave were not significantly correlated with porosity and mean intercept lengths (MILs) (R2 ≤ 0.29). However, the backscatter coefficients of the slow wave were significantly correlated with porosity (R2 = 0.45–0.67) and MIL of the pore part in the ultrasound direction (R2 = 0.64–0.80).

Mechanical Characterization of Stir Cast Al-7075/B4C/Graphite Reinforced Hybrid Metal Matrix Composites

Abstract The modern technology requires the materials with light weight, high strength, high stiffness and superior mechanical properties. The mechanical properties of metal matrix composites (MMCs) are critical to their potential application as structural materials. A systematic examination is required to study the effect of particulate weight fraction on the mechanical properties. Aluminium based metal matrix composites find varied applications in aerospace, defence, automobile, sports equipment and electronics due to their favourable properties. Al 7075 is a light weight castable alloy with moderate hardness and strength and finds applications in automotive and aerospace. The addition of refractory reinforcement generally improves the hardness, tensile strength and high temperature properties of the material. The present investigation focuses on characterization of Stir cast Al-7075/B4C/Graphite reinforced Hybrid Metal Matrix Composites. Adding B4C with varying reinforcement of three cases, in first case 2% constant with varying graphite 1%, 3%, and 5%, in second case 4%, and in third case 6% constant with varying same graphite percentage, the aluminum matrix hybrid composites have been fabricated by stir-casting method at 650 °C. Castings for tensile testing were prepared in circular metal mold of diameter 20 mm and length 120 mm. The specimens of 55×10×10 mm with 2 mm notch for impact test, 20×10×10 mm for microscopy analysis and hardness test are cut from a cast ingot of 100×50×10 mm using CNC EDM wire cutting. Specimens are prepared as per the ASTM standards and Microstructure investigation, ultimate tensile strength, impact strength and hardness measurements have been correlated with the percentage of B4C and Graphite particles. The effects of B4C and Graphite particle content on the mechanical properties were investigated. The grain size by using the mean intercept length method, Standard deviation and 95% confidence intervals were determined at different weight fractions.

Transport through random bimodal and multimodal fiber structures

Random walk simulation results are reported for the transport and structural properties of random bimodal fibrous media for a range of values of the porosity, relative fiber size, and relative fiber density. Analytical expressions are derived for the mean intercept length of random bimodal and multimodal fiber structures, and are validated through simulations. A fiber dispersity factor emerges from the derivations, accounting for the deviation of the mean intercept length of such structures from that of unimodal fiber beds of the same porosity. Tortuosity factors in all diffusion regimes for in-plane and transverse flow through bimodal fibrous media of moderate or high porosity are practically independent of the relative fiber size and density and equal to those reported earlier for beds of unimodal fibers. The same holds for the formation factor of such structures, accounting for the dimensionless effective bulk diffusivity, thermal and electrical conductivity, magnetic permeability, dielectric constant and refractive index. The dimensionless viscous permeability of bimodal and multimodal fiber structures of moderate or high porosity may be obtained from that of unimodal fiber structures through simple multiplication by the square of the dispersity factor. This result is in line with a multitude of experimental data of the literature.

Microstructure anisotropy of La0.6Sr0.4Co0.2Fe0.8O3-δ film on rigid Gd0.1Ce0.9O1.95 substrate during constrained sintering

La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF) cathodes on rigid Gd0.1Ce0.9O1.95 (GDC) substrate were sintered to different densities, and their three dimensional (3D) microstructures were characterized using focused ion beam-scanning electronic microscopy (FIB-SEM) tomography. The microstructure anisotropies of the green and constrainedly sintered cathodes were studied using 3D mean intercept length (MIL) method and the two dimensional (2D) best-fit ellipse method and 3D best-fit ellipsoid method. It shows that in the constrained sintering of LSCF films, the microstructures were transversely isotropic in the plane parallel to the substrate, while the microstructures in the thickness direction were anisotropic. Density and grain size gradients were observed and quantified along the cathode thickness direction during constrained sintering. The pores were preferentially oriented and elongated in the thickness direction. The anisotropy factor increased as increasing the sintering time or sintering temperature in the current density range. Cross-sectional 2D measurements underestimated the pore anisotropy, but showed qualitative agreement with 3D measurements.

Relationship between the anisotropy tensor calculated through global and object measurements in high‐resolution X‐ray tomography on cellular and composite materials

Structural anisotropy of two-phase materials can be evaluated through global measurements, as volume orientation or mean-intercept length methods do, or through statistics performed on a set of individual measurements. This last procedure is encouraged by recent improvements in the spatial resolution of conventional X-ray tomography. In this paper, the above-described approaches were compared in three case studies: a foam subjected to an in situ compression test, a second foam with a completely different cell morphology and a plastic material reinforced with short fibres. The approach based on the subdivision into distinguishable objects of the considered material phase has proved to be more sensitive in highlighting small deformations in the structure or small irregularities in an otherwise isotropic structure. On the other hand, the other approach is more general and is always usable. The two methods for calculating the fabric tensor tend to converge as the average anisotropy of individual objects in the statistical population increases. The use of Lambert's cylindrical equal-area projection of cell/fibre directions or local volume orientations is suggested, because the density of points is preserved from the sphere to the plane surface. Finally, a quick vector method to evaluate the anisotropy of the directions distribution has been presented, by defining a coherence index of the average direction.

Assessment of vertebral wedge strength using cancellous textural properties derived from digital tomosynthesis and density properties from dual energy X-ray absorptiometry and high resolution computed tomography

The purpose of this study was to examine the potential of digital tomosynthesis (DTS) derived cancellous bone textural measures to predict vertebral strength under conditions simulating a wedge fracture. 40 vertebral bodies (T6, T8, T11, and L3 levels) from 5 male and 5 female cadaveric donors were utilized. The specimens were scanned using dual energy X-ray absorptiometry (DXA) and high resolution computed tomography (HRCT) to obtain measures of bone mineral density (BMD) and content (BMC), and DTS to obtain measures of bone texture. Using a custom loading apparatus designed to deliver a nonuniform displacement resulting in a wedge deformity similar to those observed clinically, the specimens were loaded to fracture and their fracture strength was recorded. Mixed model regressions were used to determine the associations between wedge strength and DTS derived textural variables, alone and in the presence of BMD or BMC information. DTS derived fractal, lacunarity and mean intercept length variables correlated with wedge strength, and individually explained up to 53% variability. DTS derived textural variables, notably fractal dimension and lacunarity, contributed to multiple regression models of wedge strength independently from BMC and BMD. The model from a scan orientation transverse to the spine axis and in the anterior-posterior view resulted in highest explanatory capability (R2adj = 0.91), with a scan orientation parallel to the spine axis and in the lateral view offering an alternative (R2adj = 0.88). In conclusion, DTS can be used to examine cancellous texture relevant to vertebral wedge strength, and potentially complement BMD in assessment of vertebral fracture risk.