Theoretical explanation of the relationship between backscattered electron and x-ray linear attenuation coefficients in calcified tissues

X-ray absorption and backscattered electron (BSE) microscopies are two commonly used techniques for estimating mineral contents in calcified tissues. The resolution in BSE images is usually higher than in x-ray images, but due to the previous lack of good standards to quantify the grey levels in BSE images of bones and teeth, x-ray microtomog-raphy (XMT) images of the same specimens have been used for calibration. However, the physics of these two techniques is different: for a specimen with a given composition, the x-ray linear attenuation coefficient is proportional to density, but there is no such relation with the BSE coefficient. To understand the reason that this calibration appears to be valid, the behaviour of simulated bone samples was investigated. In this, the bone samples were modelled as having three phases: hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂), protein, and void (either empty or completely filled with polymethylmethacrylate (PMMA), a resin which is usually used for embedding bones and teeth in microscopic studies). The x-ray linear attenuation coefficients (calculated using published data) and the BSE coefficients (calculated using Monte Carlo simulation) were compared for samples of various phase proportions. It was found that the BSE coefficient correlated only with the x-ray attenuation coefficient for samples with PMMA infiltration. This was attributed to the properties of PMMA (density and mean atomic number) being very similar to those of the protein; therefore, the sample behaves like a two-phase system which allows the establishment of a monotonic relation between density and BSE coefficient. With the newly developed standards (brominated and iodinated dimethacrylate esters) for BSE microscopy of bone, grey levels can be converted to absolute BSE coefficients by linear interpolation, from which equivalent densities can be determined.     

Evaluation of bone strength: correlation between measurements of bone mineral density and drilling force

Bone drilling is a major part of modern orthopaedic surgery which involves the internal fixation of fractured bones. The investigation of bone drilling described in this paper demonstrates the contribution of automation technology towards the study of bone strength. The aim of this preliminary investigation is to establish a relationship between bone drilling forces and measurements of bone mineral density (BMD) by dual energy X-ray absorptiometry (DXA). A linear relationship with a high coefficient of correlation has been found between average drilling forces and BMD measurements at both the greater trochanter and the femoral head of porcine femurs when drilling in the anterior-posterior (AP) direction (i.e. the direction of the DXA scan). It has also been found that in the normal drilling direction (i.e. in the cervical axis direction), which is orthogonal to the DXA scanning direction, there are similar trends between the drilling forces and BMD levels in regions where bone density is more consistent (e.g. the femoral head). The findings of this investigation indicate that analysis of bone drilling forces has the potential to provide useful information about the strength of bone.     

Scanning and transmission electron microscopy for evaluation of order/disorder in bone structure

A comparative characterization of the structure of normal and abnormal (osteoporotic) human lumbar and thoracic vertebrae samples was carried out to reveal the type of possible disorder. Samples from the bone fragments extracted during the surgery due to vertebra fractures were examined by scanning electron microscopy (SEM), conventional and high resolution transmission electron microscopy (TEM and HRTEM), and X-ray energy dispersive spectroscopy (EDS). Contrary to what might be expected in accordance with possible processes of dissolution, formation and remineralization of hard tissues, no changes in phase composition of mineral part, crystal sizes (length, width, and thickness), and arrangement of crystals on collagen fibers were detected in abnormal bones compared to the normal ones. The following sizes were determined by HRTEM for all bone samples: 相似文献   

Acoustic and ultrasonic tissue characterization--assessment of osteoporosis.

Osteoporosis, often termed the 'silent epidemic', has been defined as 'a decrease in bone mass and architectural deterioration of bone tissue, leading to enhanced bone fragility and consequent increase in fracture risk'. In the United Kingdom alone, the annual health costs are in excess of 750 million Pounds, with 60,000 patients suffering a hip fracture each year. A quarter of these will die within 12 months of their fracture, half of the remainder will never regain independent living. The established procedure for assessing the risk of osteoporotic fracture is via bone mineral density (BMD) assessment using dual-energy X-ray absorptiometry (DXA). However, DXA is an expensive technique and is not widely available. Within the past 15 years, ultrasound assessment of bone has rapidly advanced in scientific understanding, technical development and clinical utility. Measurements of cancellous bone (particularly at the calcaneus) are generally performed in preference to those of cortical bone (tibial cortex). There are currently 15 commercial systems available and over 3500 systems are in use world-wide. The low cost and portability offered by ultrasound systems should enable an integrated community-based screening programme to be established in the near future. Ultrasound measurements of bone are generally obtained using transmission rather than pulse-echo techniques owing to its highly attenuating nature. Ultrasound velocity and attenuation measurements are utilized. For velocity, there are well-defined fundamental relationships describing the dependence upon the elasticity and density of bone.     

Estimation of femoral neck bone mineral density by ultrasound scanning: Preliminary results and feasibility

Aim of this paper was to assess the diagnostic accuracy of a novel ultrasound (US) approach for femoral neck densitometry. A total of 173 female patients (56–75 years) were recruited and all of them underwent a dual X-ray absorptiometry (DXA) of the proximal femur and an US scan of the same anatomical district. Acquired US data were analysed through a novel algorithm that performed a series of spectral and statistical analyses in order to calculate bone mineral density employing an innovative method. Diagnostic accuracy of US investigations was quantitatively assessed through a direct comparison with DXA results. The average diagnostic agreement resulted pretty good (85.55%), with a maximum (88.00%) in correspondence of the youngest investigated patients (56–60 y). Overall, diagnostic accuracy showed only minimal variations with patient age, indicating that the proposed approach has the potential to be effectively employable for osteoporosis diagnosis in the whole considered age interval.     

基于自回归倒谱法估计骨小梁间距

基于超声背散射信号，本文提出用自回归（AR）倒谱法来估计松质骨中骨小梁的间距。对牛胫骨和人离体跟骨松质骨中的超声背散射信号采用AR倒谱法进行了分析，并估计了牛胫骨和人离体跟骨中骨小梁的平均间距。结果表明，松质骨的密度与骨小梁的平均间距具有密切的关系，随松质骨表观密度的减小，骨小梁的平均间距增大，用AR倒谱能比较准确地估计出松质骨中骨小梁的平均间距。     

A preliminary dual-energy X-ray absorptiometry-based finite element model for assessing osteoporotic hip fracture risk

To more accurately assess osteoporotic hip fracture risk in a specific patient, a dual-energy X-ray absorptiometry (DXA)-based finite element model was constructed from the patient's femur DXA image. The outermost contour of the femur bone segmented from the DXA image was used to generate a finite element mesh. Bone mechanical properties, such as Young's modulus, are correlated with areal bone mineral density (BMD) captured in the DXA image. A quasi-static loading condition representing a sideway fall was applied to the finite element model. Three fracture risk indices were introduced and expressed as ratios of internal forces caused by impact forces occurring in sideway fall to bone ultimate cross-section strength at the three critical locations, i.e. the femoral neck, the intertrochanteric region, and the subtrochanteric region. The proposed finite element modelling procedure was validated against six representative clinical cases extracted from the Manitoba BMD database, where initial and follow-up DXA images have been taken to monitor longitudinal variation of areal BMD in individual patients. It was found from the clinical validation that variations in the proposed fracture risk indices have the same trends as those indicated by the conventional areal BMD and T-score. In addition, by the three proposed fracture risk indices it is possible to further identify the specific fracture location. It was also found that for the same subject, the variations in the three fracture risk indices have quite different magnitudes, with intertrochanteric region the largest and subtrochanteric region the smallest, which is probably owing to the different content of trabecular and cortical bones in the three regions. With further development, it is promising that the proposed DXA-based finite element model will be a useful tool for accurate assessment of osteoporosis development and for treatment monitoring.     

Elemental distributions in femoral bone of rat under osteoporosis preventive treatments

One of the abnormalities of bone architecture is osteoporosis as occurring in post‐menopausal women. Especially long bones, such as femur, become more fragile and more prone to fracture. The efficiency of several osteoporosis preventative treatments based on oestrogen and progestin in bone structure and mineral recovery was studied using ovariectomized Wistar rats as an osteoporosis experimental model. Diagonal cross‐sections of the proximal epiphysis of femoral bones were analysed using nuclear microscopy techniques in order to map and determine the concentration profiles of P, Ca, S, Fe and Zn from the epiphysis to diaphysis and across the cortical and trabecular bone structures. In control animals (not ovariectomized), the S and Zn contents significantly characterized differences between cortical and trabecular bone structures, whereas P and Ca showed increased gradients from the epiphyseal region to the diaphysis. After ovariectomy the differences observed were differential according to the type of hormonal supplementation. A significant decrease in P and Ca contents and depletion of minor and trace minerals, such as S, Fe and Zn, were found for both cortical and trabecular bone structures after ovariectomy relative to controls. Bone mineral contents were reversed to control levels by synthetic oestrogen supplementation, and combined oestrogen and progesterone treatment. Recovery was more evident in the femoral epiphysis and neck than in the diaphysis. The use of oestrogen alone did not lead to bone recovery after ovariectomy. Alterations in bone mineral composition observed for animals receiving synthetic oestrogen and combined oestrogen and progesterone supplement might reflect beneficial structural changes in critical regions of long bones, mostly affected in post‐menopausal osteoporosis.     

Systemically alendronate was incorporated into dental tissues but did not cause morphological or mechanical changes in rats teeth

This study evaluated the effect of the systemic use of sodium alendronate in rats in vivo. Forty‐five Wistar rats aged 36 to 42 days and weighing 200 to 230 g were randomly assigned to a control group (n = 20), which received distilled water, and an experimental group (n = 25), which received 2 weekly doses of 1 mg/kg of chemically pure sodium alendronate. The animals were killed after 60 days of treatment. The tibias were removed for analysis of bone mineral density by dual‐energy X‐ray absorptiometry (DXA). Then, the maxillary incisors were extracted for analysis of the mineralized dental tissues using fluorescence spectroscopy (FS), scanning electron microscopy (SEM), bright field microscopy (BFM), and cross‐sectional microhardness (CSMH) testing. DXA and CSMH data were subjected to statistical analysis by Kruskal‐Wallis test (5% significance level). The experimental group presented higher bone mineral density than the control group by DXA. FS analysis revealed presence of alendronate in the mineralized dental tissues of the specimens of the experimental group. Significant morphological differences were not found by SEM and BFM. Enamel and dentin (100 and 300 μm from the dentinoenamel junction) CSMH data did not show significant difference between the control and experimental groups. Based on the obtained results, we conclude that while alendronate increased the bone mineral density and was incorporated into the mineralized dental tissues it did not cause significant alterations in the morphology and microhardness of rat incisor enamel and dentin. Microsc. Res. Tech. 75:1265–1271, 2012. © 2012 Wiley Periodicals, Inc.     

Errors in quantitative backscattered electron analysis of bone standardized by energy-dispersive x-ray spectrometry

Backscattered electron (BSE) imaging has proven to be a useful method for analyzing the mineral distribution in microscopic regions of bone. However, an accepted method of standardization has not been developed, limiting the utility of BSE imaging for truly quantitative analysis. Previous work has suggested that BSE images can be standardized by energy-dispersive x-ray spectrometry (EDX). Unfortunately, EDX-standardized BSE images tend to underestimate the mineral content of bone when compared with traditional ash measurements. The goal of this study is to investigate the nature of the deficit between EDX-standardized BSE images and ash measurements. A series of analytical standards, ashed bone specimens, and unembedded bone specimens were investigated to determine the source of the deficit previously reported. The primary source of error was found to be inaccurate ZAF corrections to account for the organic phase of the bone matrix. Conductive coatings, methyl-methacrylate embedding media, and minor elemental constituents in bone mineral introduced negligible errors. It is suggested that the errors would remain constant and an empirical correction could be used to account for the deficit. However, extensive preliminary testing of the analysis equipment is essential.     

Analysis of plastic deformation in cortical bone after insertion of coated and non-coated self-tapping orthopaedic screws

Insertion of internal fracture fixation devices, such as screws, mechanically weakens the bone. Diamond-like carbon has outstanding tribology properties which may decrease the amount of damage in tissue. The purpose of this study was to investigate methods for quantification of cortical bone damage after orthopaedic bone screw insertion and to evaluate the effect of surface modification on tissue damage. In total, 48 stainless steel screws were inserted into cadaver bones. Half of the screws were coated with a smooth amorphous diamond coating. Geometrical data of the bones was determined by peripheral quantitative computed tomography. Thin sections of the bone samples were prepared after screw insertion, and histomorphometric evaluation of damage was performed on images obtained using light microscopy. Micro-computed tomography and scanning electron microscopy were also used to examine tissue damage. A positive correlation was found between tissue damage and the geometric properties of the bone. The age of the cadaver significantly affected the bone mineral density, as well as the damage perimeter and diameter of the screw hole. However, the expected positive effect of surface modification was probably obscured by large variations in the results and, thus, statistically significant differences were not found in this study. This can be explained by natural variability in bone tissue, which also made automated image analysis difficult.     

Computation of bone remodelling after Duracon knee arthroplasty using a thermodynamic-based model

The present study utilizes a recently developed literature model for the bone remodelling process to predict the evolution of bone density following Duracon total knee arthroplasty (TKA). In this model, which is based on chemical kinetics and irreversible thermodynamics, bone is treated as a self-organizing system capable of exchanging matter, energy, and entropy with its surroundings. Unlike previous models in which mechanical loading is regarded as the only stimulus for bone remodelling, the present model establishes a unique coupling between mechanical loading and the chemical reactions involved in the process of bone remodelling. This model was incorporated into the finite element software ANSYS by means of a macro to compute density distribution in distal femoral bone both before and after TKA. Consistent with dual-energy X-ray absorptiometry (DEXA) scans reported in the literature, the results showed that the most severe bone loss occurs in the anterior region of the distal femur and that there is more bone resorption in the lateral than the medial condyle following TKA. Furthermore, the bone density distribution predicted using the present model showed a gradual and uniform pattern and thus a more realistic bone evolution contrary to the strain energy density model, where there is no gradual bone density evolution.     

Accumulation of in-vivo fatigue microdamage and its relation to biomechanical properties in ageing human cortical bone

Bone matrix accumulates microdamage in the form of microcracks as a result of everyday cyclic loading activities. In two very recent studies, which used conventional histological stains and light microscopy techniques, the amount of this in-vivo microdamage in the cortices of long bones has been shown to increase with age. These articles have suggested that in-vivo microcracks may have an effect on the material properties of the tissue. However, a precise quantitative relationship between the number of microcracks and the mechanical properties of these same bones has not been produced before, and in particular the way the microcracks may affect the stiffness, the strength or possibly the toughness of the tissue. This article presents an examination of the in-vivo microdamage in human bones by the use of laser scanning confocal microscopy, which offers better discrimination and allows examination of the cracks in-situ . Quantification of in-vivo fatigue microcracks was performed by counting the microcrack numerical density and surface density in specimens for which we have previously derived a full set of mechanical properties as a function of age. It is shown that bone microdamage relates more to the toughness (measured by three different measures) of ageing bone tissue than to its stiffness and strength. The result allows us (i) to re-evaluate the fragility of ageing human bone and put more emphasis on its energy-related resistance to fracture than perhaps on its stiffness or strength and also (ii) to understand more fully the causal relationship and interactions between microcracks and tissue toughness.     

Sensitivity of proximal femoral stiffness and areal bone mineral density to changes in bone geometry and density

Areal bone mineral density (aBMD) is the most common surrogate measurement for assessing the bone strength of the proximal femur associated with osteoporosis. Additional factors, however, contribute to the overall strength of the proximal femur, primarily the anatomical geometry. Finite element analysis (FEA) is an effective and widely used computer-based simulation technique for modelling mechanical loading of various engineering structures, providing predictions of displacement and induced stress distribution due to the applied load. FEA is therefore inherently dependent upon both density and anatomical geometry. FEA may be performed on both three-dimensional and two-dimensional models of the proximal femur derived from radiographic images, from which the mechanical stiffness may be predicted. It is examined whether the outcome measures of two-dimensional FEA, two-dimensional, finite element analysis of X-ray images (FEXI), and three-dimensional FEA computed stiffness values of the proximal femur are more sensitive than aBMD to changes in trabecular bone density and femur geometry. It is assumed that if an outcome measure follows known trends with changes in density and geometric parameters, then an increased sensitivity will be indicative of an improved prediction of bone strength. All three outcome measures increased non-linearly with trabecular bone density, increased linearly with cortical shell thickness and neck width, decreased linearly with neck length, and were relatively insensitive to neck-shaft angle. For femoral head radius, aBMD was relatively insensitive, with two-dimensional FEXI and three-dimensional FEA demonstrating a non-linear increase and decrease in sensitivity respectively. For neck anteversion, aBMD decreased non-linearly, whereas both two-dimensional FEXI and three-dimensional FEA demonstrated a parabolic-type relationship, with the maximum stiffness being achieved at an angle of approximately 15 degrees. Multi-parameter analysis showed that all three outcome measures demonstrated their highest sensitivity to a change in cortical thickness. When changes in all input parameters were considered simultaneously, three and two-dimensional FEA had statistically equal sensitivities (0.41 +/- 0.20 and 0.42 +/- 0.16 respectively, p = ns) that were significantly higher than the sensitivity of aBMD (0.24 +/- 0.07; p = 0.014 and 0.002 for three-dimensional and two-dimensional FEA respectively). This simulation study suggests that since mechanical integrity and FEA are inherently dependent on anatomical geometry, FEXI stiffness, being derived from conventional two-dimensional radiographic images, may provide an improvement in the prediction of bone strength of the proximal femur than currently provided by aBMD.     

Density measurements of noncrystalline materials at high pressure with diamond anvil cell

We describe an x-ray absorption method for in situ density measurement of non-crystalline materials in the diamond anvil cell using a monochromatic synchrotron x-ray microbeam. Sample thickness, which is indispensable in the absorption method, can be determined precisely by extrapolating the thickness profile of the gasket obtained by x-ray absorption and diffraction measurements. Diamond deformation across the sample chamber becomes noticeable at high pressures above 10 GPa, which can be monitored with a precision better than 1%, as demonstrated by measurements on crystalline Ag. We have applied the developed method to measure densities of the classic network-forming GeO(2) glass in octahedral form at pressures up to 56 GPa. The fit to the pressure-volume data with the Birch-Murnaghan equation from 13 to 56 GPa gives parameters of V(0)=23.2+/-0.4 cm(3)mol and K=35.8+/-3.0 GPa, assuming that K(')=4. This method could be applicable for in situ determination of the density of liquids and other noncrystalline materials using a diamond anvil cell up to ultrahigh pressures.     

Parametric investigation of load-induced structure remodeling in the proximal femur

The process of adaptive bone remodeling can be simulated with a self-optimizing finite element method. The basic remodeling rules attempt to obtain a constant value for the strain energy per unit bone mass, by adapting density. The precise solution is dependent on the loads, initial conditions, and the parameters of the remodeling rule. While there are several investigations on developing algorithms leading to the bone density distribution in the proximal femur, these algorithms often require a large number of iterations. The aim of this study was to develop a more efficient adaptive bone remodeling algorithm, and to identify how the bone density distribution of the proximal femur was affected by parameters that govern the remodeling process. The forces at different phases of the gait cycle were applied as boundary conditions. The bone density distributions from these forces were averaged to estimate the density distribution in the proximal femur. The effect of varying the initial bone density, spatial influence function, non-linear order of the adaptive algorithm, and the influence range on the converged solution were investigated. The proposed procedure was shown to converge in a fewer number of iterations and requiring less computational time, while still generating a realistic bone density distribution. It was also shown that varying the identified parameters within reasonable upper and lower bounds had very little impact on the qualitative form of the converged solution. In contrast, the convergence rate was affected to a greater degree by variation of these parameters. In all cases, the solutions obtained are comparable with the actual density in the proximal femur, as measured by Dual-energy X-ray absorptiometry (DEXA) scans.     

Mineral content changes in bone associated with damage induced by the electron beam

Energy-dispersive x-ray (EDX) spectroscopy and backscattered electron (BSE) imaging are finding increased use for determining mineral content in microscopic regions of bone. Electron beam bombardment, however, can damage the tissue, leading to erroneous interpretations of mineral content. We performed elemental (EDX) and mineral content (BSE) analyses on bone tissue in order to quantify observable deleterious effects in the context of (1) prolonged scanning time, (2) scan versus point (spot) mode, (3) low versus high magnification, and (4) embedding in poly-methylmethacrylate (PMMA). Undemineralized cortical bone specimens from adult human femora were examined in three groups: 200x embedded, 200x unembedded, and 1000x embedded. Coupled BSE/EDX analyses were conducted five consecutive times, with no location analyzed more than five times. Variation in the relative proportions of calcium (Ca), phosphorous (P), and carbon (C) were measured using EDX spectroscopy, and mineral content variations were inferred from changes in mean gray levels ("atomic number contrast") in BSE images captured at 20 keV. In point mode at 200x, the embedded specimens exhibited a significant increase in Ca by the second measurement (7.2%, p < 0.05); in scan mode, a small and statistically nonsignificant increase (1.0%) was seen by the second measurement. Changes in P were similar, although the increases were less. The apparent increases in Ca and P likely result from decreases in C: -3.2% (p < 0.05) in point mode and -0.3% in scan mode by the second measurement. Analysis of unembedded specimens showed similar results. In contrast to embedded specimens at 200x, 1000x data showed significantly larger variations in the proportions of Ca, P, and C by the second or third measurement in scan and point mode. At both magnifications, BSE image gray level values increased (suggesting increased mineral content) by the second measurement, with increases up to 23% in point mode. These results show that mineral content measurements can be reliable when using coupled BSE/EDX analyses in PMMA-embedded bone if lower magnifications are used in scan mode and if prolonged exposure to the electron beam is avoided. When point mode is used to analyze minute regions, adjustments in accelerating voltages and probe current may be required to minimize damage.     

一种CR-CR型自动变速器的运动分析和效率计算

以CR- CR双排行星齿轮机构四挡自动变速器为例,运用单排行星齿轮机构一般运动规律的特性方程式对该类变速器进行运动分析,采用啮合功率法将行星齿轮机构转化为定轴轮系机构,对自动变速箱的传动效率进行计算.所述方法为其进一步自动变速箱的结构改进和性能提高提供了一定的理论基础.     

倒装芯片封装结构中SnAgCu焊点热疲劳寿命预测方法研究

由于焊点区非协调变形导致的热疲劳失效是倒装芯片封装（包括无铅封装）结构的主要失效形式.到目前为止,仍无公认的焊点寿命和可靠性的评价方法.文中分别采用双指数和双曲正弦本构模型描述SnAgCu焊点的变形行为,通过有限元方法计算焊点累积蠕变应变和累积蠕变应变能密度,进而据此预测倒装芯片封装焊点的热疲劳寿命.通过实验验证,评价上述预测方法的可行性.结果表明,倒装芯片的寿命可由芯片角焊点的寿命表征;根据累积蠕变应变能密度预测的焊点热疲劳寿命比根据累积蠕变应变预测的焊点热疲劳寿命更接近实测数据;根据累积蠕变应变预测的热疲劳寿命比根据累积蠕变应变能密度预测的热疲劳寿命长;采用双指数本构模型时,预测的焊点热疲劳寿命也较长.     

Applicability of sheep and pig models for cancellous bone in human vertebral bodies

The mineral content of cancellous bone from sheep and pig vertebral bodies was determined by ashing at 800 degrees C. The results were compared with published results for human vertebral cancellous bone. The results for sheep (0.37 +/- 0.06 gcm(-3), mean +/- standard deviation) were not significantly different (p = 0.127) to those from pigs (0.33 +/- 0.03 gcm(-3)). The results from both species were significantly higher (p < 0.001) than those from human bones (0.15 +/- 0.02 gcm(-3)). This means that cancellous bone from sheep and pig vertebral bodies is not a good model for corresponding human bone. However, sheep and pig bone are useful, for example, for providing stringent tests of cutting instruments to be used in human spinal surgery.