The contribution of cancellous bone to long bone strength and rigidity

A recent article (Burr and Piotrowski, 1982) suggested that structural analyses of long bone cross-sectional geometry will be inaccurate and should be considered inappropriate when cancellous bone accounts for 10-15% or more of the cross-sectional area. Consideration of material property differences between compact and cancellous bone, however, indicates that even significant proportions of cancellous bone (10-40% of total cross-sectional area) will very likely have negligible effects on bone strength and rigidity, and can be effectively ignored in geometrical analyses of diaphyseal sections. In metaphyseal and epiphyseal regions, however, geometric analyses of section properties such as area moments of inertia are inappropriate, both because of significant trabecular bone effects, and because of the inherent constraints of mechanical beam models.     

The effects of tensile-compressive loading mode and microarchitecture on microdamage in human vertebral cancellous bone

The amount of microdamage in bone tissue impairs mechanical performance and may act as a stimulus for bone remodeling. Here we determine how loading mode (tension vs. compression) and microstructure (trabecular microarchitecture, local trabecular thickness, and presence of resorption cavities) influence the number and volume of microdamage sites generated in cancellous bone following a single overload. Twenty paired cylindrical specimens of human vertebral cancellous bone from 10 donors (47–78 years) were mechanically loaded to apparent yield in either compression or tension, and imaged in three dimensions for microarchitecture and microdamage (voxel size 0.7×0.7×5.0 μm³). We found that the overall proportion of damaged tissue was greater (p=0.01) for apparent tension loading (3.9±2.4%, mean±SD) than for apparent compression loading (1.9±1.3%). Individual microdamage sites generated in tension were larger in volume (p<0.001) but not more numerous (p=0.64) than sites in compression. For both loading modes, the proportion of damaged tissue varied more across donors than with bone volume fraction, traditional measures of microarchitecture (trabecular thickness, trabecular separation, etc.), apparent Young?s modulus, or strength. Microdamage tended to occur in regions of greater trabecular thickness but not near observable resorption cavities. Taken together, these findings indicate that, regardless of loading mode, accumulation of microdamage in cancellous bone after monotonic loading to yield is influenced by donor characteristics other than traditional measures of microarchitecture, suggesting a possible role for tissue material properties.     

A method for the determination of the residual chloroform in defatted cancellous bone transplants

The removal of fat from cancellous bone tissue promotes the clinical healing of the transplant and improves the penetration of chemical sterilisation media into the tissue. Treatment using chloroform/methanol (2:1, 2 h) is frequently used as a defatting procedure. Eight rinses with methanol followed by two rinses with aqua ad iniectabilia (20 min each, with ultrasonic effect) ensure depletion in the level of chloroform from defatted cancellous bone to a concentration below 25 ppm (limit value). For the necessary routine quality checks on the production process, a gas chromatography method has been developed that determines the level of chloroform in cancellous bone, for which the detection limit is 0.003 ppm.     

Nanostructure and elastic modulus of single trabecula in bovine cancellous bone

We aimed to investigate the elastic modulus of trabeculae using tensile tests and assess the effects of nanostructure at the hydroxyapatite (HAp) crystal scale on the elastic modulus. In the experiments, 18 trabeculae that were at least 3 mm in length in the proximal epiphysis of three adult bovine femurs were used. Tensile tests were conducted using a small tensile testing device coupled with microscopy under air-dried condition. The c-axis orientation of HAp crystals and the degree of orientation were measured by X-ray diffraction. To observe the deformation behavior of HAp crystals under tensile loading, the same tensile tests were conducted in X-ray diffraction measurements. The mineral content of specimens was evaluated using energy dispersive X-ray spectrometry. The elastic modulus of a single trabecula varied from 4.5 to 23.6 GPa, and the average was 11.5±5.0 GPa. The c-axis of HAp crystals was aligned with the trabecular axis and the crystals were lineally deformed under tensile loading. The ratio of the HAp crystal strain to the tissue strain (strain ratio) had a significant correlation with the elastic modulus (r=0.79; P<0.001). However, the mineral content and the degree of orientation did not vary widely and did not correlate with the elastic modulus in this study. It suggests that the strain ratio may represent the nanostructure of a single trabecula and would determine the elastic modulus as well as mineral content and orientation.     

3D analysis from micro-MRI during in situ compression on cancellous bone

A mini-compression jig was built to perform in situ tests on bovine trabecular bone monitored by micro-MRI. The MRI antenna provided an isotropic resolution of 78 μm that allows for a volume correlation method to be used. Three-dimensional displacement fields are then evaluated within the bone sample during the compression test. The performances of the correlation method are evaluated and discussed to validate the technique on trabecular bone. By considering correlation residuals and estimates of acquisition noise, the measured results are shown to be trustworthy. By analyzing average strain levels for different interrogation volumes along the loading direction, it is shown that the sample size is less than that of a representative volume element. This study shows the feasibility of the 3D-displacement and strain field analyses from micro-MRI images. Other biological tissues could be considered in future work.     

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 (R²_adj = 0.91), with a scan orientation parallel to the spine axis and in the lateral view offering an alternative (R²_adj = 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.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

Orthotropic properties of cancellous bone modelled as parameterized cellular material

Analysis of stresses and strains in bone tissues and simulation of their adaptive remodelling require exhaustive information about distribution of constitutive properties of cancellous bone and their relationships to microstructural parameters. Homogenization of “equivalent” trabecular microstructures appears to be an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. The models, based on a space-filling dodecahedron, are fully three-dimensional and are parameterized with four shape parameters. Variation of the parameters allows to imitate most of typical microstructure patterns observed in real bones, along with a variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Coefficients of elastic orthotropic stiffness matrix are determined as tabularized functions of elastic constants versus the shape parameters. Additionally, they are correlated to apparent density and principal fabric tensor values. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement.     

Age-related changes of bone mineral density in human calcaneus, talus, and scaphoid bone

To examine whether the bone mineral density (BMD) decreases uniformly with aging in any spongy bones, the authors investigated age-related changes of BMD in the calcaneus, talus, and scaphoid bone. After the ordinary dissection by medical students was finished, calcanei, tali, and scaphoid bones were resected from the subjects, and BMDs were measured by dual-energy X-ray absorptiometry. Their BMDs seemed to decrease gradually with aging in the calcanei, tali, and scaphoid bones. It was found that there were statistically significant relationships between age and BMD in the men’s and women’s scaphoid bones, women’s tali, and women’s calcanei, but not in the men’s tali and calcanei. It should be noted that there were significant relationships between age and BMD in both men’s and women’s scaphoid bones. In regard to relationship in BMD between the bones of the upper and lower limbs in individuals, it was found that the relationship between the calcaneus and talus was higher than that between the calcaneus and scaphoid bone. This suggests that there is a higher relationship in BMD between the two tarsal bones compared with that between the tarsal and carpal bones.     

The effect of restriction of dietary calcium on trabecular and cortical bone mineral density in the rats

This study aimed to investigate effects of restricted calcium intake on cortical and trabecular bone density in white rats. Low Ca diet was fed for six weeks, and bone density and bone metabolism parameters were assessed in blood. This study was carried out on 12 male white rats aged 12 weeks (Sprague-Dawley; SD). These rats were bred for 1 week and randomly assigned to the standard calcium diet group (SCa group, n = 6) and the low calcium diet group (LCa group; n = 6). The SCa group was given a modified AIN-93M mineral mix (with 0.5% Ca), which was made by adding calcium to a standard AIN93 diet, and the LCa Group was fed a modified AIN-93 Mineral mix (with 0.1% Ca). Femoral BMD and BMC were measured by DEXA in each rat. After trabecular bone was separated from cortical bone, volumetric bone mineral density (vBMD) was measured using pQCT. Serum Ca and P levels were measured as parameters of bone metabolism, and S-ALP, S-TrACP and-Dpd levels were also measured. The results revealed no significant differences in weight, growth rate, feed consumption and feed efficiency between the two groups before and after calcium-restricted diet (p > .05). No significant differences were also observed in bone length and bone mass between the two groups (p > .05). Although bilateral femoral BMDs were not significantly different between the two groups, bilateral femoral BMCs significantly decreased in the LCa group, compared with the SCa group (p = .023, p = .047). Bilateral cortical MDs were not significantly different between the two groups, either. However, trabecular BMD significantly decreased in the LCa group, compared with the SCa group (p = .041). U-Dpd and S-TrACP levels significantly declined in the LCa group, compared to the SCa group (p = .039, p = .010). There were no significant differences in serum Ca and P levels between the two groups (p > .05). However, a significant decrease in urinary Ca level (p = .001) and a significant increase in urinary P (p = .001) were observed in the LCa group, compared to the Sca group. These findings described that six-week low calcium diet led to decreased trabecular bone density, reduced urinary excretion of Ca and increased urinary excretion of P. As a result, Ca hemeostasis can be maintained.     

Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions

Strong correspondence between the uniaxial apparent strength and stiffness of cancellous bone allows the use of stiffness as a predictor of bone strength. Measured values of mechanical properties in cancellous bone can be different between experiments due to different experimental conditions. In the current study, bone volume fraction, experimentally determined and finite element (FE) predicted stiffness were examined as predictors of cancellous bone ultimate strength in two different groups each of which was tested using a different end constraint. It is demonstrated that, although always significant, the relationships of strength with bone volume fraction and experimentally determined stiffness are different between test groups. Apparent stiffness, estimated by FE modeling, predicts the ultimate strength of human cancellous bone consistently for all examined experimental protocols.     

The effect of surface charge density on valinomycin-K+ complex formation in model membranes

The model membrane approach was used to investigate the surface charge effect on the ion-antibiotic complexation process. Mixed monolayers of valinomycin and lipids were spread on subphases containing K⁺ or Na⁺. The surface charge density was modified by spreading ionizable valinomycin analogs on aqueous subphases of different pH or by changing the nature of the lipid (neutral, negatively charged) in the mixed film. Surface pressure and surface potential measurements demonstrated that a neutral lipid (phosphatidylcholine) or positively charged valinomycin analogs didn't enhance the antibiotic complexing capacity. However, a maximal complexation is reached for a critical lipid concentration in the valinomycin-phosphatidylserine mixed film. The role of the surface charge on the valinomycin complexing properties was examined in terms of the Gouy-Chapman theory. As a consequence of the negative charge of the lipid monolayer, the K⁺ concentration near the surface is larger than the bulk concentration, by a Boltzmann factor. A good agreement was observed between the experimental results and the theoretical predictions. Conductance measurements of asymmetric bilayers containing a neutral lipid (egg lecithin) on one side and a negatively charged lipid (phosphatidylserine) on the other, confirm the role of the surface charge. Indeed, addition of K⁺ to the neutral side of the bilayer containing valinomycin had no effect on the conductance whereas addition of K⁺ to the charged side of the bilayer caused a 80-fold conductance increase.     

Design and validation of a testing system to assess torsional cancellous bone failure in conjunction with time-lapsed micro-computed tomographic imaging

When compressed axially, cancellous bone often fails at an oblique angle along well-defined bands, highlighting the importance of cancellous bone shear properties. Torsion testing to determine shear properties of cancellous bone has often been conducted under conditions appropriate only for axis-symmetric specimens comprised of homogeneous and isotropic materials. However, most cancellous bone specimens do not meet these stringent test conditions. Therefore, the aim of this study was to design and validate a uniaxial, incremental torsional testing system for non-homogeneous orthotropic or non-axis-symmetric specimens.Precision and accuracy of the newly designed torsion system was validated by using Plexiglas rods and beams, where obtained material properties were compared to those supplied by the manufacturer. Additionally, the incremental step-wise application of angular displacement and simultaneous time-lapsed μCT imaging capability of the system was validated using whale cancellous bone specimens, with step-wise application of angular displacement yielding similar torsional mechanical properties to continuous application of angular displacement in a conventional torsion study.In conclusion, a novel torsion testing system for non-homogeneous, orthotropic materials using the incremental step-wise application of torsion and simultaneous time-lapsed μCT imaging was designed and validated.     

百岁以上老人跟骨骨密度和骨强度的相关性分析

目的研究广西巴马百岁以上女性老人的年龄、身高、体重、BMI与跟骨骨密度、骨强度之间的关系。方法采用定量超声骨密度测定仪,对广西巴马16名百岁以上女性老人的跟骨骨密度、骨强度进行测定,并记录相应年龄,同时行人工测量身高、体重、BMI指数,应用SPSS16.0软件分别计算年龄、身高、体重、BMI与跟骨骨密度、骨强度的pearson的相关系数。结果年龄、身高、体重、BMI均与百岁以上女性老人的跟骨骨密度、骨强度有相关关系,但相关性均无显著性(P0.05)。其中年龄、身高、体重与跟骨骨密度、骨强度呈负相关关系;BMI与跟骨骨密度、骨强度呈正相关关系,但相关性均无显著性(P0.05)。结论年龄、身高、体重、BMI均是广西巴马百岁以上女性老人骨密度、骨强度的影响因素,但相关性均无显著性,或需探讨新的评价指标衡量百岁以上女性老人的骨密度及骨强度,为百岁以上女性老人早期预防和诊断骨质疏松提供科学依据。     

Mathematical analysis of trabecular 'trajectories' in apparent trajectorial structures: the unfortunate historical emphasis on the human proximal femur

Wolff's "law" of the functional adaptation of bone is rooted in the trajectory hypothesis of cancellous bone architecture. Wolff often used the human proximal femur as an example of a trajectorial structure (i.e. arched trabecular patterns appear to be aligned along tension/compression stress trajectories). We examined two tenets of the trajectory hypothesis; namely, that the trabecular tracts from the tension- and compression-loaded sides of a bending environment will: (1) follow 'lines' (trajectories) of tension/compression stress that resemble an arch with its apex on a neutral axis, and (2) form orthogonal (90 degrees ) intersections. These predictions were analysed in proximal femora of chimpanzees and modern humans, and in calcanei of sheep and deer. Compared to complex loading of the human femoral neck, the chimpanzee femoral neck reputedly receives relatively simpler loading (i.e. temporally/spatially more consistent bending), and the artiodactyl calcaneus is even more simply loaded in bending. In order to directly consider Wolff's observations, measurements were also made on two-dimensional, cantilevered beams and curved beams, each with intersecting compression/tension stress trajectories. Results in the calcanei showed: (1) the same nonlinear equation best described the dorsal ("compression") and plantar ("tension") trabecular tracts, (2) these tracts could be exactly superimposed on the corresponding compression/tension stress trajectories of the cantilevered beams, and (3) trabecular tracts typically formed orthogonal intersections. In contrast, trabecular tracts in human and chimpanzee femoral necks were non-orthogonal (mean approximately 70 degrees ), with shapes differing from trabecular tracts in calcanei and stress trajectories in the beams. Although often being described by the same equations, the trajectories in the curved beams had lower r(2) values than calcaneal tracts. These results suggest that the trabecular patterns in the calcanei and stress trajectories in short beams are consistent with basic tenets of the trajectory hypothesis while those in human and chimpanzee femoral necks are not. Compared to calcanei, the more complexly loaded human and chimpanzee femoral necks probably receive more prevalent/predominant shear, which is best accommodated by non-orthogonal, asymmetric trabecular tracts. The asymmetrical trabecular patterns in the proximal femora may also reflect the different developmental 'fields' (trochanteric vs. neck/head) that formed these regions, of which there is no parallel in the calcanei.     

Experimental charge density of sucrose at 20K: bond topological, atomic, and intermolecular quantitative properties

The charge density of sucrose was determined from a high-resolution X-ray data set measured at 20 K. The density distribution so obtained was analyzed quantitatively by application of Bader’s atoms in molecules (AIM) formalism, and a comparison was made with corresponding results from a B3LYP (6-311++G(3df,3pd)) calculation at the experimental geometry. Bond topological and atomic properties (volumes and charges) were derived and compared. The influence of hydrogen bonding on the experimental charge density was also studied qualitatively and quantitatively by means of topological properties. In terms of the hydrogen-bond energies, a grouping into strong, medium and very weak hydrogen bonds was made, the latter of which were involved in a bifurcated bond.     

Influence of mastication and edentulism on mandibular bone density

The aim of this study was to demonstrate that external loading due to daily activities, including mastication, speech and involuntary open–close cycles of the jaw contributes to the internal architecture of the mandible. A bone remodelling algorithm that regulates the bone density as a function of stress and loading cycles is incorporated into finite element analysis. A three-dimensional computational model is constructed on the basis of computerised tomography (CT) images of a human mandible. Masticatory muscle activation involved during clenching is modelled by static analysis using linear optimisation. Other loading conditions are approximated by imposing mandibular flexure. The simulations predict that mandibular bone density distribution results in a tubular structure similar to what is observed in the CT images. Such bone architecture is known to provide the bone optimum strength to resist bending and torsion during mastication while reducing the bone mass. The remodelling algorithm is used to simulate the influence of edentulism on mandibular bone loss. It is shown that depending on the location and number of missing teeth, up to one-third of the mandibular bone mass can be lost due to lack of adequate mechanical stimulation.     

1.8 mT不同频率正弦交变电磁场对青年大鼠骨密度及骨形态计量的影响比较

比较不同频率的正弦交变电磁场对SD青年大鼠骨密度及骨形态计量指标的影响,筛选可有效提升大鼠骨密度的频率参数。将32只8周龄SD雌性大鼠随机分为4组:对照组、15 Hz组、30 Hz组、45 Hz组;除对照组外,实验组大鼠每天都给予相应频率的1.8 m T正弦交变电磁场干预,干预时间为90 min。磁场干预8周后,双能X射线骨密度仪检测大鼠全身骨密度、右侧股骨骨密度和椎骨骨密度,ELISA分析血清中骨形成与骨吸收生化指标的含量,右侧胫骨进行荧光间距测量与骨形态计量分析。相比于对照组,15 Hz组、45 Hz组大鼠的全身骨密度、股骨骨密度、椎骨骨密度均明显升高(P0.05),血清中骨钙素与骨保护素含量也显著提升(P0.05);实验组大鼠的胫骨双荧光间距与骨组织静态参数均高于对照组(P0.05)。结果表明,15 Hz、45 Hz正弦交变电磁场可有效提升青年大鼠的骨密度,从而可预防骨质疏松的发生。