Trabecular Shear Stresses Predict <Emphasis Type="Italic">In Vivo</Emphasis> Linear Microcrack Density but not Diffuse Damage in Human Vertebral Cancellous Bone

Linear microcracks and diffuse damage (staining over a broad region) are two types of microscopic damage known to occur in vivo in human vertebral trabecular bone. These damage types might be associated with vertebral failure. Using microcomputed tomography and finite element analysis for specimens of cancellous bone, we estimated the stresses in the trabeculae of human vertebral tissue for inferosuperior loading. Microdamage was quantified histologically. The density of in vivo linear microcracks was, but the diffuse damage area was not, related to the estimates of von Mises stress distribution in the tissue. In vivo linear microcrack density increased with increasing coefficient of variation of the trabecular von Mises stress and with increasing average trabecular von Mises stress generated per superoinferior apparent axial stress. Nonlinear increase in linear crack density, similar to the increase of the coefficient of variation of trabecular shear stresses, with decreasing bone stiffness and bone volume fraction suggests that damage may accumulate rather rapidly in diseases associated with low bone density due to the dramatic increase of shear stresses in the tissue. © 2003 Biomedical Engineering Society. PAC2003: 8719Rr, 8719Xx, 8759Ls, 8759Fm, 8710+e     

股骨头坏死中松质骨微观力学特性的演变规律

目的采用结合显微CT和显微有限元分析方法,即基于显微CT图像建立三维有限元模型并进行数值模拟仿真分析,无创研究不同分期的坏死股骨头松质骨的微结构和微观力学性能,以期了解在股骨头坏死的发展过程中,松质骨微结构和微观力学特性的变化规律,为临床预测股骨头坏死提供理论基础。方法采集10例股骨头坏死患者的股骨头标本的显微CT图像,按照国际骨循环研究学会分期标准分为Ⅱ期样本3例,Ⅲ期3例,Ⅳ期4例。将图像中骨组织进行阈值分割,分区域建立坏死区、侧向区、硬化区和远端区的松质骨块三维有限元模型(边长8 mm),并根据CT值赋予非均匀材料属性。利用ImageJ软件中的BoneJ插件通过识别显微CT组图像,计算测量各区域松质骨的微结构参数,包括骨体积分数、骨小梁厚度、骨小梁间隙、结构模型指数。对松质骨块施加表观应变为1%的压缩载荷,计算骨组织应力和松质骨表观刚度等参数,对比分析各分期、各分区结果。结果在松质骨微结构方面,Ⅳ期较Ⅱ期的股骨头内部硬化区和坏死区的变化最为明显,硬化区的骨体积分数不断上升,骨小梁间隙下降,结构模型指数减小,而坏死区域与之相反;在骨组织微观受力方面,Ⅱ期到Ⅲ期坏死区域的应力并没有明显变化,而硬化区域随着分期增加应力不断上升,侧向区的应力不断下降。表观刚度变化与应力变化一致。结论随着股骨头坏死程度的加剧,硬化区的松质骨微结构和力学性能变化最大,应作为临床早期诊断中重点关注的区域。此外,微结构参数并不能准确体现松质骨的力学行为,而股骨头塌陷最终取决于其力学特性,因此结合有限元分析方法可更加全面了解股骨头坏死的微观力学演变规律。     

The Influence of Mineralization on Intratrabecular Stress and Strain Distribution in Developing Trabecular Bone

The load-transfer pathway in trabecular bone is largely determined by its architecture. However, the influence of variations in mineralization is not known. The goal of this study was to examine the influence of inhomogeneously distributed degrees of mineralization (DMB) on intratrabecular stresses and strains. Cubic mandibular condylar bone specimens from fetal and newborn pigs were used. Finite element models were constructed, in which the element tissue moduli were scaled to the local DMB. Disregarding the observed distribution of mineralization was associated with an overestimation of average equivalent strain and underestimation of von Mises equivalent stress. From the surface of trabecular elements towards their core the strain decreased irrespective of tissue stiffness distribution. This indicates that the trabecular elements were bent during the compression experiment. Inhomogeneously distributed tissue stiffness resulted in a low stress at the surface that increased towards the core. In contrast, disregarding this tissue stiffness distribution resulted in high stress at the surface which decreased towards the core. It was concluded that the increased DMB, together with concurring alterations in architecture, during development leads to a structure which is able to resist increasing loads without an increase in average deformation, which may lead to damage.     

Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels

The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000–25,000 με. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unload-recovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship.     

Trabecular Microarchitecture of Hominoid Thoracic Vertebrae

Spontaneous vertebral fractures are a common occurrence in modern humans, yet these fractures are not documented in other hominoids. Differences in vertebral bone strength between humans and apes associated with trabecular bone microarchitecture may contribute to differences in fracture incidence. We used microcomputed tomography to examine trabecular bone microarchitecture in the T8 vertebra of extant young adult hominoids. Scaled volumes of interest from the anterior vertebral body were analyzed at a resolution of 46 μm, and bone volume fraction, trabecular thickness, trabecular number, trabecular separation, structure model index, and degree of anisotropy were compared among species. As body mass increased, so did trabecular thickness, but bone volume fraction, structure model index, and degree of anisotropy were independent of body mass. Bone volume fraction was not significantly different between the species. Degree of anisotropy was not significantly different among the species, suggesting similarity of loading patterns in the T8 vertebra due to similar anatomical and postural relationships within each species' spine. Degree of anisotropy was negatively correlated with bone volume fraction (r² = 0.85, P < 0.05) in humans, whereas the apes demonstrated no such relationship. This suggested that less dense human trabecular bone was more preferentially aligned to habitual loading. Furthermore, we theorize that trabeculae in ape thoracic vertebrae would not be expected to become preferentially aligned if bone volume fraction was decreased. The differing relationship between bone volume fraction and degree of anisotropy in humans and apes may cause less dense human bone to be more fragile than less dense ape bone. Anat Rec, 2009. © 2009 Wiley‐Liss, Inc.     

The Effect of Regional Variations of the Trabecular Bone Properties on the Compressive Strength of Human Vertebral Bodies

Cancellous centrum is a major component of the vertebral body and significantly contributes to its structural strength and fracture risk. We hypothesized that the variability of cancellous bone properties in the centrum is associated with vertebral strength. Microcomputed tomography (micro-CT)-based gray level density (GLD), bone volume fraction (BV/TV), and finite element modulus (E) were examined for different regions of the trabecular centrum and correlated with vertebral body strength determined experimentally. Two sets of images in the cancellous centrum were digitally prepared from micro-CT images of eight human vertebral bodies (T10–L5). One set included a cubic volume (1 per vertebral centrum, n = 8) in which the largest amount of cancellous material from the centrum was included but all the shell materials were excluded. The other set included cylindrical volumes (6 per vertebral centrum, n = 48) from the anterior (4 regions: front, center, left, and right of the midline of vertebra) and the posterior (2 regions: left and right) regions of the centrum. Significant positive correlations of vertebral strength with GLD (r ² = 0.57, p = 0.03) and E (r ² = 0.63, p = 0.02) of the whole centrum and with GLD (r ² = 0.65, p = 0.02), BV/TV (r ² = 0.72, p = 0.01) and E (r ² = 0.85, p = 0.001) of the central region of the vertebral centrum were found. Vertebral strength decreased with increasing coefficient of variation of GLD, BV/TV, and E calculated from subregions of the vertebral centrum. The values of GLD, BV/TV, and E in centrum were significantly smaller for the anterior region than for the posterior region. Overall, these findings supported the significant role of regional variability of centrum properties in determining the whole vertebral strength.     

Laterality and grip strength influence hand bone micro‐architecture in modern humans,an HRpQCT study

It is widely hypothesized that mechanical loading, specifically repetitive low‐intensity tasks, influences the inner structure of cancellous bone. As such, there is likely a relationship between handedness and bone morphology. The aim of this study is to determine patterns in trabecular bone between dominant and non‐dominant hands in modern humans. Seventeen healthy patients between 22 and 32 years old were included in the study. Radial carpal bones (lunate, capitate, scaphoid, trapezium, trapezoid, 1st, 2nd and 3rd metacarpals) were analyzed with high‐resolution micro‐computed tomography. Additionally, crush and pinch grip were recorded. Factorial analysis indicated that bone volume ratio, trabeculae number (Tb.N), bone surface to volume ratio (BS.BV), body weight, stature and crush grip were all positively correlated with principal components 1 and 2 explaining 78.7% of the variance. Volumetric and trabecular endostructural parameters (BV/TV, BS/BV or Tb.Th, Tb.N) explain the observed inter‐individual variability better than anthropometric or clinical parameters. Factors analysis regressions showed correlations between these parameters and the dominant side for crush strength for the lunate (r² = 0.640, P < 0.0001), trapezium (r² = 0.836, P < 0.0001) and third metacarpal (r² = 0.763). However, despite a significant lateralization in grip strength for all patients, the endostructural variability between dominant and non‐dominant sides was limited in perspective to inter‐individual differences. In conclusion, handedness is unlikely to generate trabecular patterns of asymmetry. It appears, however, that crush strength can be considered for endostructural analysis in the modern human wrist.     

Progression of osteoporosis in cancellous bone depending on trabecular structure

Progression of osteoporosis is caused by a decline in bone formation activity relative to the resorption activity. In this paper, the authors carried out a theoretical analysis of the progression of osteoporosis to estimate the osteoporotic change in the upper end of the femur. According to this analysis, the progression rate of osteoporosis in cancellous bone depends on the product of remodeling activity,R _act, and the trabecular structure parameter,K _tr. To confirm that the theoretical results were reasonably comparable to actual osteoporotic change, these two factors were measured in rabbits. From the results, it was concluded that the highest progression rate was shown in bar/barlike trabecular structure (type 3); the next highest rate, was shown in plate/bar-like structure (type 2); and the plate/plate-like structure (type 1) was the most insensible. Furthermore, the bone volume fractions of cancellous bone were measured at the upper end of human femurs with and without osteoporosis. Then the measured value was compared with the theoretical value for each type of trabecular structure. Results showed that the decrease in bone volume fraction predicted by Eq. 7 was well in accord with the actual decrease.     

Optimizing bone cement stiffness for vertebroplasty through biomechanical effects analysis based on patient-specific three-dimensional finite element modeling

Vertebroplasty is a common and effective treatment for symptomatic osteoporotic vertebral compression fractures. However, the cemented and adjacent vertebras have a risk of recollapse due to largely unassured mechanisms, among which excessive stiffness of bone cement may be an important risk factor. This study aimed to find the most appropriate range of bone cement stiffness by analyzing its biomechanical effects on the augmented and adjacent vertebras of individual patient after vertebroplasty. A three-dimensional finite element model of T11-L1 osteoligamentous vertebras was reconstructed according to individual computed tomography data and validated by post mortem human subject experiment in literatures. Bone cement of varying stiffness was injected into the trabecular core of the T12 vertebra simulatively. The maximum von Mises stresses on cancellous and cortical bones of T11-L1 vertebras were analyzed under the loading conditions of flexion, extension, bending, and torsion. For the adjacent T11 and L1 vertebras, the stepwise elevation of the bone cement elastic modulus increased the maximum von Mises stress on the cancellous bone, but its effect on cortical bone was negligible. For the augmented T12 vertebra, the stresses on cancellous bone increased slightly under the loading condition of lateral bending and remained no impact on cortical bone. The linear interpolation revealed that the most suitable range of cement elastic modulus is 833.1 and 1408.1 Mpa for this patient. Increased elastic modulus of bone cement may lead to a growing risk of recollapse for the cemented vertebra as well as the adjacent vertebras. Our study provides a fresh perspective in clinical optimization of individual therapy in vertebroplasty.

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Lumbar Vertebral Body Bone Microstructural Scaling in Small to Medium‐Sized Strepsirhines

Bone mass, architecture, and tissue mineral density contribute to bone strength. As body mass (BM) increases any one or combination of these properties could change to maintain structural integrity. To better understand the structural origins of vertebral fragility and gain insight into the mechanisms that govern bone adaptation, we conducted an integrative analysis of bone mass and microarchitecture in the last lumbar vertebral body from nine strepsirhine species, ranging in size from 42 g (Microcebus rufus) to 2,440 g (Eulemur macaco). Bone mass and architecture were assessed via µCT for the whole body and spherical volumes of interest (VOI). Allometric equations were estimated and compared with predictions for geometric scaling, assuming axial compression as the dominant loading regime. Bone mass, microarchitectural, and vertebral body geometric variables predominantly scaled isometrically. Among structural variables, the degree of anisotropy (Tb.DA) was the only parameter independent of BM and other trabecular architectural variables. Tb.DA was related to positional behavior. Orthograde primates had higher average Tb.DA (1.60) and more craniocaudally oriented trabeculae while lorisines had the lowest Tb.DA (1.25), as well as variably oriented trabeculae. Finally, lorisines had the highest ratio of trabecular bone volume to cortical shell volume (～3x) and while there appears to be flexibility in this ratio, the total bone volume (trabecular + cortical) scales isometrically (BM^1.23, r² = 0.93) and appears tightly constrained. The common pattern of isometry in our measurements leaves open the question of how vertebral bodies in strepsirhine species compensate for increased BM. Anat Rec, 2013. © 2013 Wiley Periodicals, Inc.     

Single-trabecula building block for large-scale finite element models of cancellous bone

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) ‘building-block’ of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of ∼ 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of ∼30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.     

膝关节单髁置换胫骨优化截骨设计的生物力学研究

目的 比较膝关节单髁置换术(unicompartmental knee arthroplasty, UKA)常规截骨、保留圆角截骨及全新扩大圆角截骨方法对术后胫骨近端生物力学特性的影响。方法 基于Sawbones胫骨的CT数据,构建完整胫骨模型及不同截骨方式下UKA术后胫骨模型,采用轴向压缩工况对模型进行有限元分析,比较不同模型间胫骨近端应变情况及骨水泥应力差异。结果 在轴向压缩工况下,扩大圆角组其截骨区皮质骨von Mises应变峰值较常规截骨组与保留圆角组有所增加,而松质骨von Mises应变峰值则分别减少24.3%～42.9%、26.0%～48.7%。对比截骨区松质骨与皮质骨von Mises应变峰值差Δε_peak,发现扩大圆角组其Δε_peak远远小于其余两组。UKA后不同模型间胫骨前内侧皮质骨最小主应变无明显差异,但较完整胫骨模型增加23.3%～34.5%。扩大圆角组骨水泥单元平均von Mises应力随着圆角半径增大呈现下降趋势,且整体均小于常规截骨组与保留圆角组。结论 全新扩大圆角截骨方法可使健康骨质条件下胫骨近端应力传递更均匀...     

Paradoxical Effects of Partial Leptin Deficiency on Bone in Growing Female Mice

Morbidly obese, leptin‐deficient ob/ob mice display low bone mass, mild osteoclast‐rich osteopetrosis, and increased bone marrow adiposity. While partial leptin deficiency results in increased weight, the skeletal manifestations of partial leptin deficiency are less well defined. We therefore analyzed femora and lumbar vertebrae in growing (7‐week‐old) female C57BL/6 wildtype (WT) mice, partial leptin‐deficient ob/+ mice, and leptin‐deficient ob/ob mice. The bones were evaluated by dual energy absorptiometry, microcomputed tomography and histomorphometry. As expected, ob/+ mice were heavier, had more white adipose tissue, and lower serum leptin than WT mice, but were lighter and had less white adipose tissue than ob/ob mice. With a few exceptions, cancellous bone architecture, cell (osteoblast, osteoclast, and adipocyte), and dynamic measurements did not differ between WT and ob/+ mice. In contrast, compared to WT and ob/+ mice, ob/ob mice had lower cancellous bone volume fraction, and higher bone marrow adiposity in the femur metaphysis, and higher cancellous bone volume fraction in lumbar vertebra. Paradoxically, ob/+ mice had greater femoral bone volume than either WT or ob/ob mice. There was a positive correlation between body weight and femur volume in all three genotypes. However, the positive effect of weight on bone occurred with lower body weight in leptin‐producing mice. The paradoxical differences in bone size among WT, ob/+, and ob/ob mice may be explained if leptin, in addition to stimulating bone growth and cancellous bone turnover, acts to lower the set‐point at which increased body weight leads to a commensurate increase in bone size. Anat Rec, 298:2018–2029, 2015. © 2015 Wiley Periodicals, Inc.     

Adaptations of Trabecular Bone to Low Magnitude Vibrations Result in More Uniform Stress and Strain Under Load

Extremely low magnitude mechanical stimuli (<10 microstrain) induced at high frequencies are anabolic to trabecular bone. Here, we used finite element (FE) modeling to investigate the mechanical implications of a one year mechanical intervention. Adult female sheep stood with their hindlimbs either on a vibrating plate (30 Hz, 0.3 g) for 20 min/d, 5 d/wk or on an inactive plate. Microcomputed tomography data of 1 cm bone cubes extracted from the medial femoral condyles were transformed into FE meshes. Simulated compressive loads applied to the trabecular meshes in the three orthogonal directions indicated that the low level mechanical intervention significantly increased the apparent trabecular tissue stiffness of the femoral condyle in the longitudinal (+17%, p < 0.02), anterior–posterior (+29%, p < 0.01), and medial-lateral (+37%, p < 0.01) direction, thus reducing apparent strain magnitudes for a given applied load. For a given apparent input strain (or stress), the resultant stresses and strains within trabeculae were more uniformly distributed in the off-axis loading directions in cubes of mechanically loaded sheep. These data suggest that trabecular bone responds to low level mechanical loads with intricate adaptations beyond a simple reduction in apparent strain magnitude, producing a structure that is stiffer and less prone to fracture for a given load. © 2003 Biomedical Engineering Society.     

Ultrasonic characterisation in determining elastic modulus of trabecular bone material

The pulse transmission ultrasonic technique is used to characterise the actual pathway and the wavelength dependence in relation to the bone specimen and microstructural dimensions. The average velocity through individual trabecular bone is 2901 m s⁻¹ (SD 161), and the mean velocity through cylindrical cancellous bone specimens is 2717 m s⁻¹ (SD 171). Thus, the velocity through the cylindrical cancellous bone specimens is underestimated by as much as 6.4% of that through individual trabeculae. There is statistically significant difference in the ultrasonic velocity between individual trabeculae and cylindrical cancellous bone specimens (p=0.0012).     

种植体不同设计参数对下颌骨牙齿种植的影响

目的 建立不同设计参数的种植体-下颌骨模型,观测种植体及周围骨质应力分布,分析不同设计参数对下颌骨牙齿种植的影响。方法 基于结构特征参数（种植体直径、螺纹深度、基台穿龈高度、螺纹形态）,设计8组种植体模型,并分别进行下颌骨整体模型的装配。对模型施加静态150 N垂直、斜向45°两种载荷,分析骨组织和种植体von Mises应力峰值,探讨对von Mises应力峰值最敏感的种植体结构参数变量。结果 斜向载荷比垂直载荷对颌骨会产生更大的应力峰值。种植体直径是影响皮质骨von Mises应力峰值的关键因素;螺纹深度是影响松质骨von Mises应力峰值的关键因素;基台穿龈高度也会对颌骨von Mises应力峰值产生影响,但影响程度不如螺纹深度和种植体直径明显;螺纹形态对颌骨von Mises应力峰值几乎没有影响。结论 不同的种植体设计参数会影响颌骨不同组织的应力峰值,对于个性化种植需要慎重考虑种植体参数的选择。研究结果为口腔种植体的结构参数设计提供理论指导,为口腔种植手术精准预测提供参考。     

Regional Variations in the Apparent and Tissue-Level Mechanical Parameters of Vertebral Trabecular Bone with Aging Using Micro-Finite Element Analysis

The aim of this study was to obtain the apparent and tissue-level mechanical parameters of vertebral cancellous bones using micro-finite element analysis, and to identify the regional variations and their relative differences with respect to aging. Ninety trabecular specimens were obtained from six normal L4 vertebral bodies of six male cadavers in two age groups, three aged 62 years and three aged 69 years, and then were scanned using a high-resolution micro-Computed Tomography (micro-CT) system. The obtained micro-CT reconstruction models were then converted to micro-finite element models. Micro-finite element analyses were done to determine the apparent Young’s moduli and tissue-level Von Mises stress distribution for each trabecular specimen on the longitudinal direction, and medial–lateral and anterior–posterior directions (transverse directions), respectively. Regional variations about the mechanical parameters at both apparent and tissue levels in different transverse layers and vertical columns within and between the two age groups were then analyzed. The results showed significant decreases in the apparent Young’s moduli in each direction with aging, and those in the two transverse directions decreased more with aging compared with the longitudinal direction. Furthermore, there were no statistically significant differences between the mechanical parameters in the two transverse directions in both age groups. This study offered an insight into the distributions and variations of mechanical properties within a vertebral body. The mechanical parameters calculated from this study may help in a better understanding of regional fracture risks and the vertebral fracture mechanism in the prevention of osteoporotic fracture in elder individuals.     

How to select the elastic modulus for cancellous bone in patient-specific continuum models of the spine

Patient-specific finite element (FE) modelling is a promising technology that is expected to support clinical assessment of the spine in the near future. To allow rapid, robust and economic patient-specific modelling of the whole spine or of large spine segments, it is practicable to consider vertebral cancellous bone in the spine as a continuum material, but the elastic modulus of that continuum material must reflect the quality of the individual vertebral bone. A numerical parametric model of lattice trabecular architecture has been developed for determining the apparent elastic modulus of cancellous bone E_cb in vertebrae. The model inputs were apparent morphological parameters (trabecular thickness Tb_Th and trabecular separation Tb_Sp) and the bone mineral density (BMD), which can all be measuredin vivo, using the spatial resolution of current clinical quantitative computed tomography (QCT) commercial whole-body scanners. The model predicted that E_cb values between 30 and 110 MPa represent normal morphology and BMD of human spinal cancellous bone. The present E_cb to Tb_Th, Tb_Sp and BMD relationships pave the way for automatic generation of patientspecific continuum FE spine models that consider the individual's osteoporotic or other degenerative condition of cancellous bone.     

Ultrasound velocity and attenuation in relation to maximum trabecula stress in the patella

The ultrasound velocity and attenuation were examined in 16 sets of human patellae. The average ultrasound velocity of patella was shown to be greater in the superior/inferior direction than in the anterior/posterior and medial/lateral directions. The distribution of bone mineral density (BMD) was also examined. The BMD of the patella varied with location. BMD values were largest at the superior and lateral regions and decreased inferiorly and medially. A two-dimensional finite element analysis was performed on each patella. The maximum von Mises stress occurred along the cortical shell on the non-articular surface. The trabecular von Mises stress existed in the posterior region of the patella. Correlation study showed that patellar BMD was significantly associated with each of three directional ultrasound velocities. The relationship between BMD and ultrasound attenuation was not significant. It was also found that the ultrasound velocity and attenuation were not significantly correlated with the maximum von Mises stress.