松质骨弹性模量与表观密度的关系-基于杆-杆结构和带孔板结构相结合的模型

从杆-杆结构模型开始，然后以此框架为基础逐渐填加固体物质形成带孔板的框架模型，从而将松质骨的两种微结构模型结合起来，利用均匀化理论计算松质骨的弹性模量，通过对所得结果的分析，讨论了松质骨的弹性模量与表观密度的关系。得出弹性模量与表观密度的关系为E=1．78p^1.88（GPa），该结果与用胞元结构理论导出的关系式比较接近，可能更合理。     

改变力学环境后松质骨胞元结构的预测

松质骨是骨的重要组成部分,结构疏松、多孔,由针状、片状骨小梁组成多种胞体,其结构称为胞元结构。正常生理状态下,骨质的形成与吸收呈平衡态,骨结构稳定,当骨所处的力学环境发生变化时,骨的结构形态也随之变化。松质骨细观结构数值模拟变化的力学环境与骨结构的关系目前未见报道,本文是采用带有生理限定应力的自适应生理模型与有限元相结合的方法,在力学环境发生变化后用计算机预测松质骨胞元结构;定量的研究了松质骨胞元结构从一种优化平衡态到另一种平衡态与其力学环境的关系,模拟了松质骨胞元结构的变化与力学环境的适应性。把这种骨结构预测从宏观水平提高到细观水平。     

基于损伤修复理论的各向异性骨再造自我组织控制模型

Wolff定律指出 :骨能够响应力学激励来改变其表观密度和骨小梁分布的方向 ,表明骨再造是各项异性行为。本研究基于各项异性损伤修复理论并结合自我组织控制模型 ,提出更符合骨再造实际生理行为的基于损伤修复理论的各向异性自我组织控制骨再造模型 ,并以股骨近端为例进行了模拟 ,得到的结果在密度分布与主应力迹线分布上和实际都非常一致。     

多载荷下带有生理限定应力的松质骨细观结构模拟

松质是骨的重要组成部分，属多胞体结构，由于构成松质骨的小梁骨尺寸较小，形状多变，因此给松质骨的研究增加了困难。本文把负反馈调节的生理特征引入骨再造模拟中，提出带有生理限定应力的骨再造自适应模型。模型具有骨再造局部适应的正反馈调节与整体控制的负反馈调节的生理调整过程，使骨结构内的应力控制在生理限定应力以下，维持骨力学环境的稳定。使用此模型在几种不同的力学环境下模拟了松质骨结构，定量地预测了松质骨细观结构与其力学环境的对应关系，同时表明了松质骨细观结构与力学环境的适应性。模拟结果与真实松质骨细观结构的典型部分相一致。     

松质骨表观密度和弹性模量间关系的均匀化理论模型

本文利用理想化特征胞元模型对松质骨的刚度进行了研究,提出了松质骨的二级微结构均匀化模型,考虑了骨小梁中的微结构的影响。结果表明,松质骨的弹性模量与表观密度间接近线性关系,二级均匀化松质骨模型较各向同性骨小粱松质骨模型计算出的结果偏高。     

骨质疏松的数值模拟研究

目的对骨质疏松松质骨的力学性质进行数值模拟研究。方法利用均匀化理论研究骨质疏松松质骨的力学性质。结果松质骨的弹性模量（E）与表观密度（ρ）和断裂度（γ）三者之间的数值关系为E=0．38^3.6p-3.76γ,这一结果不仅具有理论意义．更具有重要的实践价值。结论研究表明松质骨的表观密度和断裂度是影响松质骨力学性质的最主要因素．进一步强调了骨微结构对骨强度的影响。     

带有力学调控系统的各向异性骨再造模型

目前，骨再造数值模型在生理上和力学上都不能复制骨再造的实际生理过程。本文引入了骨再造的生理机制和骨力学性质的各向异性，在损伤修复理论的基础上，建立了带有力学调控系统的各向异性骨再造模型，使骨再造的数值模拟趋向和生理过程一致，并以二维方板模型为例进行了计算机模拟，得到了和实际较为一致的结果。本模型可用于在一定力学环境下或力学环境改变后．骨结构的模拟，还可用于植入物植入后骨结构发生结构变化的模拟。     

胞元结构形式、材料性质对松质骨力学性能的影响

将均匀化理论与有限元方法相结合 ,讨论了骨小梁的弹性模量、泊松比和构成松质骨微结构的形式对松质骨力学性质的影响。结果表明微结构的形式和固体体分比确定时 ,松质骨的弹性模量与骨小梁弹性模量之间存在着确定的数量关系 ;当微结构的固体体分比较小时 ,骨小梁的泊松比对松质骨的弹性模量几乎没有影响。讨论了微结构形式对松质骨弹性模量的影响。     

松质骨表现密度和弹性模量间关系的均匀化理论模型

本文利用理想化特征胞元模型对松质骨的刚度进行了研究，提出了松质骨的二级微结构均匀化模型，考虑了骨小梁中的微结构的影响，结果表明，松质骨的弹性模量与清观密度间接近线性关系，二级均匀化松质骨模型较各向同性骨小梁松质骨模型计算出的结果偏高。     

基于均匀化理论的功能梯度材料力学性质的研究

目的利用均匀化理论讨论了功能梯度材料的细观结构形式对其宏观性能的影响。方法利用均匀化理论，研究组分材料泊松比、表观密度、弹性模量硬分布的影响。结果组分材料的泊松比对功能梯度材料的弹性模量的影响不仅与泊松比的大小有关．而且与组分材料的分布形式有关；组分材料的表观密度对功能梯度材料弹性模量的影响可用指数函数模拟；组分材料的弹性模最对功能梯度材料弹性模量的影响可用线性函数模拟；组分材料的分布对功能梯度材料弹性模量的影响甚微。结论功能梯度材料的弹性模量是受组分材料的泊松比影响的。     

Comparison of mechanical and ultrasound elastic modulus of ovine tibial cortical bone

Finite element models of bones can be created by deriving geometry from an X-ray CT scan. Material properties such as the elastic modulus can then be applied using either a single or set of homogeneous values, or individual elements can have local values mapped onto them. Values for the elastic modulus can be derived from the CT density values using an elasticity versus density relationship.Many elasticity–density relationships have been reported in the literature for human bone. However, while ovine in vivo models are common in orthopaedic research, no work has been done to date on creating FE models of ovine bones. To create these models and apply relevant material properties, an ovine elasticity–density relationship needs to be determined.Using fresh frozen ovine tibias the apparent density of regions of interest was determined from a clinical CT scan. The bones were the sectioned into cuboid samples of cortical bone from the regions of interest. Ultrasound was used to determine the elastic modulus in each of three directions – longitudinally, radially and tangentially. Samples then underwent traditional compression testing in each direction.The relationships between apparent density and both ultrasound, and compression modulus in each direction were determined. Ultrasound testing was found to be a highly repeatable non-destructive method of calculating the elastic modulus, particularly suited to samples of this size.The elasticity–density relationships determined in the longitudinal direction were very similar between the compression and ultrasound data over the density range examined. A clear difference was seen in the elastic modulus between the longitudinal and transverse directions of the bone samples, and a transverse elasticity–density relationship is also reported.     

全髋关节置换术中压电股骨重建的边光滑有限元分析

目的 针对传统有限元法(finite element method, FEM)分析全髋关节置换(total hip arthroplasty, THA)后压电股骨重建时精度低的问题,采用边光滑有限元法(edge-based smoothed finite element method, ES-FEM)对植入假体后压电股骨近端的骨重建进行仿真分析。方法 根据自适应骨重建理论,建立假体-压电股骨模型。基于模型的背景网格构建光滑域,引入梯度光滑技术,求解出光滑的重建刺激,进而得到术后压电股骨近端的密度分布。结果 植入假体后,受力点由股骨头转移到假体,出现应力屏蔽现象,股骨内部表观密度的分布发生明显变化。相比于FEM,ES-FEM在一定程度上能软化数值模型,提高仿真精度。在相同的网格下,电势和密度的求解精度分别提高27%和30%左右。结论 采用ES-FEM能够更精确地模拟出THA术后压电股骨近端的骨重建进程,为THA临床研究提供有效的理论依据。     

Glucocorticoid-treated sheep as a model for osteopenic trabecular bone in biomaterials research

The purpose of this study was to determine the alterations in ovine trabecular bone induced by a combination of ovariectomy and steroid treatment. Twenty-four female skeletally mature Merino sheep were randomly assigned to ovariectomy alone (OVX), ovariectomy combined with glucocorticoid treatment for 6 months (OVX + GC), or no treatment (control). Biopsies of trabecular bone were harvested 6 and 12 months after the beginning of the study from the proximal tibia. The biopsies were scanned for apparent bone mineral density by quantitative computed tomography and were mechanically tested. Three-dimensional bone reconstructions were obtained by micro-computed tomography. Trabecular bone from the OVX + GC animals had a markedly reduced apparent bone mineral density (27% less than control), bone volume (34%), and elastic modulus (36%) at 6 months. At 12 months, the reductions in apparent bone mineral density (33%), bone volume (37%), and elastic modulus (62%) appeared to be even more pronounced. Ovariectomy alone did not result in a perceptible reduction in any parameter. The combination of ovariectomy and glucocorticoid treatment in sheep resulted in a successful induction of substantial loss of trabecular bone and thus may serve as a large-animal model for osteopenic trabecular bone for the development and testing of orthopedic implants and techniques under osteoporotic conditions.     

Parametric sensitivity analysis applied to a specific one-dimensional internal bone remodelling problem

The relative importance of the various parameters in inducing bone mass loss and osteoclastic perforations is still controversial. Therefore, there is a significant motivation to better understand the parameters behind such dynamic response, and great interest to carry out a parametric sensitivity study as it can provide useful information. As an application, the widely-accepted bone remodelling equation [M.G. Mullender, R. Huiskes, H. Weinans, A physiological approach to the simulation of bone remodeling as self organizational control process, J. Biomech. 27 (1994) 1389.] is investigated using the "n units" model [M. Zidi, S. Ramtani, Bone remodeling theory applied to the study of n unit-elements model, J Biomech. 32 (1999) 743.]. This analysis pointed out that the power in the modulus density relationship p and the power to which density is raised in normalizing the energy stimulus q, known as strongly implicated in the stability condition of the remodelling process, were also stated as insensitive parameters in the bone loss area.     

基于骨骼自适应理论优化模型的骨重建数值模拟

我们根据骨重建的自适应理论以及结构优化方法,建立了骨重建数值模拟的反问题求解模型和算法.由材料密度分布描述骨内部重建,材料密度的变化通过优化方法求解.股骨、长骨干和腰椎体冠状面(外部形状和内部结构)重建模拟的计算结果,符合实际情况,反映了骨结构对荷载环境的自适应特征,表明本文方法是骨重建研究的一种有效数值方法.     

Comparison of the influences of structural characteristics on bulk mechanical behaviour: experimental study using a bone surrogate

An experimental study was conducted to classify the influence of trabecular architecture and cortical shell thickness on the mechanical properties using a bone surrogate. Thirty-six rectangular prisms and 18 vertebral-shaped specimens were fabricated with fused deposition modelling (FDM) as a bone surrogate with controlled structural characteristics (cortical wall thickness, strut spacing, strut angle and strut orientation). The apparent density of the FDM specimens was evaluated using quantitative computed tomography (QCT) imaging and related to the apparent elastic modulus measured with compression testing. The effects of the structural parameters on the apparent elastic modulus were analysed using analysis of variance (ANOVA). The results obtained corroborate that the structural parameters have a significant effect on the apparent mechanical properties of the bulk material. The cortical shell thickness was found to have more influence than trabecular architecture. Therefore, accurate modelling of the cortical shell thickness should be considered more important than trabecular architecture in development of bone finite element models and bone surrogates.     

Experimental and numerical analyses of local mechanical properties measured by atomic force microscopy for sheared endothelial cells

Local mechanical properties were measured for bovine endothelial cells exposed to shear stress using an atomic force microscopy (AFM), and the AFM indentations were simulated using a finite element method (FEM) to determine the elastic modulus. After exposure to shear stress, the endothelial cells showed marked elongation and orientation in the flow direction, together with significant decrease in the peak cell height. The applied force-indentation depth curve was obtained at seven different locations on the major axis of the cell surface and quantitatively expressed by the quadratic equation. The elastic modulus was determined by comparison of the experimental and numerical results. The modulus using our FEM model significantly became higher from 12.2+/-4.2 to 18.7+/-5.7 kPa with exposure to shear stress. Fluorescent images showed that stress fibers of F-actin bundles were mainly formed in the central portion of the sheared cells. The significant increase in the modulus may be due to this remodeling of cytoskeletal structure. The moduli using the Hertz model are 0.87+/-0.23 and 1.75+/-0.43 kPa for control and sheared endothelial cells respectively. This difference can be attributable to the differences in approximation functions to determine the elastic modulus. The elastic modulus would contribute a better understanding of local mechanical properties of the cells.