单髁膝关节置换胫骨元件不同固定柱形状的有限元分析

目的针对单髁膝关节置换后胫骨前内侧疼痛、胫骨元件松动以及对侧关节炎恶化的问题,通过有限元方法比较分析胫骨元件固定柱的不同几何形状对胫骨应力分布的影响。方法建立有效的单髁膝关节置换有限元模型,对胫骨元件固定柱的形状进行设计。在相同的加载条件下,分别对双柱形、单脊形、双脊形和十字星形胫骨元件进行有限元分析,并与完整膝关节模型进行对比,评估胫骨元件固定柱不同形状设计对胫骨前内侧皮质骨应力、胫骨截骨面松质骨应力、胫骨对侧软骨应力的影响。结果单髁置换后胫骨前内侧皮质骨应力峰值均增大。与完整膝关节相比,在双柱形、单脊形、双脊形和十字星形胫骨元件固定柱的模型中,胫骨前内侧皮质骨应力峰值分别增加56.1%、55.9%、54.5%和68.4%。单脊形和双脊形胫骨元件松质骨截骨面应力峰值比完整胫骨分别减小8.1%和15.6%,而双柱形和十字星形则分别增大67.9%和121.5%,超过松质骨的疲劳屈服应力。双柱形、单脊形、双脊形和十字星形胫骨固定柱对应的胫骨对侧软骨应力峰值相比于完整胫骨分别减小42.1%、26.6%、24.2%和28.5%。结论单髁膝关节置换改变了胫骨内外侧的载荷分布,使置换侧承受更大的载荷。单脊形和双脊形胫骨元件在降低胫骨前内侧皮质骨和截骨面松质骨应力方面效果更好,其中单脊形胫骨元件更接近完整膝关节胫骨的应力分布。研究结果可为设计更符合膝关节力学性能的单髁膝关节假体提供理论依据。     

Fixation response of two cementless tibial implants under static and fatigue compression loading.

The short- and long-term success of tibial cementless implants depend on the initial fixation stability often provided by posts and screws. Excessive relative interface motions are known to inhibit bone ingrowth and, hence, biologic fixation. In the present study, the stability of two cementless tibial implants under static and cyclic loading was studied. An apparatus was developed to perform compression tests on tibial components fixed by screws or posts onto resurfaced tibiae. Motion transducers were placed to record liftoff and subsidence displacements. A load of 1000 N was eccentrically applied on the medial plateau via the femoral component. The response was measured under static and repetitive loading up to 4000 cycles at 1 Hz. Experimental results showed that the screw fixation yielded the stiffer response and, hence, provided greater initial stability. The tibial component fixed with posts demonstrated larger lift off displacements. Comparison of measured results of static tests before and after fatigue indicated that the load-displacement behavior was not significantly affected by the cyclic fatigue loading under 1000 N up to 4000 cycles at 1 Hz. Nevertheless, much larger permanent displacements were recorded for the post fixation systems. In contrast to screw fixation, posts fixation systems demonstrated marked deterioration under larger compression loads of approximately 2000 N.     

Mechanical characterization in shear of human femoral cancellous bone: torsion and shear tests

In order to investigate and compare the mechanical behaviour of human cancellous bone during different shear loading modes, two tests were performed to characterise human femoral cancellous bone in shear: a torsion test until failure and a shear test using a sharpened stainless steel tube. Paired cylindrical samples were core drilled from 12 human femoral heads, symmetrically with respect to the coronal plane and along the primary trabecular direction. The distal part of the sample was assigned to a torsion test and the shear test was performed on the proximal part along two perpendicular anatomical directions. Apparent densities and tissue densities were measured on both torsion and shear specimens. The mean torsion properties were shear modulus G, 289 (183) MPa, ultimate stress tau(torsion), 6.1 (2.7) MPa, ultimate strain gamma(ultimate), 4.6 (1.3)%, yield stress tau(yield), 4.3 (1.9) MPa and yield strain gamma(yield), 1.8 (0.3)%. Strong correlation was obtained between G and tau(torsion) (r'=0.853, p<0.001). These torsion properties were correlated with apparent density of torsion specimens showing, respectively: r'=0.713, p=0.005 and r'=0.671, p=0. 008. Properties from the shear test were invariable with regard to the two tested directions then isotropic ultimate shear stress and isotropic elementary shear stress, which represent the mean values of the two tested directions were, respectively, tau(shear), 10.0 (4. 5) MPa and tau(elem), 18.8 (6.1) MPa. Both shear stresses were correlated with apparent density of shear specimens: tau(shear), r'=0.564, p=0.045 and tau(elem), r'=0.636, p=0.024. Apparent densities for shear specimens were superior than for torsion specimens (p=0.06) and the comparison was the opposite for tissue densities (p=0.028), showing strong density gradients of cancellous bone in the femoral head. These torsion and shear tests which permit the evaluation of cancellous bone behavior under two different types of shear loading, may be performed on different human sites and the measured shear properties may be compared to structural properties of cancellous bone.     

远中邻牙合腭面缺损的上颌第 1 磨牙纤维桩-树脂核修复的有限元分析

目的 探究根管治疗后远中邻 腭面(disto-occluso-palatal,DOP)缺损的上颌第 1 磨牙纤维桩-树脂核修复策 略。 方法 建立 8 种不同的纤维桩-树脂核修复策略修复后的上颌第 1 磨牙有限元模型。 若多根桩在髓腔内存在 干扰,则将较细的桩在重叠部分下方 1 mm 处水平截断作为辅桩,较粗的桩保留原长作为主桩。 分别加载与牙体长 轴平行的 800 N 垂直力和与牙体长轴呈 45°的 225 N 侧向力。 通过有限元分析计算牙体组织和纤维桩内的等效应 力及桩-树脂水门汀、树脂水门汀-根管壁界面上的切应力。 结果 在相同载荷下,不同组间在牙体组织外表面的应 力分布形式相似。 垂直加载时,应力集中于根干的腭侧面;侧向加载时,应力集中于根干的近中颊侧面。 置入纤维 桩的根管中 1 / 3 处内表面最大等儿应力上升,而根管颈 1 / 3 处内表面最大等效应力下降。 垂直、侧向载荷下所受 应力最大的桩分别是腭桩和近颊桩。 垂直载荷下,在同一根管内主桩较辅桩在桩-树脂水门汀界面上的切应力大; 侧向载荷下,近中颊桩的桩-树脂水门汀界面切应力最大。 垂直载荷下,树脂水门汀-根管壁界面上最大切应力在腭 根内放置纤维桩时最大;侧向载荷下,界面上的最大切应力在近颊根放置纤维桩时最大。 结论 对于 DOP 缺损的 上颌第 1 磨牙,纤维桩修复能有效地将 力向根方传导,改善剩余牙体组织中的应力分布。 在腭根内置入单根纤 维桩进行纤维桩-树脂核-全瓷冠修复可能是其最佳修复策略。     

Stress distribution in porous surfaced medullary implants

Finite element stress analysis has been applied to examine the stress patterns in a prosthesis requiring fixation in the medullary shaft of a long bone. No specific prosthesis is considered but rather a generally applicable geometry has been chosen. This consists of a cylindrical section of cortical bone within which is implanted a prosthesis composed of a solid central rod surrounded by a porous coating. The finite element analysis utilized an axisymmetric model to determine the distribution of stresses throughout the system. The effect of changes in length of prosthesis, thickness of porous coating, depth and type of tissue ingrowth, and type of porous coating material were studied under conditions of axisymmetric loading. The results indicate that with complete bone ingrowth, the maximum shear stress and the distance necessary for load transfer are both independent of implant length. However, with incomplete ingrowth, increasing implant length reduces shear. Incomplete growth also produces lower shear stresses but higher shear strains in areas without ingrowth. In addition, a porous polyethylene coating gives a more even load transfer and lower shear than a porous coating of a high modulus material.     

Finite element analysis of a glass fibre reinforced composite endodontic post

In this work the mechanical response to external applied loads of a new glass fibre reinforced endodontic post is simulated by finite element (FE) analysis of a bidimensional model. The new post has a cylindrical shape with a smooth conical end in order to adequately fit the root cavity, and to avoid edges that could act as undesired stress concentrators. Mechanical data obtained by three-point bending tests on some prototypes fabricated in the laboratory are presented and used in the FE model. Under various loading conditions, the resulting stress component fields are hence compared with those obtained in the case of two commercial endodontic posts (i.e. a cast metal post and a carbon fibre post) and with the response of a natural tooth. The gold cast post-and-core produces the greatest stress concentration at the post-dentin interface. On the other hand, fibre-reinforced composite posts do present quite high stresses in the cervical region due to their flexibility and also to the presence of a less stiff core material. The glass fibre composite shows the lowest peak stresses inside the root because its stiffness is much similar to dentin. Except for the force concentration at the cervical margin, the glass fibre composite post induces a stress field quite similar to that of the natural tooth.     

Predicting time-dependent remodeling of bone around immediately loaded dental implants with different designs

The purpose of this study was to predict time-dependent biomechanics of bone around cylindrical screw dental implants with different macrogeometric designs under simulated immediate loading condition. The remodeling of bone around a parallel-sided and a tapered dental implant of same length was studied under 100 N oblique load by implementing the Stanford theory into three-dimensional finite element models. The results of the analyses were examined in five time intervals consisting loading immediately after implant placement, and after 1, 2, 3 and 4 weeks following implantation. Maximum principal stress, minimum principal stress, and strain energy density in peri-implant bone and displacement in x-(implant lateral direction with a projection of the oblique force) and y-(implant longitudinal direction) axes of the implant were evaluated. The highest value of the maximum and minimum principal stresses around both implants increased in cortical bone and decreased in trabecular bone. The maximum and minimum principal stresses in cortical bone were higher around the tapered cylindrical implant, but stresses in the trabecular bone were higher around the parallel-sided cylindrical implant. Strain energy density around both implants increased in cortical bone, slightly decreased in trabecular bone, and higher values were obtained for the parallel-sided cylindrical implant. Displacement values slightly decreased in time in x-axis, and an initial decrease followed by a slight increase was observed in the y-axis. Bone responded differently in remodeling for the two implant designs under immediate loading, where the cortical bone carried the highest load. Application of oblique loading resulted in increase of stiffness in the peri-implant bone.     

Mechanical analysis of fixation methods for anterior cruciate ligament reconstruction with hamstring tendon graft. An experimental study in sheep knees

This study evaluates the structural properties of the femur-anterior cruciate ligament (ACL) graft-tibia complex, comparing different graft fixation techniques in sheep knees. Four fixation devices were tested both for femoral fixation (Transfix, absorbable screw, RCI screw and Linx-HT) and tibial fixation (bone plug with metal screw, absorbable screw with staple, RCI screw and cancellous screw with spiked washer). The graft used for ACL reconstruction was fresh ovine doubled Achilles tendon (DAT). Femurs and tibias were tested separately. Two mechanical test series were performed on the specimens: a load-to-failure test and a cyclic loading test. On the femoral side, transcondylar screw showed the greatest fixation strength and stiffness and the lowest elongation at cyclic loading. Tibial fixation complexes seemed to have poorer structural properties in comparison to femoral fixation. Among the tibial fixation devices, absorbable screw with staple fixation showed the greatest strength and stiffness. Spiked washer fixation showed the greatest elongation under cyclic loading.     

脊柱胸腰段骨折后路经伤椎单节段固定与常规短节段固定的力学性能比较

目的 应用三维有限元技术构建胸腰椎骨折经伤椎单节段固定及常规短节段固定模型,研究经伤椎单节段固定的生物力学特点,论证其在胸腰椎骨折治疗中应用的可行性。方法 选取青壮年健康男性志愿者,利用CT扫描数据建立脊柱T10~L2正常模型、T12骨折模型以及经伤椎单节段固定和短节段固定模型;分析在轴向压缩、前屈、后伸、侧屈及轴向旋转下各个节段的最大位移差及内固定物的应力情况。结果 骨折模型T10~11、T11~12、T12~L1的最大位移差较正常模型在大多数加载情况时明显增大,经短节段或者经伤椎单节段固定后,该值明显减小,两种固定方式无显著差异。内固定物应力方面：在轴向压缩及前屈时,经伤椎单节段固定模型中螺钉应力明显低于短节段固定;而在后伸、侧屈及轴向旋转时,螺钉应力无明显差异。对于固定棒,轴向压缩及前屈时,两种固定方式无差异;后伸及侧屈时经伤椎节段固定应力高于短节段固定,而旋转时则恰恰相反。结论 对于胸腰段单节段不完全骨折,经伤椎单节段固定可以提供与常规短节段固定相近的生物力学稳定性,是治疗胸腰椎不完全骨折的一种良好的选择。     

Surgical and Morphological Factors that Affect Internal Mechanical Loads in Soft Tissues of the Transtibial Residuum

The residual limb of transtibial amputation (TTA) prosthetic users is threatened daily by pressure ulcers (PU) and deep tissue injury (DTI) caused mainly by sustained mechanical strains and stresses. Several risk factors dominate the extent of internal tissue loads in the residuum. In this study, we developed a set of three-dimensional finite element (FE) models that were variants of a patient-specific FE model, built from magnetic resonance imaging scans. The set of FE modes was utilized to assess the impact of the following risk factors on the strain/stress distribution in the muscle flap: (i) the tibial length, (ii) the tibial bevelment, (iii) a fibular osteophyte, (iv) the mechanical properties of the muscle, and (v) scarring in different locations and depths. A total of 12 nonlinear FE model configurations, representing variations in these factors, were built and solved. We present herein calculations of compression, tension and shear strains and stresses, von Mises stresses, and strain energy density averaged in critical locations in the muscle flap as well as volumes of concentration of elevated stresses in these areas. Our results overall show higher stresses accumulating in the bone proximity rather than in outlying soft tissues. The longer bone configurations spread the loads toward the external surfaces of the muscle flap. When shortening the truncated bones from 11.2 to 9.2 cm, the von Mises stresses at the distal edges of the bones were relieved considerably (by up to 80%), which indicates a predicted decreased risk for DTI. Decreasing the tibial bevelment mildly, from 52.3° to 37.7° caused propagation of internal stresses from the bone proximity toward the more superficial soft tissues of the residuum, thereby also theoretically reducing the risk for DTI. An osteophyte at the distal fibular end increased the strain and stress distributions directly under the fibula but had little effect (<1%) on stresses at other sites, e.g., under the tibia. Elevation of muscle stiffness (instantaneous shear modulus increase from 8.5 to 16.2 kPa), simulating variation between patients, and muscle flap contraction or spasm, showed the most substantial effect by an acute rise of the von Mises stresses at the bone proximity. The mean von Mises stresses at the bone proximity were approximately twofold higher in the contracted/spastic muscle when compared to the flaccid muscle. Locating a surgical scar in different sites and depths of the residuum had the least influence on the overall loading of the muscle flap (where stresses changed by <7%). Pending further validation by epidemiological PU and DTI risk factor studies, the conclusions of this study can be incorporated as guidelines for TTA surgeons, physical therapists, prosthetists, and the TTA patients themselves to minimize the onset of PU and DTI in this population. Additionally, the present analyses can be used to guide or focus epidemiological research of PU and DTI risk factors in the TTA population.     

Stress shielding in periprosthetic bone following a total knee replacement: Effects of implant material,design and alignment

Periprosthetic bone strain distributions in some of the typical cases of total knee replacement (TKR) were studied with regard to the selection of material, design and the alignments of tibial components to examine which conditions are more forgiving than the others to stress shielding post a TKR. Four tibial components with two implant designs (cruciate sacrificing and cruciate retaining) and material properties (metal-backed (MB) and all-polyethylene (AP)) were considered in a specimen-specific finite element tibia bone model loaded in a neutral position. The influence of tibial material and design on the periprosthetic bone strain response was investigated under the peak loads of walking and stair descending/ascending. Two of the models were also modified to examine the effect of selected implant malalignment conditions (7° posterior, 5° valgus and 5° varus) on stress shielding in the bone, where the medio-lateral load share ratios were adjusted accordingly. The predicted increases of bone density due to implantation for the selected cases studied were also presented.For the cases examined, the effect of stress shielding on the periprosthetic bone seems to be more significantly influenced by the implant material than by the implant geometry. Significant stress shielding is found in MB cases, as opposed to increase in bone density found in AP cases, particularly in the bones immediately beneath the baseplate. The effect of stress shielding is reduced somewhat for the MB components in the malaligned positions compared with the neutral case. In AP cases, the effect of stress shielding is mostly low except in the varus position, possibly due to off-loading of lateral condyle. Increases in bone density are found in both MB and AP cases for the malaligned conditions.     

Bone–cement interfacial behaviour under mixed mode loading conditions

Interfacial behaviour of the bone–cement interface has been studied under tensile, shear and mixed mode loading conditions. Bovine cancellous bone was used to bond with acrylic bone cement to form bone–cement interface samples, which were mechanically tested under selected tensile, shear and mixed mode loading conditions. The influence of the loading angle and the extent of the cement penetration on the interfacial behaviour were examined. The failure mechanisms with regard to loading mode were examined using micro-focus computed tomography. The measured tensile and shear responses were utilized in a cohesive zone constitutive model, from which the pre-yield linear and the post-yield exponential strain softening behaviour under mixed mode loading conditions was predicted. The implications of the work on the studies of cemented joint replacements are also discussed.     

大鼠牙槽骨理想模型的流固耦合数值模拟研究

载荷作用下松质骨孔隙中的液体流动是刺激骨组织细胞产生生物学响应并调控骨重建的主要因素。因此,阐明牙槽骨内孔隙结构中的液体流动情况对于深入理解力学作用在牙槽骨内的传导过程以及牙齿发育、正畸牙移动等细胞水平的调控机制具有重要意义。此工作首先进行了大鼠牙齿正畸的动物实验,并基于微计算机断层扫描(micro-CT)图像构建了牙齿-牙周韧带-牙槽骨有限元模型,分析了咬合力或正畸力作用下牙槽骨中的应变状态;进而构建了理想模型,应用流固耦合数值模拟方法,分析了动态咬合力加载下无正畸加载、正畸拉伸加载、正畸压缩加载三种情况下骨内液体的流动情况。模拟结果表明,动态咬合力作用下,沿咬合方向排列的骨小梁表面流体剪应力水平高于非咬合方向排列的骨小梁,正畸力对骨内液体的流动没有影响。上述结果说明,临床上通过调整牙齿咬合面形状等方法改变咬合力的方向,会在牙槽骨表面引起不同水平的流体剪应力,进而刺激骨组织表面的细胞产生响应,最终调控牙槽骨的结构重建。     

Role of cell location and morphology in the mechanical environment around meniscal cells

Fibrochondrocytes within meniscal tissue have been shown to alter their biochemical activity in response to changes in their mechanical environment. Meniscal tissue is known to contain both spherical (chondrocytic-like) and elliptical (fibroblastic-like) cells. We hypothesize that a cell's mechanical environment is governed by local material properties of the tissue around the cell, the cell morphology and the cell's position within the tissue. A two-dimensional, non-linear, fiber (collagen) reinforced, multi-scale, finite element model was utilized to quantify changes in the stress, strain, fluid velocity and fluid flow induced shear stress (FFISS) within and around fibrochondrocytes. Cells differing in morphology and size were modeled at different locations within an explant 6mm in diameter and 5mm thick, under 5% unconfined compression. Cellular stresses were an order of magnitude less than surrounding extracellular matrix stresses but cellular strains were higher. Cell size affected both the stress and strain levels within the cell, with smaller cells being exposed to smaller principal stresses and strains than larger cells of the same shape. The pericellular matrix of an elliptical cell was less effective at shielding the cell from large principal strains and stresses. FFISS were largest around small circular cells ( approximately 0.13Pa), and were dramatically affected by the position of the cell relative to the axis of the explant, with cells closer to the periphery experiencing greater FFISS than cells near the central axis of the explant. These results will allow biosynthetic activity of fibrochondrocytes to be correlated with position and morphology in the future.     

Stress distributions in maxillary central incisors restored with various types of post materials and designs

Different dental post designs and materials affect the stability of restoration of a tooth. This study aimed to analyse and compare the stability of two shapes of dental posts (parallel-sided and tapered) made of five different materials (titanium, zirconia, carbon fibre and glass fibre) by investigating their stress transfer through the finite element (FE) method. Ten three-dimensional (3D) FE models of a maxillary central incisor restored with two different designs and five different materials were constructed. An oblique loading of 100 N was applied to each 3D model. Analyses along the centre of the post, the crown-cement/core and the post-cement/dentine interfaces were computed, and the means were calculated. One-way ANOVAs followed by post hoc tests were used to evaluate the effectiveness of the post materials and designs (p = 0.05). For post designs, the tapered posts introduced significantly higher stress compared with the parallel-sided post (p < 0.05), especially along the centre of the post. Of the materials, the highest level of stress was found for stainless steel, followed by zirconia, titanium, glass fibre and carbon fibre posts (p < 0.05). The carbon and glass fibre posts reduced the stress distribution at the middle and apical part of the posts compared with the stainless steel, zirconia and titanium posts. The opposite results were observed at the crown-cement/core interface.     

Comparison of volumetric bone mineral density in the tibial region of interest for ACL reconstruction

Adequate tibial bone mineral density (BMD) is essential to soft tissue graft fixation during anterior cruciate ligament (ACL) reconstruction. The purpose of this study was to compare volumetric bone plug density measurements at the tibial region of interest for ACL reconstruction using a standardized immersion technique and Archimedes’ principle. Cancellous bone cores were harvested from the proximal, middle, and distal metaphyseal regions of the lateral tibia and from the standard tibial tunnel location used for ACL reconstruction of 18 cadaveric specimens. Proximal tibial cores displayed 32.6% greater BMD than middle tibial cores and 31.8% greater BMD than distal tibial cores, but did not differ from the BMD of the tibial tunnel cores. Correlational analysis confirmed that the cancellous BMD in the tibial tunnel related to the cancellous BMD of the proximal and distal lateral tibial metaphysis. In conjunction with its adjacent cortical bone, the cancellous BMD of the region used for standard tibial tunnel placement provides an effective foundation for ACL graft fixation. In tibia with poor BMD, bicortical fixation that incorporates cortical bone from the distal tibial tunnel region is recommended.     

牙科即刻种植中不同螺纹形态及深度设计参数种植体的生物力学性能

目的分析牙科即刻种植中不同螺纹形态和螺纹深度种植体周围骨质应力分布情况,为种植体的设计和选择提供依据。方法利用Geomagic Studio、Solid Works和ANSYS Workbench建立下颌骨骨块、种植体及下颌磨牙简化模型,施加垂直载荷和斜向载荷,观察不同螺纹形态和螺纹深度的种植体及其周围骨组织应力分布情况。结果垂直载荷作用下,种植体、皮质骨、松质骨应力峰值变化范围分别为120. 51～129. 63 MPa、9. 94～13. 25 MPa、3. 92～8. 01 MPa,V形、矩形、支撑形、反支撑形种植体周围皮质骨在螺纹深度0. 40～0. 45 mm范围内应力变化平稳;斜向载荷作用下,种植体、皮质骨、松质骨应力峰值变化范围分别为220. 23～286. 51 MPa、33. 39～45. 08 MPa、4. 96～12. 5 MPa。螺纹深度为0. 45 mm,V形、支撑形、反支撑形种植体应力最小。结论 V形、支撑形、反支撑形螺纹种植体选择螺纹深度为0. 45 mm,矩形种植体选择螺纹深度0. 40 mm,呈现出较好的生物力学特性。     

Mechanobiological bone growth: comparative analysis of two biomechanical modeling approaches

Mechanobiological growth is the process whereby bone growth is modulated by mechanical loading. Analytical formulations of mechanobiological growth have been developed by Stokes et al. (J Orthop Res 17(5):646–653, 1990) and Carter et al. (J Orthop Res 6:804–816, 1988). The purpose of this study was to compare these two modeling approaches in a finite element model of a vertebra to investigate whether growth pattern induced by these models were equivalent. A finite element model of a thoracic vertebra, integrating a conceptual model of the growth plate, was developed and combined with the mechanobiological growth models. This model was further used to simulate vertebral growth modulation resulting from different physiological loading conditions. Different growth magnitudes were obtained under compression and combined tension/shear loading, whereas dissimilar growth patterns were triggered by shear forces and combined compression/shear. These two models represent mechanobiological bone growth under limited mechanical environment. Carter’s model takes into account three-dimensional stress stimuli, but does not intrinsically incorporate the resulting growth orientation. Stokes’ model adequately represents the mechanobiological contribution of axial stresses but does not take into account the contribution of non-axial stresses, which can occur in complex mechanical environment.     

国人胫骨松质骨力学性质的实验研究

本文对国人胫骨近端松质骨的拉伸、压缩、扭转、剪切、弯曲的宏观力学性质及实验方法进行了实验研究和探讨。得到了一系列相应的常规力学性质,以及回归分析所拟合的曲线关系。可为临床医学提供参考。     

The dependence between the strength and stiffness of cancellous and cortical bone tissue for tension and compression: extension of a unifying principle

A strong positive correlation between the apparent ultimate strength and stiffness of bone tissue that can be expressed by a unified relationship has been observed for cortical bone in tension and low-density cancellous bone in compression. For practical purposes, the existence of a relationship between strength and stiffness is significant in that bone stiffness can be measured in vivo using non-invasive methods. It is generally accepted that bone strength is greater in compression than in tension whereas there is no substantial evidence that bone stiffness in compression is different from that in tension. This might suggest that compressive strength would relate to the stiffness, if at all, in a way that is different from tensile strength. In order to examine similarities and differences in the way strength is associated with stiffness between modes of loading and tissue type, we tested equine cortical bone and bovine cancellous bone in compression and examined these data together with previously reported data from compression testing of human cancellous bone as well as tensile testing of cortical bone from various sources. We have found for cortical bone that (i) the sensitivity of strength to stiffness is the same for tension and compression (p>0.75, ANCOVA), and (ii) the difference between the magnitudes of compressive and tensile strength for cortical bone is the result of an additive, rather than a multiplicative factor (52.1 MPa after adjusting to 1 microstrain/s, p<0.0001, ANOVA). High-density bovine tibial cancellous bone, on the other hand, has a steeper slope for its compressive strength-stiffness relationship than that for cortical bone and human cancellous bone, resulting in a transitional relationship between compressive strength and stiffness for a range of bone types and densities. Based on the current results and previous work, it is suggested that the offset strength in the compressive strength-stiffness relationship may be a direct manifestation of the difference between the compressive and tensile strengths of the bone material that constitutes the building blocks of the bone structure. Deviation of high-density cancellous bone compressive behavior from the other bone types and densities is attributed to stress distribution differences between the bone types.