Influence of the stiffness of bone defect implants on the mechanical conditions at the interface--a finite element analysis with contact

The study focused on the influence of the implant material stiffness on stress distribution and micromotion at the interface of bone defect implants. We hypothesized that a low-stiffness implant with a modulus closer to that of the surrounding trabecular bone would yield a more homogeneous stress distribution and less micromotion at the interface with the bony bed. To prove this hypothesis we generated a three-dimensional, non-linear, anisotropic finite element (FE) model. The FE model corresponded to a previously developed animal model in sheep. A prismatic implant filled a standardized defect in the load-bearing area of the trabecular bone beneath the tibial plateau. The interface was described by face-to-face contact elements, which allow press fits, friction, sliding, and gapping. We assumed a physiological load condition and calculated contact pressures, shear stresses, and shear movements at the interface for two implants of different stiffness (titanium: E=110GPa; composite: E=2.2GPa). The FE model showed that the stress distribution was more homogeneous for the low-stiffness implant. The maximum pressure for the composite implant (2.1 MPa) was lower than for the titanium implant (5.6 MPa). Contrary to our hypothesis, we found more micromotion for the composite (up to 6 microm) than for the titanium implant (up to 4.5 microm). However, for both implants peak stresses and micromotion were in a range that predicts adequate conditions for the osseointegration. This was confirmed by the histological results from the animal studies.     

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing: a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.     

Nanoindentation measurements of biomechanical properties in mature and newly formed bone tissue surrounding an implant

The characterization of the biomechanical properties of newly formed bone tissue around implants is important to understand the osseointegration process. The objective of this study is to investigate the evolution of the hardness and indentation modulus of newly formed bone tissue as a function of healing time. To do so, a nanoindentation device is employed following a multimodality approach using histological analysis. Coin-shaped implants were placed in vivo at a distance of 200 μm from the cortical bone surface, leading to an initially empty cavity of 200 μm * 4.4 mm. Three New Zealand White rabbits were sacrificed after 4, 7, and 13 weeks of healing time. The bone samples were embedded and analyzed using histological analyses, allowing to distinguish mature and newly formed bone tissue. The bone mechanical properties were then measured in mature and newly formed bone tissue. The results are within the range of hardness and apparent Young's modulus values reported in previous literature. One-way ANOVA test revealed a significant effect of healing time on the indentation modulus (p < 0.001, F = 111.24) and hardness (p < 0.02, F = 3.47) of bone tissue. A Tukey-Kramer analysis revealed that the biomechanical properties of newly formed bone tissue (4 weeks) were significantly different from those of mature bone tissue. The comparison with the results obtained in Mathieu et al. (2011, "Micro-Brillouin Scattering Measurements in Mature and Newly Formed Bone Tissue Surrounding an Implant," J. Biomech. Eng., 133, 021006). shows that bone mass density increases by approximately 13.5% between newly formed bone (7 weeks) and mature bone tissue.     

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box–Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.     

Improving stress shielding following total hip arthroplasty by using a femoral stem made of β type Ti-33.6Nb-4Sn with a Young’s modulus gradation

Stress shielding-related bone loss occurs after total hip arthroplasty because the stiffness of metallic implants differs from that of the host femur. Although reducing stem stiffness can ameliorate the bone resorption, it increases stress at the bone–implant interface and can inhibit fixation. To overcome this complication, a novel cementless stem with a gradient in Young’s modulus was developed using Ti-33.6Nb-4Sn (TNS) alloy. Local heat treatment applied at the neck region for increasing its strength resulted in a gradual decrease in Young’s modulus from the proximal to the distal end, from 82.1 to 51.0 GPa as calculated by a heat transfer simulation. The Young’s modulus gradient did not induce the excessive interface stress which may cause the surface debonding. The main purpose of this study was to evaluate bone remodeling with the TNS stem using a strain-adaptive bone remodeling simulation based on finite element analysis. Our predictions showed that, for the TNS stem, bone reduction in the calcar region (Gruen zone 7) would be 13.6% at 2 years, 29.0% at 5 years, and 45.8% at 10 years postoperatively. At 10 years, the bone mineral density for the TNS stem would be 42.6% higher than that for the similar Ti-6Al-4V alloy stem. The stress–strength ratio would be lower for the TNS stem than for the Ti-6Al-4V stem. These results suggest that although proximal bone loss cannot be eliminated completely, the TNS stem with a Young’s modulus gradient may have bone-preserving effects and sufficient stem strength, without the excessive interface stress.     

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly (p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly (p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.     

Assessment of the effect of mesh density on the material property discretisation within QCT based FE models: a practical example using the implanted proximal tibia

A three-dimensional, quantitative computed tomography based finite element model of a proximal implanted tibia was analysed in order to assess the effect of mesh density on material property discretisation and the resulting influence on the predicted stress distribution. The mesh was refined on the contact surfaces (matched meshes) with element sizes of 3, 2, 1.4, 1 and 0.8 mm. The same loading conditions were used in all models (bi-condylar load: 60% medial, 40% lateral). Significant variations were observed in the modulus distributions between the coarsest and finest mesh densities. Poor discretisation of the material properties also resulted in poor correlations of the stresses and risk ratios between the coarsest and finest meshes. Little difference in Young's modulus, von Mises stress and risk ratio distributions were observed between the three finest models; hence, it was concluded that for this particular case an element size of 1.4 mm on the contact surfaces was enough to properly describe the stiffness, stress and risk ratio distributions within the bone. Poor convergence of the material property distribution occurred when the element size was significantly larger than the pixel size of the source CT data. It was concluded that unless there is convergence in the Young's modulus distribution, convergence of the stress field or of other parameters of interest will not occur either.     

Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur

PURPOSE: In a meta-analysis of the literature we evaluated the present knowledge of the material properties of cortical and cancellous bone to answer the question whether the available data are sufficient to realize anisotropic finite element (FE)-models of the proximal femur. MATERIAL AND METHOD: All studies that met the following criteria were analyzed: Young's modulus, tensile, compressive and torsional strengths, Poisson's ratio, the shear modulus and the viscoelastic properties had to be determined experimentally. The experiments had to be carried out in a moist environment and at room temperature with freshly removed and untreated human cadaverous femurs. All material properties had to be determined in defined load directions (axial, transverse) and should have been correlated to apparent density (g/cm(3)), reflecting the individually variable and age-dependent changes of bone material properties. RESULTS: Differences in Young's modulus of cortical [cancellous] bone at a rate of between 33% (58%) (at low apparent density) and 62% (80%) (at high apparent density), are higher in the axial than in the transverse load direction. Similar results have been seen for the compressive strength of femoral bone. For the tensile and torsional strengths, Poisson's ratio and the shear modulus, only ultimate values have been found without a correlation to apparent density. For the viscoelastic behaviour of bone only data of cortical bone and in axial load direction have been described up to now. CONCLUSIONS: Anisotropic FE-models of the femur could be realized for most part with the summarized material properties of bone if characterized by apparent density and load directions. Because several mechanical properties have not been correlated to these main criteria, further experimental investigations will be necessary in future.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

Is callus calcium content an indicator of the mechanical strength of healing fractures? An experimental study in rat metatarsals

Changes in the mechanical properties and the calcium content of healing fracture callus were followed, using rat metatarsals. By 24 weeks post-fracture the mean ultimate tensile stress and elastic modulus were still less than half that of the contralateral unfractured bone, whereas the mean torsional modulus had almost reached that of the unfractured bone. The calcium content of the callus formed immediately between the fractured ends of the bone showed changes which coincided with the increases in mechanical strength and the moduli, thus measurement of callus calcium content would enable the prediction of the strength of a healing fracture.     

Mechanical aspects of the development of artificial heart valves

The development of an antithrombogenic coating permits a hybrid design for artificial heart valves. A substrate material optimized for its application is coated to meet the electrochemical requirements of improved hemocompatibility. But future progress in artificial heart valves requires an improvement in design as well as of the material. The basis of both aspects is the determination of such fundamental mechanical properties as the elasticity and plasticity of the valve ring and the deformation and fraction behaviour of the occluder. Analytical and numerical calculations of various different models result in different requirements for the substrate of ring and occluder. A combination of high elastic temper and low resistance to flow requires a ring material with a Young's modulus of 40 GPa or more, and a 0.2% proof stress to (Young's modulus)2/3 ratio of 0.3 MPa1/3. The best occluder materials should have a Young's modulus of more than 50 GPa and a flexural strength of at least 800 MPa. On the basis of these criteria, a heart valve consisting of a TiA15Fe2,5 ring and occluders made partially stabilized zirconia is introduced.     

The effect of roughness on biophysical stimuli at the bone-cartilage interface

Numerical simulations are often used to investigate the effect of mechanical environment on fracture healing. Although these models exhibit biologically relevant mechanical parameters at the bone-callus interface, this interface is modelled as perfectly smooth when in fact it is rough. In this study, a macro-micro-two-scale finite element model was used to determine if roughness significantly alters calculated local mechanical parameters. An idealized fracture healing poroelastic model with a small micro-modelled sub-domain of cartilaginous callus adjacent to rough bone was subjected to cyclic loading. The shear stress, tangential fluid velocity, and pore pressure were investigated. With roughness similar to that at the growth plate, solid matrix shear stress differed substantially with interface roughness, whereas interstitial fluid velocity and pore pressure were only slightly affected. Hence, when modelling local micro-mechanical environments near hard-soft tissue interfaces, interface roughness should be considered.     

低强度脉冲超声波辐照与泡沫TiC/Ti对犬节段性骨缺修复的促进作用

目的探讨低强度脉冲超声波辐照对节段性骨缺损修复效果的影响。方法将直径12 mm长20mm泡沫TiC/Ti植入6只Beagle犬的左侧胫骨节段性骨缺损区。随机分为超声组和对照组,超声组采用低强度脉冲超声波辐照（频率1.5 MHz、强度30 mW/cm2、脉冲宽度200μs、脉冲周期1 kHz、20 min/次、1次/d）,对照组为不开功率源的假辐照,术后4、8周后分别行X线检查及骨密度测定,观察及分析材料周围骨愈合情况。结果 6只beagle犬均进入结果分析。术后4周超声组骨早期成熟度优于对照组,表现在材料周围骨痂影密度增高,骨痂影由两端向中央生长;对照组仅见骨痂区密度低,还可见部分骨痂缺如。术后8周超声组新生骨痂面积优于对照组,骨干结构相对稳定;对照组骨缺损区未闭合,在骨干两侧看到少量骨痂,愈合较差。骨密度测定结果显示,4周时超声组高于对照组,两组间存在统计学差异;8周时超声组略高于对照组,但两组间没有统计学差异。结论通过联合应用低强度脉冲超声波辐照与人工骨材料修复可提高新骨形成速度及骨组织密度,缩短节段性骨缺损的骨愈合时间。     

The application of a homogeneous half-space model in the analysis of endothelial cell micropipette measurements

Experimental studies have shown that endothelial cells which have been exposed to shear stress maintain a flattened and elongated shape after detachment. Their mechanical properties, which are studied using the micropipette experiments, are influenced by the level as well as the duration of the shear stress. In the present paper, we analyze these mechanical properties with the aid of two mathematical models suggested by the micropipette technique and by the geometry peculiar to these cells in their detached post-exposure state. The two models differ in their treatment of the contact zone between the cell and the micropipette. The main results are expressions for an effective Young's modulus for the cells, which are used in conjunction with the micropipette data to determine an effective Young's modulus for bovine endothelial cells, and to discuss the dependence of this modulus upon exposure to shear stress.     

Apparent Young's modulus of human radius using inverse finite-element method

The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.     

The underestimation of Young's modulus in compressive testing of cancellous bone specimens

In order to determine the accuracy of measurements of Young's modulus of cancellous bone by conventional compression testing, two independent strain measurements were made simultaneously during non-destructive uniaxial compression to 0.8% strain of rectangular specimens (n = 18). Strain was measured by an extensometer attached to the compression anvils close to the specimen and by an optical system covering the central half of the specimens. Mean Young's modulus determined by the extensometer technique was 689 MPa, but was 871 MPa when determined by the optical technique (mean difference = 182 MPa, SED = 50 MPa, p less than 0.002). Uneven strain distribution due to lack of support of cut vertical trabeculae at the anvil-specimen interface is believed to be causing the underestimation of Young's modulus measured by the extensometer technique. The influence of friction at the specimen-anvil interface was studied by performing a finite element analysis. It is concluded that Young's modulus of specimens of the chosen geometry on average is underestimated by about 20% by conventional compressing testing. The underestimation seems not to be dependent upon specimen density.     

The biomechanics of human femurs in axial and torsional loading: comparison of finite element analysis, human cadaveric femurs, and synthetic femurs

To assess the performance of femoral orthopedic implants, they are often attached to cadaveric femurs, and biomechanical testing is performed. To identify areas of high stress, stress shielding, and to facilitate implant redesign, these tests are often accompanied by finite element (FE) models of the bone/implant system. However, cadaveric bone suffers from wide specimen to specimen variability both in terms of bone geometry and mechanical properties, making it virtually impossible for experimental results to be reproduced. An alternative approach is to utilize synthetic femurs of standardized geometry, having material behavior approximating that of human bone, but with very small specimen to specimen variability. This approach allows for repeatable experimental results and a standard geometry for use in accompanying FE models. While the synthetic bones appear to be of appropriate geometry to simulate bone mechanical behavior, it has not, however, been established what bone quality they most resemble, i.e., osteoporotic or osteopenic versus healthy bone. Furthermore, it is also of interest to determine whether FE models of synthetic bones, with appropriate adjustments in input material properties or geometric size, could be used to simulate the mechanical behavior of a wider range of bone quality and size. To shed light on these questions, the axial and torsional stiffness of cadaveric femurs were compared to those measured on synthetic femurs. A FE model, previously validated by the authors to represent the geometry of a synthetic femur, was then used with a range of input material properties and change in geometric size, to establish whether cadaveric results could be simulated. Axial and torsional stiffnesses and rigidities were measured for 25 human cadaveric femurs (simulating poor bone stock) and three synthetic "third generation composite" femurs (3GCF) (simulating normal healthy bone stock) in the midstance orientation. The measured results were compared, under identical loading conditions, to those predicted by a previously validated three-dimensional finite element model of the 3GCF at a variety of Young's modulus values. A smaller FE model of the 3GCF was also created to examine the effects of a simple change in bone size. The 3GCF was found to be significantly stiffer (2.3 times in torsional loading, 1.7 times in axial loading) than the presently utilized cadaveric samples. Nevertheless, the FE model was able to successfully simulate both the behavior of the 3GCF, and a wide range of cadaveric bone data scatter by an appropriate adjustment of Young's modulus or geometric size. The synthetic femur had a significantly higher stiffness than the cadaveric bone samples. The finite element model provided a good estimate of upper and lower bounds for the axial and torsional stiffness of human femurs because it was effective at reproducing the geometric properties of a femur. Cadaveric bone experiments can be used to calibrate FE models' input material properties so that bones of varying quality can be simulated.     

Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique

The Hopkinson bar stress technique and a universal testing machine (Instron 1125) have been used to investigate the dynamic and static mechanical properties of cortical bone taken from a human femur respectively. We found that the average dynamic Young's modulus value (Ed = 19.9 GPa) to be 23% higher than the average static Young's modulus value (Ed = 16.2 GPa). Furthermore, the Poisson's ratio did not exhibit any significant variation for the two different types of loading. No difference was observed between the values of the dynamic Young's modulus in tension and those found in compression. A comparison was made of the results of this study with those found by other researchers using different techniques, such as ultrasonics, and it was found that they agree well with most of the results of previous studies. Finally, the viscosity for cortical bone found in this study correlates with viscosity reported by Tennyson et al. [Expl Mech. 12, 502-507 (1972)] for ten days post mortem age specimens.     

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens.

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens was studied by non-destructive uniaxial compression to 0.4% strain using cylindrical specimens with different sizes and length-to-diameter ratios, and by comparing cubic and cylindrical specimens with the same cross-sectional area. Both the length and the cross-sectional area of the specimen had a highly significant influence on the mechanical behaviour (p less than 0.0001). Within the actual range of length (2.75-11.0 mm) the normalized stiffness (Young's modulus) was related nearly linearly to the specimen length. This dependency on specimen length is suggested to be caused mainly by structural disintegrity of the trabecular specimens near the surface. The normalized stiffness (Young's modulus) was also positively correlated to the cross-sectional area. This dependency on cross-sectional area is probably due to friction-induced stress inhomogeneity at the platen-specimen interface. A cube with side length 6.5 mm or a cylindrical specimen with 7.5 mm diameter and 6.5 mm length are suggested as standard specimens for comparative studies on trabecular bone mechanics.