Structural properties of a new design of composite replicate femurs and tibias

The purpose of this study was to compare the structural properties of a new vs. established design of composite replicate femurs and tibias. The new design has a cortical bone analog consisting of short-glass-fiber-reinforced (SGFR) epoxy, rather than the fiberglass-fabric-reinforced (FFR) epoxy in the currently available design. The hypothesis was that this new cortical bone analog would improve the uniformity of structural properties between specimens, while having mean stiffness values in the range of natural human bones. The composite replicate bones were tested under bending, axial, and torsional loads. In general, the new SGFR bones were significantly less stiff than the FFR bones, although both bone designs reasonably approximated the structural stiffnesses of natural human bones. With the exceptions of the FFR bone axial tests, the highest variability between specimens was 6.1%. The new SGFR bones had similar variability in structural properties when compared to the FFR bones under bending and torsional loading, but had significantly less variability under axial loading. Differences in epiphyseal geometry between the FFR and SGFR bones, and subsequent seating in the testing fixtures, may account for some of the differences in structural properties; axial stiffness was especially dependent on bone alignment. Stiffness variabilities for the composite replicate bones were much smaller than those seen with natural human bones. Axial strain distribution along the proximal-medial SGFR femur had a similar shape to what was observed on natural human femurs by other investigators, but was considerably less stiff in the more proximal locations.     

Structural properties of fourth-generation composite femurs and tibias

The purpose of this study was to measure the structural properties of the latest design (fourth-generation) of composite femurs and tibias from Pacific Research Laboratories, Inc. Fourth-generation composite bones have the same geometries as the third-generation bones, but the cortical bone analogue material was changed to one with increased fracture and fatigue resistance, tensile and compressive properties, thermal stability, and moisture resistance. The stiffnesses of the femurs and tibias were tested under bending, axial, and torsional loading, and the longitudinal strain distribution along the proximal-medial diaphysis of the femur was also determined. The fourth-generation composite bones had average stiffnesses and strains that were for the most part closer to corresponding values measured for natural bones, than was the case for third-generation composite bones; all measurements were taken by the same investigator in separate studies using identical methodology. For the stiffness tests, variability between the specimens was less than 10% for all cases, and setup variability was less than 6%.     

Assessment of the bilateral asymmetry of human femurs based on physical,densitometric, and structural rigidity characteristics

The purpose of this study was to perform a comprehensive geometric, densitometric, biomechanical, and statistical analysis of paired femurs for an adult population over a wide age range using three imaging modalities to quantify the departure from symmetry in size, bone mineral density, and cross-sectional structural rigidities.Femur measurements were obtained from 20 pairs of cadaveric femurs. Dimensions of these anatomic sites were measured using calipers directly on the bone and plain radiographs. Dual energy X-ray absorptiometry was used to measure bone mineral density. Bone mineral content and axial and bending rigidities were determined from the CT imaging.No differences were observed between the geometric measurements, DXA based bone mineral density and axial and bending rigidities of left and right femurs (P>0.05 for all cases). Left and right proximal femurs are not significantly different based on geometric, densitometric, and structural rigidity measurements. However, absolute left–right differences for individual patients can be substantial. When using the contralateral femur as a control, the number of femur pairs required to assess significant changes in anatomic dimensions and structural properties induced by a tumor, infection, fracture, or implanted device can range from 3 to 165 pairs depending on the desired effect size or sensitivity (5% or 10% difference).This information is important both for femoral arthroplasty implant design and the use of the contralateral femur as an intra-subject control for clinical assessment and research studies. In addition, our statistical analysis provides sample size estimates for planning future orthopedic research studies.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).     

Cortical screw pullout strength and effective shear stress in synthetic third generation composite femurs

BACKGROUND: The use of artificial bone analogs in biomechanical testing of orthopaedic fracture fixation devices has increased, particularly due to the recent development of commercially available femurs such as the third generation composite femur that closely reproduce the bulk mechanical behavior of human cadaveric and/or fresh whole bone. The purpose of this investigation was to measure bone screw pullout forces in composite femurs and determine whether results are comparable to cadaver data from previous literature. METHOD OF APPROACH: The pullout strengths of 3.5 and 4.5 mm standard bicortical screws inserted into synthetic third generation composite femurs were measured and compared to existing adult human cadaveric and animal data from the literature. RESULTS: For 3.5 mm screws, the measured extraction shear stress in synthetic femurs (23.70-33.99 MPa) was in the range of adult human femurs and tibias (24.4-38.8 MPa). For 4.5 mm screws, the measured values in synthetic femurs (26.04-34.76 MPa) were also similar to adult human specimens (15.9-38.9 MPa). Synthetic femur results for extraction stress showed no statistically significant site-to-site effect for 3.5 and 4.5 mm screws, with one exception. Overall, the 4.5 mm screws showed statistically higher stress required for extraction than 3.5 mm screws. CONCLUSIONS: The third generation composite femurs provide a satisfactory biomechanical analog to human long-bones at the screw-bone interface. However, it is not known whether these femurs perform similarly to human bone during physiological screw "toggling."     

A biomechanical comparison of composite femurs and cadaver femurs used in experiments on operated hip fractures

Fourth generation composite femurs (4GCFs, models #3406 and #3403) simulate femurs of males <80 years with good bone quality. Since most hip fractures occur in old women with fragile bones, concern is raised regarding the use of standard 4GCFs in biomechanical experiments. In this study the stability of hip fracture fixations in 4GCFs was compared to human cadaver femurs (HCFs) selected to represent patients with hip fractures.Ten 4GCFs (Sawbones, Pacific Research Laboratories, Inc., Vashon, WA, USA) were compared to 24 HCFs from seven females and five males >60 years. Proximal femur anthropometric measurements were noted. Strain gauge rosettes were attached and femurs were mounted in a hip simulator applying a combined subject-specific axial load and torque. Baseline measurements of resistance to deformation were recorded. Standardized femoral neck fractures were surgically stabilized before the constructs were subjected to 20,000 load-cycles. An optical motion tracking system measured relative movements.Median (95% CI) head fragment migration was 0.8 mm (0.4 to 1.1) in the 4GCF group versus 2.2 mm (1.5 to 4.6) in the cadaver group (p=0.001). This difference in fracture stability could not be explained by observed differences in femoral anthropometry or potential overloading of 4GCFs. 4GCFs failed with fracture-patterns different from those observed in cadavers.To conclude, standard 4GCFs provide unrealistically stable bone-implant constructs and fail with fractures not observed in cadavers. Until a validated osteopenic or osteoporotic composite femur model is provided, standard 4GCFs should only be used when representing the biomechanical properties of young healthy femurs.     

Experimental validation of a finite element model of a human cadaveric tibia

Finite element (FE) models of long bones are widely used to analyze implant designs. Experimental validation has been used to examine the accuracy of FE models of cadaveric femurs; however, although convergence tests have been carried out, no FE models of an intact and implanted human cadaveric tibia have been validated using a range of experimental loading conditions. The aim of the current study was to create FE models of a human cadaveric tibia, both intact and implanted with a unicompartmental knee replacement, and to validate the models against results obtained from a comprehensive set of experiments. Seventeen strain rosettes were attached to a human cadaveric tibia. Surface strains and displacements were measured under 17 loading conditions, which consisted of axial, torsional, and bending loads. The tibia was tested both before and after implantation of the knee replacement. FE models were created based on computed tomography (CT) scans of the cadaveric tibia. The models consisted of ten-node tetrahedral elements and used 600 material properties derived from the CT scans. The experiments were simulated on the models and the results compared to experimental results. Experimental strain measurements were highly repeatable and the measured stiffnesses compared well to published results. For the intact tibia under axial loading, the regression line through a plot of strains predicted by the FE model versus experimentally measured strains had a slope of 1.15, an intercept of 5.5 microstrain, and an R(2) value of 0.98. For the implanted tibia, the comparable regression line had a slope of 1.25, an intercept of 12.3 microstrain, and an R(2) value of 0.97. The root mean square errors were 6.0% and 8.8% for the intact and implanted models under axial loads, respectively. The model produced by the current study provides a tool for simulating mechanical test conditions on a human tibia. This has considerable value in reducing the costs of physical testing by pre-selecting the most appropriate test conditions or most favorable prosthetic designs for final mechanical testing. It can also be used to gain insight into the results of physical testing, by allowing the prediction of those variables difficult or impossible to measure directly.     

Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion

Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.     

An improved method to assess torsional properties of rodent long bones

Torsion is an important testing modality commonly used to calculate structural properties of long bones. However, the effects of size and geometry must be excluded from the overall structural response in order to compare material properties of bones of different size, age and species. We have developed a new method to analyze torsional properties of bones using actual cross-sectional information and length-wise geometrical variations obtained by micro-computed topographic (μCT) imaging. The proposed method was first validated by manufacturing three rat femurs through rapid prototyping using a plastic with known material properties. The observed variations in calculated torsional shear modulus of the hollow elliptical model of mid-shaft cross-section (Ekeland et al.), multi-prismatic model of five true cross-sections (Levenston et al.) and multi-slice model presented in this study were 96%, ?7% and 6% from the actual properties of the plastic, respectively. Subsequently, we used this method to derive relationships expressing torsional properties of rat cortical bone as a function of μCT-based bone volume fraction or apparent density over a range of normal and pathologic bone densities. Results indicate that a regression model of shear modulus or shear strength and bone volume fraction or apparent density described at least 81% of the variation in torsional properties of normal and pathologic bones. Coupled with the structural rigidity analysis technique introduced by the authors, the relationships reported here can provide a non-invasive tool to assess fracture risk in bones affected by pathologies and/or treatment options.     

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.     

Allometry between length and cross-sectional dimensions of the femur and tibia in Homo sapiens sapiens

Allometric equations relating length and cross-sectional geometric properties of the femur and tibia are generated using skeletal remains from three recent human population samples. Approximate isometry, or geometric similarity, is found both within and between samples. Cross-sectional areas scale to approximately length2, while second moments of area scale to approximately length4. It is shown that this is consistent with the maintenance of equivalent mechanical stress in long bones of different length under dynamic loadings in vivo. Other evidence indicates that bending and torsional loadings are more critical than axial loadings in the determination of lower limb bone cross-sectional dimensions.     

Principles of determination and verification of muscle forces in the human musculoskeletal system: Muscle forces to minimise bending stress

While there are a growing number of increasingly complex methodologies available to model geometry and material properties of bones, these models still cannot accurately describe physical behaviour of the skeletal system unless the boundary conditions, especially muscular loading, are correct. Available in vivo measurements of muscle forces are mostly highly invasive and offer no practical way to validate the outcome of any computational model that predicts muscle forces. However, muscle forces can be verified indirectly using the fundamental property of living tissue to functional adaptation and finite element (FE) analysis. Even though the mechanisms of the functional adaptation are not fully understood, its result is clearly seen in the shape and inner structure of bones. The FE method provides a precise tool for analysis of the stress/strain distribution in the bone under given loading conditions. The present work sets principles for the determination of the muscle forces on the basis of the widely accepted view that biological systems are optimized light-weight structures with minimised amount of unloaded/underloaded material and hence evenly distributed loading throughout the structure. Bending loading of bones is avoided/compensated in bones under physiological loading. Thus, bending minimisation provides the basis for the determination of the musculoskeletal system loading. As a result of our approach, the muscle forces for a human femur during normal gait and sitting down (peak hip joint force) are obtained such that the bone is loaded predominantly in compression and the stress distribution in proximal and diaphyseal femur corresponds to the material distribution in bone.     

Computer-integrated finite element modeling of human middle ear

 The objective of this study was to produce an improved finite element (FE) model of the human middle ear and to compare the model with human data. We began with a systematic and accurate geometric modeling technique for reconstructing the middle ear from serial sections of a freshly frozen temporal bone. A geometric model of a human middle ear was constructed in a computer-aided design (CAD) environment with particular attention to geometry and microanatomy. Using the geometric model, a working FE model of the human middle ear was created using previously published material properties of middle ear components. This working FE model was finalized by a cross-calibration technique, comparing its predicted stapes footplate displacements with laser Doppler interferometry measurements from fresh temporal bones. The final FE model was shown to be reasonable in predicting the ossicular mechanics of the human middle ear. Received: 18 February 2002 / Accepted: 6 June 2002 The preparation of temporal bone histological sections of Robert K. Dyer, Jr., MD is gratefully recognized. The Whitaker Foundation supported this work (Research Grant RG-98-0305).     

Long bone torsion: I. Effects of heterogeneity, anisotropy and geometric irregularity

The influences of heterogeneity, anisotropy and geometric irregularity on the unrestrained, linearly elastic torsional response of long bones are assessed. Longitudinal geometric variations contribute insignificantly to the torsional response for typical long bone geometries. Anisotropy, heterogeneity and transverse geometric irregularity significantly influence the torsional response. A procedure is discussed which uses an approximate means to characterize both heterogeneity and anisotropy in predicting the torsional response. The accuracy of circular and elliptical annulus models of the bone cross-sectional geometry are assessed by comparing the stress predictions of these simple models to those of finite element models of the bone geometry.     

Biomechanical measurements of torsion-tension coupling in human cadaveric femurs

The mechanical behavior of human femurs has been described in the literature with regard to torsion and tension but only as independent measurements. However, in this study, human femurs were subjected to torsion to determine if a simultaneous axial tensile load was generated. Fresh frozen human femurs (n=25) were harvested and stripped of soft tissue. Each femur was mounted rigidly in a specially designed test jig and remained at a fixed axial length during all experiments. Femurs were subjected to external and internal rotation applied at a constant angulation rate of 0.1 deg/s to a maximum torque of 12?N?m. Applied torque and generated axial tension were monitored simultaneously. Outcome measurements were extracted from torsion-versus-tension graphs. There was a strong relationship between applied torsion and the resulting tension for external rotation tests (torsion/tension ratio=551.7±283.8?mm, R(2)=0.83±0.20, n=25), internal rotation tests (torsion/tension ratio=495.3±233.1?mm, R(2)=0.87±0.17, n=24), left femurs (torsion/tension ratio=542.2±262.4?mm, R(2)=0.88±0.13, n=24), and right femurs (torsion/tension ratio=506.7±260.0?mm, R(2)=0.82±0.22, n=25). No statistically significant differences were found for external versus internal rotation groups or for left versus right femurs when comparing torsion/tension ratios (p=0.85) or R(2) values (p=0.54). A strongly coupled linear relationship between torsion and tension for human femurs was exhibited. This suggests an interplay between these two factors during activities of daily living and injury processes.     

Comparison of micro-level and continuum-level voxel models of the proximal femur

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density–modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.     

Determination of orthotropic bone elastic constants using FEA and modal analysis

Finite element models have been widely employed in an effort to quantify the stress and strain distribution around implanted prostheses and to explore the influence of these distributions on their long-term stability. In order to provide meaningful predictions, such models must contain an appropriate reflection of mechanical properties. Detailed geometrical and density information is now readily available from CT scanning. However, despite the use of phantoms, a method of determining mechanical properties (or elastic constants) from bone density has yet to be made available in a usable form.In this study, a cadaveric bone was CT scanned and its natural frequencies were measured using modal analysis. Using the geometry obtained from the CT scan data, a finite element mesh was created with the distribution of density established by matching the mass of the FE bone model with the mass of the cadaveric bone. The maximum values of the orthotropic elastic constants were then established by matching the predictions from FE modal analyses to the experimental natural frequencies, giving a maximum error of 7.8% over 4 modes of vibration. Finally, the elastic constants of the bone derived from the analyses were compared with those measured using ultrasound techniques. This produced a difference of <1% for both the maximum density and axial Young's Modulus. This study has thereby produced an orthotropic finite element model of a human femur. More importantly, however, is the implication that it is possible to create a valid FE model by simply comparing the FE results with the measured resonant frequency of the CT scanned bone.     

Use of a statistical model of the whole femur in a large scale,multi-model study of femoral neck fracture risk

Interpatient variability is often overlooked in orthopaedic computational studies due to the substantial challenges involved in sourcing and generating large numbers of bone models. A statistical model of the whole femur incorporating both geometric and material property variation was developed as a potential solution to this problem. The statistical model was constructed using principal component analysis, applied to 21 individual computer tomography scans. To test the ability of the statistical model to generate realistic, unique, finite element (FE) femur models it was used as a source of 1000 femurs to drive a study on femoral neck fracture risk. The study simulated the impact of an oblique fall to the side, a scenario known to account for a large proportion of hip fractures in the elderly and have a lower fracture load than alternative loading approaches. FE model generation, application of subject specific loading and boundary conditions, FE processing and post processing of the solutions were completed automatically. The generated models were within the bounds of the training data used to create the statistical model with a high mesh quality, able to be used directly by the FE solver without remeshing. The results indicated that 28 of the 1000 femurs were at highest risk of fracture. Closer analysis revealed the percentage of cortical bone in the proximal femur to be a crucial differentiator between the failed and non-failed groups. The likely fracture location was indicated to be intertrochantic. Comparison to previous computational, clinical and experimental work revealed support for these findings.     

Influences of geometrical and mechanical properties of bone tissues in mandible behaviour – experimental and numerical predictions

The properties and geometry of bone in the mandible play a key role in mandible behaviour during a person’s lifetime, and attention needs to be paid to the influence of bone properties. We analysed the effect of bone geometry, size and bone properties in mandible behaviour, experimenting on cadaveric mandibles and FE models. The study was developed using the geometry of a cadaveric mandible without teeth. Three models of cadaveric condyles were experimentally tested with instrumented with four rosettes, and a condyle reaction of 300 N. Four finite element models were considered to validate the experiments and analyse mandible behaviour. One numeric model was simulated with 10 muscles in a quasi-static condition. The experimental results present different condyle stiffness’s, of 448, 215 and 254 N/mm. The values presented in the rosettes are influenced by bone geometry and bone thickness; maximum value was ?600 με in rosette #4, and the maximum strain difference between mandibles was 111%. The numerical results show that bone density decreases and strain distribution increases in the thinner mandible regions. Nevertheless, the global behaviour of the structure remains similar, but presents different strain magnitudes. The study shows the need to take into account bone characteristics and their evolutions in order to improve implant design and fixation throughout the patient life. The change in bone stiffness promotes a change in maximum strain distribution with same global behaviour.