Design and validation of a surrogate humerus for biomechanical testing

At present biomechanical testing of fracture plating strategies is conducted using animal or cadaveric whole bone models. This may introduce experimental error into these studies. This communication summarises the design and validation of a novel bone and fibre-reinforced plastic construct conceived to minimise intra-experimental error. A tubular surrogate humerus was produced with dimension and strength matched to that of the human humerus. Bone inserts placed into the wall of the tube allow for the fixation of the plates with bone screws. Three-point bending tests of the flexural rigidity of the surrogate humerus (EI=100.1 (SD 6.0)Nm(2)) showed it to be comparable to the human humerus. Further, pull-out tests of the screws showed that the bone slots adequately mimicked the whole bone scenario. This testing construct will be used for a comparative study of humeral plating techniques.     

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.     

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.     

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.     

Bone modeling response to voluntary exercise in the hindlimb of mice

The functional adaptation of juvenile mammalian limb bone to mechanical loading is necessary to maintain bone strength. Diaphyseal size and shape are modified during growth through the process of bone modeling. Although bone modeling is a well-documented response to increased mechanical stress on growing diaphyseal bone, the effect of proximodistal location on bone modeling remains unclear. Distal limb elements in cursorial mammals are longer and thinner, most likely to conserve energy during locomotion because they require less energy to move. Therefore, distal elements are hypothesized to experience greater mechanical loading during locomotion and may be expected to exhibit a greater modeling response to exercise. In this study, histomorphometric comparisons are made between femora and tibiae of mice treated with voluntary exercise and a control group (N = 20). We find that femora of exercised mice exhibit both greater bone growth rates and growth areas than do controls (P < 0.05). The femora of exercised mice also have significantly greater cortical area, bending rigidity, and torsional rigidity (P < 0.05), although bending and torsional rigidity are comparable when standardized by bone length. Histomorphometric and cross-section geometric properties of the tibial midshaft of exercised and control mice did not differ significantly, although tibial length was significantly greater in exercised mice (P < 0.05). Femora of exercised mice were able to adapt to increased mechanical loading through increases in compressive, bending, and torsional rigidity. No such adaptations were found in the tibia. It is unclear if this is a biomechanical adaptation to greater stress in proximal elements or if distal elements are ontogenetically constrained in a tradeoff of bone strength of distal elements for bioenergetic efficiency during locomotion.     

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.     

Design and testing of external fixator bone screws

In external fixation, bone screw loosening still presents a major clinical problem. For this study, the design factors influencing the mechanics of the bone-screw interface were analysed and various experimental screws designed with the intention of maximizing the strength and stiffness of the inserted screw. Push-in, pull-out and bending tests were then carried out on the three experimental screws, and on two commercially available screws in both a synthetic material and in cadaveric bone; photoelastic tests on different screw threadforms were also performed. The results of the push-in and pull-out tests indicate that both the screw threadform and cutting head have a significant effect on the holding strength of the screw. The photoelastic tests show that most of the applied load is distributed over the first few threads closest to the load, and that the area between the thread crests is subjected to high shear stresses.     

Estimation of torsional rigidity in primate long bones

Comparative studies of long bone biomechanics in primates frequently use the polar moment of inertia (J ) as a variable reflecting overall mechanical rigidity, average bending rigidity, or resistance to torsional shear stresses. While the use of this variable for characterizing the first two properties is appropriate, it is potentially a highly misleading measure of torsional resistance. Errors result from violations of assumptions required for the use of the polar moment of inertia; in particular, the predictive utility of J diminishes with departures from axial symmetry (i.e., a cylindrical cross-sectional shape). The magnitude of these errors is estimated both theoretically and experimentally. It is argued that the use of the polar moment of inertia for estimating long bone torsional rigidity should be restricted to samples of relatively invariant and/or cylindrical geometry. Alternative measures for torsional resistance are evaluated and reviewed.     

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."     

In vitro sodium fluoride exposure decreases torsional and bending strength and increases ductility of mouse femora

Fluoride exposure in vivo can reduce the material strength of bone, an effect that has been attributed to a change in mineral structure. An in vitro model of fluoride exposure offers the potential to study directly the effects of fluoride on bone mineral. Previous investigators have reported that soaking bones in sodium fluoride in vitro reduces bone strength. However, long soaking times and the absence of physiological buffering ions from their treatment solutions may have caused mineral dissolution that contributed to the decrease in bone strength. Our objectives were to further characterize the effects of in vitro fluoride exposure on bone mechanical properties and to determine if the changes reported in previous studies of bovine cortical bone would be observed for whole rodent bones. We soaked 60 mouse femora in sodium fluoride solutions, with and without physiological buffering ions, and evaluated their torsional and bending properties. Fluoride soaked bones had a 30-fold increase in fluoride content and a 23% increase in water content compared to controls. These changes were associated with average reductions in ultimate load of 45%, reductions in rigidity of 70%, and increases in deformation to failure of 80%. The effect of fluoride was similar for bones treated in buffered and non-buffered solutions, and was observed in both torsion and bending. Our findings confirm those of previous studies and highlight the strong effect that in vitro fluoride exposure has on bone mechanical properties. The in vitro model of fluoride exposure offers a tool to further study the effects of ion substitution in bone.     

Central screw use delays implant dislodgement in osteopenic bone but not synthetic surrogates: A comparison of reverse total shoulder models

Adequate glenoid baseplate fixation in reverse total shoulder arthroplasty (rTSA) is important to achieve, but may prove challenging in the context of glenoid bone loss or osteopenia. Current rTSA testing standards rely upon synthetic bone surrogates, but it is unclear if these models accurately recapitulate the mechanics of osteoporotic bone. Additionally, it also unknown if the use of a central screw effectively provides resistance to micromotion in the milieu of poor quality bone. The purpose of this experiment was to create a novel cyclic load test protocol that elicited clinically relevant failures, so that comparisons of relative motion between baseplates and bones could be made with: (1) synthetic bones and poor quality cadaveric bones, and (2) the use or omission of a central screw. rTSA components were implanted into cadaveric and synthetic bones with and without a central screw. To model a range of loads that may be experienced during abduction, increasing cyclic loads were applied to shoulder joints in 30° of humeral abduction. Cycles and loads prior to permanent deformation exceeding 150 µm, 1 mm, and joint failure were determined using measurements from the test frame and from 3-D motion analysis. Synthetic bones demonstrated significantly more resistance to micromotion in comparison to cadaveric bones. Use of the central screw improved resistance to dislodgement, which was only observed in the cadaveric specimens. This study highlights the need for biomechanical testing with cadaveric specimens, especially when assessing osteopenic or osteoporotic populations.     

Mechanical validation of whole bone composite tibia models

Composite synthetic models of the human tibia have recently become commercially available as substitutes for cadaveric specimens. Their use is justified by the advantages they offer as a substitute for real tibias. The present investigation concentrated on an extensive experimental validation of the mechanical behaviour of the whole bone composite model, compared to human specimens for different loading conditions. The stiffness of the tibias was measured with a torsional load applied along the long axis, and with a bending load applied both in the latero-medial and in the antero-posterior direction. The bending stiffness of the composite tibias matched well with that of the cadaveric specimens. This was not true for the torsional stiffness. In fact, the composite tibias were much stiffer than the cadaveric specimens, possibly due to the structure of the reinforcement material. The inter-specimen variability for the composite tibias was much lower than that for the cadaveric specimens. Thus, it seems that the composite tibias are suitable to replace cadaveric specimens for certain types of test, whereas they might be unsuitable for others, depending on the loading regimen.     

Scaling of long bone fracture strength with animal mass

Most long bone fractures are the result of bending and/or torsional loading. To allometrically relate bone torsional and bending strength to animal mass (M), we define the bone strength index SB = J/dl where J = midshaft cross section polar moment of inertia, d = diameter, and l = length. In geometrically similar scaling, one would expect SB alpha M2/3. In this study, long bone geometric parameters were measured for 12 species of Artiodactyls. The relationships determined for length and diameter are similar to those reported by previous investigators (l alpha d3/4, l alpha M1/4). For the Artiodactyls studied, we found that SB alpha M0.82. Data previously collected by Biewener on a wide range of mammals (non-Artiodactyls) showed different scaling characteristics (l alpha d0.89, l alpha M0.31). However, our analysis of his data suggests roughly similar scaling of the torsional and bending strength index, SB alpha M0.77. It therefore appears that, in spite of differences in scaling of length and external diameter, the bending and torsional strengths scale similarly across a broad range of animals.     

Bone abnormalities in adolescent leptin-deficient mice

Ob/ob and db/db mice have different aberrations in leptin signaling that both lead to abnormalities in bone mineral density (BMD), and bone histological and histomorphometric outcomes. A few studies have directly compared bone metabolism in ob/ob and db/db mice, and biomechanical strength properties that are surrogate measures of fracture risk, have not been extensively studied. This study compared bone mineral content (BMC), BMD and biomechanical strength properties of femurs and lumbar vertebrae among 10 week old male ob/ob, db/db and C57Bl/6 wildtype (WT) mice. Femurs and lumbar vertebrae were specifically studied to determine if trabecular and cortical bone are regulated by leptin in a similar manner in ob/ob and db/db mice. Femurs of ob/ob and db/db mice had lower BMC, BMD and biomechanical strength properties, including peak load, compared to WT mice. In contrast, lumbar vertebrae BMC and BMD did not differ among genotypes, nor did the peak load from compression testing of an individual lumbar vertebra differ among groups. These findings suggest that leptin deficiency in adolescent male mice first results in changes in femurs, a representative long bone, and alterations in lumbar vertebrae may occur later in life.     

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%.     

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.     

Micro-computed tomography prediction of biomechanical strength in murine structural bone grafts

Correlating massive bone graft strength to parameters derived from non-invasive imaging is important for pre-clinical and clinical evaluation of therapeutic adjuvants designed to improve graft repair. Towards that end, univariate and multivariate regression between measures of graft and callus geometry from micro-CT imaging and torsional strength and rigidity were investigated in a mouse femoral graft model. Four millimeter mid-diaphyseal defects were grafted with live autografts or processed allografts and allowed to heal for 6, 9, 12, or 18 weeks. We observed that allograft remodeling and incorporation into the host remained severely impaired compared to autografts mainly due to the extent of callus formation around the graft, the rate and extent of the graft resorption, and the degree of union between the graft and host bone as judged by post-mechanical testing analysis of the mode of failure. The autografts displayed greater ultimate torque and torsional rigidity compared to the allografts over time. However the biomechanical properties of allografts were equivalent to autografts by 9 weeks but significantly decreased at 12 and 18 weeks. Multivariate regression analysis demonstrated significant statistical correlations between combinations of the micro-CT parameters (graft and callus volume and cross-sectional polar moment of inertia) with the measured ultimate torque and torsional rigidity (adjusted R(2)=44% and 50%, respectively). The statistical correlations approach used in this mouse study could be useful in guiding future development of non-invasive predictors of the biomechanical properties of allografts using clinical CT.     

Micro-CT and micro-FE analysis of pedicle screw fixation under different loading conditions

Anchorage of pedicle screw instrumentation in the elderly spine with poor bone quality remains challenging. In this study, micro finite element (µFE) models were used to assess the specific influence of screw design and the relative contribution of local bone density to fixation mechanics. These were created from micro computer tomography (µCT) scans of vertebras implanted with two types of pedicle screws, including a full region-or-interest of 10 mm radius around each screw, as well as submodels for the pedicle and inner trabecular bone of the vertebral body. The local bone volume fraction (BV/TV) calculated from the µCT scans around different regions of the screw (pedicle, inner trabecular region of the vertebral body) were then related to the predicted stiffness in simulated pull-out tests as well as to the experimental pull-out and torsional fixation properties mechanically measured on the corresponding specimens. Results show that predicted stiffness correlated excellently with experimental pull-out strength (R² > 0.92, p < .043), better than regional BV/TV alone (R2 = 0.79, p = .003). They also show that correlations between fixation properties and BV/TV were increased when accounting only for the pedicle zone (R² = 0.66–0.94, p ≤ .032), but with weaker correlations for torsional loads (R² < 0.10). Our analyses highlight the role of local density in the pedicle zone on the fixation stiffness and strength of pedicle screws when pull-out loads are involved, but that local apparent bone density alone may not be sufficient to explain resistance in torsion.     

Structural behaviour and strain distribution of the long bones of the human lower limbs

Although stiffness and strength of lower limb bones have been investigated in the past, information is not complete. While the femur has been extensively investigated, little information is available about the strain distribution in the tibia, and the fibula has not been tested in vitro. This study aimed at improving the understanding of the biomechanics of lower limb bones by: (i) measuring the stiffness and strain distributions of the different low limb bones; (ii) assessing the effect of viscoelasticity in whole bones within a physiological range of strain-rates; (iii) assessing the difference in the behaviour in relation to opposite directions of bending and torsion. The structural stiffness and strain distribution of paired femurs, tibias and fibulas from two donors were measured. Each region investigated of each bone was instrumented with 8–16 triaxial strain gauges (over 600 grids in total). Each bone was subjected to 6–12 different loading configurations. Tests were replicated at two different loading speeds covering the physiological range of strain-rates. Viscoelasticity did not have any pronounced effect on the structural stiffness and strain distribution, in the physiological range of loading rates explored in this study. The stiffness and strain distribution varied greatly between bone segments, but also between directions of loading. Different stiffness and strain distributions were observed when opposite directions of torque or opposite directions of bending (in the same plane) were applied. To our knowledge, this study represents the most extensive collection of whole-bone biomechanical properties of lower limb bones.     

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.