The effects of testing methods on the flexural fatigue life of human cortical bone

A flexural model of four-point bending fatigue that has been experimentally validated for human cortical bone under load control was used to determine how load and displacement control testing affects the fatigue behavior of human cortical bone in three-point and symmetric four-point bending. Under load control, it was predicted that three-point bending produced no significant differences in fatigue life when compared to four-point bending. However, three-point bending produced less stiffness loss with increasing cycles than four-point bending. In four-point bending, displacement control was predicted to produce about one and a half orders of magnitude greater fatigue life when compared to load control. This prediction agrees with experimental observations of equine cannon bone tested in load and displacement control (Gibson et al., 1998). Displacement controlled three-point bending was found to produce approximately a 25% greater fatigue life when compared to load control. The prediction of longer fatigue life under displacement control may have clinical relevance for the repair of damaged bone. The model can also be adapted to other geometric configurations, including modeling of whole long bones, and with appropriate fatigue data, other cortical bone types.     

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.     

Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy

The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several steps. The specimens were prepared to control damage localization during four-point bending fatigue cycling and to unambiguously identify resonant modes for NRUS measurements. NRUS measurements were achieved to follow the evolution of the nonlinear hysteretic elastic behavior during fatigue-induced damage. After each fatigue step, a small number of specimens was removed from the protocol and set apart to quantitatively assess the microcrack number density and length using synchrotron radiation micro-computed tomography (SR-µCT). The results showed a significant effect of damage steps on the nonlinear hysteretic elastic behavior. No significant change in the overall length of microcracks was observed in damaged regions compared to the load-free control regions. Only an increased number of shortest microcracks, those in the lowest quartile, was noticed. This was suggestive of newly formed microcracks during the early phases of damage accumulation. The variation of nonlinear hysteretic elastic behavior was significantly correlated to the variation of the density of short microcracks. Our results suggest that the nonlinear hysteretic elastic behavior is sensitive to early bone microdamage. Therefore NRUS technique can be used to monitor fatigue microdamage progression in in vitro experiments.     

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.     

Quantitative measures of femoral fracture repair in rats derived by micro-computed tomography

Although fracture healing is frequently studied in pre-clinical models of long bone fractures using rodents, there is a dearth of objective quantitative techniques to assess successful healing. Biomechanical testing is possibly the most quantitative and relevant to a successful clinical outcome, but it is a destructive technique providing little insight into the cellular mechanisms associated with healing. The advent of X-ray computed tomography (CT) has provided the opportunity to quantitatively and non-destructively assess bone structure and density, but it is unknown how measurements derived using this technology relate to successful healing. To examine possible relationships, we used a pre-clinical model to test for statistically significant correlations between quantitative characteristics of the callus by micro-CT (μCT) and the bending strength, stiffness, and energy-to-failure of the callus as assessed by three-point bending of excised bones. A closed, transverse fracture was generated in the mid-shaft of rat femurs by impact loading. Shortly thereafter, the rats received a one-time, local injection of either the vehicle or one of four doses of lovastatin. Following sacrifice after 4 weeks of healing, fractured femurs were extracted for μCT analysis and then three-point bending. Setting the region of interest to be 3.2 mm above and below the fracture line, we acquired standard and new μCT-derived measurements. The mineralized callus volume and the mineral density of the callus correlated positively with callus strength (r_xy=?0.315, p=0.016 and r_xy=0.444, p<0.0005, respectively) and stiffness (r_xy=?0.271, p=0.040 and r_xy=0.325, p=0.013, respectively), but the fraction of the callus that mineralized and the moment of inertia of the callus did not. This fraction did correlate with energy-to-failure (r_xy=?0.343, p=0.0085). Of the μCT-derived measurements, quantifying defects within the outer bridging cortices of the callus produced the strongest correlation with both callus strength (r_xy=0.557, p<0.0001) and stiffness (r_xy=0.468, p=0.0002). By both reducing structural defects and increasing mineralization, lovastatin appears to increase the callus strength.     

Design and validation of a testing system to assess torsional cancellous bone failure in conjunction with time-lapsed micro-computed tomographic imaging

When compressed axially, cancellous bone often fails at an oblique angle along well-defined bands, highlighting the importance of cancellous bone shear properties. Torsion testing to determine shear properties of cancellous bone has often been conducted under conditions appropriate only for axis-symmetric specimens comprised of homogeneous and isotropic materials. However, most cancellous bone specimens do not meet these stringent test conditions. Therefore, the aim of this study was to design and validate a uniaxial, incremental torsional testing system for non-homogeneous orthotropic or non-axis-symmetric specimens.Precision and accuracy of the newly designed torsion system was validated by using Plexiglas rods and beams, where obtained material properties were compared to those supplied by the manufacturer. Additionally, the incremental step-wise application of angular displacement and simultaneous time-lapsed μCT imaging capability of the system was validated using whale cancellous bone specimens, with step-wise application of angular displacement yielding similar torsional mechanical properties to continuous application of angular displacement in a conventional torsion study.In conclusion, a novel torsion testing system for non-homogeneous, orthotropic materials using the incremental step-wise application of torsion and simultaneous time-lapsed μCT imaging was designed and validated.     

Influence of phase angle between axial and torsional loadings on fatigue fractures of bone

Fatigue fractures of cortical bone involve combined axial-torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0 degrees and 90 degrees phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures.     

Pure moment testing for spinal biomechanics applications: fixed versus 3D floating ring cable-driven test designs

Pure moment testing has become a standard protocol for in vitro assessment of the effect of surgical techniques or devices on the bending rigidity of the spine. Of the methods used for pure moment testing, cable-driven set-ups are popular due to their low requirements and simple design. Fixed loading rings are traditionally used in conjunction with these cable-driven systems. However, the accuracy and validity of the loading conditions applied with fixed ring designs have raised some concern, and discrepancies have been found between intended and prescribed loading conditions for flexion-extension. This study extends this prior work to include lateral bending and axial torsion, and compares this fixed ring design with a novel "3D floating ring" design. A complete battery of multi-axial bending tests was conducted with both rings in multiple different configurations using an artificial lumbar spine. Applied moments were monitored and recorded by a multi-axial load cell at the base of the specimen. Results indicate that the fixed ring design deviates as much as 77% from intended moments and induces non-trivial shear forces (up to 18 N) when loaded to a non-destructive maximum of 4.5 Nm. The novel 3D floating ring design largely corrects the inherent errors in the fixed ring design by allowing additional directions of unconstrained motion and producing uniform loading conditions along the length of the specimen. In light of the results, it is suggested that the 3D floating ring set-up be used for future pure moment spine biomechanics applications using a cable-driven apparatus.     

The contribution of the cruciate ligaments to the load-displacement characteristics of the human knee joint

Human knee specimens were subjected to anterior-posterior, medial-lateral, varus-valgus, and torsional displacement tests. Loads were recorded for the intact joint and for the joint with all soft tissues cut except for the cruciate ligaments. The effect of condylar interference was determined for anterior-posterior, medial-lateral, and torsional displacements. The variation in load with flexion angle was considerable for medial-lateral (0-90-deg flexion) displacements, and less for varus-valgus (0-45-deg flexion) displacements. The cruciates were found to carry almost the entire anterior-posterior load; they carried a significant percentage of the medial-lateral load which varied considerably with flexion angle. A small, but not insignificant percentage of the varus-valgus load was carried by the cruciates and the variations with flexion angle were small. In torsion, the cruciates resisted only internal rotation. In the tested displacement ranges, condylar interference had a small effect on the medial-lateral load but did not affect anterior-posterior or torsional loads.     

A comparison of stereology, structural rigidity and a novel 3D failure surface analysis method in the assessment of torsional strength and stiffness in a mouse tibia fracture model

In attempting to develop non-invasive image based measures for the determination of the biomechanical integrity of healing fractures, traditional μCT based measurements have been limited. This study presents the development and evaluation of a tool for assessment of fracture callus mechanical properties through determination of the geometric characteristics of the fracture callus, specifically along the surface of failure identified during destructive mechanical testing. Fractures were created in tibias of ten male mice and subjected to μCT imaging and biomechanical torsion testing. Failure surface analysis, along with previously described image based measures was calculated using the μCT image data, and correlated with mechanical strength and stiffness. Three-dimensional measures along the surface of failure, specifically the surface area and torsional rigidity of bone, were shown to be significantly correlating with mechanical strength and stiffness. It was also shown that surface area of bone along the failure surface exhibits stronger correlations with both strength and stiffness than measures of average and minimum torsional rigidity of the entire callus. Failure surfaces observed in this study were generally oriented at 45° to the long axis of the bone, and were not contained exclusively within the callus. This work represents a proof of concept study, and shows the potential utility of failure surface analysis in the assessment of fracture callus stability.     

Temporal trends in femoral diaphyseal torsional asymmetry among the Arikara associated with postural behavior

Average femoral torsion has been reported to differ among populations, and several studies have observed a relatively high prevalence of femoral anteversion asymmetry in Native Americans, especially females. This study investigates sexual dimorphism and temporal trends in femoral torsional asymmetry among the Arikara from the seventeenth to the early nineteenth century. To establish if there are population differences, femoral torsion was first measured using a direct method on a diverse comparative sample of Native Americans from the Southwest, Midwest, and Great Plains as well as American Whites and Blacks. To examine temporal trends among the Arikara, femoral torsion was examined using the orientation of the maximum bending rigidity at subtrochanteric in 154 females and 164 males from three temporal variants of the Arikara Coalescent tradition. There is significant sexual dimorphism in femoral torsional directional and absolute asymmetry among most Native American samples, but not among American Whites and Blacks. Among the Arikara there is significant sexual dimorphism in femoral torsional asymmetry in all three temporal variants, and asymmetry in femoral torsional asymmetry increased significantly from the protohistoric to the early historic period among females. The increased femoral torsional asymmetry is likely associated with a common side‐sitting posture observed in historic photographs of Great Plains females. Historic Arikara females may have habitually sat in this compulsory position for extended periods while conducting domestic chores. The dramatic change from the protohistoric to historic period suggests a cultural change in sitting posture among females that was widespread across the Northern Plains. Am J Phys Anthropol 154:512–524, 2014. © 2014 Wiley Periodicals, Inc.     

On the origin of the temperature dependence of the supercoiling free energy.

Monte Carlo simulations using temperature-invariant torsional and bending rigidities fail to predict the rather steep decline of the experimental supercoiling free energy with increasing temperature, and consequently fail to predict the correct sign and magnitude of the supercoiling entropy. To illustrate this problem, values of the twist energy parameter (E(T)), which governs the supercoiling free energy, were simulated using temperature-invariant torsion and bending potentials and compared to experimental data on pBR322 over a range of temperatures. The slope, -dE(T)/dT, of the simulated values is also compared to the slope derived from previous calorimetric data. The possibility that the discrepancies arise from some hitherto undetected temperature dependence of the torsional rigidity was investigated. The torsion elastic constant of an 1876-bp restriction fragment of pBR322 was measured by time-resolved fluorescence polarization anisotropy of intercalated ethidium over the range 278-323 K, and found to decline substantially over that interval. Simulations of a 4349-bp model DNA were performed using these measured temperature-dependent torsional rigidities. The slope, -dE(T)/dT, of the simulated data agrees satisfactorily with the slope derived from previous calorimetric measurements, but still lies substantially below that of Duguet's data. Models that involve an equilibrium between different secondary structure states with different intrinsic twists and torsion constants provide the most likely explanation for the variation of the torsion constant with T and other pertinent observations.     

Structural consequences of transcortical holes in long bones loaded in torsion

Finite element models were used to predict the structural consequences of transcortical holes through long bones loaded in torsion. Several parameters were investigated including hole size, anelastic behavior of the bone, cortical wall thickness, cortical wall symmetry, curvature along the bone's long axis and the axial length of the defect. Finite element model predictions of percent intact bone strength were compared to experimental data for sheep femora with transcortical drill holes loaded to failure in torsion. Hole size was expressed as hole diameter divided by the outer bone diameter. Linear finite element model predictions were in conservative agreement with the experimental data for large hole sizes. A transcortical hole with a diameter 50% of the outer bone diameter reduced the torsional strength by 60%. However, the linear models predict a 40% drop in strength for small holes whereas in vitro data suggest that small holes have no significant effect on strength. Models which represent non-linear anelastic behavior in bone over-predicted torsional strengths. Asymmetric cortical wall thickness and long bone bowing have minor effects, while the length of an elongated defect strongly influences the torsional strength. Strength reductions are greatest for bones with thin cortical walls.     

Mechanical properties of single bovine trabeculae are unaffected by strain rate

For a better understanding of traumatic bone fractures, knowledge of the mechanical behavior of bone at high strain rates is required. Importantly, it needs to be clarified how quasistatic mechanical testing experiments relate to real bone fracture. This merits investigating the mechanical behavior of bone with an increase in strain rate. Various studies examined how cortical and trabecular bone behave at varying strain rates, but no one has yet looked at this question using individual trabeculae. In this study, three-point bending tests were carried out on bovine single trabeculae excised from a proximal femur to test the trabecular material's strain rate sensitivity. An experimental setup was designed, capable of measuring local strains at the surface of such small specimens, using digital image correlation. Microdamage was detected using the bone whitening effect. Samples were tested through two orders of magnitude, at strain rates varying between 0.01 and 3.39 s(-1). No linear relationship was observed between the strain rate and the Young's modulus (1.13-16.46 GPa), the amount of microdamage, the maximum tensile strain at failure (14.22-61.65%) and at microdamage initiation (1.95-12.29%). The results obtained in this study conflict with previous studies reporting various trends for macroscopic cortical and trabecular bone samples with an increase in strain rate. This discrepancy might be explained by the bone type, the small sample geometry, the limited range of strain rates tested here, the type of loading and the method of microdamage detection. Based on the results of this study, the strain rate can be ignored when modeling trabecular bone.     

A comparison of mechanical properties derived from multiple skeletal sites in mice

Laboratory mice provide a versatile experimental model for studies of skeletal biomechanics. In order to determine the strength of the mouse skeleton, mechanical testing has been performed on a variety of bones using several procedures. Because of differences in testing methods, the data from previous studies are not comparable. The purpose of this study was to determine which long bone provides the values closest to the published material properties of bone, while also providing reliable and reproducible results. To do this, the femur, humerus, third metatarsal, radius, and tibia of both the low bone mass C57BL/6H (B6) and high bone mass C3H/HeJ (C3H) mice were mechanically tested under three-point bending. The biomechanical tests showed significant differences between the bones and between mouse strains for the five bones tested (p < 0.05). Computational models of the femur, metatarsal, and radius were developed to visualize the types of measurement error inherent in the three-point bending tests. The models demonstrated that measurement error arose from local deformation at the loading point, shear deformation and ring-type deformation of the cylindrical cross-section. Increasing the aspect ratio (bone length/width) improved the measurement of Young's modulus of the bone for both mouse strains (p < 0.01). Bones with the highest aspect ratio and largest cortical thickness to radius ratio were better for bending tests since less measurement error was observed in the computational models. Of the bones tested, the radius was preferred for mechanical testing because of its high aspect ratio, minimal measurement error, and low variability.     

Influence of shear stress on behaviors of piezoelectric voltages in bone

The piezoelectric properties of bone play an important role in the bone remodeling process and can be employed in clinical bone repair. In this study, the piezo-voltage of bone between two surfaces of a bone beam under bending deformation was measured using an ultra-high-input impedance bioamplifier. The influence of shear stress on the signs of piezo-voltages in bone was determined by comparing and contrasting the results from three-point and four-point bending experiments. From the three-point bending experiment, the study found that the signs of piezo-voltages depend only on shear stress and are not sensitive to the normal stress.     

Torsional Tribological Behavior and Torsional Friction Model of Polytetrafluoroethylene against 1045 Steel

In this work, the plane-on-plane torsional fretting tribological behavior of polytetrafluoroethylene (PTFE) was studied. A model of a rigid, flat-ended punch acting on an elastic half-space was built according to the experimental conditions. The results indicate that the shape of T–θ curves was influenced by both the torsional angle and the normal load. The torsion friction torque and wear rate of PTFE exponentially decreased when the torsion angle rose. The torsional torque increased from 0.025 N·m under a normal load of 43 N to 0.082 N·m under a normal load of 123 N. With sequentially increasing normal load, the value of torque was maintained. With rising normal load, the wear mass loss of PTFE disks was increased and the wear rate was decreased. Good agreement was found with the calculated torque according to the model and the experimental torque except for that under a normal load of 163 N. The difference under a normal load of 163 N was caused by the coefficient of friction. Usually the coefficient of friction of a polymer decreases with increasing normal load, whereas a constant coefficient of friction was applied in the model.     

Microtensile measurements of single trabeculae stiffness in human femur

In this paper, the authors perform microtensile tests of single trabeculae excised from a human femur head. One of the main issues of this work is to establish some experimental procedures for preparing and testing the specimens. The use of a well-characterized microtensile apparatus allows for a low intraspecimen dispersion of the measured stiffness. Tensile/compressive tests were chosen because they appear less sensitive to errors in the cross-sectional area measurements with respect to bending tests. By these considerations, some tensile/compressive tests of plate-like trabecular specimens have been carried out. Typical stiffness values are 74.2+/-0.7Nmm(-1) for tensile tests, and 58.9+/-0.6Nmm(-1) for compressive test. Another compressive test performed on a shorter specimen yielded a stiffness value of 148.3+/-5.3Nmm(-1). The maximum applied load was about 0.5N. Rough measurements of specimens sizes yielded a Young's modulus value ranging from 1.41 to 1.89GPa.     

Comparison of two systems for tibial external fixation in rabbits

BACKGROUND AND PURPOSE: Use of rabbits in orthopedic investigations is common. In this study, focus is on factors that influence bone healing and on distraction osteogenesis. Biomechanical characteristics of two external fixator systems (Orthofix device and Hoffmann device) for long bones were tested. METHODS: Twelve freshly dissected tibiae were obtained from six skeletally mature New Zealand White rabbits, and four-point bending stiffness in two planes (90 and 180 degrees to the fixator pins) and torsional stiffness and strength of the bone-fixator complex were evaluated by use of a material testing machine. RESULTS: In four-point bending, Orthofix device had higher stiffness and strength, compared with Hoffmann device. When the load was applied 180 degrees to the pins, both devices had higher stiffness, compared with that at 90 degrees. In torsional testing, Orthofix device had significantly higher stiffness and strength. CONCLUSIONS: Significant differences in structural properties between the two systems were evident. Loading direction and gap conditions were important factors in determining properties of the systems. Therefore, type of external fixation system and fixation technique should be considered when designing experiments, using the rabbit long bone model.     

Novel Intramedullary-Fixation Technique for Long Bone Fragility Fractures Using Bioresorbable Materials

Almost all of the currently available fracture fixation devices for metaphyseal fragility fractures are made of hard metals, which carry a high risk of implant-related complications such as implant cutout in severely osteoporotic patients. We developed a novel fracture fixation technique (intramedullary-fixation with biodegradable materials; IM-BM) for severely weakened long bones using three different non-metallic biomaterials, a poly(l-lactide) (PLLA) woven tube, a nonwoven polyhydroxyalkanoates (PHA) fiber mat, and an injectable calcium phosphate cement (CPC). The purpose of this work was to evaluate the feasibility of IM-BM with mechanical testing as well as with an animal experiment. To perform mechanical testing, we fixed two longitudinal acrylic pipes with four different methods, and used them for a three-point bending test (N = 5). The three-point bending test revealed that the average fracture energy for the IM-BM group (PLLA + CPC + PHA) was 3 times greater than that of PLLA + CPC group, and 60 to 200 times greater than that of CPC + PHA group and CPC group. Using an osteoporotic rabbit distal femur incomplete fracture model, sixteen rabbits were randomly allocated into four experimental groups (IM-BM group, PLLA + CPC group, CPC group, Kirschner wire (K-wire) group). No rabbit in the IM-BM group suffered fracture displacement even under full weight bearing. In contrast, two rabbits in the PLLA + CPC group, three rabbits in the CPC group, and three rabbits in the K-wire group suffered fracture displacement within the first postoperative week. The present work demonstrated that IM-BM was strong enough to reinforce and stabilize incomplete fractures with both mechanical testing and an animal experiment even in the distal thigh, where bone is exposed to the highest bending and torsional stresses in the body. IM-BM can be one treatment option for those with severe osteoporosis.