The effect of wire plane tilt and olive wires on proximal tibia fracture fragment stability and fracture site motion

To analyze the effect of the tilt angle relationship between the crossed wire plane and the bone axis on the stiffness of fine wire external fixation, load-deformation behavior was compared across different tilt angles (0 degree, 10 degrees, and 20 degrees) of the plane containing crossed smooth or olive wires under identical conditions of central axial compression, medial compression-bending, posterior compression-bending, posteromedial compression-bending, and torsion. Stiffness values were calculated from the load-deformation and torque-angle curves. A tilt angle of 20 degrees with olive wires provided significantly greater stiffness compared to smooth wires at any angle in any loading condition (p < 0.05). A tilt angle of 20 degrees with olive wires was also significantly more stiff than a tilt angle of 0 degree with olive wires in any loading condition. In torsion, olive wires with 10 degrees and 20 degrees tilt were not significantly different, while in posterior bending olive wires with 10 degrees tilt were significantly stiffer than olive wires with 0 degree or 20 degrees tilt. With smooth wires, tilting the wire plane caused a decrease in stiffness in posterior bending, posteromedial bending, and torsion. Overall, the use of olive wires in conjunction with tilting the wire plane enhances the fixation stiffness for proximal tibia fractures while allowing more options for wire configurations that avoid neurovascular and musculotendinous structures, and wounds.     

Compressive fatigue behavior of human vertebral trabecular bone

Damage accumulation under compressive fatigue loading is believed to contribute significantly to non-traumatic, age-related vertebral fractures in the human spine. Only few studies have explored trabecular bone fatigue behavior under compressive loading and none examined the influence of trabecular architecture on fatigue life. In this study, trabecular bone samples of human lumbar and thoracic vertebrae (4 donors from age 29 to 86, n=29) were scanned with a microCT system prior to compressive fatigue testing to determine morphology-mechanical relationships for this relevant loading mode. Inspired from previous fabric-based relationships for elastic properties and quasi-static strength of trabecular bone, a simple power relationship between volume fraction, fabric eigenvalue, applied stress and the number of cycles to failure is proposed. The experimental results demonstrate a high correlation for this relationship (R2=0.95) and detect a significant contribution of the degree of anisotropy towards prediction of fatigue life. Step-wise regression for total and residual strains at failure suggested a weak, but significant correlation with volume fraction. From the obtained results, we conclude that the applied stress normalized by volume fraction and axial fabric eigenvalue can estimate fatigue life of human vertebral trabecular bone in axial compressive loading.     

Axial-shear interaction effects on microdamage in bovine tibial trabecular bone

Because many osteoporotic fractures occur during a fall, understanding the effect of off-axis loads on initiation and propagation of microdamage in trabecular bone should provide further insight into the biomechanics of age-related fractures. Fourteen on-axis cylindrical specimens were prepared from 12 bovine tibiae. Fluorescent stains were used to label the microdamage due to a sequence of compressive and torsional damaging loads. The mean decrease in Young's modulus was over four times greater than that in the shear modulus after the compressive overload, while there was no difference between the decrease in the axial and torsional stiffnesses after the torsional overload. The total microcrack density due to compression was uniform across the radius of the cylindrical specimens, while the mean density of microcracks due to torsional overloading increased from the axis of the cylindrical specimen to the circumference. The high density of microcracks near the axis of the specimen following torsional overloading was unexpected because of the low strains. Nearly 40% of the microcracks due to torsion propagated from pre-existing microcracks caused by axial compression, indicating that existing microcracks may extend at relatively low strain if the loading mode changes. The propagating microcracks were, on average, longer than the initiating microcracks due to either compressive or torsional loading. Damage due to axial compression appears to increase the susceptibility of trabecular bone to damage propagation during subsequent torsional loads, but it has little effect on the elastic properties in shear.     

Collagen fiber orientation and geometry effects on the mechanical properties of secondary osteons.

The effects of collagen fiber orientation and osteon geometry on the mechanical properties of secondary osteons under axial compression/tension and combined loadings (compression, bending and torsion) were investigated using a composite-beam finite-element model. Three cross-sectional shapes of secondary osteons were studied to show the effect of geometry. The results of stiffness are presented using the tension and compression properties for each lamella. The model shows that the mechanical properties of osteons are enhanced in bending and torsion when collagen fibers are oriented within 30 degrees of the loading axis. Osteons with alternating lamellar orientation are not well adapted to resist torsional moments, but alternate collagen fiber orientation has virtually no effect on the bending stiffness of osteons. Fiber orientation affects the mechanical properties less significantly when osteons are non-circular. Collagen fiber orientation and osteon geometry interact to determine the mechanical behavior of the osteon, and may act in a compensatory manner in the adaptive process.     

Analysis of bone tissue mechanical properties

This paper deals with the torsional moment depending on the angle of torsion of the compact bone in laboratory animals and humans. Based on the data from laboratory animals, obtained by measurement, the data on dependence of the torsional moment and the angle of torsion were assumed for humans. Measurements were carried out on four groups of compact bone in laboratory animals. One was the control group, and three other groups were treated by various vitamin D3 metabolites. Equal measurements were performed in only one group of compact bone in humans, due to the impossibility to treat humans with vitamin D3 metabolites. Functional relations between the angle of torsion and the torsional moment for all groups of animal body tissue were determined by measurements, and the results were used to assume the reaction of human compact bone tissue if treated by vitamin D3 metabolites.     

Model for computer simulation of bone tissue

The paper deals with the dependence of the torsional moment on the angle of the compact bone torsion in laboratory animals and humans. Based on the data for laboratory animals obtained by measurements, the data on dependence of the torsional moment and the angle of torsion were predicted for humans. The measurements were carried out in four groups of laboratory animals. One was the control group, and the other three groups were treated by various vitamin D3 metabolites. The same measurements were performed also in only one group of humans, due to the impossibility to treat humans with vitamin D3 metabolites. The functional relationship between the angle of torsion and the torsional moment for all the groups of animal bone tissue were determined by measurements, and results were used to predict the reaction of the human compact bone tissue if treated by vitamin D3 metabolites.     

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.     

On high-cycle fatigue of 316L stents

This paper deals with fatigue life prediction of 316L stainless steel cardiac stents. Stents are biomedical devices used to reopen narrowed vessels. Fatigue life is dominated by the cyclic loading due to the systolic and diastolic pressure and the design against premature mechanical failure is of extreme importance. Here, a life assessment approach based on the Dang Van high cycle fatigue criterion and on finite element analysis is applied to explore the fatigue reliability of 316L stents subjected to multiaxial fatigue loading. A finite element analysis of the stent vessel subjected to cyclic pressure is performed to carry out fluctuating stresses and strain at some critical elements of the stent where cracks or complete fracture may occur. The obtained results show that the loading path of the analysed stent subjected to a pulsatile load pressure is located in the safe region concerning infinite lifetime.     

Twist buckling of veins under torsional loading

Veins are often subjected to torsion and twisted veins can hinder and disrupt normal blood flow but their mechanical behavior under torsion is poorly understood. The objective of this study was to investigate the twist deformation and buckling behavior of veins under torsion. Twist buckling tests were performed on porcine internal jugular veins (IJVs) and human great saphenous veins (GSVs) at various axial stretch ratio and lumen pressure conditions to determine their critical buckling torques and critical buckling twist angles. The mechanical behavior under torsion was characterized using a two-fiber strain energy density function and the buckling behavior was then simulated using finite element analysis. Our results demonstrated that twist buckling occurred in all veins under excessive torque characterized by a sudden kink formation. The critical buckling torque increased significantly with increasing lumen pressure for both porcine IJV and human GSV. But lumen pressure and axial stretch had little effect on the critical twist angle. The human GSVs are stiffer than the porcine IJVs. Finite element simulations captured the buckling behavior for individual veins under simultaneous extension, inflation, and torsion with strong correlation between predicted critical buckling torques and experimental data (R² = 0.96). We conclude that veins can buckle under torsion loading and the lumen pressure significantly affects the critical buckling torque. These results improve our understanding of vein twist behavior and help identify key factors associated in the formation of twisted veins.     

Microdamage Caused by Fatigue Loading in Human Cancellous Bone: Relationship to Reductions in Bone Biomechanical Performance

Vertebral fractures associated with osteoporosis are often the result of tissue damage accumulated over time. Microscopic tissue damage (microdamage) generated in vivo is believed to be a mechanically relevant aspect of bone quality that may contribute to fracture risk. Although the presence of microdamage in bone tissue has been documented, the relationship between loading, microdamage accumulation and mechanical failure is not well understood. The aim of the current study was to determine how microdamage accumulates in human vertebral cancellous bone subjected to cyclic fatigue loading. Cancellous bone cores (n = 32) from the third lumbar vertebra of 16 donors (10 male, 6 female, age 76±8.8, mean ± SD) were subjected to compressive cyclic loading at σ/E₀ = 0.0035 (where σ is stress and E₀ is the initial Young’s modulus). Cyclic loading was suspended before failure at one of seven different amounts of loading and specimens were stained for microdamage using lead uranyl acetate. Damage volume fraction (DV/BV) varied from 0.8±0.5% (no loading) to 3.4±2.1% (fatigue-loaded to complete failure) and was linearly related to the reductions in Young’s modulus caused by fatigue loading (r² = 0.60, p<0.01). The relationship between reductions in Young’s modulus and proportion of fatigue life was nonlinear and suggests that most microdamage generation occurs late in fatigue loading, during the tertiary phase. Our results indicate that human vertebral cancellous bone tissue with a DV/BV of 1.5% is expected to have, on average, a Young’s modulus 31% lower than the same tissue without microdamage and is able to withstand 92% fewer cycles before failure than the same tissue without microdamage. Hence, even small amounts of microscopic tissue damage in human vertebral cancellous bone may have large effects on subsequent biomechanical performance.     

Region Specific Response of Intervertebral Disc Cells to Complex Dynamic Loading: An Organ Culture Study Using a Dynamic Torsion-Compression Bioreactor

The spine is routinely subjected to repetitive complex loading consisting of axial compression, torsion, flexion and extension. Mechanical loading is one of the important causes of spinal diseases, including disc herniation and disc degeneration. It is known that static and dynamic compression can lead to progressive disc degeneration, but little is known about the mechanobiology of the disc subjected to combined dynamic compression and torsion. Therefore, the purpose of this study was to compare the mechanobiology of the intervertebral disc when subjected to combined dynamic compression and axial torsion or pure dynamic compression or axial torsion using organ culture. We applied four different loading modalities [1. control: no loading (NL), 2. cyclic compression (CC), 3. cyclic torsion (CT), and 4. combined cyclic compression and torsion (CCT)] on bovine caudal disc explants using our custom made dynamic loading bioreactor for disc organ culture. Loads were applied for 8 h/day and continued for 14 days, all at a physiological magnitude and frequency. Our results provided strong evidence that complex loading induced a stronger degree of disc degeneration compared to one degree of freedom loading. In the CCT group, less than 10% nucleus pulposus (NP) cells survived the 14 days of loading, while cell viabilities were maintained above 70% in the NP of all the other three groups and in the annulus fibrosus (AF) of all the groups. Gene expression analysis revealed a strong up-regulation in matrix genes and matrix remodeling genes in the AF of the CCT group. Cell apoptotic activity and glycosaminoglycan content were also quantified but there were no statistically significant differences found. Cell morphology in the NP of the CCT was changed, as shown by histological evaluation. Our results stress the importance of complex loading on the initiation and progression of disc degeneration.     

Loading Mode Interactions in Simulations of Long Bone Cross-Sectional Adaptation

Although many bone adaptation theories have been formulated to address both trabecular and cortical adaptation, most applications have focused on trabecular adaptation. Thus far, no thorough investigations of the influence of different types of loading on predicted patterns of long bone cross-sectional adaptation have been reported. In the current study, we present a new model for long bone cross-sectional adaptation that incorporates axial, bending and torsional loading components. We found that bending moments have a strong potential to modulate cross-sectional geometry, but can produce unforseen (and unrealistic) geometric instabilities. Torsional moments have the ability to suppress these instabilities, suggesting that torsion may play a more significant role in guiding long bone development than previously recognized. Our results also call into question the concept of strict "remodeling equilibrium," suggesting that long bones do not necessarily approach a state of uniform mechanical stimulation. This modeling approach provides an additional perspective on experimental studies, and may lead to a greater understanding of the interaction between mechanics and biology in long bone adaptation.     

Loading Mode Interactions in Simulations of Long Bone Cross-Sectional Adaptation

Although many bone adaptation theories have been formulated to address both trabecular and cortical adaptation, most applications have focused on trabecular adaptation. Thus far, no thorough investigations of the influence of different types of loading on predicted patterns of long bone cross-sectional adaptation have been reported. In the current study, we present a new model for long bone cross-sectional adaptation that incorporates axial, bending and torsional loading components. We found that bending moments have a strong potential to modulate cross-sectional geometry, but can produce unforseen (and unrealistic) geometric instabilities. Torsional moments have the ability to suppress these instabilities, suggesting that torsion may play a more significant role in guiding long bone development than previously recognized. Our results also call into question the concept of strict “remodeling equilibrium,” suggesting that long bones do not necessarily approach a state of uniform mechanical stimulation. This modeling approach provides an additional perspective on experimental studies, and may lead to a greater understanding of the interaction between mechanics and biology in long bone adaptation.     

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.     

Creep contributes to the fatigue behavior of bovine trabecular bone.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.     

The influence of immune cross-reaction on phase structure in resonant solutions of a multi-strain seasonal SIR model

Resonance in seasonally forced SIR epidemiological models may lead to stable solutions in which the epidemic period is an integer multiple of the forcing period. We examine the influence of immune cross-protection and cross-enhancement on the epidemic phase relationship of resonance solutions in an annually forced two-strain SIR model. Solutions with epidemics of the two strains in-phase commonly occur for wide ranges of cross-reaction intensity. Solutions with epidemics out-of-phase are less common and limited to narrow ranges of cross-reaction intensity. This is broadly as predicted by the two natural periods of the system. The natural period corresponding to out-of-phase solutions is sensitive to changes in the cross-reaction parameter but the natural period corresponding to in-phase solutions is constant. Bifurcation analysis indicates that the stability of in-phase orbits is controlled by pitchfork and period doubling bifurcations while out-of-phase orbits may also be influenced by Andronov-Hopf bifurcations. In order to develop an intuitive understanding of the epidemiological factors governing the occurrence of different solutions we consider how the susceptible, infected and removed components of the system must interact to form a stable solution. This shows that the impact of cross-reaction is moderated by in-phase structures but amplified by out-of-phase structures. Although the average infection rate over long time periods is not affected by phase structure, this analysis indicates that in-phase epidemic patterns are likely to be more consistent and thus allow more effective health care management.     

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.     

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.     

Comparison between Different Methods for Biomechanical Assessment of Ex Vivo Fracture Callus Stiffness in Small Animal Bone Healing Studies

For ex vivo measurements of fracture callus stiffness in small animals, different test methods, such as torsion or bending tests, are established. Each method provides advantages and disadvantages, and it is still debated which of those is most sensitive to experimental conditions (i.e. specimen alignment, directional dependency, asymmetric behavior). The aim of this study was to experimentally compare six different testing methods regarding their robustness against experimental errors. Therefore, standardized specimens were created by selective laser sintering (SLS), mimicking size, directional behavior, and embedding variations of respective rat long bone specimens. For the latter, five different geometries were created which show shifted or tilted specimen alignments. The mechanical tests included three-point bending, four-point bending, cantilever bending, axial compression, constrained torsion, and unconstrained torsion. All three different bending tests showed the same principal behavior. They were highly dependent on the rotational direction of the maximum fracture callus expansion relative to the loading direction (creating experimental errors of more than 60%), however small angular deviations (<15°) were negligible. Differences in the experimental results between the bending tests originate in their respective location of maximal bending moment induction. Compared to four-point bending, three-point bending is easier to apply on small rat and mouse bones under realistic testing conditions and yields robust measurements, provided low variation of the callus shape among the tested specimens. Axial compressive testing was highly sensitive to embedding variations, and therefore cannot be recommended. Although it is experimentally difficult to realize, unconstrained torsion testing was found to be the most robust method, since it was independent of both rotational alignment and embedding uncertainties. Constrained torsional testing showed small errors (up to 16.8%, compared to corresponding alignment under unconstrained torsion) due to a parallel offset between the specimens’ axis of gravity and the torsional axis of rotation.     

The fatigue strength of compact bone in torsion

We have conducted a series of fatigue tests on samples of bovine compact bone loaded in cyclic torsion. The fatigue strength (i.e. the range of stress needed to cause failure in a given number of cycles) was found to be lower than the fatigue strength of the same material in compression by more than a factor of two. We also tested intact chicken metatarsals and found a similar reduction in strength compared to compression testing of chicken tibiae. These results were predicted using a theoretical model in which fatigue failure was assumed to be dependent on the growth of microcracks, oriented approximately parallel to the bone's longitudinal axis but having misorientation angles of up to 30 degrees. An effective stress range was derived which is a function of the normal and shear stresses, and thus of the Mode I and Mode II stress intensities experienced by the crack. These results may have important consequences for the understanding of fatigue in bone in vivo; relatively small amounts of longitudinal shear stress, which are often ignored in analysis, may contribute significantly to fatigue failures. This may shed light on the phenomenon of stress fractures and on the need for repair and adaptation in living bone.