The thickness of the walls of tubular bones

Some bones have slender marrow cavities and relatively thick walls. Others have wide cavities and thinner walls. Such differences are described by a quantity K , the ratio of the internal to the external diameter. A theoretical analysis shows that the optimum value of K , which allows the mass of a bone to be minimized, depends on whether the bone is selected principally for yield or fatigue strength, for ultimate strength, for impact strength or for stiffness. It also depends on whether the cavity is filled with marrow or with gas. The values of K found in the limb bones of mammals, birds and a few reptiles are surveyed, and compared to the theoretical optima.     

Wall thickness of gas- and marrow-filled avian long bones: measurements on humeri, femora and tibiotarsi in crows (Corvus corone cornix) and magpies (Pica pica)

We studied how the ratio K of the internal to external diameter of gas- and marrow-filled avian long bones follows the biomechanical optima derived for tubular bones with minimum mass designed to fulfil various mechanical requirements. We evaluated radiographs of numerous humeri, femora and tibiotarsi in Corvus corone cornix and Pica pica. The K-values of the gas-filled humerus (K=0.78+/-0.03) and the marrow-filled femur (K=0.79+/-0.02) in Corvus are practically the same, while K of the marrow-filled tibiotarsus (K=0.71+/-0.04) is significantly smaller. The same is true for the gas-filled humerus (K=0.78+/-0.02) and the marrow-filled femur (K=0.77+/-0.02) and tibiotarsus (K=0.67+/-0.05) in Pica. K in Corvus is slightly larger than K in Pica, but the differences are statistically not significant. The standard deviation DeltaK of the tibiotarsi (DeltaK=0.04-0.05) is approximately two times as large as that of the humeri (DeltaK=0.02-0.03) and femora (DeltaK=0.02) in both species. Accepting the assumption of earlier authors that the ratio Q of the marrow to bone density is 0.5, our data show that the marrow-filled tibiotarsi of Corvus and Pica are optimized for stiffness, while the marrow-filled femora are far from any optimum. The relative wall thickness W=1-K of the gas-filled avian humeri studied is much larger than the theoretical optimum W*=1-K*=0.07, and thus these bones are thicker-walled than the optimal gas-filled tubular bone with minimum mass.     

Gender specific LRP5 influences on trabecular bone structure and strength

A mutation in LRP5 (low-density lipoprotein receptor-related protein 5) has been shown to increase bone mass and density in humans and animals. Transgenic mice expressing the LRP5 mutation (G171V) demonstrate an increase in bone mass as compared to non-transgenic (NTG) littermates. This study evaluated LRP5 gene and gender-related influences on the structural and biomechanical strength properties of trabecular and cortical bone in femurs and vertebrae (L5) of 17-week-old mice. Micro-computed tomography was used to evaluate the trabecular bone structure of distal femurs and vertebrae ex vivo. Mechanical testing of the trabecular bone in the distal femur was done to determine biomechanical strength. Differences due to genotype and gender were tested using two-way ANOVA at a significance level of p<0.05. Trabecular bone structural parameters (BV/TV, trabecular thickness, number, etc.) at the distal femur, femoral neck, and vertebral body sites were greater in the transgenic as compared to the NTG mice. In addition, vertebral cortical thickness and trabecular strength parameters (ultimate and yield loads, stiffness, ultimate and yield stresses) in the distal femur were greater in the transgenic mice as compared to NTG. The increasing trends of cortical thickness were also noted in the transgenic mice as compared to NTG. Within LRP5 (G171V) mutant mice, there were significant gender-related differences in some of the trabecular bone structural parameters at all the sites (distal femur, femoral neck, and vertebral body). However, unlike trabecular structural parameters, the gender-specific differences were not found in the trabecular strength of LRP5 transgenic mice. In summary, these findings suggest that the LRP5 (G171V) mutation results in greater trabecular bone structure and strength at both the distal femurs and vertebral bodies as compared to NTG. In addition, only the trabecular structure parameters were affected by gender within the LRP5 (G171V) mutation.     

Effects of tissue preservation on murine bone mechanical properties

Murine bone specimens are used extensively in skeletal research to assess the effects of environmental, physiologic and pathologic factors on their mechanical properties. Given the destructive nature of mechanical testing, it is normally performed as a terminal procedure, where specimens must be preserved without affecting their mechanical properties. To this end, we aimed to study the effects of tissue preservation (freezing and formalin fixation) on the elastic and viscoelastic mechanical properties of murine femur and vertebrae. A total of 120 femurs and 180 vertebral bodies (L3–L5) underwent non-destructive cyclic loading to assess their viscoelastic properties followed by mono-cyclic loading to failure to assess their elastic properties. All specimens underwent re-hydration in 0.9% saline for 30 min prior to mechanical testing. Analysis indicated that stiffness, modulus of elasticity, yield load, yield strength, ultimate load and ultimate strength of frozen and formalin-fixed femurs and vertebrae were not different from fresh specimens. Cyclic loading of both femurs and vertebrae indicated that loss, storage and dynamic moduli were not affected by freezing. However, formalin fixation altered their viscoelastic properties. Our findings suggest that freezing and formalin fixation over a 2-week period do not alter the elastic mechanical properties of murine femurs and vertebrae, provided that specimens are re-hydrated for at least half an hour prior to testing. However, formalin fixation weakened the viscoelastic properties of murine bone by reducing its ability to dissipate viscous energy. Future studies should address the long-term effects of both formalin fixation and freezing on the mechanical properties of murine bone.     

Quantitative trait loci for tibial bone strength in C57BL/6J and C3H/HeJ inbred strains of mice

Three-point bending technology has been widely used in the measurement of bone strength. Quantitative trait loci (QTLs) for bone strength have been identified using mouse femurs. In this study, we investigate the use of mouse tibiae in identification of QTLs that regulate bone strength. Mouse tibiae were from a F₂ population derived from C57BL/6J (B6) and C3H/HeJ (C3H). Three-point bending was measured using ISO 4049, with the support width adjustable to accommodate specimen sizes outside the scope of ISO 4049. The strain rate is selectable from 0.05 to 500 mm per min. All stress strain diagrams are recorded and retrieved in digital electronic form. Genome scan was performed in The Jackson Laboratory (TJL). QTL mapping was conducted using Map Manager QTX software. Data show that (i) both elastic modulus (stiffness) and maximum loading (strength) value appear as normal distributions, suggesting that multiple genetic factors control the bone strength; (ii) 11 QTLs, accounting for 90% of variation for strength, have been detected. More than half QTLs of three-point bending are located on the same locations of bone density earlier identified from mouse femurs; (iii) a major QTL of femoral and vertebral bone mineral density (BMD) was not detected for bone strength of tibiae; (iv) the QTL on chromosome 4 has extremely high LOD score of 31.8 and represents 60% of the variation of bone strength; and (v) four QTLs of stiffness (chromosomes 2, 11, 15 and 19) have been identified.     

Scaling effects in the fatigue strength of bones from different animals

The bones of vertebrates are all made from the same basic material, despite a huge variation in size from one species to another. This introduces a problem: large structures are more prone to fatigue failure (stress fracture) than smaller structures made of the same material. This implies that bones in larger animals cannot withstand as much stress in daily use as bones in smaller animals. In fact, this is not the case, because all bones experience approximately the same stresses and strains in use. This implies a variation in the underlying material: bone material in large animals must have superior fatigue properties to offset the disadvantages of size. This hypothesis is tested here by reference to fatigue data from the literature, taken from a range of animals from cows to mice. Fatigue strength was plotted as a function of stressed volume and modelled mathematically using a Weibull distribution. This shows a general tendency for fatigue strength to reduce as volume increases. But when the volume effect is taken into account, there remains a tendency for bones from smaller animals to have lower fatigue strength. This can be modelled by a simple variation in one of the parameters in the Weibull equation, which defines the intrinsic fatigue strength of the material. When extrapolated to the size of the whole bone for each animal, all bones were found to have the same fatigue strength. This resolves the anomaly and implies a complex system in which the underlying structure of bone varies with animal size in order to cancel out scaling effects.     

Type I collagen mutation alters the strength and fatigue behavior of Mov13 cortical tissue

Despite advances in understanding the molecular basis of Osteogenesis Imperfecta, the mechanisms by which type I collagen mutations compromise whole bone function are not well understood. Previously, we have shown that a heterozygous type I collagen mutation is associated with increased brittleness of long bones from Mov13 transgenic mice, a model of the mild form of Osteogenesis Imperfecta. In the current study, we investigated tissue-level damage processes by testing the hypothesis that the fatigue properties of Mov13 tissue were significantly compromised relative to littermate controls. We also quantified tissue structure and mineral content to explain variations in the fatigue behavior. Micro-beam specimens were machined from the anterior and posterior quadrants of Mov13 and control femurs and subjected to cyclic bending at one of four stress levels. Mov13 tissue exhibited a 22–25% reduction in tissue bending strength and a similar reductions in fatigue life and the stress level at which damage was apparent. These results provided tissue-level evidence that damage accumulation mechanisms were significantly compromised in Mov13 cortical tissue. Given that significant alterations in tissue structure were observed in Mov13 femurs, the results of this study support the idea that Mov13 femurs were brittle because alterations in tissue structure associated with the mutation interfered with normal damage processes. These results provide new insight into the pathogenesis of Osteogenesis Imperfecta and are consistent with bone behaving as a damaging composite material, where damage accumulation is central to bone fracture.     

Femoral Strength after Induced Lesions in Rats (Rattus norvegicus)

Rats are a common model for the study of bone healing, with the cranium, femur, and tibia being the bones studied most frequently. This study examines noncritical-sized lesions that would allow rats to continue to bear weight without the need for fixation but that are sufficiently large to enable characterization of the healing process. We compared the femoral bone strength associated with 3 lesion sizes selected for use in future studies. Sprague–Dawley rats (age, 10 to 16 wk) were used to assess the ultimate breaking strength, stress, and break force of normal, unmanipulated femurs. We then created lesions of 3 different sizes in the mid- to distal diaphysis of the left and right femurs and characterized the associated decreases in bone strength. Femurs (n= 85) for this study were collected through tissue sharing from rats used in other acute surgical procedures and were tested by using a 3-point bending flexural materials-testing machine. Our hypothesis was that, as a model for bone healing, 3 induced lesions of different sizes would show incremental and proportional decreases in femoral strength, with the intermediate-sized (1.5-mm) lesion demonstrating a decrease of 20% to 40%. A lesion of 1.5 mm yielded a decrease in strength of 17% for both the left and right femurs. The strength of left femurs carrying intermediate lesions was significantly less than that of control, uninjured femur bones. In addition to providing validation for our own future bone-healing project, these data are a useful baseline for other investigators studying bone healing in a rat femur model.Rodents, particularly rats, represent a reliable and affordable model for conducting basic research involving the skeleton.² Although biomechanical techniques for testing bone strength have been well documented, few studies define the theory, methods, and experimental procedures for evaluating the fracture toughness of bone (fracture resistance), especially whole-bone testing in small animals.¹⁰ This said, femurs are still the ideal rat and mouse bones to use to evaluate the fracture toughness properties in small-animal model studies.^4,10 Bending tests are useful to assess the mechanical properties of bones from rodents and other small animals.¹⁵ Even though this method of testing is referred to as a ‘bending test,’ the material (in this case, bone) is actually fractured to assess fracture toughness or breaking. For bending tests, long bones are loaded mainly in bending or compression during normal movement of the animals and are subject to both intrinsic and extrinsic large bending forces.^4,14 In rodents, locomotion results in alternating tension and compression on the cortex of weight-supporting bones during the gait cycle, with no limit on the magnitude or direction in which these forces can be exerted.⁸ This makes testing of bending, compression, torsion or any combination of methods potentially applicable. Therefore we chose to conduct 3-point bending testing on rat femurs. Bones were stressed to the point of fracture and the values required were recorded for computer-assisted analysis.In the testing of bone, the fundamental structural properties of greatest importance are stiffness, strength, and toughness.^8,10 Measured and calculated values of importance are peak force (ultimate breaking strength), fatigue resistance, stress, strain, break force, and energy to break. We chose to collect and compare peak force (measured data) as well as stress and break force (both calculated data). We made these choices because the most important biomechanical property from a clinical point of view is the peak force, which corresponds to the ability of a patient''s leg to resist high loading before a fracture or irreversible deformation occurs.Strength can be tested as tension, compression, bending, or shear.^8,10 Strength as a material parameter is defined as the ultimate stress at which failure occurs, but strength is defined structurally as the ultimate load (or force) when failure of the system occurs.⁸ In the current study, we tested the strength of rat femurs via 3-point bending. We hypothesized that the 1.5-mm lesion, which involved 39% of the bone circumference, would yield a 20% to 40% decrease in strength. In addition, the femurs with induced lesions showed a consistent decrease in strength, with larger lesions associated with lower peak force on both the right and left sides.     

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.     

Relationship Between Structure and Mechanical Function of the Tissues of the Intervertebral Joint

This paper reviews our current understanding of the relationshipbetween the structures and properties of the tissues of thespine and their mechanical functions. Emphasis is on the humanlumbar spine. Vertebrae consist of a core of cancellous bone(low density) surrounded by a shell of cortical bone (high stiffness);as a result they have high stiffness but low mass. The intervertebraldisc is able to withstand compression because of the swellingpressure exerted by the nucleus pulposus which is constrained,radially, by the annulus fibrosus. Thus the disc acts as a thick-walledpressure vessel. Collagen fibers within the annulus providereinforcement during compression, bending and torsion of thedisc. Collagen fibers also provide tensile reinforcement andprevent tears spreading across ligaments. The ligamenta flavacontain elastic fibers (low stiffness and low strength) withcollagen fibers (high stiffness and high strength). In the unstretchedligamenta flava, the collagen fibers have almost random orientationsbut they become aligned as the ligament is stretched. This structureenables the high extensibility of elastic fibers to be exploitedbut protects them from damage at high strains. The structureof the interspinous ligament suggests that its main functionis to attach the thoracolumbar fascia to the posterior spine.Thus the fascia is maintained in tension when stretched by theabdominal muscles. This and other observations indicate theimportance of muscles for maintaining the stability of the spinalcolumn.     

Femoral strength is better predicted by finite element models than QCT and DXA.

Clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in-vivo were available. A group of 51 human femurs (age range 21-93; 23 females, 28 males) were evaluated for bone density and geometry using quantitative computed tomography (QCT) and dual energy X-ray absorptiometry (DXA). Regional bone density and dimensions obtained from QCT and DXA were used to develop statistical models to predict femoral strength ex vivo. The QCT data also formed the basis of a three-dimensional finite element (FE) models to predict structural stiffness. The femurs were separated into two groups; a model training set (n = 25) was used to develop statistical models to predict ultimate load, and a test set (n = 26) was used to validate these models. The main goal of this study was to test the ability of DXA, QCT and FE techniques to predict fracture load non-invasively, in a simple load configuration which produces predominantly femoral neck fractures. The load configuration simulated the single stance phase portion of normal gait; in 87% of the specimens, clinical appearing sub-capital fractures were produced. The training/test study design provided a tool to validate that the predictive models were reliable when used on specimens with "unknown" strength characteristics. The FE method explained at least 20% more of the variance in strength than the DXA models. Planned refinements of the FE technique are expected to further improve these results. Three-dimensional FE models are a promising method for predicting fracture load, and may be useful in monitoring strength changes in vivo.     

The influence of water removal on the strength and toughness of cortical bone

Although the effects of dehydration on the mechanical behavior of cortical bone are known, the underlying mechanisms for such effects are not clear. We hypothesize that the interactions of water with the collagen and mineral phases each have a unique influence on mechanical behavior. To study this, strength, toughness, and stiffness were measured with three-point bend specimens made from the mid-diaphysis of human cadaveric femurs and divided into six test groups: control (hydrated), drying in a vacuum oven at room temperature (21 degrees C) for 30 min and at 21, 50, 70, or 110 degrees C for 4 h. The experimental data indicated that water loss significantly increased with each increase in drying condition. Bone strength increased with a 5% loss of water by weight, which was caused by drying at 21 degrees C for 4 h. With water loss exceeding 9%, caused by higher drying temperatures (> or =70 degrees C), strength actually decreased. Drying at 21 degrees C (irrespective of time in vacuum) significantly decreased bone toughness through a loss of plasticity. However, drying at 70 degrees C and above caused toughness to decrease through decreases in strength and fracture strain. Stiffness linearly increased with an increase in water loss. From an energy perspective, the water-mineral interaction is removed at higher temperatures than the water-collagen interaction. Therefore, we speculate that loss of water in the collagen phase decreases the toughness of bone, whereas loss of water associated with the mineral phase decreases both bone strength and toughness.     

The Relationship Between Lesion Size and Load to Failure After Stabilization of Simulated Metastatic Lesions of the Proximal Femur

BackgroundAs overall cancer survival continues to improve, the incidence of metastatic lesions to the bone continues to increase. The subsequent skeletal related events that can occur with osseous metastasis can be debilitating. Complete and impending pathologic femur fractures are common with patients often requiring operative fixation. However, the efficacy of an intramedullary nail construct, on providing stability, continue to be debated. Therefore, the purpose of this study was to utilize a synthetic femur model to determine 1) how proximal femur defect size and cortical breach impact femur load to failure (strength) and stiffness, and 2) and how the utilization of an IMN, in a prophylactic fashion, subsequently alters the overall strength and stiffness of the proximal femur.MethodsA total of 21 synthetic femur models were divided into four groups: 1) intact (no defect), 2) 2 cm defect, 3) 2.5 cm defect, and 4) 4 cm defect. An IMN was inserted in half of the femur specimens that had a defect present. This procedure was performed using standard antegrade technique. Specimens were mechanically tested in offset torsion. Force-displacement curves were utilized to determine each constructs load to failure and overall torsional stiffness. The ultimate load to failure and construct stiffness of the synthetic femurs with defects were compared to the intact synthetic femur, while the femurs with the placement of the IMN were directly compared to the synthetic femurs with matching defect size.ResultsThe size of the defect invertedly correlated with the load the failure and overall stiffness. There was no difference in load to failure or overall stiffness when comparing intact models with no defect and the 2 cm defect group (p=0.98, p=0.43). The 2.5 cm, and 4.5 cm defect groups demonstrated significant difference in both load to failure and overall stiffness when compared to intact models with results demonstrating 1313 N (95% CI: 874-1752 N; p<0.001) and 104 N/mm (95% CI: 98-110 N/mm; p=0.03) in the 2.5 cm defect models, and 512 N (95% CI: 390-634 N, p<0.001) and 21 N/mm (95% CI: 9-33 N/mm, p<0.001) in the models with a 4 cm defect. Compared to the groups with defects, the placement an IMN increased overall stiffness in the 2.5 cm defect group (125 N/mm; 95% CI:114-136 N/mm; p=0.003), but not load to failure (p=0.91). In the 4 cm defect group, there was a significant increase in load to failure (1067 N; 95% CI: 835-1300 N; p=0.002) and overall stiffness (57 N/mm; 95% CI:46-69 N/mm; p=0.001).ConclusionProphylactic IMN fixation significantly improved failure load and overall stiffness in the group with the largest cortical defects, but still demonstrated a failure loads less than 50% of the intact model. This investigation suggests that a cortical breach causes a loss of strength that is not completely restored by intramedullary fixation. Level of Evidence: II     

Development of a parametric finite element model of the proximal femur using statistical shape and density modelling

Skeletal fractures associated with bone mass loss are a major clinical problem and economic burden, and lead to significant morbidity and mortality in the ageing population. Clinical image-based measures of bone mass show only moderate correlative strength with bone strength. However, engineering models derived from clinical image data predict bone strength with significantly greater accuracy. Currently, image-based finite element (FE) models are time consuming to construct and are non-parametric. The goal of this study was to develop a parametric proximal femur FE model based on a statistical shape and density model (SSDM) derived from clinical image data. A small number of independent SSDM parameters described the shape and bone density distribution of a set of cadaver femurs and captured the variability affecting proximal femur FE strength predictions. Finally, a three-dimensional FE model of an 'unknown' femur was reconstructed from the SSDM with an average spatial error of 0.016 mm and an average bone density error of 0.037 g/cm(3).     

The relationship between whole bone stiffness and strength is age and sex dependent

Accurately estimating whole bone strength is critical for identifying individuals that may benefit from prophylactic treatments aimed at reducing fracture risk. Strength is often estimated from stiffness, but it is not known whether the relationship between stiffness and strength varies with age and sex. Cadaveric proximal femurs (44 Male: 18–78 years; 40 Female: 24–95 years) and radial (36 Male: 18–89 years; 19 Female: 24–95 years) and femoral diaphyses (34 Male: 18–89 years; 19 Female: 24–95 years) were loaded to failure to evaluate how the stiffness-strength relationship varies with age and sex. Strength correlated significantly with stiffness at all sites and for both sexes, as expected. However, females exhibited significantly less strength for the proximal femur (58% difference, p < 0.001). Multivariate regressions revealed that stiffness, age and PYD were significant negative independent predictors of strength for the proximal femur (Age: M: p = 0.005, F: p < 0.001, PYD: M: p = 0.022, F: p = 0.025), radial diaphysis (Age: M = 0.055, PYD: F = 0.024), and femoral diaphysis (Age: M: p = 0.014, F: p = 0.097, PYD: M: p = 0.003, F: p = 0.091). These results indicated that older bones tended to be significantly weaker for a given stiffness than younger bones. These results suggested that human bones exhibit diminishing strength relative to stiffness with aging and with decreasing PYD. Incorporating these age- and sex-specific factors may help to improve the accuracy of strength estimates.     

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.     

Bone density and the lightweight skeletons of birds

The skeletons of birds are universally described as lightweight as a result of selection for minimizing the energy required for flight. From a functional perspective, the weight (mass) of an animal relative to its lift-generating surfaces is a key determinant of the metabolic cost of flight. The evolution of birds has been characterized by many weight-saving adaptations that are reflected in bone shape, many of which strengthen and stiffen the skeleton. Although largely unstudied in birds, the material properties of bone tissue can also contribute to bone strength and stiffness. In this study, I calculated the density of the cranium, humerus and femur in passerine birds, rodents and bats by measuring bone mass and volume using helium displacement. I found that, on average, these bones are densest in birds, followed closely by bats. As bone density increases, so do bone stiffness and strength. Both of these optimization criteria are used in the design of strong and stiff, but lightweight, manmade airframes. By analogy, increased bone density in birds and bats may reflect adaptations for maximizing bone strength and stiffness while minimizing bone mass and volume. These data suggest that both bone shape and the material properties of bone tissue have played important roles in the evolution of flight. They also reconcile the conundrum of how bird skeletons can appear to be thin and delicate, yet contribute just as much to total body mass as do the skeletons of terrestrial mammals.     

High-impact exercise strengthens bone in osteopenic ovariectomized rats with the same outcome as Sham rats.

The effect of jump exercise on middle-aged osteopenic rats was investigated. Forty-two 9-mo-old female rats were either sham-operated (Sham) or ovariectomized (OVX). Three months after surgery, the rats were divided into the following groups: Sham sedentary, Sham exercised, OVX sedentary, and OVX exercised. Rats in the exercise groups jumped 10 times/day, 5 days/wk, for 8 wk, with a jumping height of 40 cm. Less than 1 min was required for the jump training. After the experiment, the right tibia and femur were dissected, and blood was obtained from each rat. OVX rats were observed to have increased body weights and decreased bone mass in their tibiae and femurs. Jump-exercised rats, on the other hand, had significantly increased tibial bone mass, strength, and cortical areas. The bone mass and strength of OVX exercised rats increased to approximately the same extent as Sham exercised rats, despite estrogen deficiency or osteopenia. Our data suggest that jump exercise has beneficial effects on lower limb bone mass, strength, bone mineral density, and morphometry in middle-aged osteopenic rats, as well as in Sham rats.     

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

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

Purification of recombinant enhanced green fluorescent protein expressed in Escherichia coli with new immobilized metal ion affinity magnetic absorbents

A new immobilized metal ion affinity (IMA) adsorbent containing superparamagnetic nanoparticles and coated with hydrophilic resins are proposed here to improve the purification of His-tagged proteins. The magnetic chelating resin was prepared by radical polymerization of magnetite (Fe3O4), styrene, divinyl benzene (DVB) and glycidyl methacrylate-iminodiacetic acid (GMA-IDA) in ethanol/water medium. IDA is immobilized on magnetite as a ligand and pre-charged Cu2+, Zn2+ and Ni2+ as metal ions. To identify the GMA-IDA magnetic particles easily, we named these particles MPGI. The MPGI adsorbent was used to test their suitability for the direct recovery of an intracellular, polyhistidine-tagged protein, enhanced green fluorescent protein [EGFP-(His)(6)], from Escherichia coli lysates in a single step. Parameters influencing the purification efficiencies such as pH, ionic strength and imidazole concentration were optimized to achieve improved separation. The optimal selectively was observed in binding buffer (0.2M NaCl, 0.02M imidazole), washing buffer (0.4M NaCl, 0.03 M imidazole) and elution buffer (0.50M imidazole). The Cu2+-charged MPGI adsorbent had the highest yield and purification factor at 70.4% and 12.3, respectively. The calculated isotherm parameters (Q(m)=53.5 mg/g, K(d)=5.84 mg/mL and Q(m)/K(d)=9.2 mL/g) indicated that the MPGI adsorbent could be used as a suitable adsorbent for EGFP from an aqueous solution.