Volume effects on fatigue life of equine cortical bone

Materials, including bone, often fail due to loading in the presence of critical flaws. The relative amount, location, and interaction of these flaws within a stressed volume of material play a role in determining the failure properties of the structure. As materials are generally imperfect, larger volumes of material have higher probabilities of containing a flaw of critical size than do smaller volumes. Thus, larger volumes tend to fail at fewer cycles compared with smaller volumes when fatigue loaded to similar stress levels. A material is said to exhibit a volume effect if its failure properties are dependent on the specimen volume. Volume effects are well documented in brittle ceramics and composites and have been proposed for bone. We hypothesized that (1) smaller volumes of cortical bone have longer fatigue lives than similarly loaded larger volumes and (2) that compared with microstructural features, specimen volume was able to explain comparable amounts of variability in fatigue life. In this investigation, waisted rectangular specimens (n=18) with nominal cross-sections of 3×4 mm and gage lengths of 10.5, 21, or 42 mm, were isolated from the mid-diaphysis of the dorsal region of equine third metacarpal bones. These specimens were subjected to uniaxial load controlled fatigue tests, with an initial strain range of 4000 microstrain. The group having the smallest volume exhibited a trend of greater log fatigue life than the larger volume groups. Each volume group exhibited a significant positive correlation between the logarithm of fatigue life and the cumulative failure probability, indicating that the data follow the two-parameter Weibull distribution. Additionally, log fatigue life was negatively correlated with log volume, supporting the hypothesis that smaller stressed volumes of cortical bone possess longer fatigue lives than similarly tested larger stressed volumes.     

Dynamic strain similarity in vertebrates; an alternative to allometric limb bone scaling

Galileo (1638) observed that "nature cannot grow a tree nor construct an animal beyond a certain size, while retaining the proportions which suffice in the case of a smaller structure". However, subsequent measurement has shown that limb bone dimensions are scaled geometrically with body size (Alexander et al., 1979a), and that the material properties of their constituent bone tissue are similar in animals over a wide range of body weight (Sedlin & Hirsch, 1966; Yamada, 1970; Burstein et al., 1972; Biewener, 1982). If, as suggested in previous scaling arguments (McMahon, 1973; Biewener, 1982), vigorous locomotion involved the same proportional forces over a wide range of animal size, this would create a paradox since large animals would be in far greater danger of skeletal failure than small ones. However, in vivo strain gauge implantations have shown that, during high speed running, axial force as a proportion of body weight (G) in the limb bones of animals decreases as a function of body size from 6.9 G in a 7 kg turkey to 2.8 G in a small (130 kg) horse. Estimates of axial force in larger animals suggest that this is further reduced to 0.8 G in a 2500 kg elephant. Nevertheless, it appears that, regardless of animal size or locomotory style, the peak stresses in the bones of these animals are remarkably similar. Therefore, throughout the range of animals considered (350 times differences in mass), we suggest that similar safety factors to failure are maintained, not by allometrically scaling bone dimensions, but rather by allometrically scaling the magnitude of the peak forces applied to them during vigorous locomotion.(ABSTRACT TRUNCATED AT 250 WORDS)     

Trabecular bone scales allometrically in mammals and birds

Many bones are supported internally by a latticework of trabeculae. Scaling of whole bone length and diameter has been extensively investigated, but scaling of the trabecular network is not well characterized. We analysed trabecular geometry in the femora of 90 terrestrial mammalian and avian species with body masses ranging from 3 g to 3400 kg. We found that bone volume fraction does not scale substantially with animal size, while trabeculae in larger animals' femora are thicker, further apart and fewer per unit volume than in smaller animals. Finite element modelling indicates that trabecular scaling does not alter the bulk stiffness of trabecular bone, but does alter strain within trabeculae under equal applied loads. Allometry of bone's trabecular tissue may contribute to the skeleton's ability to withstand load, without incurring the physiological or mechanical costs of increasing bone mass.     

An improved method to assess torsional properties of rodent long bones

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

Fatigue damage,remodeling, and the minimization of skeletal weight

The skeleton has provided many advantages during the course of vertebrate evolution, but it has also contained limitations that have strongly influenced bone biology. These limitations have included weight and the potential for fatigue failure. Calcified bone tissue is approximately twice as heavy as other tissues, so it is important to minimize the size of the skeleton, but this implies increasing bone stresses and strains and the potential for fatigue fracture. This paper first explores the role of fatigue damage removal by remodeling in extending a long bone's fatigue life to match the animal's lifetime. Next, an estimate is obtained for the amount that the cross-sectional area of a bone would have to be increased in lieu of remodeling to achieve the same extension of fatigue life, provided that the associated muscle mass remained constant. The result illustrates how remodeling can provide a gracile bone the same fatigue life as a substantially more robust bone lacking remodeling. Finally, it is shown that if muscle mass increases in linear proportion to bone mass, as experimental data suggest, extending a bone's fatigue life by increasing its cross-sectional dimensions may not be effective because the inertia of bigger bones would result in larger muscles and increased skeletal loads. Thus, bone remodeling to remove fatigue damage may be essential for the existence of relatively large, long-lived vertebrates.     

The effect of normal development and of severe undernutrition on some minor components of cortical bone

1. The amounts of calcium, magnesium, sodium and citric acid in the bones of undernourished pigs 1 year old were compared with the amounts in the bones of smaller newborn animals, normal animals of the same weight aged 4 weeks and of the same age weighing 170kg. 2. The differences that were found between 4 weeks and 1 year of age in the normal animals were expected as effects of aging. However, between birth and 4 weeks of age the changes in composition were in the opposite direction to those between 4 weeks and 1 year. 3. Undernutrition produced a bone that resembled chemically that of an animal 1 year old.     

The Effect of Naturally Occurring Chronic Kidney Disease on the Micro-Structural and Mechanical Properties of Bone

Chronic kidney disease (CKD) is a growing public health concern worldwide, and is associated with marked increase of bone fragility. Previous studies assessing the effect of CKD on bone quality were based on biopsies from human patients or on laboratory animal models. Such studies provide information of limited relevance due to the small size of the samples (biopsies) or the non-physiologic CKD syndrome studied (rodent models with artificially induced CKD). Furthermore, the type, architecture, structure and biology of the bone of rodents are remarkably different from human bones; therefore similar clinicopathologic circumstances may affect their bones differently. We describe the effects of naturally occurring CKD with features resembling human CKD on the skeleton of cats, whose bone biology, structure and composition are remarkably similar to those of humans. We show that CKD causes significant increase of resorption cavity density compared with healthy controls, as well as significantly lower cortical mineral density, cortical cross-sectional area and cortical cross-sectional thickness. Young''s modulus, yield stress, and ultimate stress of the cortical bone material were all significantly decreased in the skeleton of CKD cats. Cancellous bone was also affected, having significantly lower trabecular thickness and bone volume over total volume in CKD cats compared with controls. This study shows that naturally occurring CKD has deleterious effects on bone quality and strength. Since many similarities exist between human and feline CKD patients, including the clinicopathologic features of the syndrome and bone microarchitecture and biology, these results contribute to better understanding of bone abnormalities associated with CKD.     

Blood circulation of long bones in trained growing rats and mice.

The effect of physical training on the blood circulation of long bones was studied in growing rats and mice of NMRI-strain. The animals to be trained and their controls were about 2 weeks old at the beginning of the training. The training took place on a 5 degree inclined treadmill 5 days a week for 3 weeks in experiment I and 7 weeks in experiments II and III. The duration of the daily exercise was progressively increased over 3 weeks. The final exercise bouts were 80 min for moderate and 180 min for intensive training programs. The circulating red cell volume (ml/100 g bone) of the humeral, femoral and tibial bones of the trained animals was lower compared to the controls in all three experiments mainly due to reduced hematocrit values. The circulating blood volume (ml/100 g bone) decreased in the tibial bones of the trained animals in experiment I and showed a decreasing tendency in experiment III, but no significant differences between the groups were observed in the humeral and femoral bones. Yet, when related to the volume of the bones the circulating blood volume (ml/100 ccm bone) was significantly higher in the femoral bones of the trained animals, while the changes in the humeral bones were negligible (experiment III). The results suggest that the vascularity of long bones is affected by physical training. The varying responses in different bones are perhaps due to the amount of mechanical stress during physical activity.     

A computational assessment of the independent contribution of changes in canine trabecular bone volume fraction and microarchitecture to increased bone strength with suppression of bone turnover

This study addressed the effects of changes in trabecular microarchitecture induced by suppressed bone turnover-including changes to the remodeling space-on the trabecular bone strength-volume fraction characteristics independent of changes in tissue material properties. Twenty female beagle dogs, aged 1-2 years, were treated daily with either oral saline (n=10 control) or high doses of oral risedronate (0.5mg/kg/day, n=10 suppressed) for a period of 1 year, the latter designed (and confirmed) to substantially suppress bone turnover. High-resolution micro-CT-based finite element models (18-mum voxel size) of canine trabecular bone cores (n=2 per vertebral body) extracted from the T-10 vertebrae were analyzed in both compressive and torsional loading cases. The same tissue-level material properties were used in all models, thus providing measures of tissue-normalized strength due only to changes in the microarchitecture. Suppressed bone turnover resulted in more plate-like architecture with a thicker and more dense trabecular structure, but the relationship between the microarchitectural parameters and volume fraction was unaltered (p>0.05). Though the suppressed group had a greater tissue-normalized strength as compared to the control group (p<0.001) for both compressive and torsional loading, the relationship between tissue-normalized strength and volume fraction was not significantly altered for compression (p>0.13) or torsion (p>0.09). In this high-density, non-osteoporotic animal model, the increases in tissue-normalized strength seen with suppression of bone turnover were entirely commensurate with increases in bone volume fraction and thus, no evidence of microarchitecture-related or "stress-riser" effects which may disproportionately affect strength were found.     

Low-frequency acoustic sweep monitoring of bone integrity and osteoporosis.

We developed a noninvasive method to evaluate bone structural integrity. It is based on the measurement of the dynamic characteristics of the bone using sweeping sound excitation in the range of acoustic frequencies. The Quality Factor (a measure of material damping) has been used as an indicator of the tendency of the bone to fracture. Results of animal studies have supported this hypothesis since linear correlations were observed between bone density, quality factor, and impact strength. A vibration excitation in the form of an acoustic sweep signal is applied to a bone to measure the quality factor. Rat bones were tested, obtained from animals with osteoporosis age-dependent (tested in vitro) or ovariectomy-induced (tested in vivo), and compared with bones of healthy (control) rats. The change in damping was, on average, equal or greater to the change in density. Moreover, excellent correlation of the quality factor was obtained with bone fracture energy measured with an impact test. During a vibration cycle, the changing strain results in temperature changes due to the reciprocity of temperature and strain. Nonreversible conduction of heat due to the unequal temperature change results in entropy production that is enhanced due to the stress concentration about the voids associated with bone porosity. Damping is a measure of the production of entropy. Its measure, the quality factor, represents a potentially useful tool for monitoring bone integrity, which is deteriorating in diseases characterized by disruption of the trabecular architecture, such as osteoporosis. A computational model yielded results that are in good correlation with the experimental results.     

Correlations between rates of epiphyseal and diaphyseal elongation in the short bones of the hand

Serial annual radiographs of the hand have been used to analyze the rates of elongation of the epiphyses and diaphyses of the metacarpals and phalanges in children at ages from 3 to 13 years. The rates of elongation for many corresponding ephiphyses and diaphyses (i.e., of the same bone) are negatively correlated but to an extent that is not statistically significant for any particular bone. This tendency toward negative correlations is found for most of these bones although the correlation coefficients for most of the metacarpals are positive in each sex. Within rays, the correlation indices between the rates of elongation for corresponding epiphyses and diaphyses (i.e., of the same bone) have larger negative or smaller positive values than for those between either adjacent and non-corresponding or non-adjacent and non-corresponding epiphyses and diaphyses (i.e., not of the same bone but of either adjacent or non-adjacent bones). The communality indices for the ratio between the rates of epiphyseal and diaphyseal elongation in particular bones are more highly correlated in the girls than in the boys and within the rows than within the rays. Some implications of the tendency to negative correlations between the rates of elongation of corresponding epiphyses and diaphyses have been discussed.     

Three‐dimensional characterization of osteocyte volumes at multiple scales,and its relationship with bone biology and genome evolution in ray‐finned fishes

Osteocytes, cells embedded within the bone mineral matrix, inform on key aspects of vertebrate biology. In particular, a relationship between volumes of the osteocytes and bone growth and/or genome size has been proposed for several tetrapod lineages. However, the variation in osteocyte volume across different scales is poorly characterized and mostly relies on incomplete, two‐dimensional information. In this study, we characterize the variation of osteocyte volumes in ray‐finned fishes (Actinopterygii), a clade including more than half of modern vertebrate species in which osteocyte biology is poorly known. We use X‐ray synchrotron micro‐computed tomography (SRµCT) to achieve a three‐dimensional visualization of osteocyte lacunae and direct measurement of their size (volumes). Our specimen sample is designed to characterize variation in osteocyte lacuna morphology at three scales: within a bone, among the bones of one individual and among species. At the intra‐bone scale, we find that osteocyte lacunae vary noticeably in size between zones of organized and woven bone (being up to six times larger in woven bone), and across cyclical bone deposition. This is probably explained by differences in bone deposition rate, with larger osteocyte lacunae contained in bone that deposits faster. Osteocyte lacuna volumes vary 3.5‐fold among the bones of an individual, and this cannot readily be explained by variation in bone growth rate or other currently observable factors. Finally, we find that genome size provides the best explanation of variation in osteocyte lacuna volume among species: actinopterygian taxa with larger genomes (polyploid taxa in particular) have larger osteocyte lacunae (with a ninefold variation in median osteocyte volume being measured). Our findings corroborate previous two‐dimensional studies in tetrapods that also observed similar patterns of intra‐individual variation and found a correlation with genome size. This opens new perspectives for further studies on bone evolution, physiology and palaeogenomics in actinopterygians, and vertebrates as a whole.     

Effects of differences in mineralization on the mechanical properties of bone

There is a considerable variation in the mineralization of bone; normal, non-pathological compact bone has ash masses ranging from 45 to 85% by mass. This range of mineralization results in an even greater range of mechanical properties. The Young modulus of elasticity can range from 4 to 32 GPa, bending strength from 50 to 300 MPa, and the work of fracture from 200 to 7000 Jm-2. It is not possible for any one type of bone to have high values for all three properties. Very high values of mineralization produce high values of Young modulus but low values of work of fracture (which is a measure of fracture toughness). Rather low values of mineralization are associated with high values of work of fracture but low values of Young modulus and intermediate values of bending strength. The reason for the high value for the Young modulus associated with high mineralization is intuitively obvious, but has not yet been rigorously modelled. The low fracture toughness associated with high mineralization may be caused by the failure of various crack-stopping mechanisms that can act when the mineral crystals in bone have not coalesced, but which become ineffective when the volume fraction of mineral becomes too high. The adoption of different degrees of mineralization by different bones, leading to different sets of mechanical properties, is shown to be adaptive in most cases studied, but some puzzles still remain.     

A Fatigue-Based Model of Disuse Osteoporosis

A theoretical model has been developed for predicting the extent of bone adaptation as a function of exercise level. The model works by estimating the amount of fatigue damage which will occur for a given cyclic strain. This allowed us to predict that there would be a difference in the strengths of bones taken from sedentary individuals compared to those from more active individuals. The predicted difference, expressed as the ratio of the fatigue strengths of the two bones, was 1.53.

Experimental tests were carried out using bones from chickens, comparing those kept in battery cages (who are unable to engage in any strenuous activity) with those kept in normal free-range conditions. A finite element model was used to ensure that the in vitro fatigue tests were conducted at strain levels within the physiological range. Significant differences in both static and fatigue strength were found for the radius and tibia bones. These differences could be accurately predicted by the theoretical model, after a slight difference in weight between the two groups was allowed for. Additional evidence for these predictions can also be found in the literature. This work supports the concept that bone adaptation is driven by the need to optimise fatigue damage accumulation.     

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.     

A torsional strength comparison of vascularized and nonvascularized bone grafts

Comparisons of torsional strength are made on the ulnae from the forelegs of short haired hounds where a nonvascularized graft was performed on one leg and a vascularized graft performed on the other. By using the forelegs of a dog as the experimental model and microsurgical techniques, a vascularized bone segment was used to graft a five centimeter nonunion in one leg and at the same time a conventional bone graft was performed on a similar nonunion in the other leg. Similar segments of rib bone were used for each graft. Torsional strength data are shown for nine experimental animals. A successful method for mounting the bones for testing of torsional strength in a torsion machine is given. In each case for which the bones healed properly, the vascularized bone graft proved to be significantly stronger in torsion.     

Ontogeny and limb bone scaling in two new world marsupials,Monodelphis domestica and Didelphis virginiana

This study examines the growth of two species of marsupials who share common ancestry and are born at the same neonatal size of a little less than 1 g. Despite this similarity at birth, adult size of these two species differs by about 50 times, with the smaller species believed to be the more ancestral. We quantified the growth in the limb bones (humerus, femur, ulna, tibia, metacarpal, and metatarsal) beginning around 40 days of age until adult size was reached. Results indicate that the larger species grows at a higher rate of growth as well as for a longer period of time to reach its larger adult size. Despite these differences in growth, there were few differences observed in the scaling over time of length to width in the various limb bones that were measured. The two species, although different in their adult size and the patterns of growth, maintain the same length to width proportions in each limb bone. The biggest difference between species in scaling was observed in the bones of the hands and feet, which may suggest adaptation to size and/or locomotor performance as body size increases. Despite variation in size, these heterochronic patterns do not affect the shape among adults or over evolutionary time. J Morphol 231:117–130, 1997. © 1997 Wiley-Liss, Inc.     

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.     

Compressive axial mechanical properties of rat bone as functions of bone volume fraction,apparent density and micro-ct based mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure–function properties of the skeleton. With recent advances in computing power of personal computers, virtual alternatives to mechanical testing are gaining acceptance and use. We have previously introduced such a technique called structural rigidity analysis to assess mechanical strength of skeletal tissue with defects. The application of this technique is predicated upon the use of relationships defining the strength of bone as a function of its density for a given loading mode. We are to apply this technique in rat models to assess their compressive skeletal response subjected to a host of biological and pharmaceutical stimulations. Therefore, the aim of this study is to derive a relationship expressing axial compressive mechanical properties of rat cortical and cancellous bone as a function of equivalent bone mineral density, bone volume fraction or apparent density over a range of normal and pathologic bones.We used bones from normal, ovariectomized and partially nephrectomized animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial compression to failure.We obtained univariate relationships describing 71–78% of the mechanical properties of rat cortical and cancellous bone based on equivalent mineral density, bone volume fraction or apparent density over a wide range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity analysis introduced by the authors to provide a non-invasive method to assess the compressive strength of bones affected by pathology and/or treatment options.     

Diametral compression of non-circular diaphyseal bone sections

Many research endeavors involve strength testing of long bones, frequently using whole-bone four-point bending models. Recently, diametral compression of short sections has been used to quantify local mechanical parameters and effects of treatment, but testing of biologically derived samples entails a number of added complications, such as the non-circularity of bone sections, ambiguity of load orientation during testing, thickness variation in a section, and size and shape variation between sections in a single sample. In order to quantify the effects of these confounding factors, finite element diametral compression models of a number of bone sections were compared with simplified circular and elliptical sections. Each anatomic section was tested in all rotationally stable load configurations. A high degree of correlation was observed between the anatomic sections and their circular and elliptic analogs, indicating that meaningful comparisons may be made between bone sections of disparate geometry. The aspect ratio and shape of the bone sections did not have a significant impact on the maximum in-plane principal stresses, whereas stresses were strongly dependant on the mean thickness and spatial thickness variation. Some variation due to load orientation was observed. These results indicate that diametral ring compression testing of anatomic sections can be used effectively to measure structural and material parameters of long bones, and that anatomic variation can be successfully accommodated. The ability to use diametral compression testing should allow researchers to obtain many more samples from each specimen than whole-bone bending without the difficulty of extracting solid core or dog-bone samples.