Strain rate dependence of work of fracture tests on bone and similar tissues: Reflections on testing methods and mineral content effects.

This paper is concerned with the effect of different strain rate on the Work of Fracture (Wf) of various vertebrate mineralised tissues, controlling for the effect of mineral content and Young's modulus of elasticity. Using specimens of uniform shape and size values for the Work of Fracture of specimens tested at various deformation rates, and also the energy absorbed by notched specimens in impact, are reported. The results indicated that, of those tested, for most bone specimens the Work of Fracture measurements were constant like in the case for a 'material property'. Variations due to loading conditions (deformation rate) were small, with the exemption of antler, which is relatively poorly mineralised and in which the Work of Fracture values increased by a factor of 4 across the range from quasistatic loading to impact. The Tattersall and Tappin (1966) test has shown itself to offer some great advantages: if the quest is for a fracture toughness test for an unknown tissue it offers reliability, it is perhaps more forgiving to handling errors, it also suffers less of the influence of strain rate effects and uses relatively simple instrumentation. It is also able to demonstrate the remarkable toughness of antler bone which other more commonly used fracture toughness methods cannot do.

Does nutrition affect bone porosity and mineral tissue distribution in deer antlers? The relationship between histology, mechanical properties and mineral composition.

It is well known that porosity has an inverse relationship with the mechanical properties of bones. We examined cortical and trabecular porosity of antlers, and mineral composition, thickness and mechanical properties in the cortical wall. Samples belonged to two deer populations: a captive population of an experimental farm having a high quality diet, and a free-ranging population feeding on plants of lower nutritive quality. As shown for minerals and mechanical properties in previous studies by our group, cortical and trabecular porosity increased from the base distally. Cortical porosity was always caused by the presence of incomplete primary osteons. Porosity increased along the length of the antler much more in deer with lower quality diet. Despite cortical porosity being inversely related to mechanical properties and positively with K, Zn and other minerals indicating physiological effort, it was these minerals and not porosity that statistically better explained variability in mechanical properties. Histochemistry showed that the reason for this is that Zn is located around incomplete osteons and also in complete osteons that were still mineralizing, whereas K is located in non-osteonal bone, which constitutes a greater proportion of bone where osteons are incompletely mineralized. This suggests that, K, Zn and other minerals indicate reduction in mechanical performance even with little porosity. If a similar process occurred in internal bones, K, Zn and other minerals in the bone may be an early indicator of decrease in mechanical properties and future osteoporosis. In conclusion, porosity is related to diet and physiological effort in deer.

The canine baculum: the structure and mechanical properties of an unusual bone.

The baculum is an extraskeletal bone located in the penis of a few species in several orders of mammals such as carnivores, insectivores, rodents, bats and primates. This study aims to describe the structure, architecture and mechanical properties of the canine baculum. To this end canine bacula from castrated and uncastrated dogs were collected and examined by light microscopy, micro-computed tomography (microCT) scanning, histological staining, and mechanical testing. Their mineral density and mechanical properties were compared with those of a typical skeletal bone (the radius) in the same dog. Furthermore, a numerical model of a representative baculum was created and its mechanical performance analyzed using the finite element method, in order to try to elucidate its function. Examination of light microscopy images of transverse sections shows that the baculum consists of a typical sandwich structure, with two cortical plates separated, and joined, by loose cancellous bone. MicroCT scans reveal that the mineral density is lower in the baculum than in the radius, both in castrated as well as in uncastrated dogs, resulting in much lower stiffness. Castration was found to decrease the mineral density in both the baculum and the radius. The most likely function of the baculum of the dog is to stiffen the penis to assist intromission, and its much lower mineral density compared to that of the radius may be a mechanism designed to decrease the stiffness somewhat, and thus reduce the risk of fracture during copulation.

Do drastic weather effects on diet influence changes in chemical composition, mechanical properties and structure in deer antlers?

We attempted to determine why after an exceptionally hard winter deer antlers fractured more often than usual. We assessed mechanical properties, structural variables and mineral composition of deer antlers grown in a game estate (LM) after freezing temperatures (late winter frosts, LWF), which resulted in high incidence of antler fractures despite being grown later in the year, and those grown after a standard winter (SW). Within each year, specimens from broken and intact antlers were assessed. LWF was associated with reduced impact energy (U) and somewhat reduced work to peak force (W), Young's modulus (E) and physical density, as well as cortical thickness. LWF was associated with considerably increased Si and reduced Na. In each year, broken antlers had lower Mn, P and physical density, and they had more Na and B than unbroken antlers. Because no such effect was found in farmed deer fed whole meal, and because freezing in plants usually produces an increase in Si content, which in turn reduces Mn, it is likely that LWF produced a diet rich in Si and low in Mn. Because antlers are grown transferring calcium phosphate from the own skeleton and Ca/P levels were slightly reduced, it seems likely that Mn reduction may have increased antler fractures. A comparison between farm deer and those in another game estate (LI) also shows a link between lower Mn content and lower W. Thus, small changes in minor bone minerals, probably induced by diet, may have marked effects in mechanical properties of bone.

Mechanical properties and adaptations of some less familiar bony tissues.

This review attempts to show the bone community that there are many ways of being a 'bone', and that the range of mechanical properties of bone material is much greater than is conventionally thought to be the case. However the structure-function relationships have in many cases hardly moved beyond mere assertion. There is a pressing need for an examination of some material properties of a whole variety of bones, always using exactly the same testing method, for instance nanoindentation of wet material, so that firm comparisons can be made.

The mechanical properties of red deer antler bone when used in fighting.

We assessed the hydration state of antlers and its effect on antler mechanical properties compared with wet femur. Red deer antlers were removed from the head at various times, from a few days after velvet shedding till late in the season, and weighed weekly until after casting time. Antlers cut just after losing their velvet lost weight rapidly in the first few weeks, then settled down and changed weight very little, the latter changes correlating with air relative humidity. Antlers cut later showed little weight change at any time. The water content of cortical and trabecular parts of the contralateral antler was assessed after cutting. Most of the weight loss was from the cancellous, not the cortical, part of the antler. Wet and dry specimens from the antlers, and wet specimens from deer femora, were tested mechanically. Compared with wet bone, wet antler had a much lower modulus of elasticity and bending strength, but a higher work to fracture. Compared with wet bone, dry antler showed a somewhat lower Young's modulus, but a considerably higher bending strength and a much higher work to fracture. The impact energy absorption of dry antler was much greater than that of wet bone. In red deer, the antler is effectively dry during its use in fights, at least in southern Spain. In addition, dry antler, compared with ordinary bone, shows mechanical properties that suit it admirably for its fighting function.

Influence of physiological effort of growth and chemical composition on antler bone mechanical properties.

Antler is a good model to study bone biology both because it is accessible and because it grows and is shed every year. Previous studies have shown that chemical composition changes as the antler is grown, implying constraints in mineral availability and the physiological effort made to grow it. This study aimed at examining antler mechanical properties to assess whether they reflect physiological effort and whether they are associated with precise mineral bone composition rather than just ash content, which is usually the main factor affecting mechanical properties. We examined Young's modulus of elasticity (E), strength, and work to maximum load, as well as bone mineral composition, along the antler shaft. Then we compared trends between antlers from two populations: captive, well-fed, health-managed deer (n=15), and free-ranging deer with lower food quality and no health treatment (n=10). Greater E, strength and work were found for better fed and health managed deer. In addition, antler chemical composition of both populations differed in Na, Mg, K, Fe and Si, and marginally in Zn, but not in ash or Ca content. Significant and clear divergent trends in mechanical properties supporting greater physiological exhaustion in free-ranging deer were found for all mechanical variables. Detailed models showed that, in addition to ash content, independent factors extracted from principal component analyses on composition affected E and strength, but not work to maximum load. The results suggest that there is an association between bone chemical composition and mechanical properties independently of ash content.

Anisotropic Poisson's ratio and compression modulus of cortical bone determined by speckle interferometry.

Young's modulus and Poisson's ratios of 6mm-sized cubes of equine cortical bone were measured in compression using a micro-mechanical loading device. Surface displacements were determined by electronic speckle pattern-correlation interferometry. This method allows for non-destructive testing of very small samples in water. Analyses of standard materials showed that the method is accurate and precise for determining both Young's modulus and Poisson's ratio. Material properties were determined concurrently in three orthogonal anatomic directions (axial, radial and transverse). Young's modulus values were found to be anisotropic and consistent with values of equine cortical bone reported in the literature. Poisson's ratios were also found to be anisotropic, but lower than those previously reported. Poisson's ratios for the radial-transverse and transverse-radial directions were 0.15+/-0.02, for the axial-transverse and axial-radial directions 0.19+/-0.04, and for the transverse-axial and radial-axial direction 0.09+/-0.02 (mean+/-SD). Cubes located only millimetres apart had significantly different elastic properties, showing that significant spatial variation occurs in equine cortical bone.

The importance of the elastic and plastic components of strain in tensile and compressive fatigue of human cortical bone in relation to orthopaedic biomechanics.

The longevity, success, or failure of an orthopaedic implant is dependent on its osseointegration especially within the initial six months of the initial surgery. The development of strains plays a crucial role in both bone modelling and remodelling. For remodelling, in particular, strains of substantial values are required to activate the osteoblastic and osteoclastic activity for the osseointegration of the implant. Bone, however, is subject to "damage" when strain levels exceed a certain threshold level. Damage is manifested in the form of microcracks; it is linked to increased elastic strain amplitudes and is accompanied by the development of "plastic" (irrecoverable, residual) strains. Such strains increase the likelihood for the implant to subside or loosen. The present study examines the rates (per cycle) by which these two components of strain (elastic and "plastic") develop during fatigue cycling in two loading modes, tension and compression. The results of this study show that these strain rates depend on the applied stress in both loading modes. It also shows that elastic and plastic strain rates can be linked to each other through simple power law relationships so that one can calculate or predict the latter from the former and vice versa. We anticipate that such basic bone biomechanics data would be of great benefit to both clinicians and bioengineers working in the field of FEA modelling applications and orthopaedic implant surgery.

Strain patterns during tensile, compressive, and shear fatigue of human cortical bone and implications for bone biomechanics.

It is a common theme in basic bone biomechanics and in biomechanical applications that much of the behavior can be determined and is dictated by the level of strain, whether this pertains to bone physiology, bone remodeling, osseoinduction, osseointegration, or the development of damage. The development of damage, demonstrated by stiffness loss measurements, has already been reported in detail in the literature. However, the systematic study of the development of "plastic" (residual) strains, which are associated with the inelastic mechanical behavior of bone tissue, has generally been overlooked. The present study compares the rates at which the elastic (e(a)) and plastic components (e(p)) of strain developed during tensile, compressive, and shear fatigue in human cortical bone of six individuals aged between 53 and 79 years. The overall hypothesis of this investigation is that there is a common underlying factor in the damage-related behavior of bone, which may allow us to link together the various aspects of the damage related behavior of bone. The rate of development of plastic strain (Deltae(p)/DeltaN) and the rate of growth in elastic strain amplitude (Deltae(a)/DeltaN) are described as a function of the stress (sigma), and/or stress normalized by the modulus of elasticity (sigma/E). The implications of our findings are discussed with respect to simple models/mechanisms, which may underlie the observed behavior.

Total hip replacement in a patient with systemic mastocytosis: a case report.

Systemic mastocytosis is a rare condition that often involves the bone marrow. We report the case of a patient with systemic mastocytosis who underwent total hip replacement. Technical difficulties encountered during the procedure included a narrow medullary canal and abnormally hard bone, later confirmed by laboratory measurements. Follow-up at five years showed a good clinical and radiological outcome.

The many adaptations of bone.

Studies concerned with the "adaptations" in bones usually deal with modelling taking place during the individual's lifetime. However, many adaptations are produced over evolutionary time. This survey samples some adaptations of bone that may occur over both length scales, and tries to show whether short- or long-term adaptation is important. (a) Woven and lamellar bone. Woven bone is less mechanically competent than lamellar bone but is frequently found in bones that grow quickly. (b) Stress concentrations in bone. Bone is full of cavities that potentially may act as stress concentrators. Usually these cavities are oriented to minimise their stress-concentrating effect. Furthermore, the "flow" of lamellae round the cavities will still further reduce their stress-concentrating effect, but the elastic anisotropy of bone will, contrarily, tend to enhance it in normal loading situations. (c) Stiffness versus toughness. The mineral content of bone is the main determinant of differences in mechanical properties. Different bones have different mineral contents that optimise the mix of stiffness and toughness needed. (d) Synergy of whole bone architecture and material properties. As bone material properties change during growth the architecture of the whole bone is modified concurrently, to produce an optimum mechanical behaviour of the whole bone. (e) Secondary remodelling. The formation of secondary osteones in general weakens bone. Various suggestions that have been put forward to account for secondary remodelling: enabling mineral homeostasis; removing dead bone; changing the grain of the bone; taking out microcracks. (f) The hollowness of bones. It is shown how the degree of hollowness is adapted to the life of the animal.

The microhardness and fracture surface of the petrodentine of Lepidosiren (Dipnoi), and of other mineralised tissues.

The South American lungfish Lepidosiren has toothplates bearing an extremely hard version of dentine: petrodentine. The hardness of this tissue, and its associated ordinary dentine, was compared with that of the enamel, dentine and cement of mammalian teeth, and also with that of other mammalian bony tissues. The hardnesses of petrodentine and dentine of Lepidosiren were found to be similar to those of enamel and dentine in other, mammalian, teeth. Furthermore, the anatomical arrangement of the Lepidosiren tissues was similar to that found in the incisors of rodents, and they presumably function in the same way to keep a sharp chisel edge at the tip of the tooth. Comparison of fracture surfaces of Lepidosiren petrodentine and that of rat incisor showed, however, that petrodentine does not have the refined, crack-stopping structure found in rat incisor enamel.

Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation.

The elastic modulus and hardness of secondary osteonal and interstitial bone was examined through the thickness of the cortex of human femora of various ages by nano-indentation. There was a clear difference between the stiffness and hardness of secondary osteonal and interstitial bone, the latter being stiffer (F(1,48)=56.0, P<0.001). There were some differences between the bones of different subjects; however, there were no differences that could be reliably associated with the chronological age of the subject, or with differences in location through the thickness of the cortex (F(2,48)=0.21, P=0.810). Previous studies have been equivocal in relating changes in the macroscopic 'composite' material stiffness of bone to the age of the individual. By combining the results of the nano-tests with histological measures, we were able to produce a good relationship of the microstructural properties at the matrix level with the bending modulus of whole bone (R(2)=0.88, P<0.001) and this improved further by taking into account the age of the individual (R(2)=0.94, P<0.001). Our results suggest that using differences in the volumetric proportions of secondary osteons versus interstitial bone, and the properties of these elements/structures in isolation may be a more accurate method of determining differences in elastic modulus of whole bone between individuals of various ages.

The role of root system architecture and root hairs in promoting anchorage against uprooting forces in Allium cepa and root mutants of Arabidopsis thaliana.

The role played by lateral roots and root hairs in promoting plant anchorage, and specifically resistance to vertical uprooting forces has been determined experimentally. Two species were studied, Allium cepa (onion) which has a particularly simple root system and two mutants of Arabidopsis thaliana, one without root hairs (rhd 2-1) and another with reduced lateral root branching (axr 4-2). Maximum strength of individual onion roots within a plant increased with plant age. In uprooting tests on onion seedlings, resistance to uprooting could be resolved into a series of events associated with the breakage of individual roots. Peak pulling resistance was explained in a regression model by a combination of a measure of plant size and the extent to which the uprooting resistance of individual roots was additive. This additive effect is termed root co-operation. A simple model is presented to demonstrate the role played by root co-operation in uprooting resistance. In similar uprooting tests on Arabidopsis thaliana, the mutant axr 4-2, with very restricted lateral development, showed a 14% reduction in peak pulling resistance when compared with the wild-type plants of similar shoot dry weight. The uprooting force trace of axr 4-2 was different to that of the wild type, and the main axis was a more significant contributor to anchorage than in the wild type. By contrast, the root hair-deficient mutant rhd 2-1 showed no difference in peak pulling resistance compared with the wild type, suggesting that root hairs do not normally play a role in uprooting resistance. The results show that lateral roots play an important role in anchorage, and that co-operation between roots may be the most significant factor.

Tensile fatigue in bone: are cycles-, or time to failure, or both, important?

In life, bones are subjected to fatigue loading which has different frequency and amplitude components, as well as various kinds of loading modes like tension, compression, shear and combinations of them. Considerable variability is observed in fatigue results of bone, which may be caused by these experimental variables or by the bone itself. In past studies the effect of magnitude and mode of loading have been examined in standard fatigue strength (stress vs. cycles to failure) diagrams. The effect of frequency is not clear, but there is clear evidence (from Carter & co-workers) that, at least in human bone, tension "fatigue" failure was determined solely by time rather than by cycles. We sought to confirm these results in the same and a different species. We cycled human and bovine bone in tension at two frequencies: 0.5 and 5 Hz. There was no cycle number effect; the results from the tests at the two frequencies were different if plotted and analysed as a function of cycles to failure, but were not separable if plotted and analysed as a function of time to failure. In this respect bone differs from tendon, in which failure in tension is a function of both cycles and time.

The anisotropic Young's modulus of equine secondary osteones and interstitial bone determined by nanoindentation.

The equine radius is a useful subject for examining the adaptation of bone histology to loading because in life the anterior cortex is loaded almost entirely in tension, the posterior cortex in compression. The histology of the two cortices is correspondingly different, the osteones and the interstitial lamellae in the posterior cortex having a more transversely oriented fibre arrangement than those in the anterior cortex. Presumably as a result of this histological difference, the posterior cortex is stronger in compression than the anterior cortex; the anterior cortex is stronger in tension than the posterior cortex. We here use nanoindentation to examine how the Young's modulus of elasticity of secondary osteones and interstitial lamellae in the anterior and posterior cortices varied as a function of angle. The anterior osteones were stiffer than the posterior osteones when tested in the direction parallel to the bone's long axis, but became progressively relatively less stiff as the angle increased; at 90 degrees, they were less stiff than the posterior osteones. Although the interstitial lamellae were stiffer than their neighbouring osteones, the same relationship between anterior and posterior interstitial lamellae as a function of angle was found as for the osteones. The anisotropy of these Young's moduli determined by nanoindentation shows a close relationship with what was to be expected from the histological findings.

Mechanical properties of nacre and highly mineralized bone.

We compared the mechanical properties of 'ordinary' bovine bone, the highly mineralized bone of the rostrum of the whale Mesoplodon densirostris, and mother of pearl (nacre) of the pearl oyster Pinctada margaritifera. The rostrum and the nacre are similar in having very little organic material. However, the rostral bone is much weaker and more brittle than nacre, which in these properties is close to ordinary bone. The ability of nacre to outperform rostral bone is the result of its extremely well-ordered microstructure, with organic material forming a nearly continuous jacket round all the tiny aragonite plates, a design well adapted to produce toughness. In contrast, in the rostrum the organic material, mainly collagen, is poorly organized and discontinuous, allowing the mineral to join up to form, in effect, a brittle stony material.