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.     

Allometry and curvature in the long bones of quadrupedal mammals

The allometric relationships between basic structural proportions in long bones are examined in the humerus, radius, femur and tibia for a diverse group of 42 terrestrial quadrupedal mammals that span a size range from 0.02–6000 kg. Non-linear scaling is found for length vs. diameter in the tibia and radius, suggesting that the mechanical constraints on the skeleton differ within large and small body-size mammals. Curvature normalized to mid-shaft radius scales differently in the different long bones. Curvature is poorly related to size in the proximal limb bones (humerus and femur) while it decreases systematically with size in the tibia (mass exponent −0.13). The scaling of normalized curvature in the radius is unique among long bones. Variability of curvature in the radius is reduced at any size in comparison to that found in the other long bones. Normalized curvature is constant within the small body size group (0.02 to approximately 100 kg) while it decreases sharply with size within animals over 100 kg body mass. The unusual scaling found in the radius is probably the result of this bone's close alignment with the extrinsic forces which act on it during locomotion. The change in scaling within the radius for animals of different size may be indicative of more general size-dependent mechanical trade-offs which are masked by the complex loading circumstances of the other long bones.     

Functional differentiation of long bones in lorises

The external dimensions of the limb bones and the geometry of their midshaft cross-sections were determined for Loris tardigradus and Nycticebus coucang. Relative cortical thickness, cortical area, and second moment of area were calculated and contrasted with locomotor stresses. The difference in shape-related strength of the bones between the smaller- and the larger-bodied species is more pronounced than can be expected from stresses acting during normal locomotion. The Nycticebus skeleton has a much higher safety margin overall and seems to be dimensioned for infrequent but critical stresses of high magnitude. Lorisine gaits in general are characterized by low ground reaction forces, great mobility in all joints, and a nearly equal share in propulsion and weight-bearing by the fore- and hindlimb. Accordingly, the long bones of lorises (especially those of L. tardigradus) tend to be less rigid than those of other mammalian species (including other primates), they lack a preferential plane of higher bending strength, and femur and humerus do not differ markedly in their capacity to withstand mechanical stresses. External dimensions of the humerus and femur of the two African lorisine species parallel and corroborate these results. Some more general implications for the relationships between bone shape and locomotor stresses are also discussed.     

Synostosis dynamics in human long tubular bones

More than 8,000 roentgenograms and electroroentgenograms of brachial, ulnar, radiocarpal, coxofemoral, knee, talocrural joints have been studied in persons of both sex at the age from birth up to 25 years. The synostosis degree is appreciated by the six-mark system. The roentgenological data are corroborate histologically. The method of appreciation applied makes it possible to reveal cases of initially forming synostosis long before puberty. Three stages of synostosis process are defined. The first stage--slow increase of the synostosis mark. The second--quick synostosis formation. The third--final stage. According to the stages defined, a comparative analysis of the synostosis process in all metaepiphyseal zones of all long tubular bones, peculiarities of the process depending on the sex are demonstrated. The data on the time, when the points of ossification appear, on the beginning and completion of synostosis process in all metaepiphyseal zones of the long tubular bones are presented.     

Allometry of the limb long bones of insectivores and rodents

In an attempt to investigate the relationships between allometry and locomotory adaptations, we studied the long limb bones of 45 species of insectivores and rodents. Animals ranged from a few grams to about 50 kilograms. Diameter and length of the bones and body mass (when known) were recorded. Regressions of diameter to length, diameter to body mass, and length to body mass were calculated by the least-squares and Model II, or major axis, methods. The results obtained do not agree with the predictions of either the theory of geometric similarity or the theory of elastic similarity. The discrepancies could be due to the fact that animals studied exhibit various modes of locomotion. Moreover, the allometric relationships of the different locomotor patterns are better reflected in insectivores and rodents than in other groups of mammals. The use of a single regression analysis seems to be inadequate when the sample includes a large range of body sizes.     

Estimation of torsional rigidity in primate long bones

Comparative studies of long bone biomechanics in primates frequently use the polar moment of inertia (J ) as a variable reflecting overall mechanical rigidity, average bending rigidity, or resistance to torsional shear stresses. While the use of this variable for characterizing the first two properties is appropriate, it is potentially a highly misleading measure of torsional resistance. Errors result from violations of assumptions required for the use of the polar moment of inertia; in particular, the predictive utility of J diminishes with departures from axial symmetry (i.e., a cylindrical cross-sectional shape). The magnitude of these errors is estimated both theoretically and experimentally. It is argued that the use of the polar moment of inertia for estimating long bone torsional rigidity should be restricted to samples of relatively invariant and/or cylindrical geometry. Alternative measures for torsional resistance are evaluated and reviewed.     

A biomechanical study of the long bones in platyrrhines.

The long bones of 72 individuals of extant platyrrhines, belonging to 17 species (11 genera) were studied by regressions of length, diameters and curvature. Cross-sectional shapes at midshaft and axial and bending strength indicators were also calculated. Results show that forelimb bones scale faster than hindlimb bones, for both length and diameters. Curvature scales faster in the femur than in other bones. Strength indicators showed a high variability in the relative importance of axial and bending loadings. Results are consistent with field observations of locomotor behaviour, mainly as regards quadrupedalism versus suspensory locomotion.     

Incidence and mechanical significance of pneumatization in the long bones of birds

The incidence of pneumatization in avian long bones was studied, by direct observation, in a large sample of species. Only proximal bones (humerus and femur) presented pneumatization in the sample studied. The incidence obtained was related to the variation of the maximum cortical thickness and mechanical properties, such as bending strength and flexural Young's modulus. Cortical thickness, bending strength and flexural Young's modulus were significantly lower in pneumatized bones than in marrow-filled bones. Furthermore, some congruence was found between pneumatization and systematic groups when compared. In this sense, Charadriformes was the only order studied with total absence of long bone pneumatization. Results on cortical thickness appear to be in agreement with modelling predictions previously made and with results obtained on other groups of flying vertebrates. The possible selective advantage of reduction in cortical thickness in relation to flying is suggested.     

Development of the clavicles in birds and mammals

Clavicles (collar bones) are variably present in mammals. Furculae (wishbones)--which may or may not be homologous with clavicles--are variably present and/or fused in birds and present in theropod dinosaurs. In this overview the development of clavicles and furculae is discussed with special attention to modes of skeletogenesis (whether intramembranous or endochondral), numbers of centres of ossification (one in chick furculae; two in murine clavicles), presence of cartilage (primary in clavicles, secondary in furculae), evidence from experimental analysis and from mutations for dependence of both clavicular and furcular growth on mechanical stimulation, and syndromes and mutations affecting clavicular development leading to both under and over development. J. Exp. Zool. 289:153-161, 2001.     

Avian long bones, flight and bipedalism.

Morphological, geometrical, chemical and mechanical characteristics of avian long bones are reviewed. Important differences exist between long bones of birds and mammals. Differences are also present in appendicular bones of birds, either between wing bones and leg bones or proximal (stylopodial) long bones and distal (zeugopodial) long bones. Special emphasis is put on pneumatization, in terms of both phylogenetic origin and geometrical and mechanical characteristics linked to it. Cortical thickness, bending strength and flexural Young's modulus were significantly lower in pneumatized bones than in marrow-filled bones. Possible adaptive reasons for the differences shown are discussed.