Fabricational morphology of oblique ribs in bivalves

Most analyses on allometry of long bones in terrestrial mammals have focused on dimensional allometry, relating external bone measurements either to each other or to body mass. In this article, an analysis of long bone mass to body mass in 64 different species of mammals, spanning three orders of magnitude in body mass, is presented. As previously reported from analyses on total skeletal mass to body mass in terrestrial vertebrates, the masses of most appendicular bones scale with significant positive allometry. These include the pectoral and pelvic girdles, humerus, radius+ulna, and forelimb. Total hindlimb mass and the masses of individual hindlimb bones (femur, tibia, and metatarsus) scale isometrically. Metapodial mass correlates more poorly with body mass than the girdles or any of the long bones. Metapodial mass probably reflects locomotor behavior to a greater extent than do the long bones. Long bone mass in small mammals (<50 kg) scales with significantly greater positive allometry than bone mass in large (>50 kg) mammals, probably because of the proportionally shorter long bones of large mammals as a means of preserving resistance to bending forces at large body sizes. The positive allometric scaling of the skeleton in terrestrial animals has implications for the maximal size attainable, and it is possible that the largest sauropod dinosaurs approached this limit.     

Curvature of the forelimb bones of anthropoid primates: Overall allometric patterns and specializations in suspensory species

It has previously been reported that brachiating primates, particularly gibbons, are characterized by distinctively straight forelimb long bones, yet no hypotheses have been proposed to explain why straight limb bones may be adaptive to suspensory locomotion. This study explores quantitatively the curvature of the long bones in 13 species of anthropoid primates and analyzes the functional consequences of curvature in biomechanical terms. These analyses demonstrate that, whereas the humeri of gibbons and spider monkeys are functionally less curved than those of other taxa, the ulnae of brachiators are neither more nor less curved than those of other anthropoids, and the gibbon radius is far more curved than would be predicted from body size alone. The humerus is likely significantly less curved in brachiators because of its torsion-dominated loading regime and the greatly increased stress magnitude developed in torsionally loaded curved beams. The large curvature of the radius is localized in the region of attachment of the supinator muscle. Analysis presented here of muscle mass allometry in catarrhines demonstrates that gibbons are characterized by an extremely massive supinator, and the large radial curvature is therefore most likely due to forearm muscle mechanics. This study also demonstrates that the overall pattern of limb bone curvature for anthropoids is distinct from the pattern reported for mammals as a whole. This distinctive scaling relationship may be related to the increased length of the limb bones of primates in comparison to other mammals.     

Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Giraffes have remarkably long and slender limb bones, but it is unknown how they grow with regard to body mass, sex, and neck length. In this study, we measured the length, mediolateral (ML) diameter, craniocaudal (CC) diameter and circumference of the humerus, radius, metacarpus, femur, tibia, and metatarsus in 10 fetuses, 21 females, and 23 males of known body masses. Allometric exponents were determined and compared. We found the average bone length increased from 340 ± 50 mm at birth to 700 ± 120 mm at maturity, while average diameters increased from 30 ± 3 to 70 ± 11 mm. Fetal bones increased with positive allometry in length (relative to body mass) and in diameter (relative to body mass and length). In postnatal giraffes bone lengths and diameters increased iso‐ or negatively allometric relative to increases in body mass, except for the humerus CC diameter which increased with positive allometry. Humerus circumference also increased with positive allometry, that of the radius and tibia isometrically and the femur and metapodials with negative allometry. Relative to increases in bone length, both the humerus and femur widened with positive allometry. In the distal limb bones, ML diameters increased isometrically (radius, metacarpus) or positively allometric (tibia, metatarsus) while the corresponding CC widths increased with negative allometry and isometrically, respectively. Except for the humerus and femur, exponents were not significantly different between corresponding front and hind limb segments. We concluded that the patterns of bone growth in males and females are identical. In fetuses, the growth of the appendicular skeleton is faster than it is after birth which is a pattern opposite to that reported for the neck. Allometric exponents seemed unremarkable compared to the few species described previously, and pointed to the importance of neck elongation rather than leg elongation during evolution. Nevertheless, the front limb bones and especially the humerus may show adaptation to behaviors such as drinking posture. J. Morphol. 276:503–516, 2015. © 2014 Wiley Periodicals, Inc.     

华南地区男性成年人由长骨长度推算身长的回归方程

从近年来收集的华南地区汉族成年男性50具已知生前身长的骨骼材料,算出从各长骨推算身长的常数(a)及回归系数(b),并算出长骨长度与身高的相关系数(r)数值在0.516—0.913之间,表明相关度较为密切,在此基础上算出10个由各长骨的估计身长的回归方程。并采用校正值:0.6毫米×(年龄—30),校正因年龄所造成的身长误差。从肱骨、腓骨及肱骨加桡骨、股骨加胫骨的长度推算身长最为理想。本文所得的回归方程,适用于华南人。     

Sagittal long bone curvature in birds

The maximum sagittal curvature of the long bones (humeras, radius, ulna, femur, tibiotarsus and tarsometatarsus) of 45 specimens of birds, belonging to 36 species, was measured and regressed to the corresponding body mass. Mathematical results show a tendency of curvature to scale with strong positive allometry. Within the species studied, those with more characteristic flapping flight tend to show relatively low values of curvature in the wing bones. To check the agreement of the present results with current hypotheses on the origin of long bone curvature, previous results on scaling of myological and cross-sectional parameters in birds are considered. Indirect evidence suggests that curvature tends to increase bone stresses. Hypotheses that consider curvature as a consequence of the mechanical action of muscle allocation and optimization of functional strains are discussed at length. The possible double genetic-epigenetic determinism of the curvature character is evoked.     

Shape and size of the body vs. musculoskeletal stress markers

The objective of this paper is to assess the relationship between the degree of development of muscle attachment sites (musculoskeletal stress markers - MSM1) and the length and circumference measurements of long bones and the body build expressed with the reconstructed values of body height (BH) and body mass (BM). The bone material (102 male and 99 female skeletons) used in the study was collected in the medieval burial ground in Cedynia, Poland. The authors analyzed 10 musculoskeletal stress markers located on the scapula (2), humerus (2), radius (2), femur (2) and tibia (2). The frequency and the degree of expression of muscle attachment size was carried out using the scale prepared by Myszka (2007). The scale encompassed three degrees of expression of muscle attachment size. Only changes of robusticity type (nonpathological changes) were taken into account. The assessment of body build of individuals was carried out according to the method proposed by Vancata & Charvátová (2001). Body height was reconstructed from the length of the humerus and femur using eight equations. Body mass was reconstructed from the measurements of the breadth of the proximal and distal sections of the femur and tibia (mechanical method) using twenty one equations. The equations were developed for different reference populations. The same equations were used for men and women. The correlation between the MSM and the length and circumference measurements of the bones was analyzed using the principal components analysis and the Gamma correlation coefficient. The strength of the correlation between the reconstructed body build traits (BH, BM) and the moderate degree of musculoskeletal stress markers expression was studied based on the principal components method and the Pearson correlation coefficient. A linear correlation was found between musculoskeletal stress markers and the circumference measurements and the reconstructed body mass, but no relationship with body height and the length measurements of long bones was revealed. From previous research it is evident that the relationship between the MSM and metric skeletal traits does not occur in every population. Divergent findings necessitate further corroboration of results on diverse skeletal material.     

Differential long bone growth of children between two months and eleven years of age

Diaphyseal lengths of the humerus, radius, femur and tibia of upper-middle class White children between two months and 11 years of age show positive allometric growth, indicating substantial shape or proportional change. The segments of the lower extremity display greater allometric increase than the humerus and radius; variation in relative growth within each extremity is small and inconsistent. Sex differences are consistent, with slightly greater proportional increases demonstrated for boys. The results suggest that absolute intralimb variation in growth, following a disto-proximo growth or maturity gradient, is due to initial differences in size or scale and not to differences in patterns of growth. Developmental variation between extremities is due to scaling plus variation in relative growth patterns.     

Catch-up growth in the limbs of rats undernourished for different lengths of time during suckling

Male rats were undernourished for one of three periods of time during suckling. They were subjected to undernutrition from birth to 8 days post-partum, birth to 15 days or birth to 22 days. The growth of the humerus, radius, femur and tibia was followed radiographically during the undernutrition and recovery periods. It was found that the lengths of these bones in animals undernourished from birth to 8 days were able to recover completely, while after the two longer periods of undernutrition, the animals were unable to recover. The results are not in complete agreement with those of previous workers and it is suggested that this may be due to differing rates of growth and maturation between the animals used in different studies.     

Geometry and evolutionary parallelism in the long bones of cavioid rodents and small artiodactyls

Morphological parallelism between South American cavioid rodents and small artiodactyls from the Old World has been postulated for a long time. Our study deals with this question from the point of view of biomechanical characteristics of the long bones. For this, cross-sectional area, second moment of the area, polar moment, athletic ability indicators and strength were calculated for the long bones (i.e. humerus, radius, femur and tibia) of five species of cavioids and two species of artiodactyls. Regressions of all these variables to body mass were established. Regarding the cross-sectional area, the confidence intervals show that the exponents calculated are not significantly different from the geometrical predicted value. The exponents obtained for the second moment of area and the polar moment are not significantly different from the geometrical prediction, except for the humerus. The two indicators of athletic ability scaled as expected, but the bending indicator of athletic ability of the femur was not correlated to body mass. The exponent calculated for femur strength is not different from zero, while the strength of the humerus decreases slightly with the body mass. Additional statistical tests (ANCOVAs) showed no difference between the values of these variables calculated for the samples studied of artiodactyls and rodents. The present results are consistent with the hypothesis that there is significant evolutionary parallelism between cavioid rodents and small artiodactyls.     

The variation of the cross-sectional shape in the long bones of birds and mammals

The transverse and sagittal diameters of the long bones were measured in a sample of 53 species of eutherian mammals and 36 species of birds. The scaling of the transverse and sagittal diameters of each bone to body mass was calculated. For each bone the ratio of sagittal/transverse diameter was calculated, as an expression of the cross-sectional shape of the bones. The distributions of the ratios were not significantly different from normality in all the avian bones and in the mammalian femur and tibia. In most cases, the mean of the distribution was significantly different from 1 (circular shape). The analysis shows that changes in the ratio can be caused by selective factors, considering the correlation predicted between the breaking moments and the radii, but at the same time the cross-sectional shape of mammalian and avian long bones may have a phylogenetic basis. Finally, the previous assumption of relationship between bone curvature and stress predictability, is also discussed.     

Modern humans are not (quite) isometric

Allometric relationships are important sources of information for many types of anthropological and biological research. The baseline for all allometric relationships is isometry (or geometric similarity), the principal that shape is invariant of size. Here, we formally test for geometric similarity in modern humans, looking at the maximum lengths of four long bones (humerus, radius, femur, and tibia). We use Jolicoeur's multivariate allometry method to examine globally distributed samples of human populations, both collectively and individually. Results indicate that humans are not geometrically similar, although morphological deviations from isometry are small.     

Body size, locomotion, and long bone cross-sectional geometry in indriid primates.

The geometry of the midshaft cross-sections of the femur and humerus of five indriid species was analysed. Internal (marrow cavity) and external diameters were measured on X-rays in the anteroposterior (a-p) and mediolateral (m-l) planes; cross-sectional areas, second moments of area, and section moduli were calculated using formulae for a hollow ellipse. Cortical thickness, robusticity indices (relating external diameters to the length of the bones), and a-p/m-l shape variables were also calculated. Model II regression was supplemented by analyses of correlation between size and shape. Indriids are saltatory, i.e., their locomotion is dominated by the hind limbs. Accordingly, the femur is more rigid than the humerus, and it shows a consistent difference between the a-p and m-l planes in measures related to bending strength. Cortical thickness varies considerably both within and across species. The type specimen of the new species Propithecus tattersalli is virtually indistinguishable from P. verreauxi on the basis of its long bone cross-sectional geometry. Femoral robusticity is uncorrelated with size, but humeral robusticity decreases significantly with increasing size. Femoral shape variables (a-p/m-l) are all negatively correlated with body size, indicating that m-l dimensions of the femur increase at a faster rate than do a-p dimensions. The highly loaded plane of movement seems to be more reinforced in the smaller species. Contrary to static biomechanical scaling predictions of positive allometry, all cross-sectional parameters scale relatively close to isometry. It is concluded that either changes in locomotor performance must compensate for the weight-related increase in forces and moments or that the larger-bodied animals operate appreciably closer to the limits of their safety margins.     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

Skeletal lesions and anemia associated with ascorbic acid deficiency in juvenile rhesus macaques.

Young rhesus macaques housed in outdoor corn cribs and fed a commercially prepared primate diet became weak, depressed, were reluctant to move, and expressed locomotor abnormalities. Thirteen severely affected animals were hospitalized for evaluation. Physical examination disclosed swellings and instabilities involving the ends of long bones. Radiography confirmed physeal fractures in 11 of 13 animals. Affected bones included the distal femur, proximal humerus, distal tibia/fibula, and distal radius/ulna. Other, less obvious changes were noted on radiographs. Anemia was a consistent finding. Ascorbic acid deficiency was suspected and therapy was initiated that consisted of vitamin supplements, diet change, cage rest, and support bandages. Feed samples were submitted to a laboratory for analysis and were confirmed deficient in vitamin C. Follow-up radiographs showed large calcifying subperiosteal hematomas in epiphyseometaphyseal regions, consistent with a diagnosis of scurvy. Twelve of 13 animals recovered clinically. Subsequent radiographs documented improvement of initially severe angular deformities associated with displaced fractures.     

A comparison of mechanical properties derived from multiple skeletal sites in mice

Laboratory mice provide a versatile experimental model for studies of skeletal biomechanics. In order to determine the strength of the mouse skeleton, mechanical testing has been performed on a variety of bones using several procedures. Because of differences in testing methods, the data from previous studies are not comparable. The purpose of this study was to determine which long bone provides the values closest to the published material properties of bone, while also providing reliable and reproducible results. To do this, the femur, humerus, third metatarsal, radius, and tibia of both the low bone mass C57BL/6H (B6) and high bone mass C3H/HeJ (C3H) mice were mechanically tested under three-point bending. The biomechanical tests showed significant differences between the bones and between mouse strains for the five bones tested (p < 0.05). Computational models of the femur, metatarsal, and radius were developed to visualize the types of measurement error inherent in the three-point bending tests. The models demonstrated that measurement error arose from local deformation at the loading point, shear deformation and ring-type deformation of the cylindrical cross-section. Increasing the aspect ratio (bone length/width) improved the measurement of Young's modulus of the bone for both mouse strains (p < 0.01). Bones with the highest aspect ratio and largest cortical thickness to radius ratio were better for bending tests since less measurement error was observed in the computational models. Of the bones tested, the radius was preferred for mechanical testing because of its high aspect ratio, minimal measurement error, and low variability.     

Allometric patterning in the limb skeleton of bats: Implications for the mechanics and energetics of powered flight

Allometric analysis was employed to compare linear dimensions of forelimb and hindlimb bones (humeri, radii, third and fifth metacarpals, third and fifth manual phalanges, femora, and tibiae) of 227 species of bats and 105 species of nonvolant mammals of varying degrees of phylogenetic affinity to bats. After accounting for body size, all forelimb bones are longer in bats than in nonvolant species, with the exception of humeri and radii of a few highly arboreal primates. Hindlimb bones are generally, but not uniformly, shorter in bats than in other mammals. For the humerus, radius, and metacarpals, midshaft diameters are greater in bats than in their comparably sized relatives. Proximal phalangeal midshaft diameters are statistically indistinguishable from those of other mammals, and distal phalanges show significantly reduced outer diameters. The pattern of relative reduction in wing bone diameters along the wing's proximodistal axis parallels the reduction in bone mineralization along the same axis, and a similar pattern of change in cortical thickness from the smallest wall thicknesses among mammals in the humerus and radius to the greatest wall thicknesses among mammals in the phalanges. The combination of altered cross-sectional geometry and mineralization appears significantly to reduce the mass moment of inertia of the bat wing relative to a theoretical condition in which elongated bones preserve primitive mammalian mineralization levels and patterns of scaling of long bone diameters. This intercorrelated suite of skeletal specializations may significantly reduce the inertial power of flight, contributing significant energetic savings to the total energy budgets of the only flying mammals. J. Morphol. 234: 277–294, 1997. © 1997 Wiley-Liss, Inc.     

Structural study of spongiosa tissue in growing sheep.

A study was made of 160 long bones taken from 40 native Merino sheep of both sexes. These animals, which represented uniform growth (mean growth-curve values), were divided into four groups which were slaughtered consecutively at 0, 45, 105 and 270 days old (0, 6.4, 15 and 38.5 weeks, respectively). The following bones were studied; humerus, femur, tibia and os coxae. Thin lamellae taken from the metaphyses of the bones obtained were fixed, decalcified and stained with hematoxylin-eosin to assess the development of the various components of growing bony tissue. The bones studied followed the same maturation pattern; the os coxae proved to be the best histological indicator in differentiating the age of the animals studied.     

Bone length and muscle weight in mice subjected to genetic selection for the relative length of the tibia and radius

Mice which had undergone 5 generations of selection for high and low values of the tibia length/radius length ratio were compared with unselected controls at 10 weeks of age. The ratio responded to selection in both directions. The length of the radius was increased in the low line while the response in the high line was due to an increase in the length of the tibia and a small but statistically insignificant decrease in radius length. High and low line mice were heavier than the controls. The responses of the tibia and femur and of the radius and humerus were generally similar, suggesting the existence of an association between the genetic control of the lengths of the bones of a limb. There were also correlated responses in the weight of the tibialis anterior, biceps brachii and sternomastoid, and there is some evidence to suggest that the weight of a muscle may be influenced by the length of a bone to which it is attached.     

Skeletal growth and function in the California gull (Larus californicus)

Although the bones of rapidly growing animals are composed of weak tissue, they often must function in locomotor activity. We address the conflict between development and skeletal function by analysing the ontogeny of skeletal strength in the California gull, Larus californicus. Changes in shape and mechanical properties of the femur, tibia, tarsometatarsus, humerus, ulna and carpometacarpus were analysed in a complete post-hatching growth series. During post-hatching growth, strength and stiffness of the skeletal tissue increases six- to ten-fold. At hatching, long bones of the wing are relatively weak and they remain so throughout the major portion of the growth period. However, in the hind limb, relatively thick bones in juveniles compensate for the weak tissue such that the force required to break the bones remains constant relative to body mass. This difference between hind limb and wing parallels the development of locomotor function; young gulls begin to walk within a day or two of hatching, but they do not fly until they are fully grown. Thus, in the bones of the hind limb, the conflict between rapid growth and skeletal function is solved by negative allometry of bone thickness.
After young gulls reach adult size, the breaking strength of the wing bones increases three- to four-fold, the mass of the pectoralis muscle triples and the surface area of the wing doubles. The one aspect of wing development that is not delayed until shortly before fledging is linear growth of the bones. Bones of the wing increase in length at a rapid and relatively constant rate from the time of hatching to the attainment of adult size. Relatively early initiation of linear growth of the wing bones suggests that the rate at which bones grow in length may be the rate limiting factor in wing development.     

Curvature, length, and cross-sectional geometry of the femur and humerus in anthropoid primates

The aims of this study were to describe the curvature of anthropoid limb bones quantitatively, to determine how limb bone curvature scales with body mass, and to discuss how bone curvature influences static measures of bone strength. Femora and humeri in six anthropoid genera of Old World monkeys, New World monkeys, and gibbons were used. Bone length, curvature, and cross-sectional properties were incorporated into the analysis. These variables were obtained by a new method using three-dimensional morphological data reconstructed from consecutive CT images. This method revealed the patterns of curvature of anthropoid limb bones. Log-transformed scaling analyses of the characters revealed that bone length and especially bone curvature strongly reflected taxonomic/locomotor differences. As compared with Old World monkeys, New World monkeys and gibbons in particular have a proportionally long and less curved femur and humerus relative to body mass. It is also revealed that the section modulus relative to body mass varies less between taxonomic/locomotor groups in anthropoids. Calculation of theoretical bending strengths implied that Old World monkeys achieve near-constant bending strength in accordance with the tendency observed in general terrestrial mammals. Relatively shorter bone length and larger A-P curvature of Old World monkeys largely contribute to this uniformity. Bending strengths in New World monkeys and gibbons were, however, a little lower under lateral loading and extremely stronger and more variable under axial loading as compared with Old World monkeys, due to their relative elongated and weakly curved femora and humeri. These results suggest that arboreal locomotion, including quadrupedalism and suspension, requires functional demands quite dissimilar to those required in terrestrial quadrupedalism.