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

Humeri under external load: Mechanical implications of differing bone curvature in American otter and honey badger

The mechanical properties of limb long bones are impacted by bone shape and especially curvature, which is therefore likely to be of adaptive value. We use finite element analysis to compare the mechanical properties of humeri of the closely related American otter and honey badger under external loads, and to analyze the significance of bone curvature. We simulate the effects generated by loads applied in directions that differ relative to the humeral longitudinal axes, and then compare the stress characteristics with a series of humerus-inspired abstracted curved structures with increasing ratio (C/R) of eccentricity C to radius of cross section R. The humeri of the two species differ in bone curvature, with C/R of 0.6201 and 0.8752, respectively. Our analysis shows that the peak and mean stress values found within the sampling line of bone models reach a minimum when the directions of loads are 105 ± 5°, and the humerus of the American otter always experienced lower stress values than those of the honey badger in the sampling line. An analysis of stress distribution in abstract curved structures showed the greatest reduction in stress when the direction of external load was equal or greater than 95°. This suggests that the variability of the direction of external loads is an important determinant of bone curvature, and should be accounted for when assessing load carrying capacity. This study provides a basis for biomechanics research and yields insight into the form-function relationship of nature's structural elements within limbs. It potentially contributes to the design of biomimetic robots while also highlighting the functional significance of humeral bone curvature in mammals.

Ape femoral-humeral rigidities and arboreal locomotion

OBJECTIVES

This study investigates patterns of bone functional adaptations in extant apes through comparing hindlimb to forelimb bone rigidity ratios in groups with varying levels of arboreality.

MATERIALS AND METHODS

Using CT scans, bone rigidity (J) was calculated at three regions of interest (ROI) along femoral and humeral diaphyses in Homo, Pongo, Pan, and Gorilla with further comparisons made between species and subspecies divisions within Pan and Gorilla.

RESULTS

Consistent with previous work on extant hominoids, species exhibited differences in midshaft femoral to humeral (F/H) rigidity ratios. Results of the present study confirm that these midshaft differences extend to 35% and 65% diaphyseal ROIs. Modern humans, exhibiting larger ratios, and orangutans, exhibiting smaller ratios, bracketed the intermediate African apes in comparisons. Within some African apes, limb rigidity ratios varied significantly between taxonomic groups. Eastern gorillas exhibited the highest mean ratios and chimpanzees the lowest at all three ROIs. In posthoc comparisons, chimpanzees and bonobos did not differ in relative limb rigidity ratios at any of the three ROIs. However, western gorillas were more similar to bonobos than eastern gorillas at 50% and 35% ROIs, but not at the 65% ROI.

CONCLUSION

Species, and to a lesser extent subspecies, can be distinguished by F/H limb rigidity ratios according to broad positional behavior patterns at multiple regions of interest along the diaphyses. Similarity of bonobos and western gorillas is in line with behavioral data of bonobos being the most terrestrial of Pan species, and western gorillas the most arboreal of the Gorilla groups.

Anatomy applied to image diagnosis of the hind limb in the black-striped capuchin (Sapajus libidinosus Spix, 1823)

The knowledge of anatomy and imaging exams emerges as an important tool in the study of evolutionary processes of a species, in the elaboration of diagnosis, and the successful choice of the appropriate clinical and surgical procedures. Therefore, this study aims to describe the osteology of the hind limb of Sapajus libidinosus by means of gross, radiographic, and tomographic images. Four cadavers were used in the macroscopic analysis and five animals for the imaging exams, of which four were eventually euthanized and added to the macroscopic study. For imaging exams, they were kept anesthetized. All bones of the hind limb were documented, their structures were described, and compared with data in the literature from human and nonhuman primates. We have performed Student's t test for independent samples. There was no statistical difference between the sexes regarding the length of the hind limb bones. The coxal bone was largely well described using imaging methods. A small penile bone was present at the tip of the penis and it could be identified by all analysis methods. The femur, as well as the tibia and fibula, were not well portrayed in their proximal and distal epiphyses by radiography (Rx). However, they were well identified on tomography. No third trochanter was observed in the femur and the patella had a triangular shape. All the structures described by gross anatomy of the tarsus and metatarsus could be identified by Rx and tomography. More subtle structures, such as the popliteal notch on the tibia, and the gluteal tuberosity pectineal line and facies aspera on the coxal bone, were not identified by medical imaging. S. libidinosus presented anatomical characteristics that were similar to those of larger New World and Old World monkeys, including man. This suggests it's value as an experimental model for studies in recent primates.

Application of Methods for a Morphological Analysis of the Femoral Diaphysis Based on Clinical CT Images to Prehistoric Human Bone: Comparison of Modern Japanese and Jomon Populations from Hegi Cave, Oita, Japan

A morphological analysis of ancient human bones is essential for understanding life history, medical history, and genetic characteristics. In addition to external measurements, a three-dimensional structural analysis using CT will provide more detailed information. The present study examined adult male human skeletons excavated from Hegi cave, Nakatsu city, Oita Prefecture. CT images were taken from the femurs of adult males (Initial/Early Jomon Period (n = 10) and Late Jomon Period (n = 5)). Cross-sectional images of the diaphysis from below the lesser trochanter to above the adductor tubercle were obtained using the method established by Imamura et al. (2019) and Imamura et al. (2021). Using Excel formulas and macros, the area of cortical bone, thickness, and degree of curvature were quantitatively analyzed. The results were compared with data on modern Japanese. The maximum thickness of cortical bone in the diaphysis and the degree of the anterior curvature were significantly greater in Late Jomon humans than in the other groups. In contrast to modern humans, the majority of Jomon femurs showed the S-shaped curvature with the medial side at the top position and the lateral side at the lower position. The present results demonstrate that Late Jomon humans had a wider range of activity than the other groups and also provide insights into diseases in the hip and knee joints of Jomon humans.

Morphological divergence in the curvature of human femoral diaphyses: Tracing the central mass distributions of cross-sections

The diaphysis of the human femoral bone has a physiological anterior curvature; additionally, there is a curvature to the medial side or lateral side. In addition to compression stress from gravity during standing, walking, and running, these bones are continuously exposed to complex stresses from the traction forces of the various strong muscles attached to them. The femoral diaphysis is subjected to these mechanical stresses, and the direction and size of its curvature are defined according to Wolff's law and the mechanostat theory of Frost. The purpose of this study was to quantitatively evaluate the curvature of the femoral diaphysis in Japanese skeletons by determining the curve connecting the central mass distributions (CMD) of cross-sectional images. A total of 90 right femora (46 males and 44 females) were randomly selected from modern Japanese skeletal specimens. Full-length images of these bones were acquired using a clinical computed tomography scanner. The range between the lower end of the lesser trochanter and the adductor tubercle of each femur was divided at regular intervals to obtain ten planes, and nine levels were analyzed. The CMD curve was determined by connecting the CMDs of each of the nine cross-sections. First, the CMD of a cross-section in each of the nine slices was calculated, and the nine trajectories were superimposed from above. Then, by converting the shape of the entire CMD curve to superimpose the coordinates of the endpoint on the starting point, a closed arc representing the curvature of the femur was determined. For both males and females, the patterns varied from mostly medial to largely lateral curvature. The size of the curvature also varied for individuals. By analyzing only the coordinates of the vertex of the CMD curve of each femoral bone, the outlines of the diaphyseal curvatures could be recognized. The femora were thereby divided into two groups: medial bending and lateral bending. Considering males and females together, the number in the lateral-curvature group (n = 51) was larger than that in the medial-curvature group (n = 39). Moreover, the average age of the lateral-curvature group was significantly higher than that of the medial-curvature group (p < 0.05). In males, with an increase in the cortical bone proportion of the cross-sectional area, the anterior vertex of diaphyseal bending tended to be more prominent. This cortical proportion was significantly higher in the medial-curvature groups than in the lateral-curvature group (p < 0.01). The phenomena observed in this study may be related to pathophysiologies such as atypical fractures of the femur and osteoarthritis of the knee joints.

Three-dimensional geometry of human tibial anterior curvature in chronologically distinct population samples of Central Europeans (2900 BC - 21st century AD)

Several lines of bioarchaeological research have confirmed the gradual decline in lower limb loading among past human populations, beginning with the transition to agriculture. The goal of this study was to assess whether human tibial curvature reflects this decline, with a special emphasis on the time-span during which the pace of technological change has been the most rapid. Our study is the first (1) to apply longitudinal curvature analysis in the antero-posterior (A–P) and medio-lateral (M–L) planes to the human tibia, and (2) that incorporates a broad temporal population sample including the periods of intensification of agriculture, urbanization and industrialization (from 2900 BC to the 21^st century AD; N = 435) within Czech territories. Using three-dimensional geometric morphometrics, we investigated whether anterior tibial curvature mirrors assumed diminishing lower limb loading between prehistoric and industrialized societies and explored its shape in all three dimensions. Results showed the continuous trend of A–P straightening of the shaft. This straightening was associated with a relative sigmoidal curve accentuation in the M-L plane. Given the timescale involved and the known phenomenon of declining mobility, such adaptive changes in bone geometry can be interpreted in terms of the diminishing biomechanical demands on the tibia under different living conditions.

Three-dimensional geometry of human tibial anterior curvature in chronologically distinct population samples of Central Europeans (2900 BC - 21st century AD)

Several lines of bioarchaeological research have confirmed the gradual decline in lower limb loading among past human populations, beginning with the transition to agriculture. The goal of this study was to assess whether human tibial curvature reflects this decline, with a special emphasis on the time-span during which the pace of technological change has been the most rapid. Our study is the first (1) to apply longitudinal curvature analysis in the antero-posterior (A-P) and medio-lateral (M-L) planes to the human tibia, and (2) that incorporates a broad temporal population sample including the periods of intensification of agriculture, urbanization and industrialization (from 2900 BC to the 21^st century AD; N = 435) within Czech territories. Using three-dimensional geometric morphometrics, we investigated whether anterior tibial curvature mirrors assumed diminishing lower limb loading between prehistoric and industrialized societies and explored its shape in all three dimensions. Results showed the continuous trend of A-P straightening of the shaft. This straightening was associated with a relative sigmoidal curve accentuation in the M-L plane. Given the timescale involved and the known phenomenon of declining mobility, such adaptive changes in bone geometry can be interpreted in terms of the diminishing biomechanical demands on the tibia under different living conditions.

Cross-sectional properties of the humeral diaphysis of Paranthropus boisei: Implications for upper limb function

A ∼1.52 Ma adult upper limb skeleton of Paranthropus boisei (KNM-ER 47000) recovered from the Koobi Fora Formation, Kenya (FwJj14E, Area 1A) includes most of the distal half of a right humerus (designated KNM-ER 47000B). Natural transverse fractures through the diaphysis of KNM-ER 470000B provide unobstructed views of cortical bone at two sections typically used for analyzing cross-sectional properties of hominids (i.e., 35% and 50% of humerus length from the distal end). Here we assess cross-sectional properties of KNM-ER 47000B and two other P. boisei humeri (OH 80-10, KNM-ER 739). Cross-sectional properties for P. boisei associated with bending/torsional strength (section moduli) and relative cortical thickness (%CA; percent cortical area) are compared to those reported for nonhuman hominids, AL 288-1 (Australopithecus afarensis), and multiple species of fossil and modern Homo. Polar section moduli (Z_p) are assessed relative to a mechanically relevant measure of body size (i.e., the product of mass [M] and humerus length [HL]). At both diaphyseal sections, P. boisei exhibits %CA that is high among extant hominids (both human and nonhuman) and similar to that observed among specimens of Pleistocene Homo. High values for Z_p relative to size (M × HL) indicate that P. boisei had humeral bending strength greater than that of modern humans and Neanderthals and similar to that of great apes, A. afarensis, and Homo habilis. Such high humeral strength is consistent with other skeletal features of P. boisei (reviewed here) that suggest routine use of powerful upper limbs for arboreal climbing.

Finite element analysis of a femur to deconstruct the paradox of bone curvature

Most long limb bones in terrestrial mammals exhibit a longitudinal curvature and have been found to be loaded in bending. Bone curvature poses a paradox in terms of the mechanical function of limb bones, for many believe the curvature in these bones increases bending stress, potentially reducing the bone's load carrying capacity (i.e., its mechanical strength). The aim of this study is to investigate the role of longitudinal bone curvature in the design of limb bones. In particular, it has been hypothesized that bone curvature results in a trade-off between the bone's mechanical strength and its bending predictability. We employed finite element analysis (FEA) of abstract and realistic human femora to address this issue. Geometrically simplified human femur models with different curvatures were developed and analyzed with a commercial FEA tool to examine how curvature affects the bone's bending predictability and load carrying capacity. Results were post-processed to yield probability density functions (PDFs) describing the circumferential location of maximum equivalent stress for various curvatures in order to assess bending predictability. To validate our findings, a finite element model was built from a CT scan of a real human femur and compared to the simplified femur model. We found general agreement in trends but some quantitative differences most likely due to the geometric differences between the digitally reconstructed and the simplified finite element models. As hypothesized by others, our results support the hypothesis that bone curvature can increase bending predictability, but at the expense of bone strength.

Role of Nonbehavioral Factors in Adjusting Long Bone Diaphyseal Structure in Free-ranging Pan troglodytes

Limb bones deform during locomotion and can resist the deformations by adjusting their shapes. For example, a tubular-shaped diaphysis best resists variably-oriented deformations. As behavioral profiles change during adulthood, patterns of bone deformation may exhibit age trends. Habitat characteristics, e.g., annual rainfall, tree density, and elevation changes, may influence bone deformations by eliciting individual components of behavioral repertoires and suppressing others, or by influencing movements during particular components. Habituated chimpanzee communities provide a unique opportunity to examine these factors because of the availability of morphological data and behavioral observations from known-age individuals inhabiting natural habitats. We evaluated adult femora and humeri of 18 female and 10 male free-ranging chimpanzees (Pan troglodytes) from communities in Gombe (Tanzania), Mahale Mountains (Tanzania), and Taï Forest (Côte d'Ivoire) National Parks. We compare cross sections at several locations (35%, 50%, 65% diaphyseal lengths). Community comparisons highlight different diaphyseal shapes of Taï females relative to Mahale and Gombe females, particularly in humeral diaphyses. Age trends in diaphyseal shapes are consistent with reduced activity levels in general, not only reduced arboreal activity. Age-related bone loss is apparent among community females, but is less striking among males. Community trends in diaphyseal shape are qualitatively consistent with ranked annual rainfall at localities, tree density, and elevation change or ruggedness of terrain. Habitat characteristics may contribute to variation in diaphyseal shape among chimpanzee communities, much like among modern human groups, but verification awaits further rigorous experimental and comparative analyses.

Locomotor behavior and long bone morphology in individual free-ranging chimpanzees

We combine structural limb data and behavioral data for free-ranging chimpanzees from Taï (Ivory Coast) and Mahale National Parks (Tanzania) to begin to consider the relationship between individual variation in locomotor activity and morphology. Femoral and humeral cross sections of ten individuals were acquired via computed tomography. Locomotor profiles of seven individuals were constructed from 3387 instantaneous time-point observations (87.4 hours). Within the limited number of suitable chimpanzees, individual variation in locomotor profiles displayed neither clear nor consistent trends with diaphyseal cross-sectional shapes. The percentages of specific locomotor modes did not relate well to diaphyseal shapes since neither infrequent nor frequent locomotor modes varied consistently with shapes. The percentage of arboreal locomotion, rather than estimated body mass, apparently had comparatively greater biological relevance to variation in diaphyseal shape. The mechanical consequences of locomotor modes on femoral and humeral diaphyseal shapes (e.g., orientation of bending strains) may overlap between naturalistic modes more than currently is recognized. Alternatively, diaphyseal shape may be unresponsive to mechanical demands of these specific locomotor modes. More data are needed in order to discern between these possibilities. Increasing the sample to include additional free-ranging chimpanzees, or primates in general, as well as devoting more attention to the mechanics of a greater variety of naturalistic locomotor modes would be fruitful to understanding the behavioral basis of diaphyseal shapes.