The Role of Cross-Sectional Geometry, Curvature, and Limb Posture in Maintaining Equal Safety Factors: A Computed Tomography Study

Endostructural and periosteal growth of the human humerus

The growth and development of long bones are of considerable interests in the fields of comparative anatomy and palaeoanthropology, as evolutionary changes and adaptations to specific physical activity patterns are expected to be revealed during bone ontogeny. Traditionally, the cross-sectional geometry of long bones has been examined at discrete locations usually placed at set intervals or fixed percentage distances along the midline axis of the bone shaft. More recently, the technique of morphometric mapping has enabled the continuous analysis of shape variation along the shaft. Here we extend this technique to the full sequence of late fetal and postnatal development of the humeral shaft in a modern human population sample, with the aim of establishing the shape changes during growth and their relationship with the development of the arm musculature and activity patterns. A sample of modern human humeri from individuals of age ranging from 24 weeks in utero to 18 years was imaged using microtomography at multiple resolutions and custom Matlab scripts. Standard biomechanical properties, cortical thickness, surface curvature, and pseudo-landmarks were extracted along radial vectors spaced at intervals of 1° at each 0.5% longitudinal increment measured along the shaft axis. Heat maps were also generated for cortical thickness and surface curvature. The results demonstrate that a whole bone approach to analysis of cross-sectional geometry is more desirable where possible, as there is a continuous pattern of variation along the shaft. It is also possible to discriminate very young individuals and adolescents from other groups by relative cortical thickness, and also by periosteal surface curvature.

Analyzing Modeled Torque Profiles to Understand Scale-Dependent Active Muscle Responses in the Hip Joint

Animal locomotion is influenced by a combination of constituent joint torques (e.g., due to limb inertia and passive viscoelasticity), which determine the necessary muscular response to move the limb. Across animal size-scales, the relative contributions of these constituent joint torques affect the muscular response in different ways. We used a multi-muscle biomechanical model to analyze how passive torque components change due to an animal’s size-scale during locomotion. By changing the size-scale of the model, we characterized emergent muscular responses at the hip as a result of the changing constituent torque profile. Specifically, we found that activation phases between extensor and flexor torques to be opposite between small and large sizes for the same kinematic motion. These results suggest general principles of how animal size affects neural control strategies. Our modeled torque profiles show a strong agreement with documented hindlimb torque during locomotion and can provide insights into the neural organization and muscle activation behavior of animals whose motion has not been extensively documented.

Computational model of endochondral ossification: Simulating growth of a long bone

Mechanical loading is a crucial factor in joint and bone development. Using a computational model, we investigated the role of mechanics on cartilage growth rate, ossification of the secondary center, formation of the growth plate, and overall bone shape. A computational algorithm was developed and implemented into finite element models to simulate the endochondral ossification for symmetric and asymmetric motion in a generic diarthrodial joint. Under asymmetric loading condition the secondary center ossifies asymmetrically leaning toward the external load and results in tilted growth plate. Also the mechanics seems to have greater influence in the early onset of the ossification of the secondary center rather than later progression of the center. While previous models have simulated select stages of skeletal development, our model can simulate growth and ossification during the entirety of post-natal development. Such computational models of skeletal development may provide insight into specific loading conditions that cause bone and joint deformities, and the required timing for rehabilitative repair.

Extensive chondroid bone in juvenile duck limbs hints at accelerated growth mechanism in avian skeletogenesis

Modern altricial birds are the fastest growing vertebrates, whereas various degrees of precocity (functional maturity) result in slower growth. Diaphyseal osteohistology, the best proxy for inferring relative growth rates in fossils, suggests that in the earliest birds, posthatching growth rates were more variable than in modern representatives, with some showing considerably slow growth that was attributed to their assumed precocial flight abilities. For finding clues how precocial or altricial skeletogenesis and related growth acceleration could be traced in avian evolution, as a case study we investigated the growing limb diaphyseal histology in an ontogenetic series of ducks which, among several other avian taxa, show a combination of altricial wing and precocial leg development. Here we report the unexpected discovery that chondroid bone, a skeletal tissue family intermediate between cartilage and bone, extensively contributes to the development of limb bone shaft in ducks up to at least 30 days posthatching age. To our knowledge, chondroid bone has never been reported in such quantities and with an ontogenetically extended deposition period in post‐embryonic, non‐pathological periosteal bone formation of any tetrapod limb. It shows transitional cellular/lacunar morphologies and matrix staining properties between cartilage and woven bone and takes a significant part in the diametric growth of the limb bone shaft. Its amount and distribution through duckling ontogeny seems to be associated with the disparate functional and growth trajectories of the altricial wings vs. precocial legs characteristic of duck limb development. The presence of isogenous cell groups in the periosteal chondroid bone implies that cartilage‐like interstitial growth took place before matrix mineralization complementing appositional bone growth. Based on these characteristics and on its fast formation rate in all previously reported normal as well as pathological cases, we suggest that chondroid bone in ducks significantly accelerates diametric limb bone growth. Related to this growth acceleration, we hypothesize that chondroid bone may be generally present in the growing limb bones of modern birds and hence may have key skeletogenic importance in achieving extreme avian growth rates and placing birds among the fastest growing vertebrates. Thus, we encourage future studies to test this hypothesis by investigating the occurrence of chondroid bone in a variety of precocial and altricial bird species, and to explore the presence of similar tissues in the growing limbs of other extant and extinct tetrapods in order to understand the evolutionary significance of chondroid bone in accelerated appendicular skeletogenesis.

Convergent metatarsal fusion in jerboas and chickens is mediated by similarities and differences in the patterns of osteoblast and osteoclast activities

In many vertebrate animals that run or leap, the metatarsals and/or metacarpals of the distal limb are fused into a single larger element, likely to resist fracture due to high ground-reaction forces during locomotion. Although metapodial fusion evolved independently in modern birds, ungulates, and jerboas, the developmental basis has only been explored in chickens, which diverged from the mammalian lineage approximately 300 million years ago. Here, we use a bipedal rodent, the lesser Egyptian jerboa (Jaculus jaculus), to understand the cellular processes of metatarsal fusion in a mammal, and we revisit the developing chicken to assess similarities and differences in the localization of osteoblast and osteoclast activities. In both species, adjacent metatarsals align along flat surfaces, osteoblasts cross the periosteal membrane to unite the three elements in a single circumference, and osteoclasts resorb bone at the interfaces leaving a single marrow cavity. However, the pattern of osteoclast activity differs in each species; osteoclasts are highly localized to resorb bone at the interfaces of neighboring jerboa metatarsals and are distributed throughout the endosteum of chicken metatarsals. Each species, therefore, provides an opportunity to understand mechanisms that pattern osteoblast and osteoclast activities to alter bone shape during development and evolution.

Cancellous bone and theropod dinosaur locomotion. Part I-an examination of cancellous bone architecture in the hindlimb bones of theropods

This paper is the first of a three-part series that investigates the architecture of cancellous ('spongy') bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and has previously been used to infer locomotor biomechanics in extinct tetrapod vertebrates, especially primates. Despite great promise, cancellous bone architecture has remained little utilized for investigating locomotion in many other extinct vertebrate groups, such as dinosaurs. Documentation and quantification of architectural patterns across a whole bone, and across multiple bones, can provide much information on cancellous bone architectural patterns and variation across species. Additionally, this also lends itself to analysis of the musculoskeletal biomechanical factors involved in a direct, mechanistic fashion. On this premise, computed tomographic and image analysis techniques were used to describe and analyse the three-dimensional architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs for the first time. A comprehensive survey across many extant and extinct species is produced, identifying several patterns of similarity and contrast between groups. For instance, more stemward non-avian theropods (e.g. ceratosaurs and tyrannosaurids) exhibit cancellous bone architectures more comparable to that present in humans, whereas species more closely related to birds (e.g. paravians) exhibit architectural patterns bearing greater similarity to those of extant birds. Many of the observed patterns may be linked to particular aspects of locomotor biomechanics, such as the degree of hip or knee flexion during stance and gait. A further important observation is the abundance of markedly oblique trabeculae in the diaphyses of the femur and tibia of birds, which in large species produces spiralling patterns along the endosteal surface. Not only do these observations provide new insight into theropod anatomy and behaviour, they also provide the foundation for mechanistic testing of locomotor hypotheses via musculoskeletal biomechanical modelling.

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis

The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis) to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex—long argued to indicate competent running ability—would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

A study of the progression of damage in an axially loaded Branta leucopsis femur using X-ray computed tomography and digital image correlation

This paper uses X-ray computed tomography to track the mechanical response of a vertebrate (Barnacle goose) long bone subjected to an axial compressive load, which is increased gradually until failure. A loading rig was mounted in an X-ray computed tomography system so that a time-lapse sequence of three-dimensional (3D) images of the bone’s internal (cancellous or trabecular) structure could be recorded during loading. Five distinct types of deformation mechanism were observed in the cancellous part of the bone. These were (i) cracking, (ii) thinning (iii) tearing of cell walls and struts, (iv) notch formation, (v) necking and (vi) buckling. The results highlight that bone experiences brittle (notch formation and cracking), ductile (thinning, tearing and necking) and elastic (buckling) modes of deformation. Progressive deformation, leading to cracking was studied in detail using digital image correlation. The resulting strain maps were consistent with mechanisms occurring at a finer-length scale. This paper is the first to capture time-lapse 3D images of a whole long bone subject to loading until failure. The results serve as a unique reference for researchers interested in how bone responds to loading. For those using computer modelling, the study not only provides qualitative information for verification and validation of their simulations but also highlights that constitutive models for bone need to take into account a number of different deformation mechanisms.

Convex-hull mass estimates of the dodo (Raphus cucullatus): application of a CT-based mass estimation technique

The external appearance of the dodo (Raphus cucullatus, Linnaeus, 1758) has been a source of considerable intrigue, as contemporaneous accounts or depictions are rare. The body mass of the dodo has been particularly contentious, with the flightless pigeon alternatively reconstructed as slim or fat depending upon the skeletal metric used as the basis for mass prediction. Resolving this dichotomy and obtaining a reliable estimate for mass is essential before future analyses regarding dodo life history, physiology or biomechanics can be conducted. Previous mass estimates of the dodo have relied upon predictive equations based upon hind limb dimensions of extant pigeons. Yet the hind limb proportions of dodo have been found to differ considerably from those of their modern relatives, particularly with regards to midshaft diameter. Therefore, application of predictive equations to unusually robust fossil skeletal elements may bias mass estimates. We present a whole-body computed tomography (CT) -based mass estimation technique for application to the dodo. We generate 3D volumetric renders of the articulated skeletons of 20 species of extant pigeons, and wrap minimum-fit ‘convex hulls’ around their bony extremities. Convex hull volume is subsequently regressed against mass to generate predictive models based upon whole skeletons. Our best-performing predictive model is characterized by high correlation coefficients and low mean squared error (a = − 2.31, b = 0.90, r² = 0.97, MSE = 0.0046). When applied to articulated composite skeletons of the dodo (National Museums Scotland, NMS.Z.1993.13; Natural History Museum, NHMUK A.9040 and S/1988.50.1), we estimate eviscerated body masses of 8–10.8 kg. When accounting for missing soft tissues, this may equate to live masses of 10.6–14.3 kg. Mass predictions presented here overlap at the lower end of those previously published, and support recent suggestions of a relatively slim dodo. CT-based reconstructions provide a means of objectively estimating mass and body segment properties of extinct species using whole articulated skeletons.

Musculoskeletal modelling of an ostrich (Struthio camelus) pelvic limb: influence of limb orientation on muscular capacity during locomotion

We developed a three-dimensional, biomechanical computer model of the 36 major pelvic limb muscle groups in an ostrich (Struthio camelus) to investigate muscle function in this, the largest of extant birds and model organism for many studies of locomotor mechanics, body size, anatomy and evolution. Combined with experimental data, we use this model to test two main hypotheses. We first query whether ostriches use limb orientations (joint angles) that optimize the moment-generating capacities of their muscles during walking or running. Next, we test whether ostriches use limb orientations at mid-stance that keep their extensor muscles near maximal, and flexor muscles near minimal, moment arms. Our two hypotheses relate to the control priorities that a large bipedal animal might evolve under biomechanical constraints to achieve more effective static weight support. We find that ostriches do not use limb orientations to optimize the moment-generating capacities or moment arms of their muscles. We infer that dynamic properties of muscles or tendons might be better candidates for locomotor optimization. Regardless, general principles explaining why species choose particular joint orientations during locomotion are lacking, raising the question of whether such general principles exist or if clades evolve different patterns (e.g., weighting of muscle force-length or force-velocity properties in selecting postures). This leaves theoretical studies of muscle moment arms estimated for extinct animals at an impasse until studies of extant taxa answer these questions. Finally, we compare our model's results against those of two prior studies of ostrich limb muscle moment arms, finding general agreement for many muscles. Some flexor and extensor muscles exhibit self-stabilization patterns (posture-dependent switches between flexor/extensor action) that ostriches may use to coordinate their locomotion. However, some conspicuous areas of disagreement in our results illustrate some cautionary principles. Importantly, tendon-travel empirical measurements of muscle moment arms must be carefully designed to preserve 3D muscle geometry lest their accuracy suffer relative to that of anatomically realistic models. The dearth of accurate experimental measurements of 3D moment arms of muscles in birds leaves uncertainty regarding the relative accuracy of different modelling or experimental datasets such as in ostriches. Our model, however, provides a comprehensive set of 3D estimates of muscle actions in ostriches for the first time, emphasizing that avian limb mechanics are highly three-dimensional and complex, and how no muscles act purely in the sagittal plane. A comparative synthesis of experiments and models such as ours could provide powerful synthesis into how anatomy, mechanics and control interact during locomotion and how these interactions evolve. Such a framework could remove obstacles impeding the analysis of muscle function in extinct taxa.

Scaling of convex hull volume to body mass in modern primates, non-primate mammals and birds

The volumetric method of ‘convex hulling’ has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol_CH) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (M_b) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol_CH has remained unclear. Specifically, when vol_CH scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of M_b to vol_CH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r² = 0.97–0.99) and low mean percentage prediction error (11–20%). Results suggest non-primate mammals scale body mass to vol_CH isometrically (b = 0.92, 95%CI = 0.85–1.00, p = 0.08). Birds scale body mass to vol_CH with negative allometry (b = 0.81, 95%CI = 0.70–0.91, p = 0.011) and apparent density (vol_CH/M_b) therefore decreases with mass (r² = 0.36, p<0.05). In contrast, primates scale body mass to vol_CH with positive allometry (b = 1.07, 95%CI = 1.01–1.12, p = 0.05) and apparent density therefore increases with size (r² = 0.46, p = 0.025). We interpret such departures from isometry in the context of the ‘missing mass’ of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat.

More than one way of being a moa: differences in leg bone robustness map divergent evolutionary trajectories in Dinornithidae and Emeidae (Dinornithiformes)

The extinct moa of New Zealand included three families (Megalapterygidae; Dinornithidae; Emeidae) of flightless palaeognath bird, ranging in mass from <15 kg to >200 kg. They are perceived to have evolved extremely robust leg bones, yet current estimates of body mass have very wide confidence intervals. Without reliable estimators of mass, the extent to which dinornithid and emeid hindlimbs were more robust than modern species remains unclear. Using the convex hull volumetric-based method on CT-scanned skeletons, we estimate the mass of a female Dinornis robustus (Dinornithidae) at 196 kg (range 155–245 kg) and of a female Pachyornis australis (Emeidae) as 50 kg (range 33–68 kg). Finite element analysis of CT-scanned femora and tibiotarsi of two moa and six species of modern palaeognath showed that P. australis experienced the lowest values for stress under all loading conditions, confirming it to be highly robust. In contrast, stress values in the femur of D. robustus were similar to those of modern flightless birds, whereas the tibiotarsus experienced the highest level of stress of any palaeognath. We consider that these two families of Dinornithiformes diverged in their biomechanical responses to selection for robustness and mobility, and exaggerated hindlimb strength was not the only successful evolutionary pathway.

Ontogenetic scaling of fore- and hind limb posture in wild chacma baboons (Papio hamadryas ursinus)

Large-scale interspecific studies of mammals ranging between 0.04–280 kg have shown that larger animals walk with more extended limb joints. Within a taxon or clade, however, the relationship between body size and joint posture is less straightforward. Factors that may affect the lack of congruence between broad and narrow phylogenetic analyses of limb kinematics include limited sampling of (1) ranges of body size, and/or (2) numbers of individuals. Unfortunately, both issues are inherent in laboratory-based or zoo locomotion research. In this study, we examined the relationship between body mass and elbow and knee joint angles (our proxies of fore- and hind limb posture, respectively) in a cross-sectional ontogenetic sample of wild chacma baboons (Papio hamadryas ursinus) habituated in the De Hoop Nature Reserve, South Africa. Videos were obtained from 33 individuals of known age (12 to ≥108 months) and body mass (2–29.5 kg) during walking trials. Results show that older, heavier baboons walk with significantly more extended knee joints but not elbow joints. This pattern is consistent when examining only males, but not within the female sample. Heavier, older baboons also display significantly less variation in their hind limb posture compared to lighter, young animals. Thus, within this ontogenetic sample of a single primate species spanning an order of magnitude in body mass, hind limb posture exhibited a postural scaling phenomenon while the forelimbs did not. These findings may further help explain 1) why younger mammals (including baboons) tend to have relatively stronger bones than adults, and 2) why humeri appear relatively weaker than femora (in at least baboons). Finally, this study demonstrates how field-acquired kinematics can help answer fundamental biomechanical questions usually addressed only in animal gait laboratories.