Integration of feedforward and feedback control in the neuromechanics of vertebrate locomotion: a review of experimental, simulation and robotic studies

Animal locomotion is the result of complex and multi-layered interactions between the nervous system, the musculo-skeletal system and the environment. Decoding the underlying mechanisms requires an integrative approach. Comparative experimental biology has allowed researchers to study the underlying components and some of their interactions across diverse animals. These studies have shown that locomotor neural circuits are distributed in the spinal cord, the midbrain and higher brain regions in vertebrates. The spinal cord plays a key role in locomotor control because it contains central pattern generators (CPGs) - systems of coupled neuronal oscillators that provide coordinated rhythmic control of muscle activation that can be viewed as feedforward controllers - and multiple reflex loops that provide feedback mechanisms. These circuits are activated and modulated by descending pathways from the brain. The relative contributions of CPGs, feedback loops and descending modulation, and how these vary between species and locomotor conditions, remain poorly understood. Robots and neuromechanical simulations can complement experimental approaches by testing specific hypotheses and performing what-if scenarios. This Review will give an overview of key knowledge gained from comparative vertebrate experiments, and insights obtained from neuromechanical simulations and robotic approaches. We suggest that the roles of CPGs, feedback loops and descending modulation vary among animals depending on body size, intrinsic mechanical stability, time required to reach locomotor maturity and speed effects. We also hypothesize that distal joints rely more on feedback control compared with proximal joints. Finally, we highlight important opportunities to address fundamental biological questions through continued collaboration between experimentalists and engineers.

Scaling and relations of morphology with locomotor kinematics in the sidewinder rattlesnake Crotalus cerastes

The movement of limbless terrestrial animals differs fundamentally from that of limbed animals, yet few scaling studies of their locomotor kinematics and morphology are available. We examined scaling and relations of morphology and locomotion in sidewinder rattlesnakes (Crotalus cerastes). During sidewinding locomotion, a snake lifts sections of its body up and forward while other sections maintain static ground contact. We used high-speed video to quantify whole-animal speed and acceleration; the height to which body sections are lifted; and the frequency, wavelength, amplitude and skew angle (degree of tilting) of the body wave. Kinematic variables were not sexually dimorphic, and most did not deviate from isometry, except wave amplitude. Larger sidewinders were not faster, contrary to many results from limbed terrestrial animals. Free from the need to maintain dynamic similarity (because their locomotion is dominated by friction rather than inertia), limbless species may have greater freedom to modulate speed independently of body size. Path analysis supported: (1) a hypothesized relationship between body width and wavelength, indicating that stouter sidewinders form looser curves; (2) a strong relationship between cycle frequency and whole-animal speed; and (3) weaker effects of wavelength (positive) and amplitude (negative) on speed. We suggest that sidewinding snakes may face a limit on stride length (to which amplitude and wavelength both contribute), beyond which they sacrifice stability. Thus, increasing frequency may be the best way to increase speed. Finally, frequency and skew angle were correlated, a result that deserves future study from the standpoint of both kinematics and physiology.

Post-hatching growth of the limbs in an altricial bird species

The fore‐ and hindlimbs of birds are specialized to perform different functions. The growth patterns of limb bones and their relationship with the ontogeny of locomotion are critical to our understanding of variation in morphological, physiological and life‐history traits within and among species. Unfortunately, the ontogenetic development of limb bones has not been well explored, especially in altricial birds. In this study, we sampled the entire measurements of the pigeon (Columba livia) of individual skeletons, to investigate the ontogenetic allometry of limb bones by reduced major axis regression. The ulna and humerus were found to be positively allometric in relation to body mass, with the ulna growing more rapidly than the humerus. Together with previous data, this suggests that strong positive allometric growth in forelimb bones could be a common trend among diverse Carinatae groups. Hindlimb was dominated by positive allometry, but was variable in the growth of the tarsometatarsus which included three allometric patterns. A greater dorsoventral diameter in the midsection of the humerus and ulna confers superior bending resistance and is ideal for flapping/gliding flight. Shape variation in the midsection of different hindlimb components reflects different mechanical loading, and the markedly inverse trend between the tibiotarsus and tarsometatarsus before 28 days of age also suggests loading change before fledging. Before fledging, the growth of the leg bones was prior to that of the wing bones. This kind of asynchronous development of the fore‐ and hindlimbs was associated with the establishment and improvement of different functions, and with shifts in the importance of different functions over time.

Ontogenetic shape changes in the pelvis of the Greater Rhea (Aves, Palaeognathae) and their relationships with cursorial locomotion: a geometric morphometric approach

Knowledge of the ontogenetic pattern of morphological features is essential to improve biological interpretations. The study of morphological features of the pelvic girdle and hind limb apparatus throughout growth is an excellent approach to understand how the skeletal morphology and muscles are interrelated during growth in a bird with a specialized mode of locomotion. The Greater Rhea (Rhea americana) is a large cursorial palaeognathous bird with long legs and powerful musculature. The postnatal shape changes of the pelvis of this bird were studied with geometric morphometric techniques, using landmarks and semilandmarks. In addition, regression analyses were used to explore the association between pelvic shape changes with muscle and body mass. The pelvises of 16 specimens of Rhea americana from 1 month old to adulthood were studied in dorsal and lateral views. Noticeable differences in pelvic shape were noted between ages, particularly in lateral view. In young birds, the pre- and post-acetabular ilium was subequal in length, whereas in adults the pre-acetabular ilium became shorter. In dorsal view, the main shape changes observed were the progressive thinning of both ilium portions and the elongation of the vertex craniolateralis ilii from chicks to adulthood. In this view, the only clear differentiation was between young and adult birds. Shape differences were influenced by body mass and pelvic muscles; the post-acetabular muscle mass explained the highest percentage of the variation. The specialized locomotion of Greater Rhea is reflected in their pelvic musculoskeletal system, in which the change to a longer post-acetabular ilium correlates with the growth of the powerful post-acetabular muscles. The actions of these muscles provide the necessary strength to support the body mass, minimize the body swinging movements and propel the body forward during locomotion. Bone morphology is affected by the forces produced by body mass and the muscle activity, demonstrating the presence of common growth mechanisms, which are primordial and gave rise to a functional and properly proportioned adult.

Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots

Bipedal animals have diverse morphologies and advanced locomotion abilities. Terrestrial birds, in particular, display agile, efficient, and robust running motion, in which they exploit the interplay between the body segment masses and moment of inertias. On the other hand, most legged robots are not able to generate such versatile and energy-efficient motion and often disregard trunk movements as a means to enhance their locomotion capabilities. Recent research investigated how trunk motions affect the gait characteristics of humans, but there is a lack of analysis across different bipedal morphologies. To address this issue, we analyze avian running based on a spring-loaded inverted pendulum model with a pronograde (horizontal) trunk. We use a virtual point based control scheme and modify the alignment of the ground reaction forces to assess how our control strategy influences the trunk pitch oscillations and energetics of the locomotion. We derive three potential key strategies to leverage trunk pitch motions that minimize either the energy fluctuations of the center of mass or the work performed by the hip and leg. We suggest how these strategies could be used in legged robotics.

Rat bone properties and their relationship to gait during growth

Allometric relationships have been studied over different Orders of mammals to understand how bone accommodates the mechanical demands associated with increasing mass. However, less attention has been given to the scaling of bone within a single lifetime. We aimed to determine how bone morphology and tissue density are related to (1) bending and compressive strength, and (2) gait dynamics. Longitudinal in vivo computed tomography of the hindlimbs and gait data were collected from female rats (n=5, age 8-20 weeks). Cross-sectional properties and tissue density were measured at the diaphysis, distal and proximal regions of the tibia and scaling exponents were calculated. Finite element models of the tibia were used to simulate loading during walking using joint forces from inverse dynamics calculation to determine the strain energy density and longitudinal strain at the midshaft. Second moment of area at the diaphysis followed strain similarity-based allometry, while bone area trended towards positive allometry. Strain energy in the diaphysis under transverse loading was lower than axial loading throughout growth. While both axial and transverse loading resulted in bending, tensile strains were mitigated by a change in the neutral axis and resulted in overall lower longitudinal tensile strains. The tissue density and cross-sectional properties initially increased and converged by 11 weeks of age and were correlated with changes in ground reaction forces. The scaling analyses imply that rodent tibia is (re)modeled in order to sustain bending at the midshaft during growth. The finite element results and relatively constant density after 10 weeks of age indicate that structural parameters may be the primary determinant of bone strength in the growing rodent tibia. The correlations between bone properties and joint angles imply that the changes in posture may affect bone growth in specific regions.

Ontogenetic scaling of pelvic limb muscles, tendons and locomotor economy in the ostrich (Struthio camelus)

In rapidly growing animals there are numerous selective pressures and developmental constraints underpinning the ontogenetic development of muscle-tendon morphology and mechanical properties. Muscle force generating capacity, tendon stiffness, elastic energy storage capacity and efficiency were calculated from muscle and tendon morphological parameters and in vitro tendon mechanical properties obtained from a growth series of ostrich cadavers. Ontogenetic scaling relationships were established using reduced major axis regression analysis. Ostrich pelvic limb muscle mass and cross-sectional area broadly scaled with positive allometry, indicating maintained or relatively greater capacity for maximum isometric force generation in larger animals. The length of distal limb tendons was found to scale with positive allometry in several tendons associated with antigravity support and elastic energy storage during locomotion. Distal limb tendon stiffness scaled with negative allometry with respect to body mass, with tendons being relatively more compliant in larger birds. Tendon material properties also appeared to be size-dependent, suggesting that the relative increased compliance of tendons in larger ostriches is due in part to compensatory distortions in tendon material properties during maturation and development, not simply from ontogenetic changes in tendon geometry. Our results suggest that the previously reported increase in locomotor economy through ontogeny in the ostrich is due to greater potential for elastic energy storage with increasing body size. In fact, the rate of this increase may be somewhat greater than the conservative predictions of previous studies, thus illustrating the biological importance of elastic tendon structures in adult ostriches.

Ontogeny of effective mechanical advantage in eastern cottontail rabbits (Sylvilagus floridanus)

Juvenile animals must survive in the same environment as adults despite smaller sizes, immature musculoskeletal tissues, general ecological naïveté and other limits of performance. Developmental changes in muscle leverage could constitute one mechanism to promote increased performance in juveniles despite ontogenetic limitations. We tested this hypothesis using a holistic dataset on growth and locomotor development in wild eastern cottontail rabbits (Sylvilagus floridanus) to examine ontogenetic changes in hindlimb muscle effective mechanical advantage (EMA). EMA is a dimensionless index of muscle leverage, equal to the quotient of average muscle lever length and the load arm length of the ground reaction force (GRF), effectively representing the magnitude of output force arising from a given muscle force. We found that EMA at the hip and ankle joints, as well as overall hindlimb EMA, significantly declined across ontogeny in S. floridanus, whereas EMA at the knee joint remained unchanged. Ontogenetic decreases in EMA were due to isometric scaling of muscle lever arm lengths alongside positive ontogenetic allometry of GRF load arm lengths - which in turn was primarily related to positive allometry of hindlimb segment lengths. Greater EMA limits the estimated volume of hindlimb extensor muscle that has to be activated in young rabbits, likely mitigating the energetic cost of locomotion and saving metabolic resources for other physiological functions, such as growth and tissue differentiation. An additional examination of limb growth allometry across a diverse sample of mammalian taxa suggests that ontogenetic decreases in limb joint EMA may be a common mammalian trend.

Ontogenetic allometry and architectural properties of the paravertebral and hindlimb musculature in Eastern cottontail rabbits (Sylvilagus floridanus): functional implications for developmental changes in locomotor performance

Due to small body size, an immature musculoskeletal system, and other growth-related limits on performance, juvenile mammals frequently experience a greater risk of predation than their adult counterparts. As a result, behaviorally precocious juveniles are hypothesized to exhibit musculoskeletal advantages that permit them to accelerate rapidly and evade predation. This hypothesis was tested through detailed quantitative evaluation of muscle growth in wild Eastern cottontail rabbits (Sylvilagus floridanus). Cottontail rabbits experience high rates of mortality during the first year of life, suggesting that selection might act to improve performance in growing juveniles. Therefore, it was predicted that muscle properties associated with force and power capacity should be enhanced in juvenile rabbits to facilitate enhanced locomotor performance. We quantified muscle architecture from 24 paravertebral and hindlimb muscles across ontogeny in a sample of n = 29 rabbits and evaluated the body mass scaling of muscle mass (MM), physiological cross-sectional area (PCSA), isometric force (Fmax ), and instantaneous power (Pinst ), along with several dimensionless architectural indices. In contrast to our hypothesis, MM and PCSA for most muscles change with positive allometry during growth by scaling at M b 1.3 and M b 1.1 , respectively, whereas Fmax and Pinst generally scale indistinguishably from isometry, as do the architectural indices tested. However, scaling patterns indicate that the digital flexors and ankle extensors of juvenile S. floridanus have greater capacities for force and power, respectively, than those in adults, suggesting these muscle properties may be a part of several compensatory features that promote enhanced acceleration performance in young rabbits. Overall, our study implies that body size constraints place larger, more mature rabbits at a disadvantage during acceleration, and that adults must develop hypertrophied muscles in order to maintain mechanical similarity in force and power capacities across development. These findings challenge the accepted understanding that juvenile animals are at a performance detriment relative to adults. Instead, for prey-predator interactions necessitating short intervals of high force and power generation relative to body mass, as demonstrated by rapid acceleration of cottontail rabbits fleeing predators, it may be the adults that struggle to keep pace with juveniles.

An instrumented centrifuge for studying mouse locomotion and behaviour under hypergravity

Gravity may influence multiple aspects of legged locomotion, from the periods of limbs moving as pendulums to the muscle forces required to support the body. We present a system for exposing mice to hypergravity using a centrifuge and studying their locomotion and activity during exposure. Centrifuge-induced hypergravity has the advantages that it both allows animals to move freely, and it affects both body and limbs. The centrifuge can impose two levels of hypergravity concurrently, using two sets of arms of different lengths, each carrying a mouse cage outfitted with a force and speed measuring exercise wheel and an infrared high-speed camera; both triggered automatically when a mouse begins running on the wheel. Welfare is monitored using infrared cameras. As well as detailing the design of the centrifuge and instrumentation, we present example data from mice exposed to multiple levels of hypergravity and details of how they acclimatized to hypergravity.

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.

Using step width to compare locomotor biomechanics between extinct, non-avian theropod dinosaurs and modern obligate bipeds

How extinct, non-avian theropod dinosaurs locomoted is a subject of considerable interest, as is the manner in which it evolved on the line leading to birds. Fossil footprints provide the most direct evidence for answering these questions. In this study, step width-the mediolateral (transverse) distance between successive footfalls-was investigated with respect to speed (stride length) in non-avian theropod trackways of Late Triassic age. Comparable kinematic data were also collected for humans and 11 species of ground-dwelling birds. Permutation tests of the slope on a plot of step width against stride length showed that step width decreased continuously with increasing speed in the extinct theropods (p < 0.001), as well as the five tallest bird species studied (p < 0.01). Humans, by contrast, showed an abrupt decrease in step width at the walk-run transition. In the modern bipeds, these patterns reflect the use of either a discontinuous locomotor repertoire, characterized by distinct gaits (humans), or a continuous locomotor repertoire, where walking smoothly transitions into running (birds). The non-avian theropods are consequently inferred to have had a continuous locomotor repertoire, possibly including grounded running. Thus, features that characterize avian terrestrial locomotion had begun to evolve early in theropod history.

The influence of speed and size on avian terrestrial locomotor biomechanics: Predicting locomotion in extinct theropod dinosaurs

How extinct, non-avian theropod dinosaurs moved is a subject of considerable interest and controversy. A better understanding of non-avian theropod locomotion can be achieved by better understanding terrestrial locomotor biomechanics in their modern descendants, birds. Despite much research on the subject, avian terrestrial locomotion remains little explored in regards to how kinematic and kinetic factors vary together with speed and body size. Here, terrestrial locomotion was investigated in twelve species of ground-dwelling bird, spanning a 1,780-fold range in body mass, across almost their entire speed range. Particular attention was devoted to the ground reaction force (GRF), the force that the feet exert upon the ground. Comparable data for the only other extant obligate, striding biped, humans, were also collected and studied. In birds, all kinematic and kinetic parameters examined changed continuously with increasing speed, while in humans all but one of those same parameters changed abruptly at the walk-run transition. This result supports previous studies that show birds to have a highly continuous locomotor repertoire compared to humans, where discrete 'walking' and 'running' gaits are not easily distinguished based on kinematic patterns alone. The influences of speed and body size on kinematic and kinetic factors in birds are developed into a set of predictive relationships that may be applied to extinct, non-avian theropods. The resulting predictive model is able to explain 79-93% of the observed variation in kinematics and 69-83% of the observed variation in GRFs, and also performs well in extrapolation tests. However, this study also found that the location of the whole-body centre of mass may exert an important influence on the nature of the GRF, and hence some caution is warranted, in lieu of further investigation.

Radiographic Anatomy of the Metatarsophalangeal Joint and Digits of the Ostrich (Struthio camelus)

The aim of this study was to develop a detailed and accessible set of reference images of the normal radiographic anatomy of the digits of the ostrich (Struthio camelus), with emphasis on the metatarsophalangeal joint and its arthrography. The distal excised pelvic limbs of 10 normal ostriches of different ages (ranging from 10 to 365 days of age) obtained from an abattoir were radiographed, and 2 arthrograms were performed. To illustrate the normal radiographic anatomy of the tarsometatarsal bone, 39 images were selected, labelled, and presented along with detailed descriptions and corresponding images of the bony skeleton. These results provide a valuable dataset to assist in understanding the normal anatomy of the ostrich metatarsophalangeal joint and digits and allow comparison of abnormal corresponding structures in clinical cases in ostriches.

Preferred gait and walk-run transition speeds in ostriches measured using GPS-IMU sensors

The ostrich (Struthio camelus) is widely appreciated as a fast and agile bipedal athlete, and is a useful comparative bipedal model for human locomotion. Here, we used GPS-IMU sensors to measure naturally selected gait dynamics of ostriches roaming freely over a wide range of speeds in an open field and developed a quantitative method for distinguishing walking and running using accelerometry. We compared freely selected gait-speed distributions with previous laboratory measures of gait dynamics and energetics. We also measured the walk-run and run-walk transition speeds and compared them with those reported for humans. We found that ostriches prefer to walk remarkably slowly, with a narrow walking speed distribution consistent with minimizing cost of transport (CoT) according to a rigid-legged walking model. The dimensionless speeds of the walk-run and run-walk transitions are slower than those observed in humans. Unlike humans, ostriches transition to a run well below the mechanical limit necessitating an aerial phase, as predicted by a compass-gait walking model. When running, ostriches use a broad speed distribution, consistent with previous observations that ostriches are relatively economical runners and have a flat curve for CoT against speed. In contrast, horses exhibit U-shaped curves for CoT against speed, with a narrow speed range within each gait for minimizing CoT. Overall, the gait dynamics of ostriches moving freely over natural terrain are consistent with previous lab-based measures of locomotion. Nonetheless, ostriches, like humans, exhibit a gait-transition hysteresis that is not explained by steady-state locomotor dynamics and energetics. Further study is required to understand the dynamics of gait transitions.

Phalangeal joints kinematics during ostrich (Struthio camelus) locomotion

The ostrich is a highly cursorial bipedal land animal with a permanently elevated metatarsophalangeal joint supported by only two toes. Although locomotor kinematics in walking and running ostriches have been examined, these studies have been largely limited to above the metatarsophalangeal joint. In this study, kinematic data of all major toe joints were collected from gaits with double support (slow walking) to running during stance period in a semi-natural setup with two selected cooperative ostriches. Statistical analyses were conducted to investigate the effect of locomotor gait on toe joint kinematics. The MTP3 and MTP4 joints exhibit the largest range of motion whereas the first phalangeal joint of the 4th toe shows the largest motion variability. The interphalangeal joints of the 3rd and 4th toes present very similar motion patterns over stance phases of slow walking and running. However, the motion patterns of the MTP3 and MTP4 joints and the vertical displacement of the metatarsophalangeal joint are significantly different during running and slow walking. Because of the biomechanical requirements, osctriches are likely to select the inverted pendulum gait at low speeds and the bouncing gait at high speeds to improve movement performance and energy economy. Interestingly, the motions of the MTP3 and MTP4 joints are highly synchronized from slow to fast locomotion. This strongly suggests that the 3rd and 4th toes really work as an “integrated system” with the 3rd toe as the main load bearing element whilst the 4th toe as the complementary load sharing element with a primary role to ensure the lateral stability of the permanently elevated metatarsophalangeal joint.

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.

Ontogenetic scaling patterns and functional anatomy of the pelvic limb musculature in emus (Dromaius novaehollandiae)

Emus (Dromaius novaehollandiae) are exclusively terrestrial, bipedal and cursorial ratites with some similar biomechanical characteristics to humans. Their growth rates are impressive, as their body mass increases eighty-fold from hatching to adulthood whilst maintaining the same mode of locomotion throughout life. These ontogenetic characteristics stimulate biomechanical questions about the strategies that allow emus to cope with their rapid growth and locomotion, which can be partly addressed via scaling (allometric) analysis of morphology. In this study we have collected pelvic limb anatomical data (muscle architecture, tendon length, tendon mass and bone lengths) and calculated muscle physiological cross sectional area (PCSA) and average tendon cross sectional area from emus across three ontogenetic stages (n = 17, body masses from 3.6 to 42 kg). The data were analysed by reduced major axis regression to determine how these biomechanically relevant aspects of morphology scaled with body mass. Muscle mass and PCSA showed a marked trend towards positive allometry (26 and 27 out of 34 muscles respectively) and fascicle length showed a more mixed scaling pattern. The long tendons of the main digital flexors scaled with positive allometry for all characteristics whilst other tendons demonstrated a less clear scaling pattern. Finally, the two longer bones of the limb (tibiotarsus and tarsometatarsus) also exhibited positive allometry for length, and two others (femur and first phalanx of digit III) had trends towards isometry. These results indicate that emus experience a relative increase in their muscle force-generating capacities, as well as potentially increasing the force-sustaining capacities of their tendons, as they grow. Furthermore, we have clarified anatomical descriptions and provided illustrations of the pelvic limb muscle–tendon units in emus.

Ontogenetic scaling of the hindlimb muscles of the greater rhea (Rhea americana)

The greater rhea (Rhea americana) is the largest South American bird. It is a cursorial, flightless species with long powerful legs and reduced forelimbs. The goal of this study was to explore how hindlimb muscles scale with body mass during postnatal growth and to analyze whether the specialized locomotion of this species affects the growth of muscle masses. The mass of 19 muscles and body mass were weighed in 21 specimens ranging from 1-month-old individuals to adults. Seventeen muscles scaled with positive allometry with respect to body mass, whereas two muscles scaled isometrically. The predominance of positive allometric growth in hindlimb muscles results in a limb with massive and powerful muscles specialized to support a large body mass and to attain relatively high running speeds. Analysis of muscle mass scaling is a simple and useful way to compare possible differences between locomotor styles, and it is valuable in studies that reconstruct the paleobiology of extinct taxa.

Long-axis rotation: a missing degree of freedom in avian bipedal locomotion

Ground-dwelling birds are typically characterized as erect bipeds having hind limbs that operate parasagittally. Consequently, most previous research has emphasized flexion/extension angles and moments as calculated from a lateral perspective. Three-dimensional motion analyses have documented non-planar limb movements, but the skeletal kinematics underlying changes in foot orientation and transverse position remain unclear. In particular, long-axis rotation of the proximal limb segments is extremely difficult to measure with topical markers. Here we present six degree of freedom skeletal kinematic data from maneuvering guineafowl acquired by marker-based XROMM (X-ray Reconstruction of Moving Morphology). Translations and rotations of the hips, knees, ankles, and pelvis were derived from animated bone models using explicit joint coordinate systems. We distinguished sidesteps, sidestep yaws, crossover yaws, sidestep turns, and crossover turns, but birds often performed a sequence of blended partial maneuvers. Long-axis rotation of the femur (up to 38°) modulated the foot's transverse position. Long-axis rotation of the tibiotarsus (up to 65°) also affected medio-lateral positioning, but primarily served to either reorient a swing phase foot or yaw the body about a stance phase foot. Tarsometatarsal long-axis rotation was minimal, as was hip, knee, and ankle abduction/adduction. Despite having superficially hinge-like joints, birds coordinate substantial long-axis rotations of the hips and knees to execute complex 3-D maneuvers while striking a diversity of non-planar poses.

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.

Mechanical and energetic scaling relationships of running gait through ontogeny in the ostrich (Struthio camelus)

It is unclear whether small animals, with their high stride frequency and crouched posture, or large animals, with more tendinous limbs, are more reliant on storage and return of elastic energy during locomotion. The ostrich has a limb structure that appears to be adapted for high-speed running with long tendons and short muscle fibres. Here we investigate biomechanics of ostrich gait through growth and, with consideration of anatomical data, identify scaling relationships with increasing body size, relating to forces acting on the musculoskeletal structures, effective mechanical advantage (EMA) and mechanical work. Kinematic and kinetic data were collected through growth from running ostriches. Joint moments scaled in a similar way to the pelvic limb segments as a result of consistent posture through growth, such that EMA was independent of body mass. Because no postural change was observed, relative loads applied to musculoskeletal tissues would be predicted to increase during growth, with greater muscle, and hence tendon, load allowing increased potential for elastic energy storage with increasing size. Mass-specific mechanical work per unit distance was independent of body mass, resulting in a small but significant increase in the contribution of elastic energy storage to locomotor economy in larger ostriches.

Comparative intralimb coordination in avian bipedal locomotion

Analyses of how intralimb coordination during locomotion varies within and across different taxa are necessary for understanding the morphological and neurological basis for locomotion in general. Previous findings suggest that intralimb proportions are the major source of kinematic variation that governs intralimb coordination across taxa. Also, independence of kinematics from habitat preference and phylogenetic position has been suggested for mammals. This leads to the hypothesis that among equally-sized bird species exhibiting equal limb proportions similar kinematics can be observed. To test this hypothesis, the bipedal locomotion of two distantly related ground-dwelling bird species (Eudromia elegans and Coturnix coturnix) and of a less terrestrial species (Corvus monedula) was investigated by means of a biplanar high-speed x-ray videographic analysis. Birds were exhibiting similar intralimb proportions and were filmed over a broad range of speed while moving on a treadmill. Joint- and limb element angles, as well as pelvic rotations, were quantified. Regarding fore-aft motions of the limb joints and elements, a congruent pattern of intralimb coordination was observed among all experimental species. The sample of species suggests that it is largely independent of their habitat preference and systematic position and it seems to be related to demands for coping with an irregular terrain with a minimum of necessary control. Hence, the initial hypothesis was confirmed. However, this congruence is not found when looking at medio-lateral limb motions and pelvic rotations, showing distinct differences between ground-dwellers (e.g., largely restricted to a parasagittal plane) and Corvus (e.g., an increased mobility of the hip joint).

A computational analysis of limb and body dimensions in Tyrannosaurus rex with implications for locomotion, ontogeny, and growth

The large theropod dinosaur Tyrannosaurus rex underwent remarkable changes during its growth from <10 kg hatchlings to >6000 kg adults in <20 years. These changes raise fascinating questions about the morphological transformations involved, peak growth rates, and scaling of limb muscle sizes as well as the body's centre of mass that could have influenced ontogenetic changes of locomotion in T. rex. Here we address these questions using three-dimensionally scanned computer models of four large, well-preserved fossil specimens as well as a putative juvenile individual. Furthermore we quantify the variations of estimated body mass, centre of mass and segment dimensions, to characterize inaccuracies in our reconstructions. These inaccuracies include not only subjectivity but also incomplete preservation and inconsistent articulations of museum skeletons. Although those problems cause ambiguity, we conclude that adult T. rex had body masses around 6000-8000 kg, with the largest known specimen ("Sue") perhaps ∼9500 kg. Our results show that during T. rex ontogeny, the torso became longer and heavier whereas the limbs became proportionately shorter and lighter. Our estimates of peak growth rates are about twice as rapid as previous ones but generally support previous methods, despite biases caused by the usage of scale models and equations that underestimate body masses. We tentatively infer that the hindlimb extensor muscles masses, including the large tail muscle M. caudofemoralis longus, may have decreased in their relative size as the centre of mass shifted craniodorsally during T. rex ontogeny. Such ontogenetic changes would have worsened any relative or absolute decline of maximal locomotor performance. Regardless, T. rex probably had hip and thigh muscles relatively larger than any extant animal's. Overall, the limb "antigravity" muscles may have been as large as or even larger than those of ratite birds, which themselves have the most muscular limbs of any living animal.