Computational modelling of muscle fibre operating ranges in the hindlimb of a small ground bird (Eudromia elegans), with implications for modelling locomotion in extinct species.

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle-tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle-tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

Appendicular Muscle Physiology and Biomechanics in Crocodylus niloticus.

Archosaurian reptiles (including living crocodiles and birds) had an explosive diversification of locomotor form and function since the Triassic approximately 250 million years ago. Their limb muscle physiology and biomechanics are pivotal to our understanding of how their diversity and evolution relate to locomotor function. Muscle contraction velocity, force, and power in extinct archosaurs such as early crocodiles, pterosaurs, or non-avian dinosaurs are not available from fossil material, but are needed for biomechanical modeling and simulation. However, an approximation or range of potential parameter values can be obtained by studying extant representatives of the archosaur lineage. Here, we study the physiological performance of three appendicular muscles in Nile crocodiles (Crocodylus niloticus). Nile crocodile musculature showed high power and velocity values-the flexor tibialis internus 4 muscle, a small "hamstring" hip extensor, and knee flexor actively used for terrestrial locomotion, performed particularly well. Our findings demonstrate some physiological differences between muscles, potentially relating to differences in locomotor function, and muscle fiber type composition. By considering these new data from a previously unstudied archosaurian species in light of existing data (e.g., from birds), we can now better bracket estimates of muscle parameters for extinct species and related extant species. Nonetheless, it will be important to consider the potential specialization and physiological variation among muscles, because some archosaurian muscles (such as those with terrestrial locomotor function) may well have close to double the muscle power and contraction velocity capacities of others.

Les archosaures, le groupe de reptiles incluant les oiseaux et les crocodiles actuels, sont caractérisés par une diversification importante de leurs formes et fonctions locomotrices depuis le Trias il y a environ 250 millions d'années. Des études biomécaniques et musculaires centrées sur les membres appendiculaires sont donc essentielles pour comprendre le lien qui unit les fonctions locomotrices des archosaures avec leur histoire évolutive et leur forte diversité. Les données les plus fréquemment utilisées, telles que la vitesse de contraction et la force musculaire, ne sont pas accessibles pour les archosaures éteints tels que ceux issus de la lignée fossile des crocodiles (pseudosuchiens), les ptérosaures ainsi que les dinosaures non-aviens. Ces données sont pourtant nécessaires à l'établissement de modélisations et de simulations biomécaniques à l'échelle du groupe. Il est cependant possible d'obtenir une estimation de ces paramètres à partir des archosaures actuels. Cette étude présente en détails la physiologie de trois Crocodiles du Nil (Crocodylus niloticus) en détaillant les performances musculaires de leur appareil locomoteur. Les muscles des Crocodiles du Nil présentent des forces et des vitesses de contraction élevées. Les performances du muscle flexeur tibialis internus 4, qui est un petit muscle ischio-jambier entre la hanche et le genou fréquemment sollicité chez les animaux terrestres, s'avèrent être particulièrement élevées. Notre étude met en évidence des différences de physiologie entre les muscles, potentiellement liées aux différences de fonctions locomotrices et à la composition des différents types de fibres musculaires. En couplant ces nouvelles données avec celles déjà connues chez les oiseaux, il est possible de mieux estimer les paramètres musculaires d'espèces éteintes ainsi que d'espèces actuelles phylogénétiquement proches. Il est également essentiel de considérer les différentes spécialisations ainsi que les variations de physiologie musculaire. En effet, les muscles de certains archosaures, en particulier ceux dotés d'un mode de locomotion terrestre, pourrait présenter des forces et vitesses de contractions musculaires bien supérieures à celles d'autres espèces.By Romain Pintore, RVC.

Variation in limb loading magnitude and timing in tetrapods.

Comparative analyses of locomotion in tetrapods reveal two patterns of stride cycle variability. Tachymetabolic tetrapods (birds and mammals) have lower inter-cycle variation in stride duration than bradymetabolic tetrapods (amphibians, lizards, turtles and crocodilians). This pattern has been linked to the fact that birds and mammals share enlarged cerebella, relatively enlarged and heavily myelinated Ia afferents, and γ-motoneurons to their muscle spindles. Both tachymetabolic tetrapod lineages also possess an encapsulated Golgi tendon morphology, thought to provide more spatially precise information on muscle tension. The functional consequence of this derived Golgi tendon morphology has never been tested. We hypothesized that one advantage of precise information on muscle tension would be lower and more predictable limb bone stresses, achieved in tachymetabolic tetrapods by having less variable substrate reaction forces than bradymetabolic tetrapods. To test this hypothesis, we analyzed hindlimb substrate reaction forces during locomotion of 55 tetrapod species in a phylogenetic comparative framework. Variation in species means of limb loading magnitude and timing confirm that, for most of the variables analyzed, variance in hindlimb loading and timing is significantly lower in species with encapsulated versus unencapsulated Golgi tendon organs. These findings suggest that maintaining predictable limb loading provides a selective advantage for birds and mammals by allowing energy savings during locomotion, lower limb bone safety factors and quicker recovery from perturbations. The importance of variation in other biomechanical variables in explaining these patterns, such as posture, effective mechanical advantage and center-of-mass mechanics, remains to be clarified.

Ontogenetic changes in the body plan of the sauropodomorph dinosaur Mussaurus patagonicus reveal shifts of locomotor stance during growth.

Ontogenetic information is crucial to understand life histories and represents a true challenge in dinosaurs due to the scarcity of growth series available. Mussaurus patagonicus was a sauropodomorph dinosaur close to the origin of Sauropoda known from hatchling, juvenile and mature specimens, providing a sufficiently complete ontogenetic series to reconstruct general patterns of ontogeny. Here, in order to quantify how body shape and its relationship with locomotor stance (quadruped/biped) changed in ontogeny, hatchling, juvenile (~1 year old) and adult (8+ years old) individuals were studied using digital models. Our results show that Mussaurus rapidly grew from about 60 g at hatching to ~7 kg at one year old, reaching >1000 kg at adulthood. During this time, the body's centre of mass moved from a position in the mid-thorax to a more caudal position nearer to the pelvis. We infer that these changes of body shape and centre of mass reflect a shift from quadrupedalism to bipedalism occurred early in ontogeny in Mussaurus. Our study indicates that relative development of the tail and neck was more influential in determining the locomotor stance in Sauropodomorpha during ontogeny, challenging previous studies, which have emphasized the influence of hindlimb vs. forelimb lengths on sauropodomorph stance.

Relating neuromuscular control to functional anatomy of limb muscles in extant archosaurs.

Electromyography (EMG) is used to understand muscle activity patterns in animals. Understanding how much variation exists in muscle activity patterns in homologous muscles across animal clades during similar behaviours is important for evaluating the evolution of muscle functions and neuromuscular control. We compared muscle activity across a range of archosaurian species and appendicular muscles, including how these EMG patterns varied across ontogeny and phylogeny, to reconstruct the evolutionary history of archosaurian muscle activation during locomotion. EMG electrodes were implanted into the muscles of turkeys, pheasants, quail, guineafowl, emus (three age classes), tinamous and juvenile Nile crocodiles across 13 different appendicular muscles. Subjects walked and ran at a range of speeds both overground and on treadmills during EMG recordings. Anatomically similar muscles such as the lateral gastrocnemius exhibited similar EMG patterns at similar relative speeds across all birds. In the crocodiles, the EMG signals closely matched previously published data for alligators. The timing of lateral gastrocnemius activation was relatively later within a stride cycle for crocodiles compared to birds. This difference may relate to the coordinated knee extension and ankle plantarflexion timing across the swing-stance transition in Crocodylia, unlike in birds where there is knee flexion and ankle dorsiflexion across swing-stance. No significant effects were found across the species for ontogeny, or between treadmill and overground locomotion. Our findings strengthen the inference that some muscle EMG patterns remained conservative throughout Archosauria: for example, digital flexors retained similar stance phase activity and M. pectoralis remained an 'anti-gravity' muscle. However, some avian hindlimb muscles evolved divergent activations in tandem with functional changes such as bipedalism and more crouched postures, especially M. iliotrochantericus caudalis switching from swing to stance phase activity and M. iliofibularis adding a novel stance phase burst of activity.

Reverse-engineering the locomotion of a stem amniote.

Reconstructing the locomotion of extinct vertebrates offers insights into their palaeobiology and helps to conceptualize major transitions in vertebrate evolution1-4. However, estimating the locomotor behaviour of a fossil species remains a challenge because of the limited information preserved and the lack of a direct correspondence between form and function5,6. The evolution of advanced locomotion on land-that is, locomotion that is more erect, balanced and mechanically power-saving than is assumed of anamniote early tetrapods-has previously been linked to the terrestrialization and diversification of amniote lineages7. To our knowledge, no reconstructions of the locomotor characteristics of stem amniotes based on multiple quantitative methods have previously been attempted: previous methods have relied on anatomical features alone, ambiguous locomotor information preserved in ichnofossils or unspecific modelling of locomotor dynamics. Here we quantitatively examine plausible gaits of the stem amniote Orobates pabsti, a species that is known from a complete body fossil preserved in association with trackways8. We reconstruct likely gaits that match the footprints, and investigate whether Orobates exhibited locomotor characteristics that have previously been linked to the diversification of crown amniotes. Our integrative methodology uses constraints derived from biomechanically relevant metrics, which also apply to extant tetrapods. The framework uses in vivo assessment of locomotor mechanics in four extant species to guide an anatomically informed kinematic simulation of Orobates, as well as dynamic simulations and robotics to filter the parameter space for plausible gaits. The approach was validated using two extant species that have different morphologies, gaits and footprints. Our metrics indicate that Orobates exhibited more advanced locomotion than has previously been assumed for earlier tetrapods7,9, which suggests that advanced terrestrial locomotion preceded the diversification of crown amniotes. We provide an accompanying website for the exploration of the filters that constrain our simulations, which will allow revision of our approach using new data, assumptions or methods.

Forelimb muscle and joint actions in Archosauria: insights from Crocodylus johnstoni (Pseudosuchia) and Mussaurus patagonicus (Sauropodomorpha).

Many of the major locomotor transitions during the evolution of Archosauria, the lineage including crocodiles and birds as well as extinct Dinosauria, were shifts from quadrupedalism to bipedalism (and vice versa). Those occurred within a continuum between more sprawling and erect modes of locomotion and involved drastic changes of limb anatomy and function in several lineages, including sauropodomorph dinosaurs. We present biomechanical computer models of two locomotor extremes within Archosauria in an analysis of joint ranges of motion and the moment arms of the major forelimb muscles in order to quantify biomechanical differences between more sprawling, pseudosuchian (represented the crocodile Crocodylus johnstoni) and more erect, dinosaurian (represented by the sauropodomorph Mussaurus patagonicus) modes of forelimb function. We compare these two locomotor extremes in terms of the reconstructed musculoskeletal anatomy, ranges of motion of the forelimb joints and the moment arm patterns of muscles across those ranges of joint motion. We reconstructed the three-dimensional paths of 30 muscles acting around the shoulder, elbow and wrist joints. We explicitly evaluate how forelimb joint mobility and muscle actions may have changed with postural and anatomical alterations from basal archosaurs to early sauropodomorphs. We thus evaluate in which ways forelimb posture was correlated with muscle leverage, and how such differences fit into a broader evolutionary context (i.e. transition from sprawling quadrupedalism to erect bipedalism and then shifting to graviportal quadrupedalism). Our analysis reveals major differences of muscle actions between the more sprawling and erect models at the shoulder joint. These differences are related not only to the articular surfaces but also to the orientation of the scapula, in which extension/flexion movements in Crocodylus (e.g. protraction of the humerus) correspond to elevation/depression in Mussaurus. Muscle action is highly influenced by limb posture, more so than morphology. Habitual quadrupedalism in Mussaurus is not supported by our analysis of joint range of motion, which indicates that glenohumeral protraction was severely restricted. Additionally, some active pronation of the manus may have been possible in Mussaurus, allowing semi-pronation by a rearranging of the whole antebrachium (not the radius against the ulna, as previously thought) via long-axis rotation at the elbow joint. However, the muscles acting around this joint to actively pronate it may have been too weak to drive or maintain such orientations as opposed to a neutral position in between pronation and supination. Regardless, the origin of quadrupedalism in Sauropoda is not only linked to manus pronation but also to multiple shifts of forelimb morphology, allowing greater flexion movements of the glenohumeral joint and a more columnar forelimb posture.

Analysis of the moment arms and kinematics of ostrich (Struthio camelus) double patellar sesamoids.

The patella ("kneecap") is a biomechanically important feature of the tendinous insertion of the knee extensor muscles, able to alter the moment arm lengths between its input and output tendons, and so modify the mechanical advantage of the knee extensor muscle. However, patellar gearing function is little-explored outside of humans, and the patella is often simplified or ignored in biomechanical models. Here, we investigate patellar gearing and kinematics in the ostrich-frequently used as an animal analogue to human bipedal locomotion and unusual in its possession of two patellae at the knee joint. We use x-ray reconstruction of moving morphology (XROMM) techniques to capture the kinematics of the patellae in an adult ostrich cadaver, passively manipulated in flexion-extension. Moment arm ratios between the input and output tendons of each patella are calculated from kinematically determined centers of patellofemoral joint rotation. Both patellae are found to decrease the mechanical advantage of the extensor muscle-tendon complex, decreasing the tendon output force for a given muscle input force, but potentially increasing the relative speed of knee extension. Mechanically and kinematically, the proximal patella behaves similarly to the single patella of most other species, whereas the distal patella has properties of both a fixed retroarticular process and a moving sesamoid. It is still not clear why ostriches possess two patellae, but we suggest that the configuration in ostriches benefits their rapid locomotion and provides tendon protection.

Temporal and phylogenetic evolution of the sauropod dinosaur body plan.

The colossal size and body plan of sauropod dinosaurs are unparalleled in terrestrial vertebrates. However, to date, there have been only limited attempts to examine temporal and phylogenetic patterns in the sauropod bauplan. Here, we combine three-dimensional computational models with phylogenetic reconstructions to quantify the evolution of whole-body shape and body segment properties across the sauropod radiation. Limitations associated with the absence of soft tissue preservation in fossils result in large error bars about mean absolute body shape predictions. However, applying any consistent skeleton : body volume ratio to all taxa does yield changes in body shape that appear concurrent with major macroevolutionary events in sauropod history. A caudad shift in centre-of-mass (CoM) in Middle Triassic Saurischia, associated with the evolution of bipedalism in various dinosaur lineages, was reversed in Late Triassic sauropodomorphs. A craniad CoM shift coincided with the evolution of quadrupedalism in the Late Triassic, followed by a more striking craniad shift in Late Jurassic-Cretaceous titanosauriforms, which included the largest sauropods. These craniad CoM shifts are strongly correlated with neck enlargement, a key innovation in sauropod evolution and pivotal to their gigantism. By creating a much larger feeding envelope, neck elongation is thought to have increased feeding efficiency and opened up trophic niches that were inaccessible to other herbivores. However, we find that relative neck size and CoM position are not strongly correlated with inferred feeding habits. Instead the craniad CoM positions of titanosauriforms appear closely linked with locomotion and environmental distributions, potentially contributing to the continued success of this group until the end-Cretaceous, with all other sauropods having gone extinct by the early Late Cretaceous.

A Three-Dimensional Skeletal Reconstruction of the Stem Amniote Orobates pabsti (Diadectidae): Analyses of Body Mass, Centre of Mass Position, and Joint Mobility.

Orobates pabsti, a basal diadectid from the lower Permian, is a key fossil for the understanding of early amniote evolution. Quantitative analysis of anatomical information suffers from fragmentation of fossil bones, plastic deformation due to diagenetic processes and fragile preservation within surrounding rock matrix, preventing further biomechanical investigation. Here we describe the steps taken to digitally reconstruct MNG 10181, the holotype specimen of Orobates pabsti, and subsequently use the digital reconstruction to assess body mass, position of the centre of mass in individual segments as well as the whole animal, and study joint mobility in the shoulder and hip joints. The shape of most fossil bone fragments could be recovered from micro-focus computed tomography scans. This also revealed structures that were hitherto hidden within the rock matrix. However, parts of the axial skeleton had to be modelled using relevant isolated bones from the same locality as templates. Based on the digital fossil, mass of MNG 10181 was estimated using a model of body shape that was varied within a plausible range to account for uncertainties of the dimension. In the mean estimate model the specimen had an estimated mass of circa 4 kg. Varying of the mass distribution amongst body segments further revealed that Orobates carried most of its weight on the hind limbs. Mostly unrestricted joint morphology further suggested that MNG 10181 was able to effectively generate propulsion with the pelvic limbs. The digital reconstruction is made available for future biomechanical studies.

Comparative architectural properties of limb muscles in Crocodylidae and Alligatoridae and their relevance to divergent use of asymmetrical gaits in extant Crocodylia.

Crocodiles and their kin (Crocodylidae) use asymmetrical (bounding and galloping) gaits when moving rapidly. Despite being morphologically and ecologically similar, it seems alligators and their kin (Alligatoridae) do not. To investigate a possible anatomical basis for this apparent major difference in locomotor capabilities, we measured relative masses and internal architecture (fascicle lengths and physiological cross-sectional areas) of muscles of the pectoral and pelvic limbs of 40 individuals from six representative species of Crocodylidae and Alligatoridae. We found that, relative to body mass, Crocodylidae have significantly longer muscle fascicles (increased working range), particularly in the pectoral limb, and generally smaller muscle physiological cross-sectional areas (decreased force-exerting capability) than Alligatoridae. We therefore hypothesise that the ability of some crocodylians to use asymmetrical gaits may be limited more by the ability to make large, rapid limb motions (especially in the pectoral limb) than the ability to exert large limb forces. Furthermore, analysis of scaling patterns in muscle properties shows that limb anatomy in the two clades becomes more divergent during ontogeny. Limb muscle masses, fascicle lengths and physiological cross-sectional areas scale with significantly larger coefficients in Crocodylidae than Alligatoridae. This combination of factors suggests that inter-clade disparity in maximal limb power is highest in adult animals. Therefore, despite their apparent morphological similarities, both mean values and scaling patterns suggest that considerable diversity exists in the locomotor apparatus of extant Crocodylia.

Three-dimensional anatomy of the ostrich (Struthio camelus) knee joint.

The three-dimensional anatomy of the ostrich (Struthio camelus) knee (femorotibial, femorofibular, and femoropatellar) joint has scarcely been studied, and could elucidate certain mechanobiological properties of sesamoid bones. The adult ostrich is unique in that it has double patellae, while another similar ratite bird, the emu, has none. Understanding why these patellae form and what purpose they may serve is dually important for future studies on ratites as well as for understanding the mechanobiological characteristics of sesamoid bone development. For this purpose, we present a three-dimensional anatomical study of the ostrich knee joint, detailing osteology, ligaments and menisci, and myology. We have identified seven muscles which connect to the two patellae and compare our findings to past descriptions. These descriptions can be used to further study the biomechanical loading and implications of the double patella in the ostrich.

Linking the evolution of body shape and locomotor biomechanics in bird-line archosaurs.

Locomotion in living birds (Neornithes) has two remarkable features: feather-assisted flight, and the use of unusually crouched hindlimbs for bipedal support and movement. When and how these defining functional traits evolved remains controversial. However, the advent of computer modelling approaches and the discoveries of exceptionally preserved key specimens now make it possible to use quantitative data on whole-body morphology to address the biomechanics underlying this issue. Here we use digital body reconstructions to quantify evolutionary trends in locomotor biomechanics (whole-body proportions and centre-of-mass position) across the clade Archosauria. We use three-dimensional digital reconstruction to estimate body shape from skeletal dimensions for 17 archosaurs along the ancestral bird line, including the exceptionally preserved, feathered taxa Microraptor, Archaeopteryx, Pengornis and Yixianornis, which represent key stages in the evolution of the avian body plan. Rather than a discrete transition from more-upright postures in the basal-most birds (Avialae) and their immediate outgroup deinonychosauria, our results support hypotheses of a gradual, stepwise acquisition of more-crouched limb postures across much of theropod evolution, although we find evidence of an accelerated change within the clade Maniraptora (birds and their closest relatives, such as deinonychosaurs). In addition, whereas reduction of the tail is widely accepted to be the primary morphological factor correlated with centre-of-mass position and, hence, evolution of hindlimb posture, we instead find that enlargement of the pectoral limb and several associated trends have a much stronger influence. Intriguingly, our support for the onset of accelerated morpho-functional trends within Maniraptora is closely correlated with the evolution of flight. Because we find that the evolution of enlarged forelimbs is strongly linked, via whole-body centre of mass, to hindlimb function during terrestrial locomotion, we suggest that the evolution of avian flight is linked to anatomical novelties in the pelvic limb as well as the pectoral.

Computational modelling of locomotor muscle moment arms in the basal dinosaur Lesothosaurus diagnosticus: assessing convergence between birds and basal ornithischians.

Ornithischia (the 'bird-hipped' dinosaurs) encompasses bipedal, facultative quadrupedal and quadrupedal taxa. Primitive ornithischians were small bipeds, but large body size and obligate quadrupedality evolved independently in all major ornithischian lineages. Numerous pelvic and hind limb features distinguish ornithischians from the majority of other non-avian dinosaurs. However, some of these features, notably a retroverted pubis and elongate iliac preacetabular process, appeared convergently in maniraptoran theropods, and were inherited by their avian descendants. During maniraptoran/avian evolution these pelvic modifications led to significant changes in the functions of associated muscles, involving alterations to the moment arms and the activation patterns of pelvic musculature. However, the functions of these features in ornithischians and their influence on locomotion have not been tested and remain poorly understood. Here, we provide quantitative tests of bipedal ornithischian muscle function using computational modelling to estimate 3D hind limb moment arms for the most complete basal ornithischian, Lesothosaurus diagnosticus. This approach enables sensitivity analyses to be carried out to explore the effects of uncertainties in muscle reconstructions of extinct taxa, and allows direct comparisons to be made with similarly constructed models of other bipedal dinosaurs. This analysis supports some previously proposed qualitative inferences of muscle function in basal ornithischians. However, more importantly, this work highlights ambiguities in the roles of certain muscles, notably those inserting close to the hip joint. Comparative analysis reveals that moment arm polarities and magnitudes in Lesothosaurus, basal tetanuran theropods and the extant ostrich are generally similar. However, several key differences are identified, most significantly in comparisons between the moment arms of muscles associated with convergent osteological features in ornithischians and birds. Craniad migration of the iliofemoralis group muscles in birds correlates with increased leverage and use of medial femoral rotation to counter stance phase adduction moments at the hip. In Lesothosaurus the iliofemoralis group maintains significantly higher moment arms for abduction, consistent with the hip abduction mode of lateral limb support hypothesized for basal dinosaurs. Sensitivity analysis highlights ambiguity in the role of musculature associated with the retroverted pubis (puboischiofemoralis externus group) in ornithischians. However, it seems likely that this musculature may have predominantly functioned similarly to homologous muscles in extant birds, activating during the swing phase to adduct the lower limb through lateral rotation of the femur. Overall the results suggest that locomotor muscle leverage in Lesothosaurus (and by inference basal ornithischians in general) was more similar to that of other non-avian dinosaurs than the ostrich, representing what was probably the basal dinosaur condition. This work thereby contradicts previous hypotheses of ornithischian-bird functional convergence.

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.

Functional specialization and ontogenetic scaling of limb anatomy in Alligator mississippiensis.

Crocodylians exhibit a fascinating diversity of terrestrial gaits and limb motions that remain poorly described and are of great importance to understanding their natural history and evolution. Their musculoskeletal anatomy is pivotal to this diversity and yet only qualitative studies of muscle-tendon unit anatomy exist. The relative masses and internal architecture (fascicle lengths and physiological cross-sectional areas) of muscles of the pectoral and pelvic limbs of American alligators (Alligator mississippiensis Daudin 1801) were recorded for an ontogenetic series of wild specimens (n = 15, body masses from 0.5 to 60 kg). The data were analysed by reduced major axis regression to determine scaling relationships with body mass. Physiological cross-sectional areas and therefore muscle force-generating capacity were found to be greater in the extensor (anti-gravity) muscles of the pelvic limb than in the pectoral limb, reflecting how crocodylians differ from mammals in having greater loading of the hindlimbs than the forelimbs. Muscle masses and architecture were generally found to scale isometrically with body mass, suggesting an ontogenetic decrease in terrestrial athleticism. This concurs with the findings of previous studies showing ontogenetic decreases in limb bone length and the general scaling principle of a decline of strength : weight ratios with increasing size in animals. Exceptions to isometric scaling found included positive allometry in fascicle length for extensor musculature of both limbs, suggesting an ontogenetic increase in working range interpreted as increasing postural variability - in particular the major hip extensors - the interpretation of which is complicated by previous described ontogenetic increase of moment arms for these muscles.

Biomechanics of running indicates endothermy in bipedal dinosaurs.

BACKGROUND: One of the great unresolved controversies in paleobiology is whether extinct dinosaurs were endothermic, ectothermic, or some combination thereof, and when endothermy first evolved in the lineage leading to birds. Although it is well established that high, sustained growth rates and, presumably, high activity levels are ancestral for dinosaurs and pterosaurs (clade Ornithodira), other independent lines of evidence for high metabolic rates, locomotor costs, or endothermy are needed. For example, some studies have suggested that, because large dinosaurs may have been homeothermic due to their size alone and could have had heat loss problems, ectothermy would be a more plausible metabolic strategy for such animals. METHODOLOGY/PRINCIPAL FINDINGS: Here we describe two new biomechanical approaches for reconstructing the metabolic rate of 14 extinct bipedal dinosauriforms during walking and running. These methods, well validated for extant animals, indicate that during walking and slow running the metabolic rate of at least the larger extinct dinosaurs exceeded the maximum aerobic capabilities of modern ectotherms, falling instead within the range of modern birds and mammals. Estimated metabolic rates for smaller dinosaurs are more ambiguous, but generally approach or exceed the ectotherm boundary. CONCLUSIONS/SIGNIFICANCE: Our results support the hypothesis that endothermy was widespread in at least larger non-avian dinosaurs. It was plausibly ancestral for all dinosauriforms (perhaps Ornithodira), but this is perhaps more strongly indicated by high growth rates than by locomotor costs. The polarity of the evolution of endothermy indicates that rapid growth, insulation, erect postures, and perhaps aerobic power predated advanced "avian" lung structure and high locomotor costs.

Variation in center of mass estimates for extant sauropsids and its importance for reconstructing inertial properties of extinct archosaurs.

Inertial properties of animal bodies and segments are critical input parameters for biomechanical analysis of standing and moving, and thus are important for paleobiological inquiries into the broader behaviors, ecology and evolution of extinct taxa such as dinosaurs. But how accurately can these be estimated? Computational modeling was used to estimate the inertial properties including mass, density, and center of mass (COM) for extant crocodiles (adult and juvenile Crocodylus johnstoni) and birds (Gallus gallus; junglefowl and broiler chickens), to identify the chief sources of variation and methodological errors, and their significance. High-resolution computed tomography scans were segmented into 3D objects and imported into inertial property estimation software that allowed for the examination of variable body segment densities (e.g., air spaces such as lungs, and deformable body outlines). Considerable biological variation of inertial properties was found within groups due to ontogenetic changes as well as evolutionary changes between chicken groups. COM positions shift in variable directions during ontogeny in different groups. Our method was repeatable and the resolution was sufficient for accurate estimations of mass and density in particular. However, we also found considerable potential methodological errors for COM related to (1) assumed body segment orientation, (2) what frames of reference are used to normalize COM for size-independent comparisons among animals, and (3) assumptions about tail shape. Methods and assumptions are suggested to minimize these errors in the future and thereby improve estimation of inertial properties for extant and extinct animals. In the best cases, 10%-15% errors in these estimates are unavoidable, but particularly for extinct taxa errors closer to 50% should be expected, and therefore, cautiously investigated. Nonetheless in the best cases these methods allow rigorous estimation of inertial properties.

The evolutionary continuum of limb function from early theropods to birds.

The bipedal stance and gait of theropod dinosaurs evolved gradually along the lineage leading to birds and at some point(s), flight evolved. How and when did these changes occur? We review the evidence from neontology and paleontology, including pectoral and pelvic limb functional morphology, fossil footprints/trackways and biomechanical models and simulations. We emphasise that many false dichotomies or categories have been applied to theropod form and function, and sometimes, these impede research progress. For example, dichotomisation of locomotor function into 'non-avian' and 'avian' modes is only a conceptual crutch; the evidence supports a continuous transition. Simplification of pelvic limb function into cursorial/non-cursorial morphologies or flexed/columnar poses has outlived its utility. For the pectoral limbs, even the classic predatory strike vs. flight wing-stroke distinction and separation of theropods into non-flying and flying--or terrestrial and arboreal--categories may be missing important subtleties. Distinguishing locomotor function between taxa, even with quantitative approaches, will always be fraught with ambiguity, making it difficult to find real differences if that ambiguity is properly acknowledged. There must be an 'interpretive asymptote' for reconstructing dinosaur limb function that available methods and evidence cannot overcome. We may be close to that limit, but how far can it be stretched with improved methods and evidence, if at all? The way forward is a combination of techniques that emphasises integration of neontological and paleontological evidence and quantitative assessment of limb function cautiously applied with validated techniques and sensitivity analysis of unknown variables.