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

Static versus dynamic muscle modelling in extinct species: a biomechanical case study of the Australopithecus afarensis pelvis and lower extremity

The force a muscle generates is dependent on muscle structure, in which fibre length, pennation angle and tendon slack length all influence force production. Muscles are not preserved in the fossil record and these parameters must be estimated when constructing a musculoskeletal model. Here, we test the capability of digitally reconstructed muscles of the Australopithecus afarensis model (specimen AL 288-1) to maintain an upright, single-support limb posture. Our aim was to ascertain the influence that different architectural estimation methods have on muscle specialisation and on the subsequent inferences that can be extrapolated about limb function. Parameters were estimated for 36 muscles in the pelvis and lower limb and seven different musculoskeletal models of AL 288-1 were produced. These parameters represented either a 'static' Hill-type muscle model (n = 4 variants) which only incorporated force, or instead a 'dynamic' Hill-type muscle model with an elastic tendon and fibres that could vary force-length-velocity properties (n = 3 variants). Each muscle's fibre length, pennation angle, tendon slack length and maximal isometric force were calculated based upon different input variables. Static (inverse) simulations were computed in which the vertical and mediolateral ground reaction forces (GRF) were incrementally increased until limb collapse (simulation failure). All AL 288-1 variants produced somewhat similar simulated muscle activation patterns, but the maximum vertical GRF that could be exerted on a single limb was not consistent between models. Three of the four static-muscle models were unable to support >1.8 times body weight and produced models that under-performed. The dynamic-muscle models were stronger. Comparative results with a human model imply that similar muscle group activations between species are needed to sustain single-limb support at maximally applied GRFs in terms of the simplified static simulations (e.g., same walking pose) used here. This approach demonstrated the range of outputs that can be generated for a model of an extinct individual. Despite mostly comparable outputs, the models diverged mostly in terms of strength.

Investigating the quadrupedal abilities of Scutellosaurus lawleri and its implications for locomotor behavior evolution among dinosaurs

A reversion to secondary quadrupedality is exceptionally rare in nature, yet the convergent re-evolution of this locomotor style occurred at least four separate times within Dinosauria. Facultative quadrupedality, an intermediate state between obligate bipedality and obligate quadrupedality, may have been an important transitional step in this locomotor shift, and is proposed for a range of basal ornithischians and sauropodomorphs. Advances in virtual biomechanical modeling and simulation have allowed for the investigation of limb anatomy and function in a range of extinct dinosaurian species, yet this technique has not been widely applied to explore facultatively quadrupedal gait generation. This study places its focus on Scutellosaurus, a basal thyreophoran that has previously been described as both an obligate biped and a facultative quadruped. The functional anatomy of the musculoskeletal system (myology, mass properties, and joint ranges of motion) has been reconstructed using extant phylogenetic bracketing and comparative anatomical datasets. This information was used to create a multi-body dynamic locomotor simulation that demonstrates that whil quadrupedal gaits were physically possible, they did not outperform bipedal gaits is any tested metric. Scutellosaurus cannot therefore be described as an obligate biped, but we would predict its use of quadrupedality would be very rare, and perhaps restricted to specific activities such as foraging. This finding suggests that basal thyreophorans are still overwhelmingly bipedal but is perhaps indicative of an adaptive pathway for later evolution of quadrupedality.

Modern three-dimensional digital methods for studying locomotor biomechanics in tetrapods

Here, we review the modern interface of three-dimensional (3D) empirical (e.g. motion capture) and theoretical (e.g. modelling and simulation) approaches to the study of terrestrial locomotion using appendages in tetrapod vertebrates. These tools span a spectrum from more empirical approaches such as XROMM, to potentially more intermediate approaches such as finite element analysis, to more theoretical approaches such as dynamic musculoskeletal simulations or conceptual models. These methods have much in common beyond the importance of 3D digital technologies, and are powerfully synergistic when integrated, opening a wide range of hypotheses that can be tested. We discuss the pitfalls and challenges of these 3D methods, leading to consideration of the problems and potential in their current and future usage. The tools (hardware and software) and approaches (e.g. methods for using hardware and software) in the 3D analysis of tetrapod locomotion have matured to the point where now we can use this integration to answer questions we could never have tackled 20 years ago, and apply insights gleaned from them to other fields.

Dots on a screen: The past, present, and future of morphometrics in the study of nonavian dinosaurs

Using morphometrics to study nonavian dinosaur fossils is a practice that predates the origin of the word "dinosaur." By the 1970s, linear morphometrics had become established as a valuable tool for analyzing intra- and interspecific variation in nonavian dinosaurs. With the advent of more recent techniques such as geometric morphometrics and more advanced statistical approaches, morphometric analyses of nonavian dinosaurs have proliferated, granting unprecedented insight into many aspects of their biology and evolution. I outline the past, present, and future of morphometrics as applied to the study of nonavian dinosaurs zeroing in on five aspects of nonavian dinosaur paleobiology where morphometrics has been widely utilized to advance our knowledge: systematics, sexual dimorphism, locomotion, macroevolution, and trackways. Morphometric methods are especially susceptible to taphonomic distortion. As such, the impact of taphonomic distortion on original fossil shape is discussed as are current and future methods for quantifying and accounting for distortion with the goal of reducing the taphonomic noise to biological signal ratio. Finally, the future of morphometrics in nonavian dinosaur paleobiology is discussed as paleobiologists move into a "virtual paleobiology" framework, whereby digital renditions of fossils are captured via methods such as photogrammetry and computed tomography. These primary data form the basis for three-dimensional (3D) geometric morphometric analyses along with a slew of other forms of analyses. These 3D specimen data form part of the extended specimen and help to democratize paleobiology, unlocking the specimen from the physical museum and making the specimen available to researchers across the world.

Convergent evolution of quadrupedality in ornithischian dinosaurs was achieved through disparate forelimb muscle mechanics

The secondary evolution of quadrupedality from bipedal ancestry is a rare evolutionary transition in tetrapods yet occurred convergently at least three times within ornithischian dinosaurs. Despite convergently evolving quadrupedal gait, ornithischians exhibited variable anatomy, particularly in the forelimbs, which underwent a major functional change from assisting in foraging and feeding in bipeds to becoming principal weight-bearing components of the locomotor system in quadrupeds. Here, we use three-dimensional multi-body dynamics models to demonstrate quantitatively that different quadrupedal ornithischian clades evolved distinct forelimb musculature, particularly around the shoulder. We find that major differences in glenohumeral abduction-adduction and long axis rotation muscle leverages were key drivers of mechanical disparity, thereby refuting previous hypotheses about functional convergence in major clades. Elbow muscle leverages were also disparate across the major ornithischian lineages, although high elbow extension muscle leverages were convergent between most quadrupeds. Unlike in ornithischian hind limbs, where differences are more closely tied to functional similarity than phylogenetic relatedness, mechanical disparity in ornithischian forelimbs appears to have been shaped primarily by phylogenetic constraints. Differences in ancestral bipedal taxa within each clade may have resulted in disparate ecomorphological constraints on the evolutionary pathways driving divergence in their quadrupedal descendants.

Anatomically grounded estimation of hindlimb muscle sizes in Archosauria

In vertebrates, active movement is driven by muscle forces acting on bones, either directly or through tendinous insertions. There has been much debate over how muscle size and force are reflected by the muscular attachment areas (AAs). Here we investigate the relationship between the physiological cross-sectional area (PCSA), a proxy for the force production of the muscle, and the AA of hindlimb muscles in Nile crocodiles and five bird species. The limbs were held in a fixed position whilst blunt dissection was carried out to isolate the individual muscles. AAs were digitised using a point digitiser, before the muscle was removed from the bone. Muscles were then further dissected and fibre architecture was measured, and PCSA calculated. The raw measures, as well as the ratio of PCSA to AA, were studied and compared for intra-observer error as well as intra- and interspecies differences. We found large variations in the ratio between AAs and PCSA both within and across species, but muscle fascicle lengths are conserved within individual species, whether this was Nile crocodiles or tinamou. Whilst a discriminant analysis was able to separate crocodylian and avian muscle data, the ratios for AA to cross-sectional area for all species and most muscles can be represented by a single equation. The remaining muscles have specific equations to represent their scaling, but equations often have a relatively high success at predicting the ratio of muscle AA to PCSA. We then digitised the muscle AAs of Coelophysis bauri, a dinosaur, to estimate the PCSAs and therefore maximal isometric muscle forces. The results are somewhat consistent with other methods for estimating force production, and suggest that, at least for some archosaurian muscles, that it is possible to use muscle AA to estimate muscle sizes. This method is complementary to other methods such as digital volumetric modelling.

Producing non-steady-state gaits (starting, stopping, and turning) in a biologically realistic quadrupedal simulation

Multibody dynamic analysis (MDA) has become part of the standard toolkit used to reconstruct the biomechanics of extinct animals. However, its use is currently almost exclusively limited to steady state activities such as walking and running at constant velocity. If we want to reconstruct the full range of activities that a given morphology can achieve then we must be able to reconstruct non-steady-state activities such as starting, stopping, and turning. In this paper we demonstrate how we can borrow techniques from the robotics literature to produce gait controllers that allow us to generate non-steady-state gaits in a biologically realistic quadrupedal simulation of a chimpanzee. We use a novel proportional-derivative (PD) reach controller that can accommodate both the non-linear contraction dynamics of Hill-type muscles and the large numbers of both single-joint and two-joint muscles to allow us to define the trajectory of the distal limb segment. With defined autopodial trajectories we can then use tegotae style locomotor controllers that use decentralized reaction force feedback to control the trajectory speed in order to produce quadrupedal gait. This combination of controllers can generate starting, stopping, and turning kinematics, something that we believe has never before been achieved in a simulation that uses both physiologically realistic muscles and a high level of anatomical fidelity. The gait quality is currently relatively low compared to the more commonly used feedforward control methods, but this can almost certainly be improved in future by using more biologically based foot trajectories and increasing the complexity of the underlying model and controllers. Understanding these more complex gaits is essential, particularly in fields such as paleoanthropology where the transition from an ancestral hominoid with a diversified repertoire to a bipedal hominin is of such fundamental importance, and this approach illustrates one possible avenue for further research in this area.

One step further in biomechanical models in palaeontology: a nonlinear finite element analysis review

Finite element analysis (FEA) is no longer a new technique in the fields of palaeontology, anthropology, and evolutionary biology. It is nowadays a well-established technique within the virtual functional-morphology toolkit. However, almost all the works published in these fields have only applied the most basic FEA tools i.e., linear materials in static structural problems. Linear and static approximations are commonly used because they are computationally less expensive, and the error associated with these assumptions can be accepted. Nonetheless, nonlinearities are natural to be used in biomechanical models especially when modelling soft tissues, establish contacts between separated bones or the inclusion of buckling results. The aim of this review is to, firstly, highlight the usefulness of non-linearities and secondly, showcase these FEA tool to researchers that work in functional morphology and biomechanics, as non-linearities can improve their FEA models by widening the possible applications and topics that currently are not used in palaeontology and anthropology.

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

Accurate muscle reconstructions can offer new information on the anatomy of fossil organisms and are also important for biomechanical analysis (multibody dynamics and finite-element analysis (FEA)). For the sake of simplicity, muscles are often modelled as point-to-point strands or frustra (cut-off cones) in biomechanical models. However, there are cases in which it is useful to model the muscle morphology in three dimensions, to better examine the effects of muscle shape and size. This is especially important for fossil analyses, where muscle force is estimated from the reconstructed muscle morphology (rather than based on data collected in vivo). The two main aims of this paper are as follows. First, we created a new interactive tool in the free open access software Blender to enable interactive three-dimensional modelling of muscles. This approach can be applied to both palaeontological and human biomechanics research to generate muscle force magnitudes and lines of action for FEA. Second, we provide a guide on how to use existing Blender tools to reconstruct distorted or incomplete specimens. This guide is aimed at palaeontologists but can also be used by anatomists working with damaged specimens or to test functional implication of hypothetical morphologies.

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

Accurate muscle reconstructions can offer new information on the anatomy of fossil organisms and are also important for biomechanical analysis (multibody dynamics and finite-element analysis (FEA)). For the sake of simplicity, muscles are often modelled as point-to-point strands or frustra (cut-off cones) in biomechanical models. However, there are cases in which it is useful to model the muscle morphology in three dimensions, to better examine the effects of muscle shape and size. This is especially important for fossil analyses, where muscle force is estimated from the reconstructed muscle morphology (rather than based on data collected in vivo). The two main aims of this paper are as follows. First, we created a new interactive tool in the free open access software Blender to enable interactive three-dimensional modelling of muscles. This approach can be applied to both palaeontological and human biomechanics research to generate muscle force magnitudes and lines of action for FEA. Second, we provide a guide on how to use existing Blender tools to reconstruct distorted or incomplete specimens. This guide is aimed at palaeontologists but can also be used by anatomists working with damaged specimens or to test functional implication of hypothetical morphologies.

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

Accurate muscle reconstructions can offer new information on the anatomy of fossil organisms and are also important for biomechanical analysis (multibody dynamics and finite-element analysis (FEA)). For the sake of simplicity, muscles are often modelled as point-to-point strands or frustra (cut-off cones) in biomechanical models. However, there are cases in which it is useful to model the muscle morphology in three dimensions, to better examine the effects of muscle shape and size. This is especially important for fossil analyses, where muscle force is estimated from the reconstructed muscle morphology (rather than based on data collected in vivo). The two main aims of this paper are as follows. First, we created a new interactive tool in the free open access software Blender to enable interactive three-dimensional modelling of muscles. This approach can be applied to both palaeontological and human biomechanics research to generate muscle force magnitudes and lines of action for FEA. Second, we provide a guide on how to use existing Blender tools to reconstruct distorted or incomplete specimens. This guide is aimed at palaeontologists but can also be used by anatomists working with damaged specimens or to test functional implication of hypothetical morphologies.

Body size, shape and ecology in tetrapods

Body size and shape play fundamental roles in organismal function and it is expected that animals may possess body proportions that are well-suited to their ecological niche. Tetrapods exhibit a diverse array of body shapes, but to date this diversity in body proportions and its relationship to ecology have not been systematically quantified. Using whole-body skeletal models of 410 extinct and extant tetrapods, we show that allometric relationships vary across individual body segments thereby yielding changes in overall body shape as size increases. However, we also find statistical support for quadratic relationships indicative of differential scaling in small-medium versus large animals. Comparisons of locomotor and dietary groups highlight key differences in body proportions that may mechanistically underlie occupation of major ecological niches. Our results emphasise the pivotal role of body proportions in the broad-scale ecological diversity of tetrapods.

Here, the authors examine how body size, shape, and segment proportions correspond to ecology in models of 410 tetrapods. They find variable allometric relationships, differential scaling in small and large animals, and body proportions as a potential niche occupation mechanism.

Paleomimetics: A Conceptual Framework for a Biomimetic Design Inspired by Fossils and Evolutionary Processes

In biomimetic design, functional systems, principles, and processes observed in nature are used for the development of innovative technical systems. The research on functional features is often carried out without giving importance to the generative mechanism behind them: evolution. To deeply understand and evaluate the meaning of functional morphologies, integrative structures, and processes, it is imperative to not only describe, analyse, and test their behaviour, but also to understand the evolutionary history, constraints, and interactions that led to these features. The discipline of palaeontology and its approach can considerably improve the efficiency of biomimetic transfer by analogy of function; additionally, this discipline, as well as biology, can contribute to the development of new shapes, textures, structures, and functional models for productive and generative processes useful in the improvement of designs. Based on the available literature, the present review aims to exhibit the potential contribution that palaeontology can offer to biomimetic processes, integrating specific methodologies and knowledge in a typical biomimetic design approach, as well as laying the foundation for a biomimetic design inspired by extinct species and evolutionary processes: Paleomimetics. A state of the art, definition, method, and tools are provided, and fossil entities are presented as potential role models for technical transfer solutions.

Three-dimensional polygonal muscle modelling and line of action estimation in living and extinct taxa

Biomechanical models and simulations of musculoskeletal function rely on accurate muscle parameters, such as muscle masses and lines of action, to estimate force production potential and moment arms. These parameters are often obtained through destructive techniques (i.e., dissection) in living taxa, frequently hindering the measurement of other relevant parameters from a single individual, thus making it necessary to combine multiple specimens and/or sources. Estimating these parameters in extinct taxa is even more challenging as soft tissues are rarely preserved in fossil taxa and the skeletal remains contain relatively little information about the size or exact path of a muscle. Here we describe a new protocol that facilitates the estimation of missing muscle parameters (i.e., muscle volume and path) for extant and extinct taxa. We created three-dimensional volumetric reconstructions for the hindlimb muscles of the extant Nile crocodile and extinct stem-archosaur Euparkeria, and the shoulder muscles of an extant gorilla to demonstrate the broad applicability of this methodology across living and extinct animal clades. Additionally, our method can be combined with surface geometry data digitally captured during dissection, thus facilitating downstream analyses. We evaluated the estimated muscle masses against physical measurements to test their accuracy in estimating missing parameters. Our estimated muscle masses generally compare favourably with segmented iodine-stained muscles and almost all fall within or close to the range of observed muscle masses, thus indicating that our estimates are reliable and the resulting lines of action calculated sufficiently accurately. This method has potential for diverse applications in evolutionary morphology and biomechanics.

A proposed standard for quantifying 3-D hindlimb joint poses in living and extinct archosaurs

The last common ancestor of birds and crocodylians plus all of its descendants (clade Archosauria) dominated terrestrial Mesozoic ecosystems, giving rise to disparate body plans, sizes, and modes of locomotion. As in the fields of vertebrate morphology and paleontology more generally, studies of archosaur skeletal structure have come to depend on tools for acquiring, measuring, and exploring three‐dimensional (3‐D) digital models. Such models, in turn, form the basis for many analyses of musculoskeletal function. A set of shared conventions for describing 3‐D pose (joint or limb configuration) and 3‐D kinematics (change in pose through time) is essential for fostering comparison of posture/movement among such varied species, as well as for maximizing communication among scientists. Following researchers in human biomechanics, we propose a standard methodological approach for measuring the relative position and orientation of the major segments of the archosaur pelvis and hindlimb in 3‐D. We describe the construction of anatomical and joint coordinate systems using the extant guineafowl and alligator as examples. Our new standards are then applied to three extinct taxa sampled from the wider range of morphological, postural, and kinematic variation that has arisen across >250 million years of archosaur evolution. These proposed conventions, and the founding principles upon which they are based, can also serve as starting points for measuring poses between elements within a hindlimb segment, for establishing coordinate systems in the forelimb and axial skeleton, or for applying our archosaurian system more broadly to different vertebrate clades.

Modeling tooth enamel in FEA comparisons of skulls: Comparing common simplifications with biologically realistic models

Palaeontologists often use finite element analyses, in which forces propagate through objects with specific material properties, to investigate feeding biomechanics. Teeth are usually modeled with uniform properties (all bone or all enamel). In reality, most teeth are composed of pulp, dentine, and enamel. We tested how simplified teeth compare to more realistic models using mandible models of three reptiles. For each, we created models representing enamel thicknesses found in extant taxa, as well as simplified models (bone, dentine or enamel). Our results suggest that general comparisons of stress distribution among distantly related taxa do not require representation of dental tissues, as there was no noticeable effect on heatmap representations of stress. However, we find that representation of dental tissues impacts bite force estimates, although magnitude of these effects may differ depending on constraints. Thus, as others have shown, the detail necessary in a biomechanical model relates to the questions being examined.

Predictive simulations of running gait reveal a critical dynamic role for the tail in bipedal dinosaur locomotion

Locomotion has influenced the ecology, evolution, and extinction of species throughout history, yet studying locomotion in the fossil record is challenging. Computational biomechanics can provide novel insight by mechanistically relating observed anatomy to whole-animal function and behavior. Here, we leverage optimal control methods to generate the first fully predictive, three-dimensional, muscle-driven simulations of locomotion in an extinct terrestrial vertebrate, the bipedal non-avian theropod dinosaur Coelophysis. Unexpectedly, our simulations involved pronounced lateroflexion movements of the tail. Rather than just being a static counterbalance, simulations indicate that the tail played a crucial dynamic role, with lateroflexion acting as a passive, physics-based mechanism for regulating angular momentum and improving locomotor economy, analogous to the swinging arms of humans. We infer this mechanism to have existed in many other bipedal non-avian dinosaurs as well, and our methodology provides new avenues for exploring the functional diversity of dinosaur tails in the future.

Convex hull estimation of mammalian body segment parameters

Obtaining accurate values for body segment parameters (BSPs) is fundamental in many biomechanical studies, particularly for gait analysis. Convex hulling, where the smallest-possible convex object that surrounds a set of points is calculated, has been suggested as an effective and time-efficient method to estimate these parameters in extinct animals, where soft tissues are rarely preserved. We investigated the effectiveness of convex hull BSP estimation in a range of extant mammals, to inform the potential future usage of this technique with extinct taxa. Computed tomography scans of both the skeleton and skin of every species investigated were virtually segmented. BSPs (the mass, position of the centre of mass and inertial tensors of each segment) were calculated from the resultant soft tissue segments, while the bone segments were used as the basis for convex hull reconstructions. We performed phylogenetic generalized least squares and ordinary least squares regressions to compare the BSPs calculated from soft tissue segments with those estimated using convex hulls, finding consistent predictive relationships for each body segment. The resultant regression equations can, therefore, be used with confidence in future volumetric reconstruction and biomechanical analyses of mammals, in both extinct and extant species where such data may not be available.

The evolutionary biomechanics of locomotor function in giant land animals

Giant land vertebrates have evolved more than 30 times, notably in dinosaurs and mammals. The evolutionary and biomechanical perspectives considered here unify data from extant and extinct species, assessing current theory regarding how the locomotor biomechanics of giants has evolved. In terrestrial tetrapods, isometric and allometric scaling patterns of bones are evident throughout evolutionary history, reflecting general trends and lineage-specific divergences as animals evolve giant size. Added to data on the scaling of other supportive tissues and neuromuscular control, these patterns illuminate how lineages of giant tetrapods each evolved into robust forms adapted to the constraints of gigantism, but with some morphological variation. Insights from scaling of the leverage of limbs and trends in maximal speed reinforce the idea that, beyond 100-300 kg of body mass, tetrapods reduce their locomotor abilities, and eventually may lose entire behaviours such as galloping or even running. Compared with prehistory, extant megafaunas are depauperate in diversity and morphological disparity; therefore, turning to the fossil record can tell us more about the evolutionary biomechanics of giant tetrapods. Interspecific variation and uncertainty about unknown aspects of form and function in living and extinct taxa still render it impossible to use first principles of theoretical biomechanics to tightly bound the limits of gigantism. Yet sauropod dinosaurs demonstrate that >50 tonne masses repeatedly evolved, with body plans quite different from those of mammalian giants. Considering the largest bipedal dinosaurs, and the disparity in locomotor function of modern megafauna, this shows that even in terrestrial giants there is flexibility allowing divergent locomotor specialisations.

Natural Frequency Method: estimating the preferred walking speed of Tyrannosaurus rex based on tail natural frequency

Locomotor energetics are an important determinant of an animal's ecological niche. It is commonly assumed that animals minimize locomotor energy expenditure by selecting gait kinematics tuned to the natural frequencies of relevant body parts. We demonstrate that this allows estimation of the preferred step frequency and walking speed of Tyrannosaurus rex, using an approach we introduce as the Natural Frequency Method. Although the tail of bipedal dinosaurs was actively involved in walking, it was suspended passively by the caudal interspinous ligaments. These allowed for elastic energy storage, thereby reducing the metabolic cost of transport. In order for elastic energy storage to be high, step and natural frequencies would have to be matched. Using a 3D morphological reconstruction and a spring-suspended biomechanical model, we determined the tail natural frequency of T. rex (0.66 s^-1, range 0.41-0.84), and the corresponding walking speed (1.28 m s^-1, range 0.80-1.64), which we argue to be a good indicator of preferred walking speed (PWS). The walking speeds found here are lower than earlier estimations for large theropods, but agree quite closely with PWS of a diverse group of extant animals. The results are most sensitive to uncertainties regarding ligament moment arms, vertebral kinematics and ligament composition. However, our model formulation and method for estimation of walking speed are unaffected by assumptions regarding muscularity, and therefore offer an independent line of evidence within the field of dinosaur locomotion.

Predictive Simulations of Musculoskeletal Function and Jumping Performance in a Generalized Bird

Jumping is a common, but demanding, behavior that many animals employ during everyday activity. In contrast to jump-specialists such as anurans and some primates, jumping biomechanics and the factors that influence performance remains little studied for generalized species that lack marked adaptations for jumping. Computational biomechanical modeling approaches offer a way of addressing this in a rigorous, mechanistic fashion. Here, optimal control theory and musculoskeletal modeling are integrated to generate predictive simulations of maximal height jumping in a small ground-dwelling bird, a tinamou. A three-dimensional musculoskeletal model with 36 actuators per leg is used, and direct collocation is employed to formulate a rapidly solvable optimal control problem involving both liftoff and landing phases. The resulting simulation raises the whole-body center of mass to over double its standing height, and key aspects of the simulated behavior qualitatively replicate empirical observations for other jumping birds. However, quantitative performance is lower, with reduced ground forces, jump heights, and muscle–tendon power. A pronounced countermovement maneuver is used during launch. The use of a countermovement is demonstrated to be critical to the achievement of greater jump heights, and this phenomenon may only need to exploit physical principles alone to be successful; amplification of muscle performance may not necessarily be a proximate reason for the use of this maneuver. Increasing muscle strength or contractile velocity above nominal values greatly improves jump performance, and interestingly has the greatest effect on more distal limb extensor muscles (i.e., those of the ankle), suggesting that the distal limb may be a critical link for jumping behavior. These results warrant a re-evaluation of previous inferences of jumping ability in some extinct species with foreshortened distal limb segments, such as dromaeosaurid dinosaurs.

Simulations prédictives de la fonction musculo-squelettique et des performances de saut chez un oiseau généralisé Sauter est un comportement commun, mais exigeant, que de nombreux animaux utilisent au cours de leurs activités quotidiennes. Contrairement aux spécialistes du saut tels que les anoures et certains primates, la biomécanique du saut et les facteurs qui influencent la performance restent peu étudiés pour les espèces généralisées qui n’ont pas d’adaptations marquées pour le saut. Les approches de modélisation biomécanique computationnelle offrent un moyen d’aborder cette question de manière rigoureuse et mécaniste. Ici, la théorie du contrôle optimal et la modélisation musculo-squelettique sont intégrées pour générer des simulations prédictives du saut en hauteur maximal chez un petit oiseau terrestre, le tinamou. Un modèle musculo-squelettique tridimensionnel avec 36 actionneurs par patte est utilisé, et une méthode numérique nommée “direct collocation” est employée pour formuler un problème de contrôle optimal rapidement résoluble impliquant les phases de décollage et d’atterrissage. La simulation qui en résulte élève le centre de masse du corps entier à plus du double de sa hauteur debout, et les aspects clés du comportement simulé reproduisent qualitativement les observations empiriques d’autres oiseaux sauteurs. Cependant, les performances quantitatives sont moindres, avec une réduction des forces au sol, des hauteurs de saut et de la puissance musculo-tendineuse. Une manœuvre de contre-mouvement prononcée est utilisée pendant le lancement. Il a été démontré que l’utilisation d’un contre-mouvement est essentielle à l’obtention de hauteurs de saut plus importantes, et il se peut que ce phénomène doive exploiter uniquement des principes physiques pour réussir; l’amplification de la performance musculaire n’est pas nécessairement une raison immédiate de l’utilisation de cette manœuvre. L’augmentation de la force musculaire ou de la vitesse de contraction au-dessus des valeurs nominales améliore grandement la performance de saut et, fait intéressant, a le plus grand effet sur les muscles extenseurs des membres plus distaux (c'est-à-dire ceux de la cheville), ce qui suggère que le membre distal peut être un lien critique pour le comportement de saut. Ces résultats justifient une réévaluation des déductions précédentes de la capacité de sauter chez certaines espèces éteintes avec des segments de membres distaux raccourcis, comme les dinosaures droméosauridés.

Voorspellende simulaties van musculoskeletale functie en springprestaties bij een gegeneraliseerde vogel Springen is een veel voorkomend, maar veeleisend, gedrag dat veel dieren toepassen tijdens hun dagelijkse bezigheden. In tegenstelling tot de springspecialisten zoals de anura en sommige primaten, is de biomechanica van het springen en de factoren die de prestaties beïnvloeden nog weinig bestudeerd voor algemene soorten die geen uitgesproken adaptaties voor het springen hebben. Computationele biomechanische modelbenaderingen bieden een manier om dit op een rigoureuze, mechanistische manier aan te pakken. Hier worden optimale controle theorie en musculoskeletale modellering geïntegreerd om voorspellende simulaties te genereren van maximale hoogtesprong bij een kleine grondbewonende vogel, een tinamou. Een driedimensionaal musculoskeletaal model met 36 actuatoren per poot wordt gebruikt, en directe collocatie wordt toegepast om een snel oplosbaar optimaal controleprobleem te formuleren dat zowel de opstijg-als de landingsfase omvat. De resulterende simulatie verhoogt het lichaamszwaartepunt tot meer dan het dubbele van de stahoogte, en belangrijke aspecten van het gesimuleerde gedrag komen kwalitatief overeen met empirische waarnemingen voor andere springende vogels. De kwantitatieve prestaties zijn echter minder, met verminderde grondkrachten, spronghoogtes en spierpeeskracht. Tijdens de lancering wordt een uitgesproken tegenbewegingsmanoeuvre gebruikt. Aangetoond is dat het gebruik van een tegenbeweging van cruciaal belang is voor het bereiken van grotere spronghoogten, en dit fenomeen hoeft alleen op fysische principes te berusten om succesvol te zijn; versterking van de spierprestaties hoeft niet noodzakelijk een proximate reden te zijn voor het gebruik van deze manoeuvre. Het verhogen van de spierkracht of van de contractiesnelheid boven de nominale waarden verbetert de sprongprestatie aanzienlijk, en heeft interessant genoeg het grootste effect op de meer distale extensoren van de ledematen (d.w.z. die van de enkel), wat suggereert dat de distale ledematen een kritieke schakel kunnen zijn voor het springgedrag. Deze resultaten rechtvaardigen een herevaluatie van eerdere conclusies over springvermogen bij sommige uitgestorven soorten met voorgekorte distale ledematen, zoals dromaeosauride dinosauriërs.

Prädiktive Simulationen der muskuloskelettalen Funktion und Sprungleistung bei einem generalisierten Vogel Springen ist ein übliches jedoch anstrengendes Verhalten, das viele Tiere bei ihren täglichen Aktivitäten einsetzen. Im Gegensatz zu Springspezialisten, wie Fröschen und einigen Primaten, sind bei allgemeinen Arten, welche keine ausgeprägten Anpassung für Sprungverhalten aufweisen, die Biomechanik beim Springen und die Faktoren, welche die Leistungsfähigkeit beeinflussen, noch wenig untersucht. Computergestützte biomechanische Modellierungsverfahren bieten hier eine Möglichkeit, dies in einer gründlichen, mechanistischen Weise anzugehen. In dieser Arbeit werden die optimale Steuerungstheorie und Muskel-Skelett-Modellierung zusammen eingesetzt, um die maximale Sprunghöhe eines kleinen bodenlebenden Vogels, eines Perlsteisshuhns, zu simulieren und zu prognostizieren. Es wird ein dreidimensionales Muskel-Skelett-Modell mit 36 Aktuatoren pro Bein verwendet, und durch direkte Kollokation wird ein schnell lösbares optimales Steuerungsproblem formuliert, das sowohl die Abstoss- als auch die Landephase umfasst. Die daraus folgende Simulation bringt den Ganzkörperschwerpunkt auf mehr als das Doppelte seiner Standhöhe und entscheidende Aspekte des simulierten Verhaltens entsprechen qualitativ empirischen Beobachtungen für andere springende Vögel. Allerdings ist die quantitative Leistungsfähigkeit geringer, mit reduzierten Bodenkräften, Sprunghöhen und Muskel-Sehnen-Kräften. Beim Abstossen wird ein ausgeprägtes Gegenbewegungsmanöver durchgeführt. Die Durchführung einer Gegenbewegung ist nachweislich entscheidend für das Erreichen grösserer Sprunghöhen, wobei dieses Phänomen möglicherweise nur physikalische Prinzipien auszuschöpfen braucht, um erfolgreich zu sein. Die Verstärkung der Muskelleistung ist daher möglicherweise nicht zwingend ein unmittelbarer Grund für die Verwendung dieses Manövers. Eine Erhöhung der Muskelkraft oder der Kontraktionsgeschwindigkeit über die Nominalwerte hinaus führt zu einer erheblichen Zunahme der Sprungleistung und hat interessanterweise den grössten Effekt bei den weiter distal gelegenen Streckmuskeln der Beine (d.h. bei denjenigen des Sprunggelenks), was darauf hindeutet, dass die distale Gliedmasse ein entscheidendes Element für das Sprungverhalten sein könnte. Diese Ergebnisse geben Anlass zur Überprüfung früherer Schlussfolgerungen hinsichtlich der Sprungfähigkeit einiger ausgestorbener Arten mit verkürzten distalen Gliedmassen, wie beispielsweise bei dromaeosauriden Dinosauriern.

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.

Maniraptoran pelvic musculature highlights evolutionary patterns in theropod locomotion on the line to birds

Locomotion is a fundamental aspect of palaeobiology and often investigated by comparing osteological structures and proportions. Previous studies document a stepwise accumulation of avian-like features in theropod dinosaurs that accelerates in the clade Maniraptora. However, the soft tissues that influenced the skeleton offer another perspective on locomotory adaptations. Examination of the pelvis for osteological correlates of hind limb and tail musculature allowed reconstruction of primary locomotory muscles across theropods and their closest extant relatives. Additionally, the areas of pelvic muscle origins were quantified to measure relative differences within and between taxa, to compare morphological features associated with cursoriality, and offer insight into the evolution of locomotor modules. Locomotory inferences based on myology often corroborate those based on osteology, although they occasionally conflict and indicate greater complexity than previously appreciated. Maniraptoran pelvic musculature underscores previous studies noting the multifaceted nature of cursoriality and suggests that a more punctuated step in caudal decoupling occurred at or near the base of Maniraptora.

Evolutionary biomechanics: hard tissues and soft evidence?

Biomechanical modelling is a powerful tool for quantifying the evolution of functional performance in extinct animals to understand key anatomical innovations and selective pressures driving major evolutionary radiations. However, the fossil record is composed predominantly of hard parts, forcing palaeontologists to reconstruct soft tissue properties in such models. Rarely are these reconstruction approaches validated on extant animals, despite soft tissue properties being highly determinant of functional performance. The extent to which soft tissue reconstructions and biomechanical models accurately predict quantitative or even qualitative patterns in macroevolutionary studies is therefore unknown. Here, we modelled the masticatory system in extant rodents to objectively test the ability of current muscle reconstruction methods to correctly identify quantitative and qualitative differences between macroevolutionary morphotypes. Baseline models generated using measured soft tissue properties yielded differences in muscle proportions, bite force, and bone stress expected between extant sciuromorph, myomorph, and hystricomorph rodents. However, predictions from models generated using reconstruction methods typically used in fossil studies varied widely from high levels of quantitative accuracy to a failure to correctly capture even relative differences between macroevolutionary morphotypes. Our novel experiment emphasizes that correctly reconstructing even qualitative differences between taxa in a macroevolutionary radiation is challenging using current methods. Future studies of fossil taxa should incorporate systematic assessments of reconstruction error into their hypothesis testing and, moreover, seek to expand primary datasets on muscle properties in extant taxa to better inform soft tissue reconstructions in macroevolutionary studies.

The accuracy and precision of body mass estimation in non-avian dinosaurs

Inferring the body mass of fossil taxa, such as non-avian dinosaurs, provides a powerful tool for interpreting physiological and ecological properties, as well as the ability to study these traits through deep time and within a macroevolutionary context. As a result, over the past 100 years a number of studies advanced methods for estimating mass in dinosaurs and other extinct taxa. These methods can be categorized into two major approaches: volumetric-density (VD) and extant-scaling (ES). The former receives the most attention in non-avian dinosaurs and advanced appreciably over the last century: from initial physical scale models to three-dimensional (3D) virtual techniques that utilize scanned data obtained from entire skeletons. The ES approach is most commonly applied to extinct members of crown clades but some equations are proposed and utilized in non-avian dinosaurs. Because both approaches share a common goal, they are often viewed in opposition to one another. However, current palaeobiological research problems are often approach specific and, therefore, the decision to utilize a VD or ES approach is largely question dependent. In general, biomechanical and physiological studies benefit from the full-body reconstruction provided through a VD approach, whereas large-scale evolutionary and ecological studies require the extensive data sets afforded by an ES approach. This study summarizes both approaches to body mass estimation in stem-group taxa, specifically non-avian dinosaurs, and provides a comparative quantitative framework to reciprocally illuminate and corroborate VD and ES approaches. The results indicate that mass estimates are largely consistent between approaches: 73% of VD reconstructions occur within the expected 95% prediction intervals of the ES relationship. However, almost three quarters of outliers occur below the lower 95% prediction interval, indicating that VD mass estimates are, on average, lower than would be expected given their stylopodial circumferences. Inconsistencies (high residual and per cent prediction deviation values) are recovered to a varying degree among all major dinosaurian clades along with an overall tendency for larger deviations between approaches among small-bodied taxa. Nonetheless, our results indicate a strong corroboration between recent iterations of the VD approach based on 3D specimen scans suggesting that our current understanding of size in dinosaurs, and hence its biological correlates, has improved over time. We advance that VD and ES approaches have fundamentally (metrically) different advantages and, hence, the comparative framework used and advocated here combines the accuracy afforded by ES with the precision provided by VD and permits the rapid identification of discrepancies with the potential to open new areas of discussion.

Subject-specific muscle properties from diffusion tensor imaging significantly improve the accuracy of musculoskeletal models

Musculoskeletal modelling is an important platform on which to study the biomechanics of morphological structures in vertebrates and is widely used in clinical, zoological and palaeontological fields. The popularity of this approach stems from the potential to non-invasively quantify biologically important but difficult-to-measure functional parameters. However, while it is known that model predictions are highly sensitive to input values, it is standard practice to build models by combining musculoskeletal data from different sources resulting in 'generic' models for a given species. At present, there are little quantitative data on how merging disparate anatomical data in models impacts the accuracy of these functional predictions. This issue is addressed herein by quantifying the accuracy of both subject-specific human limb models containing individualised muscle force-generating properties and models built using generic properties from both elderly and young individuals, relative to experimental muscle torques obtained from an isokinetic dynamometer. The results show that subject-specific models predict isokinetic muscle torques to a greater degree of accuracy than generic models at the ankle (root-mean-squared error - 7.9% vs. 49.3% in elderly anatomy-based models), knee (13.2% vs. 57.3%) and hip (21.9% vs. 32.8%). These results have important implications for the choice of musculoskeletal properties in future modelling studies, and the relatively high level of accuracy achieved in the subject-specific models suggests that such models can potentially address questions about inter-subject variations of muscle functions. However, despite relatively high levels of overall accuracy, models built using averaged generic muscle architecture data from young, healthy individuals may lack the resolution and accuracy required to study such differences between individuals, at least in certain circumstances. The results do not wholly discourage the continued use of averaged generic data in musculoskeletal modelling studies but do emphasise the need for to maximise the accuracy of input values if studying intra-species form-function relationships in the musculoskeletal system.

More than one way to be a giant: Convergence and disparity in the hip joints of saurischian dinosaurs

Saurischian dinosaurs evolved seven orders of magnitude in body mass, as well as a wide diversity of hip joint morphology and locomotor postures. The very largest saurischians possess incongruent bony hip joints, suggesting that large volumes of soft tissues mediated hip articulation. To understand the evolutionary trends and functional relationships between body size and hip anatomy of saurischians, we tested the relationships among discrete and continuous morphological characters using phylogenetically corrected regression. Giant theropods and sauropods convergently evolved highly cartilaginous hip joints by reducing supraacetabular ossifications, a condition unlike that in early dinosauromorphs. However, transitions in femoral and acetabular soft tissues indicate that large sauropods and theropods built their hip joints in fundamentally different ways. In sauropods, the femoral head possesses irregularly rugose subchondral surfaces for thick hyaline cartilage. Hip articulation was achieved primarily using the highly cartilaginous femoral head and the supraacetabular labrum on the acetabular ceiling. In contrast, theropods covered their femoral head and neck with thinner hyaline cartilage and maintained extensive articulation between the fibrocartilaginous femoral neck and the antitrochanter. These findings suggest that the hip joints of giant sauropods were built to sustain large compressive loads, whereas those of giant theropods experienced compression and shear forces.

Testing the function of dromaeosaurid (Dinosauria, Theropoda) 'sickle claws' through musculoskeletal modelling and optimization

Dromaeosaurids were a clade of bird-like, carnivorous dinosaurs that are well known for their characteristic morphology of pedal digit II, which bore an enlarged, sickle-shaped claw and permitted an extreme range of flexion–extension. Proposed functions for the claw often revolve around predation, but the exact manner of use varies widely. Musculoskeletal modelling provides an avenue to quantitatively investigate the biomechanics of this enigmatic system, and thereby test different behavioural hypotheses. Here, a musculoskeletal model of the hindlimb and pes of Deinonychus was developed, and mathematical optimization was used to assess the factors that maximize production of force at the claw tip. Optimization revealed that more crouched hindlimb postures (i.e., more flexed knees and ankles) and larger flexor muscle volumes consistently increased claw forces, although the optimal degree of digit flexion or extension depended on assumptions of muscle activity and fibre operating range. Interestingly, the magnitude of force capable of being produced at the claw tip was relatively small, arguing against regular transmission of a large proportion of body weight into a substrate principally via the claw tip. Such transmission would therefore likely have needed to occur via more proximal parts of the foot. Collectively, the results best support a grasping function for digit II (e.g., restraint of prey smaller than the dromaeosaurid’s own body size), although other behaviours involving flexed hindlimbs cannot be excluded.

The importance of muscle architecture in biomechanical reconstructions of extinct animals: a case study using Tyrannosaurus rex

Functional reconstructions of extinct animals represent a crucial step towards understanding palaeocological interactions, selective pressures and macroevolutionary patterns in the fossil record. In recent years, computational approaches have revolutionised the field of 'evolutionary biomechanics' and have, in general, resulted in convergence of quantitative estimates of performance on increasingly narrow ranges for well studied taxa. Studies of body mass and locomotor performance of Tyrannosaurus rex - arguably the most intensively studied extinct animal - typify this pattern, with numerous independent studies predicting similar body masses and maximum locomotor speeds for this animal. In stark contrast to this trend, recent estimates of maximum bite force in T. rex vary considerably (> 50%) despite use of similar quantitative methodologies. Herein we demonstrate that the mechanistic causes of these disparate predictions are indicative of important and underappreciated limiting factors in biomechanical reconstructions of extinct organisms. Detailed comparison of previous models of T. rex bite force reveals that estimations of muscle fibre lengths and architecture are the principal source of disagreement between studies, and therefore that these parameters represents the greatest source of uncertainty in these reconstructions, and potentially therefore extinct animals generally. To address the issue of fibre length and architecture estimation in extinct animals we present data tabulated from the literature of muscle architecture from over 1100 muscles measured in extant terrestrial animals. Application of this dataset in a reanalysis of T. rex bite force emphasises the need for more data on jaw musculature from living carnivorous animals, alongside increased sophistication of modelling approaches. In the latter respect we predict that implementing limits on skeletal loading into musculoskeletal models will narrow predictions for T. rex bite force by excluding higher-end estimates.

Cancellous bone and theropod dinosaur locomotion. Part III-Inferring posture and locomotor biomechanics in extinct theropods, and its evolution on the line to birds

This paper is the last of a three-part series that investigates the architecture of cancellous 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 highly sensitive to its prevailing mechanical environment, and may therefore help further understanding of locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part III, the biomechanical modelling approach derived previously was applied to two species of extinct, non-avian theropods, Daspletosaurus torosus and Troodon formosus. Observed cancellous bone architectural patterns were linked with quasi-static, three-dimensional musculoskeletal and finite element models of the hindlimb of both species, and used to derive characteristic postures that best aligned continuum-level principal stresses with cancellous bone fabric. The posture identified for Daspletosaurus was largely upright, with a subvertical femoral orientation, whilst that identified for Troodon was more crouched, but not to the degree observed in extant birds. In addition to providing new insight on posture and limb articulation, this study also tested previous hypotheses of limb bone loading mechanics and muscular control strategies in non-avian theropods, and how these aspects evolved on the line to birds. The results support the hypothesis that an upright femoral posture is correlated with bending-dominant bone loading and abduction-based muscular support of the hip, whereas a crouched femoral posture is correlated with torsion-dominant bone loading and long-axis rotation-based muscular support. Moreover, the results of this study also support the inference that hindlimb posture, bone loading mechanics and muscular support strategies evolved in a gradual fashion along the line to extant birds.

Building a Bird: Musculoskeletal Modeling and Simulation of Wing-Assisted Incline Running During Avian Ontogeny

Flapping flight is the most power-demanding mode of locomotion, associated with a suite of anatomical specializations in extant adult birds. In contrast, many developing birds use their forelimbs to negotiate environments long before acquiring "flight adaptations," recruiting their developing wings to continuously enhance leg performance and, in some cases, fly. How does anatomical development influence these locomotor behaviors? Isolating morphological contributions to wing performance is extremely challenging using purely empirical approaches. However, musculoskeletal modeling and simulation techniques can incorporate empirical data to explicitly examine the functional consequences of changing morphology by manipulating anatomical parameters individually and estimating their effects on locomotion. To assess how ontogenetic changes in anatomy affect locomotor capacity, we combined existing empirical data on muscle morphology, skeletal kinematics, and aerodynamic force production with advanced biomechanical modeling and simulation techniques to analyze the ontogeny of pectoral limb function in a precocial ground bird (Alectoris chukar). Simulations of wing-assisted incline running (WAIR) using these newly developed musculoskeletal models collectively suggest that immature birds have excess muscle capacity and are limited more by feather morphology, possibly because feathers grow more quickly and have a different style of growth than bones and muscles. These results provide critical information about the ontogeny and evolution of avian locomotion by (i) establishing how muscular and aerodynamic forces interface with the skeletal system to generate movement in morphing juvenile birds, and (ii) providing a benchmark to inform biomechanical modeling and simulation of other locomotor behaviors, both across extant species and among extinct theropod dinosaurs.

A Dynamic Simulation of Musculoskeletal Function in the Mouse Hindlimb During Trotting Locomotion

Mice are often used as animal models of various human neuromuscular diseases, and analysis of these models often requires detailed gait analysis. However, little is known of the dynamics of the mouse musculoskeletal system during locomotion. In this study, we used computer optimization procedures to create a simulation of trotting in a mouse, using a previously developed mouse hindlimb musculoskeletal model in conjunction with new experimental data, allowing muscle forces, activation patterns, and levels of mechanical work to be estimated. Analyzing musculotendon unit (MTU) mechanical work throughout the stride allowed a deeper understanding of their respective functions, with the rectus femoris MTU dominating the generation of positive and negative mechanical work during the swing and stance phases. This analysis also tested previous functional inferences of the mouse hindlimb made from anatomical data alone, such as the existence of a proximo-distal gradient of muscle function, thought to reflect adaptations for energy-efficient locomotion. The results do not strongly support the presence of this gradient within the mouse musculoskeletal system, particularly given relatively high negative net work output from the ankle plantarflexor MTUs, although more detailed simulations could test this further. This modeling analysis lays a foundation for future studies of the control of vertebrate movement through the development of neuromechanical simulations.

Quadrupedal locomotor simulation: producing more realistic gaits using dual-objective optimization

In evolutionary biomechanics it is often considered that gaits should evolve to minimize the energetic cost of travelling a given distance. In gait simulation this goal often leads to convincing gait generation. However, as the musculoskeletal models used get increasingly sophisticated, it becomes apparent that such a single goal can lead to extremely unrealistic gait patterns. In this paper, we explore the effects of requiring adequate lateral stability and show how this increases both energetic cost and the realism of the generated walking gait in a high biofidelity chimpanzee musculoskeletal model. We also explore the effects of changing the footfall sequences in the simulation so it mimics both the diagonal sequence walking gaits that primates typically use and also the lateral sequence walking gaits that are much more widespread among mammals. It is apparent that adding a lateral stability criterion has an important effect on the footfall phase relationship, suggesting that lateral stability may be one of the key drivers behind the observed footfall sequences in quadrupedal gaits. The observation that single optimization goals are no longer adequate for generating gait in current models has important implications for the use of biomimetic virtual robots to predict the locomotor patterns in fossil animals.

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.