Predicting the metabolic energy costs of bipedalism using evolutionary robotics

A three-dimensional musculoskeletal model of the pelvis and lower limb of Australopithecus afarensis

OBJECTIVES

Musculoskeletal modeling is a powerful approach for studying the biomechanics and energetics of locomotion. Australopithecus (A.) afarensis is among the best represented fossil hominins and provides critical information about the evolution of musculoskeletal design and locomotion in the hominin lineage. Here, we develop and evaluate a three-dimensional (3-D) musculoskeletal model of the pelvis and lower limb of A. afarensis for predicting muscle-tendon moment arms and moment-generating capacities across lower limb joint positions encompassing a range of locomotor behaviors.

MATERIALS AND METHODS

A 3-D musculoskeletal model of an adult A. afarensis pelvis and lower limb was developed based primarily on the A.L. 288-1 partial skeleton. The model includes geometric representations of bones, joints and 35 muscle-tendon units represented using 43 Hill-type muscle models. Two muscle parameter datasets were created from human and chimpanzee sources. 3-D muscle-tendon moment arms and isometric joint moments were predicted over a wide range of joint positions.

RESULTS

Predicted muscle-tendon moment arms generally agreed with skeletal metrics, and corresponded with human and chimpanzee models. Human and chimpanzee-based muscle parameterizations were similar, with some differences in maximum isometric force-producing capabilities. The model is amenable to size scaling from A.L. 288-1 to the larger KSD-VP-1/1, which subsumes a wide range of size variation in A. afarensis.

DISCUSSION

This model represents an important tool for studying the integrated function of the neuromusculoskeletal systems in A. afarensis. It is similar to current human and chimpanzee models in musculoskeletal detail, and will permit direct, comparative 3-D simulation studies.

Biomechanics and the origins of human bipedal walking: The last 50 years

Motion analysis, as applied to evolutionary biomechanics, has experienced its own evolution over the last 50 years. Here we review how an ever-increasing fossil record, together with continuing advancements in biomechanics techniques, have shaped our understanding of the origin of upright bipedal walking. The original, and long-established hypothesis held by Lamarck (1809), Darwin (1859) and Keith (1934), amongst others, maintained that bipedality originated in an arboreal context. However, the first field studies of gorilla and chimpanzees from the 1960's, highlighted their so-called 'knucklewalking' quadrupedalism, leading scientists to assume, semi-automatically, that knucklewalking must have been the precursor to bipedality. It would not be until the discovery of skeletons of early human relatives Australopithecus afarensis and Australopithecus prometheus, and the inclusion of methods of analysis from computer science, biomechanics, sports science and medicine, that the knucklewalking hypothesis would be most robustly challenged. Their short, but human-like lower limbs and human-like hand indicated that knucklewalking was not part of our ancestral locomotor repertoire. Rather, most current research in evolutionary biomechanics agrees it was a combination of climbing and bipedalism, both in an arboreal context, which facilitated upright, terrestrial, bipedal walking over short distances.

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.

Forward dynamic simulation of Japanese macaque bipedal locomotion demonstrates better energetic economy in a virtualised plantigrade posture

A plantigrade foot with a large robust calcaneus is regarded as a distinctive morphological feature of the human foot; it is presumably the result of adaptation for habitual bipedal locomotion. The foot of the Japanese macaque, on the other hand, does not have such a feature, which hampers it from making foot-ground contact at the heel during bipedal locomotion. Understanding how this morphological difference functionally affects the generation of bipedal locomotion is crucial for elucidating the evolution of human bipedalism. In this study, we constructed a forward dynamic simulation of bipedal locomotion in the Japanese macaque based on a neuromusculoskeletal model to evaluate how virtual manipulation of the foot structure from digitigrade to plantigrade affects the kinematics, dynamics, and energetics of bipedal locomotion in a nonhuman primate whose musculoskeletal anatomy is not adapted to bipedalism. The normal bipedal locomotion generated was in good agreement with that of actual Japanese macaques. If, as in human walking, the foot morphology was altered to allow heel contact, the vertical ground reaction force profile became double-peaked and the cost of transport decreased. These results suggest that evolutionary changes in the foot structure were important for the acquisition of human-like efficient bipedal locomotion.

Inferring cost of transport from whole-body kinematics in three sympatric turtle species with different locomotor habits

Chelonians are mechanically unusual vertebrates as an exoskeleton limits their body wall mobility. They generally move slowly on land and have aquatic or semi-aquatic lifestyles. Somewhat surprisingly, the limited experimental work that has been done suggests that their energetic cost of transport (CoT) are relatively low. This study examines the mechanical evidence for CoT in three turtle species that have differing degrees of terrestrial activity. Our results show that Apolone travels faster than the other two species, and that Chelydra has higher levels of yaw. All the species show poor mean levels of energy recovery, and, whilst there is considerable variation, never show the high levels of energy recovery seen in cursorial quadrupeds. The mean mechanical CoT is 2 to 4 times higher than is generally seen in terrestrial animals. We therefore find no mechanical support for a low CoT in these species. This study illustrates the need for research on a wider range of chelonians to discover whether there are indeed general trends in mechanical and metabolic energy costs.

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.

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.

A 3D musculoskeletal model of the western lowland gorilla hind limb: moment arms and torque of the hip, knee and ankle

Three-dimensional musculoskeletal models have become increasingly common for investigating muscle moment arms in studies of vertebrate locomotion. In this study we present the first musculoskeletal model of a western lowland gorilla hind limb. Moment arms of individual muscles around the hip, knee and ankle were compared with previously published data derived from the experimental tendon travel method. Considerable differences were found which we attribute to the different methodologies in this specific case. In this instance, we argue that our 3D model provides more accurate and reliable moment arm data than previously published data on the gorilla because our model incorporates more detailed consideration of the 3D geometry of muscles and the geometric constraints that exist on their lines-of-action about limb joints. Our new data have led us to revaluate the previous conclusion that muscle moment arms in the gorilla hind limb are optimised for locomotion with crouched or flexed limb postures. Furthermore, we found that bipedalism and terrestrial quadrupedalism coincided more regularly with higher moment arms and torque around the hip, knee and ankle than did vertical climbing. This indicates that the ability of a gorilla to walk bipedally is not restricted by musculoskeletal adaptations for quadrupedalism and vertical climbing, at least in terms of moment arms and torque about hind limb joints.

A comparison of muscle energy models for simulating human walking in three dimensions

The popular Hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions. These extended models differ considerably in their approach to computing energy expenditure, particularly in their treatment of active lengthening and eccentric work, but their predictive abilities have never been compared. In this study, we compared the predictions of five different Hill-based muscle energy models in 3D forward dynamics simulations of normal human walking. In a data-tracking simulation that minimized muscle fatigue, the energy models predicted metabolic costs that varied over a three-fold range (2.45-7.15 J/m/kg), with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate. In predictive simulations that optimized neuromuscular control to minimize the metabolic cost, all five models predicted similar speeds, step lengths, and stance phase durations. However, some of the models predicted a hip circumduction strategy to minimize metabolic cost, while others did not, and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used. The results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure, the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3D musculoskeletal model, the potential for using such models to predict energetically-optimal gait modifications, and the room for improvement in existing muscle energy models and locomotion simulation frameworks.

Exploring diagonal gait using a forward dynamic three-dimensional chimpanzee simulation

Primates are unusual among terrestrial quadrupedal mammals in that at walking speeds they prefer diagonal rather than lateral gaits. A number of reasons have been proposed for this preference in relation to the arboreal ancestry of modern primates: stability, energetic cost, neural control, skeletal loading, and limb interference avoiding. However, this is a difficult question to explore experimentally since most primates only occasionally use anything other than diagonal gaits. An alternative approach is to produce biologically realistic computer simulations of primate gait that enable the constraints of biomechanical loading and the energetics of different modes of locomotion to be explored. In this paper we describe such a model for the chimpanzee Pan troglodytes. The simulation is able to produce spontaneous quadrupedal locomotion, and the footfall sequences generated are split between lateral and diagonal footfall sequences with no obvious energetic benefit associated with either option. However, out of 10 successful simulation runs, 5 were lateral sequence/lateral couplet gaits indicating a preference for a specific lateral footfall sequence with a relatively tightly constrained phase difference between the fore- and hindlimbs. This suggests that the choice of diagonal walking gaits in chimpanzees is not a simple mechanical phenomenon and that diagonal walking gaits in primates are selected for by multiple factors.

Humans, geometric similarity and the Froude number: is ''reasonably close'' really close enough?

Understanding locomotor energetics is imperative, because energy expended during locomotion, a requisite feature of primate subsistence, is lost to reproduction. Although metabolic energy expenditure can only be measured in extant species, using the equations of motion to calculate mechanical energy expenditure offers unlimited opportunities to explore energy expenditure, particularly in extinct species on which empirical experimentation is impossible. Variability, either within or between groups, can manifest as changes in size and/or shape. Isometric scaling (or geometric similarity) requires that all dimensions change equally among all individuals, a condition that will not be met in naturally developing populations. The Froude number (Fr), with lower limb (or hindlimb) length as the characteristic length, has been used to compensate for differences in size, but does not account for differences in shape.To determine whether or not shape matters at the intraspecific level, we used a mechanical model that had properties that mimic human variation in shape. We varied crural index and limb segment circumferences (and consequently, mass and inertial parameters) among nine populations that included 19 individuals that were of different size. Our goal in the current work is to understand whether shape variation changes mechanical energy sufficiently enough to make shape a critical factor in mechanical and metabolic energy assessments.Our results reaffirm that size does not affect mass-specific mechanical cost of transport (Alexander and Jayes, 1983) among geometrically similar individuals walking at equal Fr. The known shape differences among modern humans, however, produce sufficiently large differences in internal and external work to account for much of the observed variation in metabolic energy expenditure, if mechanical energy is correlated with metabolic energy. Any species or other group that exhibits shape differences should be affected similarly to that which we establish for humans. Unfortunately, we currently do not have a simple method to control or adjust for size-shape differences in individuals that are not geometrically similar, although musculoskeletal modeling is a viable, and promising, alternative. In mouse-to-elephant comparisons, size differences could represent the largest source of morphological variation, and isometric scaling factors such as Fr can compensate for much of the variability. Within species, however, shape differences may dominate morphological variation and Fr is not designed to compensate for shape differences. In other words, those shape differences that are "reasonably close" at the mouse-to-elephant level may become grossly different for within-species energetic comparisons.

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.

The musculoskeletal system of humans is not tuned to maximize the economy of locomotion

Humans are known to have energetically optimal walking and running speeds at which the cost to travel a given distance is minimized. We hypothesized that "optimal" walking and running speeds would also exist at the level of individual locomotor muscles. Additionally, because humans are 60-70% more economical when they walk than when they run, we predicted that the different muscles would exhibit a greater degree of tuning to the energetically optimal speed during walking than during running. To test these hypotheses, we used electromyography to measure the activity of 13 muscles of the back and legs over a range of walking and running speeds in human subjects and calculated the cumulative activity required from each muscle to traverse a kilometer. We found that activity of each of these muscles was minimized at specific walking and running speeds but the different muscles were not tuned to a particular speed in either gait. Although humans are clearly highly specialized for terrestrial locomotion compared with other great apes, the results of this study indicate that our locomotor muscles are not tuned to specific walking or running speeds and, therefore, do not maximize the economy of locomotion. This pattern may have evolved in response to selection to broaden the range of sustainable running speeds, to improve performance in motor behaviors not related to endurance locomotion, or in response to selection for both.

The energetic cost of walking: a comparison of predictive methods

BACKGROUND

The energy that animals devote to locomotion has been of intense interest to biologists for decades and two basic methodologies have emerged to predict locomotor energy expenditure: those based on metabolic and those based on mechanical energy. Metabolic energy approaches share the perspective that prediction of locomotor energy expenditure should be based on statistically significant proxies of metabolic function, while mechanical energy approaches, which derive from many different perspectives, focus on quantifying the energy of movement. Some controversy exists as to which mechanical perspective is "best", but from first principles all mechanical methods should be equivalent if the inputs to the simulation are of similar quality. Our goals in this paper are 1) to establish the degree to which the various methods of calculating mechanical energy are correlated, and 2) to investigate to what degree the prediction methods explain the variation in energy expenditure.

METHODOLOGY/PRINCIPAL FINDINGS

We use modern humans as the model organism in this experiment because their data are readily attainable, but the methodology is appropriate for use in other species. Volumetric oxygen consumption and kinematic and kinetic data were collected on 8 adults while walking at their self-selected slow, normal and fast velocities. Using hierarchical statistical modeling via ordinary least squares and maximum likelihood techniques, the predictive ability of several metabolic and mechanical approaches were assessed. We found that all approaches are correlated and that the mechanical approaches explain similar amounts of the variation in metabolic energy expenditure. Most methods predict the variation within an individual well, but are poor at accounting for variation between individuals.

CONCLUSION

Our results indicate that the choice of predictive method is dependent on the question(s) of interest and the data available for use as inputs. Although we used modern humans as our model organism, these results can be extended to other species.

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.

Arboreality, terrestriality and bipedalism

The full publication of Ardipithecus ramidus has particular importance for the origins of hominin bipedality, and strengthens the growing case for an arboreal origin. Palaeontological techniques however inevitably concentrate on details of fragmentary postcranial bones and can benefit from a whole-animal perspective. This can be provided by field studies of locomotor behaviour, which provide a real-world perspective of adaptive context, against which conclusions drawn from palaeontology and comparative osteology may be assessed and honed. Increasingly sophisticated dynamic modelling techniques, validated against experimental data for living animals, offer a different perspective where evolutionary and virtual ablation experiments, impossible for living mammals, may be run in silico, and these can analyse not only the interactions and behaviour of rigid segments but increasingly the effects of compliance, which are of crucial importance in guiding the evolution of an arboreally derived lineage.

Locomotion and posture from the common hominoid ancestor to fully modern hominins, with special reference to the last common panin/hominin ancestor

Based on our knowledge of locomotor biomechanics and ecology we predict the locomotion and posture of the last common ancestors of (a) great and lesser apes and their close fossil relatives (hominoids); (b) chimpanzees, bonobos and modern humans (hominines); and (c) modern humans and their fossil relatives (hominins). We evaluate our propositions against the fossil record in the context of a broader review of evolution of the locomotor system from the earliest hominoids of modern aspect (crown hominoids) to early modern Homo sapiens. While some early East African stem hominoids were pronograde, it appears that the adaptations which best characterize the crown hominoids are orthogrady and an ability to abduct the arm above the shoulder - rather than, as is often thought, manual suspension sensu stricto. At 7-9 Ma (not much earlier than the likely 4-8 Ma divergence date for panins and hominins, see Bradley, 2008) there were crown hominoids in southern Europe which were adapted to moving in an orthograde posture, supported primarily on the hindlimb, in an arboreal, and possibly for Oreopithecus, a terrestrial context. By 7 Ma, Sahelanthropus provides evidence of a Central African hominin, panin or possibly gorilline adapted to orthogrady, and both orthogrady and habitually highly extended postures of the hip are evident in the arboreal East African protohominin Orrorin at 6 Ma. If the traditional idea that hominins passed through a terrestrial 'knuckle-walking' phase is correct, not only does it have to be explained how a quadrupedal gait typified by flexed postures of the hindlimb could have preadapted the body for the hominin acquisition of straight-legged erect bipedality, but we would have to accept a transition from stem-hominoid pronogrady to crown hominoid orthogrady, back again to pronogrady in the African apes and then back to orthogrady in hominins. Hand-assisted arboreal bipedality, which is part of a continuum of orthograde behaviours, is used by modern orangutans to forage among the small branches at the periphery of trees where the core hominoid dietary resource, ripe fruit, is most often to be found. Derivation of habitual terrestrial bipedality from arboreal hand-assisted bipedality requires fewer transitions, and is also kinematically and kinetically more parsimonious.

Estimating dinosaur maximum running speeds using evolutionary robotics

Maximum running speed is an important locomotor parameter for many animals-predators as well as prey-and is thus of interest to palaeobiologists wishing to reconstruct the behavioural ecology of extinct species. A variety of approaches have been tried in the past including anatomical comparisons, bone scaling and strength, safety factors and ground reaction force analyses. However, these approaches are all indirect and an alternative approach is to create a musculoskeletal model of the animal and see how fast it can run. The major advantage of this approach is that all assumptions about the animal's morphology and physiology are directly addressed, whereas the exact same assumptions are hidden in the indirect approaches. In this paper, we present simple musculoskeletal models of three extant and five extinct bipedal species. The models predict top speed in the extant species with reasonably good agreement with accepted values, so we conclude that the values presented for the five extinct species are reasonable predictions given the modelling assumptions made. Improved musculoskeletal models and better estimates of soft tissue parameters will produce more accurate values. Limited sensitivity analysis is performed on key muscle parameters but there is considerable scope for extending this in the future.

Morphological analysis of the hindlimb in apes and humans. II. Moment arms

Flexion/extension moment arms were obtained for the major muscles crossing the hip, knee and ankle joints in the orang-utan, gibbon, gorilla (Eastern and Western lowland) and bonobo. Moment arms varied with joint motion and were generally longer in proximal limb muscles than distal limb muscles. The shape of the moment arm curves (i.e. the plots of moment arm against joint angle) differed in different hindlimb muscles and in the same muscle in different subjects (both in the same and in different ape species). Most moment arms increased with increasing joint flexion, a finding which may be understood in the context of the employment of flexed postures by most non-human apes (except orang-utans) during both terrestrial and arboreal locomotion. When compared with humans, non-human great apes tended to have muscles better designed for moving the joints through large ranges. This was particularly true of the pedal digital flexors in orang-utans. In gibbons, the only lesser ape studied here, many of the moment arms measured were relatively short compared with those of great apes. This study was performed on a small sample of apes and thus differences noted here warrant further investigation in larger populations.

Stride lengths, speed and energy costs in walking of Australopithecus afarensis: using evolutionary robotics to predict locomotion of early human ancestors

This paper uses techniques from evolutionary robotics to predict the most energy-efficient upright walking gait for the early human relative Australopithecus afarensis, based on the proportions of the 3.2 million year old AL 288-1 'Lucy' skeleton, and matches predictions against the nearly contemporaneous (3.5-3.6 million year old) Laetoli fossil footprint trails. The technique creates gaits de novo and uses genetic algorithm optimization to search for the most efficient patterns of simulated muscular contraction at a variety of speeds. The model was first verified by predicting gaits for living human subjects, and comparing costs, stride lengths and speeds to experimentally determined values for the same subjects. Subsequent simulations for A. afarensis yield estimates of the range of walking speeds from 0.6 to 1.3 m s-1 at a cost of 7.0 J kg-1 m-1 for the lowest speeds, falling to 5.8 J kg-1 m-1 at 1.0 m s-1, and rising to 6.2 J kg-1 m-1 at the maximum speed achieved. Speeds previously estimated for the makers of the Laetoli footprint trails (0.56 or 0.64 m s-1 for Trail 1, 0.72 or 0.75 m s-1 for Trail 2/3) may have been underestimated, substantially so for Trail 2/3, with true values in excess of 0.7 and 1.0 m s-1, respectively. The predictions conflict with suggestions that A. afarensis used a 'shuffling' gait, indicating rather that the species was a fully competent biped.

Morphological analysis of the hindlimb in apes and humans. I. Muscle architecture

We present quantitative data on the hindlimb musculature of Pan paniscus, Gorilla gorilla gorilla, Gorilla gorilla graueri, Pongo pygmaeus abelii and Hylobates lar and discuss the findings in relation to the locomotor habits of each. Muscle mass and fascicle length data were obtained for all major hindlimb muscles. Physiological cross-sectional area (PCSA) was estimated. Data were normalized assuming geometric similarity to allow for comparison of animals of different size/species. Muscle mass scaled closely to (body mass)(1.0) and fascicle length scaled closely to (body mass)(0.3) in most species. However, human hindlimb muscles were heavy and had short fascicles per unit body mass when compared with non-human apes. Gibbon hindlimb anatomy shared some features with human hindlimbs that were not observed in the non-human great apes: limb circumferences tapered from proximal-to-distal, fascicle lengths were short per unit body mass and tendons were relatively long. Non-human great ape hindlimb muscles were, by contrast, characterized by long fascicles arranged in parallel, with little/no tendon of insertion. Such an arrangement of muscle architecture would be useful for locomotion in a three dimensionally complex arboreal environment.

Models and the scaling of energy costs for locomotion

To achieve the required generality, models designed to predict scaling relationships for diverse groups of animals generally need to be simple. An argument based on considerations of dynamic similarity predicts correctly that the mechanical cost of transport for running [power/(body mass x speed)] will be independent of body mass; but measurements of oxygen consumption for running birds and mammals show that the metabolic cost of transport is proportional to (body mass)-0.32. Thus the leg muscles seem to work more efficiently in larger animals. A model that treats birds as fixed wing aircraft predicts that the mechanical power required for flight at the maximum range speed will be proportional to (body mass)1.02, but the metabolic power is found to be proportional to (body mass)0.83; again, larger animals seem to have more efficient muscles. A model that treats hovering hummingbirds and insects as helicopters predicts mechanical power to be approximately proportional to body mass, but measurements of oxygen consumption once again show efficiency increasing with body mass. A model of swimming fish as rigid submarines predicts power to be proportional to (body mass)0.5 x (speed)2.5 or to (body mass)0.6 x (speed)2.8, depending on whether flow in the boundary layer is laminar or turbulent. Unfortunately, this prediction cannot easily be compared with available compilations of metabolic data. The finding that efficiency seems to increase with body mass, at least in running and flight, is discussed in relation to the metabolic energy costs of muscular work and force.

Comparison of inverse-dynamics musculo-skeletal models of AL 288-1 Australopithecus afarensis and KNM-WT 15000 Homo ergaster to modern humans, with implications for the evolution of bipedalism

Size and proportions of the postcranial skeleton differ markedly between Australopithecus afarensis and Homo ergaster, and between the latter and modern Homo sapiens. This study uses computer simulations of gait in models derived from the best-known skeletons of these species (AL 288-1, Australopithecus afarensis, 3.18 million year ago) and KNM-WT 15000 (Homo ergaster, 1.5-1.8 million year ago) compared to models of adult human males and females, to estimate the required muscle power during bipedal walking, and to compare this with those in modern humans. Skeletal measurements were carried out on a cast of KNM-WT 15000, but for AL 288-1 were taken from the literature. Muscle attachments were applied to the models based on their position relative to the bone in modern humans. Joint motions and moments from experiments on human walking were input into the models to calculate muscle stress and power. The models were tested in erect walking and 'bent-hip bent-knee' gait. Calculated muscle forces were verified against EMG activity phases from experimental data, with reference to reasonable activation/force delays. Calculated muscle powers are reasonably comparable to experimentally derived metabolic values from the literature, given likely values for muscle efficiency. The results show that: 1) if evaluated by the power expenditure per unit of mass (W/kg) in walking, AL 288-1 and KNM-WT 15000 would need similar power to modern humans; however, 2) with distance-specific parameters as the criteria, AL 288-1 would require to expend relatively more muscle power (W/kg.m(-1)) in comparison to modern humans. The results imply that in the evolution of bipedalism, body proportions, for example those of KNM-WT 15000, may have evolved to obtain an effective application of muscle power to bipedal walking over a long distance, or at high speed.

The metabolic costs of ‘bent-hip, bent-knee’ walking in humans

The costs of different modes of bipedalism are a key issue in reconstructing the likely gait of early human ancestors such as Australopithecus afarensis. Some workers, on the basis of morphological differences between the locomotor skeleton of A. afarensis and modern humans, have proposed that this hominid would have walked in a 'bent-hip, bent-knee' (BHBK) posture like that seen in the voluntary bipedalism of untrained chimpanzees. Computer modelling studies using inverse dynamics indicate that on the basis of segment proportions AL-288-1 should have been capable of mechanically effective upright walking, but in contrast predicted that BHBK walking would have been highly ineffective. The measure most pertinent to natural selection, however, is more likely to be the complete, physiological, or metabolic energy cost. We cannot measure this parameter in a fossil. This paper presents the most complete investigation yet of the metabolic and thermoregulatory costs of BHBK walking in humans. Data show that metabolic costs including the basal metabolic rate (BMR) increase by around 50% while the energy costs of locomotion and blood lactate production nearly double, heat load is increased, and core temperature does not return to normal within 20 minutes rest. Net effects imply that a resting period of 150% activity time would be necessary to prevent physiologically intolerable heat load. Preliminary data for children suggest that scaling effects would not significantly reduce relative costs for hominids of AL-288-1's size. Data from recent studies using forwards dynamic modelling confirm that similar total (including BMR) and locomotor metabolic costs would have applied to BHBK walking by AL-288-1. We explore some of the ecological consequences of our findings.

Evaluating alternative gait strategies using evolutionary robotics

Evolutionary robotics is a branch of artificial intelligence concerned with the automatic generation of autonomous robots. Usually the form of the robot is predefined and various computational techniques are used to control the machine's behaviour. One aspect is the spontaneous generation of walking in legged robots and this can be used to investigate the mechanical requirements for efficient walking in bipeds. This paper demonstrates a bipedal simulator that spontaneously generates walking and running gaits. The model can be customized to represent a range of hominoid morphologies and used to predict performance parameters such as preferred speed and metabolic energy cost. Because it does not require any motion capture data it is particularly suitable for investigating locomotion in fossil animals. The predictions for modern humans are highly accurate in terms of energy cost for a given speed and thus the values predicted for other bipeds are likely to be good estimates. To illustrate this the cost of transport is calculated for Australopithecus afarensis. The model allows the degree of maximum extension at the knee to be varied causing the model to adopt walking gaits varying from chimpanzee-like to human-like. The energy costs associated with these gait choices can thus be calculated and this information used to evaluate possible locomotor strategies in early hominids.

Using sensitivity analysis to validate the predictions of a biomechanical model of bite forces

Biomechanical modelling has become a very popular technique for investigating functional anatomy. Modern computer simulation packages make producing such models straightforward and it is tempting to take the results produced at face value. However the predictions of a simulation are only valid when both the model and the input parameters are accurate and little work has been done to verify this. In this paper a model of the human jaw is produced and a sensitivity analysis is performed to validate the results. The model is built using the ADAMS multibody dynamic simulation package incorporating the major occlusive muscles of mastication (temporalis, masseter, medial and lateral pterygoids) as well as a highly mobile temporomandibular joint. This model is used to predict the peak three-dimensional bite forces at each teeth location, joint reaction forces, and the contributions made by each individual muscle. The results for occlusive bite-force (1080N at M1) match those previously published suggesting the model is valid. The sensitivity analysis was performed by sampling the input parameters from likely ranges and running the simulation many times rather than using single, best estimate values. This analysis shows that the magnitudes of the peak retractive forces on the lower teeth were highly sensitive to the chosen origin (and hence fibre direction) of the temporalis and masseter muscles as well as the laxity of the TMJ. Peak protrusive force was also sensitive to the masseter origin. These result shows that the model is insufficiently complex to estimate these values reliably although the much lower sensitivity values obtained for the bite forces in the other directions and also for the joint reaction forces suggest that these predictions are sound. Without the sensitivity analysis it would not have been possible to identify these weaknesses which strongly supports the use of sensitivity analysis as a validation technique for biomechanical modelling.

Energy transformation during erect and 'bent-hip, bent-knee' walking by humans with implications for the evolution of bipedalism

We have previously reported that predictive dynamic modeling suggests that the 'bent-hip, bent-knee' gait, which some attribute to Australopithecus afarensis AL-288-1, would have been much more expensive in mechanical terms for this hominid than an upright gait. Normal walking by modern adult humans owes much of its efficiency to conservation of energy by transformation between its potential and kinetic states. These findings suggest the question if, and to what extent, energy transformation exists in 'bent-hip, bent-knee' gait. This study calculates energy transformation in humans walking upright, at three different speeds, and walking 'bent-hip, bent-knee'. Kinematic data were gathered from video sequences and kinetic (ground reaction force) data from synchronous forceplate measurement. Applying Newtonian mechanics to our experimental data, the fluctuations of kinetic and potential energy in the body centre of mass were obtained and the effects of energy transformation evaluated and compared. In erect walking the fluctuations of two forms of energy are indeed largely out-of-phase, so that energy transformation occurs and total energy is conserved. In 'bent-hip, bent-knee' walking, however, the fluctuations of the kinetic and potential energy are much more in-phase, so that energy transformation occurs to a much lesser extent. Among all modes of walking the highest energy recovery is obtained in subjectively 'comfortable' walking, the next highest in subjectively 'fast' or 'slow' walking, and the least lowest in 'bent-hip, bent-knee' walking. The results imply that if 'bent-hip, bent-knee' gait was indeed habitually practiced by early bipedal hominids, a very substantial (and in our view as yet unidentified) selective advantage would have had to accrue, to offset the selective disadvantages of 'bent-hip, bent-knee' gait in terms of energy transformation.