Center of pressure (COP) trajectories summarize the complex mechanical interaction between the foot and a contacted surface. Each trajectory itself is also complex, comprising hundreds of instantaneous vectors over the duration of stance phase. To simplify statistical analysis often a small number of scalars are extracted from each COP trajectory. The purpose of this paper was to demonstrate how a more objective approach to COP analysis can avoid particular sensitivities of scalar extraction analysis. A previously published dataset describing the effects of walking speed on plantar pressure (PP) distributions was re-analyzed. After spatially and temporally normalizing the data, speed effects were assessed using a vector-field paired Hotelling's T2 test. Results showed that, as walking speed increased, the COP moved increasingly posterior at heel contact, and increasingly laterally and anteriorly between ?60 and 85% stance, in agreement with previous independent studies. Nevertheless, two extracted scalars disagreed with these results. Furthermore, sensitivity analysis found that a relatively small coordinate system rotation of 5.5° reversed the mediolateral null hypothesis rejection decision. Considering that the foot may adopt arbitrary postures in the horizontal plane, these sensitivity results suggest that non-negligible uncertainty may exist in mediolateral COP effects. As compared with COP scalar extraction, two key advantages of the vector-field approach are: (i) coordinate system independence, (ii) continuous statistical data reflecting the temporal extents of COP trajectory changes.
It is inevitable that some important specimens will become lost or damaged over time, conservation is therefore of vital importance. The Paluxy River dinosaur tracksite is among the most famous in the world. In 1940, Roland T. Bird described and excavated a portion of the site containing associated theropod and sauropod trackways. This excavated trackway was split up and housed in different institutions, and during the process a portion was lost or destroyed. We applied photogrammetric techniques to photographs taken by Bird over 70 years ago, before the trackway was removed, to digitally reconstruct the site as it was prior to excavation. The 3D digital model offers the opportunity to corroborate maps drawn by R.T. Bird when the tracksite was first described. More broadly, this work demonstrates the exciting potential for digitally recreating palaeontological, geological, or archaeological specimens that have been lost to science, but for which photographic documentation exists.
Ornithischian dinosaurs were primitively bipedal with forelimbs modified for grasping, but quadrupedalism evolved in the clade on at least three occasions independently. Outside of Ornithischia, quadrupedality from bipedal ancestors has only evolved on two other occasions, making this one of the rarest locomotory transitions in tetrapod evolutionary history. The osteological and myological changes associated with these transitions have only recently been documented, and the biomechanical consequences of these changes remain to be examined. Here, we review previous approaches to understanding locomotion in extinct animals, which can be broadly split into form-function approaches using analogy based on extant animals, limb-bone scaling, and computational approaches. We then carry out the first systematic attempt to quantify changes in locomotor muscle function in bipedal and quadrupedal ornithischian dinosaurs. Using three-dimensional computational modelling of the major pelvic locomotor muscle moment arms, we examine similarities and differences among individual taxa, between quadrupedal and bipedal taxa, and among taxa representing the three major ornithischian lineages (Thyreophora, Ornithopoda, Marginocephalia). Our results suggest that the ceratopsid Chasmosaurus and the ornithopod Hypsilophodon have relatively low moment arms for most muscles and most functions, perhaps suggesting poor locomotor performance in these taxa. Quadrupeds have higher abductor moment arms than bipeds, which we suggest is due to the overall wider bodies of the quadrupeds modelled. A peak in extensor moment arms at more extended hip angles and lower medial rotator moment arms in quadrupeds than in bipeds may be due to a more columnar hindlimb and loss of medial rotation as a form of lateral limb support in quadrupeds. We are not able to identify trends in moment arm evolution across Ornithischia as a whole, suggesting that the bipedal ancestry of ornithischians did not constrain the development of quadrupedal locomotion via a limited number of functional pathways. Functional anatomy appears to have had a greater effect on moment arms than phylogeny, and the differences identified between individual taxa and individual clades may relate to differences in locomotor performance required for living in different environments or for clade-specific behaviours.
Locomotion in living birds (Neornithes) has two remarkable features: feather-assisted flight, and the use of unusually crouched hindlimbs for bipedal support and movement. When and how these defining functional traits evolved remains controversial. However, the advent of computer modelling approaches and the discoveries of exceptionally preserved key specimens now make it possible to use quantitative data on whole-body morphology to address the biomechanics underlying this issue. Here we use digital body reconstructions to quantify evolutionary trends in locomotor biomechanics (whole-body proportions and centre-of-mass position) across the clade Archosauria. We use three-dimensional digital reconstruction to estimate body shape from skeletal dimensions for 17 archosaurs along the ancestral bird line, including the exceptionally preserved, feathered taxa Microraptor, Archaeopteryx, Pengornis and Yixianornis, which represent key stages in the evolution of the avian body plan. Rather than a discrete transition from more-upright postures in the basal-most birds (Avialae) and their immediate outgroup deinonychosauria, our results support hypotheses of a gradual, stepwise acquisition of more-crouched limb postures across much of theropod evolution, although we find evidence of an accelerated change within the clade Maniraptora (birds and their closest relatives, such as deinonychosaurs). In addition, whereas reduction of the tail is widely accepted to be the primary morphological factor correlated with centre-of-mass position and, hence, evolution of hindlimb posture, we instead find that enlargement of the pectoral limb and several associated trends have a much stronger influence. Intriguingly, our support for the onset of accelerated morpho-functional trends within Maniraptora is closely correlated with the evolution of flight. Because we find that the evolution of enlarged forelimbs is strongly linked, via whole-body centre of mass, to hindlimb function during terrestrial locomotion, we suggest that the evolution of avian flight is linked to anatomical novelties in the pelvic limb as well as the pectoral.
The gait cycle is continuous, but for practical reasons one is often forced to analyze one or only a few adjacent cycles, for example in non-treadmill laboratory investigations and in fossilized footprint analysis. The nature of variability in long-term gait cycle dynamics has been well-investigated, but short-term variability, and specifically correlation, which are highly relevant to short gait bouts, have not. We presently tested for step-to-step autocorrelation in a total of 5243 plantar pressure (PP) distributions from ten subjects who walked at 1.1m/s on an instrumented treadmill. Following spatial foot alignment, data were analyzed both from three points of interest (POI): heel, central metatarsals, and hallux, and for the foot surface as a whole, in a mass-univariate manner. POI results revealed low average step-to-step autocorrelation coefficients (r=0.327±0.094; mean±st. dev.). Formal statistical testing of the whole-foot r distributions reached significance over an average of only 0.42±0.52% of the foots surface, even for a highly conservative uncorrected threshold of p<0.05. The common assumption, that short gait bouts consist of independent cycles, is therefore not refuted by the present PP results.
The study of a small sauropod trackway from the Late Cretaceous Fumanya tracksite (southern Pyrenees, Catalonia) and further comparisons with larger trackways from the same locality suggest a causative relationship between gait, gauge, and body proportions of the respective titanosaur trackmakers. This analysis, conducted in the context of scaling predictions and using geometric similarity and dynamic similarity hypotheses, reveals similar Froude numbers and relative stride lengths for both small and large trackmakers from Fumanya. Evidence for geometric similarity in these trackways suggests that titanosaurs of different sizes moved in a dynamically similar way, probably using an amble gait. The wide gauge condition reported in trackways of small and large titanosaurs implies that they possessed similar body (trunk and limbs) proportions despite large differences in body size. These results strengthen the hypothesis that titanosaurs possessed a distinctive suite of anatomical characteristics that are well reflected in their tracks and trackways.
Fossil evidence for longitudinal arches in the foot is frequently used to constrain the origins of terrestrial bipedality in human ancestors. This approach rests on the prevailing concept that human feet are unique in functioning with a relatively stiff lateral mid-foot, lacking the significant flexion and high plantar pressures present in non-human apes. This paradigm has stood for more than 70 years but has yet to be tested objectively with quantitative data. Herein, we show that plantar pressure records with elevated lateral mid-foot pressures occur frequently in healthy, habitually shod humans, with magnitudes in some individuals approaching absolute maxima across the foot. Furthermore, the same astonishing pressure range is present in bonobos and the orangutan (the most arboreal great ape), yielding overlap with human pressures. Thus, while the mean tendency of habitual mechanics of the mid-foot in healthy humans is indeed consistent with the traditional concept of the lateral mid-foot as a relatively rigid or stabilized structure, it is clear that lateral arch stabilization in humans is not obligate and is often transient. These findings suggest a level of detachment between foot stiffness during gait and osteological structure, hence fossilized bone morphology by itself may only provide a crude indication of mid-foot function in extinct hominins. Evidence for thick plantar tissues in Ardipithecus ramidus suggests that a human-like combination of active and passive modulation of foot compliance by soft tissues extends back into an arboreal context, supporting an arboreal origin of hominin bipedalism in compressive orthogrady. We propose that the musculoskeletal conformation of the modern human mid-foot evolved under selection for a functionally tuneable, rather than obligatory stiff structure.
Human footprints provide some of the most publically emotive and tangible evidence of our ancestors. To the scientific community they provide evidence of stature, presence, behaviour and in the case of early hominins potential evidence with respect to the evolution of gait. While rare in the geological record the number of footprint sites has increased in recent years along with the analytical tools available for their study. Many of these sites are at risk from rapid erosion, including the Ileret footprints in northern Kenya which are second only in age to those at Laetoli (Tanzania). Unlithified, soft-sediment footprint sites such these pose a significant geoconservation challenge. In the first part of this paper conservation and preservation options are explored leading to the conclusion that to record and digitally rescue provides the only viable approach. Key to such strategies is the increasing availability of three-dimensional data capture either via optical laser scanning and/or digital photogrammetry. Within the discipline there is a developing schism between those that favour one approach over the other and a requirement from geoconservationists and the scientific community for some form of objective appraisal of these alternatives is necessary. Consequently in the second part of this paper we evaluate these alternative approaches and the role they can play in a record and digitally rescue conservation strategy. Using modern footprint data, digital models created via optical laser scanning are compared to those generated by state-of-the-art photogrammetry. Both methods give comparable although subtly different results. This data is evaluated alongside a review of field deployment issues to provide guidance to the community with respect to the factors which need to be considered in digital conservation of human/hominin footprints.
It is commonly held that the major functional features of the human foot (e.g. a functional longitudinal medial arch, lateral to medial force transfer and hallucal (big-toe) push-off) appear only in the last 2 Myr, but functional interpretations of footbones and footprints of early human ancestors (hominins) prior to 2 million years ago (Mya) remain contradictory. Pixel-wise topographical statistical analysis of Laetoli footprint morphology, compared with results from experimental studies of footprint formation; foot-pressure measurements in bipedalism of humans and non-human great apes; and computer simulation techniques, indicate that most of these functional features were already present, albeit less strongly expressed than in ourselves, in the maker of the Laetoli G-1 footprint trail, 3.66 Mya. This finding provides strong support to those previous studies which have interpreted the G-1 prints as generally modern in aspect.
The large theropod dinosaur Tyrannosaurus rex underwent remarkable changes during its growth from <10 kg hatchlings to >6000 kg adults in <20 years. These changes raise fascinating questions about the morphological transformations involved, peak growth rates, and scaling of limb muscle sizes as well as the bodys centre of mass that could have influenced ontogenetic changes of locomotion in T. rex. Here we address these questions using three-dimensionally scanned computer models of four large, well-preserved fossil specimens as well as a putative juvenile individual. Furthermore we quantify the variations of estimated body mass, centre of mass and segment dimensions, to characterize inaccuracies in our reconstructions. These inaccuracies include not only subjectivity but also incomplete preservation and inconsistent articulations of museum skeletons. Although those problems cause ambiguity, we conclude that adult T. rex had body masses around 6000-8000 kg, with the largest known specimen ("Sue") perhaps ?9500 kg. Our results show that during T. rex ontogeny, the torso became longer and heavier whereas the limbs became proportionately shorter and lighter. Our estimates of peak growth rates are about twice as rapid as previous ones but generally support previous methods, despite biases caused by the usage of scale models and equations that underestimate body masses. We tentatively infer that the hindlimb extensor muscles masses, including the large tail muscle M. caudofemoralis longus, may have decreased in their relative size as the centre of mass shifted craniodorsally during T. rex ontogeny. Such ontogenetic changes would have worsened any relative or absolute decline of maximal locomotor performance. Regardless, T. rex probably had hip and thigh muscles relatively larger than any extant animals. Overall, the limb "antigravity" muscles may have been as large as or even larger than those of ratite birds, which themselves have the most muscular limbs of any living animal.
Body mass reconstructions of extinct vertebrates are most robust when complete to near-complete skeletons allow the reconstruction of either physical or digital models. Digital models are most efficient in terms of time and cost, and provide the facility to infinitely modify model properties non-destructively, such that sensitivity analyses can be conducted to quantify the effect of the many unknown parameters involved in reconstructions of extinct animals. In this study we use laser scanning (LiDAR) and computer modelling methods to create a range of 3D mass models of five specimens of non-avian dinosaur; two near-complete specimens of Tyrannosaurus rex, the most complete specimens of Acrocanthosaurus atokensis and Strutiomimum sedens, and a near-complete skeleton of a sub-adult Edmontosaurus annectens. LiDAR scanning allows a full mounted skeleton to be imaged resulting in a detailed 3D model in which each bone retains its spatial position and articulation. This provides a high resolution skeletal framework around which the body cavity and internal organs such as lungs and air sacs can be reconstructed. This has allowed calculation of body segment masses, centres of mass and moments or inertia for each animal. However, any soft tissue reconstruction of an extinct taxon inevitably represents a best estimate model with an unknown level of accuracy. We have therefore conducted an extensive sensitivity analysis in which the volumes of body segments and respiratory organs were varied in an attempt to constrain the likely maximum plausible range of mass parameters for each animal. Our results provide wide ranges in actual mass and inertial values, emphasizing the high level of uncertainty inevitable in such reconstructions. However, our sensitivity analysis consistently places the centre of mass well below and in front of hip joint in each animal, regardless of the chosen combination of body and respiratory structure volumes. These results emphasize that future biomechanical assessments of extinct taxa should be preceded by a detailed investigation of the plausible range of mass properties, in which sensitivity analyses are used to identify a suite of possible values to be tested as inputs in analytical models.
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