Musculoskeletal modelling of the Nile crocodile (Crocodylus niloticus) hindlimb: Effects of limb posture on leverage during terrestrial locomotion

Modelling take-off moment arms in an ornithocheiraean pterosaur

Take-off is a vital part of powered flight which likely constrains the size of birds, yet extinct pterosaurs are known to have reached far larger sizes. Three different hypothesised take-off motions (bipedal burst launching, bipedal countermotion launching, and quadrupedal launching) have been proposed as explanations for how pterosaurs became airborne and circumvented this proposed morphological limit. We have constructed a computational musculoskeletal model of a 5 m wingspan ornithocheiraean pterosaur, reconstructing thirty-four key muscles to estimate the muscle moment arms throughout the three hypothesised take-off motions. Range of motion constrained hypothetical kinematic sequences for bipedal and quadrupedal take-off motions were modelled after extant flying vertebrates. Across our simulations we did not find higher hindlimb moment arms for bipedal take-off motions or noticeably higher forelimb moment arms in the forelimb for quadrupedal take-off motions. Despite this, in all our models we found the muscles utilised in the quadrupedal take-off have the largest total launch applicable moment arms throughout the entire take-off sequences and for the take-off pose. This indicates the potential availability of higher leverage for a quadrupedal take-off than hypothesised bipedal motions in pterosaurs pending further examination of muscle forces.

Biomechanical modeling of musculoskeletal function related to the terrestrial locomotion of Riojasuchus tenuisceps (Archosauria: Ornithosuchidae)

Riojasuchus tenuisceps was a pseudosuchian archosaur from the Late Triassic period in Argentina. Like other ornithosuchids, it had unusual morphology such as a unique "crocodile-reversed" ankle joint, a lesser trochanter as in dinosaurs and a few other archosaurs, robust vertebrae, and somewhat shortened, gracile forelimbs. Such traits have fuelled controversies about its locomotor function-were its limbs erect or "semi-erect"? Was it quadrupedal or bipedal, or a mixture thereof? These controversies seem to persist because analyses have been qualitative (functional morphology) or correlative (morphometrics) rather than explicitly, quantitatively testing mechanistic hypotheses about locomotor function. Here, we develop a 3D whole-body model of R. tenuisceps with the musculoskeletal apparatus of the hindlimbs represented in detail using a new muscle reconstruction. We use this model to quantify the body dimensions and hindlimb muscle leverages of this enigmatic taxon, and to estimate joint ranges of motion and qualitative joint functions. Our model supports prior arguments that R. tenuisceps used an erect posture, parasagittal gait and plantigrade pes. However, some of our inferences illuminate the rather contradictory nature of evidence from the musculoskeletal system of R. tenuisceps-different features support (or are ambiguous regarding) quadrupedalism or bipedalism. Deeper analyses of our biomechanical model could move toward a consensus regarding ornithosuchid locomotion. Answering these questions would not only help understand the palaeobiology and bizarre morphology of this clade, but also more broadly if (or how) locomotor abilities played a role in the survival versus extinction of various archosaur lineages during the end-Triassic mass extinction event.

Hindlimb and pelvic anatomy of Caiman yacare (Archosauria, Pseudosuchia): Myology and osteological correlates with emphasis on lower leg and autopodial musculature

The anatomy of the archosaurian pelvis and hindlimb has adopted a diversity of successful configurations allowing a wide range of postures during the evolution of the group (e.g., erect, sprawling). For this reason, thorough studies of the structure and function of the pelvic and hindlimb musculature of crocodylians are required and provide the possibility to expand their implications for the evolution of archosaurian locomotion, as well as to identify potential new characters based on muscles and their bony correlates. In this study, we give a detailed description of the pelvic and hindlimb musculature of the South American alligator Caiman yacare, providing comprehensive novel information regarding lower limb and autopodial muscles. Particularly for the pedal muscles, we propose a new classification for the dorsal and ventral muscles of the autopodium based on the organisation of these muscles in successive layers. We have studied the myology in a global background in which we have compared the Caiman yacare musculature with other crocodylians. In this sense, differences in the arrangement of m. flexor tibialis internus 1, m. flexor tibialis externus, m. iliofibularis, mm. puboischiofemorales internii 1 and 2, between Ca. yacare and other crocodylians were found. We also discuss the muscle attachments that have different bony correlates among the crocodylian species and their morphological variation. Most of the correlates did not exhibit great variation among the species compared. The majority of the recognised correlates were identified in the pelvic girdle; additionally, some bony correlates associated with the pedal muscles are highlighted here for the first time. This research provides a wide framework for future studies on comparative anatomy and functional morphology, which could contribute to improving the character definition used in phylogenetic analyses and to understand the patterns of musculoskeletal hindlimb evolution.

Three-dimensional volumetric muscle reconstruction of the Australopithecus afarensis pelvis and limb, with estimations of limb leverage

To understand how an extinct species may have moved, we first need to reconstruct the missing soft tissues of the skeleton, which rarely preserve, with an understanding of segmental volume and muscular composition within the body. The Australopithecus afarensis specimen AL 288-1 is one of the most complete hominin skeletons. Despite 40+ years of research, the frequency and efficiency of bipedal movement in this specimen is still debated. Here, 36 muscles of the pelvis and lower limb were reconstructed using three-dimensional polygonal modelling, guided by imaging scan data and muscle scarring. Reconstructed muscle masses and configurations guided musculoskeletal modelling of the lower limb in comparison with a modern human. Results show that the moment arms of both species were comparable, hinting towards similar limb functionality. Moving forward, the polygonal muscle modelling approach has demonstrated promise for reconstructing the soft tissues of hominins and providing information on muscle configuration and space filling. This method demonstrates that volumetric reconstructions are required to know where space must be occupied by muscles and thus where lines of action might not be feasible due to interference with another muscle. This approach is effective for reconstructing muscle volumes in extinct hominins for which musculature is unknown.

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.

Quantitative biomechanical assessment of locomotor capabilities of the stem archosaur Euparkeria capensis

Birds and crocodylians are the only remaining members of Archosauria (ruling reptiles) and they exhibit major differences in posture and gait, which are polar opposites in terms of locomotor strategies. Their broader lineages (Avemetatarsalia and Pseudosuchia) evolved a multitude of locomotor modes in the Triassic and Jurassic periods, including several occurrences of bipedalism. The exact timings and frequencies of bipedal origins within archosaurs, and thus their ancestral capabilities, are contentious. It is often suggested that archosaurs ancestrally exhibited some form of bipedalism. Euparkeria capensis is a central taxon for the investigation of locomotion in archosaurs due to its phylogenetic position and intermediate skeletal morphology, and is argued to be representative of facultative bipedalism in this group. However, no studies to date have biomechanically tested if bipedality was feasible in Eupakeria. Here, we use musculoskeletal models and static simulations in its hindlimb to test the influences of body posture and muscle parameter estimation methods on locomotor potential. Our analyses show that the resulting negative pitching moments around the centre of mass were prohibitive to sustainable bipedality. We conclude that it is unlikely that Euparkeria was facultatively bipedal, and was probably quadrupedal, rendering the inference of ancestral bipedal abilities in Archosauria unlikely.

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.

Discrete element models for understanding the biomechanics of fossorial animals

The morphological features of fossorial animals have continuously evolved in response to the demands of survival. However, existing methods for animal burrowing mechanics are not capable of addressing the large deformation of substrate. The discrete element method (DEM) is able to overcome this limitation. In this study, we used DEM to develop a general model to simulate the motion of an animal body part and its interaction with the substrate. The DEM also allowed us to easily change the forms of animal body parts to examine how those different forms affected the biomechanical functions. These capabilities of the DEM were presented through a case study of modeling the burrowing process of North American Badger. In the case study, the dynamics (forces, work, and soil displacements) of burrowing were predicted for different forms of badger claw and manus, using the model. Results showed that when extra digits are added to a manus, the work required for a badger to dig increases considerably, while the mass of soil dug only increases gradually. According to the proposed efficiency index (ratio of the amount of soil dug to the work required), the modern manus with 5 digits has indeed biomechanical advantage for their fossorial lifestyle, and the current claw curvature (25.3 mm in radius) is indeed optimal. The DEM is able to predict biomechanical relationships between functions and forms for any fossorial animals. Results can provide biomechanical evidences for explaining how the selective pressures for functions influence the morphological evolution in fossorial animals.

Hip medial rotator action of gluteus medius in Japanese macaque (Macaca fuscata) and implications to adaptive significance for quadrupedal walking in primates

The gluteus medius (GM) muscle in quadrupedal primates has long been thought to mainly act as a hip extensor. However, previous reports argue that it may be a prime hip medial rotator and functions to rotate the pelvis in the horizontal plane, suggesting the functional differentiation between the GM and other hip extensors as hamstrings. In this study, we aim to quantify the muscle actions of the GM and hamstrings using muscle moment arm lengths and discuss the functional differentiation among hip extensors. Muscle attachment sites of eight specimens of Japanese macaque (Macaca fuscata) were digitized, and musculoskeletal models were constructed. Flexor-extensor, abductor-adductor, and medial-lateral rotator moment arms were calculated as the models were moved following the experimentally acquired kinematic data during walking on a pole substrate. Using electromyography, we also recorded the pattern of muscle activation. The GM showed a larger medial rotator moment arm length than the extensor moment arm length when it was activated, suggesting this muscle acts mainly as a hip medial rotator rather than as a hip extensor. The medial rotator action of the GM in the early support phase may rotate the pelvis in the horizontal plane and function to help contralateral forelimb reaching as a previous study suggested and facilitate contralateral hindlimb swinging to place the foot near the ipsilateral forelimb's hand.

Reconstructing Articular Cartilage in the Australopithecus afarensis Hip Joint and the Need for Modeling Six Degrees of Freedom

The postcranial skeleton of Australopithecus afarensis (AL 288-1) exhibits clear adaptations for bipedality, although there is some debate as to the efficiency and frequency of such upright movement. Some researchers argue that AL 288-1 walked with an erect limb like modern humans do, whilst others advocate for a "bent-hip bent-knee" (BHBK) gait, although in recent years the general consensus favors erect bipedalism. To date, no quantitative method has addressed the articulation of the AL 288-1 hip joint, nor its range of motion (ROM) with consideration for joint spacing, used as a proxy for the thickness of the articular cartilage present within the joint spacing which can affect how a joint moves. Here, we employed ROM mapping methods to estimate the joint spacing of AL 288-1's hip joint in comparison to a modern human and chimpanzee. Nine simulations assessed different joint spacing and tested the range of joint congruency (i.e., ranging from a closely packed socket to loosely packed). We further evaluated the sphericity of the femoral head and whether three rotational degrees of freedom (DOFs) sufficiently captures the full ROM or if translational DOFs must be included. With both setups, we found that the AL 288-1 hip was unlikely to be highly congruent (as it is in modern humans) because this would severely restrict hip rotational movement and would severely limit the capability for both bipedality and even arboreal locomotion. Rather, the hip was more cartilaginous than it is in the modern humans, permitting the hip to rotate into positions necessitated by both terrestrial and arboreal movements. Rotational-only simulations found that AL 288-1 was unable to extend the hip like modern humans, forcing the specimen to employ a BHBK style of walking, thus contradicting 40+ years of previous research into the locomotory capabilities of AL 288-1. Therefore, we advocate that differences in the sphericity of the AL 288-1 femoral head with that of a modern human necessitates all six DOFs to be included in which AL 288-1 could osteologically extend the hip to facilitate a human-like gait.

Walking-and Running and Jumping-with Dinosaurs and Their Cousins, Viewed Through the Lens of Evolutionary Biomechanics

Archosauria diversified throughout the Triassic Period before experiencing two mass extinctions near its end ∼201 Mya, leaving only the crocodile-lineage (Crocodylomorpha) and bird-lineage (Dinosauria) as survivors; along with the pterosaurian flying reptiles. About 50 years ago, the "locomotor superiority hypothesis" (LSH) proposed that dinosaurs ultimately dominated by the Early Jurassic Period because their locomotion was superior to other archosaurs'. This idea has been debated continuously since, with taxonomic and morphological analyses suggesting dinosaurs were "lucky" rather than surviving due to being biologically superior. However, the LSH has never been tested biomechanically. Here we present integration of experimental data from locomotion in extant archosaurs with inverse and predictive simulations of the same behaviours using musculoskeletal models, showing that we can reliably predict how extant archosaurs walk, run and jump. These simulations have been guiding predictive simulations of extinct archosaurs to estimate how they moved, and we show our progress in that endeavour. The musculoskeletal models used in these simulations can also be used for simpler analyses of form and function such as muscle moment arms, which inform us about more basic biomechanical similarities and differences between archosaurs. Placing all these data into an evolutionary and biomechanical context, we take a fresh look at the LSH as part of a critical review of competing hypotheses for why dinosaurs (and a few other archosaur clades) survived the Late Triassic extinctions. Early dinosaurs had some quantifiable differences in locomotor function and performance vs. some other archosaurs, but other derived dinosaurian features (e.g., metabolic or growth rates, ventilatory abilities) are not necessarily mutually exclusive from the LSH; or maybe even an opportunistic replacement hypothesis; in explaining dinosaurs' success.

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.

A Guide to Inverse Kinematic Marker-Guided Rotoscoping using IK Solvers

X-ray Reconstruction of Moving Morphology (XROMM) permits researchers to see beneath the skin, usually to see musculoskeletal movements. These movements can be tracked and later used to provide information regarding the mechanics of movement. Here, we discuss “IK marker-guided rotoscoping”—a method that combines inverse kinematic solvers with that of traditional scientific rotoscoping methods to quickly and efficiently overlay 3D bone geometries with the X-ray shadows from XROMM data. We use a case study of three Nile crocodiles’ (Crocodylus niloticus) forelimbs and hindlimbs to evaluate this method. Within these limbs, different marker configurations were used: some configurations had six markers, others had five markers, and all forelimb data only had three markers. To evaluate IK marker-guided rotoscoping, we systematically remove markers in the six-marker configuration and then test the magnitudes of deviation in translations and rotations of the rigged setup with fewer markers versus those of the six-marker configuration. We establish that IK marker-guided rotoscoping is a suitable method for “salvaging” data that may have too few markers.

Hind foot drumming: Volumetric micro-computed tomography investigation of the hind limb musculature of three African mole-rat species (Bathyergidae)

Several species of African mole-rats use seismic signalling by means of hind foot drumming for communication. The present study aimed to create three-dimensional reconstructions and compare volumetric measurements of 27 muscles of the hind limb of two drumming (Georychus capensis and Bathyergus suillus) and one non-drumming (Cryptomys hottentotus natalensis) species of African mole-rats. Diffusible iodine contrast-enhanced micro-computed tomography (diceCT) scans were performed on six specimens per species. Manual segmentation of the scans using VGMAX Studio imaging software allowed for individual muscles to be separated while automatically determining the volume of each muscle. The volume of the individual muscles was expressed as a percentage of the total hind limb volume and statistically compared between species. Subsequently, three-dimensional reconstructions of these muscles were created. Musculus gracilis anticus had a significantly larger percentage of the total hind limb muscle volume in both drumming species compared to the non-drumming C. h. natalensis. Furthermore, several hip and knee extensors, namely mm. gluteus superficialis, semimembranosus, gluteofemoralis, rectus femoris and vastus lateralis, had significantly larger muscle volume percentages in the two drumming species (G. capensis and B. suillus) compared to the non-drumming species. While not statistically significant, G. capensis had larger muscle volume percentages in several key hip and knee extensors compared to B. suillus. Additionally, G capensis had the largest summed percentage of the total hind limb volume in the hip flexor, hip extensor, knee extensor and ankle plantar flexor muscle groups in all the three species. This could be indicative of whole muscle hypertrophy in these muscles due to fast eccentric contractions that occur during hind foot drumming. However, significantly larger muscle volume percentages were observed in the scratch digging B. suillus compared to the other two chisel tooth digging species. Moreover, while not statistically significant, B. suillus had larger muscle volume percentages in several hip extensor and knee flexor muscles compared to G. capensis (except for m. vastus lateralis). These differences could be due to the large relative size of this species but could also be influenced by the scratch digging strategy employed by B. suillus. Therefore, while the action of hind foot drumming seems to influence certain key muscle volumes, digging strategy and body size may also play a role.

Ontogenetic changes in limb posture, kinematics, forces and joint moments in American alligators (Alligator mississippiensis)

As animals increase in size, common patterns of morphological and physiological scaling may require them to perform behaviors such as locomotion while experiencing a reduced capacity to generate muscle force and an increased risk of tissue failure. Large mammals are known to manage increased mechanical demands by using more upright limb posture. However, the presence of such size-dependent changes in limb posture has rarely been tested in animals that use non-parasagittal limb kinematics. Here, we used juvenile to subadult American alligators (total length 0.46-1.27 m, body mass 0.3-5.6 kg) and examined their limb kinematics, forces, joint moments and center of mass (CoM) to test for ontogenetic shifts in posture and limb mechanics. Larger alligators typically walked with a more adducted humerus and femur and a more extended knee. Normalized peak joint moments reflected these postural patterns, with shoulder and hip moments imposed by the ground reaction force showing relatively greater magnitudes in the smallest individuals. Thus, as larger alligators use more upright posture, they incur relatively smaller joint moments than smaller alligators, which could reduce the forces that the shoulder and hip adductors of larger alligators must generate. The CoM shifted nonlinearly from juveniles through subadults. The more anteriorly positioned CoM in small alligators, together with their compliant hindlimbs, contributes to their higher forelimb and lower hindlimb normalized peak vertical forces in comparison to larger alligators. Future studies of alligators that approach maximal adult sizes could give further insight into how animals with non-parasagittal limb posture modulate locomotor patterns as they increase in mass and experience changes in the CoM.

Validation of an Echidna Forelimb Musculoskeletal Model Using XROMM and diceCT

In evolutionary biomechanics, musculoskeletal computer models of extant and extinct taxa are often used to estimate joint range of motion (ROM) and muscle moment arms (MMAs), two parameters which form the basis of functional inferences. However, relatively few experimental studies have been performed to validate model outputs. Previously, we built a model of the short-beaked echidna (Tachyglossus aculeatus) forelimb using a traditional modelling workflow, and in this study we evaluate its behaviour and outputs using experimental data. The echidna is an unusual animal representing an edge-case for model validation: it uses a unique form of sprawling locomotion, and possesses a suite of derived anatomical features, in addition to other features reminiscent of extinct early relatives of mammals. Here we use diffusible iodine-based contrast-enhanced computed tomography (diceCT) alongside digital and traditional dissection to evaluate muscle attachments, modelled muscle paths, and the effects of model alterations on the MMA outputs. We use X-ray Reconstruction of Moving Morphology (XROMM) to compare ex vivo joint ROM to model estimates based on osteological limits predicted via single-axis rotation, and to calculate experimental MMAs from implanted muscles using a novel geometric method. We also add additional levels of model detail, in the form of muscle architecture, to evaluate how muscle torque might alter the inferences made from MMAs alone, as is typical in evolutionary studies. Our study identifies several key findings that can be applied to future models. 1) A light-touch approach to model building can generate reasonably accurate muscle paths, and small alterations in attachment site seem to have minimal effects on model output. 2) Simultaneous movement through multiple degrees of freedom, including rotations and translation at joints, are necessary to ensure full joint ROM is captured; however, single-axis ROM can provide a reasonable approximation of mobility depending on the modelling objectives. 3) Our geometric method of calculating MMAs is consistent with model-predicted MMAs calculated via partial velocity, and is a potentially useful tool for others to create and validate musculoskeletal models. 4) Inclusion of muscle architecture data can change some functional inferences, but in many cases reinforced conclusions based on MMA alone.

Modeling Sprawling Locomotion of the Stem Amniote Orobates: An Examination of Hindlimb Muscle Strains and Validation Using Extant Caiman

The stem amniote Orobates pabsti has been reconstructed to be capable of relatively erect, balanced, and mechanically power-saving terrestrial locomotion. This suggested that the evolution of such advanced locomotor capabilities preceded the origin of crown-group amniotes. We here further investigate plausible body postures and locomotion of Orobates by taking soft tissues into account. Freely available animation software BLENDER is used to first reconstruct the lines of action of hindlimb adductors and retractors for Orobates and then estimate the muscle strain of these muscles. We experimentally varied different body heights in modeled hindlimb stride cycles of Orobates to find the posture that maximizes optimal strains over the course of a stride cycle. To validate our method, we used Caiman crocodilus. We replicated the identical workflow used for the analysis of Orobates and compared the locomotor posture predicted for Caiman based on muscle strain analysis with this species’ actual postural data known from a previously published X-ray motion analysis. Since this validation experiment demonstrated a close match between the modeled posture that maximizes optimal adductor and retractor muscle strain and the in vivo posture employed by Caiman, using the same method for Orobates was justified. Generally, the use of muscle strain analysis for the reconstruction of posture in quadrupedal vertebrate fossils thus appears a promising approach. Nevertheless, results for Orobates remained inconclusive as several postures resulted in similar muscle strains and none of the postures could be entirely excluded. These results are not in conflict with the previously inferred moderately erect locomotor posture of Orobates and suggest considerable variability of posture during locomotion.

Function of the crocodilian anterior cruciate ligaments

The anterior cruciate ligament (ACL) is an important knee stabilizer that prevents the anterior subluxation of the tibia. Extant crocodiles have two ACLs, the ACL major and minor, yet their functional roles are unclear. We here examined in-situ forces within the ACL major and minor in saltwater crocodiles (Crocodylus porosus) with a 6-degree-of-freedom robotic testing system under the following loading conditions: (a) 30 N anterior tibial load at 150°, 120°, and 90° knee extension; (b) 1 Nm internal/external torque at 150° and 120° knee extension; (c) 30 N anterior tibial load +1 Nm internal/external torque at 150° and 120° knee extension. The In-situ force in the ACL minor was significantly higher than that of the ACL major in response to anterior tibial load at 90° knee extension, and anterior tibial load + external torque at both 150° and 120° knee extension. Meanwhile, the force in the ACL major was significantly higher than that of the ACL minor in response to internal torque at 120° knee extension, and anterior tibial load + internal torque at 150° knee extension. The present results showed that the ACL minor and major of saltwater crocodiles have different functions. In response to anterior tibial load + internal/external torques, either of two ACLs reacted to opposing directions of knee rotation. These suggest that two ACLs are essential for walking with long axis rotation of the knee in crocodiles.

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.