Elastic energy storage in the hopping of kangaroo rats (Dipodomys spectabilis)

Muscle-Tendon Unit Properties in Mice Bred for High Levels of Voluntary Running: Novel Physiologies, Coadaptation, Trade-Offs, and Multiple Solutions in the Evolution of Endurance Running

AbstractMuscle-tendon unit (MTU) morphology and physiology are likely major determinants of locomotor performance and therefore Darwinian fitness. However, the relationships between underlying traits, performance, and fitness are complicated by phenomena such as coadaptation, multiple solutions, and trade-offs. Here, we leverage a long-running artificial selection experiment in which mice have been bred for high levels of voluntary running to explore MTU adaptation, as well as the role of coadaptation, multiple solutions, and trade-offs, in the evolution of endurance running. We compared the morphological and contractile properties of the triceps surae complex, a major locomotor MTU, in four replicate selected lines to those of the triceps surae complex in four replicate control lines. All selected lines have lighter and shorter muscles, longer tendons, and faster muscle twitch times than all control lines. Absolute and normalized maximum shortening velocities and contractile endurance vary across selected lines. Selected lines have similar or lower absolute velocities and higher endurance than control lines. However, normalized shortening velocities are both higher and lower in selected lines than in control lines. These findings potentially show an interesting coadaptation between muscle and tendon morphology and muscle physiology, highlight multiple solutions for increasing endurance running performance, demonstrate that a trade-off between muscle speed and endurance can arise in response to selection, and suggest that a novel physiology may sometimes allow this trade-off to be circumvented.

Understanding Australia’s unique hopping species: a comparative review of the musculoskeletal system and locomotor biomechanics in Macropodoidea

Kangaroos and other macropodoids stand out among mammals for their unusual hopping locomotion and body shape. This review examines the scaling of hind- and forelimb bones, and the primary ankle extensor muscles and tendons. We find that the scaling of the musculoskeletal system is sensitive to the phylogenetic context. Tibia length increases with positive allometry among most macropodoids, but negative allometry in eastern grey kangaroos and isometry in red kangaroos. Femur length decreases with stronger negative allometry in eastern grey and red kangaroos than among other macropodoids. Muscle masses scale with negative allometry in western grey kangaroos and with isometry in red kangaroos, compared to positive allometry in other macropodoids. We further summarise the work on the hopping gait, energetics in macropodoids, and stresses in the musculoskeletal system in an evolutionary context, to determine what trade-offs may limit locomotor performance in macropodoids. When large kangaroos hop, they do not increase oxygen consumption with speed, unlike most mammals, including small hopping species. We conclude that there is not enough information to isolate the biomechanical factors that make large kangaroos so energy efficient. We identify key areas for further research to fill these gaps.

Comparative analysis of Dipodomys species indicates that kangaroo rat hindlimb anatomy is adapted for rapid evasive leaping

Body size is a key factor that influences antipredator behavior. For animals that rely on jumping to escape from predators, there is a theoretical trade-off between jump distance and acceleration as body size changes at both the inter- and intraspecific levels. Assuming geometric similarity, acceleration will decrease with increasing body size due to a smaller increase in muscle cross-sectional area than body mass. Smaller animals will likely have a similar jump distance as larger animals due to their shorter limbs and faster accelerations. Therefore, in order to maintain acceleration in a jump across different body sizes, hind limbs must be disproportionately bigger for larger animals. We explored this prediction using four species of kangaroo rats (Dipodomys spp.), a genus of bipedal rodent with similar morphology across a range of body sizes (40-150 g). Kangaroo rat jump performance was measured by simulating snake strikes to free-ranging individuals. Additionally, morphological measurements of hind limb muscles and segment lengths were obtained from thawed frozen specimens. Overall, jump acceleration was constant across body sizes and jump distance increased with increasing size. Additionally, kangaroo rat hind limb muscle mass and cross-sectional area scaled with positive allometry. Ankle extensor tendon cross-sectional area also scaled with positive allometry. Hind limb segment length scaled isometrically, with the exception of the metatarsals, which scaled with negative allometry. Overall, these findings support the hypothesis that kangaroo rat hind limbs are built to maintain jump acceleration rather than jump distance. Selective pressure from single-strike predators, such as snakes and owls, likely drives this relationship.

Elastic energy storage across speeds during steady-state hopping of desert kangaroo rats (Dipodomys deserti)

Small bipedal hoppers, including kangaroo rats, are thought to not benefit from substantial elastic energy storage and return during hopping. However, recent species-specific material properties research suggests that, despite relative thickness, the ankle extensor tendons of these small hoppers are considerably more compliant than had been assumed. With faster locomotor speeds demanding higher forces, a lower tendon stiffness suggests greater tendon deformation and thus a greater potential for elastic energy storage and return with increasing speed. Using the elastic modulus values specific to kangaroo rat tendons, we sought to determine how much elastic energy is stored and returned during hopping across a range of speeds. In vivo techniques were used to record tendon force in the ankle extensors during steady-speed hopping. Our data support the hypothesis that the ankle extensor tendons of kangaroo rats store and return elastic energy in relation to hopping speed, storing more at faster speeds. Despite storing comparatively less elastic energy than larger hoppers, this relationship between speed and energy storage offer novel evidence of a functionally similar energy storage mechanism, operating irrespective of body size or tendon thickness, across the distal muscle-tendon units of both small and large bipedal hoppers.

Immunohistochemistry of kangaroo rat hindlimb muscles

Kangaroo rats (Dipodomys spp.) use specialized bipedal hopping like that of kangaroos. In contrast to kangaroos that have elastic tendons capable of storing energy, kangaroo rats have inelastic tendons that are unable to store large amounts of energy. Thus, the musculature of the ankle joint provides the greatest power contribution to kangaroo rat hopping. Skeletal muscle can be characterized by several fiber types, including slow twitch (Type I) and fast twitch (Type II) fibers. Fast fibers are found in higher concentration in muscles that perform quick, dynamic movements, whereas slow fibers are found in higher proportion in muscles that perform slow, endurant movements. Using fiber type specific antibodies, we identified four pure (Types I, IIA, IIB, and IIX) and two hybrid (Types I/IIA and IIA/IIX) fiber types in six hindlimb muscles from three kangaroo rats (Dipodomys merriami) to investigate the relationship between fiber composition and hindlimb muscle function. Hindlimb muscles (except soleus) were dominated by Type IIB fibers, which were largest in cross-sectional area, and are known to be best suited for rapid and explosive movements. Oxidative Type IIA and Type IIX fibers were found at moderate concentrations and likely function in maintaining continual saltatory locomotion. Thus, kangaroo rats can use these two fiber type populations as "gears" for both endurant and explosive behaviors.

The menisci are not shock absorbers: A biomechanical and comparative perspective

The lateral and medial menisci are fibrocartilaginous structures in the knee that play a crucial role in normal knee biomechanics. However, one commonly cited role of the menisci is that they function as "shock absorbers." Here we provide a critique of this notion, drawing upon a review of comparative anatomical and biomechanical data from humans and other tetrapods. We first review those commonly, and often exclusively, cited studies in support of a shock absorption function and show that evidence for a shock absorptive function is dubious. We then review the evolutionary and comparative evidence to show that (1) the human menisci are unremarkable in morphology compared with most other tetrapods, and (2) "shock" during locomotion is uncommon, with humans standing out as one of the only tetrapods that regularly experiences high levels of shock during locomotion. A shock-absorption function does not explain the origin of menisci, nor are human menisci specialized in any way that would explain a unique shock-absorbing function during human gait. Finally, we show that (3) the material properties of menisci are distinctly poorly suited for energy dissipation and that (4) estimations of meniscal energy absorption based on published data are negligible, both in their absolute amount and in comparison to other well-accepted structures which mitigate shock during locomotion. The menisci are evolutionarily ancient structures crucial for joint congruity, load distribution, and stress reduction, among a number of other functions. However, the menisci are not meaningful shock absorbers, neither in tetrapods broadly, nor in humans.

Morphological determinants of jumping performance in the Iberian green frog

Predation is one of the main selective forces in nature, frequently selecting potential prey for developing escape strategies. Escape ability is typically influenced by several morphological parameters, such as morphology of the locomotor appendices, muscular capacity, body mass, or fluctuating asymmetry, and may differ between sexes and age classes. In this study, we tested the relationship among these variables and jumping performance in 712 Iberian green frogs Pelophylax perezi from an urban population. The results suggest that the main determinant of jumping capacity was body size (explaining 48% of variance). Larger frogs jumped farther, but jumping performance reached an asymptote for the largest frogs. Once controlled by structural body size, the heaviest frogs jumped shorter distances, suggesting a trade-off between fat storage and jumping performance. Relative hind limb length also determined a small but significant percentage of variance (2.4%) in jumping performance—that is, the longer the hind limbs, the greater the jumping capacity. Juveniles had relatively shorter and less muscular hind limbs than adults (for a given body size), and their jumping performance was poorer. In our study population, the hind limbs of the frogs were very symmetrical, and we found no effect of fluctuating asymmetry on jumping performance. Therefore, our study provides evidence that jumping performance in frogs is not only affected by body size, but also by body mass and hind limb length, and differ between age classes.

Functional morphology of the ankle extensor muscle-tendon units in the springhare Pedetes capensis shows convergent evolution with macropods for bipedal hopping locomotion

This study assesses the functional morphology of the ankle extensor muscle-tendon units of the springhare Pedetes capensis, an African bipedal hopping rodent, to test for convergent evolution with the Australian bipedal hopping macropods. We dissect and measure the gastrocnemius, soleus, plantaris, and flexor digitorum longus in 10 adult springhares and compare them against similar-sized macropods using phylogenetically informed scaling analyses. We show that springhares align reasonably well with macropod predictions, being statistically indistinguishable with respect to the ankle extensor mean weighted muscle moment arm (1.63 vs. 1.65 cm, respectively), total muscle mass (41.1 vs. 29.2 g), total muscle physiological cross-sectional area (22.9 vs. 19.3 cm² ), mean peak tendon stress (26.2 vs. 35.2 MPa), mean tendon safety factor (4.7 vs. 3.6), and total tendon strain energy return capacity (1.81 vs. 1.82 J). However, total tendon cross-sectional area is significantly larger in springhares than predicted for a similar-sized macropod (0.26 vs. 0.17 cm² , respectively), primarily due to a greater plantaris tendon thickness (0.084 vs. 0.048 cm² ), and secondarily because the soleus muscle-tendon unit is present in springhares but is vestigial in macropods. The overall similarities between springhares and macropods indicate that evolution has favored comparable lower hindlimb body plans for bipedal hopping locomotion in the two groups of mammals that last shared a common ancestor ~160 million years ago. The springhare's relatively thick plantaris tendon may facilitate rapid transfer of force from muscle to skeleton, enabling fast and accelerative hopping, which could help to outpace and outmaneuver predators.

Small vertebrates running on uneven terrain: a biomechanical study of two differently specialised lacertid lizards

While running, small animals frequently encounter large terrain variations relative to their body size, therefore, terrain variations impose important functional demands on small animals. Nonetheless, we have previously observed in lizards that running specialists can maintain a surprisingly good running performance on very uneven terrains. The relatively large terrain variations are offset by their capacity for leg adjustability that ensures a 'smooth ride' of the centre of mass (CoM). The question as to how the effect of an uneven terrain on running performance and locomotor costs differs between species exhibiting diverse body build and locomotor specializations remains. We hypothesise that specialized runners with long hind limbs can cross uneven terrain more efficiently than specialized climbers with a dorso-ventrally flattened body and equally short fore and hind limbs. This study reports 3D kinematics using high-speed videos (325 Hz) to investigate leg adjustability and CoM movements in two lacertid lizards (Acanthodactylus boskianus, running specialist; Podarcis muralis, climbing specialist). We investigated these parameters while the animals were running on a level surface and over a custom-made uneven terrain. We analysed the CoM dynamics, we evaluated the fluctuations of the positive and negative mechanical energy, and we estimated the overall cost of transport. Firstly, the results reveal that the climbers ran at lower speeds on flat level terrain but had the same cost of transport as the runners. Secondly, contrary to the running specialists, the speed was lower and the energy expenditure higher in the climbing specialists while running on uneven terrain. While leg movements adjust to the substrates' variations and enhance the stability of the CoM in the running specialist, this is not the case in the climbing specialist. Although their legs are kept more extended, the amplitude of movement does not change, resulting in an increase of the movement of the CoM and a decrease in locomotor efficiency. These results are discussed in light of the respective (micro-)habitat of these species and suggest that energy economy can also be an important factor for small vertebrates.

Tendons from kangaroo rats are exceptionally strong and tough

Tendons must be able to withstand the forces generated by muscles and not fail. Accordingly, a previous comparative analysis across species has shown that tendon strength (i.e., failure stress) increases for larger species. In addition, the elastic modulus increases proportionally to the strength, demonstrating that the two properties co-vary. However, some species may need specially adapted tendons to support high performance motor activities, such as sprinting and jumping. Our objective was to determine if the tendons of kangaroo rats (k-rat), small bipedal animals that can jump as high as ten times their hip height, are an exception to the linear relationship between elastic modulus and strength. We measured and compared the material properties of tendons from k-rat ankle extensor muscles to those of similarly sized white rats. The elastic moduli of k-rat and rat tendons were not different, but k-rat tendon failure stresses were much larger than the rat values (nearly 2 times larger), as were toughness (over 2.5 times larger) and ultimate strain (over 1.5 times longer). These results support the hypothesis that the tendons from k-rats are specially adapted for high motor performance, and k-rat tendon could be a novel model for improving tissue engineered tendon replacements.

Exploring Bipedal Hopping through Computational Evolution

Bipedal hopping is an efficient form of locomotion, yet it remains relatively rare in the natural world. Previous research has suggested that the tail balances the angular momentum of the legs to produce steady state bipedal hopping. In this study, we employ a 3D physics simulation engine to optimize gaits for an animat whose control and morphological characteristics are subject to computational evolution, which emulates properties of natural evolution. Results indicate that the order of gene fixation during the evolutionary process influences whether a bipedal hopping or quadrupedal bounding gait emerges. Furthermore, we found that in the most effective bipedal hoppers the tail balances the angular momentum of the torso, rather than the legs as previously thought. Finally, there appears to be a specific range of tail masses, as a proportion of total body mass, wherein the most effective bipedal hoppers evolve.

Jumping mechanics of desert kangaroo rats

Kangaroo rats are small bipedal desert rodents that use erratic vertical jumps to escape predator strikes. In this study we examined how individual hind limb joints of desert kangaroo rats (Dipodomys deserti) power vertical jumps across a range of heights. We hypothesized that increases in net work would be equally divided across hind limb joints with increases in jump height. To test this hypothesis, we used an inverse dynamics analysis to quantify the mechanical output from the hind limb joints of kangaroo rats jumping vertically over a wide range of heights. The kangaroo rats in this study reached maximal jump heights up to ∼9-times hip height. Net joint work increased significantly with jump height at the hip, knee and ankle, and decreased significantly at the metatarsal-phalangeal joint. The increase in net work generated by each joint was not proportional across joints but was dominated by the ankle, which ranged from contributing 56% of the work done on the center of mass at low jumps to 70% during the highest jumps. Therefore, the results of this study did not support our hypothesis. However, using an anatomical model, we estimated that a substantial proportion of the work delivered at the ankle (48%) was transferred from proximal muscles via the biarticular ankle extensors.

Functional capacity of kangaroo rat hindlimbs: adaptations for locomotor performance

Many cursorial and large hopping species are extremely efficient locomotors with various morphological adaptations believed to reduce mechanical demand and improve movement efficiency, including elongated distal limb segments. However, despite having elongated limbs, small hoppers such as desert kangaroo rats (Dipodomys deserti) are less efficient locomotors than their larger counterparts, which may be in part due to avoiding predators through explosive jumping movements. Despite potentially conflicting mechanical demands between the two movements, kangaroo rats are both excellent jumpers and attain high hopping speeds, likely due to a specialized hindlimb musculoskeletal morphology. This study combined experimental dissection data with a static analysis of muscle moment generating capacities using a newly developed musculoskeletal model to characterize kangaroo rat hindlimb musculoskeletal architecture and investigate how morphology has evolved to meet hopping and jumping mechanical demands. Hindlimb morphology appears biased towards generating constant moment arms over large joint ranges of motion in this species, which may balance competing requirements by reducing the need for posture and movement specific excitation patterns. The ankle extensors are a major exception to the strong positive relationship exhibited by most muscles between muscle architecture parameters (e.g. Lfibre) and joint moment arms. These muscles appear suited to meeting the high moments required for jumping: the biarticular nature of the ankle extensors is leveraged to reduce MTU strain and create a four-bar linkage that facilitates proximal force transfer. The kangaroo rat hindlimb provides an interesting case study for understanding how morphology balances the sometimes competing demands of hopping and jumping.

Why do mammals hop? Understanding the ecology, biomechanics and evolution of bipedal hopping

Bipedal hopping is a specialized mode of locomotion that has arisen independently in at least five groups of mammals. We review the evolutionary origins of these groups, examine three of the most prominent hypotheses for why bipedal hopping may have arisen, and discuss how this unique mode of locomotion influences the behavior and ecology of modern species. While all bipedal hoppers share generally similar body plans, differences in underlying musculoskeletal anatomy influence what performance benefits each group may derive from this mode of locomotion. Based on a review of the literature, we conclude that the most likely reason that bipedal hopping evolved is associated with predator avoidance by relatively small species in forested environments. Yet, the morphological specializations associated with this mode of locomotion have facilitated the secondary acquisition of performance characteristics that enable these species to be highly successful in ecologically demanding environments such as deserts. We refute many long-held misunderstandings about the origins of bipedal hopping and identify potential areas of research that would advance the understanding of this mode of locomotion.

Vertical leaping mechanics of the Lesser Egyptian Jerboa reveal specialization for maneuverability rather than elastic energy storage

BACKGROUND

Numerous historical descriptions of the Lesser Egyptian jerboa, Jaculus jaculus, a small bipedal mammal with elongate hindlimbs, make special note of their extraordinary leaping ability. We observed jerboa locomotion in a laboratory setting and performed inverse dynamics analysis to understand how this small rodent generates such impressive leaps. We combined kinematic data from video, kinetic data from a force platform, and morphometric data from dissections to calculate the relative contributions of each hindlimb muscle and tendon to the total movement.

RESULTS

Jerboas leapt in excess of 10 times their hip height. At the maximum recorded leap height (not the maximum observed leap height), peak moments for metatarso-phalangeal, ankle, knee, and hip joints were 13.1, 58.4, 65.1, and 66.9 Nmm, respectively. Muscles acting at the ankle joint contributed the most work (mean 231.6 mJ / kg Body Mass) to produce the energy of vertical leaping, while muscles acting at the metatarso-phalangeal joint produced the most stress (peak 317.1 kPa). The plantaris, digital flexors, and gastrocnemius tendons encountered peak stresses of 25.6, 19.1, and 6.0 MPa, respectively, transmitting the forces of their corresponding muscles (peak force 3.3, 2.0, and 3.8 N, respectively). Notably, we found that the mean elastic energy recovered in the primary tendons of both hindlimbs comprised on average only 4.4% of the energy of the associated leap.

CONCLUSIONS

The limited use of tendon elastic energy storage in the jerboa parallels the morphologically similar heteromyid kangaroo rat, Dipodomys spectabilis. When compared to larger saltatory kangaroos and wallabies that sustain hopping over longer periods of time, these small saltatory rodents store and recover less elastic strain energy in their tendons. The large contribution of muscle work, rather than elastic strain energy, to the vertical leap suggests that the fitness benefit of rapid acceleration for predator avoidance dominated over the need to enhance locomotor economy in the evolutionary history of jerboas.

Additional in-series compliance reduces muscle force summation and alters the time course of force relaxation during fixed-end contractions

There are high mechanical demands placed on skeletal muscles in movements requiring rapid acceleration of the body or its limbs. Tendons are responsible for transmitting muscle forces, but, because of their elasticity, can manipulate the mechanics of the internal contractile apparatus. Shortening of the contractile apparatus against the stretch of tendon affects force generation according to known mechanical properties; however, the extent to which differences in tendon compliance alter force development in response to a burst of electrical impulses is unclear. To establish the influence of series compliance on force summation, we studied electrically evoked doublet contractions in the cane toad peroneus muscle in the presence and absence of a compliant artificial tendon. Additional series compliance reduced tetanic force by two-thirds, a finding predicted based on the force-length property of skeletal muscle. Doublet force and force-time integral expressed relative to the twitch were also reduced by additional series compliance. Active shortening over a larger range of the ascending limb of the force-length curve and at a higher velocity, leading to a progressive reduction in force-generating potential, could be responsible. Muscle-tendon interaction may also explain the accelerated time course of force relaxation in the presence of additional compliance. Our findings suggest that a compliant tendon limits force summation under constant-length conditions. However, high series compliance can be mechanically advantageous when a muscle-tendon unit is actively stretched, permitting muscle fibres to generate force almost isometrically, as shown during stretch-shorten cycles in locomotor activities. Restricting active shortening would likely favour rapid force development.

Spring or string: does tendon elastic action influence wing muscle mechanics in bat flight?

Tendon springs influence locomotor movements in many terrestrial animals, but their roles in locomotion through fluids as well as in small-bodied mammals are less clear. We measured muscle, tendon and joint mechanics in an elbow extensor of a small fruit bat during ascending flight. At the end of downstroke, the tendon was stretched by elbow flexion as the wing was folded. At the end of upstroke, elastic energy was recovered via tendon recoil and extended the elbow, contributing to unfurling the wing for downstroke. Compared with a hypothetical 'string-like' system lacking series elastic compliance, the tendon spring conferred a 22.5% decrease in muscle fascicle strain magnitude. Our findings demonstrate tendon elastic action in a small flying mammal and expand our understanding of the occurrence and action of series elastic actuator mechanisms in fluid-based locomotion.

Integrating gastrocnemius force-length properties, in vivo activation, and operating lengths reveals how Anolis deal with ecological challenges

A central question in biology is how animals successfully behave under complex natural conditions. Although changes in locomotor behaviour, motor control, and force production in relation to incline are commonly examined, a wide range of other factors, including a range of perch diameters, pervades arboreal habitats. Moving on different substrate diameters requires considerable alteration of body and limb posture, likely causing significant shifts in the lengths of the muscle-tendon units powering locomotion. Thus, how substrate shape impacts in vivo muscle function remains an important, but neglected question in ecophysiology. Here, we used high-speed videography, electromyography, in situ contractile experiments, and morphology to examine gastrocnemius muscle function during arboreal locomotion in the Cuban knight anole, (Anolis equestris). The gastrocnemius contributes more to the propulsive effort on broad surfaces than on narrow surfaces. Surprisingly, substrate inclination affected the relationship between the maximum potential force and fibre recruitment; the trade-off that was present between these variables on horizontal conditions became a positive relationship on inclined surfaces. Finally, the biarticular nature of the gastrocnemius allows it to generate force isometrically, regardless of condition, despite the fact that the tendons are incapable of stretching during cyclical locomotion. Our results emphasize the importance of considering ecology and muscle function together, and the necessity of examining both mechanical and physiological properties of muscles to understand how animals move in their environment.

Epaxial muscle fiber architecture favors enhanced excursion and power in the leaper Galago senegalensis

Galago senegalensis is a habitual arboreal leaper that engages in rapid spinal extension during push-off. Large muscle excursions and high contraction velocities are important components of leaping, and experimental studies indicate that during leaping by G. senegalensis, peak power is facilitated by elastic storage of energy. To date, however, little is known about the functional relationship between epaxial muscle fiber architecture and locomotion in leaping primates. Here, fiber architecture of select epaxial muscles is compared between G. senegalensis (n = 4) and the slow arboreal quadruped, Nycticebus coucang (n = 4). The hypothesis is tested that G. senegalensis exhibits architectural features of the epaxial muscles that facilitate rapid and powerful spinal extension during the take-off phase of leaping. As predicted, G. senegalensis epaxial muscles have relatively longer, less pinnate fibers and higher ratios of tendon length-to-fiber length, indicating the capacity for generating relatively larger muscle excursions, higher whole-muscle contraction velocities, and a greater capacity for elastic energy storage. Thus, the relatively longer fibers and higher tendon length-to-fiber length ratios can be functionally linked to leaping performance in G. senegalensis. It is further predicted that G. senegalensis epaxial muscles have relatively smaller physiological cross-sectional areas (PCSAs) as a consequence of an architectural trade-off between fiber length (excursion) and PCSA (force). Contrary to this prediction, there are no species differences in relative PCSAs, but the smaller-bodied G. senegalensis trends towards relatively larger epaxial muscle mass. These findings suggest that relative increase in muscle mass in G. senegalensis is largely attributable to longer fibers. The relative increase in erector spinae muscle mass may facilitate sagittal flexibility during leaping. The similarity between species in relative PCSAs provides empirical support for previous work linking osteological features of the vertebral column in lorisids with axial stability and reduced muscular effort associated with slow, deliberate movements during anti-pronograde locomotion.

Running, hopping and trotting: tuning step frequency to the resonant frequency of the bouncing system favors larger more compliant animals

A long-lasting challenge in comparative physiology is to understand why the efficiency of the mechanical work done to maintain locomotion increases with body mass. It has been suggested that this is due to a more elastic step in larger animals. Here we show that in running, hopping trotting animals and in human running during growth the resonant frequency of the bouncing system decreases with increasing body mass with the same trend surprisingly independent of different animal species and gaits. Step frequency about equals the resonant frequency in trotting and running whereas it is about half the resonant frequency in hopping. The energy loss by elastic hysteresis during loading-unloading the bouncing system from its equilibrium position decreases with increasing body mass. Similarity to a symmetric bounce increases with increasing body mass and, for a given body mass, seems to be maximal in hopping, intermediate in trotting and minimal in running. We conclude that: i) tuning step frequency to the resonant frequency of the bouncing system coincides with a lower hysteresis loss in larger more compliant animals, ii) the mechanism of gait per se affects similarity with a symmetric bounce independent of hysteresis and iii) the greater efficiency in larger animals may be due, at least in part, to a lower hysteresis loss.

Running humans attain optimal elastic bounce in their teens

In an ideal elastic bounce of the body, the time during which mechanical energy is released during the push equals the time during which mechanical energy is absorbed during the brake, and the maximal upward velocity attained by the center of mass equals the maximal downward velocity. Deviations from this ideal model, prolonged push duration and lower upward velocity, have found to be greater in older than in younger adult humans. However it is not known how similarity to the elastic bounce changes during growth and whether an optimal elastic bounce is attained at some age. Here we show that similarity with the elastic bounce is minimal at 2 years and increases with age attaining a maximum at 13-16 years, concomitant with a mirror sixfold decrease of the impact deceleration peak following collision of the foot with the ground. These trends slowly reverse during the course of the lifespan.

Collision-based mechanics of bipedal hopping

The muscle work required to sustain steady-speed locomotion depends largely upon the mechanical energy needed to redirect the centre of mass and the degree to which this energy can be stored and returned elastically. Previous studies have found that large bipedal hoppers can elastically store and return a large fraction of the energy required to hop, whereas small bipedal hoppers can only elastically store and return a relatively small fraction. Here, we consider the extent to which large and small bipedal hoppers (tammar wallabies, approx. 7 kg, and desert kangaroo rats, approx. 0.1 kg) reduce the mechanical energy needed to redirect the centre of mass by reducing collisions. We hypothesize that kangaroo rats will reduce collisions to a greater extent than wallabies since kangaroo rats cannot elastically store and return as high a fraction of the mechanical energy of hopping as wallabies. We find that kangaroo rats use a significantly smaller collision angle than wallabies by employing ground reaction force vectors that are more vertical and center of mass velocity vectors that are more horizontal and thereby reduce their mechanical cost of transport. A collision-based approach paired with tendon morphometry may reveal this effect more generally among bipedal runners and quadrupedal trotters.

Symmetrical gaits and center of mass mechanics in small-bodied, primitive mammals

Widely accepted relationships between gaits (footfall patterns) and center of mass mechanics have been formulated from observations for cursorial mammals. However, sparse data on smaller or more generalized forms suggest a fundamentally different relationship. This study explores locomotor dynamics in one eutherian and five metatherian (marsupials) mammals-all small-bodied (<2 kg) with generalized body plans that utilize symmetrical gaits. Across our sample, trials conforming to vaulting mechanics occurred least frequently (<10% of all trials) while bouncing mechanics was obtained most commonly (60%); the remaining trials represented mixed mechanics. Contrary to the common situation in large mammals, there was no evidence for discrete gait switching within symmetrical gaits as speed increased. This was in part due to the common practice of grounded running. The adaptive advantage of different patterns of center-of-mass motion and their putative energy savings remain questionable in small-bodied mammals.

Anatomical, architectural, and biochemical diversity of the murine forelimb muscles

We characterized the architecture, fiber type, titin isoform distribution, and collagen content of 27 portions of 22 muscles in the murine forelimb. The mouse forelimb was different from the human arm in that it had the extensor digitorum lateralis muscle and no brachioradialis muscle. Architecturally, the mouse forelimb differed from humans with regard to load bearing, having a much larger contribution from extensors than flexors. In mice, the extensor : flexor PCSA ratio is 2.7, whereas in humans it is only 1.4. When the architectural difference index was calculated, similarities became especially apparent between flexors and extensors of the distal forelimb, as well as pronators. Discriminant analysis revealed that biochemical measures of collagen, titin, and myosin heavy chain were all strong between-species discriminators. In terms of composition, when compared with similar muscles in humans, mice had, on average, faster muscles with higher collagen content and larger titin isoforms. This report establishes the anatomical and biochemical properties of mouse forelimb muscles. Given the prevalence of this species in biological studies, these data will be invaluable for studying the biological basis of mouse muscle structure and function.

Terrestrial locomotion imposes high metabolic requirements on bats

The evolution of powered flight involved major morphological changes in Chiroptera. Nevertheless, all bats are also capable of crawling on the ground and some are even skilled sprinters. We asked if a highly derived morphology adapted for flapping flight imposes high metabolic requirements on bats when moving on the ground. We measured the metabolic rate during terrestrial locomotion in mastiff bats, Molossus currentium; a species that is both, a fast-flying aerial-hawking bat and an agile crawler on the ground. Metabolic rates of bats averaged 8.0 ± 4.0 ml CO2 min-1 during a one minute period of sprinting at 1.3 ± 0.6 km h-1. With rising average speed, mean metabolic rates increased, reaching peak values that were similar to those of flying conspecifics. Metabolic rates of M. currentium were higher than those of similar-sized rodents under steady-state conditions that sprinted at similar velocities. When M. currentium sprinted at peak velocities its aerobic metabolic rate was 3-5 times higher than those of rodent species running continuously in steady-state condition. Costs of transport (J kg-1 m-1) were more than ten times higher for running than for flying bats. We conclude that at the same speed bats experience higher metabolic rates during short sprints than quadruped mammals during steady-state terrestrial locomotion, yet running bats achieve higher maximal mass-specific aerobic metabolic rates than non-volant mammals such as rodents.

Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides)

A diversity of animals that run on solid, level, flat, non-slip surfaces appear to bounce on their legs; elastic elements in the limbs can store and return energy during each step. The mechanics and energetics of running in natural terrain, particularly on surfaces that can yield and flow under stress, is less understood. The zebra-tailed lizard (Callisaurus draconoides), a small desert generalist with a large, elongate, tendinous hind foot, runs rapidly across a variety of natural substrates. We use high speed video to obtain detailed three-dimensional running kinematics on solid and granular surfaces to reveal how leg, foot, and substrate mechanics contribute to its high locomotor performance. Running at ~10 body length/s (~1 m/s), the center of mass oscillates like a spring-mass system on both substrates, with only 15% reduction in stride length on the granular surface. On the solid surface, a strut-spring model of the hind limb reveals that the hind foot saves about 40% of the mechanical work needed per step, significant for the lizard's small size. On the granular surface, a penetration force model and hypothesized subsurface foot rotation indicates that the hind foot paddles through fluidized granular medium, and that the energy lost during irreversible deformation of the substrate does not differ from the reduction in the mechanical energy of the center of mass. The upper hind leg muscles must perform three times as much mechanical work on the granular surface as on the solid surface to compensate for the greater energy lost within the foot and to the substrate.

Flexible mechanisms: the diverse roles of biological springs in vertebrate movement

The muscles that power vertebrate locomotion are associated with springy tissues, both within muscle and in connective tissue elements such as tendons. These springs share in common the same simple action: they stretch and store elastic strain energy when force is applied to them and recoil to release energy when force decays. Although this elastic action is simple, it serves a diverse set of functions, including metabolic energy conservation, amplification of muscle power output, attenuation of muscle power input, and rapid mechanical feedback that may aid in stability. In recent years, our understanding of the mechanisms and importance of biological springs in locomotion has advanced significantly, and it has been demonstrated that elastic mechanisms are essential for the effective function of the muscle motors that power movement. Here, we review some recent advances in our understanding of elastic mechanisms, with an emphasis on two proposed organizing principles. First, we review the evidence that the various functions of biological springs allow the locomotor system to operate beyond the bounds of intrinsic muscle properties, including metabolic and mechanical characteristics, as well as motor control processes. Second, we propose that an energy-based framework is useful for interpreting the diverse functions of series-elastic springs. In this framework, the direction and timing of the flow of energy between the body, the elastic element and the contracting muscle determine the function served by the elastic mechanism (e.g. energy conservation vs power amplification). We also review recent work demonstrating that structures such as tendons remodel more actively and behave more dynamically than previously assumed.

The bounce of the body in hopping, running and trotting: different machines with the same motor

The bouncing mechanism of human running is characterized by a shorter duration of the brake after ‘landing’ compared with a longer duration of the push before ‘takeoff’. This landing–takeoff asymmetry has been thought to be a consequence of the force–velocity relation of the muscle, resulting in a greater force exerted during stretching after landing and a lower force developed during shortening before takeoff. However, the asymmetric lever system of the human foot during stance may also be the cause. Here, we measure the landing–takeoff asymmetry in bouncing steps of running, hopping and trotting animals using diverse lever systems. We find that the duration of the push exceeds that of the brake in all the animals, indicating that the different lever systems comply with the basic property of muscle to resist stretching with a force greater than that developed during shortening. In addition, results show both the landing–takeoff asymmetry and the mass-specific vertical stiffness to be greater in small animals than in large animals. We suggest that the landing–takeoff asymmetry is an index of a lack of elasticity, which increases with increasing the role of muscle relative to that of tendon within muscle–tendon units.

Design and fabrication of multi-material structures for bioinspired robots

New multi-material rapid prototyping processes are making possible the design and fabrication of bioinspired robot structures that share some of the desirable properties of animal appendages. The structures combine stiff and compliant materials and incorporate sensors and other discrete components, resulting in robots that are less demanding to control than traditionally designed robots and more robust. Current challenges include extending this approach to the structures that involve microscopic as well as macroscopic features.

Task-dependent force sharing between muscle synergists during locomotion in turkeys

At most joints, there is a redundancy of muscle function. For any given movement, there are a wide range of possible solutions to the problem of how force is shared among muscle synergists. A better understanding of how force is shared among muscle synergists can provide insight into the mechanics and control of movement. We examined force sharing in the gastrocnemius of wild turkeys (Meleagris gallopavo), using strain gauges bonded to bony tendons. Force was measured separately in the lateral (LG) and medial (MG)heads of the gastrocnemius, to evaluate force sharing. We also used inverse dynamics to determine the total force required during swing phase. To determine whether the pattern of force sharing varied depending on the mechanical task, we used running speed (1 to 3.5 m s–1) and limb loading (30 and 60 g added tarsometatarsal mass) to vary the force required at the intertarsal joint. We found that the distribution of force between these two heads varied depending on the phase of the stride cycle. During stance, force was shared in near equal amounts between the two heads and this distribution was unaffected by changes in running speed or limb load. During swing phase, however, there was no force sharing. Force was produced only in the lateral head, and this force was not significantly different from the total force required, as calculated from inverse dynamics. Thus, the LG produced all of the force required for limb extension during swing. This change in the pattern of force sharing between stance and swing supports the theory that force sharing between muscle synergists is task-dependent.

Hind limb scaling of kangaroos and wallabies (superfamily Macropodoidea): implications for hopping performance, safety factor and elastic savings

The aim of this study was to examine hind limb scaling of the musculoskeletal system in the Macropodoidea, the superfamily containing wallabies and kangaroos, to re-examine the effect of size on the locomotor mechanics and physiology of marsupial hopping. Morphometric musculoskeletal analyses were conducted of 15 species and skeletal specimens of 21 species spanning a size range from 0.8 to 80 kg that included representatives of 12 of the 16 extant genera of macropodoids. We found that unlike other groups, macropodoids are able to match force demands associated with increasing body size primarily through a combination of positive allometry in muscle area and muscle moment arms. Isometric scaling of primary hind limb bones suggests, however, that larger species experience relatively greater bone stresses. Muscle to tendon area ratios of the ankle extensors scale with strong positive allometry, indicating that peak tendon stresses also increase with increasing body size but to a lesser degree than previously reported. Consistent with previous morphological and experimental studies, large macropodoids are therefore better suited for elastic strain energy recovery but operate at lower safety factors, which likely poses an upper limit to body size. Scaling patterns for extant macropodoids suggest that extinct giant kangaroos (approximately 250 kg) were likely limited in locomotor capacity.

Posture, gait and the ecological relevance of locomotor costs and energy-saving mechanisms in tetrapods

A reanalysis of locomotor data from functional, energetic, mechanical and ecological perspectives reveals that limb posture has major effects on limb biomechanics, energy-saving mechanisms and the costs of locomotion. Regressions of data coded by posture (crouched vs. erect) reveal nonlinear patterns in metabolic cost, limb muscle mass, effective mechanical advantage, and stride characteristics. In small crouched animals energy savings from spring and pendular mechanisms are inconsequential and thus the metabolic cost of locomotion is driven by muscle activation costs. Stride frequency appears to be the principal functional parameter related to the decreasing cost of locomotion in crouched animals. By contrast, the shift to erect limb postures invoked a series of correlated effects on the metabolic cost of locomotion: effective mechanical advantage increases, relative muscle masses decrease, metapodial limb segments elongate dramatically (as limbs shift from digitigrade to unguligrade designs) and biological springs increase in size and effectiveness. Each of these factors leads to decreases in the metabolic cost of locomotion in erect forms resulting from real and increasing contributions of pendular savings and spring savings. Comparisons of the relative costs and ecological relevance of different gaits reveal that running is cheaper than walking in smaller animals up to the size of dogs but running is more expensive than walking in horses. Animals do not necessarily use their cheapest gaits for their predominant locomotor activity. Therefore, locomotor costs are driven more by ecological relevance than by the need to optimize locomotor economy.

How important are skeletal muscle mechanics in setting limits on jumping performance?

Jumping is an important locomotor behaviour used by many animals. The power required to perform a jump is supplied by skeletal muscle. The mechanical properties of skeletal muscle, including the power it can produce, are determined by its composition, which in turn reflects trade-offs between the differing tasks performed by the muscle. Recent studies suggest that muscles used for jumping are relatively fast compared with other limb muscles. As animals get bigger absolute jump performance tends to increase, but recent evidence suggests that adult jump performance may be relatively independent of body size. As body size increases the relative shortening velocity of muscle decreases, whereas normalised power output remains relatively constant. However, the relative shortening velocity of the fastest muscle fibre types appears to remain relatively constant over a large body size range of species. It appears likely that in many species during jumping, other factors are compensating for, or allowing for, uncoupling of jumping performance from size-related changes in the mechanical properties of muscle. In some species smaller absolute body size is compensated for by rapid development of locomotor morphology to attain high locomotor performance early in life. Smaller animal species also appear to rely more heavily on elastic storage mechanisms to amplify the power output available from skeletal muscle. Adaptations involving increased relative hindlimb length and relative mass of jumping muscles, and beneficial alteration of the origin and/or insertion of jumping muscles, have all been found to improve animal jump performance. However, further integrative studies are needed to provide conclusive evidence of which morphological and physiological adaptations are the most important in enhancing jump performance.

Scaling of elastic energy storage in mammalian limb tendons: do small mammals really lose out?

It is widely believed that elastic energy storage is more important in the locomotion of larger mammals. This is based on: (a) comparison of kangaroos with the smaller kangaroo rat; and (b) calculations that predict that the capacity for elastic energy storage relative to body mass increases with size. Here we argue that: (i) data from kangaroos and kangaroo rats cannot be generalized to other mammals; (ii) the elastic energy storage capacity relative to body mass is not indicative of the importance of elastic energy to an animal; and (iii) the contribution of elastic energy to the mechanical work of locomotion will not increase as rapidly with size as the mass-specific energy storage capacity, because larger mammals must do relatively more mechanical work per stride. We predict how the ratio of elastic energy storage to mechanical work will change with size in quadrupedal mammals by combining empirical scaling relationships from the literature. The results suggest that the percentage contribution of elastic energy to the mechanical work of locomotion decreases with size, so that elastic energy is more important in the locomotion of smaller mammals. This now needs to be tested experimentally.

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.

Tuataras and salamanders show that walking and running mechanics are ancient features of tetrapod locomotion

The lumbering locomotor behaviours of tuataras and salamanders are the best examples of quadrupedal locomotion of early terrestrial vertebrates. We show they use the same walking (out-of-phase) and running (in-phase) patterns of external mechanical energy fluctuations of the centre-of-mass known in fast moving (cursorial) animals. Thus, walking and running centre-of-mass mechanics have been a feature of tetrapods since quadrupedal locomotion emerged over 400 million years ago. When walking, these sprawling animals save external mechanical energy with the same pendular effectiveness observed in cursorial animals. However, unlike cursorial animals (that change footfall patterns and mechanics with speed), tuataras and salamanders use only diagonal couplet gaits and indifferently change from walking to running mechanics with no significant change in total mechanical energy. Thus, the change from walking to running is not related to speed and the advantage of walking versus running is unclear. Furthermore, lumbering mechanics in primitive tetrapods is reflected in having total mechanical energy driven by potential energy (rather than kinetic energy as in cursorial animals) and relative centre-of-mass displacements an order of magnitude greater than cursorial animals. Thus, large vertical displacements associated with lumbering locomotion in primitive tetrapods may preclude their ability to increase speed.

Terrestrial locomotion of the New Zealand short-tailed batMystacina tuberculataand the common vampire batDesmodus rotundus

Bats (Chiroptera) are generally awkward crawlers, but the common vampire bat (Desmodus rotundus) and the New Zealand short-tailed bat(Mystacina tuberculata) have independently evolved the ability to manoeuvre well on the ground. In this study we describe the kinematics of locomotion in both species, and the kinetics of locomotion in M. tuberculata. We sought to determine whether these bats move terrestrially the way other quadrupeds do, or whether they possess altogether different patterns of movement on the ground than are observed in quadrupeds that do not fly. Using high-speed video analyses of bats moving on a treadmill, we observed that both species possess symmetrical lateral-sequence gaits similar to the kinematically defined walks of a broad range of tetrapods. At high speeds, D. rotundus use an asymmetrical bounding gait that appears to converge on the bounding gaits of small terrestrial mammals, but with the roles of the forelimbs and hindlimbs reversed. This gait was not performed by M. tuberculata.

Many animals that possess a single kinematic gait shift with increasing speed from a kinetic walk (where kinetic and potential energy of the centre of mass oscillate out of phase from each other) to a kinetic run (where they oscillate in phase). To determine whether the single kinematic gait of M. tuberculata meets the kinetic definition of a walk, a run, or a gait that functions as a walk at low speed and a run at high speed, we used force plates and high-speed video recordings to characterize the energetics of the centre of mass in that species. Although oscillations in kinetic and potential energy were of similar magnitudes, M. tuberculata did not use pendulum-like exchanges of energy between them to the extent that many other quadrupedal animals do, and did not transition from a kinetic walk to kinetic run with increasing speed. The gait of M. tuberculata is kinematically a walk,but kinetically run-like at all speeds.