Probing the limits to muscle-powered accelerations: lessons from jumping bullfrogs

Comparative muscle anatomy of the anuran pelvis and hindlimb in relation to locomotor mode

Frogs have a highly conserved body plan, yet they employ a diverse array of locomotor modes, making them ideal organisms for investigating the relationships between morphology and locomotor function, in particular whether anatomical complexity is a prerequisite for functional complexity. We use diffusible iodine contrast-enhanced microCT (diceCT) imaging to digitally dissect the gross muscle anatomy of the pelvis and hindlimbs for 30 species of frogs representing five primary locomotor modes, including the first known detailed dissection for some of the world's smallest frogs, forming the largest digital comparative analysis of musculoskeletal structure in any vertebrate clade to date. By linking musculoskeletal dissections and phylogenetic comparative methods, we then quantify and compare relationships between anatomy and function across over 160 million years of anuran evolution. In summary, we have found that bone lengths and pelvic crest sizes are generally not reliable predictors of muscle sizes, which highlights important implications for future palaeontological studies. Our investigation also presents previously unreported differences in muscle anatomy between frogs specialising in different locomotor modes, including several of the smallest frog hindlimb muscles, which are extremely difficult to extract and measure using traditional approaches. Furthermore, we find evidence of many-to-one and one-to-many mapping of form to function across the phylogeny. Additionally, we perform the first quantitative analysis of how the degree of muscle separation can differ between frogs. We find evidence that phylogenetic history is the key contributing factor to muscle separation in the pelvis and thigh, while the separation of shank muscles is influenced more strongly by locomotor mode. Finally, our anatomical 3D reconstructions are published alongside this manuscript to contribute towards future research and serve as educational materials.

Design and control of jumping microrobots with torque reversal latches

Jumping microrobots and insects power their impressive leaps through systems of springs and latches. Using springs and latches, rather than motors or muscles, as actuators to power jumps imposes new challenges on controlling the performance of the jump. In this paper, we show how tuning the motor and spring relative to one another in a torque reversal latch can lead to an ability to control jump output, producing either tuneable (variable) or stereotyped jumps. We develop and utilize a simple mathematical model to explore the underlying design, dynamics, and control of a torque reversal mechanism, provides the opportunity to achieve different outcomes through the interaction between geometry, spring properties, and motor voltage. We relate system design and control parameters to performance to guide the design of torque reversal mechanisms for either variable or stereotyped jump performance. We then build a small (356 mg) microrobot and characterize the constituent components (e.g. motor and spring). Through tuning the actuator and spring relative to the geometry of the torque reversal mechanism, we demonstrate that we can achieve jumping microrobots that both jump with different take-off velocities given the actuator input (variable jumping), and those that jump with nearly the same take-off velocity with actuator input (stereotyped jumping). The coupling between spring characteristics and geometry in this system has benefits for resource-limited microrobots, and our work highlights design combinations that have synergistic impacts on output, compared to others that constrain it. This work will guide new design principles for enabling control in resource-limited jumping microrobots.

The effect of muscle ultrastructure on the force, displacement and work capacity of skeletal muscle

Skeletal muscle powers animal movement through interactions between the contractile proteins, actin and myosin. Structural variation contributes greatly to the variation in mechanical performance observed across muscles. In vertebrates, gross structural variation occurs in the form of changes in the muscle cross-sectional area : fibre length ratio. This results in a trade-off between force and displacement capacity, leaving work capacity unaltered. Consequently, the maximum work per unit volume-the work density-is considered constant. Invertebrate muscle also varies in muscle ultrastructure, i.e. actin and myosin filament lengths. Increasing actin and myosin filament lengths increases force capacity, but the effect on muscle fibre displacement, and thus work, capacity is unclear. We use a sliding-filament muscle model to predict the effect of actin and myosin filament lengths on these mechanical parameters for both idealized sarcomeres with fixed actin : myosin length ratios, and for real sarcomeres with known filament lengths. Increasing actin and myosin filament lengths increases stress without reducing strain capacity. A muscle with longer actin and myosin filaments can generate larger force over the same displacement and has a higher work density, so seemingly bypassing an established trade-off. However, real sarcomeres deviate from the idealized length ratio suggesting unidentified constraints or selective pressures.

Evidence for multi-scale power amplification in skeletal muscle

Many animals use a combination of skeletal muscle and elastic structures to amplify power output for fast motions. Among vertebrates, tendons in series with skeletal muscle are often implicated as the primary power-amplifying spring, but muscles contain elastic structures at all levels of organization, from the muscle tendon to the extracellular matrix to elastic proteins within sarcomeres. The present study used ex vivo muscle preparations in combination with high-speed video to quantify power output, as the product of force and velocity, at several levels of muscle organization to determine where power amplification occurs. Dynamic ramp-shortening contractions in isolated frog flexor digitorum superficialis brevis were compared with isotonic power output to identify power amplification within muscle fibers, the muscle belly, free tendon and elements external to the muscle tendon. Energy accounting revealed that artifacts from compliant structures outside of the muscle-tendon unit contributed significant peak instantaneous power. This compliance included deflection of clamped bone that stored and released energy contributing 195.22±33.19 W kg-1 (mean±s.e.m.) to the peak power output. In addition, we found that power detected from within the muscle fascicles for dynamic shortening ramps was 338.78±16.03 W kg-1, or approximately 1.75 times the maximum isotonic power output of 195.23±8.82 W kg-1. Measurements of muscle belly and muscle-tendon unit also demonstrated significant power amplification. These data suggest that intramuscular tissues, as well as bone, have the capacity to store and release energy to amplify whole-muscle power output.

The effects of temperature on elastic energy storage and release in a system with a dynamic mechanical advantage latch

Changes in temperature alter muscle kinetics and in turn affect whole-organism performance. Some organisms use the elastic recoil of biological springs, structures which are far less temperature sensitive, to power thermally robust movements. For jumping frogs, the use of elastic energy in tendons is facilitated through a geometric latching mechanism that operates through dynamic changes in the mechanical advantage (MA) of the hindlimb. Despite the well-documented use of elastic energy storage, frog jumping is a locomotor behavior that is significantly affected by changes in temperature. Here, we used an in vitro muscle preparation interacting in real time with an in silico model of a legged jumper to understand how changes in temperature affect the flow of energy in a system using a MA latch. We used the plantaris longus muscle-tendon unit (MTU) to power a virtual limb with changing MA and a mass being accelerated through a real-time feedback controller. We quantified the amount of energy stored in and recovered from elastic structures and the additional contribution of direct muscle work after unlatching. We found that temperature altered the duration of the energy loading and recovery phase of the in vitro/in silico experiments. We found that the early phase of loading was insensitive to changes in temperature. However, an increase in temperature did increase the rate of force development, which in turn allowed for increased energy storage in the second phase of loading. We also found that the contribution of direct muscle work after unlatching was substantial and increased significantly with temperature. Our results show that the thermal robustness achieved by an elastic mechanism depends strongly on the nature of the latch that mediates energy flow, and that the relative contribution of elastic and direct muscle energy likely shapes the thermal sensitivity of locomotor systems.

Amphibious Miniature Soft Jumping Robot with On-Demand In-Flight Maneuver

In nature, some semiaquatic arthropods evolve biomechanics for jumping on the water surface with the controlled burst of kinetic energy. Emulating these creatures, miniature jumping robots deployable on the water surface have been developed, but few of them achieve the controllability comparable to biological systems. The limited controllability and agility of miniature robots constrain their applications, especially in the biomedical field where dexterous and precise manipulation is required. Herein, an insect-scale magnetoelastic robot with improved controllability is designed. The robot can adaptively regulate its energy output to generate controllable jumping motion by tuning magnetic and elastic strain energy. Dynamic and kinematic models are developed to predict the jumping trajectories of the robot. On-demand actuation can thus be applied to precisely control the pose and motion of the robot during the flight phase. The robot is also capable of making adaptive amphibious locomotion and performing various tasks with integrated functional modules.

Does human foot anthropometry relate to plantar flexor fascicle mechanics and metabolic energy cost across various walking speeds?

Foot structures define the leverage in which the ankle muscles push off against the ground during locomotion. While prior studies have indicated that inter-individual variation in anthropometry (e.g. heel and hallux lengths) can directly affect force production of ankle plantar flexor muscles, its effect on the metabolic energy cost of locomotion has been inconclusive. Here, we tested the hypotheses that shorter heels and longer halluces are associated with slower plantar flexor (soleus) shortening velocity and greater ankle plantar flexion moment, indicating enhanced force potential as a result of the force-velocity relationship. We also hypothesized that such anthropometry profiles would reduce the metabolic energy cost of walking at faster walking speeds. Healthy young adults (N=15) walked at three speeds (1.25, 1.75 and 2.00 m s-1), and we collected in vivo muscle mechanics (via ultrasound), activation (via electromyography) and whole-body metabolic energy cost of transport (via indirect calorimetry). Contrary to our hypotheses, shorter heels and longer halluces were not associated with slower soleus shortening velocity or greater plantar flexion moment. Additionally, longer heels were associated with reduced metabolic cost of transport, but only at the fastest speed (2.00 m s-1, R2=0.305, P=0.033). We also found that individuals with longer heels required less increase in plantar flexor (soleus and gastrocnemius) muscle activation to walk at faster speeds, potentially explaining the reduced metabolic cost.

Muscle-tendon unit design and tuning for power enhancement, power attenuation, and reduction of metabolic cost

The contractile elements in skeletal muscle fibers operate in series with elastic elements, tendons and potentially aponeuroses, in muscle-tendon units (MTUs). Elastic strain energy (ESE), arising from either work done by muscle fibers or the energy of the body, can be stored in these series elastic elements (SEEs). MTUs vary considerably in their design in terms of the relative lengths and stiffnesses of the muscle fibers and SEEs, and the force and work generating capacities of the muscle fibers. However, within an MTU it is thought that contractile and series elastic elements can be matched or tuned to maximize ESE storage. The use of ESE is thought to improve locomotor performance by enhancing contractile element power during activities such as jumping, attenuating contractile element power during activities such as landing, and reducing the metabolic cost of movement during steady-state activities such as walking and running. The effectiveness of MTUs in these potential roles is contingent on factors such as the source of mechanical energy, the control of the flow of energy, and characteristics of SEE recoil. Hence, we suggest that MTUs specialized for ESE storage may vary considerably in the structural, mechanical, and physiological properties of their components depending on their functional role and required versatility.

Adapting small jumping robots to compliant environments

Jumping animals launch themselves from surfaces that vary widely in compliance from grasses and shrubs to tree branches. However, studies of robotic jumpers have been largely limited to those jumping from rigid substrates. In this paper, we leverage recent work describing how latches in jumping systems can mediate the transition from stored potential energy to kinetic energy. By including a description of the latch in our system model of both the jumper and compliant substrate, we can describe conditions in which a jumper can either lose energy to the substrate or recover energy from the substrate resulting in an improved jump performance. Using our mathematical model, we illustrate how the latch plays a role in the ability of a system to adapt its jump performance to a wide range of substrates that vary in their compliance. Our modelling results are validated using a 4 g jumper with a range of latch designs jumping from substrates with varying mass and compliance. Finally, we demonstrate the jumper recovering energy from a tree branch during take-off, extending these mechanistic findings to robots interacting with a more natural environment.

Muscle preactivation and the limits of muscle power output during jumping in the Cuban tree frog Osteopilus septentrionalis

Previous studies of jumping in frogs have found power outputs in excess of what is possible from direct application of muscle power and concluded that jumping requires the storage and release of elastic strain energy. Of course, the muscles must produce the work required and their power output should be consistent with known muscle properties if the total duration of muscle activity is known. Using the Cuban tree frog, Osteopilus septentrionalis, I measured jumping performance from kinematics and used EMG measurements of three major jumping muscles to determine the duration of muscle activity. Using the total mass of all the hindlimb muscles, muscle mass-specific work output up to 60 J kg-1 was recorded. Distributed over the duration of the jump, both average and peak muscle mass-specific power output increased approximately linearly with the work done, reaching values of over 750 and 2000 W kg-1, respectively. However, the muscles were activated before the jump started. Both preactivation duration and EMG amplitude increased with increasing amounts of work performed. Assuming the muscles could produce work from EMG onset until toe-off, the average muscle mass-specific power over this longer interval also increased with work done, but only up to a work output of 36 J kg-1. The mean power above this value of work was 281 W kg-1, which is approximately 65% of the estimated maximum isotonic power. Several reasons are put forward for suggesting this power output, although within the known properties of the muscles, is nevertheless an impressive achievement.

Engineered jumpers overcome biological limits via work multiplication

For centuries, scientists have explored the limits of biological jump height^1,2, and for decades, engineers have designed jumping machines^3-18 that often mimicked or took inspiration from biological jumpers. Despite these efforts, general analyses are missing that compare the energetics of biological and engineered jumpers across scale. Here we show how biological and engineered jumpers have key differences in their jump energetics. The jump height of a biological jumper is limited by the work its linear motor (muscle) can produce in a single stroke. By contrast, the jump height of an engineered device can be far greater because its ratcheted or rotary motor can 'multiply work' during repeated strokes or rotations. As a consequence of these differences in energy production, biological and engineered jumpers should have divergent designs for maximizing jump height. Following these insights, we created a device that can jump over 30 metres high, to our knowledge far higher than previous engineered jumpers and over an order of magnitude higher than the best biological jumpers. Our work advances the understanding of jumping, shows a new level of performance, and underscores the importance of considering the differences between engineered and biological systems.

Use of compliant actuators for throwing rigid projectiles

Muscles and tendons, actuators in robotics, and various sports implements are examples that exploit elasticity to accelerate objects. Tuning the mechanical properties of elastic elements connecting objects can greatly enhance the transfer of mechanical energy between the objects. Here, we study experimentally the throw of rigid projectiles by an actuator, which has a soft elastic element added to the distal end. We vary the thickness of the elastic layer and suggest a simple mass-spring chain model to find the properties of the elastic layer, which will maximize the energy transfer from the actuator to the projectile. The insertion of a soft layer, impedance matched to the ejection frequency of the projectile mass, can increase the throwing efficiency by over 400%. Finally, we identify that very thick and very soft compliant layers could potentially lead to high efficiency and flexibility simultaneously.

Tuned muscle and spring properties increase elastic energy storage

Elastic recoil drives some of the fastest and most powerful biological movements. For effective use of elastic recoil, the tuning of muscle and spring force capacity is essential. Although studies of invertebrate organisms that use elastic recoil show evidence of increased force capacity in their energy loading muscle, changes in the fundamental properties of such muscles have yet to be documented in vertebrates. Here, we used three species of frogs (Cuban tree frogs, bullfrogs and cane toads) that differ in jumping power to investigate functional shifts in muscle-spring tuning in systems using latch-mediated spring actuation (LaMSA). We hypothesized that variation in jumping performance would result from increased force capacity in muscles and relatively stiffer elastic structures, resulting in greater energy storage. To test this, we characterized the force-length property of the plantaris longus muscle-tendon unit (MTU), and quantified the maximal amount of energy stored in elastic structures for each species. We found that the plantaris longus MTU of Cuban tree frogs produced higher mass-specific energy and mass-specific forces than the other two species. Moreover, we found that the plantaris longus MTU of Cuban tree frogs had higher pennation angles than the other species, suggesting that muscle architecture was modified to increase force capacity through packing of more muscle fibers. Finally, we found that the elastic structures were relatively stiffer in Cuban tree frogs. These results provide a mechanistic link between the tuned properties of LaMSA components, energy storage capacity and whole-system performance.

Plasticity of the gastrocnemius elastic system in response to decreased work and power demand during growth

Elastic energy storage and release can enhance performance that would otherwise be limited by the force-velocity constraints of muscle. Although functional influence of a biological spring depends on tuning between components of an elastic system (the muscle, spring-driven mass and lever system), we do not know whether elastic systems systematically adapt to functional demand. To test whether altering work and power generation during maturation alters the morphology of an elastic system, we prevented growing guinea fowl (Numida meleagris) from jumping. We compared the jump performance of our treatment group at maturity with that of controls and measured the morphology of the gastrocnemius elastic system. We found that restricted birds jumped with lower jump power and work, yet there were no significant between-group differences in the components of the elastic system. Further, subject-specific models revealed no difference in energy storage capacity between groups, though energy storage was most sensitive to variations in muscle properties (most significantly operating length and least dependent on tendon stiffness). We conclude that the gastrocnemius elastic system in the guinea fowl displays little to no plastic response to decreased demand during growth and hypothesize that neural plasticity may explain performance variation.

Cooperation behavior of fore- And hindlimbs during jumping in Rana dybowskii and Xenopus laevis

Frogs are characterized by their outstanding jumping ability, depending on the rapid extension of hindlimbs to propel their bodies into air. A typical jumping cycle could be broken into four phases: preparation, takeoff, flight, and landing. Considerable research has been performed to discuss the function of hindlimbs of frogs during takeoff phase, whereas the literature of limbs' motion in jumping between different species was limited. To profile the evolution of locomotion in anurans, it is necessary to investigate on the motion of fore- and hindlimbs of frogs within different taxa. In this work, we put forward a detailed description of jumping behavior of two frog species, Rana dybowskii and Xenopus laevis. High-speed cameras were used to explore the movement of different joints in fore- and hindlimbs of these two animals, and kinematic analysis was operated to identify both homologous behaviors and significant differences between them. We found that the Rana dybowskii's fore- and hindlimbs had good cooperation during jumping, while the Xenopus laevis' uncooperative behavior in limbs may give a functional explanation for the deficiency in terrestrial jumping; besides, the R. dybowskii's landing followed the "hands-belly-feet slap" strategy, and Xenopus laevis had clumsy landing with "belly-flops" sequence. The result gained here clarifies the cooperation behavior of anuran limbs and may supply a new insight into our understanding of the anuran's evolution.

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.

Thermal robustness of biomechanical processes

Temperature influences many physiological processes that govern life as a result of the thermal sensitivity of chemical reactions. The repeated evolution of endothermy and widespread behavioral thermoregulation in animals highlight the importance of elevating tissue temperature to increase the rate of chemical processes. Yet, movement performance that is robust to changes in body temperature has been observed in numerous species. This thermally robust performance appears exceptional in light of the well-documented effects of temperature on muscle contractile properties, including shortening velocity, force, power and work. Here, we propose that the thermal robustness of movements in which mechanical processes replace or augment chemical processes is a general feature of any organismal system, spanning kingdoms. The use of recoiling elastic structures to power movement in place of direct muscle shortening is one of the most thoroughly studied mechanical processes; using these studies as a basis, we outline an analytical framework for detecting thermal robustness, relying on the comparison of temperature coefficients (Q ₁₀ values) between chemical and mechanical processes. We then highlight other biomechanical systems in which thermally robust performance that arises from mechanical processes may be identified using this framework. Studying diverse movements in the context of temperature will both reveal mechanisms underlying performance and allow the prediction of changes in performance in response to a changing thermal environment, thus deepening our understanding of the thermal ecology of many organisms.

Bioinspired high-power-density strong contractile hydrogel by programmable elastic recoil

Stimuli-responsive hydrogels have large deformability but-when applied as actuators, smart switch, and artificial muscles-suffer from low work density due to low deliverable forces (~2 kPa) and speed through the osmotic pressure-driven actuation. Inspired by the energy conversion mechanism of many creatures during jumping, we designed an elastic-driven strong contractile hydrogel through storing and releasing elastic potential energy in polymer network. It can generate high contractile force (40 kPa) rapidly at ultrahigh work density (15.3 kJ/m³), outperforming current hydrogels (~0.01 kJ/m³) and even biological muscles (~8 kJ/m³). This demonstrated elastic energy storing and releasing method endows hydrogels with elasticity-plasticity switchability, multi-stable deformability in fully reversible and programmable manners, and anisotropic or isotropic deformation. With the high power density and programmability via this customizable modular design, these hydrogels demonstrated potential for broad applications in artificial muscles, contractile wound dressing, and high-power actuators.

In vitro virtual reality: an anatomically explicit musculoskeletal simulation powered by in vitro muscle using closed-loop tissue-software interaction

Muscle force-length dynamics are governed by intrinsic contractile properties, motor stimulation and mechanical load. Although intrinsic properties are well characterised, physiologists lack in vitro instrumentation to account for combined effects of limb inertia, musculoskeletal architecture and contractile dynamics. We introduce in vitro virtual reality (in vitro-VR) which enables in vitro muscle tissue to drive a musculoskeletal jumping simulation. In hardware, muscle force from a frog plantaris was transmitted to a software model where joint torques, inertia and ground reaction forces were computed to advance the simulation at 1 kHz. To close the loop, simulated muscle strain was returned to update in vitro length. We manipulated (1) stimulation timing and (2) the virtual muscle's anatomical origin. This influenced interactions among muscular, inertial, gravitational and contact forces dictating limb kinematics and jump performance. We propose that in vitro-VR can be used to illustrate how neuromuscular control and musculoskeletal anatomy influence muscle dynamics and biomechanical performance.

Modeling the Determinants of Mechanical Advantage During Jumping: Consequences for Spring- and Muscle-Driven Movement

Systems powered by elastic recoil need a latch to prevent motion while a spring is loaded but allow motion during spring recoil. Some jumping animals that rely on elastic recoil use the increasing mechanical advantage of limb extensor muscles to accomplish latching. We examined the ways in which limb morphology affects latching and the resulting performance of an elastic-recoil mechanism. Additionally, because increasing mechanical advantage is a consequence of limb extension that may be found in many systems, we examined the mechanical consequences for muscle in the absence of elastic elements. By simulating muscle contractions against a simplified model of an extending limb, we found that increasing mechanical advantage can limit the work done by muscle by accelerating muscle shortening during limb extension. The inclusion of a series elastic element dramatically improves mechanical output by allowing for additional muscle work that is stored and released from the spring. This suggests that elastic recoil may be beneficial for more animals than expected when assuming peak isotonic power output from muscle during jumping. The mechanical output of elastic recoil depends on limb morphology; long limbs moving small loads maximize total work, but it is done at a low power, whereas shorter limbs moving larger loads do less work at a higher power. This work-power trade-off of limb morphology is true with or without an elastic element. Systems with relatively short limbs may have performance that is robust to variable conditions such as body mass or muscle activation, while long-limbed systems risk complete failure with relatively minor perturbations. Finally, a changing mechanical advantage latch allows for muscle work to be done simultaneously with spring recoil, changing the predictions for spring mechanical properties. Overall, the design constraints revealed by considering the mechanics of this particular latch will inform our understanding of the evolution of elastic-recoil mechanisms and our attempts to engineer similar systems.

Playing with Power: Mechanisms of Energy Flow in Organismal Movement

Across multiple evolutionary clades and size scales, organismal movement requires controlling the flow of energy through the body to enhance certain functions. Whether energy is released or absorbed by the organism, proper function hinges on the ability to manipulate both where and when energy is transferred. For example, both power amplification and power attenuation rely on the use of springs for the intermediate storage of energy between the body and the environment; but variation in function is the result of the path and timing of energy flow. In this symposium, we have invited speakers that demonstrate the diversity of mechanisms used to control the flow of energy through the body and into the environment. By bringing together researchers investigating movements in the context of power and energy flow, the major goal of this symposium is to facilitate fresh perspectives on the unifying mechanical themes of energy transfer in organismal movement.

Energy Flow in Multibody Limb Models: A Case Study in Frogs

A frog jump is both simple and difficult to comprehend. The center-of-mass (COM) follows a two-dimensional (2D) path; it accelerates diagonally upward, then traces a predictable arc in flight. Despite this simplicity, the leg segments trace intricate trajectories to drive the COM both upwards and forwards. Because the frog sits crouched with sprawled legs, segments must pivot, tilt, and twist; they solve a long-recognized problem of converting non-linear 3D motion of the leg segments to linear 2D motion of the COM. I use mathematical approaches borrowed from robotics to address: How do frogs manipulate the flow of kinetic energy through their body to influence jump trajectory? I address (1) transfer of motion through kinematic transmission and (2) transfer of motion through dynamic coupling of segment mass-inertia properties. Using a multi-body simulation, I explore how segment acceleration induces rotations at neighboring segments (even without accounting for bi-articular muscles). During jumps, this inertial coupling mechanism is likely crucial for modulating the direction of travel. The frog case study highlights a useful computational framework for studying how limb joints produce coordinated motion.

Hurry Up and Get Out of the Way! Exploring the Limits of Muscle-Based Latch Systems for Power Amplification

Animals can amplify the mechanical power output of their muscles as they jump to escape predators or strike to capture prey. One mechanism for amplification involves muscle-tendon unit (MT) systems in which a spring element (series elastic element [SEE]) is pre-stretched while held in place by a "latch" that prevents immediate transmission of muscle (or contractile element, CE) power to the load. In principle, this storage phase is followed by a triggered release of the latch, and elastic energy released from the SEE enables power amplification (PRATIO=PLOAD/PCE,max >1.0), whereby the peak power delivered from MT to the load exceeds the maximum power limit of the CE in isolation. Latches enable power amplification by increasing the muscle work generated during storage and reducing the duration over which that stored energy is released to power a movement. Previously described biological "latches" include: skeletal levers, anatomical triggers, accessory appendages, and even antagonist muscles. In fact, many species that rely on high-powered movements also have a large number of muscles arranged in antagonist pairs. Here, we examine whether a decaying antagonist force (e.g., from a muscle) could be useful as an active latch to achieve controlled energy transmission and modulate peak output power. We developed a computer model of a frog hindlimb driven by a compliant MT. We simulated MT power generated against an inertial load in the presence of an antagonist force "latch" (AFL) with relaxation time varying from very fast (10 ms) to very slow (1000 ms) to mirror physiological ranges of antagonist muscle. The fastest AFL produced power amplification (PRATIO=5.0) while the slowest AFL produced power attenuation (PRATIO=0.43). Notably, AFLs with relaxation times shorter than ∼300 ms also yielded greater power amplification (PRATIO>1.20) than the system driving the same inertial load using only an agonist MT without any AFL. Thus, animals that utilize a sufficiently fast relaxing AFL ought to be capable of achieving greater power output than systems confined to a single agonist MT tuned for maximum PRATIO against the same load.

Beyond power amplification: latch-mediated spring actuation is an emerging framework for the study of diverse elastic systems

Rapid biological movements, such as the extraordinary strikes of mantis shrimp and accelerations of jumping insects, have captivated generations of scientists and engineers. These organisms store energy in elastic structures (e.g. springs) and then rapidly release it using latches, such that movement is driven by the rapid conversion of stored elastic to kinetic energy using springs, with the dynamics of this conversion mediated by latches. Initially drawn to these systems by an interest in the muscle power limits of small jumping insects, biologists established the idea of power amplification, which refers both to a measurement technique and to a conceptual framework defined by the mechanical power output of a system exceeding muscle limits. However, the field of fast elastically driven movements has expanded to encompass diverse biological and synthetic systems that do not have muscles - such as the surface tension catapults of fungal spores and launches of plant seeds. Furthermore, while latches have been recognized as an essential part of many elastic systems, their role in mediating the storage and release of elastic energy from the spring is only now being elucidated. Here, we critically examine the metrics and concepts of power amplification and encourage a framework centered on latch-mediated spring actuation (LaMSA). We emphasize approaches and metrics of LaMSA systems that will forge a pathway toward a principled, interdisciplinary field.

Digital dissection of the pelvis and hindlimb of the red-legged running frog, Phlyctimantis maculatus, using Diffusible Iodine Contrast Enhanced computed microtomography (DICE μCT)

Background

The current study applies both traditional and Diffusible Iodine Contrast Enhanced computed microtomography (DICE µCT) techniques to reveal the musculoskeletal anatomy of Phlyctimantis maculatus. DICE µCT has emerged as a powerful tool to visualise intricate musculoskeletal anatomy. By generating 3D digital models, anatomical analyses can be conducted non-destructively, preserving the in situ 3D topography of the system, therefore eliminating some of the drawbacks associated with traditional methods. We aim to describe the musculature of the spine, pelvis, and hindlimb, compare the musculoskeletal anatomy and pelvic morphology of P. maculatus with functionally diverse frogs, and produce 3D digital anatomy reference data.

Method

An adult frog was stained using an aqueous Lugol’s solution and scanned in a SkyScan1176 in vivo µCT scanner. Scan images were reconstructed, resampled, and digitally segmented to produce a 3D model. A further adult female frog was dissected traditionally for visualisation of tendinous insertions.

Results

Our work revealed three main findings: (1) P. maculatus has similar gross muscular anatomy to Rana catesbeiana (bullfrog) but is distinct from those species that exhibit ancestral traits (leopelmids) and those that are highly specialised (pipids), (2) P. maculatus’s pelvic anatomy best fits the description of Emerson’s walking/hopping pelvic morphotype IIA, and (3) a split in the semimembranosus and gracilis major muscles is consistent with the reported myology in other anuran species.

Discussion

While DICE µCT methods were instrumental in characterising the 3D anatomy, traditional dissection was still required to visualise important structures such as the knee aponeurosis, tendinous insertions, and fasciae. Nonetheless, the anatomical data presented here marks the first detailed digital description of an arboreal and terrestrial frog. Further, our digital model presents P. maculatus as a good frog model system and as such has formed a crucial platform for further functional analysis within the anuran pelvis and hindlimb.

The dynamic role of the ilio-sacral joint in jumping frogs

A striking feature among jumping frogs is a sharp pelvic bend about the ilio-sacral (IS) joint, unique to anurans. Although this sagittal plane hinge has been interpreted as crucial for the evolution of jumping, its mechanical contribution has not been quantified. Using a model based on Kassina maculata and animated with kinematics from prior experiments, we solved the ground contact dynamics in MuJoCo enabling inverse dynamics without force plate measurements. We altered the magnitude, speed and direction of IS extension (leaving remaining kinematics unaltered) to determine its role in jumping. Ground reaction forces (GRFs) matched recorded data. Prior work postulated that IS rotation facilitates jumping by aligning the torso with the GRF. However, our simulations revealed that static torso orientation has little effect on GRF due to the close proximity of the IS joint with the COM, failing to support the ‘torso alignment’ hypothesis. Rather than a postural role, IS rotation has a dynamic function whereby angular acceleration (i) influences GRF direction to modulate jump direction and (ii) increases joint loading, particularly at the ankle and knee, perhaps increasing tendon elastic energy storage early in jumps. Findings suggest that the pelvic hinge mechanism is not obligatory for jumping, but rather crucial for the fine tuning of jump trajectory, particularly in complex habitats.

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.

The principles of cascading power limits in small, fast biological and engineered systems

Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

A novel kinematics analysis method using quaternion interpolation-a case study in frog jumping

Spherical Linear Interpolation (SLERP) has long been used in computer animation to interpolate movements between two 3D orientations. We developed a forward kinematics (FK) approach using quaternions and SLERP to predict how frogs modulate jump kinematics between start posture and takeoff. Frog limb kinematics have been studied during various activities, yet the causal link between differences in joint kinematics and locomotor variation remains unknown. We varied 1) takeoff angle from 8 to 60°; 2) turn angle from 0 to 18°; and 3) initial body pitch from 0 to 70°. Simulations were similar to experimentally observed frog kinematics. Findings suggest a fundamental mechanism whereby limb elevation is modulated by thigh and shank adduction. Forward thrust is produced by thigh and proximal foot retraction with little contribution from the shank except to induce asymmetries for turning. Kinematic shifts causing turns were subtle, marked only by slight counter-rotation of the left versus right shank as well as a 10% timing offset in proximal foot adduction. Additionally, inclining initial body tilt influenced the centre of mass trajectory to determine direction of travel at takeoff. Most importantly, our theory suggests firstly that the convergence of leg segment rotation axes toward a common orientation is crucial both for limb extension and for coordinating jump direction; and, secondly, the challenge of simulating 3D kinematics is simplified using SLERP because frog limbs approximately follow linear paths in unit quaternion space. Our methodology can be applied more broadly to study living and fossil frog taxa as well as to inspire new control algorithms for robotic limbs.

Effect of a prehop on the muscle-tendon interaction during vertical jumps

Many movements use stretch-shortening cycles of a muscle-tendon unit (MTU) for storing and releasing elastic energy. The required stretching of medial gastrocnemius (MG) tendinous tissue during jumps, however, requires large length changes of the muscle fascicles because of the lack of MTU length changes. This has a negative impact on the force-generating capacity of the muscle fascicles. The purpose of this study was to induce a MG MTU stretch before shortening by adding a prehop to the squat jump. Eleven well-trained athletes specialized in jumping performed a prehop squat jump (PHSJ) and a standard squat jump (SSJ). Kinematic data were collected using a 3D motion capture system and were used in a musculoskeletal model to calculate MTU lengths. B-mode ultrasonography of the MG was used to measure fascicle length and pennation angle during the jumps. By combining the muscle-tendon unit lengths, fascicle lengths, and pennation angles, the stretch and recoil of the series elastic element of MG were calculated using a simple geometric muscle-tendon model. Our results show less length changes of the muscle fascicles during the upward motion and lower maximal shortening velocities, increasing the moment-generating capacity of the plantar flexors, reflected in the higher ankle joint moment in the PHSJ compared with the SSJ. Although muscle-tendon interaction during the PHSJ was more optimal, athletes were not able to increase their jump height compared with the SSJ. NEW & NOTEWORTHY This is the first study that aimed to improve the muscle-tendon interaction in squat jumping. We effectively introduced a stretch to the medial gastrocnemius muscle-tendon unit resulting in lower maximal shortening velocities and thus an increase in the plantar flexor force-generating capacity, reflected in the higher ankle joint moment in the prehop squat jump compared with the standard squat jump. Here, we demonstrate an effective method for mechanical optimization of the muscle-tendon interaction in the medial gastrocnemius during squat jumping.

Muscle-tendon length and force affect human tibialis anterior central aponeurosis stiffness in vivo

The factors that drive variable aponeurosis behaviors in active versus passive muscle may alter the longitudinal stiffness of the aponeurosis during contraction, which may change the fascicle strains for a given muscle force. However, it remains unknown whether these factors can drive variable aponeurosis behaviors across different muscle-tendon unit (MTU) lengths and influence the subsequent fascicle strains during contraction. Here, we used ultrasound and elastography techniques to examine in vivo muscle fascicle behavior and central aponeurosis deformations of human tibialis anterior (TA) during force-matched voluntary isometric dorsiflexion contractions at three MTU lengths. We found that increases in TA MTU length increased both the length and apparent longitudinal stiffness of the central aponeurosis at low and moderate muscle forces (P < 0.01). We also found that increased aponeurosis stiffness was directly related to reduced magnitudes of TA muscle fascicle shortening for the same change in force (P < 0.01). The increase in slope and shift to longer overall lengths of the active aponeurosis force-length relationship as MTU length increased was likely due to a combination of parallel lengthening of aponeurosis and greater transverse aponeurosis strains. This study provides in vivo evidence that human aponeurosis stiffness is increased from low to moderate forces and that the fascicle strains for a given muscle force are MTU length dependent. Further testing is warranted to determine whether MTU length-dependent stiffness is a fundamental property of the aponeurosis in pennate muscles and evaluate whether this property can enhance muscle performance.

Scaling of work and power in a locomotor muscle of a frog

Muscle work and power are important determinants of movement performance in animals. How these muscle properties scale determines, in part, the scaling of performance during movements, such as jump height or distance. Muscle-mass-specific work is predicted to remain constant across a range of scales, assuming geometric similarity, while muscle-mass-specific power is expected to decrease with increasing scale. We tested these predictions by examining muscle morphology and contractile properties of plantaris muscles from frogs ranging in mass from 1.28 to 20.60 g. Scaling of muscle work and power was examined using both linear regression on log₁₀-transformed data (LR) and non-linear regressions on untransformed data (NLR). Results depended on the method of regression not because of large changes in scaling slopes, but because of changing levels of statistical significance using corrections for multiple tests, demonstrating the importance of careful consideration of statistical methods when analyzing patterns of scaling. In LR, muscle-mass-specific work decreased with increasing scale, but an accompanying positive allometry of muscle mass predicts constant movement performance at all scales. These relationships were non-significant in NLR, though scaling with geometric similarity also predicts constant jump performance across scales, because of proportional increases in available muscle energy and body mass. Both intrinsic shortening velocity and muscle-mass-specific power were positively allometric in both types of analysis. Nonetheless, scale accounts for little variation in contractile properties overall over the range examined, indicating that other sources of intraspecific variation may be more important in determining muscle performance and its effects on movement.

Enhancement of muscle and locomotor performance by a series compliance: A mechanistic simulation study

The objective was to better understand how a series compliance alters contraction kinetics and power output of muscle to enhance the work done on a load. A mathematical model was created in which a gravitational point load was connected via a linear spring to a muscle (based on the contractile properties of the sartorius of leopard frogs, Rana pipiens). The model explored the effects of load mass, tendon compliance, and delay between onset of contraction and release of the load (catch) on lift height and power output as measures of performance. Series compliance resulted in increased lift height over a relatively narrow range of compliances, and the effect was quite modest without an imposed catch mechanism unless the load was unrealistically small. Peak power of the muscle-tendon complex could be augmented up to four times that produced with a muscle alone, however, lift height was not predicted by peak power. Rather, lift height was improved as a result of the compliance synchronizing the time courses of muscle force and shortening velocity, in particular by stabilizing shortening velocity such that muscle power was sustained rather than rising and immediately falling. With a catch mechanism, enhanced performance resulted largely from energy storage in the compliance during the period of catch, rather than increased time for muscle activation before movement commenced. However, series compliance introduced a trade-off between work done before versus after release of the catch. Thus, the ability of tendons to enhance locomotor performance (i.e. increase the work done by muscle) appears dependent not only on their established role in storing energy and increasing power, but also on their ability to modulate the kinetics of muscle contraction such that power is sustained over more of the contraction, and maximizing the balance of work done before versus after release of a catch.

Muscle-spring dynamics in time-limited, elastic movements

Muscle contractions that load in-series springs with slow speed over a long duration do maximal work and store the most elastic energy. However, time constraints, such as those experienced during escape and predation behaviours, may prevent animals from achieving maximal force capacity from their muscles during spring-loading. Here, we ask whether animals that have limited time for elastic energy storage operate with springs that are tuned to submaximal force production. To answer this question, we used a dynamic model of a muscle-spring system undergoing a fixed-end contraction, with parameters from a time-limited spring-loader (bullfrog: Lithobates catesbeiana) and a non-time-limited spring-loader (grasshopper: Schistocerca gregaria). We found that when muscles have less time to contract, stored elastic energy is maximized with lower spring stiffness (quantified as spring constant). The spring stiffness measured in bullfrog tendons permitted less elastic energy storage than was predicted by a modelled, maximal muscle contraction. However, when muscle contractions were modelled using biologically relevant loading times for bullfrog jumps (50 ms), tendon stiffness actually maximized elastic energy storage. In contrast, grasshoppers, which are not time limited, exhibited spring stiffness that maximized elastic energy storage when modelled with a maximal muscle contraction. These findings demonstrate the significance of evolutionary variation in tendon and apodeme properties to realistic jumping contexts as well as the importance of considering the effect of muscle dynamics and behavioural constraints on energy storage in muscle-spring systems.

Resistance jump training may reverse the weakened biomechanical behavior of tendons of diabetic Wistar rats

ABSTRACT Background: resistance training is widely applied in non-diabetic physical protocol showing effectiveness in improving the tendon tissue. To address this gap, we assessed the effects of resistance training on aquatic environment, on the biomechanical properties of the calcaneal tendon of diabetic Wistar rats. Methods: 59 male Wistar rats were evaluated for 60 days, they were randomly divided into the following groups: Sedentary Control Group (SCG, n=15), Sedentary Diabetic Group (SDG, n=15), Trained Control Group (TCG, n=14) and Trained Diabetic Group (TDG, n=15). After randomization the animals from the SDG and the TDG were induced to Diabetes Mellitus by intraperitoneal injection of Streptozotocin (60 mg/kg). The animals on the trained groups performed resistance exercise that consisted of jumping in an aquatic environment. After nine weeks the calcaneal tendons were collected and tractioned on a conventional mechanical testing machine. Results: the analysis of biomechanical parameters showed lower values in elastic modulus (p=0.000), maximum strength tension (p=0.000) and energy/area (p=0.008) in TDG compared to SDG in addition to an increase on the cross-sectional area (p=0.002). There was no difference for the specific deformation variable. Conclusion: the training protocol used restored some biomechanical parameters of the calcaneal tendon in rats induced to diabetes, thus, resulting in an improvement of its mechanical efficiency.

Human ankle plantar flexor muscle-tendon mechanics and energetics during maximum acceleration sprinting

Tendon elastic strain energy is the dominant contributor to muscle-tendon work during steady-state running. Does this behaviour also occur for sprint accelerations? We used experimental data and computational modelling to quantify muscle fascicle work and tendon elastic strain energy for the human ankle plantar flexors (specifically soleus and medial gastrocnemius) for multiple foot contacts of a maximal sprint as well as for running at a steady-state speed. Positive work done by the soleus and medial gastrocnemius muscle fascicles decreased incrementally throughout the maximal sprint and both muscles performed more work for the first foot contact of the maximal sprint (FC1) compared with steady-state running at 5 m s(-1) (SS5). However, the differences in tendon strain energy for both muscles were negligible throughout the maximal sprint and when comparing FC1 to SS5. Consequently, the contribution of muscle fascicle work to stored tendon elastic strain energy was greater for FC1 compared with subsequent foot contacts of the maximal sprint and compared with SS5. We conclude that tendon elastic strain energy in the ankle plantar flexors is just as vital at the start of a maximal sprint as it is at the end, and as it is for running at a constant speed.

The diversity and evolution of locomotor muscle properties in anurans

Anuran jumping is a model system for linking muscle physiology to organismal performance. However, anuran species display substantial diversity in their locomotion, with some species performing powerful leaps from riverbanks or tree branches, while other species move predominantly via swimming, short hops or even diagonal-sequence gaits. Furthermore, many anurans with similar locomotion and morphology are actually convergent (e.g. multiple independent evolutions of 'tree frogs'), while closely related species may differ drastically, as with the walking toad (Melanophryniscus stelzneri) and bullfrog-like river toad (Phrynoides aspera) compared with other Bufonid toads. These multiple independent evolutionary changes in locomotion allow us to test the hypothesis that evolutionary increases in locomotor performance will be linked to the evolution of faster, high-power muscles. I tested the jumping, swimming and walking (when applicable) performance of 14 species of anurans and one salamander, followed by measurement of the contractile properties of the semimembranosus and plantaris longus muscles and anatomical measurements, using phylogenetic comparative methods. I found that increased jumping performance correlated to muscle contractile properties associated with muscle speed (e.g. time to peak tetanus, maximum shortening speed, peak isotonic power), and was tightly linked to relevant anatomical traits (e.g. leg length, muscle mass). Swimming performance was not correlated to jumping, and was correlated with fewer anatomical and muscular variables. Thus, muscle properties evolve along with changes in anatomy to produce differences in overall locomotor performance.

It's positive to be negative: Achilles tendon work loops during human locomotion

Ultrasound imaging is increasingly used with motion and force data to quantify tendon dynamics during human movement. Frequently, tendon dynamics are estimated indirectly from muscle fascicle kinematics (by subtracting muscle from muscle-tendon unit length), but there is mounting evidence that this Indirect approach yields implausible tendon work loops. Since tendons are passive viscoelastic structures, when they undergo a loading-unloading cycle they must exhibit a negative work loop (i.e., perform net negative work). However, prior studies using this Indirect approach report large positive work loops, often estimating that tendons return 2–5 J of elastic energy for every 1 J of energy stored. More direct ultrasound estimates of tendon kinematics have emerged that quantify tendon elongations by tracking either the muscle-tendon junction or localized tendon tissue. However, it is unclear if these yield more plausible estimates of tendon dynamics. Our objective was to compute tendon work loops and hysteresis losses using these two Direct tendon kinematics estimates during human walking. We found that Direct estimates generally resulted in negative work loops, with average tendon hysteresis losses of 2–11% at 1.25 m/s and 33–49% at 0.75 m/s (N = 8), alluding to 0.51–0.98 J of tendon energy returned for every 1 J stored. We interpret this finding to suggest that Direct approaches provide more plausible estimates than the Indirect approach, and may be preferable for understanding tendon energy storage and return. However, the Direct approaches did exhibit speed-dependent trends that are not consistent with isolated, in vitro tendon hysteresis losses of about 5–10%. These trends suggest that Direct estimates also contain some level of error, albeit much smaller than Indirect estimates. Overall, this study serves to highlight the complexity and difficulty of estimating tendon dynamics non-invasively, and the care that must be taken to interpret biological function from current ultrasound-based estimates.

Three dimensional reconstruction of energy stores for jumping in planthoppers and froghoppers from confocal laser scanning microscopy

Jumping in planthopper and froghopper insects is propelled by a catapult-like mechanism requiring mechanical storage of energy and its quick release to accelerate the hind legs rapidly. To understand the functional biomechanics involved in these challenging movements, the internal skeleton, tendons and muscles involved were reconstructed in 3-D from confocal scans in unprecedented detail. Energy to power jumping was generated by slow contractions of hind leg depressor muscles and then stored by bending specialised elements of the thoracic skeleton that are composites of the rubbery protein resilin sandwiched between layers of harder cuticle with air-filled tunnels reducing mass. The images showed that the lever arm of the power-producing muscle changed in magnitude during jumping, but at all joint angles would cause depression, suggesting a mechanism by which the stored energy is released. This methodological approach illuminates how miniaturized components interact and function in complex and rapid movements of small animals.

DOI:http://dx.doi.org/10.7554/eLife.23824.001

Effects of temperature and force requirements on muscle work and power output

Performance of muscle-powered movements depends on temperature through its effects on muscle contractile properties. In vitro stimulation of Cuban treefrog (Osteopilus septentrionalis) plantaris muscles reveals that interactions between force and temperature affect the mechanical work of muscle. At low temperatures (9-17°C), muscle work depends on temperature when shortening at any force, and temperature effects are greater at higher forces. At warmer temperatures (13-21°C), muscle work depends on temperature when shortening with intermediate and high forces (≥30% peak isometric tetanic force). Shortening velocity is most strongly affected by temperature at low temperatures and high forces. Power is also most strongly affected at low temperature intervals, but this effect is minimized at intermediate forces. Effects of temperature on muscle force explain these interactions; force production decreases at lower temperatures, increasing the challenge of moving a constant force relative to the muscle's capacity. These results suggest that animal performance that requires muscles to do work with low forces relative to a muscle's maximum force production will be robust to temperature changes, and this effect should be true whether muscle acts directly or through elastic-recoil mechanisms and whether force is prescribed (i.e. internal) or variable (i.e. external). Conversely, performance requiring muscles to shorten with relatively large forces is expected to be more sensitive to temperature changes.

In vivo muscle force and muscle power during near-maximal frog jumps

Frogs' outstanding jumping ability has been associated with a high power output from the leg extensor muscles. Two main theories have emerged to explain the high power output of the frog leg extensor muscles, either (i) the contractile conditions of all leg extensor muscles are optimized in terms of muscle length and speed of shortening, or (ii) maximal power is achieved through a dynamic catch mechanism that uncouples fibre shortening from the corresponding muscle-tendon unit shortening. As in vivo instantaneous power generation in frog hind limb muscles during jumping has never been measured directly, it is hard to distinguish between the two theories. In this study, we determined the instantaneous variable power output of the plantaris longus (PL) of Lithobates pipiens (also known as Rana pipiens), by directly measuring the in vivo force, length change, and speed of muscle and fibre shortening in near maximal jumps. Fifteen near maximal jumps (> 50cm in horizontal distance) were analyzed. High instantaneous peak power in PL (536 ± 47 W/kg) was achieved by optimizing the contractile conditions in terms of the force-length but not the force-velocity relationship, and by a dynamic catch mechanism that decouples fascicle shortening from muscle-tendon unit shortening. We also found that the extra-muscular free tendon likely amplifies the peak power output of the PL by modulating fascicle shortening length and shortening velocity for optimum power output, but not by releasing stored energy through recoiling as the tendon only started recoiling after peak PL power had been achieved.

Inverse dynamic modelling of jumping in the red-legged running frog, Kassina maculata

Although the red-legged running frog, Kassina maculata, is secondarily a walker/runner, it retains the capacity for multiple locomotor modes, including jumping at a wide range of angles (nearly 70 deg). Using simultaneous hind limb kinematics and single-foot ground reaction forces, we performed inverse dynamics analyses to calculate moment arms and torques about the hind limb joints during jumping at different angles in K. maculata. We show that forward thrust is generated primarily at the hip and ankle, while body elevation is primarily driven by the ankle. Steeper jumps are achieved by increased thrust at the hip and ankle and greater downward rotation of the distal limb segments. Because of its proximity to the GRF vector, knee posture appears to be important in controlling torque directions about this joint and, potentially, torque magnitudes at more distal joints. Other factors correlated with higher jump angles include increased body angle in the preparatory phase, faster joint openings and increased joint excursion, higher ventrally directed force, and greater acceleration and velocity. Finally, we demonstrate that jumping performance in K. maculata does not appear to be compromised by presumed adaptation to walking/running. Our results provide new insights into how frogs engage in a wide range of locomotor behaviours and the multi-functionality of anuran limbs.

Kinematic control of extreme jump angles in the red leg running frog (Kassina maculata)

The kinematic flexibility of frog hindlimbs enables multiple locomotor modes within a single species. Prior work has extensively explored maximum performance capacity in frogs; however, the mechanisms by which anurans modulate performance within locomotor modes remain unclear. We explored how Kassina maculata, a species known for both running and jumping abilities, modulates takeoff angle from horizontal to nearly vertical. Specifically, how do 3D motions of leg segments coordinate to move the center of mass (COM) upwards and forwards? How do joint rotations modulate jump angle? High-speed video was used to quantify 3D joint angles and their respective rotation axis vectors. Inverse kinematics was used to determine how hip, knee and ankle rotations contribute to components of COM motion. Independent of takeoff angle, leg segment retraction (rearward rotation) was twofold greater than adduction (downward rotation). Additionally, the joint rotation axis vectors reoriented through time suggesting dynamic shifts in relative roles of joints. We found two hypothetical mechanisms for increasing takeoff angle: Firstly, greater knee and ankle excursion increased shank adduction, elevating the COM. Secondly, during the steepest jumps the body rotated rapidly backwards to redirect the COM velocity. This rotation was not caused by pelvic angle extension, but rather by kinematic transmission from leg segments via reorientation of the joint rotation axes. We propose that K. maculata uses proximal leg retraction as the principal kinematic drive while dynamically tuning jump trajectory by knee and ankle joint modulation.

Robotic vertical jumping agility via series-elastic power modulation

Several arboreal mammals have the ability to rapidly and repeatedly jump vertical distances of 2 m, starting from rest. We characterize this performance by a metric we call vertical jumping agility. Through basic kinetic relations, we show that this agility metric is fundamentally constrained by available actuator power. Although rapid high jumping is an important performance characteristic, the ability to control forces during stance also appears critical for sophisticated behaviors. The animal with the highest vertical jumping agility, the galago (Galago senegalensis), is known to use a power-modulating strategy to obtain higher peak power than that of muscle alone. Few previous robots have used series-elastic power modulation (achieved by combining series-elastic actuation with variable mechanical advantage), and because of motor power limits, the best current robot has a vertical jumping agility of only 55% of a galago. Through use of a specialized leg mechanism designed to enhance power modulation, we constructed a jumping robot that achieved 78% of the vertical jumping agility of a galago. Agile robots can explore venues of locomotion that were not previously attainable. We demonstrate this with a wall jump, where the robot leaps from the floor to a wall and then springs off the wall to reach a net height that is greater than that accessible by a single jump. Our results show that series-elastic power modulation is an actuation strategy that enables a clade of vertically agile robots.

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.

The motor and the brake of the trailing leg in human walking: leg force control through ankle modulation and knee covariance

Human walking is a complex task, and we lack a complete understanding of how the neuromuscular system organizes its numerous muscles and joints to achieve consistent and efficient walking mechanics. Focused control of select influential task-level variables may simplify the higher-level control of steady-state walking and reduce demand on the neuromuscular system. As trailing leg power generation and force application can affect the mechanical efficiency of step-to-step transitions, we investigated how joint torques are organized to control leg force and leg power during human walking. We tested whether timing of trailing leg force control corresponded with timing of peak leg power generation. We also applied a modified uncontrolled manifold analysis to test whether individual or coordinated joint torque strategies most contributed to leg force control. We found that leg force magnitude was adjusted from step to step to maintain consistent leg power generation. Leg force modulation was primarily determined by adjustments in the timing of peak ankle plantar-flexion torque, while knee torque was simultaneously covaried to dampen the effect of ankle torque on leg force. We propose a coordinated joint torque control strategy in which the trailing leg ankle acts as a motor to drive leg power production while trailing leg knee torque acts as a brake to refine leg power production.

The Energy Amplification Characteristic Research of a Multimodal Actuator

A multimodal actuator is proposed to fulfil the different walking patterns of a power-assisted knee exoskeleton. With this actuator, the exoskeleton leg can realize several modes of operation, including series elastic actuation, stiff position control and energy storage and release. The energy amplification characteristics of the multimodal actuator in the series elastic mode are analysed. A dynamics model was established to study how series elasticity and the equivalent mass of transmission influence a power source, such as an electric motor. The results, in both simulation and experiment, show that series elasticity can amplify actuator power output, and the power output of a multimodal actuator is greater when the equivalent mass of the transmission mechanism is smaller. This research into multimodal actuator energy amplification supplies important insights into the design of artificial systems that can more closely approximate the performance of biological systems.