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

Universal optimal design in the vertebrate limb pattern and lessons for bioinspired design

This paper broadly summarizes the variation of design features found in vertebrate limbs and analyses the resultant versatility and multifunctionality in order to make recommendations for bioinspired robotics. The vertebrate limb pattern (e.g. shoulder, elbow, wrist and digits) has been proven to be very successful in many different applications in the animal kingdom. However, the actual level of optimality of the limb for each animal application is not clear because for some cases (e.g. whale flippers and bird wings), the basic skeletal layout is assumed to be highly constrained by evolutionary ancestry. This paper addresses this important and fundamental question of optimality by analysing six limbs with contrasting functions: human arm, whale flipper, bird wing, human leg, feline hindlimb and frog hindlimb. A central finding of this study is that the vertebrate limb pattern is highly versatile and optimal not just for arms and legs but also for flippers and wings. One key design feature of the vertebrate limb pattern is that of networks of segmented bones that enable smooth morphing of shapes as well as multifunctioning structures. Another key design feature is that of linkage mechanisms that fine-tune motions and mechanical advantage. A total of 52 biomechanical design features of the vertebrate limb are identified and tabulated for these applications. These tables can be a helpful reference for designers of bioinspired robotic and prosthetic limbs. The vertebrate limb has significant potential for the bioinspired design of robotic and prosthetic limbs, especially because of progress in the development of soft actuators.

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.

Research status and development trend of frog-inspired robots

The frog-inspired robots with amphibious locomotion ability have greatest application prospects and practical value in the fields of resource exploration and environmental reconnaissance. Although frog-inspired robots have been of interest over many years, research on frog-inspired amphibious robots is still in its infancy. Since the locomotion mechanism is the basis for the research of frog-inspired amphibious robots, the research methods of the single motion mechanism of frogs are firstly inductive analyzed, and a reference scheme is proposed to inspire the research on the amphibious motion mechanism. Then, we collect and introduce a systematic discussion of the research status of frog-inspired robots according to the locomotion mode. The characteristics of the robots are analyzed from the aspects of design concept, structural characteristics, driving method, and motion performance. Finally, the technical challenges faced by the research on the frog-inspired robots are analyzed, and the development trend is predicted. The authors hope that this study can provide an informative reference for future research in the direction of frog-inspired amphibious robot.

Dual spring force couples yield multifunctionality and ultrafast, precision rotation in tiny biomechanical systems

Small organisms use propulsive springs rather than muscles to repeatedly actuate high acceleration movements, even when constrained to tiny displacements and limited by inertial forces. Through integration of a large kinematic dataset, measurements of elastic recoil, energetic math modeling and dynamic math modeling, we tested how trap-jaw ants (Odontomachus brunneus) utilize multiple elastic structures to develop ultrafast and precise mandible rotations at small scales. We found that O. brunneus develops torque on each mandible using an intriguing configuration of two springs: their elastic head capsule recoils to push and the recoiling muscle-apodeme unit tugs on each mandible. Mandibles achieved precise, planar, circular trajectories up to 49,100 rad s-1 (470,000 rpm) when powered by spring propulsion. Once spring propulsion ended, the mandibles moved with unconstrained and oscillatory rotation. We term this mechanism a 'dual spring force couple', meaning that two springs deliver energy at two locations to develop torque. Dynamic modeling revealed that dual spring force couples reduce the need for joint constraints and thereby reduce dissipative joint losses, which is essential to the repeated use of ultrafast, small systems. Dual spring force couples enable multifunctionality: trap-jaw ants use the same mechanical system to produce ultrafast, planar strikes driven by propulsive springs and for generating slow, multi-degrees of freedom mandible manipulations using muscles, rather than springs, to directly actuate the movement. Dual spring force couples are found in other systems and are likely widespread in biology. These principles can be incorporated into microrobotics to improve multifunctionality, precision and longevity of ultrafast systems.

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.

Techniques for In Vivo Measurement of Ligament and Tendon Strain: A Review

The critical clinical and scientific insights achieved through knowledge of in vivo musculoskeletal soft tissue strains has motivated the development of relevant measurement techniques. This review provides a comprehensive summary of the key findings, limitations, and clinical impacts of these techniques to quantify musculoskeletal soft tissue strains during dynamic movements. Current technologies generally leverage three techniques to quantify in vivo strain patterns, including implantable strain sensors, virtual fibre elongation, and ultrasound. (1) Implantable strain sensors enable direct measurements of tissue strains with high accuracy and minimal artefact, but are highly invasive and current designs are not clinically viable. (2) The virtual fibre elongation method tracks the relative displacement of tissue attachments to measure strains in both deep and superficial tissues. However, the associated imaging techniques often require exposure to radiation, limit the activities that can be performed, and only quantify bone-to-bone tissue strains. (3) Ultrasound methods enable safe and non-invasive imaging of soft tissue deformation. However, ultrasound can only image superficial tissues, and measurements are confounded by out-of-plane tissue motion. Finally, all in vivo strain measurement methods are limited in their ability to establish the slack length of musculoskeletal soft tissue structures. Despite the many challenges and limitations of these measurement techniques, knowledge of in vivo soft tissue strain has led to improved clinical treatments for many musculoskeletal pathologies including anterior cruciate ligament reconstruction, Achilles tendon repair, and total knee replacement. This review provides a comprehensive understanding of these measurement techniques and identifies the key features of in vivo strain measurement that can facilitate innovative personalized sports medicine treatment.

Estimation of the force-velocity properties of individual muscles from measurement of the combined plantarflexor properties

The force-velocity (F-V) properties of isolated muscles or muscle fibers have been well studied in humans and other animals. However, determining properties of individual muscles in vivo remains a challenge because muscles usually function within a synergistic group. Modeling has been used to estimate the properties of an individual muscle from the experimental measurement of the muscle group properties. While this approach can be valuable, the models and the associated predictions are difficult to validate. In this study, we measured the in situ F-V properties of the maximally activated kangaroo rat plantarflexor group and used two different assumptions and associated models to estimate the properties of the individual plantarflexors. The first model (Mdl1) assumed that the percent contributions of individual muscles to group force and power were based upon the muscles' cross-sectional area and were constant across the different isotonic loads applied to the muscle group. The second model (Mdl2) assumed that the F-V properties of the fibers within each muscle were identical, but because of differences in muscle architecture, the muscles' contributions to the group properties changed with isotonic load. We compared the two model predictions with independent estimates of the muscles' contributions based upon sonomicrometry measurements of muscle length. We found that predictions from Mdl2 were not significantly different from sonomicrometry-based estimates while those from Mdl1 were significantly different. The results of this study show that incorporating appropriate fiber properties and muscle architecture is necessary to parse the individual muscles' contributions to the group F-V properties.

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.

Sarcomere Lengths Become More Uniform Over Time in Intact Muscle-Tendon Unit During Isometric Contractions

The seemingly uniform striation pattern of skeletal muscles, quantified in terms of sarcomere lengths (SLs), is inherently non-uniform across all hierarchical levels. The SL non-uniformity theory has been used to explain the force creep in isometric contractions, force depression following shortening of activated muscle, and residual force enhancement following lengthening of activated muscle. Our understanding of sarcomere contraction dynamics has been derived primarily from in vitro experiments using regular bright-field light microscopy or laser diffraction techniques to measure striation/diffraction patterns in isolated muscle fibers or myofibrils. However, the collagenous extracellular matrices present around the muscle fibers, as well as the complex architecture in the whole muscles may lead to different contraction dynamics of sarcomeres than seen in the in vitro studies. Here, we used multi-photon excitation microscopy to visualize in situ individual sarcomeres in intact muscle tendon units (MTUs) of mouse tibialis anterior (TA), and quantified the temporal changes of SL distribution as a function of SLs in relaxed and maximally activated muscles for quasi-steady state, fixed-end isometric conditions. The corresponding muscle forces were simultaneously measured using a force transducer. We found that SL non-uniformity, quantified by the coefficient of variation (CV) of SLs, decreased at a rate of 1.9–3.1%/s in the activated muscles, but remained constant in the relaxed muscles. The force loss during the quasi-steady state likely did not play a role in the decrease of SL non-uniformity, as similar force losses were found in the activated and relaxed muscles, but the CV of SLs in the relaxed muscles underwent negligible change over time. We conclude that sarcomeres in the mid-belly of maximally contracting whole muscles constantly re-organize their lengths into a more uniform pattern over time. The molecular mechanisms accounting for SL non-uniformity appear to differ in active and passive muscles, and need further elucidation, as do the functional implications of the SL non-uniformity.

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.

The sarcomere force-length relationship in an intact muscle-tendon unit

The periodic striation pattern in skeletal muscle reflects the length of the basic contractile unit: the sarcomere. More than half a century ago, Gordon, Huxley and Julian provided strong support for the 'sliding filament' theory through experiments with single muscle fibres. The sarcomere force-length (FL) relationship has since been extrapolated to whole muscles in an attempt to unravel in vivo muscle function. However, these extrapolations were frequently associated with non-trivial assumptions, such as muscle length changes corresponding linearly to SL changes. Here, we determined the in situ sarcomere FL relationship in a whole muscle preparation by simultaneously measuring muscle force and individual SLs in an intact muscle-tendon unit (MTU) using state-of-the-art multi-photon excitation microscopy. We found that despite great SL non-uniformity, the mean value of SLs measured from a minute volume of the mid-belly, equivalent to about 5×10-6% of the total muscle volume, agrees well with the theoretically predicted FL relationship, but only if the precise contractile filament lengths are known, and if passive forces from parallel elastic components and activation-associated sarcomere shortening are considered properly. As SLs are not uniformly distributed across the whole muscle and changes in SL with muscle length are location dependent, our results may not be valid for the proximal or distal parts of the muscle. The approach described here, and our findings, may encourage future studies to determine the role of SL non-uniformity in influencing sarcomere FL properties in different muscles and for different locations within single muscles.

Mechanical Demands at the Ankle Joint During Saut de Chat and Temps levé Jumps in Classically Trained Ballet Dancers

Background

During ballet, injuries to the Achilles tendon are associated with the take-off phase of various jumps.

Research question

The purpose of the study was to assess differences in mechanical demand on the body, specifically at the ankle, in two single-leg jumps commonly trained in ballet: a saut de chat (SDC) and a temps levé (TL).

Methods

Fifteen classically trained female dancers had 16 reflective markers placed on the lower body and each dancer performed each jump three times on a force plate. The marker position data and ground reaction forces (GRF) were captured synchronously at 250 Hz and 1000 Hz, respectively. Peak vertical GRF, mean rate of force development (RFD), peak ankle moment, and peak ankle power were determined and averaged across trials. Paired t-tests were used to determine differences between the SDC and the TL.

Results

When compared to the TL, the SDC displayed significantly higher peak vertical GRF (p = 0.003), RFD (p = 0.002), and peak ankle moment and power (p < 0.001). The effect sizes for these differences were large for all variables (Cohen’s d > 0.80).

Conclusion

The mechanical demand at the ankle joint is significantly greater for the SDC than the TL.

The influence of added mass on muscle activation and contractile mechanics during submaximal and maximal countermovement jumping in humans

Muscle contractile mechanics induced by the changing demands of human movement have the potential to influence our movement strategies. This study examined fascicle length changes of the triceps surae during jumping with added mass or increasing jump height to determine whether the chosen movement strategies were associated with relevant changes in muscle contractile properties. Sixteen participants jumped at sub-maximal and maximal intensities while total net work was matched via two distinct paradigms: (1) adding mass to the participant or (2) increasing jump height. Electromyography (EMG) and ultrasound analyses were performed to examine muscle activation, fascicle length and fascicle velocity changes of the triceps surae during jumping. Integrated EMG was significantly higher in the added mass paradigm with no difference in mean or maximal EMG, indicating that the muscle was activated for a significantly longer period of time but not activated to a greater intensity. Fascicle shortening velocity was slower with added mass compared than with increasing jump height; therefore, intrinsic force–velocity properties probably enabled increased force production. Improved fascicle contractile mechanics paired with a longer activation period probably produced a consistently larger fascicle force, enabling a greater impulse about the ankle joint. This may explain why previous research found that participants used an ankle-centred strategy for work production in the added mass paradigm and not in the jump height paradigm. The varied architecture of muscles within the lower limb may influence which muscles we choose to employ for work production under different task constraints.

On sarcomere length stability during isometric and post-active-stretch isometric contractions

Sarcomere length (SL) instability and SL non-uniformity have been used to explain fundamental properties of skeletal muscles, such as creep, force depression following active muscle shortening, and residual force enhancement following active stretching of muscles. Regarding residual force enhancement, it has been argued that active muscle stretching causes SL instability, thereby increasing SL non-uniformity. However, we recently showed that SL non-uniformity is not increased by active muscle stretching, but it remains unclear if SL stability is affected by active stretching. Here, we used single myofibrils of rabbit psoas and measured SL non-uniformity and SL instability during isometric contractions and for isometric contractions following active stretching at average SLs corresponding to the descending limb of the force-length relationship. We defined isometric contractions as contractions during which mean SL remained constant. SL instability was quantified by the rate of change of individual SLs over the course of steady state, isometric force; and SL non-uniformity was defined as deviations of SLs from the mean SL at an instant of time. We found that while the mean SL remained constant during isometric contraction, by definition, individual SLs did not. SLs were more stable in the force-enhanced, isometric state following active stretching compared to the isometric reference state. We also found that SL instability was not correlated with the rate of change of SL non-uniformity. Also, SL non-uniformity was not different in the isometric and the post-stretch isometric contractions. We conclude that since SL is more stable but similarly non-uniform in the force-enhanced compared to the corresponding isometric reference contraction, it appears unlikely that either SL instability or SL non-uniformity contribute to the residual force enhancement property of skeletal muscle.

Single sarcomere contraction dynamics in a whole muscle

The instantaneous sarcomere length (SL) is regarded as an important indicator of the functional properties of striated muscle. Previously, we found greater sarcomere elongations at the distal end compared to the mid-portion in the mouse tibialis anterior (TA) when the muscle was stretched passively. Here, we wanted to see if SL dispersions increase with activation, as has been observed in single myofibrils, and if SL dispersions differ for different locations in a muscle. Sarcomere lengths were measured at a mid- and a distal location of the TA in live mice using second harmonic generation imaging. Muscle force was measured using a tendon force transducer. We found that SL dispersions increased substantially from the passive to the active state, and were the same for the mid- and distal portions of TA. Sarcomere length non-uniformities within a segment of ~30 serial sarcomeres were up to 1.0 µm. We conclude from these findings that passive, mean SLs obtained from a single location are not necessarily representative of the distribution of SL in active muscle, and thus may be misinterpreted when deriving muscle mechanical properties, such as the force-length relationship. In view of these findings, it seems crucial to determine how SL distributions within a muscle relate to the most fundamental properties of muscle, such as the maximal isometric force.

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.

In Vivo Sarcomere Lengths Become More Non-uniform upon Activation in Intact Whole Muscle

The sarcomere force-length relationship has been extensively used to predict muscle force potential. The common practice is to measure the mean sarcomere length (SL) in a relaxed muscle at a single location and at a given length, and this mean SL is assumed to represent the SLs at other locations across the muscle. However, in a previous study, we found that SLs are highly non-uniform across an intact passive muscle. Moreover, SL non-uniformity increases during activation in single myofibril experiments. Myofibrils lack some structural proteins that comprise an intact muscle, and therefore, the increased SL dispersion upon activation seen in myofibrils may not occur in intact whole muscle. The objectives of the current study were (i) to measure the distribution of SLs in an activated intact muscle; and (ii) to assess the feasibility of using the mean SL measured at a specific location of the muscle to predict muscle force. Using state-of-the-art multi-photon microscopy and a miniature tendon force transducer, in vivo sarcomeres in the mouse tibialis anterior were imaged simultaneously with muscle force during isometric tetanic contractions. We found that in vivo SL dispersion increased substantially during activation and reached average differences of ~1.0 μm. These differences in SL are associated with theoretical force differences of 70-100% of the maximal isometric force. Furthermore, SLs measured at a single location in the passive muscle were poor predictors of active force potential. Although mean SLs in the activated muscle were better predictors of force potential, predicted forces still differed by as much as 35% from the experimentally measured maximal isometric forces.