The interaction of in vivo muscle operating lengths and passive stiffness in rat hindlimbs.

The operating length of a muscle is a key determinant of its ability to produce force in vivo. Muscles that operate near the peak of their force-length relationship will generate higher forces whereas muscle operating at relatively short length may be safe from sudden lengthening perturbations and subsequent damage. At longer lengths, passive mechanical properties have the potential to contribute to force or constrain operating length with stiffer muscle-tendon units theoretically being restricted to shorter lengths. Connective tissues typically increase in density during aging, thus increasing passive muscle stiffness and potentially limiting the operating lengths of muscle during locomotion. Here, we compare in vivo and in situ muscle strain from the medial gastrocnemius in young (7 months old) and aged (30-32 months old) rats presumed to have varying passive tissue stiffness to test the hypothesis that stiffer muscles operate at shorter lengths relative to their force-length relationship. We measured in vivo muscle operating length during voluntary locomotion on inclines and flat trackways and characterized the muscle force-length relationship of the medial gastrocnemius using fluoromicrometry. Although no age-related results were evident, rats of both age groups demonstrated a clear relationship between passive stiffness and in vivo operating length, such that shorter operating lengths were significantly correlated with greater passive stiffness. Our results suggest that increased passive stiffness may restrict muscles to operating lengths shorter than optimal lengths, potentially limiting force capacity during locomotion.

Linking in vivo muscle dynamics to force-length and force-velocity properties reveals that guinea fowl lateral gastrocnemius operates at shorter than optimal lengths.

The isometric force-length (F-L) and isotonic force-velocity (F-V) relationships characterize the contractile properties of skeletal muscle under controlled conditions, yet it remains unclear how these properties relate to in vivo muscle function. Here, we map the in situ F-L and F-V characteristics of guinea fowl (Numida meleagris) lateral gastrocnemius (LG) to the in vivo operating range during walking and running. We test the hypothesis that muscle fascicles operate on the F-L plateau, near the optimal length for force (L0) and near velocities that maximize power output (Vopt) during walking and running. We found that in vivo LG velocities are consistent with optimizing power during work production, and economy of force at higher loads. However, LG does not operate near L0 at higher loads. LG length was near L0 at the time of electromyography (EMG) onset but shortened rapidly such that force development during stance occurred on the ascending limb of the F-L curve, around 0.8L0. Shortening across L0 in late swing might optimize potential for rapid force development near the swing-stance transition, providing resistance to unexpected perturbations that require rapid force development. We also found evidence of in vivo passive force rise in late swing, without EMG activity, at lengths where in situ passive force is zero, suggesting that dynamic viscoelastic effects contribute to in vivo force development. Comparison of in vivo operating ranges with F-L and F-V properties suggests the need for new approaches to characterize muscle properties in controlled conditions that more closely resemble in vivo dynamics.

Hindlimb muscle spindles inform preparatory forelimb coordination prior to landing in toads.

Animals move across a wide range of surface conditions in real-world environments to acquire resources and avoid predation. To effectively navigate a variety of surfaces, animals rely on several mechanisms including intrinsic mechanical responses, spinal-level central pattern generators, and neural commands that require sensory feedback. Muscle spindle Ia afferents play a critical role in providing sensory feedback and informing motor control strategies across legged vertebrate locomotion, which is apparent in cases where this sensory input is compromised. Here, we tested the hypothesis that spindle Ia afferents from hindlimb muscles are important for coordinating forelimb landing behavior in the cane toad. We performed bilateral sciatic nerve reinnervations to ablate the stretch reflex from distal hindlimb muscles while allowing for motor neuron recovery. We found that toads significantly delayed the onset and reduced the activation duration of their elbow extensor muscle following spindle Ia afferent ablation in the hindlimbs. However, reinnervated toads achieved similar elbow extension at touchdown to that of their pre-surgery state. Our results suggest that while toads likely tuned the activation timing of forelimb muscles in response to losing Ia afferent sensation from the hindlimbs they were likely able to employ compensatory strategies that allowed them to continue landing effectively with reduced sensory information during take-off. These findings indicate muscle spindle Ia afferents may contribute to tuning complex movements involving multiple limbs.

Modulation of limb mechanics in alligators moving across varying grades.

Graded substrates require legged animals to modulate their limb mechanics to meet locomotor demands. Previous work has elucidated strategies used by cursorial animals with upright limb posture, but it remains unclear how sprawling species such as alligators transition between grades. We measured individual limb forces and 3D kinematics as alligators walked steadily across level, 15 deg incline and 15 deg decline conditions. We compared our results with the literature to determine how limb posture alters strategies for managing the energetic variation that accompanies shifts in grade. We found that juvenile alligators maintain spatiotemporal characteristics of gait and locomotor speed while selectively modulating craniocaudal impulses (relative to level) when transitioning between grades. Alligators seem to accomplish this using a variety of kinematic strategies, but consistently sprawl both limb pairs outside of the parasagittal plane during decline walking. This latter result suggests alligators and other sprawling species may use movements outside of the parasagittal plane as an axis of variation to modulate limb mechanics when transitioning between graded substrates. We conclude that limb mechanics during graded locomotion are fairly predictable across quadrupedal species, regardless of body plan and limb posture, with hindlimbs playing a more propulsive role and forelimbs functioning to dissipate energy. Future work will elucidate how shifts in muscle properties or function underlie such shifts in limb kinematics.

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.

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.

The Multi-Scale, Three-Dimensional Nature of Skeletal Muscle Contraction.

Muscle contraction is a three-dimensional process, as anyone who has observed a bulging muscle knows. Recent studies suggest that the three-dimensional nature of muscle contraction influences its mechanical output. Shape changes and radial forces appear to be important across scales of organization. Muscle architectural gearing is an emerging example of this process.

Fatigue resistant jaw muscles facilitate long-lasting courtship behaviour in the southern alligator lizard (Elgaria multicarinata).

The southern alligator lizard (Elgaria multicarinata) exhibits a courtship behaviour during which the male firmly grips the female's head in his jaws for many hours at a time. This extreme behaviour counters the conventional wisdom that reptilian muscle is incapable of powering high-endurance behaviours. We conducted in situ experiments in which the jaw-adductor muscles of lizards were stimulated directly while bite force was measured simultaneously. Fatigue tests were performed by stimulating the muscles with a series of tetanic trains. Our results show that a substantial sustained force gradually develops during the fatigue test. This sustained force persists after peak tetanic forces have declined to a fraction of their initial magnitude. The observed sustained force during in situ fatigue tests is consistent with the courtship behaviour of these lizards and probably reflects physiological specialization. The results of molecular analysis reveal that the jaw muscles contain masticatory and tonic myosin fibres. We propose that the presence of tonic fibres may explain the unusual sustained force properties during mate-holding behaviour. The characterization of muscle properties that facilitate extreme performance during specialized behaviours may reveal general mechanisms of muscle function, especially when done in light of convergently evolved systems exhibiting similar performance characteristics.

Lowering metabolic rate mitigates muscle atrophy in western fence lizards.

Extended periods of skeletal muscle disuse can cause a significant loss of contractile proteins, which compromises the ability to generate force, mechanical work or power, thus compromising locomotor performance. Several hibernating organisms can resist muscle atrophy despite months of inactivity. This resistance has been attributed to a reduction in body temperature and metabolic rate and activation of physiological pathways that counteract pathways of protein degradation. However, in these systems, such strategies are not mutually exclusive and the effects of these mechanisms can be difficult to separate. In this study, we used the western fence lizard, Sceloporus occidentalis, as an ectothermic model to determine whether a reduction in metabolic rate is sufficient to resist muscle atrophy. We induced atrophy through sciatic denervation of the gastrocnemius muscle and housed lizards at either 15 or 30°C for 6-7 weeks. Following treatment, we used muscle ergometry to measure maximum isometric force, the force-velocity relationship and contractile dynamics in the gastrocnemius. This approach allowed us to relate changes in the size and morphology to functional metrics of contractile performance. A subset of samples was used to histologically determine muscle fiber types. At 30°C, denervated muscles had a larger reduction in muscle mass, physiological cross-sectional area and maximum isometric force than at 15°C. Maximum shortening velocity of the muscle decreased slightly in animals housed at 30°C but did not change in those housed at 15°C. Our results suggest that metabolic rate alone can influence the rate of muscle atrophy and that ectothermic vertebrates may have an intrinsic mechanism to resist muscle atrophy during seasonal periods of inactivity.

Stuck in gear: age-related loss of variable gearing in skeletal muscle.

Skeletal muscles power a broad diversity of animal movements, despite only being able to produce high forces over a limited range of velocities. Pennate muscles use a range of gear ratios, the ratio of muscle shortening velocity to fiber shortening velocity, to partially circumvent these force-velocity constraints. Muscles operate with a high gear ratio at low forces; fibers rotate to greater angles of pennation, enhancing velocity but compromising force. At higher forces, muscles operate with a lower gear ratio; fibers rotate little so limiting muscle shortening velocity, but helping to preserve force. This ability to shift gears is thought to be due to the interplay of contractile force and connective tissue constraints. In order to test this hypothesis, gear ratios were determined in the medial gastrocnemius muscles of both healthy young rats, and old rats where the interaction between contractile and connective tissue properties was assumed to be disrupted. Muscle fiber and aponeurosis stiffness increased with age (P<0.05) from 19.1±5.0 kPa and 188.5±24.2 MPa, respectively, in young rats to 39.1±4.2 kPa and 328.0±48.3 MPa in old rats, indicating a mechanical change in the interaction between contractile and connective tissues. Gear ratio decreased with increasing force in young (P<0.001) but not old (P=0.72) muscles, indicating that variable gearing is lost in old muscle. These findings support the hypothesis that variable gearing results from the interaction between contractile and connective tissues and suggest novel explanations for the decline in muscle performance with age.

Timing matters: tuning the mechanics of a muscle-tendon unit by adjusting stimulation phase during cyclic contractions.

A growing body of research on the mechanics and energetics of terrestrial locomotion has demonstrated that elastic elements acting in series with contracting muscle are critical components of sustained, stable and efficient gait. Far fewer studies have examined how the nervous system modulates muscle-tendon interaction dynamics to optimize 'tuning' or meet varying locomotor demands. To explore the fundamental neuromechanical rules that govern the interactions between series elastic elements (SEEs) and contractile elements (CEs) within a compliant muscle-tendon unit (MTU), we used a novel work loop approach that included implanted sonomicrometry crystals along muscle fascicles. This enabled us to decouple CE and SEE length trajectories when cyclic strain patterns were applied to an isolated plantaris MTU from the bullfrog (Lithobates catesbeianus). Using this approach, we demonstrate that the onset timing of muscle stimulation (i.e. stimulation phase) that involves a symmetrical MTU stretch-shorten cycle during active force production results in net zero mechanical power output, and maximal decoupling of CE and MTU length trajectories. We found it difficult to 'tune' the muscle-tendon system for strut-like isometric force production by adjusting stimulation phase only, as the zero power output condition involved significant positive and negative mechanical work by the CE. A simple neural mechanism - adjusting muscle stimulation phase - could shift an MTU from performing net zero to net positive (energy producing) or net negative (energy absorbing) mechanical work under conditions of changing locomotor demand. Finally, we show that modifications to the classical work loop paradigm better represent in vivo muscle-tendon function during locomotion.

Geared up to stretch: pennate muscle behavior during active lengthening.

Many locomotor activities require muscles to actively lengthen, dissipate energy and decelerate the body. These eccentric contractions can disrupt cytoskeletal structures within myofibrils and reduce force output. We examined how architectural features of pennate muscles can provide a protective mechanism against eccentric muscle damage by limiting fascicle lengthening. It has been previously shown that the angled fibers of pennate muscles change orientation when shortening. This change in fiber orientation can amplify fascicle shortening, resulting in a velocity advantage at the level of the muscle-tendon unit (MTU) that is characterized by a gear ratio (MTU velocity/fascicle velocity). A muscle's architectural gear ratio (AGR) has been shown to vary as a function of force during shortening, while AGR during lengthening remains largely unknown. We independently measured fascicle length and MTU length in vitro in the bullfrog plantaris. We characterized the muscle's force-velocity curve and AGR during both shortening and lengthening across a broad range of forces (10-190% peak isometric force). AGR was measured during the isotonic portion of each contraction, to eliminate possible contributions of series elasticity to MTU length changes. We found that gear ratio varies with force during both shortening and lengthening contractions. The highest AGR was observed during lengthening contractions, indicating that lengthening of the MTU can occur with relatively little stretch of the fascicle. As fascicle strain is considered an important determinant of muscle damage, a high gear ratio may afford pennate muscles protection against the damaging effects of active lengthening.

Reduce torques and stick the landing: limb posture during landing in toads.

A controlled landing, where an animal does not crash or topple, requires enough stability to allow muscles to effectively dissipate mechanical energy. Toads (Rhinella marina) are exemplary models for understanding the mechanics and motor control of landing given their ability to land consistently during bouts of continuous hopping. Previous studies in anurans have shown that ground reaction forces (GRFs) during landing are significantly higher compared with takeoff and can potentially impart large torques about the center of mass (COM), destabilizing the body at impact. We predict that in order to minimize such torques, toads will align their COM with the GRF vector during the aerial phase in anticipation of impact. We combined high-speed videography and force-plate ergometry to quantify torques at the COM and relate the magnitude of torques to limb posture at impact. We show that modulation of hindlimb posture can shift the position of the COM by about 20% of snout-vent length. Rapid hindlimb flexion during the aerial phase of a hop moved the COM anteriorly and reduced torque by aligning the COM with the GRF vector. We found that the addition of extrinsic loads did not significantly alter landing behavior but did change the torques experienced at impact. We conclude that anticipatory hindlimb flexion during the aerial phase of a hop is a critical feature of a mechanically stable landing that allows toads to quickly string together multiple, continuous hops.

Architectural gear ratio depends on actuator spacing in a physical model of pennate muscle.

Pennate muscles are defined by the architectural arrangement of their muscle fibers, which run at an angle to the primary axis of muscle shortening. Pennation angles can vary dynamically over the course of individual contractions, influencing the speed and distance of muscle shortening. Despite their relevance to muscle performance, the physical mechanisms that drive dynamic changes in pennation angle remain poorly understood. Muscle fibers bulge radially as they shorten, a consequence of maintaining a constant internal fluid volume, and we hypothesized that radial interactions between tightly packed muscle fibers are essential to dynamic pennation angle changes. To explore this, we built physical models of pennate muscles in which the radial distance between fiber-like actuators could be experimentally altered. Models were built from pennate arrays of McKibben actuators, a type of pneumatic actuator that forcefully shortens and bulges radially when inflated with compressed air. Consistent with past studies of biological muscle and engineered pennate actuators, we found that the magnitude of pennation angle change during contraction varied with load. Importantly, however, we found that pennation angle changes were also strongly influenced by the radial distance between neighboring McKibben actuators. Increasing the radial distance between neighboring actuators reduced pennation angle change during contraction and effectively eliminated variable responses to load. Radial interactions between muscle fibers are rarely considered in theoretical and experimental analyses of pennate muscle; however, these findings suggest that radial interactions between fibers drive pennation angle changes and influence pennate muscle performance. Our results provide insight into the fundamental mechanism underlying dynamic pennation angle changes in biological muscle and highlight design considerations that can inform the development of engineered pennate arrays.

Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates.

Biological springs can be used in nature for energy conservation and ultra-fast motion. The loading and unloading rates of elastic materials can play an important role in determining how the properties of these springs affect movements. We investigate the mechanical energy efficiency of biological springs (American bullfrog plantaris tendons and guinea fowl lateral gastrocnemius tendons) and synthetic elastomers. We measure these materials under symmetric rates (equal loading and unloading durations) and asymmetric rates (unequal loading and unloading durations) using novel dynamic mechanical analysis measurements. We find that mechanical efficiency is highest at symmetric rates and significantly decreases with a larger degree of asymmetry. A generalized one-dimensional Maxwell model with no fitting parameters captures the experimental results based on the independently characterized linear viscoelastic properties of the materials. The model further shows that a broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry on efficiency. Overall, our study provides valuable insights into the interplay between material properties and unloading dynamics in both biological and synthetic elastic systems.

Anticipatory motor patterns limit muscle stretch during landing in toads.

To safely land after a jump or hop, muscles must be actively stretched to dissipate mechanical energy. Muscles that dissipate energy can be damaged if stretched to long lengths. The likelihood of damage may be mitigated by the nervous system, if anticipatory activation of muscles prior to impact alters the muscle's operating length. Anticipatory motor recruitment is well established in landing studies and motor patterns have been shown to be modulated based on the perceived magnitude of the impact. In this study, we examine whether motor recruitment in anticipation of landing can serve a protective function by limiting maximum muscle length during a landing event. We use the anconeus muscle of toads, a landing muscle whose recruitment is modulated in anticipation of landing. We combine in vivo measurements of muscle length during landing with in vitro characterization of the force-length curve to determine the muscle's operating length. We show that muscle shortening prior to impact increases with increasing hop distance. This initial increase in muscle shortening functions to accommodate the larger stretches required when landing after long hops. These predictive motor strategies may function to reduce stretch-induced muscle damage by constraining maximum muscle length, despite variation in the magnitude of impact.

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 power attenuation by tendon during energy dissipation.

An important function of skeletal muscle is deceleration via active muscle fascicle lengthening, which dissipates movement energy. The mechanical interplay between muscle contraction and tendon elasticity is critical when muscles produce energy. However, the role of tendon elasticity during muscular energy dissipation remains unknown. We tested the hypothesis that tendon elasticity functions as a mechanical buffer, preventing high (and probably damaging) velocities and powers during active muscle fascicle lengthening. We directly measured lateral gastrocnemius muscle force and length in wild turkeys during controlled landings requiring rapid energy dissipation. Muscle-tendon unit (MTU) strain was measured via video kinematics, independent of muscle fascicle strain (measured via sonomicrometry). We found that rapid MTU lengthening immediately following impact involved little or no muscle fascicle lengthening. Therefore, joint flexion had to be accommodated by tendon stretch. After the early contact period, muscle fascicles lengthened and absorbed energy. This late lengthening occurred after most of the joint flexion, and was thus mainly driven by tendon recoil. Temporary tendon energy storage led to a significant reduction in muscle fascicle lengthening velocity and the rate of energy absorption. We conclude that tendons function as power attenuators that probably protect muscles against damage from rapid and forceful lengthening during energy dissipation.

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

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

Variable gearing in pennate muscles.

Muscle fiber architecture, i.e., the physical arrangement of fibers within a muscle, is an important determinant of a muscle's mechanical function. In pennate muscles, fibers are oriented at an angle to the muscle's line of action and rotate as they shorten, becoming more oblique such that the fraction of force directed along the muscle's line of action decreases throughout a contraction. Fiber rotation decreases a muscle's output force but increases output velocity by allowing the muscle to function at a higher gear ratio (muscle velocity/fiber velocity). The magnitude of fiber rotation, and therefore gear ratio, depends on how the muscle changes shape in the dimensions orthogonal to the muscle's line of action. Here, we show that gear ratio is not fixed for a given muscle but decreases significantly with the force of contraction (P < 0.0001). We find that dynamic muscle-shape changes promote fiber rotation at low forces and resist fiber rotation at high forces. As a result, gearing varies automatically with the load, to favor velocity output during low-load contractions and force output for contractions against high loads. Therefore, muscle-shape changes act as an automatic transmission system allowing a pennate muscle to shift from a high gear during rapid contractions to low gear during forceful contractions. These results suggest that variable gearing in pennate muscles provides a mechanism to modulate muscle performance during mechanically diverse functions.