Unconstrained muscle-tendon workloops indicate resonance tuning as a mechanism for elastic limb behavior during terrestrial 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.

A Conceptual Exploration of Hamstring Muscle-Tendon Functioning during the Late-Swing Phase of Sprinting: The Importance of Evidence-Based Hamstring Training Frameworks

An eccentrically lengthening, energy-absorbing, brake-driven model of hamstring function during the late-swing phase of sprinting has been widely touted within the existing literature. In contrast, an isometrically contracting, spring-driven model of hamstring function has recently been proposed. This theory has gained substantial traction within the applied sporting world, influencing understandings of hamstring function while sprinting, as well as the development and adoption of certain types of hamstring-specific exercises. Across the animal kingdom, both spring- and motor-driven muscle-tendon unit (MTU) functioning are frequently observed, with both models of locomotive functioning commonly utilising some degree of active muscle lengthening to draw upon force enhancement mechanisms. However, a method to accurately assess hamstring muscle-tendon functioning when sprinting does not exist. Accordingly, the aims of this review article are three-fold: (1) to comprehensively explore current terminology, theories and models surrounding muscle-tendon functioning during locomotion, (2) to relate these models to potential hamstring function when sprinting by examining a variety of hamstring-specific research and (3) to highlight the importance of developing and utilising evidence-based frameworks to guide hamstring training in athletes required to sprint. Due to the intensity of movement, large musculotendinous stretches and high mechanical loads experienced in the hamstrings when sprinting, it is anticipated that the hamstring MTUs adopt a model of functioning that has some reliance upon active muscle lengthening and muscle actuators during this particular task. However, each individual hamstring MTU is expected to adopt various combinations of spring-, brake- and motor-driven functioning when sprinting, in accordance with their architectural arrangement and activation patterns. Muscle function is intricate and dependent upon complex interactions between musculoskeletal kinematics and kinetics, muscle activation patterns and the neuromechanical regulation of tensions and stiffness, and loads applied by the environment, among other important variables. Accordingly, hamstring function when sprinting is anticipated to be unique to this particular activity. It is therefore proposed that the adoption of hamstring-specific exercises should not be founded on unvalidated claims of replicating hamstring function when sprinting, as has been suggested in the literature. Adaptive benefits may potentially be derived from a range of hamstring-specific exercises that vary in the stimuli they provide. Therefore, a more rigorous approach is to select hamstring-specific exercises based on thoroughly constructed evidence-based frameworks surrounding the specific stimulus provided by the exercise, the accompanying adaptations elicited by the exercise, and the effects of these adaptations on hamstring functioning and injury risk mitigation when sprinting.

Phase shift between joint rotation and actuation reflects dominant forces and predicts muscle activation patterns

During behavior, the work done by actuators on the body can be resisted by the body's inertia, elastic forces, gravity, or viscosity. The dominant forces that resist actuation have major consequences on the control of that behavior. In the literature, features and actuation of locomotion, for example, have been successfully predicted by nondimensional numbers (e.g. Froude number and Reynolds number) that generally express the ratio between two of these forces (gravitational, inertial, elastic, and viscous). However, animals of different sizes or motions at different speeds may not share the same dominant forces within a behavior, making ratios of just two of these forces less useful. Thus, for a broad comparison of behavior across many orders of magnitude of limb length and cycle period, a dimensionless number that includes gravitational, inertial, elastic, and viscous forces is needed. This study proposes a nondimensional number that relates these four forces: the phase shift (ϕ) between the displacement of the limb and the actuator force that moves it. Using allometric scaling laws, ϕ for terrestrial walking is expressed as a function of the limb length and the cycle period at which the limb steps. Scale-dependent values of ϕ are used to explain and predict the electromyographic (EMG) patterns employed by different animals as they walk.

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.

The force response of muscles to activation and length perturbations depends on length history

Recent studies have demonstrated that muscle force is not determined solely by activation under dynamic conditions, and that length history has an important role in determining dynamic muscle force. Yet, the mechanisms for how muscle force is produced under dynamic conditions remain unclear. To explore this, we investigated the effects of muscle stiffness, activation and length perturbations on muscle force. First, submaximal isometric contraction was established for whole soleus muscles. Next, the muscles were actively shortened at three velocities. During active shortening, we measured muscle stiffness at optimal muscle length (L0) and the force response to time-varying activation and length perturbations. We found that muscle stiffness increased with activation but decreased as shortening velocity increased. The slope of the relationship between maximum force and activation amplitude differed significantly among shortening velocities. Also, the intercept and slope of the relationship between length perturbation amplitude and maximum force decreased with shortening velocity. As shortening velocities were related to muscle stiffness, the results suggest that length history determines muscle stiffness and the history-dependent muscle stiffness influences the contribution of activation and length perturbations to muscle force. A two-parameter viscoelastic model including a linear spring and a linear damper in parallel with measured stiffness predicted history-dependent muscle force with high accuracy. The results and simulations support the hypothesis that muscle force under dynamic conditions can be accurately predicted as the force response of a history-dependent viscoelastic material to length perturbations.

Reduced Achilles Tendon Stiffness Disrupts Calf Muscle Neuromechanics in Elderly Gait

Older adults walk slower and with a higher metabolic energy expenditure than younger adults. In this review, we explore the hypothesis that age-related declines in Achilles tendon stiffness increase the metabolic cost of walking due to less economical calf muscle contractions and increased proximal joint work. This viewpoint may motivate interventions to restore ankle muscle-tendon stiffness, improve walking mechanics, and reduce metabolic cost in older adults.

The influence of in vivo mechanical behaviour of the Achilles tendon on the mechanics, energetics and apparent efficiency of bouncing gaits

In this study, we used kinematic, kinetic, metabolic and ultrasound analysis to investigate the role of elastic energy utilization on the mechanical and physiological demands of a movement task (hopping) that primarily involves the plantar-flexor muscles to determine the contribution of tendon work to total mechanical work and its relationship with apparent efficiency (AE) in bouncing gaits. Metabolic power (PMET) and (positive) mechanical power at the whole-body level (PMEC) were measured during hopping at different frequencies (2, 2.5, 3 and 3.5 Hz). The (positive) mechanical power produced during the Achilles tendon recoil phase (PTEN) was obtained by integrating ultrasound data with an inverse dynamic approach. As a function of hopping frequency, PMEC decreased steadily and PMET exhibited a U-shape behaviour, with a minimum at about 3 Hz. AE (PMEC/PMET) showed an opposite trend and was maximal (about 0.50) at the same frequency when PTEN was also highest. Positive correlations were observed: (i) between PTEN and AE (AE=0.22+0.15PTEN, R2=0.67, P<0.001) and the intercept of this relationship indicates the value of AE that should be expected when tendon work is nil; (ii) between AE and tendon gearing (Gt=Δmuscle-tendon unit length/Δmuscle belly length; R2=0.50, P<0.001), where a high Gt indicates that the muscle is contracting more isometrically, thus allowing the movement to be more economical (and efficient); (iii) between Gt and PTEN (R2=0.73, P<0.001), which indicates that Gt could play an important role in the tendon's capability to store and release mechanical power.

Mechanical advantage and joint function of the lower limb during hopping at different frequencies

Mechanical output at a joint level could be influenced by its leverage characteristics and by its functional behaviour and both could change to accommodate the demands of a given locomotor task. In this study, the mechanical power generated at the knee and ankle joints and their functional indexes (i.e. damper, strut, spring and motor like-function) were calculated by using 3D kinematic and kinetic data during hopping at 2, 2.5, 3 and 3.5 Hz. The effective mechanical advantage (i.e. the ratio between internal and external moment arm) of the knee (EMA_K) and ankle (EMA_A) and joint stiffness were calculated as well. Joint stiffness increased with frequency whereas positive and negative joint power decreased with it, the ankle power values being always larger (20-50%) than those at the knee. EMA_A reached its highest value (0.4) during the propulsive phase at 3 Hz whereas no significant changes in EMA_K were observed as a function of frequency in both the absorption and propulsive phases. Knee joint-functional index shifted from a spring to a strut-like function with increasing frequency (from 56 to 8% and from 4 to 51%, respectively) while the ankle operated mainly as a spring (from 90 to 53%), its damper and motor-like indexes being negligible at all frequencies (<5%). Therefore, in hopping, the knee works to dissipate mechanical energy (the combination of its damper and strut indexes increase from 23 to 72% at these frequencies) and the primary source of mechanical power is attributable to the elastic function of the ankle.

Tuning of feedforward control enables stable muscle force-length dynamics after loss of autogenic proprioceptive feedback

Animals must integrate feedforward, feedback and intrinsic mechanical control mechanisms to maintain stable locomotion. Recent studies of guinea fowl (Numida meleagris) revealed that the distal leg muscles rapidly modulate force and work output to minimize perturbations in uneven terrain. Here we probe the role of reflexes in the rapid perturbation responses of muscle by studying the effects of proprioceptive loss. We induced bilateral loss of autogenic proprioception in the lateral gastrocnemius muscle (LG) using self-reinnervation. We compared in vivo muscle dynamics and ankle kinematics in birds with reinnervated and intact LG. Reinnervated and intact LG exhibit similar steady state mechanical function and similar work modulation in response to obstacle encounters. Reinnervated LG exhibits 23ms earlier steady-state activation, consistent with feedforward tuning of activation phase to compensate for lost proprioception. Modulation of activity duration is impaired in rLG, confirming the role of reflex feedback in regulating force duration in intact muscle.

Spike-induced ordering: Stochastic neural spikes provide immediate adaptability to the sensorimotor system

The functional advantages of using a stochastically spiking neural network (sSNN) instead of a nonspiking neural network (NS-NN) have remained largely unknown. We developed an architecture which enabled the parametric adjustment of the spikiness (i.e., impulsive dynamics and stochasticity) of the sSNN output and observed that stochastic spikes instantaneously induced the ordered motion of a dynamical system. We demonstrated the benefits of sSNNs using a musculoskeletal bipedal walker and, moreover, showed that the decrease in the spikiness of motor neuron output leads to a reduction in adaptability. Stochastic spikes may aid the adaptation of a biological system to sudden perturbations or environmental changes. Our architecture can easily be connected to the conventional NS-NN and may superimpose the on-site adaptability.

Most biological neurons exhibit stochastic and spiking action potentials. However, the benefits of stochastic spikes versus continuous signals other than noise tolerance and energy efficiency remain largely unknown. In this study, we provide an insight into the potential roles of stochastic spikes, which may be beneficial for producing on-site adaptability in biological sensorimotor agents. We developed a platform that enables parametric modulation of the stochastic and discontinuous output of a stochastically spiking neural network (sSNN) to the rate-coded smooth output. This platform was applied to a complex musculoskeletal–neural system of a bipedal walker, and we demonstrated how stochastic spikes may help improve on-site adaptability of a bipedal walker to slippery surfaces or perturbation of random external forces. We further applied our sSNN platform to more general and simple sensorimotor agents and demonstrated four basic functions provided by an sSNN: 1) synchronization to a natural frequency, 2) amplification of the resonant motion in a natural frequency, 3) basin enlargement of the behavioral goal state, and 4) rapid complexity reduction and regular motion pattern formation. We propose that the benefits of sSNNs are not limited to musculoskeletal dynamics. Indeed, a wide range of the stability and adaptability of biological systems may arise from stochastic spiking dynamics.

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.

History-dependent perturbation response in limb muscle

Muscle mediates movement but movement is typically unsteady and perturbed. Muscle is known to behave non-linearly and with history-dependent properties during steady locomotion, but the importance of history dependence in mediating muscle function during perturbations remains less clear. To explore the capacity of muscles to mitigate perturbations during locomotion, we constructed a series of perturbations that varied only in kinematic history, keeping instantaneous position, velocity and time from stimulation constant. We found that the response of muscle to a perturbation is profoundly history dependent, varying 4-fold as baseline frequency changes, and dissipating energy equivalent to ∼6 times the kinetic energy of all the limbs in 5 ms (nearly 2400 W kg^-1). Muscle energy dissipation during a perturbation is predicted primarily by the force at the onset of the perturbation. This relationship holds across different frequencies and timings of stimulation. This history dependence behaves like a viscoelastic memory producing perturbation responses that vary with the frequency of the underlying movement.

Some Challenges of Playing with Power: Does Complex Energy Flow Constrain Neuromuscular Performance?

Many studies of the flow of energy between the body, muscles, and elastic elements highlight advantages of the storage and recovery of elastic energy. The spring-like action of structures associated with muscles allows for movements that are less costly, more powerful and safer than would be possible with contractile elements alone. But these actions also present challenges that might not be present if the pattern of energy flow were simpler, for example, if power were always applied directly from muscle to motions of the body. Muscle is under the direct control of the nervous system, and precise modulation of activity can allow for finely controlled displacement and force. Elastic structures deform under load in a predictable way, but are not under direct control, thus both displacement and the flow of energy act at the mercy of the mechanical interaction of muscle and forces associated with movement. Studies on isolated muscle-tendon units highlight the challenges of controlling such systems. A carefully tuned activation pattern is necessary for effective cycling of energy between tendon and the environment; most activation patterns lead to futile cycling of energy between tendon and muscle. In power-amplified systems, "elastic backfire" sometimes occurs, where energy loaded into tendon acts to lengthen active muscles, rather than accelerate the body. Classic models of proprioception that rely on muscle spindle organs for sensing muscle and joint displacement illustrate how elastic structures might influence sensory feedback by decoupling joint movement from muscle fiber displacements. The significance of the complex flow of energy between muscles, elastic elements and the body for neuromotor control is worth exploring.

Humans falling in holes: adaptations in lower-limb joint mechanics in response to a rapid change in substrate height during human hopping

In getting from here to there, we continuously negotiate complex environments and unpredictable terrain. Our ability to stay upright in the face of obstacles, such as holes in the ground, is quite remarkable. However, we understand relatively little about how humans adjust limb mechanical behaviour to recover from unexpected perturbations. In this study, we determined how the joints of the lower-limb respond to recover from a rapid, unexpected drop in substrate height during human hopping. We recorded lower-limb kinematics and kinetics while subjects performed steady-state hopping at their preferred frequency on an elevated platform (5, 10 and 20 cm). At an unknown time, we elicited an unexpected perturbation (i.e. a hole in the ground) via the rapid removal of the platform. Based on previous research in bipedal birds, we hypothesized (i) that distal joints would play an increased role in fall recovery when compared to steady-state hopping, and (ii) that patterns of joint power redistribution would be more pronounced with increases in perturbation height. Our results suggest that humans successfully recover from falling in a hole by increasing the energy absorbed predominantly in distal lower-limb joints (i.e. the ankle) across perturbation heights ranging from 5 to 10 cm. However, with increased perturbation height (20 cm) humans increase their reliance on the more proximal lower-limb joints (i.e. the knee and the hip) to absorb mechanical energy and stabilize fall recovery. Further investigations into the muscle-tendon mechanics underlying these joint-level responses will likely provide additional insights into the neuromotor control strategies used to regain the stability following unexpected perturbations and provide biological inspiration for the future design of wearable devices capable of performing within unpredictable environments.

Effect of processing and end groups on the crystal structure of polypeptoids studied by cryogenic electron microscopy at atomic length scales

Cryogenic electron microscopy at atomic length scales was used to study the structure of self-assembled crystalline nanosheets obtained from a series of polypeptoids with the same chain architecture but with different end groups. While long-range order is enhanced by slowing down the self-assembly process, the dominant crystalline motif was found to be a sensitive function of both processing details and end group chemistry. In some cases, adjacent rows of polypeptoid molecules adopt anti-parallel V-shaped side chain conformations. In other cases, adjacent rows of polypeptoid molecules adopt parallel V-shaped side chain conformations. Interestingly, the unit cell is rectangular in both cases with dimensions a = 4.5 Å and c = 50 Å. In all cases, long-range order, quantified by the average number of concatenated unit cells of the same type, is more prevalent along the a direction.

Distinct muscle-tendon interaction during running at different speeds and in different loading conditions

The interaction between the Achilles tendon and the triceps surae muscles seems to be modulated differently with various task configurations. Here we tested the hypothesis that the increased forces and ankle joint work during running under contrasting conditions (altered speed or load) would be met by different, time-dependent adjustments at the muscle-tendon level. Ultrasonography, electromyography, kinematics, and ground reaction force measurements were used to examine Achilles tendon, gastrocnemius, and soleus muscle mechanics in 16 runners in four different running conditions, consisting of a combination of two different speeds (preferred and +20% of preferred speed) and two loading conditions (unloaded and +20% of body mass). Positive ankle joint work increased similarly (+13%) with speed and load. Gastrocnemius and soleus muscle fascicle length and peak velocity were not altered by either condition, suggesting that contractile conditions are mostly preserved despite the constraints imposed in this experimental design. However, at higher running speed, tendon length changes were unaltered but mean muscle electromyographic activity increased in gastrocnemius (+10%, P < 0.01) and soleus (+14%, P < 0.01). Conversely, when loading was increased, mean muscle activity remained similar to unloaded conditions but the mean velocity of gastrocnemius fascicles was reduced and tendon recoil increased (+29%, P < 0.01). Collectively, these results suggest that the neuromuscular system meets increased mechanical demands by favoring economical force production when enough time is available. NEW & NOTEWORTHY We demonstrate that muscle-tendon mechanics are adjusted differently when running under constraints imposed by speed or load, despite comparable increases in work. The neuromuscular system likely modulates the way force is produced as a function of availability of time and potential energy.

Operating length and velocity of human vastus lateralis muscle during walking and running

According to the force-length-velocity relationships, the muscle force potential during locomotion is determined by the operating fibre length and velocity. We measured fascicle and muscle-tendon unit length and velocity as well as the activity of the human vastus lateralis muscle (VL) during walking and running. Furthermore, we determined the VL force-length relationship experimentally and calculated the force-length and force-velocity potentials (i.e. fraction of maximum force according to the force-length-velocity curves) for both gaits. During the active state of the stance phase, fascicles showed significantly (p < 0.05) smaller length changes (walking: 9.2 ± 4.7% of optimal length (L₀); running: 9.0 ± 8.4%L₀) and lower velocities (0.46 ± 0.36 L₀/s; 0.03 ± 0.83 L₀/s) compared to the muscle-tendon unit (walking: 19.7 ± 5.3%L₀, −0.94 ± 0.32 L₀/s; running: 34.5 ± 5.8%L₀, −2.59 ± 0.41 L₀/s). The VL fascicles operated close to optimum length (L₀ = 9.4 ± 0.11 cm) in both walking (8.6 ± 0.14 cm) and running (10.1 ± 0.19 cm), resulting in high force-length (walking: 0.92 ± 0.08; running: 0.91 ± 0.14) and force-velocity (0.91 ± 0.08; 0.97 ± 0.13) potentials. For the first time we demonstrated that, in contrast to the current general conception, the VL fascicles operate almost isometrically and close to L₀ during the active state of the stance phase of walking and running. The findings further verify an important contribution of the series-elastic element to VL fascicle dynamics.

Modeling age-related changes in muscle-tendon dynamics during cyclical contractions in the rat gastrocnemius

Efficient muscle-tendon performance during cyclical tasks is dependent on both active and passive mechanical tissue properties. Here we examine whether age-related changes in the properties of muscle-tendon units (MTUs) compromise their ability to do work and utilize elastic energy storage. We empirically quantified passive and active properties of the medial gastrocnemius muscle and material properties of the Achilles tendon in young (∼6 mo) and old (∼32 mo) rats. We then used these properties in computer simulations of a Hill-type muscle model operating in series with a Hookean spring. The modeled MTU was driven through sinusoidal length changes and activated at a phase that optimized muscle-tendon tuning to assess the relative contributions of active and passive elements to the force and work in each cycle. In physiologically realistic simulations where young and old MTUs started at similar passive forces and developed similar active forces, the capacity of old MTUs to store elastic energy and produce positive work was compromised. These results suggest that the observed increase in the metabolic cost of locomotion with aging may be in part due to the recruitment of additional muscles to compensate for the reduced work at the primary MTU. Furthermore, the age-related increases in passive stiffness coupled with a reduced active force capacity in the muscle can lead to shifts in the force-length and force-velocity operating range that may significantly impact mechanical and metabolic performance. Our study emphasizes the importance of the interplay between muscle and tendon mechanical properties in shaping MTU performance during cyclical contractions.