The integrated function of muscles and tendons during locomotion

The mechanical roles of tendon and muscle contractile elements during locomotion are often considered independently, but functionally they are tightly integrated. Tendons can enhance muscle performance for a wide range of locomotor activities because muscle-tendon units shorten and lengthen at velocities that would be mechanically unfavorable for muscle fibers functioning alone. During activities that require little net mechanical power output, such as steady-speed running, tendons reduce muscular work by storing and recovering cyclic changes in the mechanical energy of the body. Tendon stretch and recoil not only reduces muscular work, but also allows muscle fibers to operate nearly isometrically, where, due to the force-velocity relation, skeletal muscle fibers develop high forces. Elastic energy storage and recovery in tendons may also provide a key mechanism to enable individual muscles to alter their mechanical function, from isometric force-producers during steady speed running to actively shortening power-producers during high-power activities like acceleration or uphill running. Evidence from studies of muscle contraction and limb dynamics in turkeys suggests that during running accelerations work is transferred directly from muscle to tendon as tendon stretch early in the step is powered by muscle shortening. The energy stored in the tendon is later released to help power the increase in energy of the body. These tendon length changes redistribute muscle power, enabling contractile elements to shorten at relatively constant velocities and power outputs, independent of the pattern of flexion/extension at a joint. Tendon elastic energy storage and recovery extends the functional range of muscles by uncoupling the pattern of muscle fiber shortening from the pattern of movement of the body.     

Effect of muscle contraction levels on the force-length relationship of the human Achilles tendon during lengthening of the triceps surae muscle-tendon unit

Findings from animal experiments are sometimes contradictory to the idea that the tendon structure is a simple elastic spring in series with muscle fibers, and suggest influence of muscle contraction on the tendon mechanical properties. The purpose of the present study was to investigate the influence of muscle contraction levels on the force-length relationship of the human Achilles tendon during lengthening of the triceps surae muscle-tendon unit. For seven subjects, ankle dorsiflexion was performed without (passive condition) and with contraction of plantar flexor muscles (eccentric conditions, at 3 contraction levels) on an isokinetic dynamometer. Deformation of the Achilles tendon during each trial was measured using ultrasonography. The Achilles tendon force corresponding to the tendon elongation of 10mm in the passive condition was significantly smaller than those in the eccentric conditions (p<0.05 or p<0.01). Within the eccentric conditions, the Achilles tendon force corresponding to the tendon elongation of 10mm was significantly greater in the maximal contraction level than those in submaximal eccentric conditions (p<0.05 or p<0.01). In addition, the tendon stiffness was greater in higher contraction levels (p<0.05 or p<0.01). Present results suggest that the human tendon structure is not a simple elastic spring in series with muscle fibers.     

Elastic mechanisms in primate locomotion

Tendons that stretch elastically and recoil, as the forces on them rise and fall, can save energy in running by enabling the animal to make do with shorter or slower muscle fascicles, that can generate force more economically. Non-human primates have rather long fascicles and thick tendons in their distal leg muscles and so seem poorly adapted to save energy in this way. Additional savings are made possible by the elastic compliance of ligaments in the foot. Though tendon and ligament compliance tend to save energy, the compliance of branches tends to increase the energy cost of arboreal locomotion.     

Behavior of fascicles and tendinous structures of human gastrocnemius during vertical jumping.

Behavior of fascicles and tendinous structures of human gastrocnemius medialis (MG) was determined by use of ultrasonography in vivo during jumping. Eight male subjects jumped vertically without countermovement (squat jump, SQJ). Simultaneously, kinematics, kinetics, and electromyography from lower leg muscles were recorded during SQJ. During phase I (-350 to -100 ms before toe-off), muscle-tendon complex (MTC) length was almost constant. Fascicles, however, shortened by 26%, and tendinous structures were stretched by 6%, storing elastic energy of 4.9 J during phase I. During phase II (-100 ms to toe-off), although fascicles generated force quasi-isometrically, MTC shortened rapidly by 5.3%, releasing prestored elastic energy with a higher peak positive power than that of fascicles. Also, the compliance of tendinous structures in vivo was somewhat higher than that of external tendon used in the simulation studies. The results demonstrate that the compliance of tendinous structures, together with no yielding of muscle fibers, allows MTC to effectively generate relatively large power at a high joint angular velocity region during the last part of push-off.     

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s^-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.     

The Control of Mechanical Power in Insect Flight

SYNOPSIS. The cost of locomotion is rarely constant, but rathervaries as an animal changes speed and direction. Ultimately,the locomotory muscles of an animal must compensate for thesechanging requirements by varying the amount of mechanical powerthat they produce. In this paper, we consider the mechanismsby which the mechanical power generated by the asynchronousflight muscles of the fruit fly, Drosophila melanogaster, isregulated to match the changing requirements during flight controlbehaviors. Our data come from individual flies flown in a flightarena under conditions in which stroke kinematics, total metaboliccost, and flight force are simultaneously measured. In orderto increase force production, flies must increase wing beatfrequency and wing stroke amplitude. Theory predicts that thesekinematics changes should result in a roughly cubic increasein the mechanical power requirements for flight. However, themechanical energy generated by muscle should increase only linearlywith stroke amplitude and frequency. This discrepancy impliesthat flight muscles must either recruit myofibrils or increaseactivation in order to generate sufficient mechanical powerto sustain elevated force production. By comparing respirometricallymeasured total metabolic power with kinematically estimatedmechanical power, we have calculated that the stress in theflight muscles of Drosophila must increase by 50% to accommodatea doubling of flight force. Electrophysiological evidence suggeststhat this change in stress may be accomplished by an increasedneural drive to the asynchronous muscles, which in turn mayact to recruit additional cross bridges through an increasein cytosolic calcium.     

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.     

Force-length properties and functional demands of cat gastrocnemius, soleus and plantaris muscles.

The purpose of this study was to measure isometric force-length properties of cat soleus, gastrocnemius and plantaris muscle-tendon units, and to relate these properties to the functional demands of these muscles during everyday locomotor activities. Isometric force-length properties were determined using an in situ preparation, where forces were measured using buckle-type tendon transducers, and muscle-tendon unit lengths were quantified through ankle and knee joint configurations. Functional demands of the muscles were assessed using direct muscle force measurements in freely moving animals. Force-length properties and functional demands were determined for soleus, gastrocnemius and plantaris muscles simultaneously in each animal. The results suggest that isometric force-length properties of cat soleus, gastrocnemius and plantaris muscles, as well as the region of the force-length relation that is used during everyday locomotor tasks, match the functional demands.     

Contractile behavior of the forelimb digital flexors during steady-state locomotion in horses (Equus caballus): an initial test of muscle architectural hypotheses about in vivo function

The forelimb digital flexors of the horse display remarkable diversity in muscle architecture despite each muscle-tendon unit having a similar mechanical advantage across the fetlock joint. We focus on two distinct muscles of the digital flexor system: short compartment deep digital flexor (DDF(sc)) and the superficial digital flexor (SDF). The objectives were to investigate force-length behavior and work performance of these two muscles in vivo during locomotion, and to determine how muscle architecture contributes to in vivo function in this system. We directly recorded muscle force (via tendon strain gauges) and muscle fascicle length (via sonomicrometry crystals) as horses walked (1.7 m s(-1)), trotted (4.1 m s(-1)) and cantered (7.0 m s(-1)) on a motorized treadmill. Over the range of gaits and speeds, DDF(sc) fascicles shortened while producing relatively low force, generating modest positive net work. In contrast, SDF fascicles initially shortened, then lengthened while producing high force, resulting in substantial negative net work. These findings suggest the long fibered, unipennate DDF(sc) supplements mechanical work during running, whereas the short fibered, multipennate SDF is specialized for economical high force and enhanced elastic energy storage. Apparent in vivo functions match well with the distinct architectural features of each muscle.     

Structure-function considerations of muscle-tendon junctions

Skeletal muscle cells transmit force across the cell membrane to the extracellular matrix and ultimately to tendons. Force transmission may occur both along the lateral surfaces of muscle fibers and at their ends. Forces within muscles may follow the path of greatest resistance. Sites of force transmission are morphologically and compositionally specialized for this function. They are also specialized to provide stress-information that feeds into the synthetic programs of the muscle cell. A detailed analysis of the structures and functions of muscle-tendon junctions is essential to a comprehensive understanding of the way in which muscles and their connective tissues are controlled to move joints and to respond to mechanical stresses.     

Analysis of the tendinous structure in human masticatory muscles.

In the masticatory muscles, the development of bundles of the tendon was examined: they were composed of many collagen fibers and a few elastic fibers. In the masseter muscle, the property of the tendon differs in the distribution and size of collagen fibers and elastic fibers in comparison with those of other masticatory muscles. This difference is concerned with the kinetic force for the stress or the stretch of each tendon and muscle during jaw movement.     

Human leg model predicts ankle muscle-tendon morphology, state, roles and energetics in walking

A common feature in biological neuromuscular systems is the redundancy in joint actuation. Understanding how these redundancies are resolved in typical joint movements has been a long-standing problem in biomechanics, neuroscience and prosthetics. Many empirical studies have uncovered neural, mechanical and energetic aspects of how humans resolve these degrees of freedom to actuate leg joints for common tasks like walking. However, a unifying theoretical framework that explains the many independent empirical observations and predicts individual muscle and tendon contributions to joint actuation is yet to be established. Here we develop a computational framework to address how the ankle joint actuation problem is resolved by the neuromuscular system in walking. Our framework is founded upon the proposal that a consideration of both neural control and leg muscle-tendon morphology is critical to obtain predictive, mechanistic insight into individual muscle and tendon contributions to joint actuation. We examine kinetic, kinematic and electromyographic data from healthy walking subjects to find that human leg muscle-tendon morphology and neural activations enable a metabolically optimal realization of biological ankle mechanics in walking. This optimal realization (a) corresponds to independent empirical observations of operation and performance of the soleus and gastrocnemius muscles, (b) gives rise to an efficient load-sharing amongst ankle muscle-tendon units and (c) causes soleus and gastrocnemius muscle fibers to take on distinct mechanical roles of force generation and power production at the end of stance phase in walking. The framework outlined here suggests that the dynamical interplay between leg structure and neural control may be key to the high walking economy of humans, and has implications as a means to obtain insight into empirically inaccessible features of individual muscle and tendons in biomechanical tasks.     

Stretching Your Energetic Budget: How Tendon Compliance Affects the Metabolic Cost of Running

Muscles attach to bones via tendons that stretch and recoil, affecting muscle force generation and metabolic energy consumption. In this study, we investigated the effect of tendon compliance on the metabolic cost of running using a full-body musculoskeletal model with a detailed model of muscle energetics. We performed muscle-driven simulations of running at 2–5 m/s with tendon force–strain curves that produced between 1 and 10% strain when the muscles were developing maximum isometric force. We computed the average metabolic power consumed by each muscle when running at each speed and with each tendon compliance. Average whole-body metabolic power consumption increased as running speed increased, regardless of tendon compliance, and was lowest at each speed when tendon strain reached 2–3% as muscles were developing maximum isometric force. When running at 2 m/s, the soleus muscle consumed less metabolic power at high tendon compliance because the strain of the tendon allowed the muscle fibers to operate nearly isometrically during stance. In contrast, the medial and lateral gastrocnemii consumed less metabolic power at low tendon compliance because less compliant tendons allowed the muscle fibers to operate closer to their optimal lengths during stance. The software and simulations used in this study are freely available at simtk.org and enable examination of muscle energetics with unprecedented detail.     

The effects of Achilles tendon compliance on triceps surae mechanics and energetics in walking

Achilles tendon (AT) compliance can affect the generation and transmission of triceps surae muscle forces, and thus has important biomechanical consequences for walking performance. However, the uniarticular soleus (SOL) and the biarticular (GAS) function differently during walking, with in vivo evidence suggesting that their associated fascicles and tendinous structures exhibit unique kinematics during walking. Given the strong association between muscle fiber length, velocity and force production, we conjectured that SOL and GAS mechanics and energetic behavior would respond differently to altered AT compliance. To test this, we characterized GAS and SOL muscle and tendon mechanics and energetics due to systematic changes in tendon compliance using musculoskeletal simulations of walking. Increased tendon compliance enlarged GAS and SOL tendon excursions, shortened fiber operation lengths and affected muscle excitation patterns. For both muscles, an optimal tendon compliance (tendon strains of approximately 5% with maximum isometric force) existed that minimized metabolic energy consumption. However, GAS muscle-tendon mechanics and energetics were significantly more sensitive to changes in tendon compliance than were those for SOL. In addition, GAS was not able to return stored tendon energy during push-off as effectively as SOL, particularly for larger values of tendon compliance. These fundamental differences between GAS and SOL sensitivity to altered tendon compliance seem to arise from the biarticular nature of GAS. These insights are potentially important for understanding the functional consequences of altered Achilles tendon compliance due to aging, injury, or disease.     

Plantarflexor fiber and tendon slack length are strong determinates of simulated single-leg heel raise height

Achilles tendon ruptures have been linked with detrimental changes in muscle-tendon structure, which may help explain long-term functional deficits. However, the causal effects of muscle-tendon structure on joint function have not been tested in a controlled setting. Therefore, the purpose of this study was to test the implications of muscle-tendon unit parameters on simulated single-leg heel raise height. We hypothesized that muscle fiber length and resting ankle angle – a clinical surrogate measure of tendon slack length – would predict single-leg heel raise height more strongly than other parameters. To test this hypothesis, we developed a two-part simulation paradigm that recreated clinically relevant muscle-tendon scenarios and then tested these parameters on single-leg heel raise height. We found that longer muscle fibers had the greatest positive effect on single-leg heel raise height. However, tendon slack length, determined by simulating resting ankle angles in a secondary analysis, revealed a stronger negative correlation with heel raise height. Our findings support previous clinical observations that both muscle fascicle length and resting tendon length are important muscle-tendon parameters for patient function. In addition to minimizing tendon elongation following rupture, treatment plans should focus on preserving plantarflexor muscle structure to mitigate functional loses following Achilles tendon ruptures.     

Springs in Swimming Animals

Animals can lower the metabolic cost of swimming by using appropriatelytuned, elastic springs. Jet-powered invertebrates use springsthat lie in functional parallel to their swimming muscles topower half the locomotor cycle. The parallel geometry constrainsthe spring to be non-linearly elastic; muscle power is divertedto load the spring only when swimming muscles are not capableof producing maximal hydrodynamic thrust. The springs of jellyfishand scallops are forced at or near their resonant frequency,producing large energy savings. Measuring the contribution ofelastic energy storage to jet-powered locomotion has been facilitatedby the relatively simple geometries of invertebrate locomotorsystems. In contrast, complex musculoskeletal systems and kinematicshave complicated the study of springs in swimming vertebrates.Skins, tendons and axial skeletons of some vertebrate swimmershave appropriate mechanical properties to act as springs. Todate, though, there exist just a handful of studies that haveinvestigated the mechanical behaviors of these locomotor structuresin swimming vertebrates, and these data have yet to be integratedwith measures of swimming power. Integrating mechanical, kinematic,hydrodynamic and metabolic data are required to understand morefully the role of elastic springs in vertebrate swimming energetics.     

Locomotor function shapes the passive mechanical properties and operating lengths of muscle

Locomotor muscles often perform diverse roles, functioning as motors that produce mechanical energy, struts that produce force and brakes that dissipate mechanical energy. In many vertebrate muscles, these functions are not mutually exclusive and a single muscle often performs a range of mechanically diverse tasks. This functional diversity has obscured the relationship between a muscle''s locomotor function and its mechanical properties. I use hopping in toads as a model system for comparing muscles that primarily produce mechanical energy with muscles that primarily dissipate mechanical energy. During hopping, hindlimb muscles undergo active shortening to produce mechanical energy and propel the animal into the air, whereas the forelimb muscles undergo active lengthening to dissipate mechanical energy during landing. Muscles performing distinct mechanical functions operate on different regions of the force–length curve. These findings suggest that a muscle''s operating length may be shaped by potential trade-offs between force production and sarcomere stability. In addition, the passive force–length properties of hindlimb and forelimb muscles vary, suggesting that passive stiffness functions to restrict the muscle''s operating length in vivo. These results inform our understanding of vertebrate muscle variation by providing a clear link between a muscle''s locomotor function and its mechanical properties.     

Properties of the tendinous structures and series elastic component of EDL muscle-tendon complex of the rat

Characteristics of the entire series elastic component and of tendinous structures separately (tendon and aponeurosis) were compared for rat EDL muscle-tendon complex during isometric contractions, to study the contribution of tendinous structures to series elastic component characteristics. Compliance of series elastic component was measured using quick length decreases during the force plateau of isometric contractions. Lengths of tendinous structures were measured using macro-photographs during passive and active muscle conditions. Length data obtained from aponeurosis showed inconsistency with respect to elastic behaviour in two ways: the difference of aponeurosis length in active muscle at short length and at optimum length exceeded the extension of series elastic component for the same force range. Furthermore, aponeurosis in passive muscle at optimum length was considerably longer than in active muscle at short length, despite the fact that muscle force in the former condition is smaller than in the latter. It is concluded that aponeurosis length does not depend exclusively on force but is also muscle length-dependent. This muscle length dependence was not found for tendon of EDL. Additional experiments showed that series elastic component compliance does not depend on muscle length. It is concluded that muscle length-dependent changes of aponeurosis length-force characteristics involve shifts of its force length curve to other aponeurosis lengths.     

Subject-specific tendon-aponeurosis definition in hill-type model predicts higher muscle forces in dynamic tasks

Neuromusculoskeletal models are a common method to estimate muscle forces. Developing accurate neuromusculoskeletal models is a challenging task due to the complexity of the system and large inter-subject variability. The estimation of muscles force is based on the mechanical properties of tendon-aponeurosis complex. Most neuromusculoskeletal models use a generic definition of the tendon-aponeurosis complex based on in vitro test, perhaps limiting their validity. Ultrasonography allows subject-specific estimates of the tendon-aponeurosis complex's mechanical properties. The aim of this study was to investigate the influence of subject-specific mechanical properties of the tendon-aponeurosis complex on a neuromusculoskeletal model of the ankle joint. Seven subjects performed isometric contractions from which the tendon-aponeurosis force-strain relationship was estimated. Hopping and running tasks were performed and muscle forces were estimated using subject-specific tendon-aponeurosis and generic tendon properties. Two ultrasound probes positioned over the muscle-tendon junction and the mid-belly were combined with motion capture to estimate the in vivo tendon and aponeurosis strain of the medial head of gastrocnemius muscle. The tendon-aponeurosis force-strain relationship was scaled for the other ankle muscles based on tendon and aponeurosis length of each muscle measured by ultrasonography. The EMG-driven model was calibrated twice - using the generic tendon definition and a subject-specific tendon-aponeurosis force-strain definition. The use of subject-specific tendon-aponeurosis definition leads to a higher muscle force estimate for the soleus muscle and the plantar-flexor group, and to a better model prediction of the ankle joint moment compared to the model estimate which used a generic definition. Furthermore, the subject-specific tendon-aponeurosis definition leads to a decoupling behaviour between the muscle fibre and muscle-tendon unit in agreement with previous experiments using ultrasonography. These results indicate the use of subject-specific tendon-aponeurosis definitions in a neuromusculoskeletal model produce better agreement with measured external loads and more physiological model behaviour.     

The series elastic shock absorber: tendon elasticity modulates energy dissipation by muscle during burst deceleration

During downhill running, manoeuvring, negotiation of obstacles and landings from a jump, mechanical energy is dissipated via active lengthening of limb muscles. Tendon compliance provides a ‘shock-absorber’ mechanism that rapidly absorbs mechanical energy and releases it more slowly as the recoil of the tendon does work to stretch muscle fascicles. By lowering the rate of muscular energy dissipation, tendon compliance likely reduces the risk of muscle injury that can result from rapid and forceful muscle lengthening. Here, we examine how muscle–tendon mechanics are modulated in response to changes in demand for energy dissipation. We measured lateral gastrocnemius (LG) muscle activity, force and fascicle length, as well as leg joint kinematics and ground-reaction force, as turkeys performed drop-landings from three heights (0.5–1.5 m centre-of-mass elevation). Negative work by the LG muscle–tendon unit during landing increased with drop height, mainly owing to greater muscle recruitment and force as drop height increased. Although muscle strain did not increase with landing height, ankle flexion increased owing to increased tendon strain at higher muscle forces. Measurements of the length–tension relationship of the muscle indicated that the muscle reached peak force at shorter and likely safer operating lengths as drop height increased. Our results indicate that tendon compliance is important to the modulation of energy dissipation by active muscle with changes in demand and may provide a mechanism for rapid adjustment of function during deceleration tasks of unpredictable intensity.