Tensile properties of calcified and uncalcified avian tendons

The mechanical properties of turkey and heron leg tendons have been investigated in dynamic tensile tests. Heron tendons have properties similar to those found for various mammalian tendons. The Young's modulus and the density of turkey tendons increase with increasing calcification. Ultimate tensile stresses are similar to those found for uncalcified tendon, but Young's modulus may reach about 16 GPa, a value normally associated with bone. Calcification lowers the amount of strain energy that can be stored temporarily in the tendons of the legs. The contribution made by elastic strain energy storage to lowering the cost of running is reduced.     

Elastic properties of the feet of deer (Cervidae)

Dynamic tests have been performed on the feet of deer, and on tendons removed from the feet, to determine their elastic properties. The results have been used to calculate the strain energy stored in each foot while it is on the ground in a fast galloping stride. This is compared with an estimate of the work done by the leg, and the energy-saving rle of tendon elasticity is assessed.     

Elastic properties of the forefoot of the Donkey, Equus asinus

The elastic properties of the forefeet of Donkeys, and of tendons removed from the feet, have been investigated in dynamic tests at a frequency chosen to simulate running. The elastic properties of the foot are explained in terms of the properties of individual tendons and check ligaments. The elastic strain energy stored in the foot, during a trotting step, is calculated to be only a little less than the optimum quantity which would minimize the work required of the muscles in this gait. Frictional and viscous energy losses were fairly small in the experiments on feet, and would probably be smaller in the intact animal.     

Elastic Energy Stores in Running Vertebrates

Large mammals save much of the energy they would otherwise needfor running by means of elastic structures in their legs. Kineticand potential energy, lost at one stage of a stride, is storedtemporarily as elastic strain energy and returned later in anelastic recoil. At high speeds, men and kangaroos seem to savein this way more than half the metabolic energy they would otherwiseneed for locomotion. It is shown by means of a generalized model that muscles andtendons could both be important as elastic energy stores. Analysisof films and force records of kangaroos hopping shows that strainenergy stored while the feet are on the ground must be storedmainly distal to the knee. The principal muscles there haveshort fibres, and most of the storage must be in tendons. Investigationof camels shows that tendons in the feet, distal to the ankleand wrist, are especially important. The scope for elastic storagewhile the feet are off the groundis also considered. Though the evidence presented in this paper comes mainly froma few species, the conclusions presumably apply to large mammalsin general.     

Elastic properties of the hind foot of the Donkey, Equus asinus

The elastic properties of the hind feet of Donkeys, and of tendons removed from the feet, have been investigated by methods similar to those used in a previous study of the forefoot. The elastic strain energy stored in the foot, during a trotting step, is calculated to be approximately the optimum which would minimize the work required of the muscles in this gait.     

Mechanical characteristics of biological soft tissue]

In a detailed study mechanical properties of tendons, muscles, nerves, blood-vessels and skin of just slaughtered pigs have been investigated in nearly stationary stress tests. Tensile tests have produced tensile strength, ultimate stress and their appropriate strains, Young's modulus and the work up to fatigue of samples. In hysteresis tests the deformation work has been determined as a function of numbers of stress cycles. The hysteresis decrease with the number of stress cycles and approaches asymptotically to cero. By preconditioning of tendons, nerves and blood-vessels to steady state significant differences of strain at tensile strength and of Young's modulus have been established. Moreover for nerves the tests have revealed significant deviations of tensile strength. Bruise tests have been carried out with muscle tissue. For the described setup the limit force can be specified, at which pathological changes appear. Subsequently conducted histological investigations have demonstrated this. In dynamical bruise tests there appeared no pathological changes in muscle tissue in spite of higher transmitted energy.     

Elastic energy storage in unmineralized and mineralized extracellular matrices (ECMs): a comparison between molecular modeling and experimental measurements

In order to facilitate locomotion and limb movement many animals store energy elastically in their tendons. In the turkey, much of the force generated by the gastrocnemius muscle is stored as elastic energy during tendon deformation and not within the muscle. As limbs move, the tendons are strained causing the collagen fibers in the extracellular matrices to be strained. During growth, avian tendons mineralize in the portions distal to the muscle and show increased tensile strength, modulus, and energy stored per unit strain as a result. In this study the energy stored in unmineralized and mineralized collagen fibers was measured and compared to the amount of energy stored in molecular models. Elastic energy storage values calculated using the molecular model were slightly higher than those obtained from collagen fibers, but display the same increases in slope as the fiber data. We hypothesize that these increases in slope are due to a change from the stretching of flexible regions of the collagen molecule to the stretching of less flexible regions. The elastic modulus obtained from the unmineralized molecular model correlates well with elastic moduli of unmineralized collagen from other studies. This study demonstrates the potential importance of molecular modeling in the design of new biomaterials.     

The mechanics of hopping by kangaroos (Macropodidae)

Force platform records and films have been made of kangaroos and a wallaby hopping.
The maximum forces exerted on the ground were about six times body weight. The force exerted on the ground changes direction, throughout the period when the feet are on the ground, so that it is always more or less in line with the centre of mass. Consequently the animal decelerates a little and then accelerates again, during the contact phase.
The fluctuations of potential energy which occur in each hop are slightly smaller at high speeds than at low ones. Fluctuations of external kinetic energy increase with speed and account for most of the energy cost of hopping at high speeds. Fluctuations of internal kinetic energy (due to acceleration and deceleration of the limbs) are relatively small. While the feet are on the ground the extensor muscles of the hip do positive work, those of the knee negative work and those of the ankle negative work followed by positive work. The energy cost of hopping is reduced substantially by elastic storage of energy in the Achilles tendon. In the case of a wallaby hopping at moderate speed the calculated saving was 40%. The maximum stresses developed in leg muscles, tendons and the tibia have been calculated and are discussed in relation to the known properties of muscle, tendon and bone. The trunk pitches as the animal hops because the two legs swing forwards and back simultaneously. Appropriate tail movements reduce, but do not eliminate, this effect. A mathematical theory of hopping is presented and used to investigate the merits of different hopping techniques.
Dawson & Taylor's (1973) discovery that the rate of oxygen consumption of kangaroos decreases a little, as hopping speed increases, is probably to be explained by the increased role of elastic storage of energy at high speeds.     

Why Change Gaits? Recruitment of Muscles and Muscle Fibers as a Function of Speed and Gait

Muscles shorten, stay the same length and are stretched whilethey are active during normal modes of terrestrial locomotion.The relative importance of these different types of muscularactivity changes as animals change gait. Energy is conservedduring a walk by an alternate storage and recovery of gravitationalpotential energy within each stride, as in an inverted pendulum.In order for this transfer of energy to take place, muscularactivity is required to hold the limb rigid while the animalrotates over it. Energy is conserved by a spring mechanism duringrunning, trotting, galloping, and hopping. Energy is storedwhen active muscles and their tendons are stretched and recoveredas they subsequently shorten. The recruitment patterns of motorunits as a function of speed therefore, depends on the typeof muscular activity as well as the force exerted. Discontinuitiesin the cross sectional area of active fibers with increasingspeed have been observed at the trot-gallop transition. It issuggested that at this point the trunk is recruited as an additionalspring enabling more energy to be stored elastically. It isconcluded that we must consider what muscles are doing duringnormal modes of locomotion before we become too involved indesigning schemes of motor unit recruitment.     

Positive force feedback in bouncing gaits?

During bouncing gaits (running, hopping, trotting), passive compliant structures (e.g. tendons, ligaments) store and release part of the stride energy. Here, active muscles must provide the required force to withstand the developing tendon strain and to compensate for the inevitable energy losses. This requires an appropriate control of muscle activation. In this study, for hopping, the potential involvement of afferent information from muscle receptors (muscle spindles, Golgi tendon organs) is investigated using a two-segment leg model with one extensor muscle. It is found that: (i) positive feedbacks of muscle-fibre length and muscle force can result in periodic bouncing; (ii) positive force feedback (F+) stabilizes bouncing patterns within a large range of stride energies (maximum hopping height of 16.3 cm, almost twofold higher than the length feedback); and (iii) when employing this reflex scheme, for moderate hopping heights (up to 8.8 cm), an overall elastic leg behaviour is predicted (hopping frequency of 1.4-3 Hz, leg stiffness of 9-27 kN m(-1)). Furthermore, F+ could stabilize running. It is suggested that, during the stance phase of bouncing tasks, the reflex-generated motor control based on feedbacks might be an efficient and reliable alternative to central motor commands.     

Differential design for hopping in two species of wallabies.

Hindlimb musculoskeletal anatomy and steady speed over ground hopping mechanics were compared in two species of macropod marsupials, tammar wallabies and yellow-footed rock wallabies (YFRW). These two species are relatively closely related and are of similar size and general body plan, yet they inhabit different environments with presumably different musculoskeletal demands. Tammar wallabies live in relatively flat, open habitat whereas yellow-footed rock wallabies inhabit steep cliff faces. The goal of this study was to explore musculoskeletal differences between tammar wallabies and yellow-footed rock wallabies and determine how these differences influence each species' hopping mechanics. We found the cross-sectional area of the combined ankle extensor tendons of yellow-footed rock wallabies was 13% greater than that of tammar wallabies. Both species experienced similar ankle joint moments during steady-speed hopping, however due to a lower mechanical advantage at this joint, tammar wallabies produced 26% more muscle force. Thus, during moderate speed hopping, yellow-footed rock wallabies operated with 38% higher tendon safety factors, while tammar wallabies were able to store 73% more elastic strain energy (2.18 J per leg vs. 1.26 J in YFRW). This likely reflects the differing demands of the environments inhabited by these two species, where selection for non-steady locomotor performance in rocky terrain likely requires trade-offs in locomotor economy.     

Continuum description of the Poisson׳s ratio of ligament and tendon under finite deformation

Ligaments and tendons undergo volume loss when stretched along the primary fiber axis, which is evident by the large, strain-dependent Poisson?s ratios measured during quasi-static tensile tests. Continuum constitutive models that have been used to describe ligament material behavior generally assume incompressibility, which does not reflect the volumetric material behavior seen experimentally. We developed a strain energy equation that describes large, strain dependent Poisson?s ratios and nonlinear, transversely isotropic behavior using a novel method to numerically enforce the desired volumetric behavior. The Cauchy stress and spatial elasticity tensors for this strain energy equation were derived and implemented in the FEBio finite element software (www.febio.org). As part of this objective, we derived the Cauchy stress and spatial elasticity tensors for a compressible transversely isotropic material, which to our knowledge have not appeared previously in the literature. Elastic simulations demonstrated that the model predicted the nonlinear, upwardly concave uniaxial stress–strain behavior while also predicting a strain-dependent Poisson?s ratio. Biphasic simulations of stress relaxation predicted a large outward fluid flux and substantial relaxation of the peak stress. Thus, the results of this study demonstrate that the viscoelastic behavior of ligaments and tendons can be predicted by modeling fluid movement when combined with a large Poisson?s ratio. Further, the constitutive framework provides the means for accurate simulations of ligament volumetric material behavior without the need to resort to micromechanical or homogenization methods, thus facilitating its use in large scale, whole joint models.     

Elastic structures in the back and their rôle in galloping in some mammals

A study of Fallow deer ( Dma dama ) and Domestic dog ( Canis familiaris ) leads to identification of an aponeurosis in the back as an important elastic strain energy store in galloping. Kinetic energy lost by the body, as the forelegs end their backward swing and the hind legs end their forward swing, is stored briefly as elastic strain energy, and recovered in an elastic recoil. Thus energy is saved, making galloping the most economical gait for high speeds. Some strain energy is also stored in muscle fibres and in the vertebral column. Mechanical tests on the aponeurosis and vertebrae lead to estimates of the quantities of energy involved.     

Effects of frozen storage temperature on the elasticity of tendons from a small murine model

The basic mechanism of reinforcement in tendons addresses the transfer of stress, generated by the deforming proteoglycan (PG)-rich matrix, to the collagen fibrils. Regulating this mechanism involves the interactions of PGs on the fibril with those in the surrounding matrix and between PGs on adjacent fibrils. This understanding is key to establishing new insights on the biomechanics of tendon in various research domains. However, the experimental designs in many studies often involved long sample preparation time. To minimise biological degradation the tendons are usually stored by freezing. Here, we have investigated the effects of commonly used frozen storage temperatures on the mechanical properties of tendons from the tail of a murine model (C57BL6 mouse). Fresh (unfrozen) and thawed samples, frozen at temperatures of -20°C and -80°C, respectively, were stretched to rupture. Freezing at -20°C revealed no effect on the maximum stress (σ), stiffness (E), the corresponding strain (ε) at σ and strain energy densities up to ε (u) and from ε until complete rupture (up). On the other hand, freezing at -80°C led to higher σ, E and u; ε and up were unaffected. The results implicate changes in the long-range order of radially packed collagen molecules in fibrils, resulting in fibril rupture at higher stresses, and changes to the composition of extrafibrillar matrix, resulting in an increase in the interaction energy between fibrils via collagen-bound PGs.     

More than energy cost: multiple benefits of the long Achilles tendon in human walking and running

Elastic strain energy that is stored and released from long, distal tendons such as the Achilles during locomotion allows for muscle power amplification as well as for reduction of the locomotor energy cost: as distal tendons perform mechanical work during recoil, plantar flexor muscle fibres can work over smaller length ranges, at slower shortening speeds, and at lower activation levels. Scant evidence exists that long distal tendons evolved in humans (or were retained from our more distant Hominoidea ancestors) primarily to allow high muscle–tendon power outputs, and indeed we remain relatively powerless compared to many other species. Instead, the majority of evidence suggests that such tendons evolved to reduce total locomotor energy cost. However, numerous additional, often unrecognised, advantages of long tendons may speculatively be of greater evolutionary advantage, including the reduced limb inertia afforded by shorter and lighter muscles (reducing proximal muscle force requirement), reduced energy dissipation during the foot–ground collisions, capacity to store and reuse the muscle work done to dampen the vibrations triggered by foot–ground collisions, reduced muscle heat production (and thus core temperature), and attenuation of work-induced muscle damage. Cumulatively, these effects should reduce both neuromotor fatigue and sense of locomotor effort, allowing humans to choose to move at faster speeds for longer. As these benefits are greater at faster locomotor speeds, they are consistent with the hypothesis that running gaits used by our ancestors may have exerted substantial evolutionary pressure on Achilles tendon length. The long Achilles tendon may therefore be a singular adaptation that provided numerous physiological, biomechanical, and psychological benefits and thus influenced behaviour across multiple tasks, both including and additional to locomotion. While energy cost may be a variable of interest in locomotor studies, future research should consider the broader range of factors influencing our movement capacity, including our decision to move over given distances at specific speeds, in order to understand more fully the effects of Achilles tendon function as well as changes in this function in response to physical activity, inactivity, disuse and disease, on movement performance.     

The mechanics of jumping by a dog (Canis familiaris)

A force platform has been used to obtain records of the forces exerted on the ground by an Alsatian dog, during take-off for running long jumps and standing scale jumps. The records have been analysed in conjunction with cinematograph film, taken simultaneously, and anatomical data. Stresses in the principal muscles of the hind limb, and in the triceps, have been calculated and the values obtained are compared with the stresses found by other investigators in isometric experiments with excised mammal muscles. Stresses in certain tendons and bones have been calculated, and the values obtained are compared with published values for the strength of tendon and bone. Evidence is presented that the gastrocnemius and plantaris muscles behave, in take-off for a jump, essentially as passive elastic bodies. Most of the elastic energy is probably stored in their tendons. A tendency for distal limb muscles to be pinnate, with much shorter fibres than proximal limb muscles, is noted and discussed.     

The structure and function of normally mineralizing avian tendons

The leg tendons of certain avian species normally calcify. The gastrocnemius, or Achilles, tendon of the domestic turkey, Meleagris gallopavo, is one such example. Its structure and biomechanical properties have been studied to model the adaptive nature of this tendon to external forces, including the means by which mineral deposition occurs and the functional role mineralization may play in this tissue. Structurally, the distal rounded, thick gastrocnemius bifurcates into two smaller proximal segments that mineralize with time. Mineral deposition occurs at or near the bifurcation, proceeding in a distal-to-proximal direction along the segments toward caudal and medial muscle insertions of the bird hip. Mineral formation appears mediated first by extracellular matrix vesicles and later by type I collagen fibrils. Biomechanical analyses indicate lower tensile strength and moduli for the thick distal gastrocnemius compared to narrow, fan-shaped proximal segments. Tendon mineralization here appears to be strain-induced, the muscle forces causing matrix deformation leading conceptually to calcium binding through the exposure of charged groups on collagen, release of sequestered calcium by proteoglycans, and increased diffusion. Functionally, the mineralized tendons limit further tendon deformation, reduce tendon strain at a given stress, and provide greater load-bearing capacity to the tissue. They also serve as important and efficient elastic energy storage reservoirs, increasing the amount of stored elastic energy by preventing flexible type I collagen regions from stretching and preserving muscle energy during locomotion of the animals.     

Elastic energy storage in tendons: mechanical differences related to function and age

We investigated the possibility that tendons that normally experience relatively high stresses and function as springs during locomotion, such as digital flexors, might develop different mechanical properties from those that experience only relatively low stresses, such as digital extensors. At birth the digital flexor and extensor tendons of pigs have identical mechanical properties, exhibiting higher extensibility and mechanical hysteresis and lower elastic modulus, tensile strength, and elastic energy storage capability than adult tendons. With growth and aging these tendons become much stronger, stiffer, less extensible, and more resilient than at birth. Furthermore, these alterations in elastic properties occur to a significantly greater degree in the high-load-bearing flexors than in the low-stress extensors. At maturity the pig digital flexor tendons have twice the tensile strength and elastic modulus but only half the strain energy dissipation of the corresponding extensor tendons. A morphometric analysis of the digital muscles provides an estimate of maximal in vivo tendon stresses and suggests that the muscle-tendon unit of the digital flexor is designed to function as an elastic energy storage element whereas that of the digital extensor is not. Thus the differences in material properties between mature flexor and extensor tendons are correlated with their physiological functions, i.e., the flexor is much better suited to act as an effective biological spring than is the extensor.     

Tendon elasticity and muscle function

Vertebrate animals exploit the elastic properties of their tendons in several different ways. Firstly, metabolic energy can be saved in locomotion if tendons stretch and then recoil, storing and returning elastic strain energy, as the animal loses and regains kinetic energy. Leg tendons save energy in this way when birds and mammals run, and an aponeurosis in the back is also important in galloping mammals. Tendons may have similar energy-saving roles in other modes of locomotion, for example in cetacean swimming. Secondly, tendons can recoil elastically much faster than muscles can shorten, enabling animals to jump further than they otherwise could. Thirdly, tendon elasticity affects the control of muscles, enhancing force control at the expense of position control.