Is Achilles tendon compliance optimised for maximum muscle efficiency during locomotion?

Tendon elasticity is important for economical locomotion; however it is unknown whether tendon stiffness is appropriate to achieve an optimal efficiency in various muscles. Here we test the hypothesis that the Achilles tendon is of an appropriate stiffness to maximise medial gastrocnemius muscle efficiency during locomotion with different power requirements. To test this hypothesis we used a three element Hill muscle model to determine how muscle fascicles would be required to change length if the series elastic element stiffness is varied, whilst the limb kinematics and muscle properties are held constant. We applied a model of muscle energetics to these data to predict muscle efficiency for a range of stiffness values in both walking and running conditions. We also compared the model results to in vivo data collected using ultrasonography. The muscle model predicted that optimal series elastic element stiffness for maximising efficiency is equal or slightly higher than that of the average Achilles tendon in running and walking, respectively. Although the peak efficiency values for running (26%) and walking (27%) are similar, the range of stiffness values achieving high efficiency in running is much smaller than that during walking. These results suggest that a compliant tendon, such as the Achilles tendon, is required for efficient running. Such a finding is important, because it describes how the stiffness of a tendon may be adapted to achieve optimal efficiency for particular athletic pursuits. The influence of varying tendon stiffness on kinematic performance may, however, play an important role in determining the efficiency of the muscle.     

Measurement of muscle and tendon stiffness in man

Human first dorsal interosseous muscle was stimulated tetanically using several levels of percutaneous electrical current which produced forces in the muscle-tendon complex of between 30% and 100% of maximum. During the tetanus the muscle was subjected to a small fast stretch. The ratio of the force response to the displacement of the muscle-tendon complex gave a measure of the stiffness of the total complex. An adaptation of the method of Morgan (1977) allowed the stiffness to be separated into two components the stiffness of the muscle fibres and the stiffness of the tendon. The results showed that at full activation the stiffness of the muscle fibres and the tendon are approximately the same. The normalised stiffness values obtained in the experiments compared well with animal data.     

Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running

Muscles generate force to resist gravitational and inertial forces and/or to undertake work, e.g. on the centre of mass. A trade-off in muscle architecture exists in muscles that do both; the fibres should be as short as possible to minimise activation cost but long enough to maintain an appropriate shortening velocity. Energetic cost is also influenced by tendon compliance which modulates the timecourse of muscle mechanical work. Here we use a Hill-type muscle model of the human medial gastrocnemius to determine the muscle fascicle length and Achilles tendon compliance that maximise efficiency during the stance phase of walking (1.2 m/s) and running (3.2 and 3.9 m/s). A broad range of muscle fascicle lengths (ranging from 45 to 70 mm) and tendon stiffness values (150-500 N/mm) can achieve close to optimal efficiency at each speed of locomotion; however, efficient walking requires shorter muscle fascicles and a more compliant tendon than running. The values that maximise efficiency are within the range measured in normal populations. A non-linear toe-region region of the tendon force-length properties may further influence the optimal values, requiring a stiffer tendon with slightly longer muscle fascicles; however, it does not alter the main results. We conclude that muscle fibre length and tendon compliance combinations may be tuned to maximise efficiency under a given gait condition. Efficiency is maximised when the required volume of muscle is minimised, which may also help reduce limb inertia and basal metabolic costs.     

Muscle mechanics and neuromuscular control

The purpose of this paper is to demonstrate that the properties of the mechanical system, especially muscle elasticity and limb mass, to a large degree determine force output and movement. This makes the control demands of the central nervous system simpler and more robust. In human triceps surae, a muscle with short fibres and a long tendon, the time courses of the total muscle+tendon length and of the length of the contractile component (CC) alone in running are completely different. The muscle tendon complex shows first an eccentric phase with negative work, followed by a concentric phase. The CC, on the other hand, is concentric all the time. Moreover, the work that is done, is done at a speed that guarantees a high energetic efficiency. It is argued that this high efficiency is an in-built property of the muscle mechanics for muscles with a compliant tendon and a low v(max). When a muscle, or a set of muscles, moves a mass, and the duration of the action is short with respect to the isometric time constant of the muscle, we may call it an 'elastic bounce contraction'. In such a case the mass-spring interaction largely determines the time course of the force, and the efficiency of muscle contraction is most of the time close to optimum. In a similar way, whole limbs can be modelled as springs, with a stiffness that can be modulated by flexing the joints more or less. The motor control task of the central nervous system is simple for such elastic bounce contractions: a block-like activation is sufficient, in which timing is critical, but activation level is not. It seems possible that a whole class of actions can be generated by an identical timing sequence, with only a modulation in activation amplitude. An example is walking or running at different speeds.     

The inverted pendulum model of bipedal standing cannot be stabilized through direct feedback of force and contractile element length and velocity at realistic series elastic element stiffness

Control of bipedal standing is typically analyzed in the context of a single-segment inverted pendulum model. The stiffness K (SE) of the series elastic element that transmits the force generated by the contractile elements of the ankle plantarflexors to the skeletal system has been reported to be smaller in magnitude than the destabilizing gravitational stiffness K ( g ). In this study, we assess, in case K (SE) + K ( g ) < 0, if bipedal standing can be locally stable under direct feedback of contractile element length, contractile element velocity (both sensed by muscle spindles) and muscle force (sensed by Golgi tendon organs) to alpha-motoneuron activity. A theoretical analysis reveals that even though positive feedback of force may increase the stiffness of the muscle-tendon complex to values well over the destabilizing gravitational stiffness, dynamic instability makes it impossible to obtain locally stable standing under the conditions assumed.     

Method and strain rate dependence of Achilles tendon stiffness

Tendon stiffness is calculated by dividing changes in tendon force by tendon elongation. For this purpose, participants are commonly asked to perform a maximal muscle contraction (“active” method). Alternatively tendon elongation can be achieved by means of a passive joint rotation (“passive” method). The purpose of this study was to compare Achilles tendon stiffness obtained from both methods across different tendon strain rates. Twenty adults performed a series of ramped maximum isometric plantarflexions of different durations. Passive ankle rotations of different angular velocities were also performed. Achilles tendon stiffness was obtained from a combination of motion analysis, isokinetic dynamometry and ultrasonography and compared across methods at three strain rates. At all strain rates, tendon stiffness obtained from the active method was 6% greater compared to the passive method. In spite of this systematic bias, there was good agreement between the methods. Intraclass correlation coefficients were greater than 0.98, and more than 95% of data points fell into the 95% confidence intervals. This agreement will be acceptable in many research contexts. We also found a linear increase in tendon stiffness with increasing strain rate, which must be taken into consideration when interpreting or reporting tendon stiffness.     

Passive mechanics of muscle tendinous junction of canine diaphragm.

The diaphragmatic muscle tendon is a biaxially loaded junction in vivo. Stress-strain relations along and transverse to the fiber directions are important in understanding its mechanical properties. We hypothesized that 1) the central tendon possesses greater passive stiffness than adjacent muscle, 2) the diaphragm muscle is anisotropic, whereas the central tendon near the junction is essentially isotropic, and 3) a gradient in passive stiffness exists as one approaches the muscle-tendinous junction (MTJ). To investigate these hypotheses, we conducted uniaxial and biaxial mechanical loading on samples of the MTJ excised from the midcostal region of dog diaphragm. We measured passive length-tension relationships of the muscle, tendon, and MTJ in the direction along the muscle fibers as well as transverse to the fibers. The MTJ was slack in the unloaded state, resulting in a J-shaped passive tension-strain curve. Generally, muscle strain was greater than that of MTJ, which was greater than tendon strain. In the muscular region, stiffness in the direction transverse to the fibers is much greater than that along the fibers. The central tendon is essentially inextensible in the direction transverse to the fibers as well as along the fibers. Our data demonstrate the existence of more pronounced anisotropy in the muscle than in the tendon near the junction. Furthermore, a gradient in muscle stiffness exists as one approaches the MTJ, consistent with the hypothesis of continuous passive stiffness across the MTJ.     

The effect of tendon viscoelastic stiffness on the dynamic performance of isometric muscle

The effect of tendons viscoelastic stiffness on the dynamic response of the cat's tibialis anterior muscle under isometric conditions was determined. It was shown that the dynamic response model of the muscle derived under sinusoidal contraction-relaxation in the range of 20-80% of its maximal isometric tension was not statistically different before and after the disection of the whole distal tendon. It was suggested that under isometric conditions in the force range of 20-80% of the maximal, the tendon acts as a very stiff force transmission linkage without significantly modifying the muscle's performance.     

Mechanical properties of aponeurosis and tendon of the cat soleus muscle during whole-muscle isometric contractions

Recent studies have suggested that the mechanical properties of aponeurosis are not similar to the properties of external tendon. In the present study, the lengths of aponeurosis, tendon, and muscle fascicles were recorded individually, using piezoelectric crystals attached to the surface of each structure during isometric contractions in the cat soleus muscle. We used a surgical microscope to observe the surface of the aponeurosis, which revealed a confounding effect on measures of aponeurosis length due to sliding of a thin layer of epimysium over the proximal aponeurosis. After correcting for this artifact, the stiffness computed for aponeurosis was similar to tendon, with both increasing from around 8 F₀/L_c (F₀ is maximum isometric force and L_c is tissue length) at 0.1 F₀ to 30 F₀/L_c at forces greater than 0.4 F₀. At low force levels only (0.1 F₀), aponeurotic stiffness increased somewhat as fascicle length increased. There was a gradient in the thickness of the aponeurosis along its length: its thickness was minimal at the proximal end and maximal at the distal end, where it converged to form the external tendon. This gradient in thickness appeared to match the gradient in tension transmitted along this structure. We conclude that the specific mechanical properties of aponeurosis are similar to those of tendon. © 1995 Wiley-Liss, Inc.     

Why are mammalian tendons so thick?

The maximum stresses to which a wide range of mammalian limb tendons could be subjected in life were estimated by considering the relative cross-sectional areas of each tendon and of the fibres of its muscle. These cross-sectional areas were derived from mass and length measurements on tendons and muscles assuming published values for the respective densities. The majority of the stresses are low. The distribution has a broad peak with maximum frequency at a stress of about 13 MPa, whereas the fracture stress for tendon in tension is about 100 MPa. Thus, the majority of tendons are far thicker than is necessary for adequate strength. Much higher stresses are found among those tendons which act as springs to store energy during locomotion. The acceptability of low safety factors in these tendons has been explained previously (Alexander, 1981). A new theory explains the thickness of the majority of tendons. The muscle with its tendon is considered as a combined system which delivers mechanical energy: the thickness of the tendon is optimized by minimizing the combined mass. A thinner tendon would stretch more. To take up this stretch, the muscle would require longer muscle fibres, which would increase the combined mass. The predicted maximum stress in a tendon of optimum thickness is about 10 MPa, which is within the main peak of the observed stress distribution. Individual variations from this value are to be expected and can be understood in terms of the functions of the various muscles.     

Evaluation of different analytical methods for subject-specific scaling of musculotendon parameters

Musculoskeletal models are often used to estimate internal muscle forces and the effects of those forces on the development of human movement. The Hill-type muscle model is an important component of many of these models, yet it requires specific knowledge of several muscle and tendon properties. These include the optimal muscle fibre length, the length at which the muscle can generate maximum force, and the tendon slack length, the length at which the tendon starts to generate a resistive force to stretch. Both of these parameters greatly influence the force-generating behaviour of a musculotendon unit and vary with the size of the person. However, these are difficult to measure directly and are often estimated using the results of cadaver studies, which do not account for differences in subject size. This paper examined several different techniques that can be used to scale the optimal muscle fibre length and tendon slack length of a musculotendon unit according to subject size. The techniques were divided into three categories corresponding to linear scaling, scaling by maintaining a constant tendon slack length throughout the range of joint motion, and scaling by maintaining muscle operating range throughout the range of joint motion. We suggest that a good rationale for scaling muscle properties should be to maintain the same force-generating characteristics of a musculotendon unit for all subjects, which is best achieved by scaling that preserves the muscle operating range when the muscle is maximally activated.     

Effects of isometric training on the elasticity of human tendon structures in vivo.

The present study aimed to investigate the effect of isometric training on the elasticity of human tendon structures. Eight subjects completed 12 wk (4 days/wk) of isometric training that consisted of unilateral knee extension at 70% of maximal voluntary contraction (MVC) for 20 s per set (4 sets/day). Before and after training, the elongation of the tendon structures in the vastus lateralis muscle was directly measured using ultrasonography while the subjects performed ramp isometric knee extension up to MVC. The relationship between the estimated muscle force and tendon elongation (L) was fitted to a linear regression, the slope of which was defined as stiffness of the tendon structures. The training increased significantly the volume (7.6+/-4.3%) and MVC torque (33.9+/-14.4%) of quadriceps femoris muscle. The L values at force production levels beyond 550 N were significantly shorter after training. The stiffness increased significantly from 67.5+/-21.3 to 106.2+/-33.4 N/mm. Furthermore, the training significantly increased the rate of torque development (35.8 +/- 20.4%) and decreased electromechanical delay (-18.4+/-3.8%). Thus the present results indicate that isometric training increases the stiffness and Young's modulus of human tendon structures as well as muscle strength and size. This change in the tendon structures would be assumed to be an advantage for increasing the rate of torque development and shortening the electromechanical delay.     

Selected contribution: plasticity of airway smooth muscle stiffness and extensibility: role of length-adaptive mechanisms.

Airway smooth muscle exhibits the property of length adaptation, which enables it to optimize its contractility to the mechanical conditions under which it is activated. Length adaptation has been proposed to result from a dynamic modulation of contractile and cytoskeletal filament organization, in which the cell structure adapts to changes in cell shape at different muscle lengths. Changes in filament organization would be predicted to alter muscle stiffness and extensibility. We analyzed the effects of tracheal muscle length at the time of contractile activation on the stiffness and extensibility of the muscle during subsequent stretch over a constant range of muscle lengths. Muscle strips were significantly stiffer and less extensible after contractile activation at a short length than after activation at a long length, consistent with the prediction of a shorter, thicker array of the cytoskeletal filaments at a short muscle length. Stretch beyond the length of contractile activation resulted in a persistent reduction in stiffness, suggesting a stretch-induced structural rearrangement. Our results support a model in which the filament organization of airway smooth muscle cells is plastic and can be acutely remodeled to adapt to the changes in the external physical environment.     

Relative shortening velocity in locomotor muscles: turkey ankle extensors operate at low V/V(max)

The force-velocity properties of skeletal muscle have an important influence on locomotor performance. All skeletal muscles produce less force the faster they shorten and typically develop maximal power at velocities of approximately 30% of maximum shortening velocity (V(max)). We used direct measurements of muscle mechanical function in two ankle extensor muscles of wild turkeys to test the hypothesis that during level running muscles operate at velocities that favor force rather than power. Sonomicrometer measurements of muscle length, tendon strain-gauge measurements of muscle force, and bipolar electromyographs were taken as animals ran over a range of speeds and inclines. These measurements were integrated with previously measured values of muscle V(max) for these muscles to calculate relative shortening velocity (V/V(max)). At all speeds for level running the V/V(max) values of the lateral gastrocnemius and the peroneus longus were low (<0.05), corresponding to the region of the force-velocity relationship where the muscles were capable of producing 90% of peak isometric force but only 35% of peak isotonic power. V/V(max) increased in response to the demand for mechanical power with increases in running incline and decreased to negative values to absorb energy during downhill running. Measurements of integrated electromyograph activity indicated that the volume of muscle required to produce a given force increased from level to uphill running. This observation is consistent with the idea that V/V(max) is an important determinant of locomotor cost because it affects the volume of muscle that must be recruited to support body weight.     

Between-day reliability of MyotonPRO for the non-invasive measurement of muscle material properties in the lower extremities of patients with a chronic spinal cord injury

Measuring the muscle properties of patients with spinal cord injuries (SCIs) is important to better understand their biomechanical features. In this study, we sought to evaluate the between-day reliability of MyotonPRO, a handheld device that can measure muscle mechanical properties, and assess whether it is reliable to measure muscle properties over time in patients with SCI. Thirteen men with complete SCIs (age 53.9 ± 6.3 years, height 171.0 ± 5.2 cm, weight 66.1 ± 5.8 kg), and injury levels ranging from L1 to T12, were enrolled. Oscillation frequency; logarithmic decrement; dynamic stiffness; mechanical stress relaxation time; and creep of the biceps femoris, medial and lateral gastrocnemius, rectus femoris, tibialis anterior, and Achilles tendon were measured on consecutive days using MyotonPRO. The intraclass coefficient for most muscles and the Achilles tendon ranged from 0.53 to 0.99 for all parameters. The percentage standard error of the measurement for many parameters in most muscles and the Achilles tendon was less than 10%. Bland-Altman analysis showed a high agreement for all mechanical properties. No significant differences were observed in any muscle or Achilles tendon properties between days (all p > 0.05). These results indicate that the MyotonPRO is reliable for between-day measurements of the mechanical properties of lower limb muscles and Achilles tendon in patients with SCI.     

Tensile properties of the in vivo human gastrocnemius tendon

In the present experiment we obtained the tensile properties of the human gastrocnemius tendon, a high-stressed tendon suitable for spring-like action during locomotion. Measurements were taken in vivo in six men. The gastrocnemius tendon elongation during tendon loading−unloading induced by muscle contraction−relaxation was measured using real-time ultrasonography. Tendon forces were calculated from the moment generated during isometric plantarflexion contraction, using tendon moment arm length data obtained in vivo with the tendon travel method. Tendon stiffness data were calculated from the slope of the tendon force−elongation curve, and were then normalized to the tendon's original dimensions, obtained from morphometric analysis of sonographs, to estimate the tendon Young's modulus. Mechanical hysteresis values were obtained from area calculations by numerical integration. The elongation of the tendon increased curvilinearly with the force acting upon it, from 1.7±1 mm (0.8±0.3% strain) at 87.5±8.5 N to 11.1±3.1 mm (4.9±1% strain) at 875±85 N. The tendon Young's modulus and mechanical hysteresis were 1.16±0.15 GPa and 18±3%, respectively. These values fall within the range of values obtained from in vitro experiments and are very similar to the respective values recently obtained from in vivo measurements in the less highly stressed human tibialis anterior tendon (1.2 GPa and 19%), thus indicating that the material properties of tendon are independent of physiological loading and function. Combining the present tendon force−elongation data with previously reported Achilles tendon force data recorded during walking indicates that the gastrocnemius tendon would provide 6% of the total external work produced by the locomotor system. This estimate illustrates the contribution of passive elastic mechanisms on the economy and efficiency of walking. The contributions would be greater in more active exercise such as running.     

Modeling short-range stiffness of feline lower hindlimb muscles

The short-range stiffness (SRS) of skeletal muscles is a critical property for understanding muscle contributions to limb stability, since it represents a muscle's capacity to resist external perturbations before reflexes or voluntary actions can intervene. A number of studies have demonstrated that a simple model, consisting of a force-dependent active stiffness connected in series with a constant passive stiffness, is sufficient to characterize the SRS of individual muscles over the entire range of obtainable forces. The purpose of this study was to determine if such a model could be used to characterize the SRS-force relationship in a number of architecturally distinct muscles. Specifically, we hypothesized that the active and passive stiffness components for a specific muscle can be estimated from anatomical measurements, assuming uniform active and passive stiffness properties across all muscles. This hypothesis was evaluated in six feline lower hindlimb muscle types with different motor unit compositions and architectures. The SRS-force relationships for each muscle type were predicted based on anatomical measurements and compared to experimental data. The model predictions were accurate to within 30%, when uniform scaling properties were assumed across all muscles. Errors were the greatest for the extensor digitorum longus (EDL). When this muscle was removed from the analysis, prediction errors dropped to less than 8%. Subsequent analyses suggested that these errors might have resulted from differences in the tendon elastic modulus, as compared to the other muscles tested.     

Passive muscle mechanical properties of the medial gastrocnemius in young adults with spastic cerebral palsy

Individuals with spastic cerebral palsy (SCP) exhibit restricted joint range of motion and increased joint stiffness due to structural alterations of their muscles. Little is known about which muscle–tendon structures are responsible for these alterations. The aim of this study was to compare the passive mechanics of the ankle joint and medial gastrocnemius (MG) muscle in young adults with SCP and typically developed (TD) individuals. Nine ambulant SCP (17±2 years) and ten TD individuals (18±2 years) participated in the study. Physiological cross sectional area was estimated using freehand 3D ultrasound and found to be 37% lower in the SCP group. An isokinetic dynamometer rotated the ankle through its range while joint torque and ultrasound images of the MG muscle fascicles were simultaneously measured. Mean ankle stiffness was found to be 51% higher and mean MG fascicle strain 47% lower in the SCP group. Increased resistance to passive ankle dorsiflexion in SCP appears to be related to the inability of MG muscle fascicles to elongate with increased force.     

Theoretical considerations for muscle-energy savings during distance running

We have recently demonstrated that the triceps surae muscles energy cost (EC_TS) represents a substantial portion of the total metabolic cost of running (E_run). Therefore, it seems relevant to evaluate the factors which dictate EC_TS, namely the amount and velocity of shortening, since it is likely these factors will dictate E_run. E_run and triceps surae morphological and AT mechanical properties were obtained in 46 trained and elite male and female distance runners using ultrasonography and dynamometry. EC_TS (J·stride⁻¹) at the speed of lactate threshold (sLT) was estimated from AT force and crossbridge mechanics and energetics. To estimate the relative impact of these factors on EC_TS, mean values for running speed, body mass, resting fascicle length (L_f), Achilles tendon stiffness and moment arm and maximum isometric plantarflexion torque were obtained. EC_TS was calculated across a range (mean ± 1 sd) of values for each independent factor. Average sLT was 233 m·min⁻¹. At this speed, EC_TS was 255 J·stride⁻¹. Estimated fascicle shortening velocity was 0.08 V_max and the level of muscle activation was 84.7% of maximum isometric torque. Compared to the EC_TS calculated from the lowest range of values obtained for each independent factor, higher AT stiffness was associated with a 39% reduction in EC_TS, 81% reduction in fascicle shortening velocity and a 31% reduction in muscle activation. Longer AT moment arms and elevated body masses were associated with an increase in EC_TS of 18% and 23%, respectively. These results demonstrate that a low EC_TS is achieved primarily from a high AT stiffness and low body mass, which is exemplified in elite distance runners.