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.     

Automatic tracking of medial gastrocnemius fascicle length during human locomotion

During human locomotion lower extremity muscle-tendon units undergo cyclic length changes that were previously assumed to be representative of muscle fascicle length changes. Measurements in cats and humans have since revealed that muscle fascicle length changes can be uncoupled from those of the muscle-tendon unit. Ultrasonography is frequently used to estimate fascicle length changes during human locomotion. Fascicle length analysis requires time consuming manual methods that are prone to human error and experimenter bias. To bypass these limitations, we have developed an automatic fascicle tracking method based on the Lucas-Kanade optical flow algorithm with an affine optic flow extension. The aims of this study were to compare gastrocnemius fascicle length changes during locomotion using the automated and manual approaches and to determine the repeatability of the automated approach. Ultrasound was used to examine gastrocnemius fascicle lengths in eight participants walking at 4, 5, 6, and 7 km/h and jogging at 7 km/h on a treadmill. Ground reaction forces and three dimensional kinematics were recorded simultaneously. The level of agreement between methods and the repeatability of the automated method were quantified using the coefficient of multiple correlation (CMC). Regardless of speed, the level of agreement between methods was high, with overall CMC values of 0.90 ± 0.09 (95% CI: 0.86-0.95). Repeatability of the algorithm was also high, with an overall CMC of 0.88 ± 0.08 (95% CI: 0.79-0.96). The automated fascicle tracking method presented here is a robust, reliable, and time-efficient alternative to the manual analysis of muscle fascicle length during gait.     

Theoretical series elastic element length in Rana pipiens sartorius muscles

Assuming a two component system for the muscle, a series elastic element and a contractile component, the analyses of the isotonic and isometric data points were related to obtain the series elastic stiffness, dP/dl_s, from the relation, See PDF for Equation From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (P₀ - P)/T for dP/dt and (P₀ - P)/(P + a) times b for v, dP/dl_s = (P + a) /bT, where P < P₀, and a, b are constants for any lengths l ≤ l₀ (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, l₀, although the series elastic, l_s, and the contractile component, l_c, are changing, the total muscle length, l₀ remains fixed and therefore the time constant, T. Integrating, See PDF for Equation the stress-strain relation for the series elastic element, See PDF for Equation is obtained; l_sc0 - l_s + l_c0where l_co equals the contractile component length for a muscle exerting a tension of P₀. For a given P/P₀, l_s is uniquely determined and must be the same whether on the isotonic or isometric length-tension-time curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other.     

Measurements of volume changes and venous pressure in the human lower leg during walking and running.

This study investigates whether walking or running prevents the formation of edema in the lower leg. In 18 volunteers changes in calf volume were measured using strain gauge plethysmography during slow (3 km/h) and fast (6 km/h) walking or running (10 km/h) on a treadmill for 20 min each. Venous pressure was measured in a superficial vein near the ankle. Low-pass filtering removed motion artifacts from the signals. Slow walking reduced the calf volume in a biphasic manner: a rapid decrease was followed by a slow decline, lasting from about minute 2 to minute 20, its mean rate being -0.073%/min. Besides a rapid initial decrease, no significant change was observed during fast walking. During running, the calf volume first increased within 7 min to a maximum of 2.5% and subsequently decreased with a mean rate of -0.096%/min. The medians of venous pressure were 84.0, 23.5, 30.4, and 29.5 mmHg during quiet standing, slow and fast walking, and running, respectively. The experimental results prove the hypothesis that walking prevents dependent edema formation. This effect, however, cannot be fully explained by the lowered venous pressures.     

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

In typical muscle models, it is often assumed that the contractile element (fascicle) length depends exclusively on the instantaneous muscle-tendon length and the instantaneous muscle force. In order to test whether the instantaneous fascicle length during dynamic contractions can be predicted from muscle-tendon length and force, fascicle lengths, muscle-tendon lengths, and muscle forces were directly measured in cat medial gastrocnemii during isometric and dynamic contractions. Two theoretical muscle models were developed: model A was based on force-time data obtained during the activation phase and model D on force-time data obtained during the deactivation phase of isometric contractions. To test the models, instantaneous fascicle lengths were predicted from muscle-tendon lengths and forces during dynamic contractions that simulated cat locomotion for speeds ranging from 0.4 to 1.6m/s. The theoretically predicted fascicle lengths were compared with the experimentally measured fascicle lengths. It was found that fascicle lengths were not uniquely associated with muscle-tendon lengths and forces; that is, for a given muscle-tendon length and force, fascicle lengths varied depending on the contractile history. Consequently, models A and D differed in fascicle length predictions; model D (maximum average error=8.5%) was considerably better than model A (maximum average error=22.3%). We conclude from this study that it is not possible to predict the exact fascicle lengths from muscle-tendon lengths and forces alone, however, adequate predictions seem possible based on such a model. The relationship between fascicle length and muscle force and muscle-tendon length is complex and highly non-linear, thus, it appears unlikely that accurate fascicle length predictions can be made without some reference contractions in which fascicle length, muscle-tendon length, and force are measured simultaneously.     

Effect of different ankle- and knee-joint positions on gastrocnemius medialis fascicle length and EMG activity during isometric plantar flexion

The purpose of this study was to provide evidence on the fact that the observed decrease in EMG activity of the gastrocnemius medialis (GM) at pronounced knee flexed positions is not only due to GM insufficiency, by examining muscle fascicle lengths during maximal voluntary contractions at different positions. Twenty-two male long distance runners (body mass: 78.5+/-6.7 kg, height: 183+/-6 cm) participated in the study. The subjects performed isometric maximal voluntary plantar flexion contractions (MVC) of their left leg at six ankle-knee angle combinations. To examine the resultant ankle joint moments the kinematics of the left leg were recorded using a Vicon 624 system with 8 cameras operating at 120 Hz. The EMG activity of GM, gastrocnemius lateralis (GL), soleus (SOL) and tibialis anterior (TA) were measured using surface electromyography. Synchronously, fascicle length and pennation angle values of the GM were obtained at rest and at the plateau of the maximal plantar flexion using ultrasonography. The main findings were: (a) identifiable differences in fascicle length of the GM at rest do not necessarily imply that these differences would also exist during a maximal isometric plantar flexion contraction and (b) the EMG activity of the biarticular GM during the MVC decreased at a pronounced flexed knee-joint position (up to 110 degrees ) despite of no differences in GM fascicle length. It is suggested that the decrease in EMG activity of the GM at pronounced knee flexed positions is due to a critical force-length potential of all three muscles of the triceps surae.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

Muscle fiber and tendon length changes in the human vastus lateralis during slow pedaling.

Muscle fascicle lengths of vastus lateralis (VL) muscle were measured in five healthy men during slow pedaling to investigate the interaction between muscle fibers and tendon. Subjects cycled at a pedaling rate of 40 rpm (98 W). During exercise, fascicle lengths changed from 91 +/- 7 (SE) to 127 +/- 5 mm. It was suggested that fascicles were on the descending limb of their force-length relationship. The average shortening velocity of fascicle was greater than that of muscle-tendon complex in the first half of the knee extension phase and was less in the second half. The maximum shortening velocity of fascicle in the knee extension phase was less than that of muscle-tendon complex by 22 +/- 9%. These discrepancies in velocities were mainly caused by the elongation of the tendinous tissue. It was suggested that the elasticity of VL tendinous tissue enabled VL fascicles to develop force at closer length to their optimal length and kept the maximum shortening velocity of VL fascicles low during slow pedaling.     

Selective activation of human soleus and medial gastrocnemius muscles during walking in water

During walking in water (WW) the vertical component of ground reaction forces decreases, while the greater propulsive force is required to move forward against the greater resistance of water. In such reduced gravity environment, Hutchison et al. (1989) have demonstrated that the relative activation of rat medial gastrocnemius (MGAS) increased compared to that of the soleus (SOL) during swimming, suggesting different effects of peripheral information on motoneuron excitability of these muscles. It is conceivable that both buoyancy and resistance of water have different effects on the activation patterns of triceps surae muscles during WW, since the reduced weight in water might decrease the peripheral inflow relating load information while greater volitional command might be needed to propel a body forward against the water resistance. The present study was designed to assess each peripheral inflow and efferent input by adjusting the load and walking speed voluntarily during WW. The aim of this study is to investigate the dissociative activation pattern between the SOL and the MGAS during WW.     

Effects of the length ratio between the contractile element and the series elastic element on an explosive muscular performance.

Effects of the length ratio between the contractile element (CE) and the series elastic element (SEE) on the behavior of the muscle tendon complex were investigated during stretch-shortening cycles. A computer simulation model of the Hill-type muscle tendon complex was constructed. The proximal end of the CE was affixed to a point in the gravitational field, and a massless supporting object was affixed to the distal end of the SEE. A mass was held on the supporting object. Initially, the muscle tendon complex was fixed at a certain length, and the CE was activated at 100%. Through this process, the CE contracted as much as the SEE was stretched. Thereafter, the supporting object was released, which caused the muscle tendon complex to propel the mass upward, simulating a stretch-shortening cycle. The length ratio between the CE and the SEE, the size of the mass and the initial length of the CE were sequentially changed. As a result, it was found that a higher performance is obtained with a longer SEE when the mass is small, while with a shorter SEE when the mass is large.     

Influence of gait velocity on gastrocnemius muscle fascicle behaviour during stair negotiation

The gastrocnemius medialis (GM) muscle plays an important role in stair negotiation. The aim of the study was to investigate the influence of cadence on GM muscle fascicle behaviour during stair ascent and descent. Ten male subjects (young adults) walked up and down a four-step staircase (with forceplates embedded in the steps) at three velocities (63, 88 and 116 steps/min). GM muscle fascicle length was measured using ultrasonography. In addition, kinematic and kinetic data of the lower legs, and GM electromyography (EMG) were measured. For both ascent and descent, the amount of fascicular shortening, shortening velocity, knee moment, ground reaction force and EMG activity increased monotonically with gait velocity. The ankle moment increased up to 88 steps/min where it reached a plateau. The lack of increase in ankle moment coinciding with further shortening of the fascicles can be explained by an increased shortening of the GM musculotendon complex (MTC), as calculated from the knee and ankle angle changes, between 88 and 116 steps/min only. For descent, the relative instant of maximum shortening, which occurred during touch down, was delayed at higher gait velocities, even to the extent that this event shifted from the double support to the single support phase.     

Empirical evaluation of gastrocnemius and soleus function during walking

Distinguishing gastrocnemius and soleus muscle function is relevant for treating gait disorders in which abnormal plantarflexor activity may contribute to pathological movement patterns. Our objective was to use experimental and computational analysis to determine the influence of gastrocnemius and soleus activity on lower limb movement, and determine if anatomical variability of the gastrocnemius affected its function. Our hypothesis was that these muscles exhibit distinct functions, with the gastrocnemius inducing limb flexion and the soleus inducing limb extension. To test this hypothesis, the gastrocnemius or soleus of 20 healthy participants was electrically stimulated for brief periods (90 ms) during mid- or terminal stance of a random gait cycle. Muscle function was characterized by the induced change in sagittal pelvis, hip, knee, and ankle angles occurring during the 200 ms after stimulation onset. Results were corroborated with computational forward dynamic gait models, by perturbing gastrocnemius or soleus activity during similar portions of the gait cycle. Mid- and terminal stance gastrocnemius stimulation induced posterior pelvic tilt, hip flexion and knee flexion. Mid-stance gastrocnemius stimulation also induced ankle dorsiflexion. In contrast mid-stance soleus stimulation induced anterior pelvic tilt, knee extension and plantarflexion, while late-stance soleus stimulation induced relatively little change in motion. Model predictions of induced hip, knee, and ankle motion were generally in the same direction as those of the experiments, though the gastrocnemius? results were shown to be quite sensitive to its knee-to-ankle moment arm ratio.     

Influence of step-height and body mass on gastrocnemius muscle fascicle behavior during stair ascent

To better understand the role of the ankle plantar flexor muscles in stair negotiation, we examined the effects of manipulation of kinematic and kinetic constraints on the behavior of the gastrocnemius medialis (GM) muscle during stair ascent. Ten subjects ascended a four-step staircase at four different step-heights (changing the kinematic constraints): standard (17 cm), 50% decreased, 50% increased and 75% increased. At the standard height, subjects also ascended the stairs wearing a weighted jacket, adding 20% of their body mass (changing the kinetic constraints). During stair ascent, kinematics and kinetics of the lower legs were determined using motion capture and ground reaction force measurements. The GM muscle fascicle length was measured during the task with ultrasonography. The amount of GM muscle fascicle shortening increased with step-height, coinciding with an increase in ankle joint moment. The increase in body mass resulted in an increased ankle joint moment, but the amount of GM muscle fascicle shortening during the lift-off phase did not increase, instead, the fascicles were shorter over the whole stride cycle. Increasing demands of stair ascent, by increasing step-height or body mass, requires higher joint moments. The increased ankle joint moment with increasing demands is, at least in part, produced by the increase in GM muscle fascicle shortening.     

Reproducibility of gastrocnemius medialis muscle architecture during treadmill running

The purpose of this study was to assess the reproducibility of fascicle length (FL) and pennation angle (PA) of gastrocnemius medialis (GM) muscle during running in vivo. Twelve male recreational long distance runners (mean ± SD; age: 24 ± 3 years, mass: 76 ± 7 kg) ran on a treadmill at a speed of 3.0 m/s, wearing their own running shoes, for two different 10 min sessions that were at least 2 days apart. For each test day 10 acceptable trials were recorded. Ankle and knee joint angle data were recorded by a Vicon 624 system with three cameras operating at 120 Hz. B-mode ultrasonography was used to examine fascicle length and pennation angle of gastrocnemius medialis muscle. The ultrasound probe was firmly secured on the muscle belly using a lightweight foam fixation. The results indicated that fascicle length and pennation angle demonstrated high reproducibility values during treadmill running both for within and between test days. The root mean square scores between the repeated waveforms of pennation angle and fascicle length were small (∼2° and ∼3.5 mm, respectively). However, ∼14 trials for pennation angle and ∼9 trials for fascicle length may be required in order to record accurate data from muscle architecture parameters. In conclusion, ultrasound measurements may be highly reproducible during dynamic movements such as treadmill running, provided that a proper fixation is used in order to assure the constant location and orientation of the ultrasound probe throughout the movement.     

Three-dimensional acceleration of the tibia during walking and running.

Measurements of tibial acceleration during walking and running were obtained by means of a triaxial accelerometer. The accelerometer was fixed to the free end of a Steinmann pin inserted into the right tibia of one volunteer subject. The patterns of tibial acceleration showed little step-to-step variation within each experimental condition. Following foot strike and depending upon footwear, the resultant tibial acceleration reached between 2.7 and 3.7 g during walking. The tibia experienced maximal accelerations of 10.6 g during running. The high values of tibial acceleration recorded in the antero-posterior (AP) and medio-lateral (ML) directions clearly revealed the importance of measuring all three components of acceleration to quantify the magnitude of the shock experienced by the lower limbs during locomotor activities.     

Passive knee movement-induced modulation of the soleus H-reflex and alteration in the fascicle length of the medial gastrocnemius muscle in humans

In humans, an inhibitory via Ia afferent pathway from the medial gastrocnemius (MG) to the soleus (SOL) motoneuron pool has been suggested. Herein, we examined the relation between MG fascicle length changes and the SOL H-reflex modulation during passive knee movement. Twelve subjects performed static and passive (5° s^?1) knee movement tasks with the ankle immobilized using an isokinetic dynamometer in sitting posture. The maximal H- and M-waves were measured at four target angles (20°, 40°, 60°, and 80° flexion from full knee extension). The MG fascicles length and velocity were measured using a B-mode ultrasonic apparatus. Results demonstrated that the SOL Hmax/Mmax; i.e., ratio of the maximal H- to M-waves, was attenuated with increasing MG fascicle length in static tasks. The SOL Hmax/Mmax at 20° was significantly attenuated compared with 60° and 80° with increasing MG fascicle length and lengthening velocity in passive knee extension. However, no significant differences in the SOL Hmax/Mmax were found across the target angles in the passive knee flexion task. In conclusion, as muscle spindles increase their discharge with lengthening fascicle velocity, but keep silent when fascicles shorten, our data suggest that lengthening the MG facilitates an inhibitory Ia pathway from MG to SOL, and modulates SOL motoneuron activity during movements.     

Muscle architecture variations along the human semitendinosus and biceps femoris (long head) length

The purpose of this study was to examine whether muscle architecture of the long head of biceps femoris (BF) and semitendinosus (ST) muscles varies along their length. The ST and BF muscles were dissected and removed from their origins in eight cadaveric specimens (age range 67.8–73.4 years). One-way analysis of variance designs were used to compare fascicle length (FL), pennation angle (PA) and muscle thickness (MT) between proximal, mid-belly and distal positions. Tendon and muscle length properties were also quantified. For the BF muscle, one-way analysis of variance tests showed a higher PA (23.96 ± 3.82°) and FL (7.12 ± 0.48 cm) proximally than distal positions (PA = 17.78 ± 1.95° and FL = 6.35 ± 0.89 cm, respectively). For the ST, there was a significantly (p < 0.05) lower PA (8.81 ± 1.22°) and FL (13.10 ± 1.54 cm) proximally than distally (PA = 14.69 ± 1.09° and FL = 15.49 ± 2.30 cm, respectively). Muscle thickness significantly increased from distal to more proximal positions (p < 0.05). These data suggest that the ST and BF architecture is not uniform and that measurement of these parameters largely depends on the measurement site. Modeling these muscles by assuming a uniform architecture along muscle length may yield less accurate representation of human hamstring muscle function.     

Relationship between lactate threshold during running and relative gastrocnemius area

This study examined the relationship between the work rate at which blood lactate accumulation begins (lactate threshold) during running and relative gastrocnemius area in four different groups. Twenty nonathletic and 11 athletic boys (age 9-12 yr), 15 female adult runners, and 11 male nonathletic students participated in this study. The muscle composition of the leg and thigh were measured by ultrasound. The lactate threshold was assessed in terms of both the absolute work rate (ml.kg-1.min-1) and relative work rate. The relative cross-sectional area of the gastrocnemius to the plantar flexor (relative gastrocnemius area) was significantly negatively related to the absolute and relative lactate threshold in all groups. These results suggest that the relative gastrocnemius area may play an important role in determining the relative and absolute lactate threshold during running.     

Effects of knee joint angle on the fascicle behavior of the gastrocnemius muscle during eccentric plantar flexions

The present study aimed to clarify the effects of knee joint angle on the behavior of the medial gastrocnemius muscle (MG) fascicles during eccentric plantar flexions. Eight male subjects performed maximal eccentric plantar flexions at two knee positions [fully extended (K0) and 90° flexed (K90)]. The eccentric actions were preceded by static plantar flexion at a 30° plantar flexed position and then the ankle joint was forcibly dorsiflexed to 15° of dorsiflexion with an isokinetic dynamometer at 30°/s and 150°/s. Tendon force was calculated by dividing the plantar flexion torque by the estimated moment arm of the Achilles tendon. The MG fascicle length was determined with ultrasonography. The tendon forces during eccentric plantar flexions were influenced by the knee joint angle, but not by the angular velocity. The MG fascicle lengths were elongated as the ankle was dorsiflexed in K0, but in K90 they were almost constant despite the identical range of ankle joint motion. These results suggested that MG fascicle behavior during eccentric actions was markedly affected by the knee joint angle. The difference in the fascicle behavior between K0 and K90 could be attributed to the non-linear force–length relations and/or to the slackness of tendinous tissues.