A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo

The study of muscle growth and muscle length adaptations requires measurement of passive length-tension properties of individual muscles, but until now such measurements have only been made in animal muscles. We describe a new method for measuring passive length-tension properties of human gastrocnemius muscles in vivo. Passive ankle torque and ankle angle data were obtained as the ankle was rotated through its full range with the knee in a range of positions. To extract gastrocnemius passive length-tension curves from passive torque-angle data it was assumed that passive ankle torque was the sum of torque due to structures which crossed only the ankle joint (this torque was a 6-parameter function of ankle joint angle) and a torque due to the gastrocnemius muscle (a 3-parameter function of knee and ankle angle). Parameter values were estimated with non-linear regression and used to reconstruct passive length-tension curves of the gastrocnemius. The reliability of the method was examined in 11 subjects by comparing three sets of measurements: two on the same day and the other at least a week later. Length-tension curves were reproducible: the average root mean square error was 5.1+/-1.1 N for pairs of measurements taken within a day and 7.3+/-1.2 N for pairs of measurements taken at least a week apart (about 3% and 6% of maximal passive tension, respectively). Length-tension curves were sensitive to mis-specification of moment arms, but changes in length-tension curves were not. The new method enables reliable measurement of passive length-tension properties of human gastrocnemius in vivo, and is likely to be useful for investigation of changes in length-tension curves over time.     

Rises in whole muscle passive tension of mammalian muscle after eccentric contractions at different lengths.

This is a report of experiments carried out on the medial gastrocnemius muscle of the anesthetized cat, investigating the effects of eccentric contractions carried out at different muscle lengths on the passive and active length-tension relationships. In one series of experiments, the motor supply to the muscle was divided into three approximately equal parts; in the other, whole muscles were used. Fifty eccentric contractions were carried out over different regions of the active length-tension curve for each partial or whole muscle. Active and passive length-tension curves were measured before and after the eccentric contractions. When eccentric contractions were carried out at longer lengths, there was a larger shift of the optimum length for active tension in the direction of longer muscle lengths and a larger fall in peak isometric tension. Passive tension was higher immediately after the eccentric contractions, and if the muscle was left undisturbed for 40 min, it increased further to higher values, particularly after contractions at longer lengths. A series of 20 passive stretches of the same speed and amplitude and covering the same length range as the active stretches, reduced the passive tension which redeveloped over a subsequent 40-min period. It is hypothesized that there are two factors influencing the level of passive tension in a muscle after a series of eccentric contractions. One is injury contractures in damaged muscle fibers tending to raise passive tension; the other is the presence of disrupted sarcomeres in series with still-functioning sarcomeres tending to reduce it.     

Myofascial force transmission between the human soleus and gastrocnemius muscles during passive knee motion

The plantarflexors of the lower limb are often assumed to act as independent actuators, but the validity of this assumption is the subject of considerable debate. This study aims to determine the degree to which passive changes in gastrocnemius muscle length, induced by knee motion, affect the tension in the adjacent soleus muscle. A second aim is to quantify the magnitude of myofascial passive force transmission between gastrocnemius and adjacent soleus. Fifteen healthy volunteers participated. Simultaneous ultrasound images of the gastrocnemius and soleus muscles were obtained during passive knee flexion (0-90°), while keeping the ankle angle fixed at either 70° or 115°. Image correlation analysis was used to quantify muscle fascicle lengths in both muscles. The data show that the soleus muscle fascicles elongate significantly during gastrocnemius shortening. The approximate change in passive soleus force as a result of the observed change in fascicle length was estimated and appears to be <5 N, but this estimate is sensitive to the assumed slack length of soleus.     

The length dependence of muscle active force: considerations for parallel elastic properties.

The purpose of this study was to choose between two popular models of skeletal muscle: one with the parallel elastic component in parallel with both the contractile element and the series elastic component (model A), and the other in which it is in parallel with only the contractile element (model B). Passive and total forces were obtained at a variety of muscle lengths for the medial gastrocnemius muscle in anesthetized rats. Passive force was measured before the contraction (passive A) or was estimated for the fascicle length at which peak total force occurred (passive B). Fascicle length was measured with sonomicrometry. Active force was calculated by subtracting passive (A or B) force from peak total force at each fascicle or muscle length. Optimal length, that fascicle length at which active force is maximized, was 13.1 +/- 1.2 mm when passive A was subtracted and 14.0 +/- 1.1 mm with passive B (P < 0.01). Furthermore, the relationship between double-pulse contraction force and length was broader when calculated with passive B than with passive A. When the muscle was held at a long length, passive force decreased due to stress relaxation. This was accompanied by no change in fascicle length at the peak of the contraction and only a small corresponding decrease in peak total force. There is no explanation for the apparent increase in active force that would be obtained when subtracting passive A from the peak total force. Therefore, to calculate active force, it is appropriate to subtract passive force measured at the fascicle length corresponding to the length at which peak total force occurs, rather than passive force measured at the length at which the contraction begins.     

Viscous elements have little impact on measured passive length-tension properties of human gastrocnemius muscle-tendon units in vivo

Several studies have measured the elastic properties of a single human muscle-tendon unit in vivo. However the viscoelastic behavior of single human muscles has not been characterized. In this study, we adapted QLV theory to model the viscoelastic behavior of human gastrocnemius muscle-tendon units in vivo. We also determined the influence of viscoelasticity on passive length-tension properties of human gastrocnemius muscle-tendon units. Eight subjects participated in the experiment, which consisted of two parts. First, the stress relaxation response of human gastrocnemius muscle-tendon units was determined at a range of knee and ankle angles. Subsequently, passive ankle torque and ankle angle were collected during cyclic dorsiflexion and plantarflexion at a range of knee angles. Viscous parameters were determined by fitting the stress relaxation experiment data with a two-term exponential function, and elastic parameters were estimated by fitting the QLV model and viscous parameters to the cyclic experiment data. The model fitted the experimental data well at slow speeds (RMSE: 1.7 ± 0.5N) and at fast speeds (RMSE: 1.9 ± 0.2N). Muscle-tendon units demonstrated a large amount of stress relaxation. Nonetheless, viscoelastic passive length-tension curves estimated with the QLV model were similar to elastic passive length-tension curves obtained using a model that ignored viscosity. There was little difference in the elastic passive length-tension curves at different loading rates. We conclude that (a) the QLV model can be used to quantify viscoelastic behaviors of relaxed human gastrocnemius muscle-tendon units in vivo, and (b) over the range of velocities we examined, the velocity of loading has little effect on the passive length-tension properties of human gastrocnemius muscle-tendon units.     

Reliability and accuracy of an automated tracking algorithm to measure controlled passive and active muscle fascicle length changes from ultrasound

Manual tracking of muscle fascicle length changes from ultrasound images is a subjective and time-consuming process. The purpose of this study was to assess the repeatability and accuracy of an automated algorithm for tracking fascicle length changes in the medial gastrocnemius (MG) muscle during passive length changes and active contractions (isometric, concentric and eccentric) performed on a dynamometer. The freely available, automated tracking algorithm was based on the Lucas–Kanade optical flow algorithm with an affine optic flow extension, which accounts for image translation, dilation, rotation and shear between consecutive frames of an image sequence. Automated tracking was performed by three experienced assessors, and within- and between-examiner repeatability was computed using the coefficient of multiple determination (CMD). Fascicle tracking data were also compared with manual digitisation of the same image sequences, and the level of agreement between the two methods was calculated using the coefficient of multiple correlation (CMC). The CMDs across all test conditions ranged from 0.50 to 0.93 and were all above 0.98 when recomputed after the systematic error due to the estimate of the initial fascicle length on the first ultrasound frame was removed from the individual fascicle length waveforms. The automated and manual tracking approaches produced similar fascicle length waveforms, with an overall CMC of 0.88, which improved to 0.94 when the initial length offset was removed. Overall results indicate that the automated fascicle tracking algorithm was a repeatable, accurate and time-efficient method for estimating fascicle length changes of the MG muscle in controlled passive and active conditions.     

Validity of Measurement of Shear Modulus by Ultrasound Shear Wave Elastography in Human Pennate Muscle

Ultrasound shear wave elastography is becoming a valuable tool for measuring mechanical properties of individual muscles. Since ultrasound shear wave elastography measures shear modulus along the principal axis of the probe (i.e., along the transverse axis of the imaging plane), the measured shear modulus most accurately represents the mechanical property of the muscle along the fascicle direction when the probe’s principal axis is parallel to the fascicle direction in the plane of the ultrasound image. However, it is unclear how the measured shear modulus is affected by the probe angle relative to the fascicle direction in the same plane. The purpose of the present study was therefore to examine whether the angle between the principal axis of the probe and the fascicle direction in the same plane affects the measured shear modulus. Shear modulus in seven specially-designed tissue-mimicking phantoms, and in eleven human in-vivo biceps brachii and medial gastrocnemius were determined by using ultrasound shear wave elastography. The probe was positioned parallel or 20° obliquely to the fascicle across the B-mode images. The reproducibility of shear modulus measurements was high for both parallel and oblique conditions. Although there was a significant effect of the probe angle relative to the fascicle on the shear modulus in human experiment, the magnitude was negligibly small. These findings indicate that the ultrasound shear wave elastography is a valid tool for evaluating the mechanical property of pennate muscles along the fascicle direction.     

Control of human eye movements: I. modelling of extraocular muscle

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

Control of human eye movements: III. dynamic characteristics of the eye tracking mechanism

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

Dependence of the length-tension relationship on agonist concentration in vascular smooth muscle

This study examines the dependence of the length-tension (L-T) relationship in vascular smooth muscle on its level of activation. A horizontal shift of the L-T relationship with a change in activation level has been shown in striated muscle when L-T curves could not be superimposed. Active force at each length was normalized to the maximum active force in each curve. Indices of a horizontal shift of a L-T curve include the initial length for an active response (Li) and the length for maximum active force (Lmax). In this study normalized L-T curves were obtained from rings of the dog anterior tibial artery at low (approximately ED50) and high (maximal activation) concentrations of potassium (K+), norepinephrine (NE), and calcium (Ca2+). The normalized curve with a low concentration of K+ or NE was shifted to the right of the curve obtained with a high concentration. Li and Lmax were significantly longer for a low concentration of K+ or NE than a high concentration. With the same concentration of NE (10(-5) M) no difference in the normalized L-T curves, in Li, or in Lmax were found when low (0.085 mM) Ca2+ experiments were compared to normal (1.7 mM) Ca2+ experiments. It may be concluded that the length-tension relationship in vascular smooth muscle is shifted to longer lengths with a decrease in the concentration of a chemical agonist but not by a decrease in external calcium. We suggest that a concentration dependent shift in the length-tension relationship may have a role in the regulation of blood flow.     

Estimation of passive ankle joint moment during standing and walking

This study estimated the passive ankle joint moment during standing and walking initiation and its contribution to total ankle joint moment during that time. The decrement of passive joint moment due to muscle fascicle shortening upon contraction was taken into account. Muscle fascicle length in the medial gastrocnemius, which was assumed to represent muscle fascicle length in plantarflexors, was measured using ultrasonography during standing, walking initiation, and cyclical slow passive ankle joint motion. Total ankle joint moment during standing and walking initiation was calculated from ground reaction forces and joint kinematics. Passive ankle joint moment during the cyclical ankle joint motion was measured via a dynamometer. Passive ankle joint moment during standing and at the time (Tp) when the MG muscle-tendon complex length was longest in the stance phase during walking initiation were 2.3 and 5.4 Nm, respectively. The muscle fascicle shortened by 2.9 mm during standing compared with the length at rest, which decreased the contribution of passive joint moment from 19.9% to 17.4%. The muscle fascicle shortened by 4.3 mm at Tp compared with the length at rest, which decreased the contribution of passive joint moment from 8.0% to 5.8%. These findings suggest that (a) passive ankle joint moment plays an important role during standing and walking initiation even in view of the decrement of passive joint moment due to muscle fascicle shortening upon muscle contraction, and (b) muscle fascicle shortening upon muscle contraction must be taken into account when estimating passive joint moment during movements.     

Fascicle length of gastrocnemius muscles in monozygous twins

A large inter-individual variation is seen in muscle fascicle length of the athletes but the reasons for this phenomenon are unclear. The purpose of this study was to determine whether genetic factors contribute to the variances in muscle architectural characteristics. Nine monozygous twin pairs (3 males and 6 females), mean age 23 years (range 17-40) were studied. Fascicle length, pennation angle, and muscle thickness of the medial (MG) and lateral (LG) gastrocnemius muscles were measured in vivo by B-mode ultrasound. In the LG muscle intrapair resemblance (P < 0.01) for fascicle length (r = 0.98), pennation angle (r = 0.94) and muscle thickness (r = 0.86) were observed. In MG muscle, however, there was no intrapair resemblance for fascicle length (r = 0.66, P > 0.05), although pennation angle (r = 0.73, P < 0.05) and muscle thickness (r = 0.86, P < 0.01) were significant. Mean percent intrapair difference in LG and MG muscles were 1.8% and 5.1% for fascicle length, 11.3% and 12.3% for pennation angle and 12.4% and 9.9% for muscle thickness, respectively. There is intrapair difference between muscle thickness and pennation angle in both MG (r = 0.69, P < 0.05) and LG (r = 0.70, P < 0.05) muscles. However, no significant correlation was observed for intrapair difference between muscle thickness and fascicle length in both muscles (MG, r = 0.46; LG, r = 0.40). It appears that genetic predisposition is the predominant factor for the determination of muscle fascicle length. However, a lack of intrapair resemblance in MG fascicle length raises the possibility that fascicle length may be further influenced by external environmental factors such as physical training.     

In vivo determination of fascicle curvature in contracting human skeletal muscles.

Fascicle curvature of human medial gastrocnemius muscle (MG) was determined in vivo by ultrasonography during isometric contractions at three (distal, central, and proximal) locations (n = 7) and at three ankle angles (n = 7). The curvature significantly (P < 0.05) increased from rest to maximum voluntary contraction (MVC) (0.4-5.2 m(-1)). In addition, the curvature at MVC became larger in the order dorsiflexed, neutral, plantar flexed (P < 0.05). Thus both contraction levels and muscle length affected the curvature. Intramuscular differences in neither the curvature nor the fascicle length were found. The direction of curving was consistent along the muscle: fascicles were concave in the proximal side. Fascicle length estimated from the pennation angle and muscle thickness, under the assumption that the fascicle was straight, was underestimated by ~6%. In addition, the curvature was significantly correlated to pennation angle and muscle thickness. These findings are particularly important for understanding the mechanical functions of human skeletal muscle in vivo.     

In vivo passive mechanical properties of the human gastrocnemius muscle belly

The purpose of the present study was to determine the in vivo passive mechanical properties, including the length below the slack length, of the gastrocnemius muscle (GAS) belly in humans. Transverse ultrasound images of the medial head of the GAS were taken in 11 subjects during passive knee extension from 80 degrees to 5 degrees with a constant ankle joint angle of 10 degrees (0 degrees is the neutral ankle position: positive values for dorsiflexion). The change in passive ankle joint moment (Mp), which is produced only by the GAS length change, was also measured during passive knee extension. The onset of Mp during passive knee extension was found to be 43+/-8 degrees (mean+/-SD) when the baseline of the Mp was set at the average Mp in the range of 55-60 degrees where the Mp was almost constant (SD<0.03 Nm). At this onset, the muscle fascicle length of the GAS (Lf) was 46+/-7 mm (slack length; Lfs). Lf at 80 degrees was 6+/-4 mm (13+/-6%) less than the Lfs, and Lf at 5 degrees was 12+/-5 mm (27+/-11%) greater than the Lfs. The passive force-resisting compression of the GAS did not produce a dorsiflexion moment in the joint angle range adopted. The passive ankle joint moment increased linearly with Lf (coefficient of determination (R2)=0.85-0.96), and the slopes of the relationships between Lf and Mp, and between the relative Lf to Lfs and Mp were 0.093+/-0.038 Nm/mm and 0.043+/-0.021 Nm/%Lfs. The findings of the present study can be implemented in musculoskeletal modeling, which would provide a more accurate evaluation of the passive mechanical properties of muscle during movement.     

Resonance in the human medial gastrocnemius muscle during cyclic ankle bending exercise.

We investigated the behavior of the muscle tendon unit (MTU) of the medial gastrocnemius muscle during cyclic ankle bending exercise at eight different frequencies (ranging from 1.33 to 3.67 Hz). The changes in the length of fascicle in the muscle during the exercises were determined by real-time ultrasound imaging. The coordinates of anatomical references and the ground reaction force were determined from video recording and a force plate, respectively. The length change of the MTU (the distance from the origin to insertion of the muscle) was calculated from changes in the knee and ankle joint angles. It was found that the amplitude ratio and phase difference between the fascicle and MTU lengths were both dependent on the movement frequency. At lower frequencies, the fascicle lengths varied almost in phase with the MTU length, whereas they varied out of phase at the higher frequencies. At intermediate frequency, the amplitude of the fascicle became very small compared with that of the MTU, which is considered resonance. We constructed a mechanical model of the MTU based on a notion of forced oscillation in a mass-spring system. The obtained data were well explained by the model. It was concluded that the behavior of the MTU highly depends on the movement frequency due to the viscoelasticity of the MTU.     

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.     

Automated regional analysis of B-mode ultrasound images of skeletal muscle movement

To understand the functional significance of skeletal muscle anatomy, a method of quantifying local shape changes in different tissue structures during dynamic tasks is required. Taking advantage of the good spatial and temporal resolution of B-mode ultrasound imaging, we describe a method of automatically segmenting images into fascicle and aponeurosis regions and tracking movement of features, independently, in localized portions of each tissue. Ultrasound images (25 Hz) of the medial gastrocnemius muscle were collected from eight participants during ankle joint rotation (2° and 20°), isometric contractions (1, 5, and 50 Nm), and deep knee bends. A Kanade-Lucas-Tomasi feature tracker was used to identify and track any distinctive and persistent features within the image sequences. A velocity field representation of local movement was then found and subdivided between fascicle and aponeurosis regions using segmentations from a multiresolution active shape model (ASM). Movement in each region was quantified by interpolating the effect of the fields on a set of probes. ASM segmentation results were compared with hand-labeled data, while aponeurosis and fascicle movement were compared with results from a previously documented cross-correlation approach. ASM provided good image segmentations (<1 mm average error), with fully automatic initialization possible in sequences from seven participants. Feature tracking provided similar length change results to the cross-correlation approach for small movements, while outperforming it in larger movements. The proposed method provides the potential to distinguish between active and passive changes in muscle shape and model strain distributions during different movements/conditions and quantify nonhomogeneous strain along aponeuroses.     

A quantitative model of intersarcomere dynamics during fixed-end contractions of single frog muscle fibers.

A numerical model of a muscle fiber as 400 sarcomeres, identical except for their initial lengths, was used to simulate fixed-end tetanic contractions of frog single fibers at sarcomere lengths above the optimum. The sarcomeres were represented by a lumped model, constructed from the passive and active sarcomere length-tension curves, the force-velocity curve, and the observed active elasticity of a single frog muscle fiber. An intersarcomere force was included to prevent large disparities in lengths of neighboring sarcomeres. The model duplicated the fast rise, slow creep rise, peak, and slow decline of tension seen in tetanic contractions of stretched living fibers. Decreasing the initial non-uniformity of sarcomere length reduced the rate of rise of tension during the creep phase, but did not decrease the peak tension reached. Limitations of the model, and other processes that might contribute to the shape of the fixed end tetanic tension record are discussed. Taking account of model and experimental results, it is concluded that the distinctive features of the tension records of fixed end tetanic contraction at lengths beyond optimum can be explained by internal motion within the fiber.     

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.     

Changes in fascicle length from rest to maximal voluntary contraction affect the assessment of voluntary activation

The purpose of this study was to investigate the effect of the differences between the actual fascicle length during a voluntary contraction and the fascicle length at rest of the triceps surae muscle on the determination of the voluntary activation (VA) by using the interpolated twitch technique. Twelve participants performed isometric voluntary maximal (MVC) and submaximal (20%, 40%, 60% and 80% MVC) contractions at two different ankle angles (75 degrees and 90 degrees ) under application of the interpolated twitch technique. Two ultrasound probes were used to determine the fascicle length of soleus, gastrocnemius medialis and gastrocnemius lateralis muscles. Further, the MVCs and the twitches were repeated for six more ankle angles (85 degrees , 95 degrees , 100 degrees , 105 degrees , 110 degrees and 115 degrees ). The VA of the triceps surae muscle were calculated (a) using the rest twitch force (RTF) measured during the same trial as the interpolated twitch force (ITF; traditional method) and (b) using the RTF at an ankle angle where the fascicle length showed similar values between ITF and RTF (fascicle length consideration method). The continuous changes in fascicle length from rest to MVC affect the accuracy of the assessment of the VA. The traditional method overestimates the assessment of the VA on average 4% to 12%, especially at 90 degrees ankle angle (i.e. short muscle length). The reason for this influence is the unequal force-length potential of the muscle at twitch application by the measure of ITF and RTF. These findings provide evidence that the fascicle length consideration method permits a more precise prediction (an improvement of 4-12%) of the voluntary contraction compared to the traditional method.