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.     

Stress relaxation of human ankles is only minimally affected by knee and ankle angle

Comprehensive characterization of stress relaxation in musculotendinous structures is needed to create robust models of viscoelastic behavior. The commonly used quasi-linear viscoelastic (QLV) theory requires that the relaxation response be independent of tissue strain (length). This study aims to characterize stress relaxation in the musculotendinous and ligamentous structures crossing the human ankle (ankle-only structures and the gastrocnemius muscle–tendon unit, which crosses the ankle and knee), and to determine whether stress relaxation is independent of the length of these structures. Two experiments were conducted on 8 healthy subjects. The first experiment compared stress relaxation over 10 min at different gastrocnemius muscle–tendon unit lengths keeping the length of ankle-joint only structures fixed. The second experiment compared stress relaxation at different lengths of ankle-joint only structures keeping gastrocnemius muscle–tendon unit length fixed. Stress relaxation data were fitted with a two-term exponential function (T=G₀+G₁e^?λ₁t+G₂e^?λ₂t). The first experiment demonstrated a significant effect of gastrocnemius muscle–tendon unit length on G₁, and the second experiment demonstrated an effect of the length of ankle-joint only structures on G₂, λ₁ and λ₂ (p<0.05). Nonetheless, the size of effects on stress relaxation was small (ΔG/G<10%), similar to experimental variability. We conclude that stress relaxation in the relaxed human ankle is minimally affected by changing gastrocnemius muscle–tendon unit length or by changing the lengths of ankle-joint only structures. Consequently quasi-linear viscoelastic models of the relaxed human ankle can use a common stress relaxation modulus at different knee and ankle angles with minimal error.     

Characterization of passive elastic properties of the human medial gastrocnemius muscle belly using supersonic shear imaging

The passive elastic properties of a muscle-tendon complex are usually estimated from the relationship between the joint angle and the passive resistive torque, although the properties of the different structures crossing the joint cannot be easily assessed. This study aimed to determine the passive mechanical properties of the gastrocnemius medialis muscle (GM) using supersonic shear imaging (SSI) that allows the measurement of localized muscle shear modulus (μ). The SSI of the GM was taken for 7 subjects during passive ankle dorsiflexion at a range of knee positions performed on an isokinetic dynamometer. The relationship between normalized μ and the length of the gastrocnemius muscle-tendon units (GMTU) was very well fitted to an exponential model (0.944相似文献   

A comparison of two Hill-type skeletal muscle models on the construction of medial gastrocnemius length-tension curves in humans in vivo

Human length-tension curves are traditionally constructed using a model that assumes passive tension does not change during contraction (model A) even though the animal literature suggests that passive tension can decrease (model B). The study's aims were threefold: 1) measure differences in human medial gastrocnemius length-tension curves using model A vs. model B, 2) test the reliability of ultrasound constructed length-tension curves, and 3) test the robustness of fascicle length-generated length-tension curves to variations between the angle and fascicle length relationship. An isokinetic dynamometer manipulated and measured ankle angle while ultrasound was used to measure medial gastrocnemius fascicle length. Supramaximal tibial nerve stimulation was used to evoke resting muscle twitches. Length-tension curves were constructed using model A {angle-torque [A-T((A))], length-torque [L-T((A))]} or model B {length-torque [L-T((B))]} in three conditions: baseline, heel-lift (where the muscle was shortened at each angle), and baseline repeated 2 h later (+2 h). Length-tension curves constructed from model B differed from those produced via model A, indicated by a significant increase in maximum torque (≈23%) when using L-T((B)) vs. L-T((A)). No parameter measured was different between baseline and +2 h for any method, indicating good reliability when using ultrasound. Length-tension curves were unaffected by the heel-lift condition when using L-T((A)) or L-T((B)) but were affected when using A-T((A)). Since the muscle model used significantly alters human length-tension curves, and given animal data indicate model B to be more accurate when passive tension is present, we recommend that model B should be used when constructing medial gastrocnemius length-tension curves in humans in vivo.     

In vivo motion transmission in the inactive gastrocnemius medialis muscle-tendon unit during ankle and knee joint rotation.

The purposes of this study were: (a) to quantify the influence of passive ankle and knee joint angular displacement on the estimated mechanical and architectural properties of the gastrocnemius medialis (GM) muscle-tendon unit, and (b) to determine the strain distribution of separate structures (tendon, aponeurosis and fascicle) during passive lengthening of the GM muscle-tendon unit at rest. Ten male subjects participated in the study. The passive ankle and knee joint movements were performed on an isokinetic dynamometer. The kinematics of the left leg were recorded using the Vicon 624 system with 8 cameras. Two ultrasound probes were used to examine the elongation of the tendon, the aponeurosis, the fascicles and the angle of pennation of the GM. To calculate the elongation of the GM muscle-tendon unit the Achilles tendon path was reconstructed using a series of small reflective markers. The results show that the passive ankle joint angular displacement has a considerable influence on the elongation of the tendinous and architectural structures of the GM muscle-tendon unit. In contrast, the influence of knee joint angular displacement on the GM fascicle length and pennation angle becomes relevant only at knee angles greater than 144 degrees . The contribution of the tendon to the elongation of the GM muscle-tendon unit at rest is relevant because of its greater resting length in comparison to the resting length of the GM fascicles. The results indicate the existence of slackness in the inactive GM muscle-tendon unit between 121 degrees and 107 degrees ankle angle and between 65 degrees and 144 degrees knee angle.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.     

The prediction of stress-relaxation of ligaments and tendons using the quasi-linear viscoelastic model

Recent studies have questioned the ability of the quasi-linear viscoelastic (QLV) model to predict stresses and strains in response to loading conditions other than those used to fit the model. The objective of this study was to evaluate the ability of several models in the literature to predict the elastic stress response of ligament and tendon at strain levels higher than the levels used to fit the model. The constitutive models were then used to evaluate the ability of the QLV model to predict the overall stress response during stress relaxation. The models expressing stress as an exponential function of strain significantly overestimated stress when used at higher strain levels. The polynomial formulation of the Mooney–Rivlin model more accurately predicted the stress–strain behavior of ligament and tendon. The results demonstrate that the ability of the QLV model to accurately predict the stress-relaxation response is dependent in part on the accuracy of the function used to model the elastic response of the soft tissue.     

The effect of overshooting the target strain on estimating viscoelastic properties from stress relaxation experiments

BACKGROUND: Tendon's mechanical behaviors have frequently been quantified using the quasi-linear viscoelastic (QLV) model. The QLV parameters are typically estimated by fitting the model to a single-step stress relaxation experiment. Unfortunately, overshoot of the target strain occurs to some degree in most experiments. This has never been formally investigated even though failing to measure, minimize, or compensate for overshoot may cause large errors in the estimation of parameters. Therefore, the objective of this study was to investigate the effect of overshoot on the estimation of QLV parameters. METHOD OF APPROACH: A simulated experiment was first performed to quantify the effect of different amounts of overshoot on the estimated QLV parameters. Experimental data from tendon was then used to determine if the errors associated with overshoot could be reduced when a direct fit is used (i.e., the actual strain history was used in the curve fit). RESULTS: We found that both the elastic and viscous QLV parameters were incorrectly estimated if overshoot was not properly accounted for in the fit. Furthermore, the errors associated with overshoot were partially reduced when overshoot was accounted for using a direct fit. CONCLUSIONS: A slow ramp rate is recommended to limit the amount of overshoot and a direct fit is recommended to limit the errors associated with overshoot, although other approaches such as adjusting the control system to limit overshoot could also be utilized.     

Rest length and compliance of non-immobilised and immobilised rabbit soleus muscle and tendon

The first aim of this study was to measure the contributions of muscle and tendon to the total compliance of resting muscle-tendon units. A second aim was to determine whether the decrease in muscle-tendon unit rest length produced by prolonged immobilisation in a shortened position is mediated primarily by adaptations of the muscle or tendon. One ankle joint from each of five rabbits was immobilised in a plantarflexed position for 14 days. The passive length-tension properties of soleus muscle fascicles and tendons from both hindlimbs were measured using a video-based tensile-testing system. In non-immobilised muscles, muscle fascicle strains exceeded tendon strains by up to four times. However, because the rest length of tendon was much greater than that of muscle fascicles, changes in tendon length accounted for nearly half of the total change in muscle-tendon unit length. The rest length of immobilised muscle-tendon units was less than that of non-immobilised muscle-tendon units from contralateral limbs. Most of this difference was attributable to a change in the rest length of the tendon; there was little change in the rest length of muscle fascicles. It is concluded that the tendon is responsible for a large part of the compliance of rabbit soleus muscle-tendon units at physiological resting tensions, and that adaptation of tendon rest length is the primary mechanism by which the rabbit soleus shortens in response to immobilisation at short lengths. Accepted: 7 May 1997     

Gastrocnemius fascicle length changes with two-joint passive movements

Predicting muscle fascicle length changes during passive movements may lead to a better understanding of muscle function. The purpose of this study was to experimentally compare fascicle length changes in the gastrocnemius during two-joint passive movements with a previously derived kinematic model based on anatomical measures from a cadaver. The ratio of passive ankle to knee motion was manipulated to generate medial gastrocnemius fascicle elongation and lateral gastrocnemius fascicle shortening. Ultrasound images from both heads of the gastrocnemius fascicles were acquired at 10 degrees knee flexion increments and compared with this kinematic model. Our results suggest that the two-joint kinematic model from which we originally based our knee and ankle movements did not adequately reflect fascicle length changes during any of the movement conditions in this study. From our data, we propose that for every degree of ankle motion the medial and lateral gastrocnemius changes 0.42 mm and 0.96 mm, respectively, whereas changes of 0.14 mm and 0.22 mm are observed for the medial and lateral gastrocnemius, respectively, during knee movements.     

A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in combination with fluid flow

Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.     

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

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

An approach to determine pressure profile generated by compression bandage using quasi-linear viscoelastic model

Understanding the stress relaxation behavior of the compression bandage could be very useful in determining the behavior of the interface pressure exerted by the bandage on a limb during the course of the compression treatment. There has been no comprehensive study in the literature to investigate the pressure profile (interface pressure with time) generated by a compression bandage when applied at different levels of strain. The present study attempts to describe the pressure profile, with the use of a quasi-linear viscoelastic model, generated by a compression bandage during compression therapy. The quasi-linear viscoelastic (QLV) theory proposed by Fung (Fung, 1972, "Stress Strain History Relations of Soft Tissues in Simple Elongation," Biomechanics: Its Foundations and Objectives, Y. C. Fung, N. Perrone, and M. Anliker, eds., Prentice-Hall, Englewood Cliffs, NJ, pp. 181-207). was used to model the nonlinear time- and history-dependent relaxation behavior of the bandage using the ramp strain approach. The regression analysis was done to find the correlation between the pressure profile and the relaxation behavior of the bandage. The parameters of the QLV model, describing the relaxation behavior of the bandage, were used to determine the pressure profile generated by the bandage at different levels of strain. The relaxation behaviors of the bandage at different levels of strain were well described by the QLV model parameters. A high correlation coefficient (nearly 0.98) shows a good correlation of the pressure profile with the stress relaxation behavior of the bandage.The prediction of the pressure profile using the QLV model parameters were in agreement with the experimental data. The pressure profile generated by a compression bandage could be predicted using the QLV model describing the nonlinear relaxation behavior of the bandage. This new application of the QLV theory helps in evaluating the bandage performance during compression therapy as scientific wound care management.     

A quasi-linear, viscoelastic, structural model of the plantar soft tissue with frequency-sensitive damping properties

Little is known about the structural properties of plantar soft-tissue areas other than the heel; nor is it known whether the structural properties vary depending on location. Furthermore, although the quasi-linear viscoelastic (QLV) theory has been used to model many soft-tissue types, it has not been employed to model the plantar soft tissue. The structural properties of the plantar soft tissue were quantified via stress relaxation experiments at seven regions (subcalcaneal, five submetatarsal, and subhallucal) across eight cadaveric feet. The cadaveric feet were 36.9 +/- 17.4 (mean +/- S.D.) years of age, all free from vascular diseases and orthopedics disorders. All tests were performed at a constant environmental temperature of 35 degrees C. Stress relaxation experiments were performed; different loads were employed for different areas based on normative gait data. A modification of the relaxation spectrum employed within the QLV theory allowed for the inclusion of frequency-sensitive relaxation properties in addition to nonlinear elastic behavior. The tissue demonstrated frequency-dependent damping properties that made the QLV theory ill suited to model the relaxation. There was a significant difference between the elastic structural properties (A) of the subcalcaneal tissue and all other areas (p = 0.004), and a trend (p = 0.067) for the fifth submetatarsal to have less viscous damping (c1) than the subhallucal, or first, second, or third submetatarsal areas. Thus, the data demonstrate that the structural properties of the foot can vary across regions, but careful consideration must be given to the applied loads and the manner in which the loads were applied.     

An improved method to analyze the stress relaxation of ligaments following a finite ramp time based on the quasi-linear viscoelastic theory

The quasi-linear viscoelastic (QLV) theory proposed by Fung (1972) has been frequently used to model the nonlinear time- and history-dependent viscoelastic behavior of many soft tissues. It is common to use five constants to describe the instantaneous elastic response (constants A and B) and reduced relaxation function (constants C, tau 1, and tau 2) on experiments with finite ramp times followed by stress relaxation to equilibrium. However, a limitation is that the theory is based on a step change in strain which is not possible to perform experimentally. Accounting for this limitation may result in regression algorithms that converge poorly and yield nonunique solutions with highly variable constants, especially for long ramp times (Kwan et al. 1993). The goal of the present study was to introduce an improved approach to obtain the constants for QLV theory that converges to a unique solution with minimal variability. Six goat femur-medial collateral ligament-tibia complexes were subjected to a uniaxial tension test (ramp time of 18.4 s) followed by one hour of stress relaxation. The convoluted QLV constitutive equation was simultaneously curve-fit to the ramping and relaxation portions of the data (r2 > 0.99). Confidence intervals of the constants were generated from a bootstrapping analysis and revealed that constants were distributed within 1% of their median values. For validation, the determined constants were used to predict peak stresses from a separate cyclic stress relaxation test with averaged errors across all specimens measuring less than 6.3 +/- 6.0% of the experimental values. For comparison, an analysis that assumed an instantaneous ramp time was also performed and the constants obtained for the two approaches were compared. Significant differences were observed for constants B, C, tau 1, and tau 2, with tau 1 differing by an order of magnitude. By taking into account the ramping phase of the experiment, the approach allows for viscoelastic properties to be determined independent of the strain rate applied. Thus, the results obtained from different laboratories and from different tissues may be compared.     

Bipedal walking and running with spring-like biarticular muscles

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.     

Linear and quasi-linear viscoelastic characterization of ankle ligaments

The objective of this study was to produce linear and nonlinear viscoelastic models of eight major ligaments in the human ankle/foot complex for use in computer models of the lower extremity. The ligaments included in this study were the anterior talofibular (ATaF), anterior tibiofibular (ATiF), anterior tibiotalar (ATT), calcaneofibular (CF), posterior talofibular (PTaF), posterior tibiofibular (PTiF), posterior tibiotalar (PTT), and tibiocalcaneal (TiC) ligaments. Step relaxation and ramp tests were performed. Back-extrapolation was used to correct for vibration effects and the error introduced by the finite rise time in step relaxation tests. Ligament behavior was found to be nonlinear viscoelastic, but could be adequately modeled up to 15 percent strain using Fung's quasilinear viscoelastic (QLV) model. Failure properties and the effects of preconditioning were also examined.     

A constituent-based model for the nonlinear viscoelastic behavior of ligaments

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.     

Ultrasound estimates of Achilles tendon exhibit unexpected shortening during ankle plantarflexion

The purpose of this study was to investigate Achilles tendon (AT) length changes during a series of tasks that involved combinations of higher/lower force, and larger/smaller length changes of the medial gastrocnemius muscle-tendon unit (MTU). We sought to determine if common ultrasound-based estimates of AT length change were consistent with expectations for a passive elastic tendon acting in series with a muscle. We tested 8 healthy individuals during restricted joint calf contractions (high force, low displacement), ankle dorsi-/plantar-flexion (DF/PF) with the foot in the air (low force, high displacement), and heel raises (high force, high displacement). We experimentally estimated AT length change using two ultrasound methods, one based on muscle-tendon junction (MTJ) tracking and one based on muscle fascicle (MF) tracking. Estimates of AT length change were consistent with model expectations during restricted calf contractions, when the MTU underwent minimal length change. However, estimates of AT length changes were inconsistent with model expectations during the ankle DF/PF and heel raise tasks. Specifically, the AT was estimated to shorten substantially, often 10–20 mm, when the ankle plantarflexed beyond neutral position, despite loading conditions in which a passive, stiff spring would be expected to either lengthen (under increasing force) or maintain its length (under low force). These unexpected findings suggest the need for improvements in how we conceptually model and/or experimentally estimate MTU dynamics in vivo during motion analysis studies, particularly when the ankle plantarflexes beyond neutral.