Fibre operating lengths of human lower limb muscles during walking

Muscles actuate movement by generating forces. The forces generated by muscles are highly dependent on their fibre lengths, yet it is difficult to measure the lengths over which muscle fibres operate during movement. We combined experimental measurements of joint angles and muscle activation patterns during walking with a musculoskeletal model that captures the relationships between muscle fibre lengths, joint angles and muscle activations for muscles of the lower limb. We used this musculoskeletal model to produce a simulation of muscle-tendon dynamics during walking and calculated fibre operating lengths (i.e. the length of muscle fibres relative to their optimal fibre length) for 17 lower limb muscles. Our results indicate that when musculotendon compliance is low, the muscle fibre operating length is determined predominantly by the joint angles and muscle moment arms. If musculotendon compliance is high, muscle fibre operating length is more dependent on activation level and force-length-velocity effects. We found that muscles operate on multiple limbs of the force-length curve (i.e. ascending, plateau and descending limbs) during the gait cycle, but are active within a smaller portion of their total operating range.     

Effects of contraction history on control and stability in explosive actions

In this model study, the effect of contraction history in skeletal muscle on joint movement and stability was investigated. A joint system was constructed with two identical (antagonistic) muscles. The muscles were modelled either according to the Hill tradition or as a modified Hill system including history-dependent properties. The joint system underwent movements with full activity of both muscles, mimicking explosive actions with high stability demands. Movements starting away from a balanced mid-position, as well as perturbation experiments, were simulated. The comparison between the Hill and modified Hill systems showed that contraction history improved stability (stiffness under perturbation) and, under certain conditions, caused a shift in the final joint position, which depended on the task characteristics (starting position and perturbations characteristics). This result indicates that modulations of muscle activity, required to move a joint to a particular end-position, do not only depend on the end-position but also on the preceding movements. This finding does not agree with the equilibrium-point hypothesis and is discussed accordingly.     

Muscle power attenuation by tendon during energy dissipation

An important function of skeletal muscle is deceleration via active muscle fascicle lengthening, which dissipates movement energy. The mechanical interplay between muscle contraction and tendon elasticity is critical when muscles produce energy. However, the role of tendon elasticity during muscular energy dissipation remains unknown. We tested the hypothesis that tendon elasticity functions as a mechanical buffer, preventing high (and probably damaging) velocities and powers during active muscle fascicle lengthening. We directly measured lateral gastrocnemius muscle force and length in wild turkeys during controlled landings requiring rapid energy dissipation. Muscle-tendon unit (MTU) strain was measured via video kinematics, independent of muscle fascicle strain (measured via sonomicrometry). We found that rapid MTU lengthening immediately following impact involved little or no muscle fascicle lengthening. Therefore, joint flexion had to be accommodated by tendon stretch. After the early contact period, muscle fascicles lengthened and absorbed energy. This late lengthening occurred after most of the joint flexion, and was thus mainly driven by tendon recoil. Temporary tendon energy storage led to a significant reduction in muscle fascicle lengthening velocity and the rate of energy absorption. We conclude that tendons function as power attenuators that probably protect muscles against damage from rapid and forceful lengthening during energy dissipation.     

A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings

The aim of this paper was to compare the effect of different optimisation methods and different knee joint degrees of freedom (DOF) on muscle force predictions during a single legged hop. Nineteen subjects performed single-legged hopping manoeuvres and subject-specific musculoskeletal models were developed to predict muscle forces during the movement. Muscle forces were predicted using static optimisation (SO) and computed muscle control (CMC) methods using either 1 or 3 DOF knee joint models. All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°). Biarticular muscles (hamstrings, rectus femoris and gastrocnemius) showed more differences in muscle force profiles when comparing between the different muscle prediction approaches where these muscles showed larger time delays for many of the comparisons. The muscle force magnitudes of vasti, gluteus maximus and gluteus medius were not greatly influenced by the choice of muscle force prediction method with low normalised root mean squared errors (<48%) observed in most comparisons. We conclude that SO and CMC can be used to predict lower-limb muscle co-contraction during hopping movements. However, care must be taken in interpreting the magnitude of force predicted in the biarticular muscles and the soleus, especially when using a 1 DOF knee. Despite this limitation, given that SO is a more robust and computationally efficient method for predicting muscle forces than CMC, we suggest that SO can be used in conjunction with musculoskeletal models that have a 1 or 3 DOF knee joint to study the relative differences and the role of muscles during hopping activities in future studies.     

Comparison of an EMG-based and a stress-based method to predict shoulder muscle forces

The estimation of muscle forces in musculoskeletal shoulder models is still controversial. Two different methods are widely used to solve the indeterminacy of the system: electromyography (EMG)-based methods and stress-based methods. The goal of this work was to evaluate the influence of these two methods on the prediction of muscle forces, glenohumeral load and joint stability after total shoulder arthroplasty. An EMG-based and a stress-based method were implemented into the same musculoskeletal shoulder model. The model replicated the glenohumeral joint after total shoulder arthroplasty. It contained the scapula, the humerus, the joint prosthesis, the rotator cuff muscles supraspinatus, subscapularis and infraspinatus and the middle, anterior and posterior deltoid muscles. A movement of abduction was simulated in the plane of the scapula. The EMG-based method replicated muscular activity of experimentally measured EMG. The stress-based method minimised a cost function based on muscle stresses. We compared muscle forces, joint reaction force, articular contact pressure and translation of the humeral head. The stress-based method predicted a lower force of the rotator cuff muscles. This was partly counter-balanced by a higher force of the middle part of the deltoid muscle. As a consequence, the stress-based method predicted a lower joint load (16% reduced) and a higher superior–inferior translation of the humeral head (increased by 1.2 mm). The EMG-based method has the advantage of replicating the observed cocontraction of stabilising muscles of the rotator cuff. This method is, however, limited to available EMG measurements. The stress-based method has thus an advantage of flexibility, but may overestimate glenohumeral subluxation.     

Motor unit firing rates during isometric voluntary contractions performed at different muscle lengths

Firing rates of motor units and surface EMG were measured from the triceps brachii muscles of able-bodied subjects during brief submaximal and maximal isometric voluntary contractions made at 5 elbow joint angles that covered the entire physiological range of muscle lengths. Muscle activation at the longest, midlength, and shortest muscle lengths, measured by twitch occlusion, averaged 98%, 97%, and 93% respectively, with each subject able to achieve complete activation during some contractions. As expected, the strongest contractions were recorded at 90 degrees of elbow flexion. Mean motor unit firing rates and surface EMG increased with contraction intensity at each muscle length. For any given absolute contraction intensity, motor unit firing rates varied when muscle length was changed. However, mean motor unit firing rates were independent of muscle length when contractions were compared with the intensity of the maximal voluntary contraction (MVC) achieved at each joint angle.     

Mechanical energy expenditure on human movement and the anthropomorphic mechanism]

Mechanical energy expenditures of the man and anthropomorphic locomotion machine during movement are compared theoretically. Sources of the mechanical energy affecting movement of human's lower extremity are modelled by 8 muscles, 3 of which are the two-joint muscles. The model of the lower extremity of anthropomorphic locomotion machine is moved by joint moments. It was shown that in the same movement the model of the human lower extremity can spend less mechanical energy than that of the model of the anthropomorphic locomotion machine. It is caused by the presence of two-joint muscles in the first model. Such an economy of mechanical energy expenditures realized by the two-joint muscle is possible at simultaneous execution of three conditions: 1) signs of the muscle powers, which are produced by that muscle at both joints, are opposite; 2) moments produced by that muscle at each of both joints have the same direction with the joint moments at these joints; 3) one-joint antagonistic muscles are not active. An expression which makes it possible to estimate the mechanical energy savings by the two-joint muscles during humans' movement was developed.     

Modeling the length dependence of isometric force in human quadriceps muscles

Functional electrical stimulation is used to restore movement and function of paralyzed muscles by activating skeletal muscle artificially. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that produce the desired force. The present study is a first step in developing a mathematical model for non-isometric muscle contractions. The goals of this study were to: (1) identify how our isometric force model's parameters vary with changes in knee joint angle, (2) identify the best knee flexion angle to parameterize this model, and (3) validate the model by comparing experimental data to predictions in response to a wide range of stimulation frequencies and muscle lengths. Results showed that by parabolically varying one of the free parameters with knee joint angle and fixing the other parameters at the values identified at 40 degrees of knee flexion, the model could predict the force responses to a wide range of stimulation frequencies and patterns at different muscle lengths. This work showed that the current isometric force model is capable of predicting the changes in skeletal muscle force at different muscle lengths.     

The muscle line of action in current models of the human cervical spine: a comparison with in vivo MRI data

Cervical muscles are commonly represented by line-of-action models. This investigation evaluates the performance of three types of model implementations, based on their ability to mimic geometric in-vivo aspects of muscles. Five prominent pairs of neck muscles were reconstructed in three head positions using magnetic resonance imaging. Based on the reconstructions, muscle approximations were created that represent the muscles with piecewise straight lines. Measured and modelled muscle approximations were compared with respect to their pulling directions at the attachment sites and the overall distance between the muscle paths. Muscle lengths were evaluated in two ways. First, length discrepancies were determined between measured and modelled muscles depending on the head position. Second, the difference of muscle lengths in neutral and deflected head positions for measurement and models were calculated. The results indicate considerable differences between models and measurements. Pulling directions, for instance, differed by up to 40°, depending on the chosen muscle and the type of muscle implementation.     

Musculotendon lengths and moment arms for a three-dimensional upper-extremity model

Generating muscle-driven forward dynamics simulations of human movement using detailed musculoskeletal models can be computationally expensive. This is due in part to the time required to calculate musculotendon geometry (e.g., musculotendon lengths and moment arms), which is necessary to determine and apply individual musculotendon forces during the simulation. Modeling upper-extremity musculotendon geometry can be especially challenging due to the large number of multi-articular muscles and complex muscle paths. To accurately represent this geometry, wrapping surface algorithms and/or other computationally expensive techniques (e.g., phantom segments) are used. This paper provides a set of computationally efficient polynomial regression equations that estimate musculotendon length and moment arms for thirty-two (32) upper-extremity musculotendon actuators representing the major muscles crossing the shoulder, elbow and wrist joints. Equations were developed using a least squares fitting technique based on geometry values obtained from a validated public-domain upper-extremity musculoskeletal model that used wrapping surface elements (Holzbaur et al., 2005). In general, the regression equations fit well the original model values, with an average root mean square difference for all musculotendon actuators over the represented joint space of 0.39 mm (1.1% of peak value). In addition, the equations reduced the computational time required to simulate a representative upper-extremity movement (i.e., wheelchair propulsion) by more than two orders of magnitude (315 versus 2.3 s). Thus, these equations can assist in generating computationally efficient forward dynamics simulations of a wide range of upper-extremity movements.     

The Obstacle-Set Method for Representing Muscle Paths in Musculoskeletal Models

A computational method is introduced for modeling the paths of muscles in the human body. The method is based on the premise that the resultant muscle force acts along the locus of the transverse cross-sectional centroids of the muscle. The path of the muscle is calculated by idealizing its centroid path as a frictionless elastic band, which moves freely over neighboring anatomical constraints such as bones and other muscles. The anatomical constraints, referred to as obstacles, are represented in the model by regular-shaped, rigid bodies such as spheres and cylinders. The obstacles, together with the muscle path, define an obstacle set. It is proposed that the path of any muscle can be modeled using one or more of the following four obstacle sets: single sphere, single cylinder, double cylinder, and sphere-capped cylinder. Assuming that the locus of the muscle centroids is known for an arbitrary joint configuration, the obstacle-set method can be used to calculate the path of the muscle for all other joint configurations. The obstacle-set method accounts not only for the interaction between a muscle and a neighboring anatomical constraint, but also for the way in which this interaction changes with joint configuration. Consequently, it is the only feasible method for representing the paths of muscles which cross joints with multiple degrees of freedom such as the deltoid at the shoulder.     

Model-based inverse estimation for active contraction stresses of tongue muscles using 3D surface shape in speech production

This paper presents a novel inverse estimation approach for the active contraction stresses of tongue muscles during speech. The proposed method is based on variational data assimilation using a mechanical tongue model and 3D tongue surface shapes for speech production. The mechanical tongue model considers nonlinear hyperelasticity, finite deformation, actual geometry from computed tomography (CT) images, and anisotropic active contraction by muscle fibers, the orientations of which are ideally determined using anatomical drawings. The tongue deformation is obtained by solving a stationary force-equilibrium equation using a finite element method. An inverse problem is established to find the combination of muscle contraction stresses that minimizes the Euclidean distance of the tongue surfaces between the mechanical analysis and CT results of speech production, where a signed-distance function represents the tongue surface. Our approach is validated through an ideal numerical example and extended to the real-world case of two Japanese vowels, /ʉ/ and /ɯ/. The results capture the target shape completely and provide an excellent estimation of the active contraction stresses in the ideal case, and exhibit similar tendencies as in previous observations and simulations for the actual vowel cases. The present approach can reveal the relative relationship among the muscle contraction stresses in similar utterances with different tongue shapes, and enables the investigation of the coordination of tongue muscles during speech using only the deformed tongue shape obtained from medical images. This will enhance our understanding of speech motor control.     

An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle-tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R(2) of 0.91 and mean residual error of approximately 12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.     

Development of software for human muscle force estimation

Muscle force estimation (MFE) has become more and more important in exploring principles of pathological movement, studying functions of artificial muscles, making surgery plan for artificial joint replacement, improving the biomechanical effects of treatments and so on. At present, existing software are complex for professionals, so we have developed a new software named as concise MFE (CMFE). CMFE which provides us a platform to analyse muscle force in various actions includes two MFE methods (static optimisation method and electromyographic-based method). Common features between these two methods have been found and used to improve CMFE. A case studying the major muscles of lower limb of a healthy subject walking at normal speed has been presented. The results are well explained from the effect of the motion produced by muscles during movement. The development of this software can improve the accuracy of the motion simulations and can provide a more extensive and deeper insight in to muscle study.     

Myofilament lengths of cat skeletal muscle: theoretical considerations and functional implications.

The cat is the primary model for neuromuscular research. However, sarcomere geometry, in particular thin-myofilament lengths of cat skeletal muscles, is not known, thus preventing adequate muscle modeling on the sarcomere level. The purpose of this study was to determine thin-myofilament lengths in cat skeletal muscle. It was found that average thin-myofilament lengths of cat tibialis anterior muscles (1.12 microns) were larger than the average values reported for frog (approximately 0.95 microns), rat (1.09 microns), and rabbit muscles (1.09 microns) and were smaller than the values reported for monkey (1.16 microns) and human skeletal muscles (1.27 microns). According to the cross-bridge theory of muscular contraction, this result implies that the range of sarcomere length on the ascending limb of the force-length relation for cat muscle is between those of frog, rat, and rabbit on the one side and monkey and human on the other side. It is speculated that the differences in thin-myofilament lengths of different animals are related to the functional demands of these muscles in everyday movement tasks. Isolated experimental observations appear to support this speculation.     

Muscles within muscles: Coordination of 19 muscle segments within three shoulder muscles during isometric motor tasks.

The aim of the present study was to determine how the intra-muscular segments of three shoulder muscles were coordinated to produce isometric force impulses around the shoulder joint and how muscle segment coordination was influenced by changes in movement direction, mechanical line of action and moment arm (ma). Twenty male subjects (mean age 22 years; range 18-30 years) with no known history of shoulder pathologies, volunteered to participate in this experiment. Utilising an electromyographic technique, the timing and intensity of contraction within 19 muscle segments of three superficial shoulder muscles (Pectoralis Major, Deltoid and Latissimus Dorsi) were studied and compared during the production of rapid (e.g. approximately 400ms time to peak) isometric force impulses in four different movement directions of the shoulder joint (flexion, extension, abduction and adduction). The results of this investigation have suggested that the timing and intensity of each muscle segment's activation was coordinated across muscles and influenced by the muscle segment's moment arm and its mechanical line of action in relation to the intended direction of shoulder movement (e.g. flexion, extension, abduction or adduction). There was also evidence that motor unit task groups were formed for individual motor tasks which comprise motor units from both adjacent and distant muscles. It was also confirmed that for any particular motor task, individual muscle segments can be functionally classified as prime mover, synergist or antagonist - classifications which are flexible from one movement to the next.     

Chimpanzee thumb muscle cross sections, moment arms and potential torques, and comparisons with humans.

This study investigates the morphological basis of differences between humans and chimpanzees in the kinematical and dynamical parameters of the musculature of the thumb. It is partly intended to test an hypothesis that human thumb muscles can exert significantly greater torques, due to larger muscle cross-sectional areas or to longer tendon moment arms or to both. We focus on the estimation of the potentials of thumb muscles to exert torques about joint axes in a sample of eight chimpanzee cadaver hands. The potential torque of a muscle is estimated by taking the product of a muscle's physiological cross-sectional area (an estimator of force) with its dynamical moment arm (derived from the slope of tendon excursion versus joint angular displacement, obtained during passive movements of cadaver thumb joints). Comparison of our results with similar data obtained for humans at the same Mayo Clinic laboratory shows significant differences between humans and chimpanzees in potential torque of most thumb muscles, those of humans generally exhibiting larger values. The primary reason for the larger torques in humans is that their average moment arms are significantly longer, permitting greater torque for a given muscle size. An additional finding is that chimpanzees and humans differ in the direction of secondary thumb metacarpal movements elicited by contraction of some muscles, as shown by differences in moment arm signs for a given movement in the same muscle. The differences appear to be related to differences in the musculo-skeletal structures of the trapeziometacarpal joint.     

A numerical simulation of muscle spindle ensemble encoding during planar movement of the human arm

We address the issue of what proprioceptive information, regarding movement of the human arm, may be provided to the central nervous system by proprioceptors located within muscles of this limb. To accomplish this we developed a numerical simulation which could provide estimates of the length regimes experienced by a set of model receptors located within some of the principal muscles of the human arm during planar movement of this limb. These receptors were assumed to have characteristics analogous to those associated with a simple model of muscle spindle signalling of movement. To this end each spindle had proprioceptive ‘channels’ associated with it. These corresponded to primary and secondary spindle afferent fibers which could provide independent afferent output regarding the parent muscle the spindle monitored. The angles of the shoulder and elbow joints attained by subjects performing a task requiring movement of the right arm in a horizontal plane to a static visual target were recorded. For this angular data the lengths and rates of change of lengths experienced by muscle fascicles, and hence the model spindles, during movement were calculated by means of the numerical simulation. The discharge rates of the simulated spindles during the movement were calculated to derive a measure of the depth of modulation, induced by the movement, for each spindle. These values were then summed for all spindles to provide a first-order approximation of spindle ensemble coding of the movement. Significant correlations (0.0001, Spearman's rank order) were found between the resulting ensemble encodings and, in order of significance, the angular velocity of the shoulder joint (), the tangential velocity of the hand (), and the angular velocity of the elbow joint (). Correlations between the angular positions of the shoulder () and elbow () were lower. These findings indicate that the ensemble profiles of the simulated muscle spindles, encode information regarding kinematic parameters of movements related to both intrinsic and extrinsic coordinate systems. This suggests that motor structures capable of deriving such an ensemble encoding would be in a position to perform the sensory-motor transformations between intrinsic and extrinsic frames of reference necessary for controlling movements planned in extrinsic coordinates. Received: 12 August 1994 / Accepted in revised form: 17 June 1996     

Effects of movement speed and joint position on knee flexor torque in healthy and post-surgical subjects

Coactivation of knee flexors during knee extension assists in joint stability by exerting an opposing torque to the anterior tibial displacement induced by the quadriceps. This opposing torque is believed to be generated by eccentric muscle actions that stiffen the knee, thereby attenuating strain to joint ligaments, particularly the anterior cruciate ligament (ACL). However, as the lengths of knee muscles vary with changes in joint position, the magnitude of flexor/extensor muscle force coupling may likewise vary, possibly affecting the capacity for active knee stabilization. The purpose of this study was to assess the effect of changes in movement speed and joint position on eccentric/concentric muscle action relationships in the knees of uninjured (UNI) and post-ACL-surgery (INJ) subjects (n = 14). All subjects were tested for maximum eccentric and concentric torque of the contralateral knee flexors and extensor muscles at four isokinetic speeds (15 degrees-60 degrees x s(-1)) and four joint position intervals (20 degrees-60 degrees of knee flexion). Eccentric flexor torque was normalized to the percentage of concentric flexor torque generated at each joint position interval for each speed tested (flexor E-C ratio). In order to estimate the capacity of the knee flexors to resist active knee extension, the eccentric-flexor/concentric-extensor ratios were also computed for each joint position interval and speed (flexor/extensor E-C ratio). The results revealed that eccentric torque surpassed concentric torque by 3%-144% across movement speeds and joint position intervals. The magnitude of the flexor E-C ratio and flexor/extensor E-C increased significantly with speed in both groups of subjects (P < 0.05) and tended to rise with muscle length as the knee was extended; peak values were generated at the most extended joint position (20 degrees-30 degrees). Although torque development patterns were symmetrical between the contralateral limbs in both groups, between-group comparisons revealed significantly higher flexor/extensor E-C ratios for the INJ group compared to the UNI group (P < 0.05), particularly at the fastest speed tested (60 degrees x s(-1)). The results indicate that joint position and movement speed influence the eccentric/concentric relationships of knee flexors and extensors. The INJ subjects appeared to accommodate to surgery by developing the eccentric function of their ACL and normal knee flexors, particularly at higher speeds and at more extended knee joint positions. This may assist in the dynamic stabilization of the knee at positions where ACL grafts have been reported to be most vulnerable to strain.     

Whole-body vibration induced adaptation in knee extensors; consequences of initial strength, vibration frequency, and joint angle

It was hypothesized that both vibration frequency and muscle length modulate the strengthening of muscles that is assumed to result from whole-body vibration (WBV). Length of knee extensor muscles during vibration is affected by the knee joint angle; the lengths of the knee extensors increase with more flexed knee joint angles. In an intervention study 28 volunteers were randomly assigned to 1 of 4 groups. Each group received 4 weeks of WBV at 1 of 3 different frequencies (20, 27, or 34 Hz) or 1 of 2 different lengths of knee extensors. Voluntary, isometric knee extension moment-angle relationship was determined. Initially, stronger subjects reacted differently to WBV than weaker participants. In stronger subjects knee extension moment did not improve; in the weaker subjects considerable improvements were observed ranging from 10 to 50%. Neither vibration frequency nor muscle length during the intervention affected the improvements. In addition to strength, the knee joint angle at which the maximal joint moment was generated (optimal joint angle) was affected. When trained at short muscle lengths, optimal angle shifted to more extend joint position. WBV training at long muscle lengths tended to induce an opposite shift. The amount of this shift tended to be influenced by vibration frequency; the lower the vibration frequency the larger the shift. Shifts of optimal lengths occurred in both weaker and stronger subjects. This study shows that muscle length during training affects the angle of knee joint at which the maximal extension moment was generated. Moreover, in weaker subjects WBV resulted in higher maximal knee joint extension moments. Vibration frequency and muscle length during vibration did not affect this joint moment gain.