Muscle-tendon Length Research Articles

Calf muscle-tendon lengths before and after Tendo-Achilles lengthenings and gastrocnemius lengthenings for equinus in cerebral palsy and idiopathic toe walking

The calf muscle-tendon lengths in children exhibiting equinus gait in two clinical populations, cerebral palsy (CP) and idiopathic toe walking (ITW), were examined to compare the effects of diagnosis and two different surgical procedures, Tendo-Achilles lengthening (TAL) versus Vulpius procedure (VP) gastrocnemius recession. Pre- and post-surgical gait data were obtained from 38 subjects (58 limbs) and 38 age-matched controls. Peak muscle-tendon lengths increased following surgery in 84% of limbs. For medial gastrocnemius (MGAS) and lateral gastrocnemius (LGAS) in stance, muscle-tendon lengths increased significantly following TAL surgeries but were not significantly different pre- and post-VP surgeries. For soleus (SOL) (swing and stance) and MGAS and LGAS (swing), muscle-tendon lengths increased significantly following both TAL and VP surgeries. Pre-operatively, muscle-tendon lengths were significantly shorter for the TAL group compared to the VP group; however, post-operatively the lengths were not significantly different between the surgeries. There were no significant differences between CP and ITW patients or indications that the surgery affected the groups differently. The change in length following surgery was well correlated to the subjects’ initial muscle-tendon length.

Invited Commentary on “Gastrocnemius-Soleus Muscle Tendon Unit Changes Over the First 12 Weeks of Adjusted Age in Infants Born Preterm”

Grant-Beuttler et al1 present an interesting report describing the measurement of gastrocnemius-soleus muscle tendon unit (MTU) lengths from term to 12 weeks of age in infants born preterm and infants born full term. This work joins that of other authors2 in suggesting that infants born preterm have a different developmental trajectory than infants born full term and they have identifiable and measurable impairments during early infancy. This study examined the differences in muscle-tendon tautness, length, and stretch over time. The authors note that a limitation of their study was the lack of measurements of knee flexion angle of newborn infants, both full term and preterm, to demonstrate extension limitations of the knee. Because the gastrocnemius is a 2-joint muscle, any degree of knee flexion may be important. It is very difficult to stretch the …

Effect of the Different Hip Joint Angle Definition on the Estimation of Muscle-Tendon Complex Length of the Hip Extensor Muscles in Counter Movement Jump

The purpose of this study was to consider the discrepancy between the trunk-based and the pelvis-based hip joint angles, and the difference between the MTC lengths estimated on the basis of the two types of hip joint angles during dynamic movement. Ten male athletes performed CMJ. Joint kinematics and the MTC length of long head of biceps femoris were compared between the trunk-based hip angle and the pelvis-based hip angle. In the CMJ, the angular displacements of the trunk-based were significantly higher than that of pelvis-based hip joints. There were no significant correlations between the two types of hip joint angles except at initial position. As for long head of biceps femoris, in contrast with the trunk-based-hip joint angle derived MTC length, which shows stretching in the descending phase and shortening in the ascending phase, the pelvis-based hip joint angle derived MTC length shows little changes. These results suggest that the trunk-based and pelvis-based hip joint angles have similar patterns of fluctuation; however, the angular displacement of each type is not equivalent. These results also suggest that we may misinterpret the type of muscle contraction because the definitions of hip joint angle are different even for the same muscle type.

Error propagation from kinematic data to modeled muscle-tendon lengths during walking

Kinematic data from 3D gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle-tendon lengths during walking. However, kinematic data are subject to soft tissue artifacts (STA), referring to skin marker displacements during movement. STA are known to significantly affect the computation of joint kinematics, and would therefore also have an effect on muscle-tendon lengths which are derived from the segmental positions. The present study aimed to introduce an analytical approach to calculate the error propagation from STA to modeled muscle-tendon lengths. Skin marker coordinates were assigned uncorrelated, isotropic error functions with given standard deviations accounting for STA. Two different musculoskeletal models were specified; one with the joints moving freely in all directions, and one with the joints constrained to rotation but no translation. Using reference kinematic data from two healthy boys (mean age 9 y 5 m), the propagation of STA to muscle-tendon lengths was quantified for semimembranosus, gastrocnemius and soleus. The resulting average SD ranged from 6% to 50% of the normalized muscle-tendon lengths during gait depending on the muscle, the STA magnitudes and the musculoskeletal model. These results highlight the potential impact STA has on the biomechanical analysis of modeled muscle-tendon lengths during walking, and suggest the need for caution in the clinical interpretation of muscle-tendon lengths derived from joint kinematics.

Hamstring muscle kinematics and activation during overground sprinting

Hamstring muscle strain injury is one of the most commonly seen injuries in sports such as track and field, soccer, football, and rugby. The purpose of this study was to advance our understanding of the mechanisms of hamstring muscle strain injuries during over ground sprinting by investigating hamstring muscle–tendon kinematics and muscle activation. Three-dimensional videographic and electromyographic (EMG) data were collected for 20 male runners, soccer or lacrosse players performing overground sprinting at their maximum effort. Hamstring muscle–tendon lengths, elongation velocities, and linear envelop EMG data were analyzed for a running gait cycle of the dominant leg. Hamstring muscles exhibited eccentric contractions during the late stance phase as well as during the late swing phase of overground sprinting. The peak eccentric contraction speeds of the hamstring muscles were significantly greater during the late swing phase than during the late stance phase ( p=0.001) while the hamstring muscle–tendon lengths at the peak eccentric contraction speeds were significantly greater during the late stance phase than during the late swing phase ( p=0.001). No significant differences existed in the maximum hamstring muscle–tendon lengths between the two eccentric contractions. The potential for hamstring muscle strain injury exists during the late stance phase as well as during the late swing phases of overground sprinting.

P083 Interacting effects of walking speed and spasticity level on muscle-tendon length and velocity in children with cerebral palsy

P083 Interacting effects of walking speed and spasticity level on muscle-tendon length and velocity in children with cerebral palsy

FUNCTIONAL MUSCLE MODEL PARAMETERS AND THE LENGTH-TENSION RELATIONSHIP

A phenomological Hill type muscle-tendon element (MTE) model can describe the force generating capacity of MTE over a range of muscle-tendon lengths. However modelling length-tension properties using fibre architecture and myofilament overlap does not accommodate the much larger changes seen in whole muscle length, underestimating functional changes in fibre length [Hoy, 1990; Delp, 1992; Legreneur, 1996; Bogert, 1998; Horsman, 2006]. To model whole muscle effects the use of a larger effective or functional fibre length has been suggested to account for complex internal architecture [Bogert, 1998]. Functional optimal fibre length, reference fibre length and reference pennation angle of the MTE were calculated using known changes in muscle belly length and isometric force characteristics over a functional range of muscle lengths. The resulting functional parameters ensured that modelled fibre lengths and pennation angles describe a range of fibre lengths inclusive of observed functional changes in muscle belly length and consistent with the operating range of fibres on the length-tension curve.

Calculated moment-arm and muscle-tendon lengths during gait differ substantially using MR based versus rescaled generic lower-limb musculoskeletal models

Biomechanical analysis of gait relies on the use of lower-limb musculoskeletal models. Most models are based on a generic model which takes into account the subject's skeletal dimensions by isotropic or anisotropic rescaling. Alternatively, personalized models can be built based on information from magnetic resonance (MR) images. We have studied the effect of these approaches on muscle-tendon lengths (MTLs) and moment-arm lengths (MALs) for 16 major muscles of the lower limb of a normal adult during both normal and pathologic gait. For most muscles, the MTL and MAL calculated using the rescaled generic models showed high correlation values, but large offsets when compared to values calculated using personalized models. MTL and MAL differences with the personalized model are only slightly smaller for an anisotropic than for an isotropic rescaled model. Gait kinematics influenced the observed inter-model differences and correlations due to an altered range of joint angles in both gait patterns. In conclusion, both generic rescaling methods failed to accurately estimate absolute values for MTL and MAL calculated using the personalized model. However, the magnitude of MTL and MAL changes during normal and pathologic gait corresponded between all three models for most muscles. Since rescaling depends strongly on modelling assumptions and cannot fully take into account subject-specific musculoskeletal geometry, interpretation of MTL and MAL even in normal adult subjects requires extreme caution.

Muscle–tendon surgery: effect on length and lengthening velocity of rectus femoris in cerebral palsy children gait

In cerebral palsy (CP), spasticity often induces troubles in muscle–tendon growth. One of the surgery purposes is to correct muscle–tendon length and the consequences of the spasticity. To improve ...

Biomechanical analysis of lower limbs for children with cerebral palsy: Gait analysis and musculo-skeletal modelling

s of the 17th Annual Meeting of ESMAC, Oral Presentations / Gait & Posture 28S (2008) S1–S48 S13 reconstructions in standing position were provided, by applying non linear deformation on 3D muscles in lying position, based on skeletal architecture. Muscle-tendon length ratio was then calculated based on specific subject muscles insertion areas on skeletal segments. Patients/Materials and Methods: An asymptomatic database for gait parameters was established to allow gait analysis data interpretations of patients with CP. Uncertainties on gait parameters were quantified. Specific subject 3D reconstructions of skeletal lower limbs in standing position were done. Skeletal malalignment was quantified by calculating clinical parameters. Uncertainties were less than 5o for most of them except for tibial torsion. Specific subject lower limbs were matched with gait analysis frames allowing display of bone movement during walking. Hip center calculated by the gait protocol was behind the femoral head center in static and dynamic trials (3.7 cm). Specific subject 3D reconstructions of 19 muscles were obtained for each lower limb side. Volumes, PCSA and lengths were calculated. Losses of muscle volumes were found and evaluated for the CP patient as compared to healthy subjects. Muscles were reconstructed in standing position. Muscle-tendon length ratios were lower for the CP patient as compared to the healthy children. Left: subject specific 3D reconstruction of lower limbs. Right: Bones 3D reconstructions.

High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models

High-frequency vibrations e.g., induced by legs impacting with the ground during terrestrial locomotion can provoke damage within tendons even leading to ruptures. So far, macroscopic Hill-type muscle models do not account for the observed high-frequency damping at low-amplitudes. Therefore, former studies proposed that protective damping might be explained by modelling the contractile machinery of the muscles in more detail, i.e., taking the microscopic processes of the actin-myosin coupling into account. In contrast, this study formulates an alternative hypothesis: low but significant damping of the passive material in series to the contractile machinery--e.g., tendons, aponeuroses, titin--may well suffice to damp these hazardous vibrations. Thereto, we measured the contraction dynamics of a piglet muscle-tendon complex (MTC) in three contraction modes at varying loads and muscle-tendon lengths. We simulated all three respective load situations on a computer: a Hill-type muscle model including a contractile element (CE) and each an elastic element in parallel (PEE) and in series (SEE) to the CE pulled on a loading mass. By comparing the model to the measured output of the MTC, we extracted a consistent set of muscle parameters. We varied the model by introducing either linear damping in parallel or in series to the CE leading to accordant re-formulations of the contraction dynamics of the CE. The comparison of the three cases (no additional damping, parallel damping, serial damping) revealed that serial damping at a physiological magnitude suffices to explain damping of high-frequency vibrations of low amplitudes. The simulation demonstrates that any undamped serial structure within the MTC enforces SEE-load eigenoscillations. Consequently, damping must be spread all over the MTC, i.e., rather has to be de-localised than localised within just the active muscle material. Additionally, due to suppressed eigenoscillations Hill-type muscle models taking into account serial damping are numerically more efficient when used in macroscopic biomechanical neuro-musculo-skeletal models.

Optimal Pennation Angle of the Primary Ankle Plantar and Dorsiflexors: Variations with Sex, Contraction Intensity, and Limb

Ultrasonography was used to measure the pennation angle of the human tibialis anterior (TA), lateral gastrocnemius (LG), medial gastrocnemius (MG), and soleus (Sol). The right and left legs of 8 male and 8 female subjects were tested at rest and during maximum voluntary contraction (MVC). Joint angles were chosen to control muscle tendon lengths so that the muscles were near their optimal length within the length-tension relationship. No differences in pennation angle were detected between the right and left legs. Another consistent finding was that the pennation angle at MVC was significantly greater than at rest for all muscles tested. Optimal pennation angles for the TA, MG, and Sol were significantly greater for the men than for the women. Optimal pennation angles for the TA, LG, MG, and Sol for the male subjects were 14.3 degrees, 23.7 degrees, 34.6 degrees, and 40.1 degrees respectively, whereas values of 12.1 degrees, 16.3 degrees, 27.3 degrees, and 26.3 degrees were recorded for the female subjects. The results of this study suggest the following: (1) similar values for pennation angle can be used for the right and left TA, LG, MG, and Sol; (2) pennation angle is significantly greater at MVC than at rest for all muscles tested; and (3) sex-specific values for optimal pennation angle should be used when modeling the force-generating potential of the primary muscles responsible for ankle plantar and dorsiflexion.

The role of estimating muscle-tendon lengths and velocities of the hamstrings in the evaluation and treatment of crouch gait

Persons with cerebral palsy frequently walk with excessive knee flexion during terminal swing and stance. This gait abnormality is often attributed to "short" or "spastic" hamstrings that restrict knee extension, and is often treated by hamstrings lengthening surgery. At present, the outcomes of these procedures are inconsistent. This study examined whether analyses of the muscle-tendon lengths and lengthening velocities of patients' hamstrings during walking may be helpful when deciding whether a candidate is likely to benefit from hamstrings surgery. One hundred and fifty-two subjects were cross-classified in a series of multi-way contingency tables based on their pre- and postoperative gait kinematics, muscle-tendon lengths, muscle-tendon velocities, and hamstrings surgeries. The lengths and velocities of the subjects' semimembranosus muscles were estimated by combining kinematic data from gait analysis with a three-dimensional computer model of the lower extremity. Log-linear analysis revealed that the subjects who walked with abnormally "short" or "slow" hamstrings preoperatively, and whose hamstrings did not operate at longer lengths or faster velocities postoperatively, were unlikely to walk with improved knee extension after treatment (p < 0.05). Subjects who did not walk with abnormally short or slow hamstrings preoperatively, and whose hamstrings did operate at longer lengths or faster velocities postoperatively, tended to exhibit unimproved or worsened anterior pelvic tilt after treatment (p < 0.05). Examination of the muscle-tendon lengths and velocities allows individuals who walk with abnormally short or slow hamstrings to be distinguished from those who do not, and thus may help to identify patients who are at risk for unsatisfactory postsurgical changes in knee extension or anterior pelvic tilt.

A Model of the Upper Extremity for Simulating Musculoskeletal Surgery and Analyzing Neuromuscular Control

Biomechanical models of the musculoskeletal system are frequently used to study neuromuscular control and simulate surgical procedures. To be broadly applicable, a model must be accessible to users, provide accurate representations of muscles and joints, and capture important interactions between joints. We have developed a model of the upper extremity that includes 15 degrees of freedom representing the shoulder, elbow, forearm, wrist, thumb, and index finger, and 50 muscle compartments crossing these joints. The kinematics of each joint and the force-generating parameters for each muscle were derived from experimental data. The model estimates the muscle-tendon lengths and moment arms for each of the muscles over a wide range of postures. Given a pattern of muscle activations, the model also estimates muscle forces and joint moments. The moment arms and maximum moment-generating capacity of each muscle group (e.g., elbow flexors) were compared to experimental data to assess the accuracy of the model. These comparisons showed that moment arms and joint moments estimated using the model captured important features of upper extremity geometry and mechanics. The model also revealed coupling between joints, such as increased passive finger flexion moment with wrist extension. The computer model is available to researchers at http://nmbl.stanford.edu.

Do the hamstrings operate at increased muscle–tendon lengths and velocities after surgical lengthening?

Children with crouch gait frequently walk with improved knee extension during the terminal swing and stance phases following hamstrings lengthening surgery; however, the mechanisms responsible for these improvements are unclear. This study tested the hypothesis that surgical lengthening enables the hamstrings of persons with cerebral palsy to operate at longer muscle–tendon lengths or lengthen at faster muscle–tendon velocities during walking. Sixty-nine subjects who had improved knee extension after surgery were retrospectively examined. The muscle–tendon lengths and velocities of the subjects’ semimembranosus muscles were estimated by combining kinematic data from gait analysis with a three-dimensional computer model of the lower extremity. Log-linear analyses confirmed that the subjects who walked with abnormally short muscle–tendon lengths and/or slow muscle–tendon velocities preoperatively tended to walk with longer lengths (21 of 29 subjects, p < 0.01 ) or faster velocities (30 of 40 subjects, p < 0.01 ) postoperatively. In these cases, surgical lengthening may have slackened the subjects’ tight hamstrings and/or diminished the hamstrings’ spastic response to stretch. Other subjects walked with muscle–tendon lengths and velocities that were neither shorter nor slower than normal preoperatively (22 of 69 subjects), and the semimembranosus muscles of most of these subjects did not operate at increased lengths or velocities after surgery; in these cases, the subjects’ postsurgical improvements in knee extension may have been unrelated to the hamstrings surgery. Analyses of muscle–tendon lengths and velocities may help to distinguish individuals who have “short” or “spastic” hamstrings from those who do not, and thus may augment conventional methods used to describe patients’ neuromusculoskeletal impairments and gait abnormalities.

Hamstring Muscle Kinematics during Treadmill Sprinting

The objective of this study was to characterize hamstring muscle kinematics during sprinting, so as to provide scientific data to better understand injury mechanisms and differences in injury rates between muscles. We conducted three-dimensional motion analyses of 14 athletes performing treadmill sprinting at speeds ranging from 80 to 100% of maximum. Scaled musculoskeletal models were used to estimate hamstring muscle-tendon lengths throughout the sprinting gait cycle for each speed. We tested the hypothesis that the biceps femoris (BF) long head would be stretched a greater amount, relative to its length in an upright posture, than the semitendinosus (ST) and semimembranosus (SM). We also tested the hypothesis that increasing from submaximal to maximal sprinting speed would both increase the magnitude and delay the occurrence of peak muscle-tendon length in the gait cycle. Maximum hamstring lengths occurred during the late swing phase of sprinting and were an average of 7.4% (SM), 8.1% (ST), and 9.5% (BF) greater than the respective muscle-tendon lengths in an upright configuration. Peak lengths were significantly larger in the BF than the ST and SM (P < 0.01), occurred significantly later in the gait cycle at the maximal speed (P < 0.01), but did not increase significantly with speed. Differences in the hip extension and knee flexion moment arms between the biarticular hamstrings account for the intermuscle variations in the peak lengths that were estimated. We conclude that intermuscle differences in hamstring moment arms about the hip and knee may be a factor contributing to the greater propensity for hamstring strain injuries to occur in the BF muscle.

An EMG-driven model of the upper extremity and estimation of long head biceps force

An electromyography (EMG) driven model of the upper extremity has been developed that incorporates musculoskeletal geometry of the glenohumeral and elbow joints, estimated relevant physiologic muscle parameters including optimal muscle lengths, and EMG activity. The model is designed to predict forces in muscles spanning the glenohumeral joint resulting from functionally relevant tasks. The model is composed of four sub-models that comprise a mathematical as well as graphical three-dimensional representation of the upper extremity: a musculoskeletal model for estimation of muscle–tendon lengths and moment arms, a Hill-based muscle force model, a model for estimating optimal muscle lengths, and a model for estimation of muscle activation from EMG signal of the biceps. The purpose of this paper is to describe the components of the model, as well as the data required to drive the model. Collection of data is described in the context of applying the model to determine biceps muscle forces for testing of functional tasks. Results obtained from applying the model to analyze the functional tasks are summarized, and model strengths and limitations are discussed.

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 ∼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.

Two Methods for Estimating Tendinous Tissue Elongation during Human Movement

During dynamic activities it is difficult to assess in vivo length changes in human tendon and aponeurosis. The present study compared the outcome of two methods during unilateral squat jump and drop jump performances of four volunteers. Tendinous tissue elongation of vastus lateralis muscle was estimated using either (a) direct measurement of in vivo fascicle length change and muscletendon length estimation (kinematic method), or (b) prediction using a quadratic force function in combination with direct tendon force measurement (force method). In the kinematic method the most critical measures contributing to the 10% uncertainty were the fascicle angle and fraction of the estimated fascicle length. The force method was most sensitive to resting length, with 1% error margin. Both methods predicted the same pattern of tendinous elongation because of the monotonic force/length relationship. The magnitude of length change, however, differed considerably between both methods. Based on the force method, the changes were only 20% (absolute values) or 30% (strain values) of those obtained with the kinematic method. On average, the maximum strains were 5% with the force method and 15% with the kinematic method. This difference can be explained by the fact that the kinematic method characterizes not only the changes in tendon length but also includes aponeurosis strain along the muscle belly. In addition, the kinematic method may be affected by non-uniform distribution of fascicle length change along the length of the muscle. When applying either method for estimating the patterns of tendon and tendinous tissue length changes during human locomotion, the given methodological considerations should be acknowledged.

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

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