Estimates of Achilles tendon moment arm differ when axis of ankle rotation is derived from ankle motion

The plantarflexor moment arm of the Achilles tendon determines the mechanical advantage of the triceps surae and also indirectly affects muscle force generation by setting the amount of muscle-tendon shortening per unit of ankle joint rotation. The Achilles tendon moment arm may be determined geometrically from an axis (or center) of joint rotation and the line of action of the tendon force, but such moment arms may be sensitive to the location of the joint axis. Using motion analysis to track an ultrasound probe overlying the Achilles tendon along with markers on the shank and foot, we measured Achilles tendon moment arm during loaded and unloaded dynamic plantarflexion motions in 15 healthy subjects. Three representations of the axis or center of rotation of the ankle were considered: (1) a functional axis, defined by motions of the foot and shank; (2) a transmalleolar axis; and (3) a transmalleolar midpoint. Moment arms about the functional axis were larger than those found using the transmalleolar axis and transmalleolar midpoint (all p < 0.001). Moment arms computed with the functional axis increased with plantarflexion angle (all p < 0.001), and increased with loading in the most plantarflexed position (p < 0.001) but these patterns were not observed when either using a transmalleolar axis or transmalleolar midpoint. Functional axis moment arms were similar to those estimated previously using magnetic resonance imaging, suggesting that using a functional axis for ultrasound-based geometric estimates of Achilles tendon moment arm is an improvement over landmark-based methods.     

In vivo measurement-based estimations of the moment arm in the human tibialis anterior muscle-tendon unit

The aim of this study was to estimate the moment arm of human tibialis anterior (TA) muscle-tendon unit at rest and during isometric dorsiflexion maximum voluntary contraction (MVC) from in vivo sagittal-plane magnetic resonance (MR) and ultrasound scans. Two methods were employed, both of them based on the assumption that the ankle joint complex and TA muscle-tendon unit operate in the sagittal plane. Using method A, moment arms were obtained from MR scans of the foot by measuring the perpendicular distance between a moving centre of rotation in the talo-crural joint and the TA tendon action line. Using method B, moment arms were calculated from the ratio of TA tendon displacement, which was estimated from a planimetric muscle model using pennation angles and muscle thickness measured by ultrasonography, to the tibial rotation around the talus, which was measured from the foot MR scans. Using either of the two methods at rest, the estimated TA moment arm decreased from approximately 4.5 to approximately 2.9 cm in the transition from dorsiflexion to plantarflexion. Using method A, moment arms during MVC were larger by 0.9-1.5 cm (33-44%, P < 0.01) than the respective resting estimations. In contrast, no difference (P > 0.05) was found between the resting and MVC moment arm estimations of method B. Limitations in the oversimplified musculoskeletal model used raise questions for the validity of both method estimations.     

A comparison of the triceps surae and residual muscle moments at the ankle during cycling

The rigid linked system model and principles of inverse dynamics have been widely used to calculate residual muscle moments during various activities. EMG driven models and optimization algorithms have also been presented in the literature in efforts to estimate skeletal muscle forces and evaluate their possible contribution to the residual muscle moment. Additionally, skeletal muscle-tendon forces have been measured, directly, in both animals and humans. The purpose of this investigation was to calculate the moment produced by the triceps surae muscles and compare it to the residual muscle moment at the ankle during cycling at three power outputs (90, 180 and 270 W). Inferences were made regarding the potential contribution made by each triceps surae component to the tendon force using EMG and muscle-tendon length changes. A buckle-type transducer was surgically implanted on the right Achilles tendon of one male subject. Achilles tendon forces measured in vivo were multiplied by their corresponding moment arms to yield the triceps surae moment during the three working conditions. Moment arm lengths were obtained in a separate experiment using magnetic resonance imaging (MRI). Pedal reaction forces, body segment accelerations (determined from high speed film), and appropriate mass parameters served as input to the inverse solution. The triceps surae moment was temporally in phase with and consistently represented approximately 65% of the residual muscle moment at the ankle. These data demonstrate the feasibility of using implanted transducers in human subjects and provide a greater understanding of musculoskeletal mechanics during normal human movements.     

Variation in the human Achilles tendon moment arm during walking

The Achilles tendon (AT) moment arm is an important determinant of ankle moment and power generation during locomotion. Load and depth-dependent variations in the AT moment arm are generally not considered, but may be relevant given the complex triceps surae architecture. We coupled motion analysis and ultrasound imaging to characterize AT moment arms during walking in 10 subjects. Muscle loading during push-off amplified the AT moment arm by 10% relative to heel strike. AT moment arms also varied by 14% over the tendon thickness. In walking, AT moment arms are not strictly dependent on kinematics, but exhibit important load and spatial dependencies.     

In vivo moment arm determination using B-mode ultrasonography

The tendon excursion of the tibialis anterior (TA) muscle was measured in vivo using B-mode ultrasonography in seven subjects under three force levels (0, 30 and 60% maximal voluntary contraction, MVC). For each force level, the TA moment arm (m) was determined by calculating the derivative of the tendon excursion relative to the ankle angle (a). A dynamometer controlled the ankle angle while force levels were monitored. The parametric model proposed by Miller and Dennis (1996), m = R sin(a + delta), where R is the largest moment arm and delta represents the offset angle of R from 90 degrees, was used in a least-squares fit of the relationship between moment arm and ankle angle. The R values at 0% MVC were significantly smaller than those at 30 and 60% MVC. The values of calculated moment arm at 0% MVC were not considered adequate estimates of the TA moment arm because of the possible confounding effect of the slackness of the relaxed muscle-tendon unit in more dorsiflexed positions. The moment arm values at 30 and 60% MVC were believed to provide reliable estimates of those of TA since the application of tension probably reduced the effects of the slackness of the muscle-tendon unit and tendon elongation on tendon excursion measurement at these force levels. Since the ultrasonographic technique is an in vivo application of the tendon excursion technique and therefore takes the functional meaning into consideration, it can yield more significant moment arms than other in vivo or cadaver techniques.     

Biarticular hip extensor and knee flexor muscle moment arms of the feline hindlimb

Moment arms are important for understanding muscular behavior and for calculating internal muscle forces in musculoskeletal simulations. Biarticular muscles cross two joints and have moment arms that depend on the angle of both joints the muscles cross. The tendon excursion method was used to measure the joint angle-dependence of hamstring (biceps femoris, semimembranosus and semitendinosus) moment arm magnitudes of the feline hindlimb at the knee and hip joints. Knee angle influenced hamstring moment arm magnitudes at the hip joint; compared to a flexed knee joint, the moment arm for semimembranosus posterior at the hip was at most 7.4 mm (25%) larger when the knee was extended. On average, hamstring moment arms at the hip increased by 4.9 mm when the knee was more extended. In contrast, moment arm magnitudes at the knee varied by less than 2.8 mm (mean=1.6 mm) for all hamstring muscles at the two hip joint angles tested. Thus, hamstring moment arms at the hip were dependent on knee position, while hamstring moment arms at the knee were not as strongly associated with relative hip position. Additionally, the feline hamstring muscle group had a larger mechanical advantage at the hip than at the knee joint.     

In vivo specific tension of human skeletal muscle.

In this study, we estimated the specific tensions of soleus (Sol) and tibialis anterior (TA) muscles in six men. Joint moments were measured during maximum voluntary contraction (MVC) and during electrical stimulation. Moment arm lengths and muscle volumes were measured using magnetic resonance imaging, and pennation angles and fascicular lengths were measured using ultrasonography. Tendon and muscle forces were modeled. Two approaches were followed to estimate specific tension. First, muscle moments during electrical stimulation and moment arm lengths, fascicular lengths, and pennation angles during MVC were used (data set A). Then, MVC moments, moment arm lengths at rest, and cadaveric fascicular lengths and pennation angles were used (data set B). The use of data set B yielded the unrealistic specific tension estimates of 104 kN/m(2) in Sol and 658 kN/m(2) in TA. The use of data set A, however, yielded values of 150 and 155 kN/m(2) in Sol and TA, respectively, which agree with in vitro results from fiber type I-predominant muscles. In fact, both Sol and TA are such muscles. Our study demonstrates the feasibility of accurate in vivo estimates of human muscle intrinsic strength.     

Knee muscle moment arms from MRI and from tendon travel.

We tested magnetic resonance imaging (MRI) as a means to collect geometric data for moment arm estimation. A knee specimen in five successive flexion postures was scanned by MRI, while simultaneously tendon positions of loaded muscles were measured (long head of biceps femoris, lateral and medial gastrocnemius, gracilis, rectus femoris, sartorius, semimembranosus, semitendinosus, and tensor fasciae latae). Discrete rotation centres were derived from MRI pictures. Moment arms were estimated as the distances from these centres to the tendons. The ratio of tendon travel over the increment of joint angulation was the alternative, more reliable estimate of the moment arm. An important principal shortcoming of MRI is the impossibility of accounting for force distribution in taut tissue. As a consequence, for some muscles, considerable inaccuracies in moment arm estimation are found in a relatively small range of joint angulation (up to about 30% for the rectus femoris and semimembranosus). For the tensor fasciae latae, the moment arm cannot be estimated by MRI, while the estimate by tendon travel is unreliable owing to the deformability and attachments of the fascia lata.     

Calcaneus length determines running economy: implications for endurance running performance in modern humans and Neandertals

The endurance running (ER) hypothesis suggests that distance running played an important role in the evolution of the genus Homo. Most researchers have focused on ER performance in modern humans, or on reconstructing ER performance in Homo erectus, however, few studies have examined ER capabilities in other members of the genus Homo. Here, we examine skeletal correlates of ER performance in modern humans in order to evaluate the energetics of running in Neandertals and early Homo sapiens. Recent research suggests that running economy (the energy cost of running at a given speed) is strongly related to the length of the Achilles tendon moment arm. Shorter moment arms allow for greater storage and release of elastic strain energy, reducing energy costs. Here, we show that a skeletal correlate of Achilles tendon moment arm length, the length of the calcaneal tuber, does not correlate with walking economy, but correlates significantly with running economy and explains a high proportion of the variance (80%) in cost between individuals. Neandertals had relatively longer calcaneal tubers than modern humans, which would have increased their energy costs of running. Calcaneal tuber lengths in early H. sapiens do not significantly differ from those of extant modern humans, suggesting Neandertal ER economy was reduced relative to contemporaneous anatomically modern humans. Endurance running is generally thought to be beneficial for gaining access to meat in hot environments, where hominins could have used pursuit hunting to run prey taxa into hyperthermia. We hypothesize that ER performance may have been reduced in Neandertals because they lived in cold climates.     

Inversion–eversion moment arms of gastrocnemius and tibialis anterior measured in vivo

In this study, the frontal plane moment arms of tibialis anterior (TA) and the lateral and medial heads of gastrocnemius (LG and MG) were determined using ultrasonography of ten healthy subjects. Analysis of variance was performed to investigate the effects of frontal plane angle, muscle activity, and plantarflexion angle on inversion–eversion moment arm for each muscle. The moment arms of each muscle were found to vary with frontal plane angle (all p<0.001). TA and LG exhibited eversion moment arms when the foot was everted, but MG was found to have a slight inversion moment arm in this position. As the ankle rotated from 0° to 20° inversion, the inversion moment arm of each increased, indicating that the three muscles became increasingly effective inverters. In neutral position, the inverter moment arm of MG was greater than that of LG (p=0.001). Muscle activity had a significant effect on both LG and MG moment arm at all frontal plane positions (all p0.005). These results demonstrate the manner in which frontal plane moment arms of gastrocnemius and TA differ across the frontal plane range of motion in healthy subjects. This method for assessing muscle action in vivo used in this study may prove useful for subject-specific planning of surgical treatments for frontal plane foot and ankle deformities.     

In vivo moment arm lengths for hip extensor muscles at different angles of hip flexion

Moment arm lengths of three hip extensor muscles, the gluteus maximus, the hamstrings and the adductor magnus, were determined at hip flexion angles from 0 degrees to 90 degrees by combining data from ten autopsy specimens and from twenty patients, the latter examined by computed tomography. A straight-line muscle model for muscle force was used for the hamstrings and adductor magnus, and for the gluteus maximus a two-segment straight-line muscle force model was used. With the joint in its anatomical position the moment arm of the gluteus maximus to the bilateral motion axis averaged 79 mm, for the hamstrings 61 mm and for the adductor magnus 15 mm. The moment arm of gluteus maximus decreased with increasing hip flexion angle. The hamstrings showed an increase in moment arm length up to an average of 35 degrees hip flexion and then a decrease with increasing hip flexion angle. The corresponding figures for the adductor magnus moment arm showed an increase up to 75 degrees and then a decrease. Statistical analysis revealed significant differences in moment arm length between men and women.     

Elastic properties of human Achilles tendon are correlated to muscle strength.

The purpose of this study was to investigate whether the mechanical properties of the Achilles tendon were correlated to muscle strength in the triceps surae in humans. Twenty-four men and twelve women exerted maximal voluntary isometric plantar flexion (MVIP) torque. The elongation (DeltaX) and strain of the Achilles tendon (epsilon), the proximal part of which is the composite of the gastrocnemius tendon and the soleus aponeurosis, at MVIP were determined from the displacement of the distal myotendinous junction of the medial gastrocnemius using ultrasonography. The Achilles tendon force at MVIP (F) was calculated from the MVIP torque and the Achilles tendon moment arm. There were no significant differences in either the F-DeltaX or F-epsilon relationships between men and women. DeltaX and epsilon were 9.8 +/- 2.6 mm and 5.3 +/- 1.6%, respectively, and were positively correlated to F (r = 0.39, P < 0.05; r = 0.39, P < 0.05), which meant that subjects with greater muscle strength could store more elastic energy in the tendon. The regression y-intercepts for the F-DeltaX (P < 0.01) and F-epsilon (P < 0.05) relationship were significantly positive. These results might indicate that the Achilles tendon was stiffer in subjects with greater muscle strength, which may play a role in reducing the probability of tendon strain injuries. It was suggested that the Achilles tendon of subjects with greater muscle strength did not impair the potential for storing elastic energy in tendons and may be able to deliver the greater force supplied from a stronger muscle more efficiently. Furthermore, the difference in the Achilles tendon mechanical properties between men and women seemed to be correlated to the difference in muscle strength rather than gender.     

Can Achilles tendon moment arm be predicted from anthropometric measures in pre-pubescent children?

Muscle-tendon moment arm magnitudes are essential variables for accurately calculating muscle forces from joint moments. Their measurement requires specialist knowledge and expensive resources. Research has shown that the patellar tendon moment arm length is related to leg anthropometry in children. Here, we asked whether the Achilles tendon moment arm (MA(AT)) can be accurately predicted in pre-pubescent children from surface anthropometry. Age, standing height, mass, foot length, inter-malleolar ankle width, antero-posterior ankle depth, tibial length, lower leg circumference, and distances from the calcaneus to the distal head of the 1st metatarsal and medial malleolus were determined in 49 pre-pubescent children. MA(AT) was calculated at three different ankle positions (neutral, 10° plantarflexion, and 10° dorsiflexion) by differentiating tendon excursion, measured via ultrasonography, with respect to ankle angle change using seven different differentiation techniques. Backwards stepwise regression analyses were performed to identify predictors of MA(AT.) When all variables were included, the regression analysis accounted for a maximum of 49% of MA(AT) variance at the neutral ankle angle when a third-order polynomial was used to differentiate tendon excursion with respect to ankle angle. For this condition, foot length and the distance between calcaneus and 1st metatarsal were the only significant predictors, accounting for 47% of the variance (p<0.05). The absolute error associated with this regression model was 3.8±4.4 mm, which would result in significant error (mean=14.5%) when estimating muscle forces from joint moments. We conclude that MA(AT) cannot be accurately predicted from anthropometric measures in children.     

Plantarflexor moment arms estimated from tendon excursion in vivo are not strongly correlated with geometric measurements

Geometric and tendon excursion methods have both been used extensively for estimating plantarflexor muscle moment arm in vivo. Geometric measures often utilize magnetic resonance imaging, which can be costly and impractical for many investigations. Estimating moment arm from tendon excursion measured with ultrasonography may provide a cost-effective alternative to geometric measures of moment arm, but how well such measures represent geometry-based moment arms remains in question. The purpose of this study was to determine whether moment arms from tendon excursion can serve as a surrogate for moment arms measured geometrically. Magnetic resonance and ultrasound imaging were performed on 19 young male subjects to quantify plantarflexor moment arm based on geometric and tendon excursion paradigms, respectively. These measurements were weakly correlated that approached statistical significance (R² = 0.21, p = 0.052), and moment arm from tendon excursion under-approximated geometric moment arm by nearly 40% (p < 0.001). This weak correlation between methods is at odds with a prior report (N = 9) of a strong correlation (R² = 0.94) in a similar study. Therefore, we performed 92,378 regression analyses (19 choose 9) to determine if such a strong correlation existed in our study population. We found that certain sub-populations of the current study generated similarly strong coefficients of determination (R² = 0.92), but 84% of all analyses revealed no correlation (p > 0.05). Our results suggest that the moment arms from musculoskeletal geometry cannot be otherwise obtained by simply scaling moment arms estimated from tendon excursion.     

The contraction-induced increase in Achilles tendon moment arm: A three-dimensional study

The present study aimed to re-examine the influence of the isometric plantarflexors contraction on the Achilles tendon moment arm (ATMA) and the factors influencing the ATMA in three-dimensions. A series of coronal magnetic resonance images of the right ankle were recorded at foot positions of 10° of dorsiflexion, neutral position, and 10° of plantarflexion for the rest condition and the plantarflexors contraction condition at 30% maximal voluntary effort. The shortest distance between the talocrural joint axis and the line of action of the Achilles tendon force projected to the orthogonal plane of the talocrural joint axis was determined as the ATMA. The ATMA determined in the contraction condition was significantly greater by 8 mm than that determined in the rest condition. The talocrural joint axis was displaced anteriorly by 3 mm and distally by 2 mm due to the muscle contraction. As the same time, the line of action of the Achilles tendon force was displaced posteriorly by 5 mm and medially by 2 mm. These linear displacements of the talocrural joint axis and the line of action of the Achilles tendon force accounted for the difference in the ATMAs between the two conditions by 35.9 and 62.4%, respectively. These angular displacements accounted for the total of 0.4% increase in the ATMA. These results confirm the previous findings reported in two-dimensional studies and found that the linear displacement of the line of action of the Achilles tendon force is the primary source of the contraction-induced increase in the ATMA.     

In vivo determination of the Achilles tendon moment arm in three-dimensions

Two-dimensional methods have been applied to determine the Achilles tendon moment arm in previous studies, although the talocrural joint rotates in three-dimension. The purpose of this study was to develop a method for determining the Achilles tendon moment arm in three-dimensions (3DMA). A series of sagittal ankle images were obtained at ankle positions of -20°, -10° (dorsiflexed position), 0° (neutral position), +10°, +20°, and +30° (plantarflexed position). The talocrural joint axis was determined as the finite helical axis of the ankle joint over 20° of displacement, and the 3DMA was determined as the shortest distance from the talocrural joint axis to the line of action of the Achilles tendon force. The corresponding 2DMA was determined with the center of rotation method using the images captured on the sagittal plane passing through the mid-point of the medio-lateral width of the tibia. The 3DMA ranged from 35 to 41 mm across various ankle positions and was, on average, 11 mm smaller than 2DMA. The difference between the two measures was attributable primarily to the deviations of the talocrural joint axis from the anatomical medio-lateral direction. The deviations on the coronal plane (21.4±20.7°) and on the transverse planes (14.8±22.6°) accounted for the errors of 1.3 mm and 3.0 mm, respectively. In addition, selecting either a medially or laterally misaligned sagittal-plane image for determining the 2DMA gave rise to error by 3.5 mm. The remaining difference was accounted for by the random measurement error.     

Ankle joint mechanics and foot proportions differ between human sprinters and non-sprinters

Recent studies of sprinters and distance runners have suggested that variations in human foot proportions and plantarflexor muscle moment arm correspond to the level of sprint performance or running economy. Less clear, however, is whether differences in muscle moment arm are mediated by altered tendon paths or by variation in the centre of ankle joint rotation. Previous measurements of these differences have relied upon assumed joint centres and measurements of bone geometry made externally, such that they would be affected by the thickness of the overlying soft tissue. Using magnetic resonance imaging, we found that trained sprinters have shorter plantarflexor moment arms (p = 0.011) and longer forefoot bones (p = 0.019) than non-sprinters. The shorter moment arms of sprinters are attributable to differences in the location of the centre of rotation (p < 0.001) rather than to differences in the path of the Achilles tendon. A simple computer model suggests that increasing the ratio of forefoot to rearfoot length permits more plantarflexor muscle work during plantarflexion that occurs at rates expected during the acceleration phase following the sprint start.     

Fascicle behavior of medial gastrocnemius muscle in extended and flexed knee positions

The present study tested the hypotheses that Achilles tendon forces during fast concentric actions do not differ between extended and flexed knee positions, and this phenomenon is attributable to the force-length characteristics and electromyograms (EMGs) of gastrocnemius muscle. Seven healthy men performed static and concentric plantarflexions at fully extended (K0) and 0.785 rad (45 degrees ) flexed (K45) knee positions with the maximal effort. In concentric actions, the angular velocities were set at 0.524 (slow) and 6.109 rad s(-1) (fast). Fascicle length of medial gastrocnemius (MG) was determined with ultrasonography. Surface EMGs of the MG were recorded during each action. Achilles tendon force was calculated from the torque and moment arm of the tendon. Peak tendon forces in fast concentric actions were similar in K0 and in K45, but those in static and slow concentric actions significantly (P<0.05) differed between the two positions. When the tendon force peaked, the fascicle lengths in each action and fascicle velocities in both concentric actions were significantly (P<0.05) greater in K0 than in K45. The EMGs were significantly (P<0.05) higher in K0 than K45 during each action. The results suggest that (1) the difference in the tendon forces between the two positions can be explained by the force-length and -velocity characteristics and the EMGs of the MG, and (2) the contribution of the MG to the tendon force in flexed knee positions is greater in concentric actions than expected from the results in static actions.     

Effects of rotator cuff tears on muscle moment arms: a computational study

Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 45 degrees internal to 45 degrees external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1-99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces.     

Hysteresis measurements in intact human tendon

Mechanical hysteresis in tendons has traditionally been quantified from tensile testing of isolated specimens. Limitations associated with tendon displacement measurement and clamping, and uncertainties as to whether in vitro material represents intact tendon function necessitate measuring hysteresis under in vivo conditions. In the present study such measurements were taken in the human tibialis anterior (TA) tendon. Having the foot fixed on a dynamometer footplate, the displacement of the TA tendon during stimulation and relaxation of the TA muscle was recorded by means of ultrasonography in six men. Combining moment data corresponding to 0, 20, 40, 60, 80 and 100% of maximum voltage moment and the respective tendon-displacement data, a hysteresis loop was obtained between the load–displacement curves during contraction and relaxation. Measurement of the hysteresis loop area yielded a value of 19%. This value agrees with results from in vitro tensile tests of low-stress tendons, suitable for tensile force transmission and joint displacement control. In fact, the human TA tendon has such functional characteristics. The methodology presented allows design of longitudinal and cross-sectional experimental protocols, and in vivo assessment of tendon function and propensity to overheat.