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.     

In vivo moment arm calculations at the ankle using magnetic resonance imaging (MRI)

In vivo moment arm lengths for the Achilles tendon and tibialis anterior (TA) were determined in 10 adult male subjects. Moment arms were measured as the perpendicular distance between the joint center of rotation (CR) and the center of the muscle's tendon on a series of sagittal plane magnetic resonance images. The first set of calculations used a fixed CR and the second a moving CR. The position of the CR was determined using a modification of the graphical method of Reuleaux. For both moving and fixed CR conditions, moment arms increased by approximately 20% for the Achilles tendon and decreased by approximately 30% for the TA when the ankle moved from maximum dorsiflexion to maximum plantarflexion. Moment arms averaged 3.1% greater for the Achilles tendon and 2.5% greater for the TA when calculated using a fixed CR. These data suggest that the averaged moment arm lengths for the Achilles tendon and the TA were relatively unaffected by the use of a fixed vs moving CR.     

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 human tendinous tissue stretch upon maximum muscle force generation

In the present study, we examined the hypothesis that stretch of tendinous tissue in the human tibialis anterior (TA) muscle-tendon unit upon isometric dorsiflexion maximum voluntary contraction (MVC) varies along the entire tendinous component length. Ultrasound-based measurements of the excursions of the TA tendon origin and proximal end of the TA central aponeurosis were taken in the transition from rest to MVC in six men. Subtracting the TA tendon origin excursion from the excursion of the aponeurosis proximal end, the aponeurosis excursion was estimated. Estimation of the aponeurosis proximal region excursion was obtained subtracting the excursion of the insertion point of a central region fascicle on the aponeurosis from the whole aponeurosis excursion. Subtracting tendon excursion from the excursion of the central fascicle insertion point, the aponeurosis distal region excursion was estimated. Strain values were calculated dividing the excursions obtained by the original resting lengths. All excursions and lengths were measured in the mid-longitudinal axis of the TA muscle-tendon unit at the neutral anatomical ankle position. Tendon excursion and strain were 0.5+/-0. 08 cm (mean+/-SE) and 3.1+/-0.2%, respectively. Aponeurosis excursion and strain were 1.1+/-0.15 cm and 6.5+/-0.6%, respectively. Aponeurosis distal region excursion and strain were 0.3+/-0.05 cm and 3.5+/-0.3%, respectively. Aponeurosis proximal region excursion and strain were 0.8+/-0.12 cm and 9.2+/-1%, respectively. Aponeurosis excursion and strain were larger by 110-120% (P<0.05) compared with tendon. Aponeurosis proximal region excursion and strain were larger by 165-170% (P<0.05) compared with aponeurosis distal region. These findings are in line with results from in vitro animal material testing and have important implications for theoretical models of muscle function.     

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.     

Predictability of in vivo changes in pennation angle of human tibialis anterior muscle from rest to maximum isometric dorsiflexion

The aim of this study was to assess the predictability of in vivo, ultrasound-based changes in human tibialis anterior (TA) pennation angle from rest to maximum isometric dorsiflexion (MVC) using a planimetric model assuming constant thickness between aponeuroses and straight muscle fibres. Sagittal sonographs of TA were taken in six males at ankle angles of -15 degrees (dorsiflexion direction), 0 degrees (neutral position), + 15 (plantarflexion direction) and + 30 degrees both at rest and during dorsiflexor MVC trials performed on an isokinetic dynamometer. At all four ankle angles scans were taken from the TA proximal, central and distal regions. TA architecture did not differ (P > 0.05) neither between its two unipennate parts nor along the scanned regions over its length at a given ankle angle and state of contraction. Comparing MVC with rest at any given ankle angle, pennation angle was larger (62-71%, P < 0.01), fibre length smaller (37-40%, P < 0.01) and muscle thickness unchanged (P > 0.05). The model used estimated accurately (P > 0.05) changes in TA pennation angle occurring in the transition from rest to MVC and therefore its use is encouraged for estimating the isometric TA ankle moment and force generating capacity using musculoskeletal modelling.     

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

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

The human patellar tendon moment arm assessed in vivo using dual-energy X-ray absorptiometry

Accurate assessment of muscle–tendon forces in vivo requires knowledge of the muscle–tendon moment arm. Dual-energy X-ray absorptiometry (DXA) can produce 2D images suitable for visualising both tendon and bone, thereby potentially allowing the moment arm to be measured but there is currently no validated DXA method for this purpose. The aims of this study were (i) to compare in vivo measurements of the patellar tendon moment arm (d_PT) assessed from 2D DXA and magnetic resonance (MR) images and (ii) to compare the reliability of the two methods. Twelve healthy adults (mean±SD: 31.4±9.5 yr; 174.0±9.5 cm; 76.2±16.6 kg) underwent two DXA and two MR scans of the fully extended knee at rest. The tibiofemoral contact point (TFCP) was used as the centre of joint rotation in both techniques, and the d_PT was defined as the perpendicular distance from the patellar tendon axis to the TFCP. The d_PT was consistently longer when assessed via DXA compared to MRI (+3.79±1.25 mm or +9.78±3.31%; P<0.001). The test–retest reliability of the DXA [CV=2.13%; ICC=0.94; ratio limits of agreement (RLA)=1.01 (?/÷1.07)] and MR [(CV=2.27%; ICC=0.96; RLA=1.00 (?/÷1.07)] methods was very high and comparable between techniques. Moreover, the RLA between the mean DXA and MRI d_PT values [1.097 (?/÷1.061)] demonstrated very strong agreement between the two methods. In conclusion, highly reproducible d_PT measurements can be determined from DXA imaging with the knee fully extended at rest. This has implications for the calculation of patellar tendon forces in vivo where MR equipment is not available.     

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

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

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.     

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.     

Moment arms of the human neck muscles in flexion, bending and rotation

There is a paucity of data available for the moment arms of the muscles of the human neck. The objective of the present study was to measure the moment arms of the major cervical spine muscles in vitro. Experiments were performed on five fresh-frozen human head-neck specimens using a custom-designed robotic spine testing apparatus. The testing apparatus replicated flexion-extension, lateral bending and axial rotation of each individual intervertebral joint in the cervical spine while all other joints were kept immobile. The tendon excursion method was used to measure the moment arms of 30 muscle sub-regions involving 13 major muscles of the neck about all three axes of rotation of each joint for the neutral position of the cervical spine. Significant differences in the moment arm were observed across sub-regions of individual muscles and across the intervertebral joints spanned by each muscle (p<0.05). Overall, muscle moment arms were larger in flexion-extension and lateral bending than in axial rotation, and most muscles had prominent moment arms in at least 2 out of the 3 joint motions investigated. This study emphasizes the importance of detailed representation of a muscle's architecture in prediction of its torque capacity about the individual joints of the cervical spine. The dataset produced may be useful in developing and validating computational models of the human neck.     

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.     

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.     

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.     

The 3D patellar tendon moment arm: quantified in vivo during volitional activity

The patellar tendon moment arm is a critical quantity in that it defines the quadriceps ability to generate a moment on the tibia. Thus, the primary purpose of this study was to establish the first in vivo three-dimensional measures of the patellar tendon moment arm, measured non-invasively and in vivo during dynamic activity in a large normative population (n=34) using a dynamic MRI technique (fast-PC MRI). The magnitude of the moment arm was defined as the shortest distance between the finite helical axis and the patellar tendon line of action. Using these data, the hypothesis that the patellar tendon moment arm is independent of gender was tested. In general, the moment arm increased from 20 to 50 mm during knee extension. There were significant differences (P<0.05) in the moment arm between gender, but these differences were eliminated when the moment arm was scaled by the femoral epicondylar width. This study took a large step forward towards the ultimate goal of defining how pathology may alter joint dynamics through alteration in moment arms by establishing the first in vivo normative data base for the patellar tendon moment arm using non-invasive measures during volitional activity in a relatively large population (n=34). The fact that the scaled moment arm was independent of gender may lend insights into impairments that tend to be gender specific, such as patellar maltracking. The next steps will be to quantify the patellar tendon moment arm in populations with specific pathologies.     

Method of determination of three dimensional index finger moment arms and tendon lines of action using high resolution MRI scans

High-resolution MRI scans, in conjunction with CAD software, were used to determine the three-dimensional moment arms and force vector direction cosines for 11 structures passing the interphalangeal and metacarpophalangeal joints of the index finger. The results are presented for five different angles of joint flexion for a single subject. The moment arm data obtained differ from previous studies, where results have been derived from tendon excursion techniques or geometrical models. These dissimilarities have been accounted for by the differences in experimental techniques.     

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 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.     

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.