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.     

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.     

Influence of muscle anatomical cross-sectional area on the moment arm length of the triceps brachii muscle at the elbow joint

The purpose of this study was to test the hypothesis that the musculotendon moment arm length is affected by the muscle anatomical cross-sectional area. The moment arm length of the triceps brachii (TB) muscle at 30°, 50°, 70°, 90°, 110° elbow flexion positions was measured in sagittal magnetic resonance images (MRI) of 18 subjects as the perpendicular distance between the center of the pulley of the humerus to the line through the center of the TB tendon. The moment arm increased as the elbow flexion angle decreased, from 1.74±0.13 cm at 110° to 2.39±0.14 cm at 30°. The maximal anatomical cross-sectional area of the TB muscle was significantly correlated with the moment arms at all joint positions (r=0.545–0.803, p<0.05). Furthermore, the circumference of the upper arm was also significantly correlated with the moment arms at all joint positions, except for 70° (r=0.504–0.702, p<0.05). These results indicate that the moment arm length of the TB muscle is affected by the muscle anatomical cross-sectional area.     

Neck muscle paths and moment arms are significantly affected by wrapping surface parameters

In this paper, we studied the effects of wrapping surfaces on muscle paths and moment arms of the neck muscle, semispinalis capitis. Sensitivities to wrapping surface size and the kinematic linkage to vertebral segments were evaluated. Kinematic linkage, but not radius, significantly affected the accuracy of model muscle paths compared to centroid paths from images. Both radius and linkage affected the moment arm significantly. Wrapping surfaces that provided the best match to centroid paths over a range of postures had consistent moment arms. For some wrapping surfaces with poor matches to the centroid path, a kinematic method (tendon excursion) predicted flexion moment arms in certain postures, whereas geometric method (distance to instant centre) predicted extension. This occurred because the muscle lengthened as it wrapped around the surface. This study highlights the sensitivity of moment arms to wrapping surface parameters and the importance of including multiple postures when evaluating muscle paths and moment arm.     

Neck muscle paths and moment arms are significantly affected by wrapping surface parameters

In this paper, we studied the effects of wrapping surfaces on muscle paths and moment arms of the neck muscle, semispinalis capitis. Sensitivities to wrapping surface size and the kinematic linkage to vertebral segments were evaluated. Kinematic linkage, but not radius, significantly affected the accuracy of model muscle paths compared to centroid paths from images. Both radius and linkage affected the moment arm significantly. Wrapping surfaces that provided the best match to centroid paths over a range of postures had consistent moment arms. For some wrapping surfaces with poor matches to the centroid path, a kinematic method (tendon excursion) predicted flexion moment arms in certain postures, whereas geometric method (distance to instant centre) predicted extension. This occurred because the muscle lengthened as it wrapped around the surface. This study highlights the sensitivity of moment arms to wrapping surface parameters and the importance of including multiple postures when evaluating muscle paths and moment arm.     

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.     

Wrist tendon moment arms: Quantification by imaging and experimental techniques

Subject-specific musculoskeletal models require accurate values of muscle moment arms. The aim of this study was to compare moment arms of wrist tendons obtained from non-invasive magnetic resonance imaging (MRI) to those obtained from an in vitro experimental approach. MRI was performed on ten upper limb cadaveric specimens to obtain the centrelines for the flexor carpi radialis (FCR), flexor carpi ulnaris (FCU), extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), and abductor pollicis longus (APL) tendons. From these, the anatomical moment arms about each of the flexion-extension (FE) and radioulnar deviation (RUD) axes of the wrist were calculated. Specimens were mounted on a physiologic wrist simulator to obtain functional measurements of the moment arms using the tendon excursion method. No differences were observed between anatomical and functional values of the FE and RUD moment arms of FCR, ECRL and ECRB, and the RUD moment arm of ECU (p > .075). Scaling the anatomical moment arms relative to ECRB in FE and ECU in RUD reduced differences in the FE moment arm of FCU and the RUD moment arm of APL to less than 15% (p > .139). However, differences persisted in moment arms of FCU in RUD, and ECU and APL in FE (p < .008). This study shows that while measurements of moment arms of wrist tendons using imaging do not always conform to values obtained using in vitro experimental approaches, a stricter protocol could result in the acquisition of subject-specific moment arms to personalise musculoskeletal models.     

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.     

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.     

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.     

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.     

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.     

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.     

Children with cerebral palsy have larger Achilles tendon moment arms than typically developing children

The effectiveness of the plantarflexor muscle group to generate desired plantarflexion moments is modulated by the geometry of the Achilles tendon moment arm (ATMA). Children with cerebral palsy (CP) frequently have reduced plantarflexion function, which is commonly attributed to impaired muscle structure and function, however little attention has been paid to the potential contribution of ATMA geometry. The use of musculoskeletal modelling for the simulation of gait and understanding of gait mechanics, rely on accuracy of ATMA estimates. This study aimed to compare 3D in-vivo estimates of ATMA of adults, children with CP and typically developing (TD) children, as well as compare 3D in-vivo estimates to linearly scaled musculoskeletal model estimates. MRI scans for eight children with CP, 11 TD children and nine healthy adults were used to estimate in-vivo 3D ATMA using a validated method. A lower limb musculoskeletal model was linearly scaled to individual tibia length to provide a scaled ATMA estimate. Normalised in-vivo 3D ATMA for children with CP was 17.2% ± 2.0 tibia length, which was significantly larger than for TD children (15.2% ± 1.2, p = 0.013) and adults (12.5% ± 0.8, p < 0.001). Scaled ATMA estimates from musculoskeletal models significantly underestimated in-vivo estimates for all groups, by up to 34.7%. The results of this study show children with CP have larger normalised 3D ATMA compared to their TD counterparts, which may have implications in understanding reduced plantarflexor function and the efficacy of surgical interventions whose aim is to modify the musculoskeletal geometry of this muscle group.     

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.     

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.     

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.     

Foot structure and knee joint kinetics during walking with and without wedged footwear insoles

The relationship between static foot structure characteristics and knee joint biomechanics during walking, or the biomechanical response to wedged insoles are currently unknown. In this study, 3D foot scanning, dual X-ray absorptiometry and gait analysis methods were used to determine structural parameters of the foot and assess their relation to knee joint loading and biomechanical response to wedged insoles in 30 patients with knee osteoarthritis. In multiple linear regression models, foot fat content, height of the medial longitudinal arch and static hind foot angle were not associated with the magnitude of the knee adduction moment (R² = 0.24, p = 0.060), knee adduction angular impulse (R² = 0.21, p = 0.099) or 3D resultant knee moment (R² = 0.23, p = 0.073) during gait. Furthermore, these foot structure parameters were not associated with the patients’ biomechanical response to medial or lateral wedge footwear insoles (all p < 0.01). These findings suggest that static foot structure is not associated with gait mechanics at the knee, and that static foot structure alone cannot be utilized to predict an individual’s biomechanical response to wedged footwear insoles in patients with knee osteoarthritis.     

Dynamic arm swinging in human walking

Humans tend to swing their arms when they walk, a curious behaviour since the arms play no obvious role in bipedal gait. It might be costly to use muscles to swing the arms, and it is unclear whether potential benefits elsewhere in the body would justify such costs. To examine these costs and benefits, we developed a passive dynamic walking model with free-swinging arms. Even with no torques driving the arms or legs, the model produced walking gaits with arm swinging similar to humans. Passive gaits with arm phasing opposite to normal were also found, but these induced a much greater reaction moment from the ground, which could require muscular effort in humans. We therefore hypothesized that the reduction of this moment may explain the physiological benefit of arm swinging. Experimental measurements of humans (n = 10) showed that normal arm swinging required minimal shoulder torque, while volitionally holding the arms still required 12 per cent more metabolic energy. Among measures of gait mechanics, vertical ground reaction moment was most affected by arm swinging and increased by 63 per cent without it. Walking with opposite-to-normal arm phasing required minimal shoulder effort but magnified the ground reaction moment, causing metabolic rate to increase by 26 per cent. Passive dynamics appear to make arm swinging easy, while indirect benefits from reduced vertical moments make it worthwhile overall.     

Mobility of elastin chains as determined by 13C nuclear magnetic resonance

Relaxation times and integrated intensities of ¹³C have been obtained from nuclear magnetic resonance spectra of elastin in unstretched calf ligamentum nuchae and indicate that about 80% of the backbone carbonyl carbons have short rotational correlation times, τ_R ～ 40 nanoseconds. τ_R is reduced by only a factor of two when the ligament is in contact with 2 m-KCNS, a strong denaturant. By contrast, the highly ordered chains of collagen in insoluble calf achilles tendon give no spectrum until denatured in 2 m-KCNS, when t_R decreases by many orders of magnitude. These results show that elastin is composed largely of highly mobile chains under physiological conditions, suggesting that configurational entropy has an important role in its elastic properties.