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

Measurement of instantaneous Achilles tendon moment arm and force during the stance phase of running

Accurate estimates of the Achilles tendon (AT) moment arm (AT_MA) are necessary for investigating triceps surae muscle-tendon unit loading and function. There are limited reported values of AT_MA during running. By combining ultrasound and motion capture, AT_MA was estimated during the stance phase of running. Group mean AT_MA was estimated at 49.2 ± 3.8 mm and 37.5 ± 5.3 mm, relative to the centre of rotation (malleoli markers midpoint) and the ankle finite helical axis respectively. Differences in the corresponding estimated AT forces reached up to 3100 N approximately. Such discrepancies can lead to misinterpretation of the whole muscle-tendon unit function.

Positional difference of malleoli-midpoint from three-dimensional geometric centre of rotation of ankle and its effect on ankle joint kinetics

BACKGROUNDS

Joint kinetic calculations are sensitive to joint centre locations. Although geometric hip and knee joint centre/axis are generally developed, the ankle joint centre (AJC) is conventionally defined as the midpoint between the malleolus lateralis and medialis (AJC_MID) in most gait analyses.

RESEARCH QUESTION

We examined the positional difference of the AJC_MID from the geometric centre of rotation (AJC_FUN) and its effect on the ankle joint kinetics in representative human gaits.

METHODS

In the first experiment, we calculated the AJC_FUN and indicated its location on the ankle MRI in 14 (seven male and seven female) participants. In the second experiment, we compared ankle kinematics/kinetics based on AJC_FUN and AJC_MID during walking and hopping at 2.6 Hz in 17 (nine male and eight female) participants.

RESULTS

In both experiments, AJC_FUN was located at positions significantly medial (-9.2 ± 5.4 mm and -10.1 ± 4.4 mm) and anterior (17.0 ± 7.4 mm and 15.3 ± 5.2 mm) from the AJC_MID. Furthermore, the AJC_MID underestimated peak dorsiflexion (AJC_MID/AJC_FUN: 52.6 ± 17.1%) and inversion (AJC_MID/AJC_FUN: 62.2 ± 11.5%) torques and their durations in walking. Additionally, AJC_MID overestimated the plantar flexion torque in both gait modes [AJC_MID/AJC_FUN: 111.3 ± 4.8% (walking) and 112.7 ± 6.3% (hopping)].

SIGNIFICANCE

We therefore concluded that the positional difference between the geometric and landmark-based AJC definitions significantly affected ankle kinetics, thereby indicating that the functional method should be used for defining AJC for gait analysis.

Considerations on the human Achilles tendon moment arm for in vivo triceps surae muscle-tendon unit force estimates

Moment arm-angle functions (MA-a-functions) are commonly used to estimate in vivo muscle forces in humans. However, different MA-a-functions might not only influence the magnitude of the estimated muscle forces but also change the shape of the muscle’s estimated force-angle relationship (F-a-r). Therefore, we investigated the influence of different literature based Achilles tendon MA-a-functions on the triceps surae muscle–tendon unit F-a-r. The individual in vivo triceps torque–angle relationship was determined in 14 participants performing maximum voluntary fixed-end plantarflexion contractions from 18.3° ± 3.2° plantarflexion to 24.2° ± 5.1° dorsiflexion on a dynamometer. The resulting F-a-r were calculated using 15 literature-based in vivo Achilles tendon MA-a-functions. MA-a-functions affected the F-a-r shape and magnitude of estimated peak active triceps muscle–tendon unit force. Depending on the MA-a-function used, the triceps was solely operating on the ascending limb (n = 2), on the ascending limb and plateau region (n = 12), or on the ascending limb, plateau region and descending limb of the F-a-r (n = 1). According to our findings, the estimated triceps muscle–tendon unit forces and the shape of the F-a-r are highly dependent on the MA-a-function used. As these functions are affected by many variables, we recommend using individual Achilles tendon MA-a-functions, ideally accounting for contraction intensity-related changes in moment arm magnitude.

Mapping the relationships between joint stiffness, modeled muscle stiffness, and shear wave velocity

Shear wave velocity is commonly assessed to infer the muscular origins of changes in joint stiffness, but the exact relationship between shear wave velocity changes in muscle and joint stiffness changes remains unknown. Here, we systematically evaluated and quantified this relationship in the plantar flexors. Our results provide evidence for the ability of shear wave velocity to elucidate the muscular origins of joint stiffness changes.

In vivo relationship between joint stiffness, joint-based estimates of muscle stiffness, and shear-wave velocity

Shear-wave (SW) ultrasound elastography is both a clinical and research tool that is increasingly being used to quantify the material properties of muscle. However, how SW velocity relates to stiffness changes on the joint- and musclelevels is poorly understood. Therefore, the purpose of this work was to develop a biomechanical model to estimate plantar flexor muscle stiffness, and measure joint stiffness, joint-based estimates of muscle stiffness, and medial gastrocnemius (MG) SW velocity under different activations (0, 20, and 40%) to quantify the relationships between 1) joint stiffness and jointbased estimates of muscle stiffness; 2) joint stiffness and MG SW velocity; and 3) joint-based estimates of muscle stiffness and MG SW velocity. Our main findings include strong relationships between 1) joint stiffness and joint-based estimates of muscle stiffness $( R^{2}\,= 0 .70)$ and 2) joint stiffness and MG SW velocity $( R^{2}\,= 0 .66)$, and a weak relationship between joint-based estimates of muscle stiffness and MG SW velocity $( R^{2}\,= 0 .24)$. These findings further our understanding of SW velocity measures in muscle and provide a biomechanical model to decompose muscle stiffness from joint stiffness.

Ankle Rotation and Muscle Loading Effects on the Calcaneal Tendon Moment Arm: An In Vivo Imaging and Modeling Study

In this combined in vivo and computational modeling study, we tested the central hypothesis that ankle joint rotation and triceps surae muscle loading have independent and combinatory effects on the calcaneal (i.e., Achilles) tendon moment arm (CTma) that are not fully captured in contemporary musculoskeletal models of human movement. We used motion capture guided ultrasound imaging to estimate instantaneous variations in the CTma during a series of isometric and isotonic contractions compared to predictions from scaled, lower extremity computational models. As hypothesized, we found that muscle loading: (i) independently increased the CTma by up to 8% and (ii) attenuated the effects of ankle joint rotation, the latter likely through changes in tendon slack and tendon curvature. Neglecting the effects of triceps surae muscle loading in lower extremity models led to an underestimation of the CTma, on average, particularly in plantarflexion when those effects were most prominent. We also found little agreement between in vivo estimates and model predictions on an individual subject by subject basis, alluding to unaccounted for variation in anatomical morphology and thus fundamental limitations in model scaling. Together, these findings contribute to improving our understanding of the physiology of ankle moment and power generation and novel opportunities for model development.

Aging effects on the Achilles tendon moment arm during walking

The Achilles tendon (AT) moment arm transforms triceps surae muscle forces into a moment about the ankle which is critical for functional activities like walking. Moreover, the AT moment arm changes continuously during walking, as it depends on both ankle joint rotation and triceps surae muscle loading (presumably due to bulging of the muscle belly). Here, we posit that aging negatively effects the architecturally complex AT moment arm during walking, which thereby contributes to well-documented reductions in ankle moment generation during push-off. We used motion capture-guided ultrasound imaging to quantify instantaneous variations in the AT moment arms of young (23.9 ± 4.3 years) and older (69.9 ± 2.6 years) adults during walking, their dependence on triceps surae muscle loading, and their association with ankle moment generation during push-off. Older adults walked with 11% smaller AT moment arms and 11% smaller peak ankle moments during push-off than young adults. Moreover, as hypothesized, these unfavourable changes were significantly and positively correlated (r² = 0.38, p < 0.01). More surprisingly, aging attenuated load-dependent increases in the AT moment arm (i.e., those between heel-strike and push-off at the same ankle angle); only young adults exhibited a significant increase in their AT moment arm due to triceps surae muscle-loading. Age-associated reductions in triceps surae volume or activation, and thus muscle bulging during force generation, may compromise the mechanical advantage of the AT during the critical push-off phase of walking in older adults. Thus, strategies to restore and/or improve locomotor performance in our aging population should consider these functionally important changes in musculoskeletal behavior.

Reliability of Achilles Tendon Moment Arm Measured In Vivo Using Freehand Three-Dimensional Ultrasound

This study investigated reliability of freehand three-dimensional ultrasound (3DUS) measurement of in vivo human Achilles tendon (AT) moment arm. Sixteen healthy adults were scanned on 2 separate occasions by a single investigator. 3DUS scans were performed over the free AT, medial malleolus, and lateral malleolus with the ankle passively positioned in maximal dorsiflexion, mid dorsiflexion, neutral, mid plantar flexion and maximal plantar flexion. 3D reconstructions of the AT, medial malleolus, and lateral malleolus were created from manual segmentation of the ultrasound images and used to geometrically determine the AT moment arm using both a straight (straight AT_MA) and curved (curved AT_MA) tendon line-of-action. Both methods were reliable within- and between-session (intra-class correlation coefficients > 0.92; coefficient of variation < 2.5 %) and revealed that AT moment arm increased by ∼ 7 mm from maximal dorsiflexion (∼ 41mm) to maximal plantar flexion (∼ 48 mm). Failing to account for tendon curvature led to a small overestimation (< 2 mm) of AT moment arm that was most pronounced in ankle plantar flexion, but was less than the minimal detectable change of the method and could be disregarded.

A Forefoot Strike Requires the Highest Forces Applied to the Foot Among Foot Strike Patterns

Ground reaction force is often used to predict the potential risk of injuries but may not coincide with the forces applied to commonly injured regions of the foot. This study examined the forces applied to the foot, and the associated moment arms made by three foot strike patterns. 10 male runners ran barefoot along a runway at 3.3 m/s using forefoot, midfoot, and rearfoot strikes. The Achilles tendon and ground reaction force moment arms represented the shortest distance between the ankle joint axis and the line of action of each force. The Achilles tendon and joint reaction forces were calculated by solving equations of foot motion. The Achilles tendon and joint reaction forces were greatest for the forefoot strike (2 194 and 3 137 N), followed by the midfoot strike (1 929 and 2 853 N), and the rearfoot strike (1 526 and 2 394 N). The ground reaction force moment arm was greater for the forefoot strike than for the other foot strikes, and was greater for the midfoot strike than for the rearfoot strike. Meanwhile, there were no differences in the Achilles tendon moment arm among all foot strikes. These differences were attributed mainly to differences in the ground reaction force moment arm among the three foot strike patterns.

Comparison of the Achilles tendon moment arms determined using the tendon excursion and three-dimensional methods

The moment arm of muscle‐tendon force is a key parameter for calculating muscle and tendon properties. The tendon excursion method was used for determining the Achilles tendon moment arm (ATMA). However, the accuracy of this method remains unclear. This study aimed to investigate the magnitude of error introduced in determining the ATMA using the tendon excursion method by comparing it with the reference three‐dimensional (3D) method. The tendon excursion method determined the ATMA as the ratio between the Achilles tendon displacement during foot rotation from 15° of dorsiflexion to 15° of plantarflexion and the joint rotation angle. A series of foot images was obtained at 15° of dorsiflexion, the neutral position, and 15° of plantarflexion. The 3D value of the ATMA was determined as the shortest distance between the talocrural joint axis and the line of action of the Achilles tendon force. The ATMA determined by the tendon excursion method was smaller by 3.8 mm than that determined using the 3D method. This error may be explained mainly by the length change in the Achilles tendon due to the change in the force applied to it, as passive plantarflexion torque was different by 11 Nm between 15° of dorsiflexion and 15° of plantarflexion. Furthermore, the ATMAs determined using the 3D and tendon excursion methods were significantly correlated but the coefficient of determination was not large (R² = 0.352). This result suggests that the tendon excursion method may not be feasible to evaluate the individual variability of the ATMA.