Direct measurement of muscle forces in vivo is highly invasive, 1 so muscle forces are typically estimated from measurement of joint moments. 2 , 3 Estimating muscle forces from joint moments requires knowledge of the muscle/tendon moment arm, that is, the perpendicular distance from the joint
Jared R. Fletcher and Brian R. MacIntosh
Steven J. Obst, Lee Barber, Ashton Miller and Rod S. Barrett
Estimates of in vivo Achilles tendon (AT) force are needed to measure tendon mechanical properties as a function of the measured net ankle joint torque, and to understand AT function using musculoskeletal modeling approaches. The AT moment arm is required to convert the measured external ankle
Norihide Sugisaki, Taku Wakahara, Koichiro Murata, Naokazu Miyamoto, Yasuo Kawakami, Hiroaki Kanehisa and Tetsuo Fukunaga
Although the moment arm of the triceps brachii muscle has been shown to be associated with the muscle’s anatomical crosssectional area, whether training-induced muscle hypertrophy alters the moment arm of the muscle remains unexplored. Therefore, the current study aimed to examine this. Eleven men underwent a 12-week resistance training program for the triceps brachii muscle. The maximum muscle anatomical cross-sectional area (ACSAmax), the moment arm of the triceps brachii muscle, and the anterior-posterior dimension of the olecranon were measured using a magnetic resonance imaging system before and after intervention. The ACSAmax (33.6 ± 11.9%, P < .001) and moment arm (5.5 ± 4.0%, P = .001) significantly increased after training, whereas the anterior-posterior dimension of the olecranon did not change (P > .05). The change in moment arm was smaller than that expected from the relationship between the ACSAmax and the moment arm before the intervention. The present results indicate that training-induced triceps brachii muscle hypertrophy could increase the muscle moment arm, but its impact can be small or negligible.
Kurt Manal, Justin D. Cowder and Thomas S. Buchanan
In this article, we outline a method for computing Achilles tendon moment arm. The moment arm is computed from data collected using two reliable measurement instruments: ultrasound and video-based motion capture. Ultrasound is used to measure the perpendicular distance from the surface of the skin to the midline of the tendon. Motion capture is used to determine the perpendicular distance from the bottom of the probe to the ankle joint center. The difference between these two measures is the Achilles tendon moment arm. Unlike other methods, which require an angular change in joint position to approximate the moment arm, the hybrid method can be used to compute the moment arm directly at a specific joint angle. As a result, the hybrid method involves fewer error-prone measurements and the moment arm can be computed at the limits of the joint range of motion. The method is easy to implement and uses modalities that are less costly and more accessible than MRI. Preliminary testing using a lamb shank as a surrogate for a human ankle revealed good accuracy (3.3% error). We believe the hybrid method outlined here can be used to measure subject-specific moment arms in vivo and thus will potentially benefit research projects investigating ankle mechanics.
A two-dimensional model has been developed to predict and explain the effects of the variation of muscle moment arms during dynamic exercises involving heavy external loads. The analytical dependence of the muscle moment arm on the joint angle and on the origin and insertion position was derived for an ideal uniaxial hinge joint, modeling the muscle as a cable following an idealized minimum distance path from the origin to insertion that wraps around the bony geometry. Analytical expressions for the ratios of muscular force and the joint restraining reaction components to the external load weight were deduced, for isokinetic and static exercises, as a function of joint angle, joint angular velocity, and the other geometric parameters defining the model. Therefore, external load weight, joint angular velocity, and constraints to joint range of motion may be adjusted reciprocally in order to control in advance the peak value of the components of the joint load during isokinetic exercises. A dynamic formulation of forearm flexion/extension was solved numerically under the condition of constant biceps force in order to highlight the key role played by the variation in muscle moment arm in preventing injury during lifting of external loads against gravity. For example, our analysis indicates that the mean and peak resultant joint loads decrease by 5% and 14%, respectively, as a result of the change in muscle moment arm that occurs over the range of motion.
Ryota Akagi, Soichiro Iwanuma, Satoru Hashizume, Hiroaki Kanehisa, Toshimasa Yanai and Yasuo Kawakami
The purpose of this study was to determine in vivo moment arm lengths (MAs) of three elbow flexors at rest and during low- and relatively high-intensity contractions, and to examine the contraction intensity dependence of MAs at different joint positions. At 50°, 80° and 110° of elbow flexion, MAs of the biceps brachii, brachialis and brachioradialis were measured in 10 young men using sagittal images of the right arm obtained by magnetic resonance imaging, at rest and during 20% and 60% of isometric maximal voluntary elbow flexion. In most conditions, MAs increased with isometric contractions, which is presumably due to the contraction-induced thickening of the muscles. This phenomenon was especially evident in the flexed elbow positions. The influence of the contraction intensities on the increases in MAs varied across the muscles. These results suggest that in vivo measurements of each elbow flexor MA during contractions are essential to properly examine the effects on the interrelationships between elbow flexion torque and individual muscle forces.
Ryota Akagi, Soichiro Iwanuma, Satoru Hashizume, Hiroaki Kanehisa, Toshimasa Yanai and Yasuo Kawakami
The purpose of this study was to investigate how the contraction-induced increase in distal biceps brachii tendon moment arm is related to that in elbow flexor muscle thickness, with a specific emphasis on the influence of the site-related differences in muscle thickness. The moment arm and muscle thickness were determined from sagittal and cross-sectional images, respectively, of the right arm obtained by magnetic resonance imaging of nine young men. The muscle thickness was measured at levels from the reference site (60% of the upper arm length from the acromial process of the scapula to the lateral epicondyle of the humerus) to 60 mm distal to it (every 10 mm; 7 measurement sites). At 80° of elbow flexion, the moment arm and muscle thickness were determined at rest and during 60% of maximal voluntary contraction (60%MVC) of isometric elbow flexion. Only the relative change from rest to 60%MVC in muscle thickness at the level 60 mm distal to the reference site correlated significantly with that of the moment arm. This result indicates that the contraction-induced increase in distal biceps brachii tendon moment arm is related to that in elbow flexor muscle thickness near the corresponding muscle-tendon junction.
Florian Fath, Anthony J. Blazevich, Charlie M. Waugh, Stuart C. Miller and Thomas Korff
The muscle-tendon moment arm is an important input parameter for musculoskeletal models. Moment arms change as a function of joint angle and contraction state and depend on the method being employed. The overall purpose was to gain insights into the interactive effects of joint angle, contraction state and method on the Achilles tendon moment arm using the center of rotation (COR) and the tendon excursion method (TE). Achilles tendon moment arms were obtained at rest (TErest, CORrest) and during a maximum voluntary contraction (CORMVC) at four angles. We found strong correlations between TErest and CORMVC for all angles (.72 ≤ r ≤ .93) with Achilles tendon moment arms using CORMVC being 33–36% greater than those obtained from TErest. The relationship between Achilles tendon moment arms and angle was similar across both methods and both levels of muscular contraction. Finally, Achilles tendon moment arms for CORMVC were 1–8% greater than for CORrest.
Ken Tokunaga, Yuki Nakai, Ryo Matsumoto, Ryoji Kiyama, Masayuki Kawada, Akihiko Ohwatashi, Kiyohiro Fukudome, Tadasu Ohshige and Tetsuo Maeda
This study evaluated the effect of foot progression angle on the reduction in knee adduction moment caused by a lateral wedged insole during walking. Twenty healthy, young volunteers walked 10 m at their comfortable velocity wearing a lateral wedged insole or control flat insole in 3 foot progression angle conditions: natural, toe-out, and toe-in. A 3-dimensional rigid link model was used to calculate the external knee adduction moment, the moment arm of ground reaction force to knee joint center, and the reduction ratio of knee adduction moment and moment arm. The result indicated that the toe-out condition and lateral wedged insole decreased the knee adduction moment in the whole stance phase. The reduction ratio of the knee adduction moment and the moment arm exhibited a close relationship. Lateral wedged insoles decreased the knee adduction moment in various foot progression angle conditions due to decrease of the moment arm of the ground reaction force. Moreover, the knee adduction moment during the toe-out gait with lateral wedged insole was the smallest due to the synergistic effect of the lateral wedged insole and foot progression angle. Lateral wedged insoles may be a valid intervention for patients with knee osteoarthritis regardless of the foot progression angle.
Yuki Uto, Tetsuo Maeda, Ryoji Kiyama, Masayuki Kawada, Ken Tokunaga, Akihiko Ohwatashi, Kiyohiro Fukudome, Tadasu Ohshige, Yoichi Yoshimoto and Kazunori Yone
The purpose of this study was to determine whether a lateral wedge insole reduces the external knee adduction moment during slope walking. Twenty young, healthy subjects participated in this study. Subjects walked up and down a slope using 2 different insoles: a control flat insole and a 7° lateral wedge insole. A three-dimensional motion analysis system and force plate were used to examine the knee adduction moment, the ankle valgus moment, and the moment arm of the ground reaction force to the knee joint center in the frontal plane. The lateral wedge insole significantly decreased the moment arm of the ground reaction force, resulting in a reduction of the knee adduction moment during slope walking, similar to level walking. The reduction ratio of knee adduction moment by the lateral wedge insole during the early stance of up-slope walking was larger than that of level walking. Conversely, the lateral wedge insole increased the ankle valgus moment during slope walking, especially during the early stance phase of up-slope walking. Clinicians should examine the utilization of a lateral wedge insole for knee osteoarthritis patients who perform inclined walking during daily activity, in consideration of the load on the ankle joint.