Muscle moment arms of pelvic limb muscles of the ostrich (Struthio camelus)

Muscle moment arms were measured for major muscles of the pelvic limb of the ostrich (Struthio camelus) in order to assess specific functional behaviour and to apply this to locomotor performance. Pelvic limbs of six juvenile ostriches were used for this study. The tendon travel technique was used to measure moment arms of 21 muscles at the hip, knee, ankle and metatarsophalangeal joints throughout the ranges of motion observed during level running. Six of the 21 muscles measured were found to have moment arms that did not change with joint angle, whilst the remainder all demonstrated angle-dependent changes for at least one of the joints crossed. Moment arm lengths tended to be longest for the large proximal muscles, whilst the largest relative changes were found for the moment arms of the distal muscles. For muscles where moment arm varied with joint angle: all hip muscles were found to have increasing moment arms with extension of the joint, knee flexors were found to have moment arms that increased with extension, knee extensor moment arms were found to increase with flexion and ankle extensor moment arms increased with extension. The greatest relative changes were observed in the flexors of the metatarsophalangeal joint, for which a three-fold increase in moment arm was observed from flexion to full extension. Changes in muscle moment arm through the range of motion studied appear to optimize muscle function during stance phase, increasing the effective mechanical advantage of these muscles.     

Probabilistic Modeling of Knee Muscle Moment Arms: Effects of Methods,Origin–Insertion,and Kinematic Variability

In musculoskeletal modeling, reliable estimates of muscle moment arms are an important step in accurately predicting muscle forces and joint moments. The degree of agreement between the two common methods of calculating moment arms—tendon excursion (TE) and geometric origin–insertion, is currently unknown for the muscles crossing the knee joint. Further, measured moment arm data are subject to variability in estimation of attachment sites as points from irregular surfaces on the bones, and due to differences in joint kinematics observed in vivo. Thus, the objectives of the present study were to compare moment arms of major muscles crossing the knee joint obtained from TE and geometric methods using a finite element-based lower extremity model, and to quantify the effects of potential muscle origin–insertion and tibiofemoral kinematic variability on the predicted moment arms using probabilistic methods. A semiconstrained, fixed bearing, posterior cruciate-retaining total knee arthroplasty was included due to available in vivo kinematic data. In this study, muscle origin and insertion locations and kinematic variables were represented as normal distributions with standard deviations of 5 mm for origin–insertion locations and up to 1.6 mm and 3.0° for the kinematic parameters. Agreement between the deterministic moment arm calculations from the two methods was excellent for the flexors, while differences in trends and magnitudes were observed for the extensor muscles. Model-predicted deterministic moment arms from both methods agreed reasonably with the experimental values from available literature. The uncertainty in input parameters resulted in substantial variability in predicted moment arms, with the size of 1–99% confidence interval being up to 41.3 and 35.8 mm for the TE and geometric methods, respectively. The sizeable range of moment arm predictions and associated excursions has the potential to affect a muscle’s operating range on the force–length curve, thus affecting joint moments. In this study, moment arm predictions were more dependent on muscle origin–insertion locations than the kinematic variables. The important parameters from the TE method were the origin and insertion locations in the sagittal plane, while the insertion location in the sagittal plane was the dominant parameter using the geometric method.     

Morphological analysis of the hindlimb in apes and humans. II. Moment arms

Flexion/extension moment arms were obtained for the major muscles crossing the hip, knee and ankle joints in the orang-utan, gibbon, gorilla (Eastern and Western lowland) and bonobo. Moment arms varied with joint motion and were generally longer in proximal limb muscles than distal limb muscles. The shape of the moment arm curves (i.e. the plots of moment arm against joint angle) differed in different hindlimb muscles and in the same muscle in different subjects (both in the same and in different ape species). Most moment arms increased with increasing joint flexion, a finding which may be understood in the context of the employment of flexed postures by most non-human apes (except orang-utans) during both terrestrial and arboreal locomotion. When compared with humans, non-human great apes tended to have muscles better designed for moving the joints through large ranges. This was particularly true of the pedal digital flexors in orang-utans. In gibbons, the only lesser ape studied here, many of the moment arms measured were relatively short compared with those of great apes. This study was performed on a small sample of apes and thus differences noted here warrant further investigation in larger populations.     

Three‐dimensional moment arms and architecture of chimpanzee (Pan troglodytes) leg musculature

The muscular and skeletal morphology of the chimpanzee ankle and foot differs from that of humans in many important respects. However, little information is available on the moment arms and architecture of the muscles that function around chimpanzee ankle and foot joints. The main goals of this study were to determine the influence of changes in leg and foot position on the moment arms of these muscle–tendon units (MTUs), and provide new measurements of their architecture. Three‐dimensional moment arm data were collected from two adult, cadaveric Pan troglodytes specimens for 11 MTUs that cross the ankle and foot joints. Tendon‐excursion measurements were made throughout the full range of plantarflexion–dorsiflexion (PF–DF) and eversion–inversion (EV–IN), including repeated measurements for mm. gastrocnemius at 0 °, 45 °, 90 ° and 135 ° of knee flexion. The total range of motion was calculated from three‐dimensional joint motion data while ensuring that foot movement was restricted to a single plane. Measurements of muscle mass, fascicle length, pennation angle and physiological cross‐sectional area were then collected for each MTU. Our results demonstrate that joint position has a significant effect on moment arm lengths, and that in some cases this effect is counterintuitive. These new data contribute to filling a significant gap in previously published chimpanzee moment arm data, providing a comprehensive characterization of the MTUs that move the chimpanzee ankle and foot joints. They also provide empirical support to the notion that chimpanzees have larger ranges of motion at these joints than humans. Comparison of osteometric estimates of moment arm lengths to direct tendon‐excursion measures provides some guidance for the use of skeletal features in estimations of PF–DF moment arms. Finally, muscle architecture data are consistent with the findings of previous studies, and increase the sample size of the chimpanzee data that are currently available.     

The moment arms of the muscles spanning the glenohumeral joint: a systematic review

The moment arm of a muscle represents its leverage or torque‐producing capacity, and is indicative of the role of the muscle in joint actuation. The objective of this study was to undertake a systematic review of the moment arms of the major muscles spanning the glenohumeral joint during abduction, flexion and axial rotation. Moment arm data for the deltoid, pectoralis major, latissimus dorsi, teres major, supraspinatus, infraspinatus, subscapularis and teres minor were reported when measured using the geometric and tendon excursion methods. The anterior and middle sub‐regions of the deltoid had the largest humeral elevator moment arm values of all muscles during coronal‐ and scapular‐plane abduction, as well as during flexion. The pectoralis major, latissimus dorsi and teres major had the largest depressor moment arms, with each of these muscles exhibiting prominent leverage in shoulder adduction, and the latissimus dorsi and teres major also in extension. The rotator cuff muscles had the largest axial rotation moment arms regardless of the axial position of the humerus. The supraspinatus had the most prominent elevator moment arms during early abduction in both the coronal and scapular planes as well as in flexion. This systematic review shows that the rotator cuff muscles function as humeral rotators and weak humeral depressors or elevators, while the three sub‐regions of the deltoid behave as substantial humeral elevators throughout the range of humeral motion. The pectoralis major, latissimus dorsi and teres major are significant shoulder depressors, particularly during abduction. This study provides muscle moment arm data on functionally relevant shoulder movements that are involved in tasks of daily living, including lifting and pushing. The results may be useful in quantifying shoulder muscle function during specific planes of movement, in designing and validating computational models of the shoulder, and in planning surgical procedures such as tendon transfer surgery.     

A comparison of the moment arms of pelvic limb muscles in horses bred for acceleration (Quarter Horse) and endurance (Arab)

Selective breeding for performance has resulted in distinct breeds of horse, such as the Quarter Horse (bred for acceleration) and the Arab (bred for endurance). Rapid acceleration, seen during Quarter Horse racing, requires fast powerful muscular contraction and the generation of large joint torques, particularly by the hind limb muscles. This study compared hind limb moment arm lengths in the Quarter Horse and Arab. We hypothesized that Quarter Horse hind limb extensor muscles would have longer moment arms when compared to the Arab, conferring a greater potential for torque generation at the hip, stifle and tarsus during limb extension. Six Quarter Horse and six Arab hind limbs were dissected to determine muscle moment arm lengths for the following muscles: gluteus medius, biceps femoris, semitendinosus, vastus lateralis, gastrocnemius (medialis and lateralis) and tibialis cranialis. The moment arms of biceps femoris (acting at the hip) and gastrocnemius lateralis (acting at the stifle) were significantly longer in the Quarter Horse, although the length of the remaining muscle moment arms were similar in both breeds of horse. All the Quarter Horse muscles were capable of generating greater muscle moments owing to their greater physiological cross-sectional area (PCSA) and therefore greater isometric force potential, which suggests that PCSA is a better determinant of muscle torque than moment arm length in these two breeds of horse. With the exception of gastrocnemius and tibialis cranialis, the observed muscle fascicle length to moment arm ratio (MFL : MA ratio) was greater for the Arab horse muscles. It appears that the Arab muscles have the potential to operate at slower velocities of contraction and hence generate greater force outputs when compared to the Quarter Horse muscles working over a similar range of joint motion; this would indicate that Arab hind limb muscles are optimized to function at maximum economy rather than maximum power output.     

A 3D musculoskeletal model of the western lowland gorilla hind limb: moment arms and torque of the hip,knee and ankle

Three‐dimensional musculoskeletal models have become increasingly common for investigating muscle moment arms in studies of vertebrate locomotion. In this study we present the first musculoskeletal model of a western lowland gorilla hind limb. Moment arms of individual muscles around the hip, knee and ankle were compared with previously published data derived from the experimental tendon travel method. Considerable differences were found which we attribute to the different methodologies in this specific case. In this instance, we argue that our 3D model provides more accurate and reliable moment arm data than previously published data on the gorilla because our model incorporates more detailed consideration of the 3D geometry of muscles and the geometric constraints that exist on their lines‐of‐action about limb joints. Our new data have led us to revaluate the previous conclusion that muscle moment arms in the gorilla hind limb are optimised for locomotion with crouched or flexed limb postures. Furthermore, we found that bipedalism and terrestrial quadrupedalism coincided more regularly with higher moment arms and torque around the hip, knee and ankle than did vertical climbing. This indicates that the ability of a gorilla to walk bipedally is not restricted by musculoskeletal adaptations for quadrupedalism and vertical climbing, at least in terms of moment arms and torque about hind limb joints.     

Internal/external rotation moment arms of muscles at the knee: moment arms for the normal knee and the ACL-deficient knee

Knowledge of the three-dimensional balance of loads at the knee joint is required to adequately assess the treatment and rehabilitation of the malfunctioning knee. This report focuses upon the moment arms for the knee in internal/external (IE) rotation motion. It augments prior work that defined flexion/extension moment arms. Muscle excursions and angular motion of the lower leg during IE rotation were measured in 17 fresh-frozen hemi-pelvis specimens. Moment arms were calculated as the derivatives of excursion with respect to the angle. Rotational motion was performed for the normal and anterior cruciate ligament (ACL)-deficient knee. Of the 13 muscles measured at the knee, seven were significant contributors to IE rotation: the biceps femoris long and short head externally rotate opposite the gracilis, sartorious, semimembranosis, semitendonosus and popliteus, functioning as internal rotators. Moment arm magnitudes were greatest with the knee in a flexed position (internal [external] rotators peaked at 70° [90°] flexion). At 30° flexion, the IE rotation moment arm minima and maxima were 10.1–11.6, 6.8–9.0, 6.0–15.7, 8.2–14.1 and 0.0–10.4 mm for the semimembranosis, semitendonosus, gracilis, sartorius and popliteus, and 14.7–27.9 and 18.5–31.5 mm for the biceps femoris short and long, respectively. Moment arms for the ACL-deficient condition were significantly changed only at extremes of flexion–extension.     

Vector-based forearm rotation moment arms – A sensitivity analysis

All existing moment arm data for muscles of the forearm derive from tendon excursion experiments. Moment arms determined this way are only valid for movement about the same generalised coordinate system as was used during the tendon excursion, which makes their implementation in more complex or realistic joint models problematic. This study used a vector-based method to calculate muscle moment arms in a three dimensional model of forearm rotation. It also evaluated the sensitivity of this method to errors in the input data. There was reasonably close agreement between the moment arms calculated in this study and those published using tendon excursion methods. Six out of eight muscles had moment arms within the range of values reported previously. However, the vector-based method was sensitive to the accuracy of the input data. This sensitivity varied between muscles and input variables. Generally, the calculations were more robust to the point of force application than the muscle lines of action and the joint's axis of rotation. A small change in these variables could produce substantial changes in the calculated moment arms. Consequently, accurate input data is important when using the vector-based method in a joint model.     

Functional specialisation of the thoracic limb of the hare (Lepus europeus)

We provide quantitative anatomical data on the muscle-tendon architecture of the hare thoracic limb (specifically muscle mass, fascicle length, pennation angle, tendon mass and length). In addition, moment arms of major thoracic limb muscles were measured. Maximum isometric force and power of muscles, the moment of force about a joint, and tendon stress and strain were estimated. Data are compared with those from other cursorial mammals. The thoracic limb of the hare consists predominantly of extrinsic musculature with long parallel fascicles, specialised for generating force over a large range. A large shoulder flexor/elbow extensor muscle mass is present, in particular Triceps brachii. The pennate nature of the long head of this muscle suggests it has an important role in stabilising the elbow joint during stance, whilst moment arm curves suggest that it may also play a role in initiating shoulder flexion. In addition, Supraspinatus and Infraspinatus are capable of generating high forces, potentially to stabilise the shoulder joint during the stance phase of locomotion. Supraspinatus may in addition play an important role in forelimb protraction. The Subscapularis muscle was capable of generating surprisingly high forces, suggesting that the hare must be able to withstand/produce high forces during activities that need medio-lateral stability, such as turning. Distally, tendons were relatively short, showing little potential for elastic energy storage when compared with both their pelvic limb counterparts and their equivalents in the horse thoracic limb. Thus, a 'stiffer' thoracic limb may be beneficial in terms of behaving like a strut, simply supporting and deflecting the body during high-speed running. This more distal/less proximal distribution of limb mass is also likely to be important in retaining the manipulative/adaptive/non-locomotor capabilities of the limb.     

Differences in muscle mechanics underlie divergent optimality criteria between feeding and locomotor systems

Tetrapod musculoskeletal diversity is usually studied separately in feeding and locomotor systems. However, direct comparisons between these systems promise important insight into how natural selection deploys the same basic musculoskeletal toolkit—connective tissues, bones, nerves, and skeletal muscle—to meet the differing performance criteria of feeding and locomotion. Recent studies using this approach have proposed that the feeding system is optimized for precise application of high forces and the locomotor system is optimized for wide and rapid joint excursions for minimal energetic expenditure. If this hypothesis is correct, then it stands to reason that other anatomical and biomechanical variables within the feeding and locomotor systems should reflect these diverging functions. To test this hypothesis, we compared muscle moment arm lengths, mechanical advantages, and force vector orientations of two jaw elevator muscles (m. temporalis and m. superficial masseter), an elbow flexor (m. brachialis) and extensor (m. triceps- lateral head), and a knee flexor (m. biceps femoris-short head) and extensor (m. vastus lateralis) across 18 species of primates. Our results show that muscles of the feeding system are more orthogonally oriented relative to the resistance arm (mandible) and operate at relatively large moment arms and mechanical advantages. Moreover, these variables show relatively little change across the range of jaw excursion. In contrast, the representative muscles of the locomotor system have much smaller mechanical advantages and, depending on joint position, smaller muscle moment arm lengths and almost parallel orientations relative to the resistance arm. These patterns are consistent regardless of phylogeny, body mass, locomotor mode, and feeding specialization. We argue that these findings reflect fundamental functional dichotomies between tetrapod locomotor and feeding systems. By organizing muscles in a manner such that moment arms and mechanical advantage are relatively small, the locomotor system can produce broad joint excursions and high angular velocities with only small muscular contraction. As such, the anatomical organization of muscles within the limbs allows striding animals to move relatively rapidly and with minimal energetic expenditure. In contrast, the anatomical configuration of muscles in the feeding system, at least m. superficial masseter and m. temporalis, favors their force-producing capacity at the expense of excursion and velocity.     

Functional variation of neck muscles and their relation to feeding style in Tyrannosauridae and other large theropod dinosaurs

Reconstructed neck muscles of large theropod dinosaurs suggest influences on feeding style that paralleled variation in skull mechanics. In all examined theropods, the head dorsiflexor m. transversospinalis capitis probably filled in the posterior dorsal concavity of the neck, for a more crocodilian‐ than avian‐like profile in this region. The tyrannosaurine tyrannosaurids Daspletosaurus and Tyrannosaurus had relatively larger moment arms for lateroflexion by m. longissimus capitis superficialis and m. complexus than albertosaurine tyrannosaurids, and longer dorsiflexive moment arms for m. complexus. Areas of dorsiflexor origination are significantly larger relative to neck length in adult Tyrannosaurus rex than in other tyrannosaurids, suggesting relatively large muscle cross‐sections and forces. Tyrannosaurids were not particularly specialized for neck ventroflexion. In contrast, the hypothesis that Allosaurus co‐opted m. longissimus capitis superficialis for ventroflexion is strongly corroborated. Ceratosaurus had robust insertions for the ventroflexors m. longissimus capitis profundus and m. rectus capitis ventralis. Neck muscle morphology is consistent with puncture‐and‐pull and powerful shake feeding in tyrannosaurids, relatively rapid strikes in Allosaurus and Ceratosaurus, and ventroflexive augmentation of weaker jaw muscle forces in the nontyrannosaurids. Anat Rec, 290:934–957, 2007. © 2007 Wiley‐Liss, Inc.     

Muscle moment arms and function of the siamang forelimb during brachiation

Moment arms have an important modulating impact on muscle function, as they represent the capacity of the muscle to convert muscle action into limb movements. In the current paper, we provide muscle moment arm data of the forelimb of four siamangs, collected by detailed dissections on unfixed cadavers. The aim of this study is to assess the role of different forelimb muscles during brachiation. Moment arm data are compared with similar published data of non‐brachiating primates such as macaques, chimpanzees and humans. Our data show that shoulder adductors and endorotators and the elbow flexors are built for force generation, whereas the shoulder abductors, flexors and exorotators are best suited to gain speed and to change direction. Compared to non‐brachiating species, both elbow and wrist flexors are particularly noticeable in terms of moment of force‐generating capacity. However, the moment of force‐generating capacity of the elbow extensor is not negligible, which indicates that the triceps also plays an active role, especially at the end of the support phase. Except for the elbow flexors, all muscles reach their maximum moment of force‐generating capacity during the support phase of brachiation. When brachiating on a more complex setup, the siamang will flex the elbows to angles that induce maximum moment arms as well.     

Neck Muscle Moment Arms Obtained <Emphasis Type="Italic">In-Vivo</Emphasis> from MRI: Effect of Curved and Straight Modeled Paths

Musculoskeletal models of the cervical spine commonly represent neck muscles with straight paths. However, straight lines do not best represent the natural curvature of muscle paths in the neck, because the paths are constrained by bone and soft tissue. The purpose of this study was to estimate moment arms of curved and straight neck muscle paths using different moment arm calculation methods: tendon excursion, geometric, and effective torque. Curved and straight muscle paths were defined for two subject-specific cervical spine models derived from in vivo magnetic resonance images (MRI). Modeling neck muscle paths with curvature provides significantly different moment arm estimates than straight paths for 10 of 15 neck muscles (p < 0.05, repeated measures two-way ANOVA). Moment arm estimates were also found to be significantly different among moment arm calculation methods for 11 of 15 neck muscles (p < 0.05, repeated measures two-way ANOVA). In particular, using straight lines to model muscle paths can lead to overestimating neck extension moment. However, moment arm methods for curved paths should be investigated further, as different methods of calculating moment arm can provide different estimates.     

The Effective Mechanical Advantage of A.L. 129‐1a for Knee Extension

The functional significance of shape differences between modern human and australopithecine distal femora remains unclear. Here, we examine the morphological component of the effective mechanical advantage (EMA) of the quadriceps muscle group in a sample of hominins that includes the fossil A.L. 129‐1a (Australopithecus afarensis) and modern humans. Quadriceps muscle moment arms were calculated from three‐dimensional computer models of specimens through a range of knee flexion. All hominins were compared using the same limb positions to allow us to examine, in isolation, the morphological component of the lengths of the pertinent moment arms. After taking into account the differences in bicondylar angle, the morphological component of the EMA was calculated as the ratio of the quadriceps muscle and ground reaction force moment arms. Our analyses reveal that A.L. 129‐1a would have possessed a morphological component of the quadriceps muscle EMA expected for a hominin of its body mass. Anat Rec, 2011. © 2011 Wiley‐Liss, Inc.     

Error associated with antagonist muscle activity in isometric knee strength testing

The purpose of this study was to determine the measurement error associated with antagonist muscle activity in isometric knee strength testing at 60° of knee flexion in both sexes. Muscle specific EMG–contraction intensity relationships were obtained from 22 young people by having them match moment targets ranging from 10% to 100% peak moment. The moments attributed to each of the quadriceps and hamstrings muscles were partitioned using a practical mathematical model. Subject specific EMG–moment relationships were defined for each muscle using second-order polynomial equations. These equations were subsequently used to predict the countermoment associated with antagonist muscle activity. Error during strength testing was calculated by expressing net antagonist moments as a percentage of net agonist moments. The net antagonist moments associated with quadriceps and hamstrings muscle activity were 11.0% and 8.7% of the peak moment values recorded when the same muscle groups were acting as agonists. The error associated with antagonist activity was significantly higher in knee flexion (20.1%) than in knee extension (4.5%). Females displayed significantly higher error in knee flexor testing (P < 0.001). Limb symmetry indices did not change significantly when the countermoments generated by the antagonist muscles were accounted for (P > 0.05). The results of this study indicate that the error associated with antagonist activity in knee extensor testing is relatively small, whereas the error in knee flexor testing is larger. This is due to the quadriceps being much stronger than the hamstrings muscles while displaying similar levels of antagonist activity.     

The distal hindlimb musculature of the cat: multiaxis moment arms at the ankle joint

The cat hindlimb muscles have been classified, traditionally, as flexors and extensors, based on their actions in the parasagittal plane and their patterns of recruitment during locomotion and reflex responses. This study provides a detailed examination of the relative magnitudes of the various moment arms of the cat ankle muscles and the interdependent effects of position in the various axes of motion. We used a method based on observing small sliding movements of tendon in response to small angular displacements of the joint. Surprisingly, we found that the ankle joint of the cat permits substantial motion in three axes (eversion/inversion and abduction/ adduction as well as extension/flexion) and many muscles crossing the ankle joint have their largest moment arms about axes other than extension/flexion. These moment arms often depended on the joint position in the axis of the moment arm and, to a lesser degree, on the extension/ flexion angle as well. For some muscles (notably peroneus longus) there was sufficient variability that the predominant action in neutral posture (axis with the largest moment arm) could change from animal to animal, which may be related to heterogeneities of locomotor and reflex recruitment reported in the companion paper.     

Musculoskeletal modelling of the Nile crocodile (Crocodylus niloticus) hindlimb: Effects of limb posture on leverage during terrestrial locomotion

We developed a three-dimensional, computational biomechanical model of a juvenile Nile crocodile (Crocodylus niloticus) pelvis and hindlimb, composed of 47 pelvic limb muscles, to investigate muscle function. We tested whether crocodiles, which are known to use a variety of limb postures during movement, use limb orientations (joint angles) that optimise the moment arms (leverages) or moment-generating capacities of their muscles during different limb postures ranging from a high walk to a sprawling motion. We also describe the three-dimensional (3D) kinematics of the crocodylian hindlimb during terrestrial locomotion across an instrumented walkway and a treadmill captured via X-ray Reconstruction of Moving Morphology (biplanar fluoroscopy; ‘XROMM’). We reconstructed the 3D positions and orientations of each of the hindlimb bones and used dissection data for muscle lines of action to reconstruct a focal, subject-specific 3D musculoskeletal model. Motion data for different styles of walking (a high, crouched, bended and two types of sprawling motion) were fed into the 3D model to identify whether any joints adopted near-optimal poses for leverage across each of the behaviours. We found that (1) the hip adductors and knee extensors had their largest leverages during sprawling postures and (2) more erect postures typically involved greater peak moment arms about the hip (flexion-extension), knee (flexion) and metatarsophalangeal (flexion) joints. The results did not fully support the hypothesis that optimal poses are present during different locomotory behaviours because the peak capacities were not always reached around mid-stance phase. Furthermore, we obtained few clear trends for isometric moment-generating capacities. Therefore, perhaps peak muscular leverage in Nile crocodiles is instead reached either in early/late stance or possibly during swing phase or other locomotory behaviours that were not studied here, such as non-terrestrial movement. Alternatively, our findings could reflect a trade-off between having to execute different postures, meaning that hindlimb muscle leverage is not optimised for any singular posture or behaviour. Our model, however, provides a comprehensive set of 3D estimates of muscle actions in extant crocodiles which can form a basis for investigating muscle function in extinct archosaurs.     

步态双支撑期下肢肌力的预测

在分析人体的运动功能时,可视人体为一个以关节连接,由肌肉所驱使的连杆系统。分析人体的运动动力问题,最后所想求得的是肌肉的力量,由于未知的肌肉作用力数目常远多于所能设定的平衡方程式的数目,因此构成所谓的肌力分布的不定问题（indeter erminant problem of muscle distribution),使得问题不得而解。肌力的量化有助于建立客观的评估标准,肌力分布的研究亦可用于了解肌肉的功能与临床之评估与预测,个别的肌肉力量至目前为止尚无法以非侵入性的力法直接量到,因此学者们尝试利用数值最佳化的技巧解此肌力不定问题,本文利用数值最佳化的方法解正常人在步态双支撑期下肢的肌肉作用与肌肉力量在肌群间的分布,以评估最佳化模式的合理性,并以最佳设计的观点探讨肌肉功能与其生理及结构的关系。本实验从肌肉之生理与结构特性中考量影响肌肉功能的因素,因为步行属于长期性且重复性的活动,故以耐力时间极大化为准则,此耐力时间的数学模式为肌肉力、最大肌力、红肌纤维比例与生理截面积的非线性函数,除了用单目标最佳化技巧外,考虑解之存在与合理性,本文并推导出一个连续最佳化数学模式,用最佳化技巧所预测的肌肉活动大致上相当符合以往学者定性研究的结果。故西文的模式初步认为相当合理,但需要进一步取得更多的运动资料加以验证,最佳化的结果目前很难验证其正确性,只能从定性的肌肉作用形式验证其合理性。虽然如此,其值仍可作为一个合理的参考值。     

Antagonist muscle moment is increased in ACL deficient subjects during maximal dynamic knee extension

IntroductionCoactivation of the hamstring muscles during dynamic knee extension may compensate for increased knee joint laxity in anterior cruciate ligament (ACL) deficient subjects. This study examined if antagonist muscle coactivation during maximal dynamic knee extension was elevated in subjects with anterior cruciate ligament (ACL) deficiency compared to age-matched healthy controls.MethodsElectromyography (EMG) and net knee joint moments were recorded during maximal concentric quadriceps and eccentric hamstring contractions, performed in an isokinetic dynamometer (ROM: 90–10°, angular speed: 30°/s). Hamstring antagonist EMG recorded during concentric quadriceps contraction was converted into antagonist moment based on the EMG–moment relationship observed during eccentric agonist contractions.ResultsThe magnitude of antagonist hamstring EMG was 65.5% higher in ACL deficient subjects compared to healthy controls (p < 0.05). Likewise, antagonist hamstring moment expressed in percentage of the measured net extension moment was elevated in ACL deficient subjects (56 ± 8 to 30 ± 6%) compared to controls (36 ± 5 to 19 ± 2%) at 20–50° of knee flexion (0° = full extension) (p < 0.05).DiscussionThe results showed a marked increase in hamstring coactivation towards more extended joint positions. Notably, this progressive rise in coactivation was greater in ACL deficient subjects, which may reflect a compensatory strategy to provide stability to the knee joint in the anterior–posterior plane during isolated knee extension. The present study encourages further investigations of hamstring coactivation in ACL deficient subjects.