An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine

Muscle force partitioning methods and musculoskeletal system simplifications are key modeling issues that can alter outcomes, and thus change conclusions and recommendations addressed to health and safety professionals. A critical modeling concern is the use of single-joint equilibrium to estimate muscle forces and joint loads in a multi-joint system, an unjustified simplification made by most lumbar spine biomechanical models. In the context of common occupational tasks, an EMG-assisted optimization method (EMGAO) is modified in this study to simultaneously account for the equilibrium at all lumbar joints (M-EMGAO). The results of this improved approach were compared to those of its conventional single-joint equivalent (S-EMGAO) counterpart, the latter method being applied to the same lumbar joints but one at a time. Despite identical geometrical configurations and passive contributions used in both models, computed outcomes clearly differed between single- and multi-joint methods, especially at larger trunk flexed postures and during asymmetric lifting. Moreover, muscle forces predicted by L5-S1 single-joint analyses do not maintain mechanical equilibrium at other spine joints crossed by the same muscles. Assuming that the central nervous system does not attempt to balance the external moments one joint at a time and that a given muscle cannot exert different forces at different joints, the proposed multi-joint method represents a substantial improvement over its single-joint counterpart. This improved approach, hence, resolves trunk muscle forces with biological integrity but without compromising mechanical equilibrium at the lumbar joints.     

Knee and ankle joint torque-angle relationships of multi-joint leg extension

The force-length-relation (F-l-r) is an important property of skeletal muscle to characterise its function, whereas for in vivo human muscles, torque-angle relationships (T-a-r) represent the maximum muscular capacity as a function of joint angle. However, since in vivo force/torque-length data is only available for rotational single-joint movements the purpose of the present study was to identify torque-angle-relationships for multi-joint leg extension. Therefore, inverse dynamics served for calculation of ankle and knee joint torques of 18 male subjects when performing maximum voluntary isometric contractions in a seated leg press. Measurements in increments of 10° knee angle from 30° to 100° knee flexion resulted in eight discrete angle configurations of hip, knee and ankle joints. For the knee joint we found an ascending-descending T-a-r with a maximum torque of 289.5° ± 43.3 Nm, which closely matches literature data from rotational knee extension. In comparison to literature we observed a shift of optimum knee angle towards knee extension. In contrast, the T-a-r of the ankle joint vastly differed from relationships obtained for isolated plantar flexion. For the ankle T-a-r derived from multi-joint leg extension subjects operated over different sections of the force-length curve, but the ankle T-a-r derived from isolated joint efforts was over the ascending limb for all subjects. Moreover, mean maximum torque of 234.7 ± 56.6 Nm exceeded maximal strength of isolated plantar flexion (185.7 ± 27.8 Nm). From these findings we conclude that muscle function between isolated and more physiological multi-joint tasks differs. This should be considered for ergonomic and sports optimisation as well as for modelling and simulation of human movement.     

Child-Adult differences in antagonist muscle coactivation: A systematic review

Antagonist coactivation is the simultaneous activation of agonist and antagonist muscles during a motor task. Age-related changes in coactivation may contribute to observed differences in muscle performance between children and adults. Our aim was to systematically summarize age-related differences in antagonist muscle coactivation during multi-joint dynamic and single-joint isometric and isokinetic contractions. Electronic databases were searched for peer-reviewed studies comparing coactivation in upper or lower extremity muscles between healthy children and adolescents/young adults. Of the 1083 studies initially identified, 25 met eligibility criteria. Thirteen studies examined multi-joint dynamic movements, 10 single-joint isometric contractions, and 2 single-joint isokinetic contractions. Of the studies investigating multi-joint dynamic contractions, 83% (11/13 studies) reported at least one significant age-related difference: In 84% (9/11 studies) coactivation was higher in children, whereas 16% (2/11 studies) reported higher coactivation in adults. Among single-joint contractions, only 25% (3/12 studies) reported significantly higher coactivation in children. Fifty six percent of studies examined females, with no clear sex-related differences. Child-adult differences in coactivation appear to be more prevalent during multi-joint dynamic contractions, where generally, coactivation is higher in children. When examining child–adult differences in muscle function, it is important to consider potential age-related differences in coactivation, specifically during multi-joint dynamic contractions.     

Total trunk muscle force and spinal compression are lower in asymmetric moments as compared to pure extension moments.

The aim of the present study was to test the assumption that asymmetric trunk loading requires a higher total muscle force and consequently entails a higher compression forces on the spine as compared to symmetric loading. When the trunk musculature is modelled in sufficient detail, optimisation shows that there is no mechanical necessity for an increase in total muscle force (or compression force) with task asymmetry. A physiologically based optimisation does also not predict an increase in total muscle force or spinal loading with asymmetry. EMG data on 14 trunk muscles collected in eight subjects showed antagonistic coactivity to be present in both conditions. However, estimates of total muscle force based on the EMG were lower when producing an asymmetric moment. In conclusion, producing an asymmetric moment appears to cause slightly lower forces on the lumbosacral joint as compared to a symmetric moment. Only lateral shear forces increase with asymmetry but these remain well below failure levels.     

The influence of dynamic factors on triaxial net muscular moments at the L5/S1 joint during asymmetrical lifting and lowering.

Asymmetrical lifting and lowering are predominant activities in the workplace. Mechanical causes are suggested for many back injuries and the dynamic conditions within which spine loading occurs are related to spine loading increase. More data on tridimensional biomechanical lumbar spine loading during asymmetrical lifting and lowering are needed. A tridimensional dynamic multisegment model was developed to compute spinal loading for asymmetrical box-handling situations. The tridimensional positions of the anatomical markers were generated by a direct linear transformation algorithm adapted for the processing of data from two real and two virtual views (mirrors). Two force platforms measured the external forces. Five male subjects performed three variations (slow, fast and accelerated) of asymmetric lifting and two variations (slow and fast) of asymmetric lowering. The torsional, extension/flexion and lateral bending net muscular moments at the L5/S1 joint were computed and peak values selected for statistical analysis. For the lifting task, the fast and accelerated conditions showed significant increases over the slow condition for torsion, extension/flexion and lateral-bending moments. The accelerated condition also showed significant increases over the fast condition for extension. A comparison between lifting and lowering tasks showed equivalent loadings for torsion and extension. The moments were compared to average maximal values measured on equivalent male subject populations by isokinetic dynamometry. This showed torsional and extension values of 30 and 83% of the maximal possible subject capacity, respectively. These results demonstrated that dynamic factors do influence the load on the spine and highlighted the influence of both lifting and lowering on the loading of the spine. This suggested that for a more complete analysis of asymmetrical handling, the maximal velocity and acceleration produced during lifting should be included.     

Sensitivity of muscle and intervertebral disc force computations to variations in muscle attachment sites

Abstract

The current paper aims at assessing the sensitivity of muscle and intervertebral disc force computations against potential errors in modeling muscle attachment sites. We perturbed each attachment location in a complete and coherent musculoskeletal model of the human spine and quantified the changes in muscle and disc forces during standing upright, flexion, lateral bending, and axial rotation of the trunk. Although the majority of the muscles caused minor changes (less than 5%) in the disc forces, certain muscle groups, for example, quadratus lumborum, altered the shear and compressive forces as high as 353% and 17%, respectively. Furthermore, percent changes were higher in the shear forces than in the compressive forces. Our analyses identified certain muscles in the rib cage (intercostales interni and intercostales externi) and lumbar spine (quadratus lumborum and longissimus thoracis) as being more influential for computing muscle and disc forces. Furthermore, the disc forces at the L4/L5 joint were the most sensitive against muscle attachment sites, followed by T6/T7 and T12/L1 joints. Presented findings suggest that modeling muscle attachment sites based on solely anatomical illustrations might lead to erroneous evaluation of internal forces and promote using anatomical datasets where these locations were accurately measured. When developing a personalized model of the spine, certain care should also be paid especially for the muscles indicated in this work.     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.     

Role of motor cortex in coordinating multi-joint movements: is it time for a new paradigm?

Reaching movements to spatial targets require motor patterns at the shoulder to be coordinated carefully with those at the elbow to smoothly move the hand through space. While the motor cortex is involved in this volitional task, considerable debate remains about how this cortical region participates in planning and controlling movement. This article reviews two opposing interpretations of motor cortical function during multi-joint movements. On the one hand, studies performed predominantly on single-joint movement generally support the notion that motor cortical activity is intimately involved in generating motor patterns at a given joint. In contrast, studies on reaching demonstrate correlations between motor cortical activity and features of movement related to the hand, suggesting that the motor cortex may be involved in more global features of the task. Although this latter paradigm involves a multi-joint motor task in which neural activity is correlated with features of movement related to the hand, this neural activity is also correlated to other movement variables. Therefore it is difficult to assess if and how the motor cortex contributes to the coordination of motor patterns at different joints. In particular, present paradigms cannot assess whether motor cortical activity contributes to the control of one joint or multiple joints during whole-arm tasks. The final point discussed in this article is the development of a new experimental device (KINARM) that can both monitor and manipulate the mechanics of the shoulder and elbow independently during multi-joint motor tasks. It is hoped that this new device will provide a new approach for examining how the motor cortex is involved in motor coordination.     

Development of a novel MATLAB-based framework for implementing mechanical joint stability constraints within OpenSim musculoskeletal models

The Static Optimization (SO) solver in OpenSim estimates muscle activations and forces that only equilibrate applied moments. In this study, SO was enhanced through an open-access MATLAB interface, where calculated muscle activations can additionally satisfy crucial mechanical stability requirements. This Stability-Constrained SO (SCSO) is applicable to many OpenSim models and can potentially produce more biofidelic results than SO alone, especially when antagonistic muscle co-contraction is required to stabilize body joints. This hypothesis was tested using existing models and experimental data in the literature. Muscle activations were calculated by SO and SCSO for a spine model during two series of static trials (i.e. simulation 1 and 2), and also for a lower limb model (supplementary material 2). In simulation 1, symmetric and asymmetric flexion postures were compared, while in simulation 2, various external load heights were compared, where increases in load height did not change the external lumbar flexion moment, but necessitated higher EMG activations. During the tasks in simulation 1, the predicted muscle activations by SCSO demonstrated less average deviation from the EMG data (6.8% −7.5%) compared to those from SO (10.2%). In simulation 2, SO predicts constant muscle activations and forces, while SCSO predicts increases in the average activations of back and abdominal muscles that better match experimental data. Although the SCSO results are sensitive to some parameters (e.g. musculotendon stiffness), when considering the strategy of the central nervous system in distributing muscle forces and in activating antagonistic muscles, the assigned activations by SCSO are more biofidelic than SO.     

An empirical approach to characterizing trunk muscle coactivation using simulation input modeling techniques

Accurately describing trunk muscle coactivation is fundamental to quantifying the spine reaction forces that occur during lifting tasks and has been the focus of a great deal of research in the spine biomechanics literature. One limitation of previous approaches has been a lack of consideration given to the variability in these coactivation strategies. The research presented in this paper is an empirical approach to quantifying and modeling trunk muscle coactivation using simulation input modeling techniques. Electromyographic (EMG) data were collected from 28 human subjects as they performed controlled trunk extension exertions. These exertions included isokinetic (10 and 45°/s) and constant acceleration (50°/s/s) trunk extensions in symmetric and asymmetric (30°) postures at two levels of trunk extension moment (30 and 80 Nm). The EMG data were collected from the right and left pairs of the erector spinae, latissimus dorsi, rectus abdominis, external obliques and internal obliques. Each subject performed nine repetitions of each combination of independent variables. The data collected during these trials were used to develop marginal distributions of trunk muscle activity as well as a 10×10 correlation matrix that described how the muscles cooperated to produce these extension torques. These elements were then combined to generate multivariate distributions describing the coactivation of the trunk musculature. An analysis of these distributions revealed that increases in extension moment, extension velocity and sagittal flexion angle created increases in both the mean and the variance of the distributions of the muscular response, while increases in the rate of trunk extension acceleration decreased both the mean and variance of the distributions of activity across all muscles considered. Increases in trunk asymmetry created a decrease in mean of the ipsi–lateral erector spinae and an increase in the mean of all other muscles considered, but there was little change in the variance of these distributions as a function of asymmetry.     

Intervertebral reaction force prediction using an enhanced assembly of OpenSim models

OpenSim offers a valuable approach to investigating otherwise difficult to assess yet important biomechanical parameters such as joint reaction forces. Although the range of available models in the public repository is continually increasing, there currently exists no OpenSim model for the computation of intervertebral joint reactions during flexion and lifting tasks. The current work combines and improves elements of existing models to develop an enhanced model of the upper body and lumbar spine. Models of the upper body with extremities, neck and head were combined with an improved version of a lumbar spine from the model repository. Translational motion was enabled for each lumbar vertebrae with six controllable degrees of freedom. Motion segment stiffness was implemented at lumbar levels and mass properties were assigned throughout the model. Moreover, body coordinate frames of the spine were modified to allow straightforward variation of sagittal alignment and to simplify interpretation of results. Evaluation of model predictions for level L1–L2, L3–L4 and L4–L5 in various postures of forward flexion and moderate lifting (8 kg) revealed an agreement within 10% to experimental studies and model-based computational analyses. However, in an extended posture or during lifting of heavier loads (20 kg), computed joint reactions differed substantially from reported in vivo measures using instrumented implants. We conclude that agreement between the model and available experimental data was good in view of limitations of both the model and the validation datasets. The presented model is useful in that it permits computation of realistic lumbar spine joint reaction forces during flexion and moderate lifting tasks. The model and corresponding documentation are now available in the online OpenSim repository.     

Modulation of shoulder muscle and joint function using a powered upper-limb exoskeleton

Robotic-assistive exoskeletons can enable frequent repetitive movements without the presence of a full-time therapist; however, human-machine interaction and the capacity of powered exoskeletons to attenuate shoulder muscle and joint loading is poorly understood. This study aimed to quantify shoulder muscle and joint force during assisted activities of daily living using a powered robotic upper limb exoskeleton (ArmeoPower, Hocoma). Six healthy male subjects performed abduction, flexion, horizontal flexion, reaching and nose touching activities. These tasks were repeated under two conditions: (i) the exoskeleton compensating only for its own weight, and (ii) the exoskeleton providing full upper limb gravity compensation (i.e., weightlessness). Muscle EMG, joint kinematics and joint torques were simultaneously recorded, and shoulder muscle and joint forces calculated using personalized musculoskeletal models of each subject’s upper limb. The exoskeleton reduced peak joint torques, muscle forces and joint loading by up to 74.8% (0.113 Nm/kg), 88.8% (5.8%BW) and 68.4% (75.6%BW), respectively, with the degree of load attenuation strongly task dependent. The peak compressive, anterior and superior glenohumeral joint force during assisted nose touching was 36.4% (24.6%BW), 72.4% (13.1%BW) and 85.0% (17.2%BW) lower than that during unassisted nose touching, respectively. The present study showed that upper limb weight compensation using an assistive exoskeleton may increase glenohumeral joint stability, since deltoid muscle force, which is the primary contributor to superior glenohumeral joint shear, is attenuated; however, prominent exoskeleton interaction moments are required to position and control the upper limb in space, even under full gravity compensation conditions. The modeling framework and results may be useful in planning targeted upper limb robotic rehabilitation tasks.     

Spinal stability and role of passive stiffness in dynamic squat and stoop lifts

The spinal stability and passive-active load partitioning under dynamic squat and stoop lifts were investigated as the ligamentous stiffness in flexion was altered. Measured in vivo kinematics of subjects lifting 180 N at either squat or stoop technique was prescribed in a nonlinear transient finite element model of the spine. The Kinematics-driven approach was utilized for temporal estimation of muscle forces, internal spinal loads and system stability. The finite element model accounted for nonlinear properties of the ligamentous spine, wrapping of thoracic extensor muscles and trunk dynamic characteristics while subject to measured kinematics and gravity/external loads. Alterations in passive properties of spine substantially influenced muscle forces, spinal loads and system stability in both lifting techniques, though more so in stoop than in squat. The squat technique is advocated for resulting in smaller spinal loads. Stability of spine in the sagittal plane substantially improved with greater passive properties, trunk flexion and load. Simulation of global extensor muscles with curved rather than straight courses considerably diminished loads on spine and increased stability throughout the task.     

Anterior hip joint force increases with hip extension, decreased gluteal force, or decreased iliopsoas force

Abnormal or excessive force on the anterior hip joint may cause anterior hip pain, subtle hip instability and a tear of the acetabular labrum. We propose that both the pattern of muscle force and hip joint position can affect the magnitude of anterior joint force and thus possibly lead to excessive force and injury. The purpose of this study was to determine the effect of hip joint position and of weakness of the gluteal and iliopsoas muscles on anterior hip joint force. We used a musculoskeletal model to estimate hip joint forces during simulated prone hip extension and supine hip flexion under four different muscle force conditions and across a range of hip extension and flexion positions. Weakness of specified muscles was simulated by decreasing the modeled maximum force value for the gluteal muscles during hip extension and the iliopsoas muscle during hip flexion. We found that decreased force contribution from the gluteal muscles during hip extension and the iliopsoas muscle during hip flexion resulted in an increase in the anterior hip joint force. The anterior hip joint force was greater when the hip was in extension than when the hip was in flexion. Further studies are warranted to determine if increased utilization of the gluteal muscles during hip extension and of the iliopsoas muscle during hip flexion, and avoidance of hip extension beyond neutral would be beneficial for people with anterior hip pain, subtle hip instability, or an anterior acetabular labral tear.     

Muscle redundancy does not imply robustness to muscle dysfunction

It is well-known that muscle redundancy grants the CNS numerous options to perform a task. Does muscle redundancy, however, allow sufficient robustness to compensate for loss or dysfunction of even a single muscle? Are all muscles equally redundant? We combined experimental and computational approaches to establish the limits of motor robustness for static force production. In computer-controlled cadaveric index fingers, we find that only a small subset (<5%) of feasible forces is robust to loss of any one muscle. Importantly, the loss of certain muscles compromises force production significantly more than others. Further computational modeling of a multi-joint, multi-muscle leg demonstrates that this severe lack of robustness generalizes to whole limbs. These results provide a biomechanical basis to begin to explain why redundant motor systems can be vulnerable to even mild neuromuscular pathology.     

An analytical model for the ergometer rowing: inverse multibody dynamics analysis

A model for the ergometer rowing exercise is presented in this paper. From the quantitative observations of a particular trajectory (motion), the model is used to determine the moment of the forces produced by the muscles about each joint. These forces are evaluated according to the continuous system of equations of motion. An inverse dynamics analysis is performed in order to predict the joint torques developed by the muscles during the execution of the task. An elementary multibody mechanical system is used as an example to discuss the assumptions and procedures adopted.     

Effect of the intra-abdominal pressure and the center of segmental body mass on the lumbar spine mechanics - a computational parametric study

Determination of physiological loads in human lumbar spine is critical for understanding the mechanisms of lumbar diseases and for designing surgical treatments. Computational models have been used widely to estimate the physiological loads of the spine during simulated functional activities. However, various assumptions on physiological factors such as the intra-abdominal pressure (IAP), centers of mass (COMs) of the upper body and lumbar segments, and vertebral centers of rotation (CORs) have been made in modeling techniques. Systematic knowledge of how these assumptions will affect the predicted spinal biomechanics is important for improving the simulation accuracy. In this paper, we developed a 3D subject-specific numerical model of the lumbosacral spine including T12 and 90 muscles. The effects of the IAP magnitude and COMs locations on the COR of each motion segment and on the joint/muscle forces were investigated using a global convergence optimization procedure when the subject was in a weight bearing standing position. The data indicated that the line connecting the CORs showed a smaller curvature than the lordosis of the lumbar spine in standing posture when the IAP was 0?kPa and the COMs were 10?mm anterior to the geometric center of the T12 vertebra. Increasing the IAP from 0 kPa to 10 kPa shifted the location of CORs toward the posterior direction (from 1.4?±?8.9 mm anterior to intervertebral disc (IVD) centers to 40.5?±?3.1 mm posterior to the IVD centers) and reduced the average joint force (from 0.78?±?0.11 Body weight (BW) to 0.31?±?0.07 BW) and overall muscle force (from 349.3?±?57.7 N to 221.5?±?84.2 N). Anterior movement of the COMs from -30 mm to 70 mm relative to the geometric center of T12 vertebra caused an anterior shift of the CORs (from 25.1?±?8.3 mm posterior to IVD centers to 7.8?±?6.2 mm anterior to IVD centers) and increases of average joint forces (from 0.78?±?0.1 BW to 0.93?±?0.1 BW) and muscle force (from 348.9?±?47.7 N to 452.9?±?58.6 N). Therefore, it is important to consider the IAP and correct COMs in order to accurately simulate human spine biomechanics. The method and results of this study could be useful for designing prevention strategies of spinal injuries and recurrences, and for enhancing rehabilitation efficiency.     

Trunk strength,muscle activity and spinal loads in maximum isometric flexion and extension exertions: A combined in vivo-computational study

Determination of the trunk maximum voluntary exertion moment capacity and associated internal spinal forces could serve in proper selection of workers for specific occupational task requirements, injury prevention and treatment outcome evaluations. Maximum isometric trunk exertion moments in flexion and extension along with surface EMG of select trunk muscles are measured in 12 asymptomatic subjects. Subsequently and under individualized measured harness-subject forces, kinematics and upper trunk gravity, an iterative kinematics-driven finite element model is used to compute muscle forces and spinal loads in 4 of these subjects. Different co-activity and intra-abdominal pressure levels are simulated. Results indicate significantly larger maximal resistant moments and spinal compression/shear forces in extension exertions than flexion exertions. The agonist trunk muscles reach their maximum force generation (saturation) to greater extent in extension exertions compared to flexion exertions. Local lumbar extensor muscles are highly active in extension exertions and generate most of the internal spinal forces. The maximum exertion attempts produce large spinal compression and shear loads that increase with the antagonist co-activity level but decrease with the intra-abdominal pressure. Intra-abdominal pressure decreases agonist muscle forces in extension exertions but generally increase them in flexion exertions.     

Residual force enhancement during voluntary contractions of knee extensors and flexors at short and long muscle lengths

Residual force enhancement (RFE) is a term describing the observation that muscle tension during a contraction that includes a stretch and hold remains above that during an isometric contraction at the hold length. RFE has been observed during in vitro and in vivo experiments, but results involving voluntary contractions are mixed, particularly with respect to large muscles. The purpose of this study was to determine if RFE can be observed in large muscles such as knee extensors and flexors at joint configurations corresponding to the ascending and descending limbs of the muscle force-length curve. Two groups of twenty participants (ten males and ten females per group) performed maximum voluntary contractions on a Biodex machine in purely isometric conditions and in isometric conditions immediately following eccentric stretch. Knee extension trials were performed at 40° (short muscles) and 100° (long muscles) flexion from full extension (0°), and knee flexion trials were performed at 70° (short muscles) and 10° (long muscles) flexion. Stretch-isometric trials terminated at these angles following 30° of eccentric motion at 30°/s. Statistically-significant RFE was observed for both tasks at long-muscle joint configurations, but was not observed for either task at short-muscle joint configurations. Passive torque enhancement was also observed following muscle relaxation at long-muscle joint configurations for both tasks, but for only knee flexion at short-muscle joint configurations. These results reinforce for voluntary contractions of large muscles the RFE behavior observed in smaller muscles, and provide further evidence that RFE occurs primarily on the descending limb of the muscle force-length curve.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.