A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings

The aim of this paper was to compare the effect of different optimisation methods and different knee joint degrees of freedom (DOF) on muscle force predictions during a single legged hop. Nineteen subjects performed single-legged hopping manoeuvres and subject-specific musculoskeletal models were developed to predict muscle forces during the movement. Muscle forces were predicted using static optimisation (SO) and computed muscle control (CMC) methods using either 1 or 3 DOF knee joint models. All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°). Biarticular muscles (hamstrings, rectus femoris and gastrocnemius) showed more differences in muscle force profiles when comparing between the different muscle prediction approaches where these muscles showed larger time delays for many of the comparisons. The muscle force magnitudes of vasti, gluteus maximus and gluteus medius were not greatly influenced by the choice of muscle force prediction method with low normalised root mean squared errors (<48%) observed in most comparisons. We conclude that SO and CMC can be used to predict lower-limb muscle co-contraction during hopping movements. However, care must be taken in interpreting the magnitude of force predicted in the biarticular muscles and the soleus, especially when using a 1 DOF knee. Despite this limitation, given that SO is a more robust and computationally efficient method for predicting muscle forces than CMC, we suggest that SO can be used in conjunction with musculoskeletal models that have a 1 or 3 DOF knee joint to study the relative differences and the role of muscles during hopping activities in future studies.     

A two-step EMG-and-optimization process to estimate muscle force during dynamic movement

The present study proposed a two-step EMG-and-optimization method for muscle force estimation in dynamic condition. Considering the strengths and the limitations of existing methods, the proposed approach exploited the advantages of min/max optimization with constraints on the contributions of the flexor and extensor muscle groups to the net joint moment estimated through an EMG-to-moment approach. Our methodology was tested at the knee joint during dynamic half squats, and was compared with traditional min/max optimization. In general, results showed significant differences in muscle force estimates from EMG-and-optimization method when compared with those from traditional min/max optimization. Muscle forces were higher – especially in the antagonist muscles – and more consistent with EMG patterns because of the ability of the proposed approach to properly account for agonist/antagonist cocontraction. In addition, muscle forces agree with mechanical constraints regarding the net, the agonist, and the antagonist moments, thus greatly improving the confidence in muscle force estimates. The proposed two-step EMG-and-optimization method for muscle force estimation is easy to implement with relatively low computational requirements and, thus, could offer interesting advantages for various applications in many fields, including rehabilitation, clinical, and sports biomechanics.     

Estimation of handgrip force using frequency-band technique during fatiguing muscle contraction

In this paper, we propose a force estimation model to compute the handgrip force from SEMG signal during fatiguing muscle contraction tasks. The appropriate frequency range was analyzed using various combinations of a wavelet scale, and the highest accuracy was achieved at a range from 242 to 365 Hz. After that, eight healthy individuals performed a series of static (70%, 50%, 30%, and 20% MVC) and dynamic (0–50% MVC) muscle contraction tasks to evaluate the performance of this technique in comparison with that of former method using the Root Mean Square of the SEMG signal. Both methods had comparable results at the beginning of the experiments, before the onset of muscle fatigue. However, differences were clearly observed as the degree of muscle fatigue began to increase toward the endurance time. Under this condition, the estimated handgrip force using the proposed method improved from 17% to 134% for static contraction tasks and 40% for dynamic contraction tasks. This study overcomes the limitation of the former method during fatiguing muscle contraction tasks and, therefore, unlocks the potential of utilizing the SEMG signal as an indirect force estimation method for various applications.     

The minimum required muscle force for a sit-to-stand task

The purpose of this study was to reveal the minimum required muscle force for a sit-to-stand task. Combining experimental procedures and computational processing, movements of various sit-to-stand patterns were obtained. Muscle forces and activations during a movement were calculated with an inverse dynamics method and a static numerical optimization method. The required muscle force for each movement was calculated with peak muscle activation, muscle physiological cross sectional area and specific tension. The robustness of the results was quantitatively evaluated with sensitivity analyses. From the results, a distinct threshold was found for the total required muscle force of the hip and knee extensors. Specifically, two findings were revealed: (1) the total force of hip and knee extensors is appropriate as the index of minimum required muscle force for a sit-to-stand task and (2) the minimum required total force is within the range of 35.3-49.2 N/kg. A muscle is not mechanically independent from other muscles, since each muscle has some synergetic or antagonistic muscles. This means that the mechanical threshold of one muscle varies with the force exertion abilities of other muscles and cannot be evaluated independently. At the same time, some kinds of mechanical threshold necessarily exist in the sit-to-stand task, since a muscle force is an only force to drive the body and people cannot stand up from a chair without muscles. These indicate that the existence of the distinct threshold in the result of the total required muscle force is reasonable.     

Development of software for human muscle force estimation

Muscle force estimation (MFE) has become more and more important in exploring principles of pathological movement, studying functions of artificial muscles, making surgery plan for artificial joint replacement, improving the biomechanical effects of treatments and so on. At present, existing software are complex for professionals, so we have developed a new software named as concise MFE (CMFE). CMFE which provides us a platform to analyse muscle force in various actions includes two MFE methods (static optimisation method and electromyographic-based method). Common features between these two methods have been found and used to improve CMFE. A case studying the major muscles of lower limb of a healthy subject walking at normal speed has been presented. The results are well explained from the effect of the motion produced by muscles during movement. The development of this software can improve the accuracy of the motion simulations and can provide a more extensive and deeper insight in to muscle study.     

Development of software for human muscle force estimation

Muscle force estimation (MFE) has become more and more important in exploring principles of pathological movement, studying functions of artificial muscles, making surgery plan for artificial joint replacement, improving the biomechanical effects of treatments and so on. At present, existing software are complex for professionals, so we have developed a new software named as concise MFE (CMFE). CMFE which provides us a platform to analyse muscle force in various actions includes two MFE methods (static optimisation method and electromyographic-based method). Common features between these two methods have been found and used to improve CMFE. A case studying the major muscles of lower limb of a healthy subject walking at normal speed has been presented. The results are well explained from the effect of the motion produced by muscles during movement. The development of this software can improve the accuracy of the motion simulations and can provide a more extensive and deeper insight in to muscle study.     

Automated estimation of ankle muscle EMG envelopes and resulting plantar-dorsi flexion torque from 64 garment-embedded electrodes uniformly distributed around the human leg

The design of personalized movement training and rehabilitation pipelines relies on the ability of assessing the activation of individual muscles concurrently with the resulting joint torques exerted during functional movements. Despite advances in motion capturing, force sensing and bio-electrical recording technologies, the estimation of muscle activation and resulting force still relies on lengthy experimental and computational procedures that are not clinically viable. This work proposes a wearable technology for the rapid, yet quantitative, assessment of musculoskeletal function. It comprises of (1) a soft leg garment sensorized with 64 uniformly distributed electromyography (EMG) electrodes, (2) an algorithm that automatically groups electrodes into seven muscle-specific clusters, and (3) a EMG-driven musculoskeletal model that estimates the resulting force and torque produced about the ankle joint sagittal plane. Our results show the ability of the proposed technology to automatically select a sub-set of muscle-specific electrodes that enabled accurate estimation of muscle excitations and resulting joint torques across a large range of biomechanically diverse movements, underlying different excitation patterns, in a group of eight healthy individuals. This may substantially decrease time needed for localization of muscle sites and electrode placement procedures, thereby facilitating applicability of EMG-driven modelling pipelines in standard clinical protocols.     

Time-frequency methods applied to muscle fatigue assessment during dynamic contractions.

This paper discusses the assessment of the electrical manifestations of muscle fatigue during dynamic contractions. In the past, the study of muscle fatigue was restricted to isometric constant force contractions because, in this contraction paradigm, the myoelectric signal may be considered as wide sense stationary over epochs lasting up to two or three seconds, and hence classic spectral estimation techniques may be applied. Recently, the availability of spectral estimation techniques specifically designed for nonstationary signal analysis made it possible to extend the employment of muscle fatigue assessment to cyclic dynamic contractions, thus increasing noticeably its possible clinical applications. After presenting the basics of time-frequency distributions, we introduce instantaneous spectral parameters well suited to tracking spectral changes due to muscle fatigue, discuss the issues of quasi-stationarity and quasi-cyclostationarity, and present different strategies of signal analysis to be utilized with cyclic dynamic contractions. We present preliminary results obtained by analyzing data collected from paraspinal muscles during repetitive lift movements, from the first dorsal interosseus during abduction-adduction movements of the index finger, and from knee flexors and extensors during isokinetic exercise. In conclusion, data herein reported demonstrate that the described techniques allow for evidencing the electrical manifestations of muscle fatigue in different paradigms of cyclic dynamic contractions. We believe that the extension of the objective assessment of the electrical manifestations of muscle fatigue from static to dynamic contractions may increase considerably the interest of researchers and clinicians and open new application fields, as ergonomics and sports medicine.     

Estimation of muscle fiber conduction velocity from two-dimensional surface EMG recordings in dynamic tasks

The aims of this study are (1) to demonstrate that multi-channel surface electromyographic (EMG) signals can be detected with negligible artifacts during fast dynamic movements with an adhesive two-dimensional (2D) grid of 64 electrodes and (2) to propose a new method for the estimation of muscle fiber conduction velocity from short epochs of 2D EMG recordings during dynamic tasks. Surface EMG signals were collected from the biceps brachii muscle of four subjects with a grid of 13 × 5 electrodes during horizontal elbow flexion/extension movements (range 120–170°) at the maximum speed, repeated cyclically for 2 min. Action potentials propagating between the innervation zone and tendon regions could be detected during the dynamic task. A maximum likelihood method for conduction velocity estimation from the 2D grid using short time intervals was developed and applied to the experimental signals. The accuracy of conduction velocity estimation, assessed from the standard deviation of the residual of the regression line with respect to time, decreased from (range) 0.20–0.33 m/s using one column to 0.02–0.15 m/s when combining five columns of the electrode grid. This novel method for estimation of muscle fiber conduction velocity from 2D EMG recordings provides an estimate which is global in space and local in time, thus representative of the entire muscle yet able to track fast changes over the execution of a task, as is required for assessing muscle properties during fast movements.     

Muscle forces during running predicted by gradient-based and random search static optimisation algorithms

Muscle forces during locomotion are often predicted using static optimisation and SQP. SQP has been criticised for over-estimating force magnitudes and under-estimating co-contraction. These problems may be related to SQP's difficulty in locating the global minimum to complex optimisation problems. Algorithms designed to locate the global minimum may be useful in addressing these problems. Muscle forces for 18 flexors and extensors of the lower extremity were predicted for 10 subjects during the stance phase of running. Static optimisation using SQP and two random search (RS) algorithms (a genetic algorithm and simulated annealing) estimated muscle forces by minimising the sum of cubed muscle stresses. The RS algorithms predicted smaller peak forces (42% smaller on average) and smaller muscle impulses (46% smaller on average) than SQP, and located solutions with smaller cost function scores. Results suggest that RS may be a more effective tool than SQP for minimising the sum of cubed muscle stresses in static optimisation.     

Adjustable passive length-tension curve in rabbit detrusor smooth muscle.

Until the 1990s, the passive and active length-tension (L-T) relationships of smooth muscle were believed to be static, with a single passive force value and a single maximum active force value for each muscle length. However, recent studies have demonstrated that the active L-T relationship in airway smooth muscle is dynamic and adapts to length changes over a period of time. Furthermore, our prior work showed that the passive L-T relationship in rabbit detrusor smooth muscle (DSM) is also dynamic and that in addition to viscoelastic behavior, DSM displays strain-softening behavior characterized by a loss of passive stiffness at shorter lengths following a stretch to a new longer length. This loss of passive stiffness appears to be irreversible when the muscle is not producing active force and during submaximal activation but is reversible on full muscle activation, which indicates that the stiffness component of passive force lost to strain softening is adjustable in DSM. The present study demonstrates that the passive L-T curve for DSM is not static and can shift along the length axis as a function of strain history and activation history. This study also demonstrates that adjustable passive stiffness (APS) can modulate total force (35% increase) for a given muscle length, while active force remains relatively unchanged (4% increase). This finding suggests that the structures responsible for APS act in parallel with the contractile apparatus, and the results are used to further justify the configuration of modeling elements within our previously proposed mechanical model for APS.     

Muscle forces during running predicted by gradient-based and random search static optimisation algorithms

Muscle forces during locomotion are often predicted using static optimisation and SQP. SQP has been criticised for over-estimating force magnitudes and under-estimating co-contraction. These problems may be related to SQP's difficulty in locating the global minimum to complex optimisation problems. Algorithms designed to locate the global minimum may be useful in addressing these problems. Muscle forces for 18 flexors and extensors of the lower extremity were predicted for 10 subjects during the stance phase of running. Static optimisation using SQP and two random search (RS) algorithms (a genetic algorithm and simulated annealing) estimated muscle forces by minimising the sum of cubed muscle stresses. The RS algorithms predicted smaller peak forces (42% smaller on average) and smaller muscle impulses (46% smaller on average) than SQP, and located solutions with smaller cost function scores. Results suggest that RS may be a more effective tool than SQP for minimising the sum of cubed muscle stresses in static optimisation.     

A calibrated EMG-informed neuromusculoskeletal model can appropriately account for muscle co-contraction in the estimation of hip joint contact forces in people with hip osteoarthritis

Abnormal hip joint contact forces (HJCF) are considered a primary mechanical contributor to the progression of hip osteoarthritis (OA). Compared to healthy controls, people with hip OA often present with altered muscle activation patterns and greater muscle co-contraction, both of which can influence HJCF. Neuromusculoskeletal (NMS) modelling is non-invasive approach to estimating HJCF, whereby different neural control solutions can be used to estimate muscle forces. Static optimisation, available within the popular NMS modelling software OpenSim, is a commonly used neural control solution, but may not account for an individual’s unique muscle activation patterns and/or co-contraction that are often evident in pathological population. Alternatively, electromyography (EMG)-assisted neural control solutions, available within CEINMS software, have been shown to account for individual activation patterns in healthy people. Nonetheless, their application in people with hip OA, with conceivably greater levels of co-contraction, is yet to be explored. The aim of this study was to compare HJCF estimations using static optimisation (in OpenSim) and EMG-assisted (in CEINMS) neural control solutions during walking in people with hip OA. EMG-assisted neural control solution was more consistent with both EMG and joint moment data than static optimisation, and also predicted significantly higher HJCF peaks (p < 0.001). The EMG-assisted neural control solution also accounted for more muscle co-contraction than static optimisation (p = 0.03), which probably contributed to these higher HJCF peaks. Findings suggest that the EMG-assisted neural control solution may estimate more physiologically plausible HJCF than static optimisation in a population with high levels of co-contraction, such as hip OA.     

A comparative study of muscle force estimates using Huxley's and Hill's muscle model

Determination of muscle forces in individual muscles is often essential to assess optimal performance of human motion. Inverse dynamic methods based on the kinematics of the given motion and on the use of optimisation approach are the most widely used for muscle force estimation. The aim of this study was to estimate how the choice of muscle model influences predicted muscle forces. Huxley's (1957, Prog Biophys Biop Chem. 7: 255–318) and Hill's (1938, Proc R Soc B. 126: 136–195) muscle models were used for determination of muscle forces of two antagonistic muscles of the lower extremity during cycling. Huxley's model is a complex model that couples biochemical and physical processes with the microstructure of the muscle whereas the Hill's model is a phenomenological model. Muscle forces predicted by both models are within the same range. Huxley's model predicts more realistic patterns of muscle activation but it is computationally more demanding. Therefore, if the overall muscle forces are to be assessed, it is reasonable to use a simpler implementation based on Hill's model.     

Changes in movement final position associated with agonist and antagonist muscle fatigue

We have tested the hypothesis that agonist and antagonist muscle fatigue could affect the final position of rapid, discrete movements. Six subjects performed consecutive elbow flexion and extension movements between two targets, with their eyes closed prior to, and after fatiguing the elbow extensor muscles. The results demonstrate that elbow extension movements performed in the post-test period systematically undershot the final position as compared to pre-test movements. However, attainment of the aimed final position in elbow flexion movements was unaffected by fatiguing of the extensor muscles. Undershoot of the final position obtained in extension movements was associated with agonist muscle fatigue, a result that was expected from the point of view of current motor control theories, and that could be explained by a reduced ability of the shortening muscle to exert force. On the other hand, the absence of the expected overshoot of the final position when the antagonist is fatigued, indicates the involvement of various reflex and/or central mechanisms operating around the stretched muscle that could contribute to returning the limb to the standard final position after a brief prominent overshoot.     

Control of human eye movements: I. modelling of extraocular muscle

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

A 'cheap' optimal control approach to estimate muscle forces in musculoskeletal systems

This paper shows a new method to estimate the muscle forces in musculoskeletal systems based on the inverse dynamics of a multi-body system associated optimal control. The redundant actuator problem is solved by minimizing a time-integral cost function, augmented with a torque-tracking error function, and muscle dynamics is considered through differential constraints. The method is compared to a previously implemented human posture control problem, solved using a Forward Dynamics Optimal Control approach and to classical static optimization, with two different objective functions. The new method provides very similar muscle force patterns when compared to the forward dynamics solution, but the computational cost is much smaller and the numerical robustness is increased. The results achieved suggest that this method is more accurate for the muscle force predictions when compared to static optimization, and can be used as a numerically 'cheap' alternative to the forward dynamics and optimal control in some applications.     

A proprioception based regulation model to estimate the trunk muscle forces

Evaluation of loads acting on the spine requires the knowledge of the muscular forces acting on it, but muscles redundancy necessitates developing a muscle forces attribution strategy. Optimisation, EMG, or hybrid models allow evaluating muscle force patterns, yielding a unique muscular arrangement or/and requiring EMG data collection. This paper presents a regulation model of the trunk muscles based on a proprioception hypothesis, which searches to avoid the spinal joint overloading. The model is also compared to other existing models for evaluation. Compared to an optimisation model, the proposed alternative muscle pattern yielded a significant spine postero-anterior shear decrease. Compared to a model based on combination of optimisation criteria, present model better fits muscle activation observed using EMG (38% improvement). Such results suggest that the proposed model, based on regulation of all spinal components, may be more relevant from a physiologic point of view.     

Extrapolation of an empirical elbow muscle co-activation relationship to a novel task set: implications for predictions of individual muscle demands

Biomechanical optimisation models applying efficiency-based objective functions often underestimate antagonist contributions. Previous work has quantified an empirical co-activation relationship in the elbow musculature, demonstrating that implementing this relationship as a constraint in an elbow muscle force prediction model improves muscle force predictions. The current study evaluated this modified model by extrapolating the co-activation relationship to 36 novel isometric unilateral, right-handed exertions, including those requiring greater intensity of effort and performed in different postures. Surface electromyography was recorded from the elbow flexors and extensors. Novel extrapolative co-activation relationships were developed and used as constraints in a muscle force prediction model. Model predictions using both constraints were compared with empirical biophysical data. Predictions by the modified model were more consistent with biophysical data than those by the original model for the novel exertions. Novel co-activation relationships did not further enhance predictions when compared with the previous relationship, suggesting that extrapolation of the previous relationship is feasible.