Estimation of muscle forces in gait using a simulation of the electromyographic activity and numerical optimization

Clinical gait analysis provides great contributions to the understanding of gait patterns. However, a complete distribution of muscle forces throughout the gait cycle is a current challenge for many researchers. Two techniques are often used to estimate muscle forces: inverse dynamics with static optimization and computer muscle control that uses forward dynamics to minimize tracking. The first method often involves limitations due to changing muscle dynamics and possible signal artefacts that depend on day-to-day variation in the position of electromyographic (EMG) electrodes. Nevertheless, in clinical gait analysis, the method of inverse dynamics is a fundamental and commonly used computational procedure to calculate the force and torque reactions at various body joints. Our aim was to develop a generic musculoskeletal model that could be able to be applied in the clinical setting. The musculoskeletal model of the lower limb presents a simulation for the EMG data to address the common limitations of these techniques. This model presents a new point of view from the inverse dynamics used on clinical gait analysis, including the EMG information, and shows a similar performance to another model available in the OpenSim software. The main problem of these methods to achieve a correct muscle coordination is the lack of complete EMG data for all muscles modelled. We present a technique that simulates the EMG activity and presents a good correlation with the muscle forces throughout the gait cycle. Also, this method showed great similarities whit the real EMG data recorded from the subjects doing the same movement.     

Effect of a pathological scapular tilt after total shoulder arthroplasty

Total shoulder arthroplasty (TSA) is an accepted and most successfully used treatment for different shoulder pathologies. Different risk factors for the failure of the prosthesis are known. A pathological scapular orientation, observed in elderly people or in patients suffering from neuromuscular diseases, could be a cause of failure, which has not been investigated yet. To test this hypothesis, a numerical musculoskeletal model of the glenohumeral joint was used to compare two TSA cases: a reference normal case and a case with a pathological anterior tilt of the scapula. An active abduction of 150° was simulated. Joint force, contact pattern, polyethylene and cement stress were evaluated for both cases. The pathological tilt slightly increased the joint force and the contact pressure, but also shifted the contact pattern. This eccentric contact increased the stress level within the polyethylene of the glenoid component and within the surrounding cement layer. This adverse effect occurred mainly during the first 60° of abduction. Therefore, a pathological orientation of the scapula may increase the risk of a failure of the cement layer around the glenoid component. These preliminary numerical results should be confirmed by a clinical study.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

A muscle-path-plane method for representing muscle contraction during joint movement

Traditional muscle paths (the straight-line model and the viapoint-line model) emphasise either the mechanical properties that arouse joint movement or the morphological characteristics of the muscles. To consider both the factors, a muscle-path-plane (MPP) method is introduced to model the paths of muscles during joint movement. This method is based on the premise that there is a MPP, constructed by origin, insertion and MPP control point, which represents the major direction of the muscle contraction for an arbitrary joint configuration at any time. Then, we can calculate the functions and the lengths of the muscle paths during instantaneous joint movement in MPP by mathematical approaches. Taking the triceps brachii as an example, the lengths of its paths during elbow flexion are calculated and compared with the relative studies reported in the literature. It is concluded that this method can provide an insight into the simulation of the muscle contraction.     

A method to determine whether a musculoskeletal model can resist arbitrary external loadings within a prescribed range

Computational models of the musculoskeletal system are prone to design errors. It is possible to create a model that cannot satisfy equilibrium conditions for a set of external loading conditions. A model is ‘loadable’ if there exists a set of muscle forces that can resist an arbitrary applied force within a prescribed range. In this study, a novel mathematical method is introduced to determine whether models are loadable. In addition, an idealised musculoskeletal model is presented in order to develop the theory behind the mathematical method. The method uses the simplex algorithm to determine feasibility of the linear programming problem and can determine loadability for an arbitrary, continuous range of external forces. The method was applied to a three-dimensional model of the shoulder and correctly determined loadability for a range of externally applied forces.     

Comparison between line and surface mesh models to represent the rotator cuff muscle geometry in musculoskeletal models

Accurate muscle geometry (muscle length and moment arm) is required to estimate muscle function when using musculoskeletal modelling. In shoulder, muscles are often modelled as a collection of independent line segments, leading to non-physiological muscles trajectory, especially for the rotator cuff muscles. To prevent this, a surface mesh model was developed and validated against 7 MRI positions in one participant. Mean moment arm errors was 11.4% for the line vs. 8.8% for the mesh model. While the model with independent lines led to some non-physiological trajectories, the mesh model gave lower misestimations of muscle lengths and moment arms.     

EMG muscle scanning: Comparison to attached surface electrodes

Electromyographic (EMG) muscle scanning measures brief samples of integrated muscle action potentials from individual muscles using a hand-held scanner with post-style electrodes. This scanning technique is widely used by biofeedback practitioners to quickly assess muscle activity in the diagnosis of musculoskeletal disorders. In an effort to compare muscle scanning with the established technique using attached surface electrodes, ten healthy subjects (25–35 years old) were scanned using 2-second sampling at five bilateral muscle sites while simultaneously monitoring the same sites with surface electrodes. This was repeated using 10-second scanning samplings. Pearson's product-moment correlations between scanning for 2 seconds and prolonged surface recording at all sites were 0.54–0.89. Scanning for 10 seconds improved the correlations to 0.68–0.91. EMG scanning for 2 seconds compares favorably with attached surface electrode recording. Comparisons are further improved by 10-second scans.     

Sensitivity analysis of an energetic muscle model applied at whole body level in recumbent pedalling

Musculoskeletal models are used in order to describe and analyse the mechanics of human movement. In order to get a complete evaluation of the human movement, energetic muscle models were developed and were shown to be promising.

The aim of this work is to determine the sensitivity of muscle mechanical and energetic model estimates to changes in parameters during recumbent pedalling.

Inputs of the model were electromyography and joint angles, collected experimentally on one participant. The sensitivity analysis was performed on muscle-specific tension, physiological cross-sectional area, muscle maximal force, tendon rest length and percentage of fast-twitch fibres using an integrated sensitivity ratio. Soleus, gastrocnemius, vasti, gluteus and medial hamstrings were selected for the analyses.

The energetic model was found to be always less sensitive to parameter changes than the mechanical model. Tendon slack length was found to be the most critical parameter for both energetic and mechanical models even if the effect on the energetic output was smaller than on muscle force and joint moments.     

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.     

An open-source model and solution method to predict co-contraction in the finger

A novel open-source biomechanical model of the index finger with an electromyography (EMG)-constrained static optimization solution method are developed with the goal of improving co-contraction estimates and providing means to assess tendon tension distribution through the finger. The Intrinsic model has four degrees of freedom and seven muscles (with a 14 component extensor mechanism). A novel plugin developed for the OpenSim modelling software applied the EMG-constrained static optimization solution method. Ten participants performed static pressing in three finger postures and five dynamic free motion tasks. Index finger 3D kinematics, force (5, 15, 30 N), and EMG (4 extrinsic muscles and first dorsal interosseous) were used in the analysis. The Intrinsic model predicted co-contraction increased by 29% during static pressing over the existing model. Further, tendon tension distribution patterns and forces, known to be essential to produce finger action, were determined by the model across all postures. The Intrinsic model and custom solution method improved co-contraction estimates to facilitate force propagation through the finger. These tools improve our interpretation of loads in the finger to develop better rehabilitation and workplace injury risk reduction strategies.     

A comprehensive and volumetric musculoskeletal model for the dynamic simulation of the shoulder function

We present a volumetric and extensive finite element model of the shoulder usable in the context of inverse control, in which the scapula is left unconstrained on the ribcage. Such a model allows for exploring various shoulder movements, which are essential for making patient-specific decisions. The proposed model consists of 23 volumetric muscles parts modelled using the finite element method. The glenohumeral, acromioclavicular and sternoclavicular joints are modelled with soft ball-socket constraints. The musculoskeletal model can be controlled by a tracking-based algorithm, finding the excitations values in the muscles needed to follow some target points. The moment arms obtained during abduction and rotation are compared with the literature, which includes results from cadaveric data and a fine FE model of the rotator cuff and the deltoid. We simulated the paralysis of serratus anterior, a main reason of scapular winging, and compared it with its physiological counterpart. A deficiency in the range of motion as well as a reduction in upward rotation were observed, which both corroborate clinical observations. This is one of the most comprehensive model of the shoulder, which can be used to study complex pathologies of the shoulder and their impact on functional outcome such as range-of-motion.     

Transformation methods for estimation of subject-specific scapular muscle attachment sites

The parameters that describe the soft tissue structures are among the most important anatomical parameters for subject-specific biomechanical modelling. In this paper, we study one of the soft tissue parameters, namely muscle attachment sites. Two new methods are proposed for transformation of the muscle attachment sites of any reference scapula to any destination scapula based on four palpable bony landmarks. The proposed methods as well as one previously proposed method have been applied for transformation of muscle attachment sites of one reference scapula to seven other scapulae. The transformation errors are compared among the three methods. Both proposed methods yield significantly less (p < 0.05) prediction error as compared to the currently available method. Furthermore, we investigate whether there exists a reference scapula that performs significantly better than other scapulae when used for transformation of muscle attachment sites. Seven different scapulae were used as reference scapula and their resulting transformation errors were compared with each other. In the considered statistical population, no such a thing as an ideal scapula was found. There was, however, one outlier scapula that performed significantly worse than the other scapulae when used as a reference. The effect of perturbations in both muscle attachment sites and other muscle properties is studied by comparing muscle force predictions of a musculoskeletal model between perturbed and non-perturbed versions of the model. It is found that 10 mm variations in muscle attachments have more significant effect on muscle force predictions than 10% variations in any of the other four analysed muscle properties.     

Using a cost function based on kinematics and electromyographic data to quantify muscle forces

A reliable evaluation of muscle forces in the human body is highly desirable for several applications in both clinical and research contexts. Several models of muscle force distribution based on non-invasive measurements have been proposed since 1836 (Weber and Weber, 1836), amongst which Crowninshield’s model (Crowninshield and Brand, 1981), which maximizes a cost-function representing the muscle fiber endurance, is the most popular. It is worth noting that Crowninshield’s model is the most widely adopted notwithstanding its major limitations of physiological coherence. Forster et al. (2004) pointed out that “these (conventional) criteria however do not predict co-contraction adequately”. Besides, electromyographic (EMG)-driven models have been proposed to assess individual muscle forces, which have not been broadly adopted due to their complexity and the need for a calibration before each test. In this context, a cost function based on kinematic and electromyographic data could provide the advantage of being physiologically more coherent with muscle activations compared to conventional cost-functions based on kinematics solely, and easier to use than the EMG-driven models. The objective of this study is to propose the first cost-function based on kinematics and electromyographic data to quantify muscle forces. When applying this new cost-function on a database of upper limb motions data of 17 subjects, healthy or with cerebral palsy, the muscle force prediction of the proposed model was 17.74% more coherent with the EMG pattern than the prediction of Crowninshield’s model. And on average, these results were more consistent whether the subjects were healthy or with cerebral palsy. In conclusion, we propose this cost-function for the quantification of muscle forces.     

Comparison between in vivo and theoretical bite performance: Using multi-body modelling to predict muscle and bite forces in a reptile skull

In biomechanical investigations, geometrically accurate computer models of anatomical structures can be created readily using computed-tomography scan images. However, representation of soft tissue structures is more challenging, relying on approximations to predict the muscle loading conditions that are essential in detailed functional analyses. Here, using a sophisticated multi-body computer model of a reptile skull (the rhynchocephalian Sphenodon), we assess the accuracy of muscle force predictions by comparing predicted bite forces against in vivo data. The model predicts a bite force almost three times lower than that measured experimentally. Peak muscle force estimates are highly sensitive to fibre length, muscle stress, and pennation where the angle is large, and variation in these parameters can generate substantial differences in predicted bite forces. A review of theoretical bite predictions amongst lizards reveals that bite forces are consistently underestimated, possibly because of high levels of muscle pennation in these animals. To generate realistic bites during theoretical analyses in Sphenodon, lizards, and related groups we suggest that standard muscle force calculations should be multiplied by a factor of up to three. We show that bite forces increase and joint forces decrease as the bite point shifts posteriorly within the jaw, with the most posterior bite location generating a bite force almost double that of the most anterior bite. Unilateral and bilateral bites produced similar total bite forces; however, the pressure exerted by the teeth is double during unilateral biting as the tooth contact area is reduced by half.     

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.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

Soft tissue structures resisting anterior instability in a computational glenohumeral joint model

The glenohumeral joint is the most dislocated joint in the body due to the lack of bony constraints and the dependence on soft tissue for stability. The roles that various structures provide to joint function are important for understanding injury treatment and orthopaedic device design purposes. The goal of this study was to develop a computational model of the glenohumeral joint whereby joint behaviour was dictated by articular contact, ligamentous constraints, muscle loading and external perturbations. The bone structure of the computational model consisted of assembled computer tomographic images of the scapula, humerus and clavicle. The soft tissue elements were composed of forces and tension-only springs that represented muscles and ligaments. Validation of this model was achieved by comparing computational predictions to the results of a cadaveric experiment in which the relative contribution of muscles and ligaments to anterior joint stability was examined. The computational model predicted an anterior subluxation force that was similar to the cadaveric experimental results in humeral external rotation. The individual structure results showed the subscapularis to be critical to stabilisation in both neutral and external rotations, the biceps stabilised the joint in neutral but not in external rotation, and the inferior glenohumeral ligament resisted anterior displacement only in external rotation. The model's predictions were similar to the conclusions of the cadaveric experiment and the literature. Knowledge gained from this type of model could assist in further understanding the contribution of soft tissue stabilisers to joint function, pre-operative planning or the design of orthopaedic implants.