A fuzzy-genetic model for estimating forces from electromyographical activity of antagonistic muscles due to planar lower arm movements: the effect of nonlinear muscle properties

The aim of this paper is to create a model for mapping the surface electromyogram (EMG) signals to the force that generated by human arm muscles. Because the parameters of each person's muscle are individual, the model of the muscle must have two characteristics: (1) The model must be adjustable for each subject. (2) The relationship between the input and output of model must be affected by the force-length and the force-velocity behaviors are proven through Hill's experiments. Hill's model is a kinematic mechanistic model with three elements, i.e. one contractile component and two nonlinear spring elements.In this research, fuzzy systems are applied to improve the muscle model. The advantages of using fuzzy system are as follows: they are robust to noise, they prove an adjustable nonlinear mapping, and are able to model the uncertainties of the muscle.Three fuzzy coefficients have been added to the relationships of force-length (active and passive) and force-velocity existing in Hill's model. Then, a genetic algorithm (GA) has been used as a biological search method that can adjust the parameters of the model in order to achieve the optimal possible fit.Finally, the accuracy of the fuzzy genetic implementation Hill-based muscle model (FGIHM) is invested as following: the FGIHM results have 12.4% RMS error (in worse case) in comparison to the experimental data recorded from three healthy male subjects. Moreover, the FGIHM active force-length relationship which is the key characteristics of muscles has been compared to virtual muscle (VM) and Zajac muscle model. The sensitivity of the FGIHM has been evaluated by adding a white noise with zero mean to the input and FGIHM has proved to have lower sensitivity to input noise than the traditional Hill's muscle model.     

A mathematical musculoskeletal shoulder model for proactive ergonomic analysis

Occupational shoulder musculoskeletal injuries and disorders are common. Generally available shoulder work analysis tools do not offer insight into specific muscle load magnitudes that may indicate increased risk, nor do they address many concerns germane to job analysis. To address these issues, a biomechanical model of the shoulder was developed to include several critical components: the systematic inclusion of kinematic and kinetic effects, population scalability, geometric realism, an empirical glenohumeral constraint, and integration with digital ergonomics analysis software tools. This unique combination of features in a single model was explored through examination of both experimental and simulated data with the developed analysis tool. The utility of the model is discussed together with a review of its specific strengths and weaknesses, and the potential for its future use in proactive ergonomic analyses and workplace simulations.     

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.     

Exploring novel objective functions for simulating muscle coactivation in the neck

Musculoskeletal modeling allows for analysis of individual muscles in various situations. However, current techniques to realistically simulate muscle response when significant amounts of intentional coactivation is required are inadequate. This would include stiffening the neck or spine through muscle coactivation in preparation for perturbations or impacts. Muscle coactivation has been modeled previously in the neck and spine using optimization techniques that seek to maximize the joint stiffness by maximizing total muscle activation or muscle force. These approaches have not sought to replicate human response, but rather to explore the possible effects of active muscle. Coactivation remains a challenging feature to include in musculoskeletal models, and may be improved by extracting optimization objective functions from experimental data. However, the components of such an objective function must be known before fitting to experimental data. This study explores the effect of components in several objective functions, in order to recommend components to be used for fitting to experimental data. Four novel approaches to modeling coactivation through optimization techniques are presented, two of which produce greater levels of stiffness than previous techniques. Simulations were performed using OpenSim and MATLAB cooperatively. Results show that maximizing the moment generated by a particular muscle appears analogous to maximizing joint stiffness. The approach of optimizing for maximum moment generated by individual muscles may be a good candidate for developing objective functions that accurately simulate muscle coactivation in complex joints. This new approach will be the focus of future studies with human subjects.     

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.     

A hill-type muscle model expansion accounting for effects of varying transverse muscle load

Recent studies demonstrated that uniaxial transverse loading (F_G) of a rat gastrocnemius medialis muscle resulted in a considerable reduction of maximum isometric muscle force (ΔF_im). A hill-type muscle model assuming an identical gearing G between both ΔF_im and F_G as well as lifting height of the load (Δh) and longitudinal muscle shortening (Δl_CC) reproduced experimental data for a single load.Here we tested if this model is able to reproduce experimental changes in ΔF_im and Δh for increasing transverse loads (0.64 N, 1.13 N, 1.62 N, 2.11 N, 2.60 N). Three different gearing ratios were tested: (I) constant G_c representing the idea of a muscle specific gearing parameter (e.g. predefined by the muscle geometry), (II) G_exp determined in experiments with varying transverse load, and (III) G_f that reproduced experimental ΔF_im for each transverse load.Simulations using G_c overestimated ΔF_im (up to 59%) and Δh (up to 136%) for increasing load. Although the model assumption (equal G for forces and length changes) held for the three lower loads using G_exp and G_f, simulations resulted in underestimation of ΔF_im by 38% and overestimation of Δh by 58% for the largest load, respectively. To simultaneously reproduce experimental ΔF_im and Δh for the two larger loads, it was necessary to reduce F_im by 1.9% and 4.6%, respectively. The model seems applicable to account for effects of muscle deformation within a range of transverse loading when using a linear load-dependent function for G.     

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90° in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.     

A simplified sliding-filament muscle model for simulation purposes

A muscle model based on the sliding filament concept is put forward. The model is simplified in such a way that it may easily be simulated on a computer (analog or digital). The model shows quite a few muscle properties rather well e.g. Hill's relation, quick-stretch and quick-release series elasticity and some dynamic transfer properties. It is found that, using an antagonistic muscle model pair and an appropriate load, realistic arm movements can be simulated.     

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 agonist and antagonist muscle strength in performance of rapid movements

Six subjects performed rapid self-terminated elbow movements under different mechanical conditions prior to, and 5 weeks after an elbow extensor strengthening programme. Despite the large difference in the strengths of elbow flexors and extensors, the pretest did not demonstrate significant differences between the movement time of flexion and extension movements performed under the same mechanical conditions. The results obtained in the posttest demonstrated a decrease in movement time (i.e. an increase in movement speed) in both elbow flexion and extension movements under some mechanical conditions. In addition, flexion movements demonstrated a relative increase in the acceleration time (acceleration time as a proportion of the movement time). It was concluded that the strength of both the agonist and antagonist muscles was important for the performance of rapid movements. Stronger agonists could increase the acceleration of the limb being moved, while stronger antagonists could facilitate the arrest of the limb movement in a shorter time, providing a longer time for acceleration.     

Influence of long-latency reflex modulation on the performance of quick adjustment movements

The effect of long-latency reflex modulation on the performance of a quick adjustment movement following a muscle stretch was studied in 26 healthy male subjects. When the subjects felt a sudden angle displacement in the direction of a wrist extension they were required to make an adjustment movement by moving a handlebar, held in the hand, to align with a target position as quickly and as accurately as possible. The index of performance (adjustment time) was the time taken to move the handle to the target position from stretch onset. A DC torque motor was used to evoke electromyographic (EMG) reflex responses on a wrist flexor. Averaging of the rectified EMG, recorded from surface electrodes placed over the flexor, showed short- and long-latency reflexes (M1 and M2 components). For all subjects, the amplitudes of the reflex components decreased during the adjustment movement because the target position for this study was fixed to the extension side of the wrist joint. The decrease in the M2 component, which is considered to be a transcortical reflex, was significantly larger than the decrease in the M1 component, which is spinal reflex. The main finding was of a positive correlation between the length of adjustment time and the degree of reduction of M1 and M2 with the adjustment movement (r = 0.602 for M1, P < 0.01; r = 0.850 for M2, P < 0.001). Moreover, there were correlations between the consistency of the voluntary response onset and the degree of M2 decrease (r = 0.577, P < 0.01), and between the consistency of the voluntary response onset and the length of the adjustment time (r = 0.603, P < 0.01). Therefore, we have concluded that the subjects who were able to perform adjustment movements within a short time could modulate the long-latency reflex of the muscle involved in such movements in order to make the function of their voluntary muscle activity more effective, and thus were able to respond appropriately. Accepted: 19 February 1997     

Effect of vibration magnitude, vibration spectrum and muscle tension on apparent mass and cross axis transfer functions during whole-body vibration exposure

Twelve seated male subjects were exposed to 15 vibration conditions to investigate the nature and mechanisms of the non-linearity in biomechanical response. Subjects were exposed to three groups of stimuli: Group A comprised three repeats of random vertical vibration at 0.5, 1.0 and 1.5 m s⁻² r.m.s. with subjects sitting in a relaxed upright posture. Group B used the same vibration stimuli as Group A, but with subjects sitting in a ‘tense’ posture. Group C used vibration where the vibration spectrum was dominated by either low-frequency motion (2–7 Hz), high-frequency motion (7–20 Hz) or a 1.0 m s⁻² r.m.s. sinusoid at the frequency of the second peak in apparent mass (about 10–14 Hz) added to 0.5 m s⁻² r.m.s. random vibration. In the relaxed posture, frequencies of the primary peak in apparent mass decreased with increased vibration magnitude. In the tense posture, the extent of the non-linearity was reduced. For the low-frequency dominated stimulus, the primary peak frequency was lower than that for the high-frequency dominated stimulus indicating that the frequency of the primary peak in the apparent mass is dominated by the magnitude of the vibration encompassing the peak. Cross-axis transfer functions showed peaks of about 15–20% and 5% of the magnitudes of the peaks in the apparent mass for x- and y-direction transfer functions, respectively, in the relaxed posture. In the tense posture, cross-axis transfer functions reduced in magnitude with increased vibration, likely indicating a reduced fore-aft pitching of the body with increased tension, supporting the hypothesis that pitching contributes to the non-linearity in apparent mass.     

A muscle controlled finite-element model of laryngeal abduction and adduction

A three-dimensional finite-element model was developed to simulate the complex movement of the laryngeal cartilages during vocal fold abduction and adduction. The model consists of cricoid and arytenoid cartilages, as well as the intralaryngeal muscles and vocal folds. The active and passive properties of the muscles were idealised by one-dimensional elements based on the Hill theory. Its controlling input value is a time dependent stimulation rate. Optimisation loops have been carried out for the arrangement of the individual stimulation rates. Since in vivo measurements are not feasible, the developed biomechanical model shall be used to analyse the force distribution within the laryngeal muscles during phonatory manoeuvres. Simulations of abduction and adduction in different pitches of voice lead to realistic tensions of the vocal folds. The model is a first step to analyse motional vocal fold diseases and to predict the consequences of phonosurgical interventions.     

A three-dimensional model of the rat hindlimb: musculoskeletal geometry and muscle moment arms

As a first step towards developing a dynamic model of the rat hindlimb, we measured muscle attachment and joint center coordinates relative to bony landmarks using stereophotogrammetry. Using these measurements, we analyzed muscle moment arms as functions of joint angle for most hindlimb muscles, and tested the hypothesis that postural change alone is sufficient to alter the function of selected muscles of the leg. We described muscle attachment sites as second-order curves. The length of the fit parabola and residual errors in the orthogonal directions give an estimate of muscle attachment sizes, which are consistent with observations made during dissection. We modeled each joint as a moving point dependent on joint angle; relative endpoint errors less than 7% indicate this method as accurate. Most muscles have moment arms with a large range across the physiological domain of joint angles, but their moment arms peak and vary little within the locomotion domain. The small variation in moment arms during locomotion potentially simplifies the neural control requirements during this phase. The moment arms of a number of muscles cross zero as angle varies within the quadrupedal locomotion domain, indicating they are intrinsically stabilizing. However, in the bipedal locomotion domain, the moment arms of these muscles do not cross zero and thus are no longer intrinsically stabilizing. We found that muscle function is largely determined by the change in moment arm with joint angle, particularly the transition from quadrupedal to bipedal posture, which may alter an intrinsically stabilizing arrangement or change the control burden.     

Three-dimensional temporomandibular joint muscle attachment morphometry and its impacts on musculoskeletal modeling

In musculoskeletal models of the human temporomandibular joint (TMJ), muscles are typically represented by force vectors that connect approximate muscle origin and insertion centroids (centroid-to-centroid force vectors). This simplification assumes equivalent moment arms and muscle lengths for all fibers within a muscle even with complex geometry and may result in inaccurate estimations of muscle force and joint loading. The objectives of this study were to quantify the three-dimensional (3D) human TMJ muscle attachment morphometry and examine its impact on TMJ mechanics. 3D muscle attachment surfaces of temporalis, masseter, lateral pterygoid, and medial pterygoid muscles of human cadaveric heads were generated by co-registering measured attachment boundaries with underlying skull models created from cone-beam computerized tomography (CBCT) images. A bounding box technique was used to quantify 3D muscle attachment size, shape, location, and orientation. Musculoskeletal models of the mandible were then developed and validated to assess the impact of 3D muscle attachment morphometry on joint loading during jaw maximal open-close. The 3D morphometry revealed that muscle lengths and moment arms of temporalis and masseter muscles varied substantially among muscle fibers. The values calculated from the centroid-to-centroid model were significantly different from those calculated using the ‘Distributed model’, which considered crucial 3D muscle attachment morphometry. Consequently, joint loading was underestimated by more than 50% in the centroid-to-centroid model. Therefore, it is necessary to consider 3D muscle attachment morphometry, especially for muscles with broad attachments, in TMJ musculoskeletal models to precisely quantify the joint mechanical environment critical for understanding TMJ function and mechanobiology.     

Effect of electrical stimulation-induced muscle force and streptomycin treatment on muscle and trabecular bone mass in early-stage disuse musculoskeletal atrophy

Objectives:

The aim was to determine whether daily muscle electrical stimulation (ES) and streptomycin treatment would have positive or negative effects on trabecular bone mass in disuse rats.

Methods:

Seven-week-old male F344 rats were randomly divided into five groups of eight animals each: an age-matched control group (CON); a sciatic denervation group (DN); a DN + direct electrical stimulation group (DN+ES); a DN + streptomycin treatment group (DN+SM); and a DN+ES+SM group. The tibialis anterior (TA) muscles in all ES groups were stimulated with 16mA at 10Hz for 30 min/day, six days/week, for one week. Bone volume and structure were evaluated using micro-CT, and histological examinations of the tibiae were performed.

Results:

Direct ES significantly reduced the disuse-induced trabecular bone loss. Osteoid thickness were also significantly greater in the ES groups than in the DN group. Micro CT and histomorphological parameters were significantly lower in the DN+ES+SM group than in the DN+ES group, while there were no significant differences between the DN and DN+SM groups.

Conclusions:

These results suggest that ES-induced muscle force reduced trabecular bone loss, and streptomycin treatment did not induce bone loss, but attenuated the effects of ES-induced muscle force on reducing the loss of disused bone.     

Distribution of prolyl oligopeptidase in the mouse whole-body sections and peripheral tissues

Prolyl oligopeptidase (POP) is a serine endopeptidase that hydrolyses proline-containing peptides shorter than 30-mer, including many bioactive peptides. The distribution of POP in the brain has been studied but little is known about the distribution of peripheral POP. We used immunohistochemistry to localize POP in mouse whole-body sections and at the cellular level in peripheral tissues. Furthermore, we used a POP activity assay to reveal the associations between POP protein and its enzymatic activity. The highest POP protein densities were found in brain, kidney, testis and thymus, but in the liver the amounts of POP protein were small. There were remarkable differences between the distribution of POP protein and activity. The highest POP activities were found in the liver and testis while kidney had the lowest activity. In peripheral tissues, POP was present in various cell types both in the cytoplasm and nucleus of the cells, in contrast to the brain where no nuclear localization was detected. These findings support the proposed role of POP in cell proliferation in peripheral tissues. The dissociation of the distribution of POP protein and its enzymatic activity points to nonhydrolytic functions of POP and to strict endogenous regulation of POP activity.     

A dynamometer for evaluation of dynamic muscle work

The validation of a new dynamometer for evaluation of dynamic muscle work is presented. The device was based on a precise measurement of load displacements of any machine using gravitational loads as external resistance. It allowed, through a sensor consisting of an infrared photo interrupter, the calculation of velocity, force and power during concentric, eccentric and stretch-shortening cycle activity. To validate the dynamometer 33 male and female track and field athletes (12 throwers and 21 jumpers) participated in the study. The throwers (4 women and 8 men) were asked to perform half-squat exercises on a slide machine with a load of 100% of the subject's body mass. The day-to-day reproducibility of half-squat exercises gave a correlation coefficient ofr = 0.88, 0.97 and 0.95 for average push-off force (AF), average push-off velocity (AV), and average push-off power (AP) respectively. Comparison of half-squat measurements was performed against jumping and running test evaluation by the jumpers (7 women and 14 men). The interrelationships among the different variables studied demonstrated a strong correlation between AF, AV and AP and sprinting and jumping parameters (r = 0.53–0.97;P < 0.05–0.001). Using values of AF, AV and AP developed in half-squat exercises executed with different loads, ranging from 35% to 210% of the subject's body mass, it was also possible to establish the force-velocity and power-velocity relationships for both male and female jumpers. In any individual case, the maximal error due to the measurement system was calculated to be less than 0.3%, 0.9% and 1.2% for AF, AV, and AP respectively. Given the accuracy of the ergometer, the high reliability found between 2 days of measurements, and the specificity of the results it is suggested that the dynamic dynamometer would be suitable for evaluation of athletes performing specific skills. In addition, because single and multiple joint movements involving appropriate muscle groups can be easily performed, physiological characteristics could be evaluated for both athletic and rehabilitation purposes. Therefore, because of its simplicity of use and application, and its low cost the dynamometer would be suitable for both laboratory and field conditions.