Muscle activity in rapid multi-degree-of-freedom elbow movements: solutions from a musculoskeletal model

The activity of certain muscles that cross the elbow joint complex (EJC) are affected by forearm position and forearm movement during elbow flexion/extension. To investigate whether these changes are based on the musculoskeletal geometry of the joint, a three-dimensional musculotendinoskeletal computer model of the EJC was used to estimate individual muscle activity in multi-degree-of-freedom (df) rapid (ballistic) elbow movements. It is hypothesized that this model could reproduce the major features of elbow muscle activity during multi-df elbow movements using dynamic optimal control theory, given a minimum-time performance criterion. Results from the model are presented and verified with experimental kinematic and electromyographic data from movements that involved both one-df elbow flexion/extension and two-df flexion/extension with forearm pronation/supination. The model demonstrated how the activity of particular muscles is affected by both forearm position and movement, as measured in these experiments and as previously reported by others. These changes were most evident in the flexor muscles and least evident in the extensor muscles. The model also indicated that, for specific one- and two-df movements, activating a muscle that is antagonistic or noncontributory to the movement could reduce the movement time. The major features of muscle activity in multi-df elbow movements appear to be highly dependent on the joint's musculoskeletal geometry and are not strictly based on neural influences or neuroanatomical substrates. Received: 9 May 1997 / Accepted in revised form: 8 December 1998     

In vivo assessment of elbow flexor work and activation during stretch-shortening cycle tasks.

The purpose of this study was to use an electromyography (EMG) based muscle model to investigate the performance enhancement of stretch-shortening cycle (SSC) tasks at different elbow flexion-extension velocities. A torque motor was used to oscillate the forearms of seven healthy male subjects (23-40 years) during SSC and non-SSC contractions at four frequencies of movement (.58, 1.5, 2.4 and 3.3Hz) over a range of 105 degrees -162 degrees of elbow extension. The torque was integrated as a function of joint angle to yield the work produced by the elbow flexors. The elbow flexors were transcutaneously stimulated with a voltage equivalent to 60% maximum voluntary isometric contraction torque for 4s at 50Hz. EMG of the elbow flexors and extensors was recorded from the biceps and triceps respectively. The processed EMG was used to drive a Hill based model to predict the torque of the elbow flexors. Results indicate that muscle work increases from non-SSC to SSC trials. Work decreases for SSC and non-SSC trials with increasing velocity. The simulated constant activation muscle model predicted work well for all trials and conditions, indicating muscle model accuracy. The EMG driven model predicted well for all non-SSC trials, but significantly underestimated the work for SSC tasks, suggesting that the contractile component is directly involved in optimising muscle work during SSC tasks.     

Shoulder muscle function depends on elbow joint position: an illustration of dynamic coupling in the upper limb

Shoulder muscle function has been documented based on muscle moment arms, lines of action and muscle contributions to contact force at the glenohumeral joint. At present, however, the contributions of individual muscles to shoulder joint motion have not been investigated, and the effects of shoulder and elbow joint position on shoulder muscle function are not well understood. The aims of this study were to compute the contributions of individual muscles to motion of the glenohumeral joint during abduction, and to examine the effect of elbow flexion on shoulder muscle function. A three-dimensional musculoskeletal model of the upper limb was used to determine the contributions of 18 major muscles and muscle sub-regions of the shoulder to glenohumeral joint motion during abduction. Muscle function was found to depend strongly on both shoulder and elbow joint positions. When the elbow was extended, the middle and anterior deltoid and supraspinatus were the greatest contributors to angular acceleration of the shoulder in abduction. In contrast, when the elbow was flexed at 90°, the anterior deltoid and subscapularis were the greatest contributors to joint angular acceleration in abduction. This dependence of shoulder muscle function on elbow joint position is explained by the existence of dynamic coupling in multi-joint musculoskeletal systems. The extent to which dynamic coupling affects shoulder muscle function, and therefore movement control, is determined by the structure of the inverse mass matrix, which depends on the configuration of the joints. The data provided may assist in the diagnosis of abnormal shoulder function, for example, due to muscle paralysis or in the case of full-thickness rotator cuff tears.     

Dependence of elbow joint stiffness measurements on speed,angle, and muscle contraction level

Elbow joint stiffness is critical to positioning the hand. Abnormal elbow joint stiffness may affect a person's ability to participate in activities of daily living. In this work, elbow joint stiffness was measured in ten healthy young adults with a device adapted from one previously used to measure stiffness in other joints. Measurements of elbow stiffness involved applying a constant-velocity rotational movement to the elbow and measuring the resultant displacement, torque, and acceleration. Elbow stiffness was then computed using a previously-established model for joint stiffness. Measurements were made at two unique elbow joint angles, two speeds, and two forearm muscle contraction levels. The results indicate that the elbow joint stiffness is significantly affected by both rotational speed and forearm muscle contraction level.     

Feasibility of using EMG driven neuromusculoskeletal model for prediction of dynamic movement of the elbow.

Neuromusculoskeletal (NMS) modeling is a valuable tool in orthopaedic biomechanics and motor control research. To evaluate the feasibility of using electromyographic (EMG) signals with NMS modeling to estimate individual muscle force during dynamic movement, an EMG driven NMS model of the elbow was developed. The model incorporates dynamical equation of motion of the forearm, musculoskeletal geometry and musculotendon modeling of four prime elbow flexors and three prime elbow extensors. It was first calibrated to two normal subjects by determining the subject-specific musculotendon parameters using computational optimization to minimize the root mean square difference between the predicted and measured maximum isometric flexion and extension torque at nine elbow positions (0-120 degrees of flexion with an increment of 15 degrees ). Once calibrated, the model was used to predict the elbow joint trajectories for three flexion/extension tasks by processing the EMG signals picked up by both surface and fine electrodes using two different EMG-to-activation processing schemes reported in the literature without involving any trajectory fitting procedures. It appeared that both schemes interpreted the EMG somewhat consistently but their prediction accuracy varied among testing protocols. In general, the model succeeded in predicting the elbow flexion trajectory in the moderate loading condition but over-drove the flexion trajectory under unloaded condition. The predicted trajectories of the elbow extension were noted to be continuous but the general shape did not fit very well with the measured one. Estimation of muscle activation based on EMG was believed to be the major source of uncertainty within the EMG driven model. It was especially so apparently when fine wire EMG signal is involved primarily. In spite of such limitation, we demonstrated the potential of using EMG driven neuromusculoskeletal modeling for non-invasive prediction of individual muscle forces during dynamic movement under certain conditions.     

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.     

Theoretical and experimental behaviour of the muscle viscosity coefficient during maximal concentric actions

The aim of this study was to calculate the theoretical variation of the nonlinear damping factor (B) as a function of the muscle shortening velocity, and then to compare the theoretical values with the experimental data obtained on both the elbow flexor and the ankle extensor muscles. The theoretical variation of the B factor was determined from a muscle model consisting of a contractile component in parallel with a viscous damper both in series with an elastic component, and by using, the charateristic equation of the force velocity curve. In this muscle model, the viscous element modelled the inability of the muscle to generate as big a contracting force (while shortening) as possible under isometric conditions. Eight volunteer subjects performed maximal concentric elbow flexions and ankle extensions on an isokinetic ergometer at angular velocities of 60, 120, 180, 240, 300 and 360°·s^–1, and held two maximal isometric actions at an elbow angle of 90° (0° corresponds to the full extension) and at an ankle angle of 0° (0° corresponds to the foot flexion of 90° relative to the leg axis). From these measurements, the force and the shortening velocity values of each muscle were determined by using a musculo-skeletal model of the joint. The results showed that the theoretical behaviour of the B factor would seem to be dependent on the shortening velocity and on the parameter which varies according to the muscle fibre type composition and affects the curvature of the force-velocity curve (a_f). For each muscle group, the experimental data of B fitted with the theoretical equation, and the best fit was obtained for an of of 0.28 for the ankle extensor and of 0.32 for the elbow flexor muscles. These results indicated that from the muscle model used in the present study it is possible to describe the mechanical behaviour of the muscle during maximal concentric action.     

Physiological considerations of muscle force through the elbow joint

An analytical model for the determination of muscle forces across the elbow joint during isometric loading conditions has been developed. The model incorporates the muscle length-tension relationship, while considering the muscle architecture. Sensitivity analyses were performed to study the effects of the geometric and architectural factors of the muscles on the distribution of muscle forces.     

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors ( < 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.     

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors (< 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.     

Individual muscle force parameters and fiber operating ranges for elbow flexion-extension and forearm pronation-supination

We have quantified individual muscle force and moment contributions to net joint moments and estimated the operating ranges of the individual muscle fibers over the full range of motion for elbow flexion/extension and forearm pronation/supination. A three dimensional computer graphics model was developed in order to estimate individual muscle contributions in each degree of freedom over the full range of motion generated by 17 muscles crossing the elbow and forearm. Optimal fiber length, tendon slack length, and muscle specific tension values were adjusted within the literature range from cadaver studies such that the net isometric joint moments of the model approximated experimental joint moments within one standard deviation. Analysis of the model revealed that the muscles operate on varying portions of the ascending limb, plateau region, and descending limb of the force-length curve. This model can be used to further understand isometric force and moment contributions of individual muscles to net joint moments of the arm and forearm and can serve as a comprehensive reference for the forces and moments generated by 17 major muscles crossing the elbow and wrist.     

A technical method using musculoskeletal model to analyse dynamic properties of muscles during human movement

An effective way to avoid invading or injuring the subjects is to use the musculoskeletal model when studying the dynamic properties of muscles in vivo. So, we put forward a joint coordinate system-based method, which mainly focuses on the coordinate's transformation of corresponding muscle attachment points, respectively, in the model and the subject in order to reproduce the movement of the subject on the model. As muscle moment arm is usually used to evaluate the dynamic properties of muscles, the moment arms in elbow flexion for each of the major muscles crossing the elbow in 50 healthy subjects (25 males and 25 females), ranging in height from 1.50 to 1.80 m (mean 1.6542 m) are calculated and compared with the measured data obtained from anatomical studies reported in the literature. The trends of the value basically coincide with each other. So, this novel method can be valid.     

The utility of an empirically derived co-activation ratio for muscle force prediction through optimization

Biomechanical optimization models that apply efficiency-based objective functions often underestimate or negate antagonist co-activation. Co-activation assists movement control, joint stabilization and limb stiffness and should be carefully incorporated into models. The purposes of this study were to mathematically describe co-activation relationships between elbow flexors and extensors during isometric exertions at varying intensity levels and postures, and secondly, to apply these co-activation relationships as constraints in an optimization muscle force prediction model of the elbow and assess changes in predictions made while including these constraints. Sixteen individuals performed 72 isometric exertions while holding a load in their right hand. Surface EMG was recorded from elbow flexors and extensors. A co-activation index provided a relative measure of flexor contribution to total activation about the elbow. Parsimonious models of co-activation during flexion and extension exertions were developed and added as constraints to a muscle force prediction model to enforce co-activation. Three different PCSA data sets were used. Elbow co-activation was sensitive to changes in posture and load. During flexion exertions the elbow flexors were activated about 75% MVC (this amount varied according to elbow angle, shoulder flexion and abduction angles, and load). During extension exertions the elbow flexors were activated about 11% MVC (this amount varied according to elbow angle, shoulder flexion angle and load). The larger PCSA values appeared to be more representative of the subject pool. Inclusion of these co-activation constraints improved the model predictions, bringing them closer to the empirically measured activation levels.     

Estimation of muscle response using three-dimensional musculoskeletal models before impact situation: a simulation study

When car crash experiments are performed using cadavers or dummies, the active muscles' reaction on crash situations cannot be observed. The aim of this study is to estimate muscles' response of the major muscle groups using three-dimensional musculoskeletal model by dynamic simulations of low-speed sled-impact. The three-dimensional musculoskeletal models of eight subjects were developed, including 241 degrees of freedom and 86 muscles. The muscle parameters considering limb lengths and the force-generating properties of the muscles were redefined by optimization to fit for each subject. Kinematic data and external forces measured by motion tracking system and dynamometer were then input as boundary conditions. Through a least-squares optimization algorithm, active muscles' responses were calculated during inverse dynamic analysis tracking the motion of each subject. Electromyography for major muscles at elbow, knee, and ankle joints was measured to validate each model. For low-speed sled-impact crash, experiment and simulation with optimized and unoptimized muscle parameters were performed at 9.4 m/h and 10 m/h and muscle activities were compared among them. The muscle activities with optimized parameters were closer to experimental measurements than the results without optimization. In addition, the extensor muscle activities at knee, ankle, and elbow joint were found considerably at impact time, unlike previous studies using cadaver or dummies. This study demonstrated the need to optimize the muscle parameters to predict impact situation correctly in computational studies using musculoskeletal models. And to improve accuracy of analysis for car crash injury using humanlike dummies, muscle reflex function, major extensor muscles' response at elbow, knee, and ankle joints, should be considered.     

A technical method using musculoskeletal model to analyse dynamic properties of muscles during human movement

An effective way to avoid invading or injuring the subjects is to use the musculoskeletal model when studying the dynamic properties of muscles in vivo. So, we put forward a joint coordinate system-based method, which mainly focuses on the coordinate's transformation of corresponding muscle attachment points, respectively, in the model and the subject in order to reproduce the movement of the subject on the model. As muscle moment arm is usually used to evaluate the dynamic properties of muscles, the moment arms in elbow flexion for each of the major muscles crossing the elbow in 50 healthy subjects (25 males and 25 females), ranging in height from 1.50 to 1.80 m (mean 1.6542 m) are calculated and compared with the measured data obtained from anatomical studies reported in the literature. The trends of the value basically coincide with each other. So, this novel method can be valid.     

Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models

A geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion/extension, forearm pronation/supination, wrist flexion/extension and radial/ulnar deviation. Model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature. Coefficients of polynomial equations were calculated for all moment arms as functions of joint angle, with special consideration to coupled muscles as a function of two joint angles. Additionally, a “normalized potential moment (NPM)” contribution index for each muscle across the elbow and wrist joints in four degrees-of-freedom was determined using each muscle's normalized physiological cross-sectional area (PCSA) and peak moment arm (MA). We hypothesize that (a) a geometric model of the elbow and wrist joints can represent the major attributes of MA versus joint angle from many literature sources of cadaver and model data and (b) an index can represent each muscle's normalized moment contribution to each degree-of-freedom at the elbow and wrist. We believe these data serve as a simple, yet comprehensive, reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance.     

The relationship between two different mechanical cost functions and muscle oxygen consumption

Inverse-dynamic models often use cost functions to solve the load-sharing problem. Although it is often assumed that energy is minimised, most cost functions are based on mechanically related measures like muscle force or stress. The aim of this study was to analyse the relationships of two cost functions with experimentally determined data on muscle energy consumption. Four subjects performed isometric contractions generating combinations of elbow flexion/extension and pro/supination moments. Muscle oxygen consumption (VO2) of the m. biceps breve, m. biceps longum, m. brachioradialis and m. triceps laterale was measured with near infrared spectroscopy. Both cost functions were implemented into an existing inverse-dynamic shoulder and elbow model and the individual cost values per muscle were calculated, normalised and subsequently compared to experimental VO2 values. The minimum stress cost function led to a good correspondence between VO2 and cost for the m. triceps laterale but for the flexor muscles cost was significantly lower. A newly proposed energy-related cost function showed, however, a far better correspondence. The inclusion of a linear term and muscle mass in the new criterion led model results to correspond better to experimental results. The energy-related cost function appeared to be a better measure for muscle energy consumption than the stress cost function and led to more realistic predictions of muscle activation.     

The role of the biceps brachii in shoulder elevation.

The biceps brachii is a bi-articular muscle affecting motion at the shoulder and elbow. While its' action at the elbow is well documented, its role in shoulder elevation is less clear. Therefore, the purpose of this project was to investigate the influence of shoulder and elbow joint angles on the shoulder elevation function of the biceps brachii. Twelve males and 18 females were tested on a Biodex dynamometer with the biceps brachii muscle selectively stimulated at a standardized level of voltage. The results indicated that both shoulder and elbow joint angles influence the shoulder joint elevation moment produced by the biceps brachii. Further analysis revealed that the elevation moment was greatest with the shoulder joint at 0 degrees and the elbow flexed 30 degrees or less. The greatest reduction in the elevation moment occurred between shoulder angles of 0 degrees and 30 degrees . The shoulder elevation moment was near zero when shoulder elevation reached or exceeded 60 degrees regardless of elbow angle. These results clarify the role of the biceps in shoulder elevation, as a dynamic stabilizer, and suggest that it is a decelerator of the arm during the throwing motion.     

Use of the latissimus dorsi muscle to restore elbow flexion in arthrogryposis

The successful use of ipsilateral pedicle latissimus dorsi muscle to restore elbow flexion in a child with arthrogryposis multiplex congenita is described. In appropriately selected patients, use of the latissimus dorsi muscle for elbow flexor reconstruction is a strong, reliable flexorplasty without significant donor-site morbidity.     

Simulated active control produces repeatable motion pathways of the elbow in an in vitro testing system.

The purpose of this study was to determine if the repeatability and pattern of elbow kinematics are affected by changing the relative magnitudes of loads applied to muscles around the elbow in vitro. In eight cadaveric upper extremities, passive and three methods of simulated active elbow flexion were tested with the forearm maintained in both pronation and supination. Passive flexion involved moving the elbow manually through a full arc of motion. Simulated active flexion used a custom designed loading system to generate elbow motion by applying loads to various tendons via pneumatic actuators. Three different simulated active loading protocols, with loading ratios based on muscle activity and physiologic cross-sectional area, were tested. Testing was performed initially on an intact elbow, and then an unstable elbow model created by transection of the lateral collateral ligament (i.e. the radial and lateral ulnar collateral ligaments). An electromagnetic tracking device was used to measure rotation of the ulna relative to the humerus. Varus-valgus angulation and internal-external rotation were less repeatable during passive flexion than simulated active flexion, regardless of the loading ratio used, in both the intact (p<0.05) and unstable (p<0.05) elbows. Throughout the arc of flexion, the motion pathways were similar for the three simulated active motion protocols employed in this study (p>0.05). The pathways followed during passive motion were different from those generated with simulated active motion, especially in the unstable elbow with the forearm supinated (p<0.001). These results suggest that using simulated active motion rather than manual passive motion can improve the repeatability of elbow kinematics generated in the laboratory, and that a wide range of muscle loading ratios may produce similar kinematic output.