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.     

A simulation analysis of the combined effects of muscle strength and surgical tensioning on lateral pinch force following brachioradialis to flexor pollicis longus transfer

Biomechanical simulations of tendon transfers performed following tetraplegia suggest that surgical tensioning influences clinical outcomes. However, previous studies have focused on the biomechanical properties of only the transferred muscle. We developed simulations of the tetraplegic upper limb following transfer of the brachioradialis (BR) to the flexor pollicis longus (FPL) to examine the influence of residual upper limb strength on predictions of post-operative transferred muscle function. Our simulations included the transfer, ECRB, ECRL, the three heads of the triceps, brachialis, and both heads of the biceps. Simulations were integrated with experimental data, including EMG and joint posture data collected from five individuals with tetraplegia and BR-FPL tendon transfers during maximal lateral pinch force exertions. Given a measured co-activation pattern for the non-paralyzed muscles in the tetraplegic upper limb, we computed the highest activation for the transferred BR for which neither the elbow nor the wrist flexor moment was larger than the respective joint extensor moment. In this context, the effects of surgical tensioning were evaluated by comparing the resulting pinch force produced at different muscle strength levels, including patient-specific scaling. Our simulations suggest that extensor muscle weakness in the tetraplegic limb limits the potential to augment total pinch force through surgical tensioning. Incorporating patient-specific muscle volume, EMG activity, joint posture, and strength measurements generated simulation results that were comparable to experimental results. Our study suggests that scaling models to the population of interest facilitates accurate simulation of post-operative outcomes, and carries utility for guiding and developing rehabilitation training protocols.     

Co-activation alters the linear versus non-linear impression of the EMG-torque relationship of trunk muscles

The use of electromyographic signals in the modeling of muscle forces and joint loads requires an assumption of the relationship between EMG and muscle force. This relationship has been studied for the trunk musculature and been shown to be predominantly non-linear, with more EMG producing less torque output at higher levels of activation. However, agonist-antagonist muscle co-activation is often substantial during trunk exertions, yet has not been adequately accounted for in determining such relationships. The purpose of this study was to revisit the EMG-moment relationship of the trunk recognizing the additional moment requirements necessitated due to antagonist muscle activity. Eight participants generated a series of isometric ramped trunk flexor and extensor moment contractions. EMG was recorded from 14 torso muscles, and the externally resisted moment was calculated. Agonist muscle moments (either flexor or extensor) were estimated from an anatomically detailed biomechanical model of the spine and fit to: the externally calculated moment alone; the externally calculated moment combined with the antagonist muscle moment. When antagonist activity was ignored, the EMG-moment relationship was found to be non-linear, similar to previous work. However, when accounting for the additional muscle torque generated by the antagonist muscle groups, the relationships became, in three of the four conditions, more linear. Therefore, it was concluded that antagonist muscle co-activation must be included when determining the EMG-moment relationship of trunk muscles and that previous impressions of non-linear EMG-force relationships should be revisited.     

A hybrid static optimisation method to estimate muscle forces during muscle co-activation

The general static optimisation (GSO) process is one of various muscle force estimation methods due to its low computational requirements. However, it can show biased muscle force estimation under muscle co-contraction. In the present study, we introduced a novel hybrid static optimisation (HSO) method to estimate reasonable muscle forces during muscle co-activation movements using more specific equality constraints, i.e. agonist and antagonist muscle moments predicted from a new correlation coefficient approach. The new method was evaluated for heel-rise movements. We found that the proposed method improved the potential of antagonist muscle force estimation in comparison to the GSO solutions. The proposed HSO method could be applied in biomechanics and rehabilitation, for example.     

A comparison of static and dynamic optimization muscle force predictions during wheelchair propulsion

The primary purpose of this study was to compare static and dynamic optimization muscle force and work predictions during the push phase of wheelchair propulsion. A secondary purpose was to compare the differences in predicted shoulder and elbow kinetics and kinematics and handrim forces. The forward dynamics simulation minimized differences between simulated and experimental data (obtained from 10 manual wheelchair users) and muscle co-contraction. For direct comparison between models, the shoulder and elbow muscle moment arms and net joint moments from the dynamic optimization were used as inputs into the static optimization routine. RMS errors between model predictions were calculated to quantify model agreement. There was a wide range of individual muscle force agreement that spanned from poor (26.4% F_max error in the middle deltoid) to good (6.4% F_max error in the anterior deltoid) in the prime movers of the shoulder. The predicted muscle forces from the static optimization were sufficient to create the appropriate motion and joint moments at the shoulder for the push phase of wheelchair propulsion, but showed deviations in the elbow moment, pronation–supination motion and hand rim forces. These results suggest the static approach does not produce results similar enough to be a replacement for forward dynamics simulations, and care should be taken in choosing the appropriate method for a specific task and set of constraints. Dynamic optimization modeling approaches may be required for motions that are greatly influenced by muscle activation dynamics or that require significant co-contraction.     

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.     

Relationships between individual isometric muscle forces, EMG activity and joint torque in monkeys

The aim of the present work was to determine the EMG activity and the moment of force developed by the main elbow flexor muscles, and to establish on this basis the degree of their participation in isometric contractions performed at various positions of the elbow. This was achieved by recording the following biomechanical parameters: EMG and tensile stress (or force) from biceps brachii (BB) and brachioradialis (BR); EMG from brachialis; external resultant force (FE). There was: a linear or quadratic relationship between the integrated EMG from each muscle and FE; a linear relationship between the force produced by BB or BR and FE. The slope of these relationships depended on the elbow angle, except for that between BB force and FE. It is proposed that iEMG changes compensate for those of the force lever arm. It has been calculated that the contribution of BR to external torque decreased from the extension to flexion while that of BB increased from 70 degrees to 90 degrees and then decreased. How far these data can be extrapolated to man is a matter of discussion based on iEMG and anthropometrical data.     

A phenomenological model and validation of shortening-induced force depression during muscle contractions

History-dependent effects on muscle force development following active changes in length have been measured in a number of experimental studies. However, few muscle models have included these properties or examined their impact on force and power output in dynamic cyclic movements. The goal of this study was to develop and validate a modified Hill-type muscle model that includes shortening-induced force depression and assess its influence on locomotor performance. The magnitude of force depression was defined by empirical relationships based on muscle mechanical work. To validate the model, simulations incorporating force depression were developed to emulate single muscle in situ and whole muscle group leg extension experiments. There was excellent agreement between simulation and experimental values, with in situ force patterns closely matching the experimental data (average RMS error <1.5 N) and force depression in the simulated leg extension exercise being similar in magnitude to experimental values (6.0% vs. 6.5%, respectively). To examine the influence of force depression on locomotor performance, simulations of maximum power pedaling with and without force depression were generated. Force depression decreased maximum crank power by 20–40%, depending on the relationship between force depression and muscle work used. These results indicate that force depression has the potential to substantially influence muscle power output in dynamic cyclic movements. However, to fully understand the impact of this phenomenon on human movement, more research is needed to characterize the relationship between force depression and mechanical work in large muscles with different morphologies.     

A three-compartment muscle fatigue model accurately predicts joint-specific maximum endurance times for sustained isometric tasks

The development of localized muscle fatigue has classically been described by the nonlinear intensity-endurance time (ET) curve (Rohmert, 1960; El Ahrache et al., 2006). These empirical intensity-ET relationships have been well-documented and vary between joint regions. We previously proposed a three-compartment biophysical fatigue model, consisting of compartments (i.e. states) for active (M(A)), fatigued (M(F)), and resting (M(R)) muscles, to predict the decay and recovery of muscle force (Xia and Frey Law, 2008). The purpose of this investigation was to determine optimal model parameter values, fatigue (F) and recovery (R), which define the "flow rate" between muscle states and to evaluate the model's accuracy for estimating expected intensity-ET curves. Using a grid-search approach with modified Monte Carlo simulations, over 1 million F and R permutations were used to predict the maximum ET for sustained isometric tasks at 9 intensities ranging from 10% to 90% of maximum in 10% increments (over 9 million simulations total). Optimal F and R values ranged from 0.00589 (F(ankle)) and 0.0182 (R(ankle)) to 0.00058 (F(shoulder)) and 0.00168 (R(shoulder)), reproducing the intensity-ET curves with low mean RMS errors: shoulder (2.7s), hand/grip (5.6s), knee (6.7s), trunk (9.3s), elbow (9.9s), and ankle (11.2s). Testing the model at different task intensities (15-95% maximum in 10% increments) produced slightly higher errors, but largely within the 95% prediction intervals expected for the intensity-ET curves. We conclude that this three-compartment fatigue model can be used to accurately represent joint-specific intensity-ET curves, which may be useful for ergonomic analyses and/or digital human modeling applications.     

Dynamic muscle force predictions from EMG: an artificial neural network approach

EMG signals of dynamically contracting muscle have never been used to predict experimentally known muscle forces across subjects. Here, we use an artificial neural network (ANN) approach to first derive an EMG–force relationship from a subset of experimentally determined EMGs and muscle forces; second, we use this relationship to predict individual muscle forces for different contractile conditions and in subjects whose EMG and force data were not used in the derivation of the EMG–force relationship; and third, we validate the predicted muscle forces against the known forces recorded in vivo. EMG and muscle forces were recorded from the cat soleus for a variety of locomotor conditions giving a data base from three subjects, four locomotor conditions, and 8–16 steps per subject and condition. Considering the conceptual differences in the tasks investigated (e.g. slow walking vs. trotting), the intra-subject results obtained here are superior to those published previously, even though the approach did not require a muscle model or the instantaneous contractile conditions as input for the force predictions. The inter-subject results are the first of this kind to be presented in the literature and they typically gave cross-correlation coefficients between actual and predicted forces of >0.90 and root mean square errors of <15%, thus they were considered excellent.

From the results of this study, it was concluded that ANNs represent a powerful tool to capture the essential features of EMG–force relationships of dynamically contracting muscle, and that ANNs might be used widely to predict muscle forces based on EMG signals.     

Human skeletal muscle fibre types and force: velocity properties

It has been reported that there is a relationship between power output and fibre type distribution in mixed muscle. The strength of this relationship is greater in the range of 3–8 rad · s^–1 during knee extension compared to slower or faster angular knee extensor speeds. A mathematical model of the force: velocity properties of muscle with various combinations of fast- and slow-twitch fibres may provide insight into why specific velocities may give better predictions of fibre type distribution. In this paper, a mathematical model of the force: velocity relationship for mixed muscle is presented. This model demonstrates that peak power and optimal velocity should be predictive of fibre distribution and that the greatest fibre type discrimination in human knee extensor muscles should occur with measurement of power output at an angular velocity just greater than 7 rad · s^–1. Measurements of torque: angular velocity relationships for knee extension on an isokinetic dynamometer and fibre type distribution in biopsies of vastus lateralis muscles were made on 31 subjects. Peak power and optimal velocity were determined in three ways: (1) direct measurement, (2) linear regression, and (3) fitting to the Hill equation. Estimation of peak power and optimal velocity using the Hill equation gave the best correlation with fibre type distribution (r > 0.5 for peak power or optimal velocity and percentage of fast-twitch fibres). The results of this study confirm that prediction of fibre type distribution is facilitated by measurement of peak power at optimal velocity and that fitting of the data to the Hill equation is a suitable method for evaluation of these parameters.     

Direct comparison of muscle force predictions using linear and nonlinear programming

Estimating forces in muscles and joints during locomotion requires formulations consistent with available methods of solving the indeterminate problem. Direct comparisons of results between differing optimization methods proposed in the literature have been difficult owing to widely varying model formulations, algorithms, input data, and other factors. We present an application of a new optimization program which includes linear and nonlinear techniques allowing a variety of cost functions and greater flexibility in problem formulation. Unified solution methods such as the one demonstrated here, offer direct evaluations of such factors as optimization criteria and constraints. This unified method demonstrates that nonlinear formulations (of the sort reported) allow more synergistic activity and in contrast to linear formulations, allow antagonistic activity. Concurrence of EMG activity and predicted forces is better with nonlinear predictions than linear predictions. The prediction of synergistic and antagonistic activity expectedly leads to higher joint force predictions. Relaxation of the requirement that muscles resolve the entire intersegmental moment maintains muscle synergism in the nonlinear formulation while relieving muscle antagonism and reducing the predicted joint contact force. Such unified methods allow more possibilities for exploring new optimization formulations, and in comparing the solutions to previously reported formulations.     

Estimates of muscle function in human gait depend on how foot-ground contact is modelled

Computational analyses of leg-muscle function in human locomotion commonly assume that contact between the foot and the ground occurs at discrete points on the sole of the foot. Kinematic constraints acting at these contact points restrict the motion of the foot and, therefore, alter model calculations of muscle function. The aim of this study was to evaluate how predictions of muscle function obtained from musculoskeletal models are influenced by the model used to simulate ground contact. Both single- and multiple-point contact models were evaluated. Muscle function during walking and running was determined by quantifying the contributions of individual muscles to the vertical, fore-aft and mediolateral components of the ground reaction force (GRF). The results showed that two factors – the number of foot-ground contact points assumed in the model and the type of kinematic constraint enforced at each point – affect the model predictions of muscle coordination. Whereas single- and multiple-point contact models produced similar predictions of muscle function in the sagittal plane, inconsistent results were obtained in the mediolateral direction. Kinematic constraints applied in the sagittal plane altered the model predictions of muscle contributions to the vertical and fore-aft GRFs, while constraints applied in the frontal plane altered the calculations of muscle contributions to the mediolateral GRF. The results illustrate the sensitivity of calculations of muscle coordination to the model used to simulate foot-ground contact.     

Estimates of muscle function in human gait depend on how foot-ground contact is modelled

Computational analyses of leg-muscle function in human locomotion commonly assume that contact between the foot and the ground occurs at discrete points on the sole of the foot. Kinematic constraints acting at these contact points restrict the motion of the foot and, therefore, alter model calculations of muscle function. The aim of this study was to evaluate how predictions of muscle function obtained from musculoskeletal models are influenced by the model used to simulate ground contact. Both single- and multiple-point contact models were evaluated. Muscle function during walking and running was determined by quantifying the contributions of individual muscles to the vertical, fore-aft and mediolateral components of the ground reaction force (GRF). The results showed that two factors--the number of foot-ground contact points assumed in the model and the type of kinematic constraint enforced at each point--affect the model predictions of muscle coordination. Whereas single- and multiple-point contact models produced similar predictions of muscle function in the sagittal plane, inconsistent results were obtained in the mediolateral direction. Kinematic constraints applied in the sagittal plane altered the model predictions of muscle contributions to the vertical and fore-aft GRFs, while constraints applied in the frontal plane altered the calculations of muscle contributions to the mediolateral GRF. The results illustrate the sensitivity of calculations of muscle coordination to the model used to simulate foot-ground contact.     

Active trunk stiffness increases with co-contraction.

Trunk dynamics, including stiffness, mass and damping were quantified during trunk extension exertions with and without voluntary recruitment of antagonistic co-contraction. The objective of this study was to empirically evaluate the influence of co-activation on trunk stiffness. Muscle activity associated with voluntary co-contraction has been shown to increase joint stiffness in the ankle and elbow. Although biomechanical models assume co-active recruitment causes increase trunk stiffness it has never been empirically demonstrated. Small trunk displacements invoked by pseudorandom force disturbances during trunk extension exertions were recorded from 17 subjects at two co-contraction conditions (minimal and maximal voluntary co-contraction recruitment). EMG data were recorded from eight trunk muscles as a baseline measure of co-activation. Increased EMG activity confirms that muscle recruitment patterns were different between the two co-contraction conditions. Trunk stiffness was determined from analyses of impulse response functions (IRFs) of trunk dynamics wherein the kinematics were represented as a second-order behavior. Trunk stiffness increased 37.8% (p < 0.004) from minimal to maximal co-activation. Results support the assumption used in published models of spine biomechanics that recruitment of trunk muscle co-contraction increases trunk stiffness thereby supporting conclusions from those models that co-contraction may contribute to spinal stability.     

Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model

The estimation of muscle fascicle behaviour is decisive in a Hill-type model as they are related to muscle force by the force–length–velocity relationship and the tendon force–strain relationship. This study was aimed at investigating the influence of subject-specific tendon force–strain relationship and initial fascicle geometry (IFG) on the estimation of muscle forces and fascicle behaviour during isometric contractions. Ultrasonography was used to estimate the in vivo muscle fascicle behaviour and compare the muscle fascicle length and pennation angle estimated from the Hill-type model. The calibration–prediction process of the electromyography-driven model was performed using generic or subject-specific tendon definition with or without IFG as constraint. The combination of subject-specific tendon definition and IFG led to muscle fascicle behaviour closer to ultrasound data and significant lower forces of the ankle dorsiflexor and plantarflexor muscles compared to the other conditions. Thus, subject-specific ultrasound measurements improve the accuracy of Hill-type models on muscle fascicle behaviour.     

Validation of a biodynamic model of pushing and pulling.

Pushing and pulling during manual material handling can increase the compressive forces on the lumbar disc region while creating high shear forces at the shoe-floor interface. A sagittal plane dynamic model derived from previous biomechanical models was developed to predict L5/S1 compressive force and required coefficients of friction during dynamic cart pushing and pulling. Before these predictions could be interpreted, however, it was necessary to validate model predictions against independently measured values of comparable quantities. This experiment used subjects of disparate stature and body mass, while task factors such as cart resistance and walking speed were varied. Predicted ground reaction forces were compared with those measured by a force platform, with correlations up to 0.67. Predicted erector spinae and rectus abdominus muscle forces were compared with muscle forces derived from RMS-EMGs of the respective muscle groups, using a static force build-up regression relationship to transform the dynamic RMS-EMGs to trunk muscle forces. Although correlations were low, this was attributed in part to the use of surface EMG on subjects of widely varied body mass. The biodynamic model holds promise as a tool for analysis of actual industrial pushing and pulling tasks, when carefully applied.     

An activation-recruitment scheme for use in muscle modeling

The derivation of a new activation-recruitment scheme and the results of a study designed to test its validity are presented. The activation scheme utilizes input data of processed surface EMG signals, muscle composition, muscle architecture, and experimentally determined activation coefficients. In the derivation, the relationship between muscle activation and muscle fiber recruitment was considered. In the experimental study, triceps muscle force was determined for isometric elbow extension tasks varying in intensity from 10 to 100% of a maximum voluntary contraction (MVC) using both a muscle model that incorporates the activation scheme, and inverse dynamics techniques. The forces calculated using the two methods were compared statistically. The modeled triceps force was not significantly different from the experimental results determined using inverse dynamics techniques for average activation levels greater than 25% of MVC, but was significantly different for activation levels less than 25% of MVC. These results lend support for use of the activation-recruitment scheme for moderate to large activation levels, and suggest that factors in addition to fiber recruitment play a role in force regulation at lower activation levels.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.