A regression model predicting isometric shoulder muscle activities from arm postures and shoulder joint moments

Tissue overloading is a major contributor to shoulder musculoskeletal injuries. Previous studies attempted to use regression-based methods to predict muscle activities from shoulder kinematics and shoulder kinetics. While a regression-based method can address co-contraction of the antagonist muscles as opposed to the optimization method, most of these regression models were based on limited shoulder postures. The purpose of this study was to develop a set of regression equations to predict the 10th percentile, the median, and the 90th percentile of normalized electromyography (nEMG) activities from shoulder postures and net shoulder moments. Forty participants generated various 3-D shoulder moments at 96 static postures. The nEMG of 16 shoulder muscles was measured and the 3-D net shoulder moment was calculated using a static biomechanical model. A stepwise regression was used to derive the regression equations. The results indicated the measured range of the 3-D shoulder moment in this study was similar to those observed during work requiring light physical capacity. The r² of all the regression equations ranged between 0.228 and 0.818. For the median of the nEMG, the average r² among all 16 muscles was 0.645, and the five muscles with the greatest r² were the three deltoids, supraspinatus, and infraspinatus. The results can be used by practitioners to estimate the range of the shoulder muscle activities given a specific arm posture and net shoulder moment.     

A model for steady isometric muscle activation

The present model of the motoneuronal (MN) pool – muscle complex (MNPMC) is deterministic and designed for steady isometric muscle activation. Time-dependent quantities are treated as time-averages. The character of the model is continuous in the sense that the motor unit (MU) population is described by a continuous density function. In contrast to most already published models, the wiring (synaptic weight) between the input fibers to the MNPMC and the MNs (about which no detailed data are known) is deduced, whereas the input–force relation is given. As suggested by experimental data, this relation is assumed to be linear during MU recruitment, but the model allows other, nonlinear relations. The input to the MN pool is defined as the number of action potentials per second in all input fibers, and the excitatory postsynaptic potential (EPSP) conductance in MNs evoked by the input is assumed to be proportional to the input. A single compartment model with a homogeneous membrane is used for a MN. The MNs start firing after passing a constant voltage threshold. The synaptic current–frequency relation is described by a linear function and the frequency–force transformation of a MU by an exponential function. The sum of the MU contraction forces is the muscle force, and the activation of the MUs obeys the size principle. The model parameters were determined a priori, i.e., the model was not used for their estimation. The analysis of the model reveals special features of the activation curve which we define as the relation between the input normalized by the threshold input of the MN pool and the force normalized by the maximal muscle force. This curve for any muscle turned out to be completely determined by the activation factor, the slope of the linear part of the activation curve (during MU recruitment). This factor determines quantitatively the relation between MU recruitment and rate modulation. This property of the model (the only known model with this property) allows a quantification of the recruitment gain (Kernell and Hultborn 1990). The interest of the activation factor is illustrated using two human muscles, namely the first dorsal interosseus muscle, a small muscle with a relatively small force at the end of recruitment, and the medial gastrocnemius muscle, a strong muscle with a relatively large force at the end of recruitment. It is concluded that the present model allows us to reproduce the main features of muscle activation in the steady state. Its analytical character facilitates a deeper understanding of these features. Received: 24 November 1997 / Accepted in revised form: 30 November 1998     

Hybrid neuromusculoskeletal modeling to best track joint moments using a balance between muscle excitations derived from electromyograms and optimization

Current electromyography (EMG)-driven musculoskeletal models are used to estimate joint moments measured from an individual?s extremities during dynamic movement with varying levels of accuracy. The main benefit is the underlying musculoskeletal dynamics is simulated as a function of realistic, subject-specific, neural-excitation patterns provided by the EMG data. The main disadvantage is surface EMG cannot provide information on deeply located muscles. Furthermore, EMG data may be affected by cross-talk, recording and post-processing artifacts that could adversely influence the EMG?s information content. This limits the EMG-driven model?s ability to calculate the multi-muscle dynamics and the resulting joint moments about multiple degrees of freedom. We present a hybrid neuromusculoskeletal model that combines calibration, subject-specificity, EMG-driven and static optimization methods together. In this, the joint moment tracking errors are minimized by balancing the information content extracted from the experimental EMG data and from that generated by a static optimization method. Using movement data from five healthy male subjects during walking and running we explored the hybrid model?s best configuration to minimally adjust recorded EMGs and predict missing EMGs while attaining the best tracking of joint moments. Minimally adjusted and predicted excitations substantially improved the experimental joint moment tracking accuracy than current EMG-driven models. The ability of the hybrid model to predict missing muscle EMGs was also examined. The proposed hybrid model enables muscle-driven simulations of human movement while enforcing physiological constraints on muscle excitation patterns. This might have important implications for studying pathological movement for which EMG recordings are limited.     

A new model for calculating muscle forces from electromyograms

A muscle model is described that uses electromyogram (EMG), muscle length and speed of contraction to predict muscle force. Physiological parameters are the Hill constants and the shape of the twitch response to a single stimulus. The model was incorporated in a jaw model of the rabbit and tested by predicting the bite force produced by the jaw muscles during mastication. The time course of the calculated force appeared to match the bite force, measured in vivo by a strain gauge, applied to the bone below the teeth. The variation in peak strain amplitude from cycle to cycle correlated with the variation predicted by the model. The peak amplitude of the integrated EMGs of individual jaw muscles showed an average correlation with peak strain of 0.41. Use of the sum of the available peak amplitudes, weighted according to their effect upon the bite force increased the correlation to 0.46; the model predicted bite forces showed a correlation of 0.57 with the strain. The increase in correlation was statistically significant. The muscle forces were calculated using a minimum number of easily obtainable constants.     

Influence of muscle mass on sympathetic neural activation during isometric exercise

The primary purpose of this study was to determine whether the sympathetic neural activation induced by isometric exercise is influenced by the size of the contracting muscle mass. To address this, in nine healthy subjects (aged 19-27 yr) we measured heart rate, systolic arterial blood pressure, and muscle sympathetic nerve activity in the leg (MSNA; peroneal nerve) before (control) and during 2.5 min of isometric handgrip exercise (30% of maximal voluntary force). Exercise was performed with the right and left arms separately and with both arms simultaneously (random order). During exercise, heart rate, systolic pressure, and MSNA increased above control under all conditions (P less than 0.05). For each variable, the magnitudes of the increases from control to the end of exercise were significantly greater when exercise was performed with two arms compared with either arm alone (P less than 0.05). In general, the increases in heart rate, systolic pressure, and MSNA elicited during two-arm exercise were significantly less than the simple sums of the responses evoked during exercise of each arm separately. These findings indicate that the magnitude of the sympathetic neural activation evoked during isometric exercise in humans is determined in part by the size of the active muscle mass. In addition, our results suggest that the sympathetic cardiovascular adjustments elicited during exercise of separate limbs are not simply additive but instead exhibit an inhibitory interaction (i.e., neural occlusion).     

Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command

This paper provides an overview of forward dynamic neuromusculoskeletal modeling. The aim of such models is to estimate or predict muscle forces, joint moments, and/or joint kinematics from neural signals. This is a four-step process. In the first step, muscle activation dynamics govern the transformation from the neural signal to a measure of muscle activation-a time varying parameter between 0 and 1. In the second step, muscle contraction dynamics characterize how muscle activations are transformed into muscle forces. The third step requires a model of the musculoskeletal geometry to transform muscle forces to joint moments. Finally, the equations of motion allow joint moments to be transformed into joint movements. Each step involves complex nonlinear relationships. The focus of this paper is on the details involved in the first two steps, since these are the most challenging to the biomechanician. The global process is then explained through applications to the study of predicting isometric elbow moments and dynamic knee kinetics.     

An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle-tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R(2) of 0.91 and mean residual error of approximately 12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.     

Predicting net joint moments during a weightlifting exercise with a neural network model

The purpose of this study was to develop and train a Neural Network (NN) that uses barbell mass and motions to predict hip, knee, and ankle Net Joint Moments (NJM) during a weightlifting exercise. Seven weightlifters performed two cleans at 85% of their competition maximum while ground reaction forces and 3-D motion data were recorded. An inverse dynamics procedure was used to calculate hip, knee, and ankle NJM. Vertical and horizontal barbell motion data were extracted and, along with barbell mass, used as inputs to a NN. The NN was then trained to model the association between the mass and kinematics of the barbell and the calculated NJM for six weightlifters, the data from the remaining weightlifter was then used to test the performance of the NN – this was repeated 7 times with a k-fold cross-validation procedure to assess the NN accuracy. Joint-specific predictions of NJM produced coefficients of determination (r²) that ranged from 0.79 to 0.95, and the percent difference between NN-predicted and inverse dynamics calculated peak NJM ranged between 5% and 16%. The NN was thus able to predict the spatiotemporal patterns and discrete peaks of the three NJM with reasonable accuracy, which suggests that it is feasible to predict lower extremity NJM from the mass and kinematics of the barbell. Future work is needed to determine whether combining a NN model with low cost technology (e.g., digital video and free digitising software) can also be used to predict NJM of weightlifters during field-testing situations, such as practice and competition, with comparable accuracy.     

Effect of quadriceps femoris muscle length on neural activation during isometric and concentric contractions.

The effect of muscle length on neural drive (here termed "neural activation") was investigated from electromyographic activities and activation levels (twitch interpolation). The neural activation was measured in nine men during isometric and concentric (30 and 120 degrees /s) knee extensions for three muscle lengths (35, 55, and 75 degrees knee flexion, i.e., shortened, intermediate, and lengthened muscles, respectively). Long (76 degrees ), medium (56 degrees ), and short (36 degrees ) ranges of motion were used to investigate the effect of the duration of concentric contraction. Neural activation was found to depend on muscle length. Reducing the duration of contraction had no effect. Neural activation was higher with short muscle length during isometric contractions and was weaker for shortened than for intermediate and lengthened muscles performing 120 degrees /s concentric contractions. Muscle length had no effect on 30 degrees /s concentric neural activation. Peripheral mechanisms and discharge properties of the motoneurons could partly explain the observed differences in the muscle length effect. We thus conclude that muscle length has a predominant effect on neural activation that would modulate the angular velocity dependency.     

A comparison of models explaining muscle activation patterns for isometric contractions

One of the main problems in motor-control research is the muscle load sharing problem, which originates from the fact that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint. As a consequence, many different possibilities exist for the activation of muscles in order to produce a desired joint torque. Several models describing muscle activation have been hypothesized over the last few decades to solve this problem. This study presents theoretical analyses of the various models and compares the predictions of these models with new data on muscle activation patterns for isometric contractions in various directions. None of the existing models fitted the experimental data in all aspects. The best fit was obtained by models based on minimization of the squared sum of muscle forces (∑ _m φ² _m , which is almost equivalent to the Moore-Penrose pseudo-inverse solution), muscle stress σ (∑ _m σ _m ²) or muscle activation α (∑ _m α _m ²). Since muscle activation patterns are different for isometric contractions and for movements, it could well be that other models or optimization criteria are better suited to describe muscle activation patterns for movements. The results of our simulations demonstrate that the predicted muscle activation patterns do not depend critically on the parameters in the model. This may explain why muscle activation patterns are highly stereotyped for all subjects irrespective of differences between subjects in many neuro-anatomical aspects, such as, for example, in the physiological cross-sectional area of muscle. Received: 24 September 1998 / Accepted in revised form: 1 March 1999     

Predicting isometric force from muscular activation using a physiologically inspired model

Motivated by biochemical processes during muscular contraction, a model is constructed that predicts isometric force from surface electromyographic signals (sEMG). The model is experimentally validated and then it is used to predict contractions from sEMG data. The calculated simulations reveal a highly non-linear relationship between sEMG and isometric force.     

A new method for estimating joint parameters from motion data

Joint centers and axes of rotation (joint parameters) are central to all branches of movement analysis. In gait analysis, the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation, anthropometric regression equations, and misplaced alignment devices. Several alternative methods have been proposed, but to date none have been shown to be accurate and reliable enough for use in the clinical setting. This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject. For the analog, the center was found to be within 3.8 mm of the geometric center and 2.0 degrees of the geometric axis (standard deviation). For the adult subject, hip centers varied on the order of 1-3 mm, knee centers by 3-9 mm, and knee axes by 2.0 degrees. The results suggest that the new method is an objective, precise, and practical alternative to the standard clinical approach.     

A phenomenological model for estimating metabolic energy consumption in muscle contraction

A phenomenological model for muscle energy consumption was developed and used in conjunction with a simple Hill-type model for muscle contraction. The model was used to address two questions. First, can an empirical model of muscle energetics accurately represent the total energetic behavior of frog muscle in isometric, isotonic, and isokinetic contractions? And second, how does such a model perform in a large-scale, multiple-muscle model of human walking? Four simulations were conducted with frog sartorius muscle under full excitation: an isometric contraction, a set of isotonic contractions with the muscle shortening a constant distance under various applied loads, a set of isotonic contractions with the muscle shortening over various distances under a constant load, and an isokinetic contraction in lengthening. The model calculations were evaluated against results of similar thermal in vitro experiments performed on frog sartorius muscle. The energetics model was then incorporated into a large-scale, multiple-muscle model of the human body for the purpose of predicting energy consumption during normal walking. The total energy estimated by the model accurately reflected the observed experimental behavior of frog muscle for an isometric contraction. The model also accurately reproduced the experimental behavior of frog muscle heat production under isotonic shortening and isokinetic lengthening conditions. The estimated rate of metabolic energy consumption for walking was 29% higher than the value typically obtained from gait measurements.     

A neural network model for estimating O2 absorption coefficient in shake-flasks

A comprehensive, simple, neural network model was constructed to replace the common semi-empirical mathematical models used for predicting individual O₂ absorption coefficients (K _L a) within Erlenmeyer and Hinton shake-flasks. Different factors that influence K _L a within shake-flasks, such as flask dimensions, working volumes, baffle-heights, and shaking speeds, were investigated and the experimental results employed to deduce the mathematical model for each type of shake-flask. Meanwhile, the K _L a values calculated from the mathematical models were used to derive a non-linear neural network estimator (NNE). The NNE for K _L a prediction was implemented to evaluate the O₂ absorption effect within the flasks and gave a promising result.     

A neural model of the dynamic activation of memory

We study an Attractor Neural Network that stores natural concepts, organized in semantic classes. The concepts are represented by distributed patterns over a space of attributes, and are related by both semantic and episodic associations. While semantic relations are expressed through an hierarchical coding over the attribute space, episodic links are realized via specific synaptic projections. Due to dynamic thresholds expressing neuronal fatigue, the network's behavior is characterized by convergence toward the concept patterns on a short time scale, and by transitions between the various patterns on a longer time scale. In its baseline, undamaged state, the network manifests semantic, episodic, and random transitions, and demonstrates the phenomen of priming. Modeling possible pathological changes, we have found that increasing the noise level or the rate of neuronal fatigue decreases the frequency of semantic transitions. When neurons characterized by large synaptic connectivity are deleted, semantic transitions decay before the episodic ones, in accordance with the findings in patients with Alzheimer's disease.     

A mathematical model of histamine-mediated neural activation during acupuncture

Acupoints (Xuewei) are the focus of acupuncture on the body in traditional Chinese medicine treatment. Mast and nerve cells share a perivascular location and are abundantly found at these acupoints. Both environmental factors and medical treatments (chemical and physical stimuli) can stimulate local mast cells (MCs) to degranulate and thus release histamine which then activates the nearby nerves and therefore contributes to a signal transmission from the peripheral to the central nervous system. In this paper, a mathematical model is constructed to describe the signaling pathways that originate from the cells located at an acupoint. We show that: (1) peripheral stimuli induce the release of histamine from MCs; (2) histamine excites receptors in primary sensory neurons and leads to membrane action potentials; (3) histamine released from MCs at an acupoint plays a key role in response to acupuncture. These results are consistent with experimental observations. Furthermore, this study may facilitate our understanding of the signal transmission process that occurs in response to peripheral stimuli as well as provide a useful modeling tool for quantitatively analyzing immune and acupuncture mechanisms that involve MCs.     

Analytical solution to isometric mechanogram of hill’s model of striated muscle

The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.     

A well-posed, embedded constraint representation of joint moments from kinesiological measurements

Joint moment estimation using the traditional inverse dynamics analysis presents two challenging problems, which limit its reliability. First, the quality of the computed moments depends directly on unreliable estimates of the segment accelerations obtained numerically by differentiating noisy marker measurements. Second, the representation of joint moments from combined video and force plate measurements belongs to a class of ill-posed problems, which does not possess a unique solution. This paper presents a well-posed representation derived from an embedded constraint equation. The proposed method, referred to as the embedded constraint representation (ECR), provides unique moment estimates, which satisfy all measurement constraints and boundary conditions and require fewer acceleration components than the traditional inverse dynamics method. Specifically, for an n-segment open chain planar system, the ECR requires n-3 acceleration components as compared to 3(n-1) components required by the traditional (from ground up) inverse dynamics analysis. Based on a simulated experiment using a simple three-segment model, the precision of the ECR is evaluated at different noise levels and compared to the traditional inverse dynamics technique. At the lowest noise levels, the inverse dynamics method is up to 50 percent more accurate while at the highest noise levels the ECR method is up to 100 percent more accurate. The ECR results over the entire range of noise levels reveals an average improvement on the order 20 percent in estimating the moments distal to the force plate and no significant improvement in estimating moments proximal to the force plate. The new method is particularly advantageous in a combined video, force plate, and accelerometery sensing strategy.     

A model for neural control of gradation of muscle force

A mathematical muscle model is presented that relates neural control signals linearly to muscle force without violating important known physiological constraints, such as the size-principle (Henneman and Mendell 1981) and non-linear twitch summation (Burke et al. 1976). This linearity implies that the neural control signals (defined as a weighted sum of activities in a nerve bundle) can be interpreted as the internal representation of total muscle force. The model allows for different relative contributions from the two force-grading mechanisms, i.e. the recruitment of motor units and the modulation of their firing frequency. It can therefore be applied to a variety of (distal and proximal) muscles. Furthermore, it permits simple mechanisms for controlling muscle force, e.g. in superposed motor tasks. The model confirms our intuitive notion that a weighted sum of activities in a nerve bundle can directly represent an external controlled variable, which in this case is exerted muscle force.     

Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.