Total shoulder and relative muscle strength in the scapular plane.

Strength profiles of the shoulder joint are measured experimentally for two arm positions in "the scapular plane" in order to present quantitative data on the shoulder strength. Apart from yielding the actual force a subject can exert in various directions, these measurements also exhibit e.g. the strongest and weakest directions, in fact the relative strength in all directions. The inter-individual variation of the direction of maximal force was at most 14 degrees (sd). The experimental profiles are compared with the corresponding theoretical profiles, obtained by using a shoulder model. The calculations were made both with default muscle parameters and individually adapted parameters. The results show that the employed shoulder model, which is based on data from an elderly population, may be adapted to other populations and that the necessary changes in relative muscle strength are those expected on biomechanical grounds. Without model changes the difference between measured (in the mean) and predicted maximal force directions was at most 50 degrees. Muscle parameter adjustment reduced this difference to 23 degrees. The strength profiles clearly indicate in what direction a person can produce larger forces and which muscles that contribute.     

Behaviour of a surface EMG based measure for motor control: Motor unit action potential rate in relation to force and muscle fatigue

Surface electromyography parameters such as root-mean-square value (RMS) and median power frequency (FMED) are commonly used to assess the input of the central nervous system (CNS) to a muscle. However, RMS and FMED are influenced not only by CNS input, but also by peripheral muscle properties. The number of motor unit action potentials (MUAPs) per second, or MUAP Rate (MR), being the sum of the firing rates of the active motor units, would reflect CNS input solely. This study explored MR behaviour in relation to force and during a fatiguing contraction in comparison to RMS and FMED.In the first experiment (n = 10) a step contraction of shoulder elevation force (20–100 N) was performed while multi-channel array EMG was recorded from the upper trapezius muscle. The sensitivity of MR for changes in force (1.8%/N) was almost twice as high as that of RMS (0.97%/N), indicating that MR may be more suitable for monitoring muscle force. The second experiment (n = 6) consisted of a 15-min isometric contraction of the biceps brachii. MR increased considerably less than RMS (0.9% vs. 4.1%), suggesting that MR selectively reflects central motor control whereas RMS also reflects peripheral changes. These results support that, at relatively low force levels, MR is a suitable parameter for non-invasive assessment of the input of the CNS to the muscle.     

A Monte Carlo analysis of muscle force estimation sensitivity to muscle-tendon properties using a Hill-based muscle model

Surface electromyography driven models are desirable for estimating subject-specific muscle forces. However, these models include parameters that come from an array of sources, thus creating uncertainty in the model-estimated force. In this study, we used Monte-Carlo simulations to evaluate the sensitivity of Hill-based model muscle forces to changes in 11 parameters in the muscle-tendon unit morphological properties and in the model force-length and force-velocity relationships. We decomposed the force variability and ranked the sensitivity of the model to the underlying parameters using the Variogram Analysis of Response Surfaces. For the analyzed running experiments and the adopted Hill model structure, our results show that the parameters are separable into four groups, where the parameters in each group have a synergistic contribution to the model global sensitivity. The first group consists of the maximum isometric force and the pennation angle. The second group contains the optimal fiber length, the tendon slack length, the tendon reference strain and the tendon shape factor. The third group contains the width and shape at the extremities of the active contractile element, along with the maximum contraction velocity and the curvature constant in the force-velocity curve. The fourth group consisted only of the force enhancement during eccentric contraction. The first two groups revealed the largest influence on the output force sensitivity. As many input parameters are difficult to measure and impact estimated forces, we propose that model estimates be presented with confidence intervals as well as inter-parameter relationships, to encourage users to explicitly consider the model uncertainty.     

Biomechanical model calculation of muscle contraction forces: a double linear programming method

This paper presents a novel scheme for the use of linear programming to calculate muscle contraction forces in models describing musculoskeletal system biomechanics. Models of this kind are frequently found in the biomechanics literature. In most cases they involve muscle contraction force calculations that are statically indeterminate, and hence use optimization techniques to make those calculations. We present a linear programming optimization technique that solves a two-objective problem with two sequential linear programs. We use the technique here to minimize muscle intensity and joint compression force, since those are commonly used objectives. The two linear program model has the advantages of low computation cost, ready implementation on a micro-computer, and stable solutions. We show how to solve the model analytically in simple cases. We also discuss the use of the dual problem of linear programming to gain understanding of the solution it provides.     

Estimation of muscle active state

A method is presented for the estimation of the complete time course of muscle active state. The method is based on the selection of a proper model for the muscle, consisting of linear and non-linear components, and on the estimation of its parameters from a simple experiment. The model's parameters are estimated, using the least square method, from measurements of a tetanized muscle's response to a change of its length. The time course of the active state is calculated from an isometric twitch tension response of the same muscle. The twitch tension response is taken as the system's output, and the active state as its input. The latter can be estimated since the system parameters have already been estimated from the tetanized muscle experiment. Experiments were performed on the gastrocnemius muscle of frogs and cats. Results are given for the whole active state time course of these muscles. The results show that the peak active state force does not reach tetanic value, and a negative force is generated during the relaxation period. Additional experiments were carried out with the purpose of verifying the existence of this force; however, no conclusive results were obtained.This research was supported by the Julius Silver Institute of Bio-Medical Engineering Sciences, Grant 050-304     

Aging alters contractile properties and fiber morphology in pigeon skeletal muscle

In this study, we tested the hypothesis that skeletal muscle from pigeons would display age-related alterations in isometric force and contractile parameters as well as a shift of the single muscle fiber cross-sectional area (CSA) distribution toward smaller fiber sizes. Maximal force output, twitch contraction durations and the force–frequency relationship were determined in tensor propatagialis pars biceps muscle from young 3-year-old pigeons, middle-aged 18-year-old pigeons, and aged 30-year-old pigeons. The fiber CSA distribution was determined by planimetry from muscle sections stained with hematoxylin and eosin. Maximal force output of twitch and tetanic contractions was greatest in muscles from young pigeons, while the time to peak force of twitch contractions was longest in muscles from aged pigeons. There were no changes in the force–frequency relationship between the age groups. Interestingly, the fiber CSA distribution in aged muscles revealed a greater number of larger sized muscle fibers, which was verified visually in histological images. Middle-aged and aged muscles also displayed a greater amount of slow myosin containing muscle fibers. These data demonstrate that muscles from middle-aged and aged pigeons are susceptible to alterations in contractile properties that are consistent with aging, including lower force production and longer contraction durations. These functional changes were supported by the appearance of slow myosin containing muscle fibers in muscles from middle-aged and aged pigeons. Therefore, the pigeon may represent an appropriate animal model for the study of aging-related alterations in skeletal muscle function and structure.     

The sensitivity of muscle force predictions to changes in physiologic cross-sectional area

The mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses. For more than a century, researchers have expressed muscle size by its 'physiological cross-sectional area' (PCSA). Researchers mathematically calculating muscle and joint forces typically use some expression of a muscle's PCSA to constrain the solution to one which is reasonable (i.e. a solution in which small muscles may not have large forces, and large muscles have large forces when expected or when there is significant electromyographic activity). It is obvious that muscle mass (and therefore any expression of PCSA) varies significantly from person to person, even in individuals of similar weight and height. Since it is not practical to predict the PCSA of each muscle in a living subject's limb or trunk, it is important to generally understand the sensitivity of muscle force solutions to possible variations in PCSA. We used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject. The PCSA (volume/muscle fiber length) of each of 47 lower limb muscle elements from two cadaver specimens and the 47 PCSA's reported by pierrynowski were input into an optimization algorithm to create three solution sets. The three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times. In contrast, the joint force solutions were within 11% of each other and, therefore, much less variable.(ABSTRACT TRUNCATED AT 250 WORDS)     

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     

Surface mechanomyogram reflects the changes in the mechanical properties of muscle at fatigue

The contractile properties of muscle are usually investigated by analysing the force signal recorded during electrically elicited contractions. The electrically stimulated muscle shows surface oscillations that can be detected by an accelerometer; the acceleration signal is termed the surface mechanomyogram (MMG). In the study described here we compared, in the human tibialis anterior muscle, changes in the MMG and force signal characteristics before, and immediately after fatigue, as well as during 6 min of recovery, when changes in the contractile properties of muscle occur. Fatigue was induced by sustained electrical stimulation. The final aim was to evaluate the reliability of the MMG as a tool to follow the changes in the mechanical properties of muscle caused by fatigue. Because of fatigue, the parameters of the force peak, the peak rate of force production and the peak of the acceleration of force production (d2F/dt2) decreased, while the contraction time and the half-relaxation time (1/2-RT) increased. The MMG peak-to-peak (p-p) also decreased. The attenuation rate of the force oscillation amplitude and MMG p-p at increasing stimulation frequency was greater after fatigue. With the exception of 1/2-RT, all of the force and MMG parameters were restored within 2 min of recovery. A high correlation was found between MMG and d2F/dt2 in un-fatigued muscle and during recovery. In conclusion, the MMG reflects specific aspects of muscle mechanics and can be used to follow the changes in the contractile properties of muscle caused by localised muscle fatigue.     

Electromyographic models to assess muscle fatigue

Muscle fatigue is a common experience in daily life. Many authors have defined it as the incapacity to maintain the required or expected force, and therefore, force, power and torque recordings have been used as direct measurements of muscle fatigue. In addition, the measurement of these variables combined with the measurement of surface electromyography (sEMG) recordings (which can be measured during all types of movements) during exercise may be useful to assess and understand muscle fatigue. Therefore, there is a need to develop muscle fatigue models that relate changes in sEMG variables with muscle fatigue. However, the main issue when using conventional sEMG variables to quantify fatigue is their poor association with direct measures of fatigue. Therefore, using different techniques, several authors have combined sets of sEMG parameters to assess muscle fatigue. The aim of this paper is to serve as a state-of-the-art summary of different sEMG models used to assess muscle fatigue. This paper provides an overview of linear and non-linear sEMG models for estimating muscle fatigue, their ability to assess power loss and their limitations due to neuromuscular changes after a training period.     

Muscle force is determined also by muscle relative position: isolated effects

Effects on force of changes of the position of extensor digitorum longus muscle (EDL) relative to surrounding tissues were investigated in rat. Connective tissue at the muscle bellies of tibialis anterior (TA), extensor hallucis longus (EHL) and EDL was left intact, to allow myofascial force transmission. The position of EDL muscle was altered, without changing EDL muscle-tendon complex length, and force exerted at proximal and distal tendons of EDL as well as summed force exerted at the distal tendons of TA and EHL muscles (TA+EHL) were measured. Proximal and distal EDL forces as well as distal TA+EHL force changed significantly on repositioning EDL muscle. These muscle position-force characteristics were assessed at two EDL lengths and two TA+EHL lengths. It was shown that changes of muscle force with length changes of a muscle is the result of the length changes per se, as well as of changes of relative position of parts of the muscle. It is concluded that in addition to length, muscle position relative to its surroundings co-determines isometric muscle force.     

A comparison of the triceps surae and residual muscle moments at the ankle during cycling

The rigid linked system model and principles of inverse dynamics have been widely used to calculate residual muscle moments during various activities. EMG driven models and optimization algorithms have also been presented in the literature in efforts to estimate skeletal muscle forces and evaluate their possible contribution to the residual muscle moment. Additionally, skeletal muscle-tendon forces have been measured, directly, in both animals and humans. The purpose of this investigation was to calculate the moment produced by the triceps surae muscles and compare it to the residual muscle moment at the ankle during cycling at three power outputs (90, 180 and 270 W). Inferences were made regarding the potential contribution made by each triceps surae component to the tendon force using EMG and muscle-tendon length changes. A buckle-type transducer was surgically implanted on the right Achilles tendon of one male subject. Achilles tendon forces measured in vivo were multiplied by their corresponding moment arms to yield the triceps surae moment during the three working conditions. Moment arm lengths were obtained in a separate experiment using magnetic resonance imaging (MRI). Pedal reaction forces, body segment accelerations (determined from high speed film), and appropriate mass parameters served as input to the inverse solution. The triceps surae moment was temporally in phase with and consistently represented approximately 65% of the residual muscle moment at the ankle. These data demonstrate the feasibility of using implanted transducers in human subjects and provide a greater understanding of musculoskeletal mechanics during normal human movements.     

Static optimization underestimates antagonist muscle activity at the glenohumeral joint: A musculoskeletal modeling study

Static optimization is commonly employed in musculoskeletal modeling to estimate muscle and joint loading; however, the ability of this approach to predict antagonist muscle activity at the shoulder is poorly understood. Antagonist muscles, which contribute negatively to a net joint moment, are known to be important for maintaining glenohumeral joint stability. This study aimed to compare muscle and joint force predictions from a subject-specific neuromusculoskeletal model of the shoulder driven entirely by measured muscle electromyography (EMG) data with those from a musculoskeletal model employing static optimization. Four healthy adults performed six sub-maximal upper-limb contractions including shoulder abduction, adduction, flexion, extension, internal rotation and external rotation. EMG data were simultaneously measured from 16 shoulder muscles using surface and intramuscular electrodes, and joint motion evaluated using video motion analysis. Muscle and joint forces were calculated using both a calibrated EMG-driven neuromusculoskeletal modeling framework, and musculoskeletal model simulations that employed static optimization. The EMG-driven model predicted antagonistic muscle function for pectoralis major, latissimus dorsi and teres major during abduction and flexion; supraspinatus during adduction; middle deltoid during extension; and subscapularis, pectoralis major and latissimus dorsi during external rotation. In contrast, static optimization neural solutions showed little or no recruitment of these muscles, and preferentially activated agonistic prime movers with large moment arms. As a consequence, glenohumeral joint force calculations varied substantially between models. The findings suggest that static optimization may under-estimate the activity of muscle antagonists, and therefore, their contribution to glenohumeral joint stability.     

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.     

Direct evidence that stomatogastric (Panulirus interruptus) muscle passive responses are not due to background actomyosin cross-bridges

Muscles respond to imposed length changes with rapid, large force changes followed by slow relaxations to new steady-state forces. These responses were originally believed to arise from background levels of actomyosin binding. Discovery of giant sarcomere-spanning proteins suggested muscle passive responses could arise from length changes of elastic domains present in these proteins. However, direct evidence that actomyosin plays little role in passive muscle force responses to imposed length changes has not been provided. We show here that a poison of actomyosin interaction, thiourea, does not alter initial force changes or subsequent relaxations of lobster stomatogastric muscles. These data provide direct evidence that background actomyosin cross-bridge formation likely plays, at most, a small role in muscle passive responses to length changes. Thiourea does not alter lobster muscle electrical responses to motor nerve stimulation, although in this species it does cause tonic motor nerve firing. This firing limits the utility of thiourea to study lobster muscle electrical responses to motor nerve stimulation. However, it is unclear whether thiourea induces such motor nerve firing in other animals. Thiourea may therefore provide a convenient technique to measure muscle electrical responses to motor nerve input without the confounding difficulties caused by muscle contraction.     

Contralateral muscle activity and fatigue in the human first dorsal interosseous muscle.

During effortful unilateral contractions, muscle activation is not limited to the target muscles but activity is also observed in contralateral muscles. The amount of this associated activity is depressed in a fatigued muscle, even after correction for fatigue-related changes in maximal force. In the present experiments, we aimed to compare fatigue-related changes in associated activity vs. parameters that are used as markers for changes in central nervous system (CNS) excitability. Subjects performed brief maximal voluntary contractions (MVCs) with the index finger in abduction direction before and after fatiguing protocols. We followed changes in MVCs, associated activity, motor-evoked potentials (MEP; transcranial magnetic stimulation), maximal compound muscle potentials (M waves), and superimposed twitches (double pulse) for 20 min after the fatiguing protocols. During the fatiguing protocols, associated activity increased in contralateral muscles, whereas afterwards the associated force was reduced in the fatigued muscle. This force reduction was significantly larger than the decline in MVC. However, associated activity (force and electromyography) remained depressed for only 5-10 min, whereas the MVCs stayed depressed for over 20 min. These decreases were accompanied by a reduction in MEP, MVC electromyography activity, and voluntary activation in the fatigued muscle. According to these latter markers, the decrease in CNS motor excitability lasted much longer than the depression in associated activity. Differential effects of fatigue on (associated) submaximal vs. maximal contractions might contribute to these differences in postfatigue behavior. However, we cannot exclude differences in processes that are specific to either voluntary or to associated contractions.     

The dependence of the twitch course of medial gastrocnemius muscle of the rat and its motor units on stretching of the muscle.

The relationship between the force of a single twitch of the medial gastrocnemius muscle of the rat and contraction and half-relaxation times, on one hand, and the load of the muscle on the other, was studied. Twitches of the whole muscle and its individual motor units were induced. The optimal load, at which the majority of motor units reached the greatest twitch force, was 10 G. Mean optimal loads for twitches of different types of motor units were very similar. Slow motor units reached a slightly greater twitch force at greater loads (12.5 G) than at 10 G. However, the optimal load for the twitch of the whole muscle was much greater. It was 47 G on the average. The contraction and half-relaxation times of motor units, as well as of the whole muscle, became longer as the force stretching the muscle increased. Half-relaxation time changed more rapidly than contraction time. Both parameters were undergoing the greatest changes in slow motor units.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

Stretch-shortening cycle: a powerful model to study normal and fatigued muscle

Stretch-shortening cycle (SSC) in human skeletal muscle gives unique possibilities to study normal and fatigued muscle function. The in vivo force measurement systems, buckle transducer technique and optic fiber technique, have revealed that, as compared to a pure concentric action, a non-fatiguing SSC exercise demonstrates considerable performance enhancement with increased force at a given shortening velocity. Characteristic to this phenomenon is very low EMG-activity in the concentric phase of the cycle, but a very pronounced contribution of the short-latency stretch-reflex component. This reflex contributes significantly to force generation during the transition (stretch-shortening) phase in SSC action such as hopping and running. The amplitude of the stretch reflex component - and the subsequent force enhancement - may vary according to the increased stretch-load but also to the level of fatigue. While moderate SSC fatigue may result in slight potentiation, the exhaustive SSC fatigue can dramatically reduce the same reflex contribution. SSC fatigue is a useful model to study the processes of reversible muscle damage and how they interact with muscle mechanics, joint and muscle stiffness. All these parameters and their reduction during SSC fatigue changes stiffness regulation through direct influences on muscle spindle (disfacilitation), and by activating III and IV afferent nerve endings (proprioseptic inhibition). The resulting reduced stretch reflex sensitivity and muscle stiffness deteriorate the force potentiation mechanisms. Recovery of these processes is long lasting and follows the bimodal trend of recovery. Direct mechanical disturbances in the sarcomere structural proteins, such as titin, may also occur as a result of an exhaustive SSC exercise bout.     

A simulation of rat edl force output based on intrinsic muscle properties

Force-velocity and force-length relations were obtained for the edl of four Wistar rats in order to characterise the contractile properties (CE) of these muscle-tendon complexes. Compliances of the undamped part of the series components (SE) were measured in quick length decreases. Force-extension relations of SEs were obtained by integration of compliance to force. A muscle model consisting of CE, SE and a visco-elastic element was used to simulate the force output of the muscle tendon complex in response to a changing muscle length lOI as input. This simulated force was compared with the experimental force of the same muscle measured in response to the same lOI as input. Tetanic contractions were used in all experiments. The results show that this muscle model can predict the experimental force within a mean maximal error not larger than approximately 14% of the force amplitude. However the comparison of simulated force with experimental force and a few additional experiments show that the muscles do not have a unique instantaneous force-velocity characteristic. As shown by several other studies, force seems to be influenced by many other variables (time, history etc.) than CE length and velocity.