Motor unit firing rates during isometric voluntary contractions performed at different muscle lengths

Firing rates of motor units and surface EMG were measured from the triceps brachii muscles of able-bodied subjects during brief submaximal and maximal isometric voluntary contractions made at 5 elbow joint angles that covered the entire physiological range of muscle lengths. Muscle activation at the longest, midlength, and shortest muscle lengths, measured by twitch occlusion, averaged 98%, 97%, and 93% respectively, with each subject able to achieve complete activation during some contractions. As expected, the strongest contractions were recorded at 90 degrees of elbow flexion. Mean motor unit firing rates and surface EMG increased with contraction intensity at each muscle length. For any given absolute contraction intensity, motor unit firing rates varied when muscle length was changed. However, mean motor unit firing rates were independent of muscle length when contractions were compared with the intensity of the maximal voluntary contraction (MVC) achieved at each joint angle.     

Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models

Hill-type models are commonly used to estimate muscle forces during human and animal movement—yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation–deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with “differential” activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r², was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r²=0.26–0.51), and all exhibited some errors (RMSE=9.63–32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.     

Does the frequency content of the surface mechanomyographic signal reflect motor unit firing rates? A brief review.

The purpose of this review is to examine the literature that has investigated the potential relationship between mechanomyographic (MMG) frequency and motor unit firing rates. Several different experimental designs/methodologies have been used to address this issue, including: repetitive electrical stimulation, voluntary muscle actions in muscles with different fiber type compositions, fatiguing and non-fatiguing isometric or dynamic muscle actions, and voluntary muscle actions in young versus elderly subjects and healthy individuals versus subjects with a neuromuscular disease(s). Generally speaking, the results from these investigations have suggested that MMG frequency is related to the rate of motor unit activation and the contractile properties (contraction and relaxation times) of the muscle fibers. Other studies, however, have reported that MMG mean power frequency (MPF) does not always follow the expected pattern of firing rate modulation (e.g. motor unit firing rates generally increase with torque during isometric muscle actions, but MMG MPF may remain stable or even decrease). In addition, there are several factors that may affect the frequency content of the MMG signal during a voluntary muscle action (i.e. muscle stiffness, intramuscular fluid pressure, etc.), independent of changes in motor unit firing rates. Despite the potential influences of these factors, most of the evidence has suggested that the frequency domain of the MMG signal contains some information regarding motor unit firing rates. It is likely, however, that this information is qualitative, rather than quantitative in nature, and reflects the global motor unit firing rate, rather than the firing rates of a particular group of motor units.     

Control of rabbit nictitating membrane movements

Our objective in this study is to synthesize existing experimental data by constructing a realistic neuromechanical control model of rabbit nictitating membrane (NM) movements. We model the retractor bulbi muscle at the motor unit level because this is the level of nervous system control and also facilitates comparison with experimental data. Our motor unit model is derived from an earlier model of muscle activation based on calcium kinetics and includes a post-activation potentiation mechanism. Motor units are combined into a model of whole muscle that includes length-tension and force-velocity effects. Finally, we incorporate the muscle model into a biomechanical model in which the globe and NM are represented as a system of inertial, viscous, and elastic elements. The model takes patterns of neural signals (in the form of impulses) as input and produces movement of the NM as output. Our muscle model quantitatively accounts for data on isometric force development and decay for twitch, double shock, and tetanic stimulation. The complete model may be used for analysis of the relationship of motoneuron activity to behavior or as a realistic response generator in models of NM conditioning. This study also highlights gaps in the experimental data on the rabbit NM effector system.     

Can co-activation reduce kinematic variability? A simulation study

Impedance modulation has been suggested as a means to suppress the effects of internal ‘noise’ on movement kinematics. We investigated this hypothesis in a neuro-musculo-skeletal model. A prerequisite is that the muscle model produces realistic force variability. We found that standard Hill-type models do not predict realistic force variability in response to variability in stimulation. In contrast, a combined motor-unit pool model and a pool of parallel Hill-type motor units did produce realistic force variability as a function of target force, largely independent of how the force was transduced to the tendon. To test the main hypothesis, two versions of the latter model were simulated as an antagonistic muscle pair, controlling the position of a frictionless hinge joint, with a distal segment having realistic inertia relative to the muscle strength. Increasing the impedance through co-activation resulted in less kinematic variability, except for the lowest levels of co-activation. Model behavior in this region was affected by the noise amplitude and the inertial properties of the model. Our simulations support the idea that muscular co-activation is in principle an effective strategy to meet accuracy demands.     

The maximum shortening velocity of muscle should be scaled with activation.

The purpose of this study was to determine whether the maximum shortening velocity (Vmax) in Hill's mechanical model (A. V. Hill. Proc. R. Soc. London Ser. B. 126: 136-195, 1938) should be scaled with activation, measured as a fraction of the maximum isometric force (Fmax). By using the quick-release method, force-velocity (F-V) relationships of the wrist flexors were gathered at five different activation levels (20-100% of maximum at intervals of 20%) from four subjects. The F-V data at different activation levels can be fitted remarkably well with Hill's characteristic equation. In general, the shortening velocity decreases with activation. With the assumption of nonlinear relationships between Hill constants and activation level, a scaled Vmax model was developed. When the F-V curves for submaximal activation were forced to converge at the Vmax obtained with maximum activation (constant Vmax model), there were drastic changes in the shape of the curves. The differences in Vmax values generated by the scaled and constant Vmax models were statistically significant. These results suggest that, when a Hill-type model is used in musculoskeletal modeling, the Vmax should be scaled with activation.     

Spinal Mechanisms May Provide a Combination of Intermittent and Continuous Control of Human Posture: Predictions from a Biologically Based Neuromusculoskeletal Model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.     

Response linearity determined by recruitment strategy in detailed model of nictitating membrane control

Many models of eyeblink conditioning assume that there is a simple linear relationship between the firing patterns of neurons in the interpositus nucleus and the time course of the conditioned response (CR). However, the complexities of muscle behaviour and plant dynamics call this assumption into question. We investigated the issue by implementing the most detailed model available of the rabbit nictitating membrane response (Bartha and Thompson in Biol Cybern 68:135-143, 1992a and in Biol Cybern 68:145-154, 1992b), in which each motor unit of the retractor bulbi muscle is represented by a Hill-type model, driven by a non-linear activation mechanism designed to reproduce the isometric force measurements of Lennerstrand (J Physiol 236:43-55, 1974). Globe retraction and NM extension are modelled as linked second order systems. We derived versions of the model that used a consistent set of SI units, were based on a physically realisable version of calcium kinetics, and used simulated muscle cross-bridges to produce force. All versions showed similar non-linear responses to two basic control strategies. (1) Rate-coding with no recruitment gave a sigmoidal relation between control signal and amplitude of CR, reflecting the measured relation between isometric muscle force and stimulation frequency. (2) Recruitment of similar strength motor units with no rate coding gave a sublinear relation between control signal and amplitude of CR, reflecting the increase in muscle stiffness produced by recruitment. However, the system response could be linearised by either a suitable combination of rate-coding and recruitment, or by simple recruitment of motor units in order of (exponentially) increasing strength. These plausible control strategies, either alone or in combination, would in effect present the cerebellum with the simplified virtual plant that is assumed in many models of eyeblink conditioning. Future work is therefore needed to determine the extent to which motor neuron firing is in fact linearly related to the nictitating membrane response.     

Can a rheological muscle model predict force depression/enhancement?

A new phenomenological model of activated muscle is presented. The model is based on a combination of a contractile element, an elastic element that engages upon activation, a linear dashpot and a linear spring. Analytical solutions for a few selected experiments are provided. This model is able to reproduce the response of cat soleus muscle to ramp shortening and stretching and, unlike standard Hill-type models, computations are stable on the descending limb of the force–length relation and force enhancement (depression) following stretching (shortening) is predicted correctly. In its linear version, the model is consistent with a linear force–velocity law, which in this model is a consequence rather than a fundamental characteristic of the material. Results show that the mechanical response of activated muscle can be mimicked by a viscoelastic system. Conceptual differences between this model and standard Hill-type models are analyzed and the advantages of the present model are discussed.     

Sensitivity of a Hill-based muscle model to perturbations in model parameters

Musculoskeletal simulations of human movement commonly use Hill muscle models to predict muscle forces, but their sensitivity to model parameter values is not well understood. The purpose of this study was to evaluate muscle model sensitivity to perturbations in 14 Hill muscle model parameters in forward dynamic simulations of running and walking by varying each by +/-50%. Three evaluations of the muscle model were performed based on: (1) calculating the sensitivity of the muscle model only, (2) determining the continuous partial derivatives of the muscle equations with respect to each parameter, and (3) evaluating the effects on the running and walking simulations. Model evaluations were found to be very sensitive (percent change in outputs greater than parameter perturbation) to parameters defining the series elastic component (tendon), force-length curve of the contractile element and maximum isometric force. For some parameters, the range of literature values was larger than the model sensitivity. Model evaluations were insensitive to parameters defining the parallel elastic element, force-velocity curve of the contractile element and muscle activation time constants. The derivative method provided similar results, but also provided a generic, continuous equation that can easily be applied to other motions. The sensitivities of the running and walking simulations were reduced compared to the sensitivity of the muscle model alone. Results demonstrate the importance of evaluating sensitivity of a musculoskeletal simulation in a controlled manner and provide an indication of which parameters must be selected most carefully based on the sensitivity of a given movement.     

Using individual-muscle specific instead of across-muscle mean data halves muscle simulation error

Hill-type parameter values measured in experiments on single muscles show large across-muscle variation. Using individual-muscle specific values instead of the more standard approach of across-muscle means might therefore improve muscle model performance. We show here that using mean values increased simulation normalized RMS error in all tested motor nerve stimulation paradigms in both isotonic and isometric conditions, doubling mean simulation error from 9 to 18 (different at p?<?0.0001). These data suggest muscle-specific measurement of Hill-type model parameters is necessary in work requiring highly accurate muscle model construction. Maximum muscle force (F _max) showed large (fourfold) across-muscle variation. To test the role of F _max in model performance we compared the errors of models using mean F _max and muscle-specific values for the other model parameters, and models using muscle-specific F _max values and mean values for the other model parameters. Using muscle-specific F _max values did not improve model performance compared to using mean values for all parameters, but using muscle-specific values for all parameters but F _max did (to an error of 14, different from muscle-specific, mean all parameters, and mean only F _max errors at p?≤ 0.014). Significantly improving model performance thus required muscle-specific values for at least a subset of parameters other than F _max, and best performance required muscle-specific values for this subset and F _max. Detailed consideration of model performance suggested that remaining model error likely stemmed from activation of both fast and slow motor neurons in our experiments and inadequate specification of model activation dynamics.     

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.     

Motor unit composition has little effect on the short-range stiffness of feline medial gastrocnemius muscle.

Studies on skinned fibers and single motor units have indicated that slow-twitch fibers are stiffer than fast-twitch fibers. This suggests that skeletal muscles with different motor unit compositions may have different short-range stiffness (SRS) properties. Furthermore, the natural recruitment of slow before fast motor units may result in an SRS-force profile that is different from electrical stimulation. However, muscle architecture and the mechanical properties of surrounding tissues also contribute to the net SRS of a muscle, and it remains unclear how these structural features each contribute to the SRS of a muscle. In this study, the SRS-force characteristics of cat medial gastrocnemius muscle were measured during natural activation using the crossed-extension reflex, which activates slow before fast motor units, and during electrical activation, in which all motor units are activated synchronously. Short, rapid, isovelocity stretches were applied using a linear puller to measure SRS across the range of muscle forces. Data were collected from eight animals. Although there was a trend toward greater stiffness during natural activation, this trend was small and not statistically significant across the population of animals tested. A simple model, in which the slow-twitch fibers were assumed to be 30% stiffer than the fast-twitch fibers, was used to simulate the experimental results. Experimental and simulated results show that motor unit composition or firing rate has little effect on the SRS property of the cat MG muscle, suggesting that architectural features may be the primary determinant of SRS.     

Use of motor cortex stimulation to measure simultaneously the changes in dynamic muscle properties and voluntary activation in human muscles.

Force responses to transcranial magnetic stimulation of motor cortex (TMS) during exercise provide information about voluntary activation and contractile properties of the muscle. Here, TMS-generated twitches and muscle relaxation during the TMS-evoked silent period were measured in fresh, heated, and fatigued muscle. Subjects performed isometric contractions of elbow flexors in two studies. Torque and EMG were recorded from elbow flexor and extensor muscles. One study (n = 6) measured muscle contraction times and relaxation rates during brief maximal and submaximal contractions in fresh and fatigued muscle. Another study (n = 7) aimed to 1) assess the reproducibility of muscle contractile properties during brief voluntary contractions in fresh muscle, 2) validate the technique for contractile properties in passively heated muscle, and 3) apply the technique to study contractile properties during sustained maximal voluntary contractions. In both studies, muscle contractile properties during voluntary contractions were compared with the resting twitch evoked by motor nerve stimulation. Measurement of muscle contractile properties during voluntary contractions is reproducible in fresh muscle and reveals faster and slower muscle relaxation rates in heated and fatigued muscle, respectively. The technique is more sensitive to altered muscle state than the traditional motor nerve resting twitch. Use of TMS during sustained maximal contractions reveals slowing of muscle contraction and relaxation with different time courses and a decline in voluntary activation. Voluntary output from the motor cortex becomes insufficient to maintain complete activation of muscle, although slowing of muscle contraction and relaxation indicates that lower motor unit firing rates are required for fusion of force.     

The resilience of the size principle in the organization of motor unit properties in normal and reinnervated adult skeletal muscles

Henneman's size principle relates the input and output properties of motoneurons and their muscle fibers to size and is the basis for size-ordered activation or recruitment of motor units during movement. After nerve injury and surgical repair, the relationship between motoneuron size and the number and size of the muscle fibers that the motoneuron reinnervates is initially lost but returns with time, irrespective of whether the muscles are self- or cross-reinnervated by the regenerated axons. Although the return of the size relationships was initially attributed to the recovery of the cross-sectional area of the reinnervated muscle fibers and their force per fiber, direct enumeration of the innervation ratio and the number of muscle fibers per motoneuron demonstrated that a size-dependent branching of axons accounts for the size relationships in normal muscle, as suggested by Henneman and his colleagues. This same size-dependent branching accounts for the rematching of motoneuron size and muscle unit size in reinnervated muscles. Experiments were carried out to determine whether the daily amount of neuromuscular activation of motor units accounts for the size-dependent organization and reorganization of motor unit properties. The normal size-dependent matching of motoneurons and their muscle units with respect to the numbers of muscle fibers per motoneuron was unaltered by synchronous activation of all of the motor units with the same daily activity. Hence, the restored size relationships and rematching of motoneuron and muscle unit properties after nerve injuries and muscle reinnervation sustain the normal gradation of muscle force during movement by size-ordered recruitment of motor units and the process of rate coding of action potentials. Dynamic modulation of size of muscle fibers and their contractile speed and endurance by neuromuscular activity allows for neuromuscular adaptation in the context of the sustained organization of the neuromuscular system according to the size principle.     

Motor unit activation patterns during concentric wrist flexion in humans with different muscle fibre composition

Muscle activity was recorded from the flexor carpi radialis muscle during static and dynamic-concentric wrist flexion in six subjects, who had exhibited large differences in histochemically identified muscle fibre composition. Motor unit recruitment patterns were identified by sampling 310 motor units and counting firing rates in pulses per second (pps). During concentric wrist flexion at 30% of maximal exercise intensity the mean firing rate was 27 (SD 13) pps. This was around twice the value of 12 (SD 5) pps recorded during sustained static contraction at 30% of maximal voluntary contraction, despite a larger absolute force level during the static contraction. A similar pattern of higher firing rates during dynamic exercise was seen when concentric wrist flexion at 60% of maximal exercise intensity [30 (SD 14) pps] was compared with sustained static contraction at 60% of maximal voluntary contraction [19 (SD 8) pps]. The increase in dynamic exercise intensity was accomplished by recruitment of additional motor units rather than by increasing the firing rate as during static contractions. No difference in mean firing rates was found among subjects with different muscle fibre composition, who had previously exhibited marked differences in metabolic response during corresponding dynamic contractions. It was concluded that during submaximal dynamic contractions motor unit firing rate cannot be deduced from observations during static contractions and that muscle fibre composition may play a minor role. Accepted: 5 May 1998     

Stochastic properties of motoneuron activity and the effect of muscular length

The activity of single motor units contributing to small tonic isometric contractions in human muscle at different muscular lengths was analyzed. The form of motor unit firing patterns shows that the interspike intervals compose independent sequences with about a 10% coefficient of variation and have a gamma distribution. The variability and the distribution shape curves show that as the mean interval decreases the variance also decreases and the interval density function becomes more symmetric. More significant is the fact that the form of the firing pattern remains unchanged when a motor unit has the same mean interval but with the muscle at different lengths. Comparison of these facts with experimental data from neuron models and cat motoneurons indicates that in the human the only relevant input-output relationship in motoneurons is that the net excitation adjusts the firing rate.     

Impedance characteristics of a neuromusculoskeletal model of the human arm I. Posture control

The mechanical impedance of neuromusculoskeletal models of the human arm is studied in this paper. The model analysis provides a better understanding of the contributions of possible intrinsic and reflexive components of arm impedance, makes clear the limitations of second-order mass-viscosity-stiffness models and reveals possible task effects on the impedance. The musculoskeletal model describes planar movements of the upper arm and forearm, which are moved by six lumped muscles with nonlinear dynamics. The motor control system is represented by a neural network which combines feedforward and feedback control. It is optimized for the control of movements or for posture control in the presence of external forces. The achieved impedance characteristics depend on the conditions during the learning process. In particular, the impedance is adapted in a suitable way to the frequency content and direction of external forces acting on the hand during an isometric task. The impedance characteristics of a model, which is optimized for movement control, are similar to experimental data in the literature. The achieved stiffness is, to a large extent, reflexively determined whereas the approximated viscosity is primarily due to intrinsic attributes. It is argued that usually applied Hill-type muscle models do not properly represent intrinsic muscle stiffness. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

Phenomenological models of the dynamics of muscle during isotonic shortening

We investigated the effectiveness of simple, Hill-type, phenomenological models of the force-length-velocity relationship for simulating measured length trajectories during muscle shortening, and, if so, what forms of the model are most useful. Using isotonic shortening data from mouse soleus and toad depressor mandibulae muscles, we showed that Hill-type models can indeed simulate the shortening trajectories with sufficiently good accuracy. However, we found that the standard form of the Hill-type muscle model, called the force-scaling model, is not a satisfactory choice. Instead, the results support the use of less frequently used models, the f-max scaling model and force-scaling with parallel spring, to simulate the shortening dynamics of muscle.