The influence of the way the muscle force is modeled on the predicted results obtained by solving indeterminate problems for a fast elbow flexion

A critical point in models of the human limbs when the aim is to investigate the motor control is the muscle model. More often the mechanical output of a muscle is considered as one musculotendon force that is a design variable in optimization tasks solved predominantly by static optimization. For dynamic conditions, the relationship between the developed force, the length and the contraction velocity of a muscle becomes important and rheological muscle models can be incorporated in the optimization tasks. Here the muscle activation can be a design variable as well. Recently a new muscle model was proposed. A muscle is considered as a mixture of motor units (MUs) with different peculiarities and the muscle force is calculated as a sum of the MUs twitches. The aim of the paper is to compare these three ways for presenting the muscle force. Fast elbow flexion is investigated using a planar model with five muscles. It is concluded that the rheological models are suitable for calculation of the current maximal muscle forces that can be used as weight factors in the objective functions. The model based on MUs has many advantages for precise investigations of motor control. Such muscle presentation can explain the muscle co-contraction and the role of the fast and the slow MUs. The relationship between the MUs activation and the mechanical output is more clear and closer to the reality.     

Modeling investigation of learning a fast elbow flexion in the horizontal plane--prediction of muscle forces and motor units action

Experimental investigation of practicing a dynamic, goal-directed movement reveals significant changes in kinematics. Modeling can provide insight into the alterations in muscle activity, associated with the kinematic adaptations, and reveal the potential motor unit (MU) firing patterns that underlie those changes. In this paper, a previously developed muscle model and software (Raikova and Aladjov, Journal of Biomechanics, 35, 2002) have been used to investigate changes in MU control, while practicing fast elbow flexion to a target in the horizontal plane. The first trial (before practice) and the last trial (after extensive practice) of two subjects have been simulated. The inputs for the simulation were the calculated external moments at the elbow joint. The external moments were countered by the action of three flexor muscles and two extensor ones. The muscles have been modeled as a mixture of MUs of different types. The software has chosen the MU firing times necessary to accomplish the movement. The muscle forces and MUs firing statistics were then calculated. Three hypotheses were tested and confirmed: (1) peak muscle forces and antagonist co-contraction increase during training; (2) there is an increase in the firing frequency and the synchronization between MUs; and (3) the recruitment of fast-twitch MUs dominates the action.     

Modeling investigation of learning a fast elbow flexion in the horizontal plane—prediction of muscle forces and motor units action

Experimental investigation of practicing a dynamic, goal-directed movement reveals significant changes in kinematics. Modeling can provide insight into the alterations in muscle activity, associated with the kinematic adaptations, and reveal the potential motor unit (MU) firing patterns that underlie those changes. In this paper, a previously developed muscle model and software (Raikova and Aladjov, Journal of Biomechanics, 35, 2002) have been used to investigate changes in MU control, while practicing fast elbow flexion to a target in the horizontal plane. The first trial (before practice) and the last trial (after extensive practice) of two subjects have been simulated. The inputs for the simulation were the calculated external moments at the elbow joint. The external moments were countered by the action of three flexor muscles and two extensor ones. The muscles have been modeled as a mixture of MUs of different types. The software has chosen the MU firing times necessary to accomplish the movement. The muscle forces and MUs firing statistics were then calculated. Three hypotheses were tested and confirmed: (1) peak muscle forces and antagonist co-contraction increase during training; (2) there is an increase in the firing frequency and the synchronization between MUs; and (3) the recruitment of fast-twitch MUs dominates the action.     

The Influence of the Way the Muscle Force is Modeled on the Predicted Results Obtained by Solving Indeterminate Problems for a Fast Elbow Flexion

A critical point in models of the human limbs when the aim is to investigate the motor control is the muscle model. More often the mechanical output of a muscle is considered as one musculotendon force that is a design variable in optimization tasks solved predominantly by static optimization. For dynamic conditions, the relationship between the developed force, the length and the contraction velocity of a muscle becomes important and rheological muscle models can be incorporated in the optimization tasks. Here the muscle activation can be a design variable as well. Recently a new muscle model was proposed [22] Raikova R.T. Aladjov H.Ts. 2002 Hierarchical genetic algorithm versus static optimization–investigation of elbow flexion and extension movements Journal of Biomechanics 35 1123 1135  [Google Scholar]. A muscle is considered as a mixture of motor units (MUs) with different peculiarities and the muscle force is calculated as a sum of the MUs twitches. The aim of the paper is to compare these three ways for presenting the muscle force. Fast elbow flexion is investigated using a planar model with five muscles. It is concluded that the rheological models are suitable for calculation of the current maximal muscle forces that can be used as weight factors in the objective functions. The model based on MUs has many advantages for precise investigations of motor control. Such muscle presentation can explain the muscle co-contraction and the role of the fast and the slow MUs. The relationship between the MUs activation and the mechanical output is more clear and closer to the reality.     

Comparative analysis of motor unit action potentials of the medial gastrocnemius muscle in cats and rats

Properties of motor unit action potentials (MUAPs) were compared for medial gastrocnemius (MG) motor units (MUs) in cats and rats. The experiments on functionally isolated MUs were performed under general anaesthesia, under comparable conditions (surgery, stimulating protocol and recording methods) for both species investigated. The proportions of motor units and contractile properties of the sample used in the study were consistent with previous studies performed on the MG muscle in both animal species, so comparisons of action potentials of individual types of MUs were acknowledged as fully reliable. The most prominent differences concerning MUAPs were observed in total duration and peak-to-peak times which for all MU types were about twice longer in cat MUs, in comparison to the rat MUs. The considerable disproportions were observed between the MUAP amplitudes of FF (fast fatigable), FR (fast resistant to fatigue) and S (slow) MUs in each species (the highest amplitudes were measured for FF and the lowest for S MUs), but there were no significant differences between cat and rat when respective types of MUs were compared. The shapes of MUAPs were commonly characterized by biphasic waveforms composed of two or three turns in all types of units, and no interspecies differences were revealed. Several factors influencing MUAP parameters were discussed indicating most of all importance of variable length of cat and rat muscle fibres and ambiguous influence of motor unit size, thickness of muscle fibres and their density around the recording electrode in the MG muscle of both species.     

Experimentally verified mathematical approach for the prediction of force developed by motor units at variable frequency stimulation patterns

During normal daily activity, muscle motor units (MUs) develop unfused tetanic contractions evoked by trains of motoneuronal firings at variable interpulse intervals (IPIs). The mechanical responses of a MU to successive impulses are not identical. The aim of this study was to develop a mathematical approach for the prediction of each response within the tetanus as well as the tetanic force itself. Experimental unfused tetani of fast and slow rat MUs, evoked by trains of stimuli at variable IPIs, were decomposed into series of twitch-shaped responses to successive stimuli using a previously described algorithm. The relationships between the parameters of the modeled twitches and the tetanic force level at which the next response begins were examined and regression equations were derived. Using these equations, profiles of force for the same and different stimulation patterns were mathematically predicted by summating modeled twitches. For comparison, force predictions were made by the summation of twitches equal to the first one. The recorded and the predicted tetanic forces were compared. The results revealed that it is possible to predict tetanic force with high accuracy by using regression equations. The force predicted in this way was much closer to the experimental record than the force obtained by the summation of equal twitches, especially for slow MUs. These findings are likely to have an impact on the development of realistic muscle models composed of MUs, and will assist our understanding of the significance of the neuronal code in motor control and the role of biophysical processes during MU contractions.     

Experimental and modelling investigation of learning a fast elbow flexion in the horizontal plane

Changes in the kinematic and electromyographic characteristics that occur while learning to move as fast as possible have been studied experimentally. Experimental investigation of what happens to the individual motor units (MUs) is more difficult. Access to each MU is impossible, and the recruitment and force developing properties of all individual MUs cannot be known. Thus, what is currently known about MU firing is based on experiments that have recorded relatively few MUs compared to what exists in the entire muscle. A recently developed muscle model (Raikova and Aladjov, 2002, J. Biomechanics, 35, 1123-1135) composed of MUs with different properties can be used for such investigation. The process of learning fast elbow flexion in the horizontal plane was simulated and the results were compared with experimentally measured data. Comparing the simulation results of the very first trial of a particular subject with those of the last trail (at the end of the learning process), it can be concluded that the speed of limb motion and muscle forces increase initially as a result of the more synchronous MUs activation and the increase of firing rate of active MUs. Further improvement necessitated an appreciable reduction in the motor task requirements (i.e. less muscle force and less MUs' activity) set in the computational algorithm by optimization criteria. This forced the next process-inclusion of additional MUs.     

Hierarchical genetic algorithm versus static optimization-investigation of elbow flexion and extension movements

The applicability of static optimization (and, respectively, frequently used objective functions) for prediction of individual muscle forces for dynamic conditions has often been discussed. Some of the problems are whether time-independent objective functions are suitable, and how to incorporate muscle physiology in models. The present paper deals with a twofold task: (1) implementation of hierarchical genetic algorithm (HGA) based on the properties of the motor units (MUs) twitches, and using multi-objective, time-dependent optimization functions; and (2) comparison of the results of the HGA application with those obtained through static optimization with a criterion "minimum of a weighted sum of the muscle forces raised to the power of n". HGA and its software implementation are presented. The moments of neural stimulation of all MUs are design variables coding the problem in the terms of HGA. The main idea is in using genetic operations to find these moments, so that the sum of MUs twitches satisfies the imposed goals (required joint moments, minimal sum of muscle forces, etc.). Elbow flexion and extension movements with different velocities are considered as proper illustration. It is supposed that they are performed by two extensor muscles and three flexor muscles. The results show that HGA is a suitable means for precise investigation of motor control. Many experimentally observed phenomena (such as antagonistic co-contraction, three-phasic behavior of the muscles during fast movements) can find their explanation by the properties of the MUs twitches. Static optimization is also able to predict three-phasic behavior and could be used as practicable and computationally inexpensive method for total estimation of the muscle forces.     

In-series fiber architecture in long human muscles

The fiber architecture of adult human sartorius and gracilis muscles was examined using a combination of fiber microdissections and histological methods. Intact fibers were dissected from fascicles of muscle strips that were digested in nitric acid. All of these fibers terminate intrafascicularly by tapering to a fine strand at one or both ends. They measure 4–20 cm after correction for shrinkage. Systematic dissections of 1 cm long blocks sampled at intervals along the muscle length suggest that tapered fiber endings occur at all locations along the muscle but are most common centrally; here they accounted for up to 14% of dissected fibers in each block. Transverse sections of muscle confirm that fiber profiles with small diameters occur at all levels of the muscle but are especially common in sections more than 5 cm from its origin or insertion. The architectural arrangement demonstrated here suggests that long human muscles, like muscles in other species, are composed of relatively short, in-series fibers. This has many implications for the neural activation and force-developing behavior of these muscles that must be considered when paralyzed muscles are reanimated using electrical stimulation. Further, it may predispose long muscles to certain types of neuromuscular damage and dysfunction. © 1993 Wiley-Liss, Inc.     

Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle

The synchronized firings of active motor units (MUs) increase the oscillations of muscle force, observed as physiological tremor. This study aimed to investigate the effects of synchronizing the firings within three types of MUs (slow—S, fast resistant to fatigue–FR, and fast fatigable–FF) on the muscle force production using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including 8 S, 23 FR, and 26 FF) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions.     

Analysis of a muscular control system in human movements

In this work, we have studied a muscular control system under experimental conditions for analyzing the dynamic behavior of individual muscles and theoretical considerations for elucidating its control strategy. Movement of human limbs is achieved by joint torques and each torque is specified as the sum of torques generated by muscle forces. The behavior of individual muscles is controlled by the neural input which is estimated by means of an electromyogram (EMG). In this study, the EMGs for a flexor and an extensor are measured in elbow joint movements and the dynamic behavior of individual muscles is analyzed. As a result, it is verified that both a flexor and an extensor are activated throughout the entire movement and that the activation of muscles is controlled above a specific limit independent of the hand-held load. Subsequently, a system model for simulating elbow joint movements is developed which includes the muscle dynamic relationship between the neural input and the isometric force. The minimum limit of muscle activation that has been confirmed in experiments is provided as a constraint of the neural input and the criterion is defined by a derivative of the isometric force of individual muscles. The optimal trajectories formulated under these conditions are quantitatively compared with the experimentally observed trajectories, and the control strategy of a muscular control system is studied. Finally, a muscular control system in multi-joint arm movements is discussed with regard to the comparative analysis between observed and optimal trajectories. Received: 7 April 1999 / Accepted in revised form: 27 July 1999     

Ultrastructural localization of lectin receptors on the bone-marrow sinusoidal endothelium of the rat

The purpose of this study was to estimate the absolute and relative masses of the three types of skeletal muscle fibers in the total hindlimb of the male Sprague-Dawley rat (Rattus norvegicus). For six rats, total body mass was recorded and the following weights taken from dissection of one hindlimb: 32 individual major muscles or muscle parts, remaining skeletal musculature (small hip muscles and intrinsic foot muscles), bone, inguinal fat pad, and skin. The fibers from the 32 muscles or muscle parts (which constituted 98% of the hindlimb skeletal muscle mass) were classified from histochemistry as fast-twitch oxidative glycolytic (FOG), fast-twitch glycolytic (FG), or slow-twitch oxidative (SO), and their populations were determined. Fiber cross-sectional areas from the same muscles were measured with a digitizer. Mass of each of the fiber types within muscles and in the total hindlimb was then calculated from fiber-type population, fiber-type area, and muscle-mass data. Skeletal muscle made up 71% of the total hindlimb mass. Of this, 76% was occupied by FG fibers, 19% by FOG fibers, and 5% by SO fibers. Thus, the FG fiber type is clearly the predominant fiber type in the rat hindlimb in terms of muscle mass. Fiber-type mass data are compared with physiological (blood flow) and biochemical (succinate dehydrogenase activities) data for the muscles taken from previous studies, and it is demonstrated that these functional properties are closely related to the proportions of muscle mass composed of the various fiber types.     

Mathematical Model for Skeletal Muscle to Simulate the Concentric and Eccentric Contraction

Skeletal muscles are responsible for the relative motion of the bones at the joints and provide the required strength. They exhibit highly nonlinear mechanical behaviour and are described by nonlinear hyperelastic constitutive relations. It is distinct from other biological soft tissue. Its hyperelastic or viscoelastic behaviour is modelled by using CE, SEE, and PEE. Contractile element simulates the behaviour of skeletal muscle when it is subjected to eccentric and concentric contraction. This research aims to estimate the stress induced in skeletal muscle in eccentric and concentric contraction with respect to the predefined strain. With the use of mathematical model for contraction of skeletal muscle for eccentric and concentric contraction, the stress induced in the skeletal muscle is estimated in this research. Mathematical model is developed for the muscle using EMG signals and Force-velocity relationship calculated. With the use of force-velocity of contraction of muscle, mathematical model is developed. This can be useful to understand the mechanical behaviour of skeletal muscles in eccentric and concentric contraction with clinical relevance. Authors are further working to develop the mathematical model with torsion force with proper activation function of muscle and experimentation for extraction of the anisotropic mechanical properties of skeletal muscle.     

Anatomy and muscle activity of the dorsal fins in bamboo sharks and spiny dogfish during turning maneuvers

Stability and procured instability characterize two opposing types of swimming, steady and maneuvering, respectively. Fins can be used to manipulate flow to adjust stability during swimming maneuvers either actively using muscle control or passively by structural control. The function of the dorsal fins during turning maneuvering in two shark species with different swimming modes is investigated here using musculoskeletal anatomy and muscle function. White‐spotted bamboo sharks are a benthic species that inhabits complex reef habitats and thus have high requirements for maneuverability. Spiny dogfish occupy a variety of coastal and continental shelf habitats and spend relatively more time cruising in open water. These species differ in dorsal fin morphology and fin position along the body. Bamboo sharks have a larger second dorsal fin area and proportionally more muscle insertion into both dorsal fins. The basal and radial pterygiophores are plate‐like structures in spiny dogfish and are nearly indistinguishable from one another. In contrast, bamboo sharks lack basal pterygiophores, while the radial pterygiophores form two rows of elongated rectangular elements that articulate with one another. The dorsal fin muscles are composed of a large muscle mass that extends over the ceratotrichia overlying the radials in spiny dogfish. However, in bamboo sharks, the muscle mass is divided into multiple distinct muscles that insert onto the ceratotrichia. During turning maneuvers, the dorsal fin muscles are active in both species with no differences in onset between fin sides. Spiny dogfish have longer burst durations on the outer fin side, which is consistent with opposing resistance to the medium. In bamboo sharks, bilateral activation of the dorsal in muscles could also be stiffening the fin throughout the turn. Thus, dogfish sharks passively stiffen the dorsal fin structurally and functionally, while bamboo sharks have more flexible dorsal fins, which result from a steady swimming trade off. J. Morphol. 274:1288–1298, 2013. © 2013 Wiley Periodicals, Inc.     

Superficial architecture of the jaw-closing muscles of the cat (Felis catus): the temporo-masseteric complex

The muscle fiber fascicles of the temporo-masseter complex of the cat were minutely dissected. Some heads were embedded in paraffin while others were put into methyl-methacrylate resin and sections were made. The results of this anatomical study demonstrate that this complex consists of the masseter muscle, the temporal muscle and two well individualized transitional fascicles: the maxillomandibularis and zygomato-comandibularis muscles. The masseter and temporal muscles are composed of individualized compartments in which the orientation and aponeuroses of the fibers of which they are composed differ with regard to the centric occlusion plane. The masseter muscle consists of a superficial fascicle made up of two layers, an intermediate fascicle, and a deep fascicle composed of two layers. The temporal muscle consists of one anterior orbital part and one posterior temporal part. This structure is in accordance with the mammalian archetype described by Gaspard and Saban. These findings should lead towards a homology-based nomenclature founded on comparative anatomy studies of mammalian species. Such a classification would permit the comparison of results obtained from physiological and histochemical studies of these complex muscle fibers when they are published by different researchers.     

Models of skeletal muscle to explain the increase in passive stiffness in desmin knockout muscle

Absence of desmin in skeletal muscle was found to induce an increase in passive stiffness. The present study aimed at developing rheological models of passive muscle to explain this stiffening. Models were elaborated by using experimental data depicting muscle viscoelastic behaviour. The experimental protocol included stepwise extension tests applied on control and desmin knockout soleus muscles from mice. Linear and non-linear models were composed of elastic and viscous elements. They were constructed with the aim at taking the presence or absence of desmin into account by simulating desmin as an elastic element. Furthermore, associated adaptation of connective tissues in absence of desmin was modelled as an additional elastic element. Differences in passive behaviour induced by absence of desmin were predicted by using a linear model and a non-linear one. The non-linear model was selected because: (1) it is able to predict experimental viscoelastic kinetics accounting for the increase in passive stiffness in muscles lacking desmin, (2) its design is consistent with morphological data, and (3) stiffness characteristics of its elements are in accordance with the literature. Finally, this modelling approach demonstrates that both absence of desmin and adaptation of connective tissue are required to explain the increase in passive stiffness in desmin knockout muscles.     

Role of biomechanics and muscle activation strategy in the production of endpoint force patterns in the cat hindlimb

We used a musculoskeletal model of the cat hindlimb to compare the patterns of endpoint forces generated by all possible combination of 12 hindlimb muscles under three different muscle activation rules: homogeneous activation of muscles based on uniform activation levels, homogeneous activation of muscles based on uniform (normalized) force production, and activation based on the topography of spinal motoneuron pools. Force patterns were compared with the patterns obtained experimentally by microstimulation of the lumbar spinal cord in spinal intact cats. Magnitude and orientation of the force patterns were compared, as well as the proportion of the types found, and the proportions of patterns exhibiting points of zero force (equilibrium points). The force patterns obtained with the homogenous activation and motoneuron topography models were quite similar to those measured experimentally, with the differences being larger for the patterns from the normalized endpoint forces model. Differences in the proportions of types of force patterns between the three models and the experimental results were significant for each model. Both homogeneous activation and normalized endpoint force models produced similar proportions of equilibrium points as found experimentally. The results suggest that muscle biomechanics play an important role in limiting the number of endpoint force pattern types, and that muscle combinations activated at similar levels reproduced best the experimental results obtained with intraspinal microstimulation.     

Responses in knee joint muscle activation patterns to different perturbations during gait in healthy subjects

PurposeTo compare the responses in knee joint muscle activation patterns to different perturbations during gait in healthy subjects.ScopeNine healthy participants were subjected to perturbed walking on a split-belt treadmill. Four perturbation types were applied, each at five intensities. The activations of seven muscles surrounding the knee were measured using surface EMG. The responses in muscle activation were expressed by calculating mean, peak, co-contraction (CCI) and perturbation responses (PR) values. PR captures the responses relative to unperturbed gait. Statistical parametric mapping analysis was used to compare the muscle activation patterns between conditions.ResultsPerturbations evoked only small responses in muscle activation, though higher perturbation intensities yielded a higher mean activation in five muscles, as well as higher PR. Different types of perturbation led to different responses in the rectus femoris, medial gastrocnemius and lateral gastrocnemius. The participants had lower CCI just before perturbation compared to the same phase of unperturbed gait.ConclusionsHealthy participants respond to different perturbations during gait with small adaptations in their knee joint muscle activation patterns. This study provides insights in how the muscles are activated to stabilize the knee when challenged. Furthermore it could guide future studies in determining aberrant muscle activation in patients with knee disorders.     

Phenotype plasticity in postural muscles of the crayfish Orconectes limosus Raf.: correlation of myofibrillar ATPase-based fiber typing with electrophysiological fiber properties and the effect of chronic nerve stimulation

The characteristics of the medial and lateral superficial extensor muscles (sem and sel) in the crayfish Orconectes limosus abdomen and their developmental and activity-dependent plasticity were studied. It was shown that both muscles are innervated by at least five excitatory and one inhibitory motor neuron in a nonuniform pattern. The muscles are composed of at least three different mATPase histochemistry-based fiber types that are all different from a fourth type in the uniform deep extensor muscles. sem and sel are composed of different ratios of these fiber types but do not show a constant fiber type pattern between segments and even between hemisegments. The three histochemically defined superficial extensor-fiber types have characteristic electrophysiological properties. The fiber types were shown to develop successively during the first postembryonic stages of development without a change in the number of muscle fibers. Based on histochemical ATPase staining after 21 days of chronic stimulation by means of an implantable, double-hook electrode, we show preliminary evidence that the fiber composition in the sem can switch from the presumably fast fiber type III to an intermediate type II. Repeated axotomy up to 53 days had no effect on the fiber type composition of the muscles.     

A method for estimating torque-vector directions of shoulder muscles using surface EMGs

In this study, a new method is proposed to estimate the torque-vector directions of each shoulder muscle. The method is based on a multiple regression model that reconstructs shoulder torque, which is calculated from the hand force and posture, from the surface EMG of many muscles recorded simultaneously. The torque-vector directions of eleven shoulder muscles of four subjects were obtained at up to 30 different arm postures with this method. The mean confidence interval ( p< 0.05) of the estimated torque-vector direction of each subject was 7.7-10.6 degrees. The correlation coefficient between the measured shoulder torque and reconstructed shoulder torque was between 0.76-0.84. The results for majority of the muscles were in accordance with previous studies, and reasonable from the viewpoint of anatomy. The torque-vector directions of a muscle, which are estimated with this method, have more of a functional meaning than a pure anatomical or mechanical one. These indicate the direction of the shoulder torque accompanying the muscle activation for a normal shoulder action that involves the cooperative contraction of many muscles.