Mechanical energy expenditure on human movement and the anthropomorphic mechanism]

Mechanical energy expenditures of the man and anthropomorphic locomotion machine during movement are compared theoretically. Sources of the mechanical energy affecting movement of human's lower extremity are modelled by 8 muscles, 3 of which are the two-joint muscles. The model of the lower extremity of anthropomorphic locomotion machine is moved by joint moments. It was shown that in the same movement the model of the human lower extremity can spend less mechanical energy than that of the model of the anthropomorphic locomotion machine. It is caused by the presence of two-joint muscles in the first model. Such an economy of mechanical energy expenditures realized by the two-joint muscle is possible at simultaneous execution of three conditions: 1) signs of the muscle powers, which are produced by that muscle at both joints, are opposite; 2) moments produced by that muscle at each of both joints have the same direction with the joint moments at these joints; 3) one-joint antagonistic muscles are not active. An expression which makes it possible to estimate the mechanical energy savings by the two-joint muscles during humans' movement was developed.     

Activation of the Shoulder-Belt and Shoulder Muscles in Two-Joint Arm Movements Performed in Humans with the Action of Opposite Loadings

In tests on four volunteers, we examined coordination of central motor commands (CMCs) controlling slow two-joint movements of the arm within the horizontal plane. Current amplitudes of EMGs recorded from six muscles of the shoulder belt and shoulder and subjected to full-wave rectifying and low-frequency filtration were considered correlates of these commands. In particular, we studied the dependence of coordination of CMCs on the direction of an external force applied to the distal forearm part. As was found, coordination of CMCs significantly depends on the direction of the force flexing the elbow joint. According to our observations, EMGs of definite muscles in the case of performance of a two-joint movement can, in a first approximation, be presented as linear combinations of the EMGs recorded in the course of separate sequential single-joint movements under conditions of shifting the reference point of the hand toward the same point of the operational space as that in the two-joint movement. These data can be interpreted as confirmation of the principle of superposition of elementary CMCs in the performance of complex movements of the extremity.     

Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation

Non-linear optimisation, such as the type presented by R.D. Crowninshield and R.A. Brand [The prediction of forces in joint structures: Distribution of intersegmental resultants, Exercise Sports Sci. Rev. 9 (1981) 159], has been frequently used to obtain a unique set of muscle forces during human or animal movements. In the past, analytical solutions of this optimisation problem have been presented for single degree-of-freedom models, and planar models with a specific number of muscles and a defined musculoskeletal geometry. Results of these studies have been generalised to three-dimensional problems and for general formulations of the musculoskeletal geometry without corresponding proofs. Here, we extend the general solution of the above non-linear, constrained, planar optimisation problem to three-dimensional systems of arbitrary geometry. We show that there always exists a set of intersegmental moments for which the given static optimisation formulation will predict co-contraction of a pair of antagonistic muscles unless they are exact antagonists. Furthermore, we provide, for a given three-dimensional system consisting of single joint muscles, a method that describes all the possible joint moments that give co-contraction for a given pair of antagonistic muscles.     

On the possibility of linear modelling the human arm neuromuscular apparatus

It has been widely claimed that linear models of the neuromuscular apparatus give very inaccurate approximations of human arm reaching movements. The present paper examines this claim by quantifying the contributions of the various non-linear effects of muscle force generation on the accuracy of linear approximation. We performed computer simulations of a model of a two-joint arm with six monarticular and biarticular muscles. The global actions of individual muscles resulted in a linear dependence of the joint torques on the joint angles and angular velocities, despite the great non-linearity of the muscle properties. The effect of time delay in force generation is much more important for model accuracy than all the non-linear effects, while ignoring this time delay in linear approximation results in large errors. Thus, the viscosity coefficients are rather underestimated and some of them can even be paradoxically estimated to be negative. Similarly, our computation showed that ignoring the time delay resulted in large errors in the estimation of the hand equilibrium trajectory. This could explain why experimentally estimated hand equilibrium trajectories may be complex, even during a simple reaching movement. The hand equilibrium trajectory estimated by a linear model becomes simple when the time delay is taken into account, and it is close to that actually used in the non-linear model. The results therefore provide a theoretical basis for estimating the hand equilibrium trajectory during arm reaching movements and hence for estimating the time course of the motor control signals associated with this trajectory, as set out in the equilibrium point hypothesis. Received: 17 February 1999 / Accepted in revised form: 22 October 1999     

A mathematical analysis of the force-stiffness characteristics of muscles in control of a single joint system

Feldman (1966) has proposed that a muscle endowed with its spinal reflex system behaves as a non-linear spring with an adjustable resting length. In contrast, because of the length-tension properties of muscles, many researchers have modeled them as non-linear springs with adjustable stiffness. Here we test the merits of each approach: Initially, it is proven that the adjustable stiffness model predicts that isometric muscle force and stiffness are linearly related. We show that this prediction is not supported by data on the static stiffness-force characteristics of reflexive muscles, where stiffness grows non-linearly with force. Therefore, an intact muscle-reflex system does not behave as a non-linear spring with an adjustable stiffness. However, when the same muscle is devoid of its reflexes, the data shows that stiffness grows linearly with force. We aim to understand the functional advantage of the non-linear stiffness-force relationship present in the reflexive muscle. Control of an inverted pendulum with a pair of antagonist muscles is considered. Using an active-state muscle model we describe force development in an areflexive muscle. From the data on the relationship of stiffness and force in the intact muscle we derive the length-tension properties of a reflexive muscle. It is shown that a muscle under the control of its spinal reflexes resembles a non-linear spring with an adjustable resting length. This provides independent evidence in support of the Feldman hypothesis of an adjustable resting length as the control parameter of a reflexive muscle, but it disagrees with his particular formulation. In order to maintain stability of the single joint system, we prove that a necessary condition is that muscle stiffness must grow at least linearly with force at isometric conditions. This shows that co-contraction of antagonist muscles may actually destabilize the limb if the slope of this stiffness-force relationship is less than an amount specified by the change in the moment arm of the muscle as a function of joint configuration. In a reflexive muscle where stiffness grows faster than linearly with force, co-contraction will always lead to an increase in stiffness. Furthermore, with the reflexive muscles, the same level of joint stiffness can be produced by much smaller muscle forces because of the non-linear stiffness-force relationship. This allows the joint to remain stable at a fraction of the metabolic energy cost associated with maintaining stability with areflexive muscles.This work was supported in part by grant no. 1R01 NS 24926 from the NIH (Michael Arbib, PI). R.S. was supported by an IBM Graduate Fellowship in Computer Science     

Peculiarities of Activation of the Upper Limb Muscles in Realization of Two-Joint Movements in Humans

In tests on humans, we recorded EMG activity from the muscles flexing and extending the forearm and shoulder in the course of realization of sequential single-joint and simultaneous two-joint movements of the upper limb. As was shown, the shoulder muscles m. biceps brachii and m. triceps brachii are involved in flexion/extension of both elbow and shoulder joints. Central commands sent to the above muscles in the course of a two-joint movement could be considered a superposition of the central commands coming to the same muscles in realization of the corresponding sequential single-joint movements with the same changes in the angles of the elbow and shoulder joints. External loadings applied in the direction of extension of the elbow and shoulder joints induced, in general, similar changes in coordination of the activity of muscles moving the forearm and shoulder under conditions of both single-joint and two-joint movements. These facts allow us to suppose that coordination of the muscle activity in two-joint movements depends to a greater extent on the forces influencing limb links than on the mode of realization of the movements (two sequential single-joint movements vs a two-joint movement corresponding to the above motor events).     

A quantitative assessment of the "tendon" action of two-joint muscles]

Two-joint muscles are able to transmit mechanical energy between the links of the body having no common joint ("tendon action" of the muscles). It is proposed to calculate difference between control moment power in a joint and the sum of powers developed by all muscles serving this joint in order to determine the direction and rate of mechanical energy transfer through the two-joint muscles. It was shown that in the shock-absorbing phase of support in running two-joint muscles the energy transfers from distal to proximal links (from foot to thigh, and from shank to pelvis), in take-off phase-from proximal links to distal ones (from pelvis to shank, and from thigh to foot).     

Peculiarities of Activation of Muscles of the Shoulder Belt in Voluntary Two-Joint Movements of the Upper Limb

We studied coordination of central motor commands (СMCs) coming to muscles of the shoulder and shoulder belt in the course of single-joint and two-joint movements including flexion and extension of the elbow and shoulder joints. Characteristics of rectified and averaged EMGs recorded from a few muscles of the upper limb were considered correlates of the CMC parameters. Special attention was paid to coordination of CMCs coming to two-joint muscles that are able to function as common flexors (m. biceps brachii, caput breve, BBcb) and common extensors (m. triceps brachii, caput longum, TBcl) of the elbow and shoulder joints. Upper limb movements used in the tests included planar shifts of the arm from one spatial point to another resulting from either simultaneous changes in the angles of the shoulder and elbow joints or isolated sequential (two-stage) changes in these joint angles. As was found, shoulder muscles providing movements of the elbow with changes in the angle of the elbow joint, i.e., BBcb and TBcl, were also intensely involved in the performance of single-joint movements in the shoulder joint. The CMCs coming to two-joint muscles in the course of two-joint movements appeared, in the first approximation, as sums of the commands received by these muscles in the course of corresponding single-joint movements in the elbow and shoulder joints. Therefore, if we interpret the isolated forearm movement performed due to a change in the angle of the elbow joint as the main motor event, while the shoulder movement is considered the accessory one, we can conclude that realization of a two-joint movement of the upper-limb distal part is based on superposition of CMCs related to basic movements (main and accessory). Neirofiziologiya/Neurophysiology, Vol. 41, No. 1, pp. 48–56, January–February, 2009.     

Oblique abdominal muscle activity in response to external perturbations when pushing a cart

Cyclic activation of the external and internal oblique muscles contributes to twisting moments during normal gait. During pushing while walking, it is not well understood how these muscles respond to presence of predictable (cyclic push-off forces) and unpredictable (external) perturbations that occur in pushing tasks. We hypothesized that the predictable perturbations due to the cyclic push-off forces would be associated with cyclic muscle activity, while external perturbations would be counteracted by cocontraction of the oblique abdominal muscles. Eight healthy male subjects pushed at two target forces and two handle heights in a static condition and while walking without and with external perturbations. For all pushing tasks, the median, the static (10th percentile) and the peak levels (90th percentile) of the electromyographic amplitudes were determined. Linear models with oblique abdominal EMGs and trunk angles as input were fit to the twisting moments, to estimate trunk stiffness. There was no significant difference between the static EMG levels in pushing while walking compared to the peak levels in pushing while standing. When pushing while walking, the additional dynamic activity was associated with the twisting moments, which were actively modulated by the pairs of oblique muscles as in normal gait. The median and static levels of trunk muscle activity and estimated trunk stiffness were significantly higher when perturbations occurred than without perturbations. The increase baseline of muscle activity indicated cocontraction of the antagonistic muscle pairs. Furthermore, this cocontraction resulted in an increased trunk stiffness around the longitudinal axis.     

Mechanical energy costs of human movement: an approach to evaluating the transfer possibilities of two-joint muscles

Different methods of calculating the mechanical energy cost of a movement presented in the literature can give results differing by an order of magnitude. The assumptions made concerning the transfer of energy between different parts of the body are part of the problem. This investigation assesses the role of transfer in energy saving and specifically, the possibility of two-joint muscles reducing the mechanical energy cost of a movement compared to a system having one-joint muscles only. An algorithm was developed which recruited one-joint or both one- and two-joint muscles to supply the net joint moments. The work performed under these two conditions was then compared. It was found that activation of both one- and two-joint musculature reduced the mechanical work cost during walking by between 7 and 29% over that required by single-joint musculature alone. This investigation supports suggestions in the literature that one of the functions of two-joint musculature is to reduce the mechanical energy cost and probably the metabolic cost of movement.     

Myofascial force transmission also occurs between antagonistic muscles located within opposite compartments of the rat lower hind limb

Force transmission via pathways other than myotendinous ones, is referred to as myofascial force transmission. The present study shows that myofascial force transmission occurs not only between adjacent synergistic muscles or antagonistic muscles in adjacent compartments, but also between most distant antagonistic muscles within a segment. Tibialis anterior (TA), extensor hallucis longus (EHL), extensor digitorum longus (EDL), peroneal muscles (PER) and triceps surae muscles of 7 male anaesthetised Wistar rats were attached to force transducers, while connective tissues at the muscle bellies were left fully intact. The TA + EHL-complex was made to exerted force at different lengths, but the other muscles were held at a constant muscle–tendon complex length. With increasing TA + EHL-complex length, active force of maximally activated EDL, PER and triceps surae decreased by maximally 5%, 32% and 16%, respectively. These decreases are for the largest part explained by myofascial force transmission. Particularly the force decrease in triceps surae muscles is remarkable, because these muscles are located furthest away from the TA + EHL-complex. It is concluded that substantial extramuscular myofascial force transmission occurs between antagonistic muscles even if the length of the path between them is considerable.     

Mechanical analysis of the sea-urchin lantern: the overall system in Paracentrotus lividus

The dental apparatus or Aristotle's lantern of sea-urchins is a complex system of interacting skeletal ossicles, joints, muscles and ligaments arranged in a rigorous geometry and involved in a variety of activities. In this paper we study the movement of the whole lantern system modelled as a rigid body. The model lantern is constrained at its apex by the peristomial membrane and its movement is controlled by five pairs of antagonistic forces (retractor and protractor muscles). The other main forces applied to the lantern are the elastic reactions of both muscles and ligamental structures (compass depressors and peristomial membrane). The lantern is allowed to perform vertical movements and lateral inclinations but cannot rotate around its main axis. The equilibrium conditions of the system have been found by means of a numerical iterative procedure for solving non-linear equations. The results of the present analysis allow simulation of the overall mechanical activity of the lantern taking into account the experimental data regarding active and passive muscular forces and the tensile constraints due to ligaments.     

Epimuscular myofascial force transmission between antagonistic and synergistic muscles can explain movement limitation in spastic paresis

Details and concepts of intramuscular, extramuscular and intermuscular myofascial force transmission are reviewed. Some new experimental data are added regarding myofascial force transmission between antagonistic muscles across the interosseal membrane of the lower hind limb of the rat. Combined with other result presented in this issue, it can be concluded that myofascial force transmission occurs between all muscles within a limb segment. This means that force generated within sarcomeres of an antagonistic muscle may be exerted at the tendon of target muscle or its synergists.

Some, in vivo, but initial indications for intersegmental myofascial force transmission are discussed. The concept of myofascial force transmission as an additional load on the muscle proved to be fruitful in the analysis of its muscular effects. In spastic paresis and for healthy muscles distal myofascial loads are often encountered, but cannot fully explain the movement limitations in spastic paresis. Therefore, the concept of simultaneous and opposing myofascial loads is analyzed and used to formulate a hypothesis for explaining the movement limitation: Myofascially transmitted antagonistic force is borne by the spastic muscle, but subsequently transmitted again to distal tendons of synergistic muscles.     

Myofascial force transmission between antagonistic rat lower limb muscles: Effects of single muscle or muscle group lengthening

Effects of lengthening of the whole group of anterior crural muscles (tibialis anterior and extensor hallucis longus muscles (TA + EHL) and extensor digitorum longus (EDL)) on myofascial interaction between synergistic EDL and TA + EHL muscles, and on myofascial force transmission between anterior crural and antagonistic peroneal muscles, were investigated. All muscles were either passive or maximally active. Peroneal muscles were kept at a constant muscle tendon complex length. Either EDL or all anterior crural muscles were lengthened so that effects of lengthening of TA + EHL could be analyzed. For both lengthening conditions, a significant difference in proximally and distally measured EDL passive and active forces, indicative of epimuscular myofascial force transmission, was present. However, added lengthening of TA + EHL significantly affected the magnitude of the active and passive load exerted on EDL. For the active condition, the direction of the epimuscular load on EDL was affected; at all muscle lengths a proximally directed load was exerted on EDL, which decreased at higher muscle lengths. Lengthening of anterior crural muscles caused a 26% decrease in peroneal active force.

Extramuscular myofascial connections are thought to be the major contributor to the EDL proximo-distal active force difference. For antagonistic peroneal complex, the added distal lengthening of a synergistic muscle increases the effects of extramuscular myofascial force transmission.     

A robotic model to investigate human motor control

The role of the mechanical properties of the neuromuscular system in motor control has been investigated for a long time in both human and animal subjects, mainly through the application of mechanical perturbations to the limb during natural movements and the observation of its corrective responses. These methods have provided a wealth of insight into how the central nervous system controls the limb. They suffer, however, from the fact that it is almost impossible to separate the active and passive components of the measured arm stiffness and that the measurement may themselves alter the stiffness characteristic of the arm. As a complement to these analyses, the implementation of a given neuroscientific hypothesis on a real mechanical system could overcome these measurement artifact and provide a tool that is, under full control of the experimenter, able to replicate the relevant functional features of the human arm. In this article, we introduce the NEURARM platform, a robotic arm intended to test hypotheses on the human motor control system. As such, NEURARM satisfies two key requirements. First, its kinematic parameters and inertia are similar to that of the human arm. Second, NEURARM mimics the main physical features of the human actuation system, specifically, the use of tendons to transfer force, the presence of antagonistic muscle pairs, the passive elasticity of muscles in the absence of any neural feedback and the non-linear elastic behaviour. This article presents the design and characterization of the NEURARM actuation system. The resulting mechanical behaviour, which has been tested in joint and Cartesian space under static and dynamic conditions, proves that the NEURARM platform can be exploited as a robotic model of the human arm, and could thus represent a powerful tool for neuroscience investigations.     

Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models

Mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces. Measurements of individual muscle forces and force sharing among individual muscles show an intensity-dependent, non-linear behavior. It has been demonstrated that the force sharing between the cat Gastrocnemius, Plantaris and Soleus shows distinct loops that change orientation systematically depending on the intensity of the movement. The purpose of this study was to prove whether or not static, non-linear optimization could inherently predict force sharing loops between agonistic muscles. Using joint moment data from a step cycle of cat locomotion, the forces in three cat ankle plantar flexors (Gastrocnemius, Plantaris and Soleus) were calculated using two popular optimization algorithms and two musculo-skeletal models. The two musculo-skeletal models included a one-degree-of-freedom model that considered the ankle joint exclusively and a two-degree-of-freedom model that included the ankle and the knee joint. The main conclusion of this study was that solutions of the one-degree-of-freedom model do not guarantee force-sharing loops, but the two-degree-of-freedom model predicts force-sharing loops independent of the specific values of the input parameters for the muscles and the musculo-skeletal geometry. The predicted force-sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment-moment graph.     

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.     

About weight factors in the non-linear objective functions used for solving indeterminate problems in biomechanics.

A lot of non-linear objective criteria are applied for solving the indeterminate problems formulated for different biomechanical models--most of them can be covered by the expression [formula in text]. It might be noted, however, that most of the suggested criteria are not applicable if considerable antagonistic co-contractions exist. This could be an effect of treating the agonistic muscles and their respective antagonists in one and the same manner in the objective function. Using a completely inverse approach (the muscle forces are supposed to be known quantities) and a simple 1DOF model (actuated by three agonistic muscles and one corresponding antagonist) it has been shown which values of the weight factors c(i) may predict different levels of muscle forces from the two antagonistic groups. Three hypothetical border variants for magnitudes of the muscle forces are considered (flexor muscles are only active, extensor muscles are only active, considerable co-contraction of flexors and extensors exists). The main conclusions are: the signs of c(i) at agonistic muscles have to be opposite to the c(i) signs at their antagonists; the signs of the weight factors depend on the direction of the net external joint moment; the closer c(i) to zero, the bigger force will be predicted in the ith muscle.     

Functional morphology of the sonic apparatus in Ophidion barbatum (Teleostei, Ophidiidae)

Most soniferous fishes producing sounds with their swimbladder utilize relatively simple mechanisms: contraction and relaxation of a unique pair of sonic muscles cause rapid movements of the swimbladder resulting in sound production. Here we describe the sonic mechanism for Ophidion barbatum, which includes three pairs of sonic muscles, highly transformed vertebral centra and ribs, a neural arch that pivots and a swimbladder whose anterior end is modified into a bony structure, the rocker bone. The ventral and intermediate muscles cause the rocker bone to swivel inward, compressing the swimbladder, and this action is antagonized by the dorsal muscle. Unlike other sonic systems in which the muscle contraction rate determines sound fundamental frequency, we hypothesize that slow contraction of these antagonistic muscles produces a series of cycles of swimbladder vibration.