What muscle variable(s) does the nervous system control in limb movements?

Tendon elasticity and positional control

The spring-like behaviour of a joint following a sudden change of torque is partly a result of the elastic properties of tendons. A large fall in a muscle with a long tendon may be accompanied by tendon recoil causing joint movements as large as 20°.

Command invariants and the frame of reference for human movement

We describe a solution to the redundancy problem related to that proposed in Feldman & Levin's target article. We suggest that the system may use a fixed mapping between commands organized at the level of degrees of freedom and commands to individual muscles. This proposal eliminates the need to maintain an explicit representation of musculoskeletalgeometry in planning movements.

Frameworks on shifting sands

Feldman and Levin present a model for movement control in which the system is said to seek equilibrium points, active movement being produced by shifting frames of reference in space. It is argued that whatever merit this model might have is limited to an understanding of “the how” and not “the why” we move. In this way the authors seem to be forced into a dualistic position leaving the upper level of the proposed control hierarchy “floating.”

Conservative or nonconservative control schemes

The conservative strategy proposed by the authors suggests a solution of the degrees-of-freedom problem of the controller. However, several simple motor control tasks cannot be explained by this strategy. A nonconservative strategy, in which more parameters of the control signal vary, can account for these simple motor tasks. However, the simplicity that distinguishes the proposed model from many others is lost.

Strategies for the control of voluntary movements with one mechanical degree of freedom

A theory is presented to explain how accurate, single-joint movements are controlled. The theory applies to movements across different distances, with different inertial loads, toward targets of different widths over a wide range of experimentally manipulated velocities. The theory is based on three propositions. (1) Movements are planned according to “strategies” of which there are at least two: a speed-insensitive (SI) and a speed-sensitive (SS) one. (2) These strategies can be equated with sets of rules for performing diverse movement tasks. The choice between SI and SS depends on whether movement speed and/or movement time (and hence appropriate muscle forces) must be constrained to meet task requirements. (3) The electromyogram can be interpreted as a low-pass filtered version of the controlling signal to the motoneuron pools. This controlling signal can be modelled as a rectangular excitation pulse in which modulation occurs in either pulse amplitude or pulse width. Movements to different distances and with loads are controlled by the SI strategy, which modulates pulse width. Movements in which speed must be explicitly regulated are controlled by the SS strategy, which modulates pulse amplitude. The distinction between the two movement strategies reconciles many apparent conflicts in the motor control literature.

The origin and use of positional frames of reference in motor control

A hypothesis about sensorimotor integration (the λ model) is described and applied to movement control and kinesthesia. The central idea is that the nervous system organizes positional frames of reference for the sensorimotor apparatus and produces active movements by shifting the frames in terms of spatial coordinates. Kinematic and electromyographic patterns are not programmed, but emerge from the dynamic interaction among the system s components, including external forces within the designated frame of reference. Motoneuronal threshold properties and proprioceptive inputs to motoneurons may be cardinal components of the physiological mechanism that produces positional frames of reference. The hypothesis that intentional movements are produced by shifting the frame of reference is extended to multi-muscle and multi-degrees-of-freedom systems with a solution of the redundancy problem that allows the control of a joint alone or in combination with other joints to produce any desired limb configuration and movement trajectory. The model also implies that for each motor behavior, the nervous system uses a strategy that minimizes the number of changeable control variables and keeps the parameters of these changes invariant. Examples are provided of simulated kinematic and electromyographic signals from single- and multi-joint arm movements produced by suggested patterns of control variables. Empirical support is provided and additional tests of the model are suggested. The model is contrasted with others based on the ideas of programming of motoneuronal activity, muscle forces, stiffness, or movement kinematics.

Origins of origins of motor control

Examination of infant spontaneous and goal-directed arm movements supports Feldman and Levin's hypothesis of a functional hierarchy. Early infant movements are dominated by biomechanical and dynamic factors without external frames of reference. Development involves not only learning to generate these frames of reference, but also protecting the higher-level goal of the movement from internal and external perturbations.

Spatial frames for motor control would be commensurate with spatial frames for vision and proprioception, but what about control of energy flows?

The model identifies a spatial coordinate frame within which the sensorimotor apparatus produces movement. Its spatial nature simplifies its coupling with spatial reference frames used concurrently by vision and proprioception. While the positional reference frame addresses the performance of spatial tasks, it seems to have little to say about movements involving energy expenditure as the principle component of the task.

Interneurons as backseat drivers and the elusive control variable

It is proposed here that the spinal network of proprioceptive feedback from length and force receptors constitutes the mechanism underlying the coordination of activation thresholds for muscles acting about the same and neighboring joints. For the most part, these circuits come between motoneurons and supraspinal signals, invalidating the idea that the activation thresholds constitute control variables for the motor system.

Two joints are more than twice one joint

An alternative multi-joint extension to the lambda model is proposed. According to this extension, the activity of a muscle depends not only on the difference between lambda and length of that muscle, but also on the difference between lambda and length of other muscles. This 2-D extension can describe more neurophysiological experiments than the extension proposed in the target article.

Control parameters, equilibria, and coordination dynamics

Important similarities exist between the dynamical concepts implicit in Feldman & Levin's extended λ model and those basic to a dynamical systems approach. We argue that careful application of the key concepts of control and order parameters, equilibria, and stability, can relate known facts of neuromuscular processes to the observables of functional, task-specific behavior.

Shifting frames of reference but the same old point of view

Models of central control variables (CVs) that are expressed in positional reference frames and rely on proprioception as the dominant specifier of muscle activation patterns have not yet been shown to be adequate for the description of fast, voluntary movement, even of single joints. An alternative model with illustrative data is proposed.

Adaptability of innate motor patterns and motor control mechanisms

The following factors underlying behavioral plasticity are discussed: (1) reflex adaptability and its role in the voluntary control of movement, (2) degrees of freedom and motor equivalence, and (3) the problem of the discrete organization of motor behavior. Our discussion concerns a variety of innate motor patterns, with emphasis on the wiping reflex in the frog.

It is proposed that central regulation of stretch reflex thresholds governs voluntary control over muscle force and length. This suggestion is an integral part of the equilibrium-point hypothesis, two versions of which are compared.

Kinematic analysis of the wiping reflex in the spinal frog has shown that each stimulated skin site is associated with a group of different but equally effective trajectories directed to the target site. Such phenomena reflect the principle of motor equivalence -the capacity of the neuronal structures responsible for movement to select one or another of a set of possible trajectories leading to the goal. Redundancy of degrees of freedom at the neuronal level as well as at the mechanical level of the body's joints makes motor equivalence possible. This sort of equivalence accommodates the overall flexibility of motor behavior.

An integrated behavioral act or a single movement consists of dynamic components. We distinguish six components for the wiping reflex, each associated with a certain functional goal, specific body positions, and motor-equivalent movement patterns. The nervous system can combine the available components in various ways in forming integrated behavioral sequences. The significance of command neuronal organization is discussed with respect to (1) the combinatory strategy of the nervous system and (2) the relation between continuous and discrete forms of motor control. We conclude that voluntary movements are effected by the central nervous system with the help of the mechanisms that underlie the variability and modifiability of innate motor patterns.

Inverse kinematic problem: Solutions by pseudoinversion, inversion and no-inversion

Kinematic properties of reaching movements reflect constraints imposed on the joint angles. Contemporary models present solutions to the redundancy problem by a pseudoinverse procedure (Whitney 1969) or without any inversion (Berkenblit et al. 1986). Feldman & Levin suggest a procedure based on a regular inversion. These procedures are considered as an outcome of a more general approach.

Natural unconstrained movements obey rules different from constrained elementary movements

The concept of a conservative control strategy minimizing the number of degrees of freedom used is criticised with reference to 3-D simple reaching and grasping experiments. The vector error in a redundant system would not be the prime controlled variable, but rather the posture for reaching, as exemplified by nearly straight displacements in joint space as opposed to curved ones in task space.

Is λ an appropriate control variable for locomotion?

The lambda model predicts that the command received by each motor nucleus during locomotion is specific for the joint at which its muscle acts and is independent of external conditions. However, investigation of the commands received by motor nuclei during fictive locomotion and of the sensitivity of these commands to feedback from the limb during locomotion indicates that neither condition is satisfied.

How far should we extend the equilibrium point (lambda) hypothesis?

A key feature of the lambda model is the hypothesis of a local spring-like muscle-reflex system defined by a central control variable that has units of position. This is intriguing, especially for a study of postural stability in large-scale systems, but it has limited direct application to skilled everyday movements. If movement is considered as a goal-directed, neuro-optimization problem, however, theavailabilityof lambda-like peripheral models (vs. conventional musculoskeletal models) deserves exploration.

The kinematic consequences of invariant dynamics in children 6-18 years of age

The effect of limb dynamics on trajectory formation is unclear. The natural frequency of a limb is the major factor in its dynamics. It has previously been shown with an indirect measurement method that the natural frequency of body segments is invariant during human growth from the age of 6 to 18. The aim of our study was to determine, using a direct measurement method, whether human growth affects: (1) lower limb dynamics (i.e. the natural frequency of the lower leg) and (2) the maximum velocities of the knee during selected motor tasks. In 20 non-disabled children, 6-18 years of age, measurements were taken of the natural frequency of the lower leg (including the foot), and the maximum velocities of knee flexion and extension during voluntary movement (MVV) and at initial and terminal swing phases of self-paced walking (WAL). The velocities were also estimated using a dynamic model and the results were compared to the measured velocities with a paired t-test. Correlations among the frequencies, velocities, and body height (an indicator of growth) were calculated. The natural frequency of the lower leg (mean+/-standard deviation, omega(0)=6.58+/-0.54s(-1)), maximum velocities of knee extension and flexion during voluntary movement (MVV(e)=10.1+/-1.8rads(-1) and MVV(f)=7.8+/-1.3rads(-1), respectively), and maximum velocities of knee flexion and extension during the swing phase of walking (WAL(f)=5.4+/-0.6rads(-1) and WAL(e)=6.3+/-0.87rads(-1), respectively) were each found to be independent of body height. The MVV measured velocities were 22% larger and WAL(f) measured velocities were 25% smaller than the velocities predicted from the dynamic model (p<0.05). The study found that a segment's dynamic properties, as well as selected kinematics, may be considered invariant with human growth.

State-space analysis of joint angle kinematics in normal treadmill walking

By restricting analysis to single averaged strides considered to be characteristic for the individual under investigation, current methods in gait analysis do not exploit the full dynamics of continuous locomotion. Therefore, a novel approach is presented that is based on long-term measurements of kinematic data during treadmill walking. The method consists of reconstructing the system attractor in the embedding space and then analyzing its geometric structure. Estimating the dimension of movement trajectories correlates well with the notion of controlling multiple degrees of freedom during performance of complex movement tasks such as walking. The influence of walking speed on the complexity of physiologic walking was investigated in 10 healthy subjects walking on a treadmill at seven fixed speeds. The results suggest that human walking becomes more complex at slower speeds. This may be associated with results from EMG studies demonstrating more irregular EMG patterns at very slow walking speeds. This study emphasizes that tools from non-linear dynamics are well suited for providing more insight into motor control in humans.

Reflex regulation of antagonist muscles for control of joint equilibrium position

A systems model of spinal neuro-musculo-skeletal system (alpha - gamma model) is developed to investigate the plausible roles of spinal proprioceptive feedback in movement control. The model is composed of a joint, a pair of antagonist muscles, length and velocity feedback from muscle spindle, as well as spinal stretch reflex, reciprocal inhibition and recurrent inhibition of Renshaw cells. A descending command modulates the background activation of alpha motoneuron pools in combination with these reflex activities. A static gamma command controls the fusimotor contraction of the spindle. Simulation results reveal that the equilibrium joint angle is linearly correlated to the level of static gamma fusimotor activity of the spindle for a wide range of external loading conditions and reflex gains, suggesting that these spinal reflexes may contribute to regulate the equilibrium position of the joint. Sensitivity analysis further shows that reflex gains and other central commands alter the quasi-linear relation in regular fashions. The reciprocal inhibition gain changes the slope of the linear theta(eq) - gamma curve; and the descending alpha excitation, the stretch reflex gain, and the external load all shift the theta(eq) - gamma curve in parallel. These results imply that reflex gains and descending alpha commands may be coordinated to maintain a unique theta(eq) - gamma curve while providing the flexibility to counteract external loads, to execute a movement, or to regulate additional muscle variables. Dynamic simulation suggests that control of a class of movements can be achieved with a triphasic, alpha pulse and a continuous gamma signal. The model study supports the notion of a dual strategy for controlling trajectories via a feedforward alpha command and for regulating the final equilibrium positions via a feedback gamma command.

Force and timing components of the motor program

Three experiments were undertaken to assess the effects of variations of force and time on both simple and choice reaction time. The first two experiments demonstrated that although latency did not vary as a function of force, timing variations, such as requiring that a response be maintained, led to consistent changes in reaction time. These results led to the development of a model of motor programming in which force and timing are dissociated as separate components. However, the data also indicated that the force component may be further analyzed into two subcomponents-force activation and force deactivation. The model predicts that the latter subcomponent may be programmed on-line provided that sufficient time elapses between the implementation of the two subcomponents. A different pair of movements was used in Experiment 3 to further demonstrate that force activation and deactivation may be preprogrammed into a single component. These results support the aspect of the proposed model that makes a distinction between operations required for program construction from those necessary for program implementation.

Review of motor control mechanisms underlying impact absorption from falls

The absorption of impacts resulting from contact with a landing surface during gait, running and drop landings has received considerable attention in the literature. This research has important clinical relevance as failure to appropriately plan and control impact absorption may lead to injuries to the musculo-skeletal system. This review attempts to summarize evidence gathered by studies on the motor control aspects of impact absorption during landing movements. Although this review focuses primarily on the control of landings from self-initiated falls or 'drop landings', an understanding of the motor control mechanisms underlying impact absorption is essential to understand common anticipatory and reflex mechanisms involved in a broader variety of movements such as running and jumping. The review is structured in three parts: the first two parts examine the preparatory muscle activity occurring during the fall (Part I) and after touch down (Part II). Part III explores the proposed sensorimotor mechanisms underlying the control of landing. The review concludes with as yet unresolved questions and directions for future research.

Somatic and intramuscular distribution of muscle spindles and their relation to muscular angiotypes

The distribution pattern of muscle spindles in the skeletal musculature has been reviewed in a large number of muscles (using the literature data especially from cat and man), and the relation of spindle content to muscle mass was quantitatively examined in 36 cat and 140 human muscles. In both species, the number of spindles increases with increasing muscle mass in a power law fashion of the form y=bx+a, whereby y denotes the logarithm of spindle content within a muscle, and x is the logarithm of muscle mass. For the cat, slope b and intercept a were estimated as 0.39 and 1.53, and for man as 0.48 and 1.33, respectively. The results show that the spindle content of a muscle may be related to its mass, confirming a similar analysis made previously by Banks and Stacey (Mechano receptors, Plenum Press, New York, 1988, pp. 263-269) in a different data set. With regard to the histological profile of muscle fibers, (as it is already well documented by many groups) muscle spindles tend to be located in deeper muscle regions where oxidative fibers predominate, and are far scarcer in superficial and flat muscle regions where glycolytic fibers predominate. These discrete muscle regions differ also in the properties of the vessel tree supplying them, for which the term oxidative and glycolytic "angiotype" has been used. The results from these three aspects of analysis (relation to muscle mass, relation to muscle regions with high oxidative index and relation to muscle regions with dense vascular supply) were combined with histological findings showing that spindles may be in systematic anatomical contact to intramuscular vessels. Based on these data a hypothesis is proposed according to which, both the number and intramuscular placement of muscle spindles are related to the oxidative angiotype supplying the muscle territories rich in oxidative fibers. The hypothesis is discussed.

The control of aerodynamics, acoustics, and perceptual characteristics during speech production

One of the most important areas of study in speech motor control is the identification of control variables, the variables controlled by the nervous system during motor tasks. The current study examined two hypotheses regarding control variables in speech production: (1) pressure and resistance in the vocal tract are controlled, and (2) perceptual and acoustic accuracy are controlled. Aerodynamic and acoustic data were collected on 20 subjects in three conditions, normally (NT), with an open air pressure bleed tube in place (TWB), and with a closed bleed tube in place (TNB). The voice recordings collected from the speakers in the production study were used in the perceptual study. Results showed that oral pressure (Po) was significantly lower in the TWB condition than in the NT and TNB conditions. The Po in the TWB condition seemed to be related to maintenance of subglottal pressure (Ps). Examination of the perceptual and acoustic data indicated that perceptual accuracy for [a] was achieved by maintaining Ps to preserve a steady sound pressure level, fundamental frequency, and voicing. Overall, it appeared speakers controlled pressure in compensating, but for the ultimate goal of maintaining acoustic and perceptual accuracy.