Optimal control of antagonistic muscle stiffness during voluntary movements

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an N-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.     

Model study of muscle spindle primary endings subjected to dynamic fusimotor activation

An earlier proposed model of the de-efferented muscle spindle mechano-receptors has been developed further to simulate the effects of the dynamic fusimotor ( _D) activation of the group Ia afferents (primary endings).The rate sensitivity of the original second order receptor model might be increased simply by increasing the overall viscous damping of the simulated polar regions of the nuclear bag fibre. However, adequate simulation of the typical time course of the stretch response of the primary endings during _D-activation required a subdivision of the polar regions into an active and a passive part. A reasonable behaviour of the model was obtained by simulating a local contraction covering about 50–90% of the polar regions of the nuclear bag fibres.The ramp response of the model showed a quick rate response component that increased by increasing the rate of the simulated stretch. This component was not significantly influenced by the simulated _D-activation.A slow rate component appeared to increase approximately in the same proportion as the intensity of the simulated _D-activation.The behaviour of the model closely corresponds to that of the biological prototype. The study demonstrates that the electrophysiological effects of activating the dynamic fusimotor fibres are indeed compatible with peripheral mechanical events associated with contraction phenomena within the polar regions of the nuclear bag intrafusal muscle fibres.     

Model-based influences on humans' choices and striatal prediction errors

The mesostriatal dopamine system is prominently implicated in model-free reinforcement learning, with fMRI BOLD signals in ventral striatum notably covarying with model-free prediction errors. However, latent learning and devaluation studies show that behavior also shows hallmarks of model-based planning, and the interaction between model-based and model-free values, prediction errors, and preferences is underexplored. We designed a multistep decision task in which model-based and model-free influences on human choice behavior could be distinguished. By showing that choices reflected both influences we could then test the purity of the ventral striatal BOLD signal as a model-free report. Contrary to expectations, the signal reflected both model-free and model-based predictions in proportions matching those that best explained choice behavior. These results challenge the notion of a separate model-free learner and suggest a more integrated computational architecture for high-level human decision-making.     

The investigation of locomotor activity control system in humans under the air-stepping conditions during passive and voluntary leg movements

The degree of activation of the central stepping program during passive leg movement was studied in healthy subjects under unloading conditions; the excitability of spinal motoneurons was studied during passive and voluntary stepping movements. Passive stepping movements with characteristics maximally close to those during voluntary stepping were accomplished by the experimenter. The bursts of muscular activity during voluntary and imposed stepping movements were compared. In addition, the influence on the leg movement of artificially created loading onto the foot was studied. The excitability of spinal motoneurons was estimated by the amplitude of modulation of the m. soleus H reflex. Changes in the H reflex (Hoffmann’s reflex) after fixation of the knee and hip joints were also studied. In most subjects, passive movements were accompanied by bursts of electromyographic (EMG) activity in the hip muscles (sometimes in shank muscles); the timing of the EMG burst during the step cycle coincided with the burst’s timing during voluntary stepping. In many cases, the bursts in EMG activity exceeded the activity of homonymous muscles during voluntary stepping. Simulation of foot loading influenced significantly the distal part of the moving extremity during both voluntary and passive movements, which was expressed in the appearance of movements in the ankle joint and an increase in the phasic EMG activity of the shank muscles. The excitability of motoneurons during passive movements was higher than during voluntary movements. Changes and modulation of the H reflex throughout the step cycle were similar without restriction of joint mobility and without hip joint mobility. Fixation of the knee joint was of great importance. It is supposed that imposed movements activate the same mechanisms of rhythm generation as supraspinal commands during voluntary movements. During passive movements, presynaptic inhibition depends mostly on the afferent influences from the moving leg rather than on the central commands. Under the conditions of “air-stepping,” the afferent influences from the foot pressure receptors are likely to interact actively with the central program of stepping and to determine the final activity pattern irrespective of the movement type (voluntary or passive).     

Estimation of muscle spindle information rate by pattern matching and the effect of gamma system activity on parallel spindles

The information transmission properties of ensembles of MSs and the effect of the gamma system on these properties were studied. Three converging lines of research were taken: (1) the development of information theoretic estimation tools, and the formulation of an operational interpretation for the information rate; (2) animal experiments in which the mutual information rate was estimated and the effect of the gamma system was quantified; (3) simulation of a muscle spindle model with gamma activation in order to corroborate the results of the animal experiments. The main hypothesis was that the gamma system will enhance information theoretic measures that quantify the quality of the sensory neural channel comprised from an ensemble of primary muscle spindle afferents. A random stimulus was applied to a muscle in the hind limb of a cat, while spike trains from several primary MS afferents were recorded simultaneously. The stimulus was administered twice, with an operative and a disconnected gamma system. The mutual information rate between the stimulus and spike trains, as well as other information theoretic measures, was estimated. The information rate of ensembles of MSs increased with increasing ensemble size. However, with an operative gamma system the ensemble effect was much higher. In addition, the ensemble effect was influenced by the stimulus spectrum. A muscle spindle population model with gamma activation was simulated with stimuli that were identical to that of the animal experiments. The simulation results supported the experimental results and corroborated the main hypothesis. The results indicate that the gamma system has an important role in enhancing information transmission from ensembles of MSs to the spinal cord.     

Non-uniform mechanical activity of quadriceps muscle during fatigue by repeated maximal voluntary contraction in humans

To determine the non-uniform surface mechanical activity of human quadriceps muscle during fatiguing activity, surface mechanomyogram (MMG), or muscle sound, and surface electromyogram (EMG) were recorded from the rectus femoris (RF), vastus lateralis (VL), and vastus medialis (VM) muscles of seven subjects during unilateral isometric knee extension exercise. Time- and frequency-domain analyses of MMG and of EMG fatigued by 50 repeated maximal voluntary contractions (MVC) for 3 s, with 3-s relaxation in between, were compared among the muscles. The mean MVC force fell to 49.5 (SEM 2.0)% at the end of the repeated MVC. Integrated EMG decreased in a similar manner in each muscle head, but a marked non-uniformity was found for the decline in integrated MMG (iMMG). The fall in iMMG was most prominent for RF, followed by VM and VL. Moreover, the median frequency of MMG and the relative decrease in that of EMG in RF were significantly greater (P < 0.05) than those recorded for VL and VM. These results would suggest a divergence of mechanical activity within the quadriceps muscle during fatiguing activity by repeated MVC. Accepted: 19 January 1999     

Effect of ouabain on electrical activity of the isolated frog muscle spindle

Changes in electrical activity of the isolated frog muscle spindle were studied in Ringer's solution containing ouabain. The presence of ouabain in the solution increased the spontaneous firing rate of the receptors up to a maximum and then reduced it quickly to zero. The amplitude of the action potentials was reduced on the average to 40% of normal. Ouabain causes initial disappearance of the hyperpolarization phase of the receptor potential and a subsequent decrease in amplitude of its dynamic phase to zero. The decrease in amplitude of the receptor potential and action potential and also the changes in firing rate in the solution with ouabain depend on the frequency of their spontaneous activity. The changes observed can be explained by depolarization of the membrane of the nerve endings and the first node of Ranvier, developing as a result of blocking of the sodium pump by ouabain.Translated from Neirofiziologiya, Vol. 5, No. 6, pp. 576–582, November–December, 1973.