Optimal posture control of a musculo-skeletal arm model

 In this paper maximal performance posture control of the human arm is investigated by means of model simulations. Recent experiments (F.C.T. van der Helm, submitted, 2000) have shown that the reflexive feedback during postural control varies with the bandwidth of the applied force disturbances. This paper focusses on the influence of the frequency content of force disturbances on the reflexive feedback gains by means of optimization. The arm is modelled by a non-linear musculo-skeletal model with two degrees of freedom and six muscles. To facilitate the optimization of the model parameters, the arm model is linearized. A performance criterion is minimized for stochastic force disturbances in a two-step procedure: (1) optimization of static muscle activations using an additional energy criterion to obtain a unique and energy-efficient solution; and (2) optimization of reflex gains using an additional control effort criterion to obtain a unique solution. The optimization reveals that for the given task and posture, the shoulder muscles have the largest contribution, whereas the bi-articular muscles have a relatively small contribution to the behaviour. The dynamics at the endpoint level are estimated so that a comparison can be made with the experiments. Compared to the experiments, the intrinsic damping of the model is relatively large (about 150%), whereas the intrinsic stiffness is relatively small (about 60%). These differences can be attributed to unmodelled mechanical effects of cross-bridges in Hill-type muscle models. The optimized reflex gains show remarkable similarities with the values found in the experiments, implying that humans can adjust their reflexive feedback gains in an optimal way, weighting the performance and energy. The approach in this paper could be useful in the study of various posture tasks, for example in the prediction of the relation between the control parameters of various musculo-skeletal models and different experimental variables. Received: 24 January 2000 / Accepted in revised form: 7 July 2000     

Changes in posture alter the attentional demands of voluntary movement.

Two simple experiments reveal that the ease with which an action is performed by the neuromuscular-skeletal system determines the attentional resources devoted to the movement. Participants were required to perform a primary task, consisting of rhythmic flexion and extension movements of the index finger, while being paced by an auditory metronome, in one of two modes of coordination: flex on the beat or extend on the beat. Using a classical dual-task methodology, we demonstrated that the time taken to react to an unpredictable visual probe stimulus (the secondary task) by means of a pedal response was greater when the extension phase of the finger movement sequence was made on the beat of the metronome than when the flexion phase was coordinated with the beat. In a second experiment, the posture of the wrist was manipulated in order to alter the operating lengths of muscles that flex and extend the index finger. The attentional demands of maintaining the extend-on-the-beat pattern of coordination were altered in a systematic fashion by changes in wrist posture, even though the effector used to respond to the visual probe stimulus was unaffected.     

Closed-loop and open-loop control of posture and movement during human trunk bending

Closed-loop (CL) and open-loop (OL) types of motor control during human forward upper trunk bending are investigated. A two-joint (hip and ankle) biomechanical model of the human body is used. The analysis is performed in terms of the movements along eigenvectors of the motion equation (“eigenmovements” or “natural synergies”). Two analyzed natural synergies are called “H-synergy” (Hip) and “A-synergy” (Ankle) according to the dominant joint in each of these synergies. Parameters of CL control were estimated using a sudden support platform displacement applied during the movement execution. The CL gain in the H-synergy increased and in the A-synergy decreased during the movement as compared with the quiet standing. The analysis of the time course of OL control signal suggests that the H-synergy (responsible for the prime movement, i.e. bending per se) is controlled according to the EP theory whereas for the associated A-synergy (responsible for posture adjustment, i.e. equilibrium maintenance) muscle forces and gravity forces are balanced for any its final amplitude and therefore the EP theory is not applicable to its control.     

Dynamic interactions between limb segments during planar arm movement

Movement of multiple segment limbs requires generation of appropriate joint torques which include terms arising from dynamic interactions among the moving segments as well as from such external forces as gravity. The interaction torques, arising from inertial, centripetal, and Coriolis forces, are not present for single joint movements. The significance of the individual interaction forces during reaching movements in a horizontal plane involving only the shoulder and elbow joints has been assessed for different movement paths and movement speeds. Trajectory formation strategies which simplify the dynamics computation are presented.     

Automatic control of limb movement and posture

Studies are reviewed that address the problem of the variables controlled by the central nervous system in the maintenance of body posture and limb movement against disturbing forces. The role of global variables of control, which take into account the dynamic state of the limb, is discussed. Neural substrates that are involved in the distributed control of kinematic and dynamic parameters are also considered.     

The effect of eye movement on the control of arm movement to a target

Abstract

The purpose of this study was to investigate the effect of eye movement on the control of arm movement to a target. Healthy humans flexed the elbow to a stationary target in response to a start tone. Simultaneously, the subject moved the eyes to the target (saccade eye movement), visually tracked a laser point moving with the arm (smooth pursuit eye movement), or gazed at a stationary start point at the midline of the horizontal visual angle (non-eye movement—NEM). Arm movement onset was delayed when saccade eye movement accompanied it. The onset of an electromyographic burst in the biceps muscle and the onset of saccade eye movement were almost simultaneous when both the arm and the eyes moved to the target. Arm movement duration during smooth pursuit eye movement was significantly longer than that during saccade eye movement or NEM. In spite of these findings, amplitudes of motor-evoked potential in the biceps and triceps brachii muscles were not significantly different among the eye movement conditions. These findings indicate that eye movement certainly affects the temporal control of arm movement, but may not affect corticospinal excitability in the arm muscles during arm movement.     

Simulation studies on the control of posture and movement in a multi-jointed limb

Simulation studies were performed to evaluate the effectiveness of different control schemes in stabilizing a multi-jointed limb (human arm) in response to force perturbations. The mechanical properties of the arm were modeled as a linear visco-elastic system and the effectiveness of negative feedback of angular position and torque was evaluated. The effectiveness of a given amount of position feedback depended strongly on the initial position of the arm and on the perturbation, while torque feedback was much more consistently effective in damping the motion of the limb.     

A spring model and equivalent neural network for arm posture control

A model is introduced for the motor program which controls final position. The first part of the model relates the biomechanical properties of the muscles to the EMG activities of the extensor and flexor muscles and thereby generates quatitative predictions for the relationships between the EMGs, final position, external forces, muscle stiffness, and muscle tension. To the extent that comparable data exist, the model is shown to give correct quantitative predictions. When only qualitative comparisons can be made, the model is consistent with the data in the literature. The model is complete and can be tested quantitatively in detail in the future. An equivalent circuit for the neural network that innervates the muscles is given. It is shown to have the advantages of making the programming of final position simple to either compute or lookup in a table. In addition, new situations, such as adapting to a force, or an unusual viewing angle, lead to very simple changes in the basic program in terms of the equivalent circuit.     

Features of learning voluntary control of posture after pyramidal and nigrostriatal lesions

The study was aimed at investigation of a deficit of learning the center-of-pressure voluntary control in patients with lesions of corticospinal and nigrostriatal systems. Thirty three patients with Parkinson's disease and 20 patients with hemiparesis after cerebrovascular accidents in the MCA participated in the investigation. The subjects stood on a force platform and in the form of a computer game were trained to match the projection of the center of pressure (a cursor) with a target on the screen under the visual feedback control. Two different postural tasks were presented. In the first task the direction of the center-of-pressure shift was not known before, so the subject learned the general strategy of the center-pressure control. In the other task a precise postural coordination should be formed. The voluntary control of the center-of-pressure position was found to be impaired in both groups of patients. In the task of moving the center of pressure in various directions (general strategy), no differences in the initial deficit of the task performance were found between the groups, but the learning was more efficient in the group of hemiparetic patients. However, in the task with precise postural coordination, despite the greater initial deficit in the parkinsonian patients, the learning in this group of patients was substantially more efficient than in hemiparetic patients. The results suggest both common and different features of the involvement of the corticospinal and nigrostriatal systems in learning voluntary control of posture.     

Relationship between the time of the beginning of the anticipatory postural components and the latent period of raising the arm in the vertical posture

The relationships between the anticipatory postural components when standing subjects raised their arms and the latent period (LP) of the motor response determined by the beginning of the deltoid muscle activation were analyzed. The LP range from the least possible to 1 s was analyzed. In the case of short LPs (approximately up to 170 ms), the anticipation time for the ipsilateral biceps femoris muscle (BFM) and sacrospinalis muscle (SSM) increased linearly with the LP; at longer LPs, it did not depend on the LP and was characterized by a wide scatter. In the case of short LPs, the delay time of the beginning of activation of postural muscles in relation to the signal for movement remained constant and was approximately 100 ms for the BFM and 120 ms for the SSM. This is explained by the fact that, with short LPs of motor response, the CNS had insufficient time to complete postural adjustments before the beginning of movement, which resulted in shortening of the anticipation time of the start of change in the activity of postural muscles and, as a consequence, the appearance of an additional initial backward inclination of the body. The results obtained are discussed in the context of organizing the interaction between the regulation of maintaining the vertical posture and the system of movement control.     

A hierarchical neural-network model for control and learning of voluntary movement

In order to control voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: the determination of a desired trajectory in the visual coordinates, the transformation of its coordinates to the body coordinates and the generation of motor command. Based on physiological knowledge and previous models, we propose a hierarchical neural network model which accounts for the generation of motor command. In our model the association cortex provides the motor cortex with the desired trajectory in the body coordinates, where the motor command is then calculated by means of long-loop sensory feedback. Within the spinocerebellum — magnocellular red nucleus system, an internal neural model of the dynamics of the musculoskeletal system is acquired with practice, because of the heterosynaptic plasticity, while monitoring the motor command and the results of movement. Internal feedback control with this dynamical model updates the motor command by predicting a possible error of movement. Within the cerebrocerebellum — parvocellular red nucleus system, an internal neural model of the inverse-dynamics of the musculo-skeletal system is acquired while monitoring the desired trajectory and the motor command. The inverse-dynamics model substitutes for other brain regions in the complex computation of the motor command. The dynamics and the inverse-dynamics models are realized by a parallel distributed neural network, which comprises many sub-systems computing various nonlinear transformations of input signals and a neuron with heterosynaptic plasticity (that is, changes of synaptic weights are assumed proportional to a product of two kinds of synaptic inputs). Control and learning performance of the model was investigated by computer simulation, in which a robotic manipulator was used as a controlled system, with the following results: (1) Both the dynamics and the inverse-dynamics models were acquired during control of movements. (2) As motor learning proceeded, the inverse-dynamics model gradually took the place of external feedback as the main controller. Concomitantly, overall control performance became much better. (3) Once the neural network model learned to control some movement, it could control quite different and faster movements. (4) The neural netowrk model worked well even when only very limited information about the fundamental dynamical structure of the controlled system was available. Consequently, the model not only accounts for the learning and control capability of the CNS, but also provides a promising parallel-distributed control scheme for a large-scale complex object whose dynamics are only partially known.     

On the cost functions for the control of the human arm movement

The aim of our investigation is to understand the mechanisms which control the movement of the human arm. The arm is here considered as a redundant system: the shoulder, elbow and wrist joints, which provide three degrees of freedom, combine to move the hand in a horizontal plane, i.e. a two dimensional space. Thus the system has one extra degree of freedom. Earlier investigations of the static situation led to the hypothesis that independent cost functions were attached to each of the three joints and that the configuration chosen for a given target position is that which provides the minimum total cost (Cruse 1986). The aim of the current investigation was to look for measurable values corresponding to the hypothetical cost functions. Experiments using pointers of different lengths attached to the hand showed that the strategy in choosing the joint angles are independent of the limb length. The muscle force necessary to reach a given angle is increased by a spring mounted across a joint. In this situation the angles of the loaded joint are changed for a given target point to give way to the force effect. This leads to the conclusion that the hypothetical cost functions are not independent of the physiological costs necessary to hold the joint at a given angle. The cost functions seem to depend on joint angle and on the force which is necessary to hold the joint in a given position. Cost functions are measured by psychophysical methods. The results showU-shaped curves which can be approximated by parabolas. The position of minimum cost (maximum comfort) for one joint showed no or weak dependency on the angles of the other joints. For each subject these psychophysical cost functions are compared with the hypothetical cost functions. The comparison showed reasonable agreement. This supports the assumption that the psychophysically measured comfort functions provide a measure for the hypothetical cost functions postulated to explain the targeting movements. Targeting experiments using a four joint arm which has two extra degrees of freedom showed a much larger scatter compared to the three joint arm. Nevertheless, the results still conform to the hypothesis that also in this case the minimum cost principle is applied to solve the redundancy problem. As the cost function for the whole arm shows a large minimum valley, quite a large range of arm positions is possible of about equal total costs. The scatter does not result from pure randomness but seems to be mainly produced by the fact that the angles at the end of the movement depend on the value of the joint angles at the beginning of the movement.