Learning the dynamics of reaching movements results in the modification of arm impedance and long-latency perturbation responses

 Some characteristics of arm movements that humans exhibit during learning the dynamics of reaching are consistent with a theoretical framework where training results in motor commands that are gradually modified to predict and compensate for novel forces that may act on the hand. As a first approximation, the motor control system behaves as an adapting controller that learns an internal model of the dynamics of the task. It approximates inverse dynamics and predicts motor commands that are appropriate for a desired limb trajectory. However, we had previously noted that subtle motion characteristics observed during changes in task dynamics challenged this simple model and raised the possibility that adaptation also involved sensory–motor feedback pathways. These pathways reacted to sensory feedback during the course of the movement. Here we hypothesize that adaptation to dynamics might also involve a modification of how the CNS responds to sensory feedback. We tested this through experiments that quantified how the motor system's response to errors during voluntary movements changed as it adapted to dynamics of a force field. We describe a nonlinear approach that approximates the impedance of the arm, i.e., force response as a function of arm displacement trajectory. We observe that after adaptation, the impedance function changes in a way that closely matches and counters the effect of the force field. This is particularly prominent in the long-latency (>100 ms) component of response to perturbations. Therefore, it appears that practice not only modifies the internal model with which the brain generates motor commands that initiate a movement, but also the internal model with which sensory feedback is integrated with the ongoing descending commands in order to respond to error during the movement. Received: 10 January 2001 / Accepted in revised form: 30 May 2001     

The discontinuous nature of motor execution II. Merging discrete and rhythmic movements in a single-joint system -- the phase entrainment effect

 Initiation of rapid discrete flexion movements is significantly altered when a secondary rhythmic movement is performed simultaneously with the same limb; the onset of a stimulus-evoked discrete movement tends to occur time-locked to the oscillation: i.e., the rhythmic movement entrains the discrete response. This nonlinear interaction may reflect a specific principle of coordination of motor tasks which are simultaneously executed with the same effector. This part II of a tripartite research report on such single-muscle multiple-task coordination investigates the contribution of the dynamic properties of the muscle and its reflex circuitry to phase entrainment. Assuming a simple threshold-linear relationship between the control signals generated by the central nervous system and the observable kinematic and electromyographic signals, a secondary rhythmic movement will cause an additional phase-dependent delay between the central “go” command and the first observable change in actual kinematics of the compound movement. Several indicators for such threshold-linear interaction are derived and tested on real data obtained in psychophysical experiments. Four healthy subjects performed rapid lateral abductions of the index finger in response to a visual “go” signal. During a portion of the experiments, subjects produced additional low-amplitude oscillatory movements before stimulus presentation with either the same finger (one-handed task), or with the index finger of the other hand (two-handed task). Results showed phase entrainment and modulation of reaction times when the cyclic and the discrete movements were simultaneously executed by the same finger. But there was no entrainment in the bimanual execution of the tasks. The model was capable of reproducing the observed effects. It is concluded that coordination of voluntary movements which are concurrently performed by the same effector involves specific discontinuous operations, which represents an essential part of the mechanism of motor coordination. Phase entrainment reflects this characteristic discontinuous behavior of the lower stages of motor execution and does not necessarily require nonlinear interaction of motor commands at higher levels of motor processing. Received: 5 September 2001 / Accepted in revised form: 19 December 2001     

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     

Nicotinic acetylcholine receptors: from structure to brain function

Nicotinic acetylcholine receptors (nAChRs) are ligand-gated ion channels and can be divided into two groups: muscle receptors, which are found at the skeletal neuromuscular junction where they mediate neuromuscular transmission, and neuronal receptors, which are found throughout the peripheral and central nervous system where they are involved in fast synaptic transmission. nAChRs are pentameric structures that are made up of combinations of individual subunits. Twelve neuronal nAChR subunits have been described, α2–α10 and β2–β4; these are differentially expressed throughout the nervous system and combine to form nAChRs with a wide range of physiological and pharmacological profiles. The nAChR has been proposed as a model of an allosteric protein in which effects arising from the binding of a ligand to a site on the protein can lead to changes in another part of the molecule. A great deal is known about the structure of the pentameric receptor. The extracellular domain contains binding sites for numerous ligands, which alter receptor behavior through allosteric mechanisms. Functional studies have revealed that nAChRs contribute to the control of resting membrane potential, modulation of synaptic transmission and mediation of fast excitatory transmission. To date, ten genes have been identified in the human genome coding for the nAChRs. nAChRs have been demonstrated to be involved in cognitive processes such as learning and memory and control of movement in normal subjects. Recent data from knockout animals has extended the understanding of nAChR function. Dysfunction of nAChR has been linked to a number of human diseases such as schizophrenia, Alzheimer's and Parkinson's diseases. nAChRs also play a significant role in nicotine addiction, which is a major public health concern. A genetically transmissible epilepsy, ADNFLE, has been associated with specific mutations in the gene coding for the α4 or β2 subunits, which leads to altered receptor properties. Electronic Publication     

Computational nature of human adaptive control during learning of reaching movements in force fields

Learning to make reaching movements in force fields was used as a paradigm to explore the system architecture of the biological adaptive controller. We compared the performance of a number of candidate control systems that acted on a model of the neuromuscular system of the human arm and asked how well the dynamics of the candidate system compared with the movement characteristics of 16 subjects. We found that control via a supra-spinal system that utilized an adaptive inverse model resulted in dynamics that were similar to that observed in our subjects, but lacked essential characteristics. These characteristics pointed to a different architecture where descending commands were influenced by an adaptive forward model. However, we found that control via a forward model alone also resulted in dynamics that did not match the behavior of the human arm. We considered a third control architecture where a forward model was used in conjunction with an inverse model and found that the resulting dynamics were remarkably similar to that observed in the experimental data. The essential property of this control architecture was that it predicted a complex pattern of near-discontinuities in hand trajectory in the novel force field. A nearly identical pattern was observed in our subjects, suggesting that generation of descending motor commands was likely through a control system architecture that included both adaptive forward and inverse models. We found that as subjects learned to make reaching movements, adaptation rates for the forward and inverse models could be independently estimated and the resulting changes in performance of subjects from movement to movement could be accurately accounted for. Results suggested that the adaptation of the forward model played a dominant role in the motor learning of subjects. After a period of consolidation, the rates of adaptation in the internal models were significantly larger than those observed before the memory had consolidated. This suggested that consolidation of motor memory coincided with freeing of certain computational resources for subsequent learning. Received: 01 January 1998 / Accepted in revised form: 26 January 1999     

Simulating a neural cross-talk model for between-hand interference during bimanual circle drawing

Studies on drawing circles with both hands in the horizontal plane have shown that this task is easy to perform across a wide range of movement frequencies under the symmetrical mode of coordination, whereas under the asymmetrical mode (both limbs moving clockwise or counterclockwise) increases in movement frequency have a disruptive effect on trajectory control and hand coordination. To account for these interference effects, we propose a simplified computer model for bimanual circle drawing based on the assumptions that (1) circular trajectories are generated from two orthogonal oscillations coupled with a phase delay, (2) the trajectories are organized on two levels, “intention” and “motor execution”, and (3) the motor systems controlling each hand are prone to neural cross-talk. The neural cross-talk consists in dispatching some fraction of any force command sent to one limb as a mirror image to the other limb. Assuming predominating coupling influences from the dominant to the nondominant limb, the simulations successfully reproduced the main characteristics of performance during asymmetrical bimanual circle drawing with increasing movement frequencies, including disruption of the circular form drawn with the nondominant hand, increasing dephasing of the hand movements, increasing variability of the phase difference, and occasional reversals of the movement direction in the nondominant limb. The implications of these results for current theories of bimanual coordination are discussed. Received: 23 June 1998 / Accepted in revised form: 20 April 1999     

Independent control of joint stiffness in the framework of the equilibrium-point hypothesis

In the framework of the equilibrium-point hypothesis, virtual trajectories and joint stiffness patterns have been reconstructed during two motor tasks practiced against a constant bias torque. One task required a voluntary increase in joint stiffness while preserving the original joint position. The other task involved fast elbow flexions over 36°. Joint stiffness gradually subsided after the termination of fast movements. In both tasks, the external torque could slowly and unexpectedly change. The subjects were required not to change their motor commands if the torque changed, i.e. “to do the same no matter what the motor did”. In both tasks, changes in joint stiffness were accompanied by unchanged virtual trajectories that were also independent of the absolute value of the bias torque. By contrast, the intercept of the joint compliant characteristic with the angle axis,r(t)-function, has demonstrated a clear dependence upon both the level of coactivation and external load. We assume that a template virtual trajectory is generated at a certain level of the motor hierarchy and is later scaled taking into account some commonly changing dynamic factors of the movement execution, for example, external load. The scaling leads to the generation of commands to the segmental structures that can be expressed, according to the equilibrium-point hypothesis, as changes in the thresholds of the tonic stretch reflex for corresponding muscles.     

Trajectory formation based on physiological characteristics of skeletal muscles

Human arm trajectories in natural unrestricted reaching movements were studied. They have particular properties such that a hand path is a rather simple straight or curved line, and a tangential velocity profile of hand is bell-shaped. Also these properties are invariant, independent of movement duration and hand-held load. In this study, trajectory formation is investigated on the basis of physiological characteristics of skeletal muscles, and a criterion prescribed by a derivative of isometric muscle torque is proposed. Subsequently, optimal trajectories are formulated under various conditions of movement to account for a planning strategy of human arm trajectories. In addition to such a theoretical approach, human arm trajectories are experimentally observed by a measuring system which provides a visual sensor and a target tracking device, enabling totally unrestricted movements. Then, optimal trajectories are quantitatively evaluated in comparison with experimental data in which essential properties of human arm trajectories are demonstrated. These results support the idea that human arm trajectories are planned in order to minimize the proposed criterion which is determined from physiological aspects. Finally, the physiological advantages of human arm trajectories are discussed with regard to the analysis of observed and optimal trajectories. Received: 2 December 1997 / Accepted in revised form: 20 March 1998     

Drifting towards a diffuse control model of exploratory motor learning: A comparison of global and within-trial performance measures

 Accurate measurement is crucial for understanding the processes that underlie exploratory patterns in motor learning. Accordingly, measures of learning should be sensitive to the changes that take place during skill acquisition. Most studies, however, use trial-based global measures that assess performance but do not actually measure gradual changes taking place within trials. The present study attempted to remedy this shortcoming by analysing a visual adaptation task, and comparing traditional global measures of learning with new, within-trial measures. Movement time was the only global measure sensitive to changes in the movement trajectory during learning. Three new measures were expected to reveal changes to the movement trajectory that are associated with learning: (i) the length of runs, (ii) change of trajectory angle in relation to the target, and (iii) drift (change in distance from the target). All three measures were sensitive to learning and indicated a gradual straightening of the movement trajectories over trials. Furthermore, three different methods to partition trajectories into segments were examined. The new within-trial measures, irrespective of partitioning method, prove promising for the development of a diffuse control model of exploratory learning. Received: 5 February 2001 / Accepted in revised form: 16 January 2002     

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.     

Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

A model of handwriting

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.     

Adjustment of the human arm viscoelastic properties to the direction of reaching

The viscoelastic properties of the human arm were measured by means of short force perturbations during fast reaching movements in two orthogonal directions. A linear spring model with time delay described the neuromuscular system of the human arm. The obtained viscoelastic parameters ensured movement stability in spite of the time delay of 50 ms. The stiffness and viscosity ellipses appeared to be predominantly orthogonal to the movement direction, which reduced the effect of force perturbation in the direction orthogonal to the reaching movement. Thus, it can be argued that the viscoelastic properties of the neuromuscular system of the human arm are adjusted to the direction of movement according to a “path preserving” strategy, which minimizes the deviation of the movement path from a straight line, when exposed to an unexpected external force.     

Memory and prediction in natural gaze control

In addition to stimulus properties and task factors, memory is an important determinant of the allocation of attention and gaze in the natural world. One way that the role of memory is revealed is by predictive eye movements. Both smooth pursuit and saccadic eye movements demonstrate predictive effects based on previous experience. We have previously shown that unskilled subjects make highly accurate predictive saccades to the anticipated location of a ball prior to a bounce in a virtual racquetball setting. In this experiment, we examined this predictive behaviour. We asked whether the period after the bounce provides subjects with visual information about the ball trajectory that is used to programme the pursuit movement initiated when the ball passes through the fixation point. We occluded a 100 ms period of the ball''s trajectory immediately after the bounce, and found very little effect on the subsequent pursuit movement. Subjects did not appear to modify their strategy to prolong the fixation. Neither were we able to find an effect on interception performance. Thus, it is possible that the occluded trajectory information is not critical for subsequent pursuit, and subjects may use an estimate of the ball''s trajectory to programme pursuit. These results provide further support for the role of memory in eye movements.     

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.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Influence of long-latency reflex modulation on the performance of quick adjustment movements

The effect of long-latency reflex modulation on the performance of a quick adjustment movement following a muscle stretch was studied in 26 healthy male subjects. When the subjects felt a sudden angle displacement in the direction of a wrist extension they were required to make an adjustment movement by moving a handlebar, held in the hand, to align with a target position as quickly and as accurately as possible. The index of performance (adjustment time) was the time taken to move the handle to the target position from stretch onset. A DC torque motor was used to evoke electromyographic (EMG) reflex responses on a wrist flexor. Averaging of the rectified EMG, recorded from surface electrodes placed over the flexor, showed short- and long-latency reflexes (M1 and M2 components). For all subjects, the amplitudes of the reflex components decreased during the adjustment movement because the target position for this study was fixed to the extension side of the wrist joint. The decrease in the M2 component, which is considered to be a transcortical reflex, was significantly larger than the decrease in the M1 component, which is spinal reflex. The main finding was of a positive correlation between the length of adjustment time and the degree of reduction of M1 and M2 with the adjustment movement (r = 0.602 for M1, P < 0.01; r = 0.850 for M2, P < 0.001). Moreover, there were correlations between the consistency of the voluntary response onset and the degree of M2 decrease (r = 0.577, P < 0.01), and between the consistency of the voluntary response onset and the length of the adjustment time (r = 0.603, P < 0.01). Therefore, we have concluded that the subjects who were able to perform adjustment movements within a short time could modulate the long-latency reflex of the muscle involved in such movements in order to make the function of their voluntary muscle activity more effective, and thus were able to respond appropriately. Accepted: 19 February 1997     

Development and Application of Stereo Camera-Based Upper Extremity Workspace Evaluation in Patients with Neuromuscular Diseases

Background

The concept of reachable workspace is closely tied to upper limb joint range of motion and functional capability. Currently, no practical and cost-effective methods are available in clinical and research settings to provide arm-function evaluation using an individual’s three-dimensional (3D) reachable workspace. A method to intuitively display and effectively analyze reachable workspace would not only complement traditional upper limb functional assessments, but also provide an innovative approach to quantify and monitor upper limb function.

Methodology/Principal Findings

A simple stereo camera-based reachable workspace acquisition system combined with customized 3D workspace analysis algorithm was developed and compared against a sub-millimeter motion capture system. The stereo camera-based system was robust, with minimal loss of data points, and with the average hand trajectory error of about 40 mm, which resulted to ∼5% error of the total arm distance. As a proof-of-concept, a pilot study was undertaken with healthy individuals (n = 20) and a select group of patients with various neuromuscular diseases and varying degrees of shoulder girdle weakness (n = 9). The workspace envelope surface areas generated from the 3D hand trajectory captured by the stereo camera were compared. Normalization of acquired reachable workspace surface areas to the surface area of the unit hemi-sphere allowed comparison between subjects. The healthy group’s relative surface areas were 0.618±0.09 and 0.552±0.092 (right and left), while the surface areas for the individuals with neuromuscular diseases ranged from 0.03 and 0.09 (the most severely affected individual) to 0.62 and 0.50 (very mildly affected individual). Neuromuscular patients with severe arm weakness demonstrated movement largely limited to the ipsilateral lower quadrant of their reachable workspace.

Conclusions/Significance

The findings indicate that the proposed stereo camera-based reachable workspace analysis system is capable of distinguishing individuals with varying degrees of proximal upper limb functional impairments.     

End-point constraints in aiming movements: effects of approach angle and speed

 The present study focuses on two trajectory-formation models of point-to-point aiming movements, viz., the minimum-jerk and the minimum torque-change model. To date, few studies on minimum-jerk and minimum torque-change trajectories have incorporated self- or externally imposed end-point constraints, such as the direction and velocity with which a target area is approached. To investigate which model accounts best for the effects on movement trajectories of such – in many circumstances – realistic end-point constraints, we adjusted both the minimum-jerk and the minimum torque-change model so that they could generate trajectories of which the final part has a specific direction and speed. The adjusted models yield realistic trajectories with a high curvature near movement completion. Comparison of simulated and measured movement trajectories show that pointing movements that are constrained with respect to final movement direction and speed can be described in terms of minimization of joint-torque changes. Received: 7 July 1999 / Accepted in revised form: 8 January 2001