Parabolic movement primitives and cortical states: merging optimality with geometric invariance

Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys’ scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.     

Kinematic invariants during cyclical arm movements

It has been observed that the motion of the arm end-point (the hand, fingertip or the tip of a pen) is characterized by a number of regularities (kinematic invariants). Trajectory is usually straight, and the velocity profile has a bell shape during point-to-point movements. During drawing movements, a two-thirds power law predicts the dependence of the end-point velocity on the trajectory curvature. Although various principles of movement organization have been discussed as possible origins of these kinematic invariants, the nature of these movement trajectory characteristics remains an open question. A kinematic model of cyclical arm movements derived in the present study analytically demonstrates that all three kinematic invariants can be predicted from a two-joint approximation of the kinematic structure of the arm and from sinusoidal joint motions. With this approach, explicit expressions for two kinematic invariants, the two-thirds power law during drawing movements and the velocity profile during point-to-point movements are obtained as functions of arm segment lengths and joint motion parameters. Additionally, less recognized kinematic invariants are also derived from the model. The obtained analytical expressions are further validated with experimental data. The high accuracy of the predictions confirms practical utility of the model, showing that the model is relevant to human performance over a wide range of movements. The results create a basis for the consolidation of various existing interpretations of kinematic invariants. In particular, optimal control is discussed as a plausible source of invariant characteristics of joint motions and movement trajectories.     

Movement Preparation and Bilateral Modulation of Beta Activity in Aging and Parkinson’s Disease

In previous studies of young subjects performing a reaction-time reaching task, we found that faster reaction times are associated with increased suppression of beta power over primary sensorimotor areas just before target presentation. Here we ascertain whether such beta decrease similarly occurs in normally aging subjects and also in patients with Parkinson’s disease (PD), where deficits in movement execution and abnormalities of beta power are usually present. We found that in both groups, beta power decreased during the motor task in the electrodes over the two primary sensorimotor areas. However, before target presentation, beta decreases in PD were significantly smaller over the right than over the left areas, while they were symmetrical in controls. In both groups, functional connectivity between the two regions, measured with imaginary coherence, increased before the target appearance; however, in PD, it decreased immediately after, while in controls, it remained elevated throughout motor planning. As in previous studies with young subjects, the degree of beta power before target appearance correlated with reaction time. The values of coherence during motor planning, instead, correlated with movement time, peak velocity and acceleration. We conclude that planning of prompt and fast movements partially depends on coordinated beta activity of both sensorimotor areas, already at the time of target presentation. The delayed onset of beta decreases over the right region observed in PD is possibly related to a decreased functional connectivity between the two areas, and this might account for deficits in force programming, movement duration and velocity modulation.     

Compositionality of arm movements can be realized by propagating synchrony

We present a biologically plausible spiking neuronal network model of free monkey scribbling that reproduces experimental findings on cortical activity and the properties of the scribbling trajectory. The model is based on the idea that synfire chains can encode movement primitives. Here, we map the propagation of activity in a chain to a linearly evolving preferred velocity, which results in parabolic segments that fulfill the two-thirds power law. Connections between chains that match the final velocity of one encoded primitive to the initial velocity of the next allow the composition of random sequences of primitives with smooth transitions. The model provides an explanation for the segmentation of the trajectory and the experimentally observed deviations of the trajectory from the parabolic shape at primitive transition sites. Furthermore, the model predicts low frequency oscillations (<10 Hz) of the motor cortex local field potential during ongoing movements and increasing firing rates of non-specific motor cortex neurons before movement onset.     

A neural model of basal ganglia-thalamocortical relations in normal and parkinsonian movement

 Anatomical, neurophysiological, and neurochemical evidence supports the notion of parallel basal ganglia–thalamocortical motor systems. We developed a neural network model for the functioning of these systems during normal and parkinsonian movement. Parkinson’s disease (PD), which results predominantly from nigrostriatal pathway damage, is used as a window to examine basal ganglia function. Simulations of dopamine depletion produce motor impairments consistent with motor deficits observed in PD that suggest the basal ganglia play a role in motor initiation and execution, and sequencing of motor programs. Stereotaxic lesions in the model’s globus pallidus and subthalamic nucleus suggest that these lesions, although reducing some PD symptoms, may constrain the repertoire of available movements. It is proposed that paradoxical observations of basal ganglia responses reported in the literature may result from regional functional neuronal specialization, and the non-uniform distributions of neurochemicals in the basal ganglia. It is hypothesized that dopamine depletion produces smaller-than-normal pallidothalamic gating signals that prevent rescalability of these signals to control variable movement speed, and that in PD can produce smaller-than-normal movement amplitudes. Received: 1 September 1994/Accepted in revised form: 16 May 1995     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

Music Attenuates Excessive Visual Guidance of Skilled Reaching in Advanced but Not Mild Parkinson's Disease

Parkinson''s disease (PD) results in movement and sensory impairments that can be reduced by familiar music. At present, it is unclear whether the beneficial effects of music are limited to lessening the bradykinesia of whole body movement or whether beneficial effects also extend to skilled movements of PD subjects. This question was addressed in the present study in which control and PD subjects were given a skilled reaching task that was performed with and without accompanying preferred musical pieces. Eye movements and limb use were monitored with biomechanical measures and limb movements were additionally assessed using a previously described movement element scoring system. Preferred musical pieces did not lessen limb and hand movement impairments as assessed with either the biomechanical measures or movement element scoring. Nevertheless, the PD patients with more severe motor symptoms as assessed by Hoehn and Yahr (HY) scores displayed enhanced visual engagement of the target and this impairment was reduced during trials performed in association with accompanying preferred musical pieces. The results are discussed in relation to the idea that preferred musical pieces, although not generally beneficial in lessening skilled reaching impairments, may normalize the balance between visual and proprioceptive guidance of skilled reaching.     

Cortical mechanisms of smooth eye movements revealed by dynamic covariations of neural and behavioral responses

Neural activity in the frontal eye fields controls smooth pursuit eye movements, but the relationship between single neuron responses, cortical population responses, and eye movements is not well understood. We describe an approach to dynamically link trial-to-trial fluctuations in neural responses to parallel variations in pursuit and demonstrate that individual neurons predict eye velocity fluctuations at particular moments during the course of behavior, while the population of neurons collectively tiles the entire duration of the movement. The analysis also reveals the strength of correlations in the eye movement predictions derived from pairs of simultaneously recorded neurons and suggests a simple model of cortical processing. These findings constrain the primate cortical code for movement, suggesting that either a few neurons are sufficient to drive pursuit at any given time or that many neurons operate collectively at each moment with remarkably little variation added to motor command signals downstream from the cortex.     

The Temporal Structure of Vertical Arm Movements

The present study investigates how the CNS deals with the omnipresent force of gravity during arm motor planning. Previous studies have reported direction-dependent kinematic differences in the vertical plane; notably, acceleration duration was greater during a downward than an upward arm movement. Although the analysis of acceleration and deceleration phases has permitted to explore the integration of gravity force, further investigation is necessary to conclude whether feedforward or feedback control processes are at the origin of this incorporation. We considered that a more detailed analysis of the temporal features of vertical arm movements could provide additional information about gravity force integration into the motor planning. Eight subjects performed single joint vertical arm movements (45° rotation around the shoulder joint) in two opposite directions (upwards and downwards) and at three different speeds (slow, natural and fast). We calculated different parameters of hand acceleration profiles: movement duration (MD), duration to peak acceleration (D PA), duration from peak acceleration to peak velocity (D PA-PV), duration from peak velocity to peak deceleration (D PV-PD), duration from peak deceleration to the movement end (D PD-End), acceleration duration (AD), deceleration duration (DD), peak acceleration (PA), peak velocity (PV), and peak deceleration (PD). While movement durations and amplitudes were similar for upward and downward movements, the temporal structure of acceleration profiles differed between the two directions. More specifically, subjects performed upward movements faster than downward movements; these direction-dependent asymmetries appeared early in the movement (i.e., before PA) and lasted until the moment of PD. Additionally, PA and PV were greater for upward than downward movements. Movement speed also changed the temporal structure of acceleration profiles. The effect of speed and direction on the form of acceleration profiles is consistent with the premise that the CNS optimises motor commands with respect to both gravitational and inertial constraints.     

Arm-plane representation of shoulder compensation during pointing movements in patients with stroke

Improvements in functional motor activities are often accompanied by motor compensations to overcome persistent motor impairment in the upper limb. Kinematic analysis is used to objectively quantify movement patterns including common motor compensations such as excessive trunk displacement during reaching. However, a common motor compensation to assist reaching, shoulder abduction, is not adequately characterized by current motion analysis approaches. We apply the arm-plane representation that accounts for the co-variation between movements of the whole arm, and investigate its ability to identify and quantify compensatory arm movements in stroke subjects when making forward arm reaches. This method has not been previously applied to the analysis of motion deficits. Sixteen adults with right post-stroke hemiparesis and eight healthy age-matched controls reached in three target directions (14 trials/target; sampling rate: 100 Hz). Arm-plane movement was validated against endpoint, joint, and trunk kinematics and compared between groups. In stroke subjects, arm-plane measures were correlated with arm impairment (Fugl-Meyer Assessment) and ability (Box and Blocks) scores and were more sensitive than clinical measures to detect mild motor impairment. Arm-plane motion analysis provides new information about motor compensations involving the co-variation of shoulder and elbow movements that may help to understand the underlying motor deficits in patients with stroke.     

Kinematic characteristics of the voluntary cyclic trunk movements in patients at the early stage of Parkinson's disease

Patients with the initial stage of Parkinson disease (PD) and matched controls performed repetitive bendings and turnings in standing position. Tasks included trunk movements in each of the anatomical planes: sagittal, frontal and axial. Electromagnetic system Flock of Birds was used for movement registration. Sensors were fixed at different segments of subject's body. Joint angles in the ankle, hip and torso as well as coordinates of the center of pressure served as output parameters. The amplitudes of joint angles were found to be lower in PD patients. Performance of the axial rotation revealed most pronounced differences. Thus, the amplitudes of joint angles of trunk movements in different anatomical planes reliably discriminate between PD patients and healthy subjects.     

Abnormal Movement Preparation in Task-Specific Focal Hand Dystonia

Electrophysiological and behavioral studies in primary dystonia suggest abnormalities during movement preparation, but this crucial phase preceding movement onset has not yet been studied specifically with functional magnetic resonance imaging (fMRI). To identify abnormalities in brain activation during movement preparation, we used event-related fMRI to analyze behaviorally unimpaired sequential finger movements in 18 patients with task-specific focal hand dystonia (FHD) and 18 healthy subjects. Patients and controls executed self-initiated or externally cued prelearnt four-digit sequential movements using either right or left hands. In FHD patients, motor performance of the sequential finger task was not associated with task-related dystonic posturing and their activation levels during motor execution were highly comparable with controls. On the other hand reduced activation was observed during movement preparation in the FHD patients in left premotor cortex / precentral gyrus for all conditions, and for self-initiation additionally in supplementary motor area, left mid-insula and anterior putamen, independent of effector side. Findings argue for abnormalities of early stages of motor control in FHD, manifesting during movement preparation. Since deficits map to regions involved in the coding of motor programs, we propose that task-specific dystonia is characterized by abnormalities during recruitment of motor programs: these do not manifest at the behavioral level during simple automated movements, however, errors in motor programs of complex movements established by extensive practice (a core feature of FHD), trigger the inappropriate movement patterns observed in task-specific dystonia.     

Motor Performance Assessment in Parkinson’s Disease: Association between Objective In-Clinic,Objective In-Home,and Subjective/Semi-Objective Measures

Advances in wearable technology allow for the objective assessment of motor performance in both in-home and in-clinic environments and were used to explore motor impairments in Parkinson’s disease (PD). The aims of this study were to: 1) assess differences between in-clinic and in-home gait speed, and sit-to-stand and stand-to-sit duration in PD patients (in comparison with healthy controls); and 2) determine the objective physical activity measures, including gait, postural balance, instrumented Timed-up-and-go (iTUG), and in-home spontaneous physical activity (SPA), with the highest correlation with subjective/semi-objective measures, including health survey, fall history (fallers vs. non-fallers), fear of falling, pain, Unified Parkinson''s Disease Rating Scale, and PD stage (Hoehn and Yahr). Objective assessments of motor performance were made by measuring physical activities in the same sample of PD patients (n = 15, Age: 71.2±6.3 years) and age-matched healthy controls (n = 35, Age: 71.9±3.8 years). The association between in-clinic and in-home parameters, and between objective parameters and subjective/semi-objective evaluations in the PD group was assessed using linear regression-analysis of variance models and reported as Pearson correlations (R). Both in-home SPA and in-clinic assessments demonstrated strong discriminatory power in detecting impaired motor function in PD. However, mean effect size (0.94±0.37) for in-home measures was smaller compared to in-clinic assessments (1.30±0.34) for parameters that were significantly different between PD and healthy groups. No significant correlation was observed between identical in-clinic and in-home parameters in the PD group (R = 0.10–0.25; p>0.40), while the healthy showed stronger correlation in gait speed, sit-to-stand duration, and stand-to-sit duration (R = 0.36–0.56; p<0.03). This suggests a better correlation between supervised and unsupervised motor function assessments in healthy controls compared to PD group. In the PD group, parameters related to velocity and range-of-motion of lower extremity within gait assessment (R = 0.58–0.84), and turning duration and velocity within iTUG test (R = 0.62–0.77) demonstrated strong correlations with PD stage (p<0.01).     

Characterising Upper Limb Movements in Huntington's Disease and the Impact of Restricted Visual Cues

Background

Voluntary motor deficits are a common feature in Huntington''s disease (HD), characterised by movement slowing and performance inaccuracies. This deficit may be exacerbated when visual cues are restricted.

Objective

To characterize the upper limb motor profile in HD with various levels of difficulty, with and without visual targets.

Methods

Nine premanifest HD (pre-HD), nine early symptomatic HD (symp-HD) and nine matched controls completed a motor task incorporating Fitts'' law, a model of human movement enabling the quantification of movement timing, via the manipulation of task difficulty (i.e., target size, and distance between targets). The task required participants to make reciprocal movements under cued and blind conditions. Dwell times (time stationary between movements), speed, accuracy and variability of movements were compared between groups.

Results

Symp-HD showed significantly prolonged and less consistent movement times, compared with controls and pre-HD. Furthermore, movement planning and online control were significantly impaired in symp-HD, compared with controls and pre-HD, evidenced by prolonged dwell times and deceleration times. Speed and accuracy were comparable across groups, suggesting that group differences observed in movement time, variability, dwell time and deceleration time were evident over and above simple performance measures. The presence of cues resulted in greater movement time variability in symp-HD, compared with pre-HD and controls, suggesting that the deficit in movement consistency manifested only in response to targeted movements.

Conclusions

Collectively, these findings provide evidence of a deficiency in both motor planning, particularly in relation to movement timing and online control, which became exacerbated as a function of task difficulty during symp-HD stages. These variables may provide a more sensitive measure of motor dysfunction than speed and/or accuracy alone in symp-HD.     

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.     

Are interlimb interactions disturbed in patients with Parkinson’s disease? A study under unloading conditions

During natural human locomotion, neural connections are activated that are typical of regulation of the quadrupedal walking. The interaction between the neural networks generating rhythmic movements of the upper and lower limbs depends on tonic state of each of these networks regulated by motor signals from the brain. Distortion of these signals in patients with Parkinson’s disease (PD) may lead to disruption of the interlimb interactions. We examined the effect of movements of the limbs of one girdle on the parameters of the motor activity of another limb girdle at their joint cyclic movements under the conditions of arm and leg unloading in 17 patients with PD and 16 healthy subjects. We have shown that, in patients, the effect of voluntary and passive movements of arms, as well as the active movement of the distal parts of arms, on the voluntary movement of legs is weak, while in healthy subjects, the effect of arm movements on the parameters of voluntary stepping is significant. The effect of arm movements on the activation of the involuntary stepping by vibrational stimulation of-legs in patients was absent, while in healthy subjects, the motor activity of arms increased the possibility of involuntary rhythmic movements activation. Differences in the effect of leg movements on the rhythmic movements of arms were found in both patients and healthy subjects. The interlimb interaction appeared after drug administration. However, the effect of the drug was not sufficient for the recovery of normal state of the neural networks in patients. In PD patients, neural networks generating stepping rhythm have an increased tonic activity, which prevents the activation and appearance of involuntary rhythmic movements facilitating the effects of arms on legs.     

The generation of handwriting with delta-lognormal synergies

This paper presents a handwriting generation model that takes advantage of the asymptotic impulse response of neuromuscular networks to produce and control complex two-dimensional synergistic movements. A parametric definition of a ballistic stroke in the context of the kinematic theory of rapid human movements is given. Two types of parameters are used: command and system parameters. The first group provides a representation of the action plan while the second takes into account the temporal properties of the neuromuscular systems executing that plan. Handwriting is described as the time superimposition of basic discontinuous strokes that results in a continuous summation of delta-lognormal velocity vectors. The model leads to trajectory reconstruction, both in the spatial and in the kinematic domain. According to this new paradigm, the angular velocity does not have to be controlled independently and continuously; it naturally emerges from the vectorial summation process. Several psychophysical phenomena related to two-dimensional movements are explained and analyzed in the context of the model: the speed/accuracy trade-offs, spatial scaling, the isochrony principle, the two-thirds power law, effector independence, etc. The overall approach also shows how basic handwriting characteristics (dimension, slant, baseline, shape, etc.) are affected and controlled using an action plan made up of virtual targets fed into a neuromuscular synergy that is governed by a delta-lognormal law. Received: 22 July 1996 / Accepted in revised form: 15 September 1997