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     

Neural control of interlimb oscillations

How do humans and other animals accomplish coordinated movements? How are novel combinations of limb joints rapidly assembled into new behavioral units that move together in in-phase or anti-phase movement patterns during complex movement tasks? A neural central pattern generator (CPG) model simulates data from human bimanual coordination tasks. As in the data, anti-phase oscillations at low frequencies switch to in-phase oscillations at high frequencies, in-phase oscillations occur at both low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, a “seagull effect” of larger errors occurs at intermediate phases, and oscillations slip toward in-phase and anti-phase when driven at intermediate phases. These oscillations and bifurcations are emergent properties of the CPG model in response to volitional inputs. The CPG model is a version of the Ellias-Grossberg oscillator. Its neurons obey Hodgkin-Huxley type equations whose excitatory signals operate on a faster time scale than their inhibitory signals in a recurrent on-center off-surround anatomy. When an equal command or GO signal activates both model channels, the model CPG can generate both in-phase and anti-phase oscillations at different GO amplitudes. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases. Received: 22 August 1994 / Accepted in revised form: 13 May 1997     

Distinguishing the noise and attractor strength of coordinated limb movements using recurrence analysis

The variability of coupled rhythmic limb movements is assumed to be a consequence of the strength of a movement’s attractor dynamic and a constant stochastic noise process that continuously perturbs the movement system away from this dynamic. Recently, it has been suggested that the nonlinear technique of recurrence analysis can be used to index the effects of noise and attractor strength on movement variability. To test this, three experiments were conducted in which the attractor strength of bimanual wrist-pendulum movements (using coordination mode, movement frequency and detuning), as well as the magnitude of stochastic perturbations affecting the variability of these movements (using a temporally fluctuating visual metronome) was manipulated. The results of these experiments demonstrate that recurrence analysis can index parametric changes in the attractor strength of coupled rhythmic limb movements and the magnitude of metronome induced stochastic perturbations independently. The results of Experiments 1 and 2 also support the claim that differences between the variability of inphase and antiphase coordination, and between slow and fast movement frequencies are due to differences in attractor strength. In contrast to the standard assumption that the noise that characterizes interlimb coordination remains constant for different magnitudes of detuning (Δ ω) the results of Experiment 3 suggest that the magnitude of noise increases with increases in |Δ ω|.     

Feedback control of the limbs position during voluntary rhythmic oscillation

The mechanisms that control the limbs position during rhythmic voluntary oscillations were investigated in ten subjects, who were asked to synchronise the lower peak of their hand or foot rhythmic oscillations to a metronome beat. The efficacy of the “position control” was estimated by measuring the degree of synchronisation between the metronome signal and the requested limb position and how it was affected by changing both the oscillation frequency (between 0.4 and 3.0 Hz) and the limbs inertial properties. With the limbs unloaded, the lower peak of both the hand and foot oscillations lagged the metronome beat of a slight amount that remained constant over the whole frequency range (mean phase delay −13.2° for the hand and −4.7° for the foot). The constancy was obtained by phase-advancing, at each frequency increment, the electromyogram (EMG) activation with respect of the clock beat of the amount necessary to compensate for the simultaneous increase of the lag between the EMG and the movement, produced by the limb mechanical impedance. After loading of either limb, the increase of the oscillation frequency induced larger EMG-movement delays and the anticipatory compensation became insufficient, so that the movement progressively phase-lagged the clock beat. The above results have been accurately simulated by a neural network connected to a pendulum model that shared the same mechanical properties of the moving limb. The network compares a central command (the intended position) to the actual position of the effector and acts as a closed-loop proportional, integrative and derivative controller. It is proposed that the synchronisation of rhythmic oscillations of either the hand or the foot is sustained by a feed-back control that conforms the position of each limb to that encoded in the central voluntary command.     

How do neural connectivity and time delays influence bimanual coordination?

Multilevel crosstalk as a neural basis for motor control has been widely discussed in the literature. Since no natural process is instantaneous, any crosstalk model should incorporate time delays, which are known to induce temporal coupling between functional elements and stabilize or destabilize a particular mode of coordination. In this article, we systematically study the dynamics of rhythmic bimanual coordination under the influence of varying connection topology as realized by callosal fibers, cortico-thalamic projections, and crossing peripheral fibers. Such connectivity contributes to various degrees of neural crosstalk between the effectors which we continuously parameterize in a mathematical model. We identify the stability regimes of bimanual coordination as a function of the degree of neural crosstalk, movement amplitude and the time delays involved due to signal processing. Prominent examples include explanations of the decreased stability of the antiphase mode of coordination in split brain patients and the role of coupling in mediating bimanual coordination.     

Levodopa influences the regularity of the ankle joint kinematics in individuals with Parkinson’s disease

The aim of the investigation was to explore the influence of levodopa therapy on the regularity of the structural variations present in the lower extremity joints of individuals with Parkinson’s disease (PD). Ten participants with PD walked on a treadmill during the states of “off” and “on” levodopa. Approximate entropy was used to quantify the regularity of the structural variations present in the joint kinematics. Additionally, a pseudo-periodic surrogation analysis was used to evaluate if changes in the regularity of the joint’s movement were associated with a noisy or deterministic motor process. This investigation provided two key findings. The first was that the structural variations present in ankle joint were more regular with levodopa therapy. The second was that changes in the structural variations were related to a deterministic motor process. This indicated that the variations present in the walking patterns of individuals with PD most likely arose from higher-order neural couplings rather than noise in the motor process. Monitoring the regularity of the structural variations present in gait may help improve the management of PD.     

Definitions of state variables and state space for brain-computer interface

Neocortical state variables are defined and evaluated at three levels: microscopic using multiple spike activity (MSA), mesoscopic using local field potentials (LFP) and electrocorticograms (ECoG), and macroscopic using electroencephalograms (EEG) and brain imaging. Transactions between levels occur in all areas of cortex, upwardly by integration (abstraction, generalization) and downwardly by differentiation (speciation). The levels are joined by circular causality: microscopic activity upwardly creates mesoscopic order parameters, which downwardly constrain the microscopic activity that creates them. Integration dominates in sensory cortices. Microscopic activity evoked by receptor input in sensation induces emergence of mesoscopic activity in perception, followed by integration of perceptual activity into macroscopic activity in concept formation. The reverse process dominates in motor cortices, where the macroscopic activity embodying the concepts supports predictions of future states as goals. These macroscopic states are conceived to order mesoscopic activity in patterns that constitute plans for actions to achieve the goals. These planning patterns are conceived to provide frames in which the microscopic activity evolves in trajectories that adapted to the immediate environmental conditions detected by new stimuli. This circular sequence forms the action-perception cycle. Its upward limb is understood through correlation of sensory cortical activity with behavior. Now brain-machine interfaces (BMI) offer a means to understand the downward sequence through correlation of behavior with motor cortical activity, beginning with macroscopic goal states and concluding with recording of microscopic MSA trajectories that operate neuroprostheses. Part 1 develops a hypothesis that describes qualitatively the neurodynamics that supports the action-perception cycle and derivative reflex arc. Part 2 describes episodic, “cinematographic” spatial pattern formation and predicts some properties of the macroscopic and mesoscopic frames by which the embedded trajectories of the microscopic activity of cortical sensorimotor neurons might be organized and controlled. URL: http://sulcus.berkeley.edu     

Rhythmic signalling and entrainment inVespa orientalis larvae: Characterization of the underlying interactions

Rhythmic “circa-second” contrations of larvae of the hornetVespa orientalis, believed to serve as hunger signals, were studied. A considerable degree of coordination among individual larvae, both in frequency and phase of these contractions, has been observed. The oscillations of singly isolated larvae are of short duration, non-constant, with increasing intervals in between and there is a substantial variability in the patterns shown by different larvae. In contrast, the association of two or more larvae leads to enhancement of their periodic behaviour and to (partial) entrainment. Communication among larvae may perhaps be mediated by the sound pulses (“scratching” noises) which are generated by these contractions. We have subjected individual and grouped larvae to external sound pulses and were able to demonstrate: (a) enhancement of rhythmic activity; (b) phase resetting; (c) entrainment to an external oscillator within a range of frequencies; (d) the existence of a subharmonic mode of entrainment. We propose a simple phenomenologic model to account for these larvae responses. Our model assumes the existence of an “energy” variable which declines with time but is upgraded, in a phase-dependent way, by external stimuli. Based in part on work performed by V. Barenholz-Paniry in partial fulfillment of the requirements for the M.Sc. degree from the Sackler Faculty of Medicine, Tel Aviv University, 1986.     

Neural activation and functional connectivity during motor imagery of bimanual everyday actions

Bimanual actions impose intermanual coordination demands not present during unimanual actions. We investigated the functional neuroanatomical correlates of these coordination demands in motor imagery (MI) of everyday actions using functional magnetic resonance imaging (fMRI). For this, 17 participants imagined unimanual actions with the left and right hand as well as bimanual actions while undergoing fMRI. A univariate fMRI analysis showed no reliable cortical activations specific to bimanual MI, indicating that intermanual coordination demands in MI are not associated with increased neural processing. A functional connectivity analysis based on psychophysiological interactions (PPI), however, revealed marked increases in connectivity between parietal and premotor areas within and between hemispheres. We conclude that in MI of everyday actions intermanual coordination demands are primarily met by changes in connectivity between areas and only moderately, if at all, by changes in the amount of neural activity. These results are the first characterization of the neuroanatomical correlates of bimanual coordination demands in MI. Our findings support the assumed equivalence of overt and imagined actions and highlight the differences between uni- and bimanual actions. The findings extent our understanding of the motor system and may aid the development of clinical neurorehabilitation approaches based on mental practice.     

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.     

A new child-friendly 3D bimanual protocol to assess upper limb movement in children with unilateral cerebral palsy: Development and validation

Unilateral cerebral palsy (uCP) causes upper limb movement disorders that impact on daily activities, especially in bimanual condition. However, a few studies have proposed bimanual tasks for 3D motion analysis. The aim of this study was to validate the new version of a child-friendly, 3D, bimanual protocol for the measurement of joint angles and movement quality variables. Twenty children with uCP and 20 typically developing children (TDC) performed the five-task protocol integrated into a game scenario. Each task specifically targeted one or two upper limb degrees of freedom. Joint angles, smoothness and trajectory straightness were calculated. Elbow extension, supination, wrist extension and adduction amplitudes were reduced; hand trajectories were less smooth and straight in children with uCP compared to TDC. Correlations between the performance-based score and kinematic variables were strong. High within and between-session reliability was found for most joint angle variables and lower reliability was found for smoothness and straightness in most tasks. The results therefore demonstrated the validity and reliability of the new protocol for the objective assessment of bimanual function in children with uCP. The evaluation of both joint angles and movement quality variables should increase understanding of pathological movement patterns and help clinicians to optimize treatment.ClinicalTrials.gov identifier: NCT03888443.     

The dynamic behavior of phycobilisome movement during light state transitions in cyanobacterium <Emphasis Type="Italic">Synechocystis</Emphasis> PCC6803

Light state transition is a physiological function of oxygenic organisms to balance the excitation of photosystem II (PSII) and photosystem I (PSI), hence a prerequisite of oxygen-evolving photosynthesis. For cyanobacteria, phycobilisome (PBS) movement during light state transition has long been expected, but never observed. Here the dynamic behavior of PBS movement during state transition in cyanobacterium Synechocystis PCC6803 is experimentally detected via time-dependent fluorescence fluctuation. Under continuous excitation of PBSs in the intact cells, time-dependent fluorescence fluctuations resemble “damped oscillation” mode, which indicates dynamic searching of a PBS in an “overcorrection” manner for the “balance” position where PSII and PSI are excited equally. Based on the parallel model, it is suggested that the “damped oscillation” fluorescence fluctuation is originated from a collective movement of all the PBSs to find the “balance” position. Based on the continuous fluorescence fluctuation during light state transition and also variety of solar spectra, it may be deduced that light state transition of oxygen-evolution organisms is a natural behavior that occurs daily rather than an artificial phenomenon at extreme light conditions in laboratory.     

Information-theoretic analysis of de-efferented single muscle spindles

 The information transmission properties of single, de-efferented primary muscle-spindle afferents from the hind limb of the cat were investigated. The gastrocnemius medialis muscle was stretched randomly while recording spike trains from several muscle-spindle afferents in the dorsal root. Two classes of input stimuli were used: (i) Gaussian noise with band-limited flat spectrum, and (ii) Gaussian noise with a more “naturalistic” 1/f ⁿ spectrum. The “reconstruction” method was used to calculate a lower bound to the information rate (in bits per second) between the muscle spindles and the spinal cord. Results show that in response to the flat-spectrum input, primary muscle-spindle afferents transfer information mainly about high frequencies, carrying 2.12 bits/spike. In response to naturalistic-spectrum inputs, primary muscle-spindle afferents transfer information about both low and high frequencies, with “spiking efficiency” increasing to 2.67 bits/spike. A simple muscle-spindle simulation model was analyzed with the same method, emphasizing the important part played by the intrafusal fiber mechanical properties in information transmission. Received: 22 January 2002 / Accepted in revised form: 17 June 2002 Correspondence to: Y. Tock (e-mail: ytock@tx.technion.ac.il, Fax: +972-4-8323041)     

The reorganization of bimanual movements during formation of a lateralized motor food skill in rats

After 48 h food deprivation adult Wistar rats were trained to obtain food from a narrow tube feeder using the forepaw under conditions of free choice of limb. At the initial stage of training animals use both paws: the grasping and extraction with one paw can be alternated with food grasping and extraction with another paw, and both paws can be alternately involved in movements preceding this grasping. Character of reorganization of bimanual movements was analyzed during training rats with different motor preference (right-handed and left-handed animals). It was shown that in the process of acquisition of both right- and left-hand skills, bimanual reactions in the anticipating attempts disappeared later than in the final successful movements. The disappearance of bimanual movements in the anticipating attempts is considered as an index of the maximum skill lateralization and acquisition of a novel lateralized movement coordination. The results suggest that left-handed rats more rapidly learn a novel movement coordination than right-handed animals.     

Mathematical biology of social behavior

When an individual grows up in a society, he learns certain behavior patterns which are “accepted” by that society. He may in general have a tendency toward behavior patterns other than those which are “accepted” by the society. This tendency toward such unaccepted behavior may be due to a process of cerebration which results in doubt as to the “correctness” of the accepted behavior. Thus, on the one hand, the individual learns to follow the accepted rules almost automatically; on the other hand, he may tend to consciously break those rules. Using a neural circuit, suggested by H. D. Landahl in his theory of learning, a neurobiophysical interpretation of the above situation is outlined. Mathematical expressions are derived which describe the social behavior of an individual as a function of his age, social status, and some neurobiophysical parameters.     

Recovery in stroke rehabilitation through the rotation of preferred directions induced by bimanual movements: a computational study

Stroke patients recover more effectively when they are rehabilitated with bimanual movement rather than with unimanual movement; however, it remains unclear why bimanual movement is more effective for stroke recovery. Using a computational model of stroke recovery, this study suggests that bimanual movement facilitates the reorganization of a damaged motor cortex because this movement induces rotations in the preferred directions (PDs) of motor cortex neurons. Although the tuning curves of these neurons differ during unimanual and bimanual movement, changes in PD, but not changes in modulation depth, facilitate such reorganization. In addition, this reorganization was facilitated only when encoding PDs are rotated, but decoding PDs are not rotated. Bimanual movement facilitates reorganization because this movement changes neural activities through inter-hemispheric inhibition without changing cortical-spinal-muscle connections. Furthermore, stronger inter-hemispheric inhibition between motor cortices results in more effective reorganization. Thus, this study suggests that bimanual movement is effective for stroke rehabilitation because this movement rotates the encoding PDs of motor cortex neurons.     

Les mouvements révolutifs des feuilles deMimosa pudica L

The nutational movements performed by the leaves of the “Sensitive plant”,Mimosa pudica L., result from periodical turgor variations taking place in the parenchymatous cells of specialized motor organs. The trajectories in the three kinds of leaf motor organs usually show irregular elliptical paths with a period ranging from 10 to 60 min. The morphological analogy of these turgor movements is discussed in relation to nutational movements observed in growing organs.      

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     

Biomechanical analysis of movement strategies in human forward trunk bending. II. Experimental study

 The large mass of the human upper trunk, its elevated position during erect stance, and the small area limited by the size of the feet, stress the importance of equilibrium control during trunk movements. The objective of the present study was to perform a biomechanical analysis of fast forward trunk movements in order to understand the coordination between movement and posture. The analysis is based on a comparison between experimentally observed bending and hypothetical “optimal bending” performed on an infinitely narrow support, as presented in a companion paper. The experimental data were obtained from 16 subjects who performed fast forward bending while standing on a wide platform or on a narrow beam. The analysis is performed by decomposition of the movement into three dynamically independent components, each representing a movement along one of the three eigenvectors of the motion equation. The eigenmovements are termed “hip”, “ankle”, and “knee” eigenmovements, according to the dominant joint. The experimentally observed movement is characterized mainly by the hip and ankle eigenmovements, whereas the knee eigenmovement is negligible. Similarly to the “optimal bending” the ankle eigenmovement starts earlier and lasts longer than the hip eigenmovement. An early forward acceleration of the center of gravity in the ankle eigenmovement is caused by anticipatory changes in the ankle joint torque. This clarifies the role of the early tibialis anterior burst and/or soleus inhibition usually observed in electromyographic recordings during forward bending. The results suggest that the hip and the ankle eigenmovements can be treated as independently controlled motion units aimed at functionally different behavioral goals: the bending per se and postural adjustment. It is proposed that the central nervous system has to control these motion units sequentially in order to perform the movement and maintain equilibrium. It is also suggested that the hip and ankle eigenmovements can be regarded as a biomechanical background for the hip and ankle strategies introduced by Horak and Nashner (1986) on the basis of electromyographic recordings and kinematic patterns in response to postural perturbations. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

Age-related changes in the spatiotemporal structure of simple cyclical graphic movements performed at the maximal rate: I. The increase in the movement rate is accounted for by reduction of the number of submovements in a movement cycle

Right-handed subjects from four age groups, including children aged 5–6, 8–9, and 11–12 years and adults, performed simple cyclical graphic movements of different degrees of coordination and serial complexity at the maximum possible rate with the right and left hands holding the stylus either with their fingers or in the fist. The period of the cyclical movement decreased with age, the decrease depending on which hand (the right or the left) was used and how the stylus was held. The frequency of submovements only slightly depended on the age, was the same for the right and left hands, but did not depend on the type of movement or the way of holding the stylus. The age-related increase in the maximal rate of graphic movements may have been almost entirely accounted for by a decrease in the number of submovements constituting the movement cycle. The results are discussed in terms of the notion of submovements as “elementary units” of graphic movements.