The Effects of Rhythmicity and Amplitude on Transfer of Motor Learning

We perform rhythmic and discrete arm movements on a daily basis, yet the motor control literature is not conclusive regarding the mechanisms controlling these movements; does a single mechanism generate both movement types, or are they controlled by separate mechanisms? A recent study reported partial asymmetric transfer of learning from discrete movements to rhythmic movements. Other studies have shown transfer of learning between large-amplitude to small-amplitude movements. The goal of this study is to explore which aspect is important for learning to be transferred from one type of movement to another: rhythmicity, amplitude or both. We propose two hypotheses: (1) Rhythmic and discrete movements are generated by different mechanisms; therefore we expect to see a partial or no transfer of learning between the two types of movements; (2) Within each movement type (rhythmic/discrete), there will be asymmetric transition of learning from larger movements to smaller ones. We used a learning-transfer paradigm, in which 70 participants performed flexion/extension movements with their forearm, and switched between types of movement, which differed in amplitude and/or rhythmicity. We found partial transfer of learning between discrete and rhythmic movements, and an asymmetric transfer of learning from larger movements to smaller movements (within the same type of movement). Our findings suggest that there are two different mechanisms underlying the generation of rhythmic and discrete arm movements, and that practicing on larger movements helps perform smaller movements; the latter finding might have implications for rehabilitation.     

Distinct timing mechanisms produce discrete and continuous movements

The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems) to accomplish varying behavioral functions such as speed constraints.     

Simulating Discrete and Rhythmic Multi-joint Human Arm Movements by Optimization of Nonlinear Performance Indices

An optimization approach applied to mechanical linkage models is used to simulate human arm movements. Predicted arm trajectories are the result of minimizing a nonlinear performance index that depends on kinematic or dynamic variables of the movement. A robust optimization algorithm is presented that computes trajectories which satisfy the necessary conditions with high accuracy. It is especially adapted to the analysis of discrete and rhythmic movements. The optimization problem is solved by parameterizing each generalized coordinate (e.g., joint angular displacement) in terms of Jacobi polynomials and Fourier series, depending on whether discrete or rhythmic movements are considered, combined with a multiple shooting algorithm. The parameterization of coordinates has two advantages. First, it provides an initial guess for the multiple shooting algorithm which solves the optimization problem with high accuracy. Second, it leads to a low dimensional representation of discrete and rhythmic movements in terms of expansion coefficients. The selection of a suitable feature space is an important prerequisite for comparison, recognition and classification of movements. In addition, the separate computational analysis of discrete and rhythmic movements is motivated by their distinct neurophysiological realizations in the cortex. By investigating different performance indices subject to different boundary conditions, the approach can be used to examine possible strategies that humans adopt in selecting specific arm motions for the performance of different tasks in a plane and in three-dimensional space.     

A dynamic theory of coordination of discrete movement

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.     

Kinematics of the Coordination of Pointing during Locomotion

In natural motor behaviour arm movements, such as pointing or reaching, often need to be coordinated with locomotion. The underlying coordination patterns are largely unexplored, and require the integration of both rhythmic and discrete movement primitives. For the systematic and controlled study of such coordination patterns we have developed a paradigm that combines locomotion on a treadmill with time-controlled pointing to targets in the three-dimensional space, exploiting a virtual reality setup. Participants had to walk at a constant velocity on a treadmill. Synchronized with specific foot events, visual target stimuli were presented that appeared at different spatial locations in front of them. Participants were asked to reach these stimuli within a short time interval after a “go” signal. We analysed the variability patterns of the most relevant joint angles, as well as the time coupling between the time of pointing and different critical timing events in the foot movements. In addition, we applied a new technique for the extraction of movement primitives from kinematic data based on anechoic demixing. We found a modification of the walking pattern as consequence of the arm movement, as well as a modulation of the duration of the reaching movement in dependence of specific foot events. The extraction of kinematic movement primitives from the joint angle trajectories exploiting the new algorithm revealed the existence of two distinct main components accounting, respectively, for the rhythmic and discrete components of the coordinated movement pattern. Summarizing, our study shows a reciprocal pattern of influences between the coordination patterns of reaching and walking. This pattern might be explained by the dynamic interactions between central pattern generators that initiate rhythmic and discrete movements of the lower and upper limbs, and biomechanical factors such as the dynamic gait stability.     

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     

Influence of Vibration on Motor Responses in the Upper Arm Muscles under Stationary Conditions and during Voluntary and Evoked Arm Movements under Limb Unloading Conditions

Locomotion of mammals, including humans, is based on the rhythmic activity of spinal cord circuitries. The functioning of these circuitries depends on multimodal afferent information and on supraspinal influences from the motor cortex. Using the method of transcranial magnetic stimulation (TMS) of arm muscle areas in the motor cortex, we studied the motor evoked potentials (MEP) in the upper arm muscles in stationary conditions and during voluntary and vibration-evoked arm movements. The study included 13 healthy subjects under arm and leg unloading conditions. In the first series of experiments, with motionless limbs, the effect of vibration of left upper arm muscles on motor responses in these muscles was evaluated. In the second series of experiments, MEP were compared in the same muscles during voluntary and rhythmic movements generated by left arm m. triceps brachii vibration (the right arm was stationary). Motionless left arm vibration led to an increase in MEP values in both vibrated muscle and in most of the non-vibrated muscles. For most target muscles, MEP was greater with voluntary arm movements than with vibration-evoked movements. At the same time, a similar MEP modulation in the cycle of arm movements was observed in the same upper arm muscles during both types of arm movements. TMS of the motor cortex significantly potentiated arm movements generated by vibration, but its effect on voluntary movements was weaker. These results indicate significant differences in the degree of motor cortex involvement in voluntary and evoked arm movements. We suppose that evoked arm movements are largely due to spinal rather than central mechanisms of generation of rhythmic movements.     

A multi-dimensional coalescent process applied to multi-allelic selection models and migration models

For a sample of two genes from a population divided into an arbitrary number of allele classes, a general mathematical framework is developed to address the expectation and variance of the time of the most recent common ancestor. Depending on the meaning of allele classes and the manner in which genes can change among them, this framework can be applied to a diversity of population genetic models. By adoption of the infinite sites model, the effect on heterozygosity is modelled for balancing selection among allele classes, mutation between allele classes, migration among populations, and gene conversion between loci. Most results are described for a continuous time approximation to a discrete generation model. It is also shown how the discrete generation model can be used to study the hitch-hiking effect of favorable mutations.     

A coupled oscillator model of disordered interlimb coordination in patients with Parkinson's disease

Coordination between the left and right limbs during cyclic movements, which can be characterized by the amplitude of each limb's oscillatory movement and relative phase, is impaired in patients with Parkinson's disease (PD). A pedaling exercise on an ergometer in a recent clinical study revealed several types of coordination disorder in PD patients. These include an irregular and burst-like amplitude modulation with intermittent changes in its relative phase, a typical sign of chaotic behavior in nonlinear dynamical systems. This clinical observation leads us to hypothesize that emergence of the rhythmic motor behaviors might be concerned with nonlinearity of an underlying dynamical system. In order to gain insight into this hypothesis, we consider a simple hard-wired central pattern generator model consisting of two identical oscillators connected by reciprocal inhibition. In the model, each oscillator acts as a neural half-center controlling movement of a single limb, either left or right, and receives a control input modeling a flow of descending signals from higher motor centers. When these two control inputs are tonic-constant and identical, the model has left-right symmetry and basically exhibits ordered coordination with an alternating periodic oscillation. We show that, depending on the intensities of these two control inputs and on the difference between them that introduces asymmetry into the model, the model can reproduce several behaviors observed in the clinical study. Bifurcation analysis of the model clarifies two possible mechanisms for the generation of disordered coordination in the model: one is the spontaneous symmetry-breaking bifurcation in the model with the left-right symmetry. The other is related to the degree of asymmetry reflecting the difference between the two control inputs. Finally, clinical implications by the model's dynamics are briefly discussed.     

Ontogeny of rhythmic motor networks in the stomatogastric nervous system

We used the lobster Homarus gammarus to study the ontogeny of neural networks involved in rhythmic behaviours. Since in the adult the neural networks belonging to the stomatogastric nervous system and controlling the rhythmic movements of the foregut are well characterised, we have studied them during ontogeny. While this foregut develops slowly throughout embryonic and larval stages, the neuronal population of these motor networks is quantitatively established since the mid-embryonic period. Moreover, in the embryo, this neural population is organised into a single functional network that displays a unique motor output. By contrast, in the adult the same neuronal elements are organised into three neural networks that express independent motor programs. Our results indicate that the multiple adult networks are partitioned progressively from a single embryonic network during development. Accepted: 23 May 1999     

Neural mechanism for generating and switching motor patterns of rhythmic movements of ovipositor valves in the cricket

In adult female crickets (Gryllus bimaculatus), rhythmic movements of ovipositor valves are produced by contractions of a set of ovipositor muscles that mediate egg-laying behavior. Recordings from implanted wire electrodes in the ovipositor muscles of freely moving crickets revealed sequential changes in the temporal pattern of motor activity that corresponded to shifts between behavioral steps: penetration of the ovipositor into a substrate, deposition of eggs, and withdrawal of the ovipositor from the substrate. We aimed in this study to illustrate the neuronal organization producing these motor patterns and the pattern-switching mechanism during the behavioral sequence. Firstly, we obtained intracellular recordings in tethered preparations, and identified 12 types of interneurons that were involved in the rhythmic activity of the ovipositor muscles. These interneurons fell into two classes: ‘initiator interneurons’ in which excitation preceded the rhythmic contractions of ovipositor muscles, and ‘oscillator interneurons’ in which the rhythmic oscillation and spike bursting occurred in sync with the oviposition motor rhythm. One of the oscillator interneurons exhibited different depolarization patterns in the penetration and deposition motor rhythms. It is likely that some of the oscillator interneurons are involved in producing different oviposition motor patterns. Secondly, we analyzed oviposition motor patterns when the mecahnosensory hairs located on the inside surface of the dorsal ovipositor valves were removed. In deafferented preparations, the sequential change from deposition to withdrawal did not occur. Therefore, the switching from deposition pattern to withdrawal pattern is signaled by the hair sensilla that detect the passage of an egg just before it is expelled.     

Search for cerebral G cluster neurons responding to taste stimulation with seaweed in Aplysia kurodai by the use of calcium imaging

The calcium imaging method can detect the spike activities of many neurons simultaneously. In the present experiments, this method was used to search for unique neurons contributing to feeding behavior in the cerebral ganglia of Aplysia kurodai. We mainly explored the neurons whose cell bodies were located in the G cluster and the neuropile region posterior to this cluster on the ventral surface of the cerebral ganglia. When the extract of the food seaweed Ulva was applied to the tentacle-lip region, many neurons stained with a calcium-sensitive dye, Calcium Green-1, showed changes in fluorescence. Some neurons showed rhythmic responses and others showed transient responses, suggesting that these neurons may be partly involved in the feeding circuits. We also identified three motor neurons among these neurons that showed rhythmic fluorescence responses to the taste stimulation. One of them was a motor neuron shortening the anterior tentacle (ATS), and the other two were motor neurons producing lip opening-like (LO(G)) and closing-like (LC(G)) movements, respectively. Application of the Ulva extract to the tentacle-lip region induced phase-locked rhythmic firing activity in these motor neurons, suggesting that these neurons may contribute to the rhythmic patterned movements of the anterior tentacles and lips during the ingestion of seaweed.     

A mathematical model of adaptive behavior in quadruped locomotion

Locomotion involves repetitive movements and is often executed unconsciously and automatically. In order to achieve smooth locomotion, the coordination of the rhythms of all physical parts is important. Neurophysiological studies have revealed that basic rhythms are produced in the spinal network called, the central pattern generator (CPG), where some neural oscillators interact to self-organize coordinated rhythms. We present a model of the adaptation of locomotion patterns to a variable environment, and attempt to elucidate how the dynamics of locomotion pattern generation are adjusted by the environmental changes. Recent experimental results indicate that decerebrate cats have the ability to learn new gait patterns in a changed environment. In those experiments, a decerebrate cat was set on a treadmill consisting of three moving belts. This treadmill provides a periodic perturbation to each limb through variation of the speed of each belt. When the belt for the left forelimb is quickened, the decerebrate cat initially loses interlimb coordination and stability, but gradually recovers them and finally walks with a new gait. Based on the above biological facts, we propose a CPG model whose rhythmic pattern adapts to periodic perturbation from the variable environment. First, we design the oscillator interactions to generate a desired rhythmic pattern. In our model, oscillator interactions are regarded as the forces that generate the desired motion pattern. If the desired pattern has already been realized, then the interactions are equal to zero. However, this rhythmic pattern is not reproducible when there is an environmental change. Also, if we do not adjust the rhythmic dynamics, the oscillator interactions will not be zero. Therefore, in our adaptation rule, we adjust the memorized rhythmic pattern so as to minimize the oscillator interactions. This rule can describe the adaptive behavior of decerebrate cats well. Finally, we propose a mathematical framework of an adaptation in rhythmic motion. Our framework consists of three types of dynamics: environmental, rhythmic motion, and adaptation dynamics. We conclude that the time scale of adaptation dynamics should be much larger than that of rhythmic motion dynamics, and the repetition of rhythmic motions in a stable environment is important for the convergence of adaptation. Received: 10 July 1997 / Accepted in revised form: 13 March 1998     

Central pattern generating networks in insect locomotion

Central pattern generators (CPGs) are neural circuits that based on their connectivity can generate rhythmic and patterned output in the absence of rhythmic external inputs. This property makes CPGs crucial elements in the generation of many kinds of rhythmic motor behaviors in insects, such as flying, walking, swimming, or crawling. Arguably representing the most diverse group of animals, insects utilize at least one of these types of locomotion during one stage of their ontogenesis. Insects have been extensively used to study the neural basis of rhythmic motor behaviors, and particularly the structure and operation of CPGs involved in locomotion. Here, we review insect locomotion with regard to flying, walking, and crawling, and we discuss the contribution of central pattern generation to these three forms of locomotion. In each case, we compare and contrast the topology and structure of the CPGs, and we point out how these factors are involved in the generation of the respective motor pattern. We focus on the importance of sensory information for establishing a functional motor output and we indicate behavior‐specific adaptations. Furthermore, we report on the mechanisms underlying coordination between different body parts. Last but not least, by reviewing the state‐of‐the‐art knowledge concerning the role of CPGs in insect locomotion, we endeavor to create a common ground, upon which future research in the field of motor control in insects can build.     

Mathematical models of eye movements in reading: a possible role for autonomous saccades

 An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory – almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes. Received: 21 March 2000 / Accepted in revised form: 10 January 2001     

Conclusions on motor control depend on the type of model used to represent the periphery

Within the field of motor control, there is no consensus on which kinematic and kinetic aspects of movements are planned or controlled. Perturbing goal-directed movements is a frequently used tool to answer this question. To be able to draw conclusions about motor control from kinematic responses to perturbations, a model of the periphery (i.e., the skeleton, muscle–tendon complexes, and spinal reflex circuitry) is required. The purpose of the present study was to determine to what extent such conclusions depend on the level of simplification with which the dynamical properties of the periphery are modeled. For this purpose, we simulated fast goal-directed single-joint movement with four existing types of models. We tested how three types of perturbations affected movement trajectory if motor commands remained unchanged. We found that the four types of models of the periphery showed different robustness to the perturbations, leading to different predictions on how accurate motor commands need to be, i.e., how accurate the knowledge of external conditions needs to be. This means that when interpreting kinematic responses obtained in perturbation experiments the level of error correction attributed to adaptation of motor commands depends on the type of model used to describe the periphery.     

Fitts' law is not continuous in reciprocal aiming

It takes longer to accomplish difficult tasks than easy ones. In the context of motor behaviour, Fitts'' famous law states that the time needed to successfully execute an aiming movement increases linearly with task difficulty. While Fitts'' explicit formulation has met criticism, the relation between task difficulty and movement time is invariantly portrayed as continuous. Here, we demonstrate that Fitts'' law is discontinuous in reciprocal aiming owing to a transition in operative motor control mechanisms with increasing task difficulty. In particular, rhythmic movements are implemented in easy tasks and discrete movements in difficult ones. How movement time increases with task difficulty differs in both movement types. It appears, therefore, that the human nervous system abruptly engages a different control mechanism when task difficulty increases.     

Rhythm Patterns Interaction - Synchronization Behavior for Human-Robot Joint Action

Interactive behavior among humans is governed by the dynamics of movement synchronization in a variety of repetitive tasks. This requires the interaction partners to perform for example rhythmic limb swinging or even goal-directed arm movements. Inspired by that essential feature of human interaction, we present a novel concept and design methodology to synthesize goal-directed synchronization behavior for robotic agents in repetitive joint action tasks. The agents’ tasks are described by closed movement trajectories and interpreted as limit cycles, for which instantaneous phase variables are derived based on oscillator theory. Events segmenting the trajectories into multiple primitives are introduced as anchoring points for enhanced synchronization modes. Utilizing both continuous phases and discrete events in a unifying view, we design a continuous dynamical process synchronizing the derived modes. Inverse to the derivation of phases, we also address the generation of goal-directed movements from the behavioral dynamics. The developed concept is implemented to an anthropomorphic robot. For evaluation of the concept an experiment is designed and conducted in which the robot performs a prototypical pick-and-place task jointly with human partners. The effectiveness of the designed behavior is successfully evidenced by objective measures of phase and event synchronization. Feedback gathered from the participants of our exploratory study suggests a subjectively pleasant sense of interaction created by the interactive behavior. The results highlight potential applications of the synchronization concept both in motor coordination among robotic agents and in enhanced social interaction between humanoid agents and humans.     

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.