A computational theory for the production of limb movements.

Motor control is a fundamental process that underlies all voluntary behavioral responses. Several different theories based on different principles (task dynamics, equilibrium-point theory, passive-motion paradigm, active inference, optimal control) account for specific aspects of how actions are produced, but fail to provide a unified view on this problem. Here, we propose a concise theory of motor control based on three principles: optimal feedback control, control with a receding time horizon, and task representation by a series of via-points updated at fixed frequency. By construction, the theory provides a suitable solution to the degrees-of-freedom problem, that is, trajectory formation in the presence of redundancies and noise. We show through computer simulations that the theory also explains the production of discrete, continuous, rhythmic, and temporally constrained movements, and their parametric and statistical properties (scaling laws, power laws, speed/accuracy trade-offs). The theory has no free parameters and only limited variations in its implementation details and in the nature of noise are necessary to guarantee its explanatory power. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

What is the nature of motor adaptation to dynamic perturbations?

When human participants repeatedly encounter a velocity-dependent force field that distorts their movement trajectories, they adapt their motor behavior to recover straight trajectories. Computational models suggest that adaptation to a force field occurs at the action selection level through changes in the mapping between goals and actions. The quantitative prediction from these models indicates that early perturbed trajectories before adaptation and late unperturbed trajectories after adaptation should have opposite curvature, i.e. one being a mirror image of the other. We tested these predictions in a human adaptation experiment and we found that the expected mirror organization was either absent or much weaker than predicted by the models. These results are incompatible with adaptation occurring at the action selection level but compatible with adaptation occurring at the goal selection level, as if adaptation corresponds to aiming toward spatially remapped targets.

Modulation of ellipses drawing by sonification.

Most studies on the regulation of speed and trajectory during ellipse drawing have used visual feedback. We used online auditory feedback (sonification) to induce implicit movement changes independently from vision. The sound was produced by filtering a pink noise with a band-pass filter proportional to movement speed. The first experiment was performed in 2D. Healthy participants were asked to repetitively draw ellipses during 45 s trials whilst maintaining a constant sonification pattern (involving pitch variations during the cycle). Perturbations were produced by modifying the slope of the mapping without informing the participants. All participants adapted spontaneously their speed: they went faster if the slope decreased and slower if it increased. Higher velocities were achieved by increasing both the frequency of the movements and the perimeter of the ellipses, but slower velocities were achieved mainly by decreasing the perimeter of the ellipses. The shape and the orientation of the ellipses were not significantly altered. The analysis of the speed-curvature power law parameters showed consistent modulations of the speed gain factor, while the exponent remained stable. The second experiment was performed in 3D and showed similar results, except that the main orientation of the ellipse also varied with the changes in speed. In conclusion, this study demonstrated implicit modulation of movement speed by sonification and robust stability of the ellipse geometry. Participants appeared to limit the decrease in movement frequency during slowing down to maintain a rhythmic and not discrete motor regimen.

Experimental and theoretical study of velocity fluctuations during slow movements in humans.

Moving smoothly is generally considered as a higher-order goal of motor control and moving jerkily as a witness of clumsiness or pathology, yet many common and well-controlled movements (e.g., tracking movements) have irregular velocity profiles with widespread fluctuations. The origin and nature of these fluctuations have been associated with the operation of an intermittent process but in fact remain poorly understood. Here we studied velocity fluctuations during slow movements, using combined experimental and theoretical tools. We recorded arm movement trajectories in a group of healthy participants performing back-and-forth movements at different speeds, and we analyzed velocity profiles in terms of series of segments (portions of velocity between 2 minima). We found that most of the segments were smooth (i.e., corresponding to a biphasic acceleration) and had constant duration irrespective of movement speed and linearly increasing amplitude with movement speed. We accounted for these observations with an optimal feedback control model driven by a staircase goal position signal in the presence of sensory noise. Our study suggests that one and the same control process can explain the production of fast and slow movements, i.e., fast movements emerge from the immediate tracking of a global goal position and slow movements from the successive tracking of intermittently updated intermediate goal positions. NEW & NOTEWORTHY We show in experiments and modeling that slow movements could result from the brain tracking a sequence of via points regularly distributed in time and space. Accordingly, slow movements would differ from fast movement by the nature of the guidance and not by the nature of control. This result could help in understanding the origin and nature of slow and segmented movements frequently observed in brain disorders.

Modifying upper-limb inter-joint coordination in healthy subjects by training with a robotic exoskeleton.

BACKGROUND: The possibility to modify the usually pathological patterns of coordination of the upper-limb in stroke survivors remains a central issue and an open question for neurorehabilitation. Despite robot-led physical training could potentially improve the motor recovery of hemiparetic patients, most of the state-of-the-art studies addressing motor control learning, with artificial virtual force fields, only focused on the end-effector kinematic adaptation, by using planar devices. Clearly, an interesting aspect of studying 3D movements with a robotic exoskeleton, is the possibility to investigate the way the human central nervous system deals with the natural upper-limb redundancy for common activities like pointing or tracking tasks. METHODS: We asked twenty healthy participants to perform 3D pointing or tracking tasks under the effect of inter-joint velocity dependant perturbing force fields, applied directly at the joint level by a 4-DOF robotic arm exoskeleton. These fields perturbed the human natural inter-joint coordination but did not constrain directly the end-effector movements and thus subjects capability to perform the tasks. As a consequence, while the participants focused on the achievement of the task, we unexplicitly modified their natural upper-limb coordination strategy. We studied the force fields direct effect on pointing movements towards 8 targets placed in the 3D peripersonal space, and we also considered potential generalizations on 4 distinct other targets. Post-effects were studied after the removal of the force fields (wash-out and follow up). These effects were quantified by a kinematic analysis of the pointing movements at both end-point and joint levels, and by a measure of the final postures. At the same time, we analysed the natural inter-joint coordination through PCA. RESULTS: During the exposition to the perturbative fields, we observed modifications of the subjects movement kinematics at every level (joints, end-effector, and inter-joint coordination). Adaptation was evidenced by a partial decrease of the movement deviations due to the fields, during the repetitions, but it occurred only on 21% of the motions. Nonetheless post-effects were observed in 86% of cases during the wash-out and follow up periods (right after the removal of the perturbation by the fields and after 30 minutes of being detached from the exoskeleton). Important inter-individual differences were observed but with small variability within subjects. In particular, a group of subjects showed an over-shoot with respect to the original unexposed trajectories (in 30% of cases), but the most frequent consequence (in 55% of cases) was the partial persistence of the modified upper-limb coordination, adopted at the time of the perturbation. Temporal and spatial generalizations were also evidenced by the deviation of the movement trajectories, both at the end-effector and at the intermediate joints and the modification of the final pointing postures towards targets which were never exposed to any field. CONCLUSIONS: Such results are the first quantified characterization of the effects of modification of the upper-limb coordination in healthy subjects, by imposing modification through viscous force fields distributed at the joint level, and could pave the way towards opportunities to rehabilitate pathological arm synergies with robots.

Balancing out dwelling and moving: optimal sensorimotor synchronization.

Sensorimotor synchronization is a fundamental skill involved in the performance of many artistic activities (e.g., music, dance). After a century of research, the manner in which the nervous system produces synchronized movements remains poorly understood. Typical rhythmic movements involve a motion and a motionless phase (dwell). The dwell phase represents a sizable fraction of the rhythm period, and scales with it. The rationale for this organization remains unexplained and is the object of this study. Twelve participants, four drummers (D) and eight nondrummers (ND), performed tapping movements paced at 0.5-2.5 Hz by a metronome. The participants organized their tapping behavior into dwell and movement phases according to two strategies: 1) Eight participants (1 D, 7 ND) maintained an almost constant ratio of movement time (MT) and dwell time (DT) irrespective of the metronome period. 2) Four participants increased the proportion of DT as the period increased. The temporal variabilities of both the dwell and movement phases were consistent with Weber's law, i.e., their variability increased with their durations, and the longest phase always exhibited the smallest variability. We developed an optimal statistical model that formalized the distribution of time into dwell and movement intervals as a function of their temporal variability. The model accurately predicted the participants' dwell and movement durations irrespective of their strategy and musical skill, strongly suggesting that the distribution of DT and MT results from an optimization process, dependent on each participant's skill to predict time during rest and movement.

A model of reward- and effort-based optimal decision making and motor control.

Costs (e.g. energetic expenditure) and benefits (e.g. food) are central determinants of behavior. In ecology and economics, they are combined to form a utility function which is maximized to guide choices. This principle is widely used in neuroscience as a normative model of decision and action, but current versions of this model fail to consider how decisions are actually converted into actions (i.e. the formation of trajectories). Here, we describe an approach where decision making and motor control are optimal, iterative processes derived from the maximization of the discounted, weighted difference between expected rewards and foreseeable motor efforts. The model accounts for decision making in cost/benefit situations, and detailed characteristics of control and goal tracking in realistic motor tasks. As a normative construction, the model is relevant to address the neural bases and pathological aspects of decision making and motor control.

A computational model of use-dependent motor recovery following a stroke: optimizing corticospinal activations via reinforcement learning can explain residual capacity and other strength recovery dynamics.

This paper describes a computational model of use-dependent recovery of movement strength following a stroke. The model frames the problem of strength recovery as that of learning appropriate activations of residual corticospinal neurons to their target motoneuronal pools. For example, for an agonist/antagonist muscle pair, we assume the motor system must learn to activate preserved agonist-exciting corticospinal neurons and deactivate preserved antagonist-exciting corticospinal neurons. The model incorporates a biologically plausible reinforcement learning algorithm for adjusting cell activation patterns-stochastic search-using generated limb force as the teaching signal to adjust the synaptic weights that determine cell activations. The model makes predictions consistent with clinical and brain imaging data, such as that patients can achieve an increase in strength after appearing to reach a recovery plateau (i.e., "residual capacity"), that the differential effect of a dose of movement practice will be greater earlier in recovery, and that force-related brain activation will increase in secondary motor areas following a stroke. An interesting prediction that could be explored clinically is that temporarily inhibiting subpopulations of more powerfully connected corticospinal neurons during late movement training will allow the motor system to optimize corticospinal neurons with a weaker influence, whose optimization was blocked by the rapid optimization of more strongly connected neurons early in training.

Dendritic signals command firing dynamics in a mathematical model of cerebellar Purkinje cells.

Dendrites of cerebellar Purkinje cells (PCs) respond to brief excitations from parallel fibers with lasting plateau depolarizations. It is unknown whether these plateaus are local events that boost the synaptic signals or they propagate to the soma and directly take part in setting the cell firing dynamics. To address this issue, we analyzed a likely mechanism underlying plateaus in three representations of a reconstructed PC with increasing complexity. Analysis in an infinite cable suggests that Ca plateaus triggered by direct excitatory inputs from parallel fibers and their mirror signals, valleys (putatively triggered by the local feed forward inhibitory network), cannot propagate. However, simulations of the model in electrotonic equivalent cables prove that Ca plateaus (resp. valleys) are conducted over the entire cell with velocities typical of passive events once they are triggered by threshold synaptic inputs that turn the membrane current inward (resp. outward) over the whole cell surface. Bifurcation analysis of the model in equivalent cables, and simulations in a fully reconstructed PC both indicate that dendritic Ca plateaus and valleys, respectively, command epochs of firing and silencing of PCs.

Active control of bias for the control of posture and movement.

Posture and movement are fundamental, intermixed components of motor coordination. Current approaches consider either that 1) movement is an active, anticipatory process and posture is a passive feedback process or 2) movement and posture result from a common passive process. In both cases, the presence of a passive component renders control scarcely robust and stable in the face of transmission delays and low feedback gains. Here we show in a model that posture and movement could result from the same active process: an optimal feedback control that drives the body from its estimated state to its goal in a given (planning) time by acting through muscles on the insertion position (bias) of compliant linkages (tendons). Computer simulations show that iteration of this process in the presence of noise indifferently produces realistic postural sway, fast goal-directed movements, and natural transitions between posture and movement.

Do robotic and non-robotic arm movement training drive motor recovery after stroke by a common neural mechanism? Experimental evidence and a computational model.

Different dose-matched, upper extremity rehabilitation training techniques, including robotic and non-robotic techniques, can result in similar improvement in movement ability after stroke, suggesting they may elicit a common drive for recovery. Here we report experimental results that support the hypothesis of a common drive, and develop a computational model of a putative neural mechanism for the common drive. We compared weekly motor control recovery during robotic and unassisted movement training techniques after chronic stroke (n = 27), as assessed with quantitative measures of strength, speed, and coordination. The results showed that recovery in both groups followed an exponential time course with a time constant of about 4-5 weeks. Despite the greater range and speed of movement practiced by the robot group, motor recovery was very similar between the groups. The premise of the computational model is that improvements in motor control are caused by improvements in the ability to activate spared portions of the damaged corticospinal system, as learned by a biologically plausible search algorithm. Robot-assisted and unassisted training would in theory equally drive this search process.

Computational motor control: feedback and accuracy.

Speed/accuracy trade-off is a ubiquitous phenomenon in motor behaviour, which has been ascribed to the presence of signal-dependent noise (SDN) in motor commands. Although this explanation can provide a quantitative account of many aspects of motor variability, including Fitts' law, the fact that this law is frequently violated, e.g. during the acquisition of new motor skills, remains unexplained. Here, we describe a principled approach to the influence of noise on motor behaviour, in which motor variability results from the interplay between sensory and motor execution noises in an optimal feedback-controlled system. In this framework, we first show that Fitts' law arises due to signal-dependent motor noise (SDN(m)) when sensory (proprioceptive) noise is low, e.g. under visual feedback. Then we show that the terminal variability of non-visually guided movement can be explained by the presence of signal-dependent proprioceptive noise. Finally, we show that movement accuracy can be controlled by opposite changes in signal-dependent sensory (SDN(s)) and SDN(m), a phenomenon that could be ascribed to muscular co-contraction. As the model also explains kinematics, kinetics, muscular and neural characteristics of reaching movements, it provides a unified framework to address motor variability.

Optimality, stochasticity, and variability in motor behavior.

Recent theories of motor control have proposed that the nervous system acts as a stochastically optimal controller, i.e. it plans and executes motor behaviors taking into account the nature and statistics of noise. Detrimental effects of noise are converted into a principled way of controlling movements. Attractive aspects of such theories are their ability to explain not only characteristic features of single motor acts, but also statistical properties of repeated actions. Here, we present a critical analysis of stochastic optimality in motor control which reveals several difficulties with this hypothesis. We show that stochastic control may not be necessary to explain the stochastic nature of motor behavior, and we propose an alternative framework, based on the action of a deterministic controller coupled with an optimal state estimator, which relieves drawbacks of stochastic optimality and appropriately explains movement variability.

Coding of movement- and force-related information in primate primary motor cortex: a computational approach.

Coordinated movements result from descending commands transmitted by central motor systems to the muscles. Although the resulting effect of the commands has the dimension of a muscular force, it is unclear whether the information transmitted by the commands concerns movement kinematics (e.g. position, velocity) or movement dynamics (e.g. force, torque). To address this issue, we used an optimal control model of movement production that calculates inputs to motoneurons that are appropriate to drive an articulated limb toward a goal. The model quantitatively accounted for kinematic, kinetic and muscular properties of planar, shoulder/elbow arm-reaching movements of monkeys, and reproduced detailed features of neuronal correlates of these movements in primate motor cortex. The model also reproduced qualitative spatio-temporal characteristics of movement- and force-related single neuron discharges in non-planar reaching and isometric force production tasks. The results suggest that the nervous system of the primate controls movements through a muscle-based controller that could be located in the motor cortex.

A new principle for information storage in an enzymatic pathway model.

Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activity-dependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans.

Computational motor control: redundancy and invariance.

The nervous system controls the behavior of complex kinematically redundant biomechanical systems. How it computes appropriate commands to generate movements is unknown. Here we propose a model based on the assumption that the nervous system: 1) processes static (e.g., gravitational) and dynamic (e.g., inertial) forces separately; 2) calculates appropriate dynamic controls to master the dynamic forces and progress toward the goal according to principles of optimal feedback control; 3) uses the size of the dynamic commands (effort) as an optimality criterion; and 4) can specify movement duration from a given level of effort. The model was used to control kinematic chains with 2, 4, and 7 degrees of freedom [planar shoulder/elbow, three-dimensional (3D) shoulder/elbow, 3D shoulder/elbow/wrist] actuated by pairs of antagonist muscles. The muscles were modeled as second-order nonlinear filters and received the dynamics commands as inputs. Simulations showed that the model can quantitatively reproduce characteristic features of pointing and grasping movements in 3D space, i.e., trajectory, velocity profile, and final posture. Furthermore, it accounted for amplitude/duration scaling and kinematic invariance for distance and load. These results suggest that motor control could be explained in terms of a limited set of computational principles.

Supervised learning in a recurrent network of rate-model neurons exhibiting frequency adaptation.

For gradient descent learning to yield connectivity consistent with real biological networks, the simulated neurons would have to include more realistic intrinsic properties such as frequency adaptation. However, gradient descent learning cannot be used straightforwardly with adapting rate-model neurons because the derivative of the activation function depends on the activation history. The objectives of this study were to (1) develop a simple computational approach to reproduce mathematical gradient descent and (2) use this computational approach to provide supervised learning in a network formed of rate-model neurons that exhibit frequency adaptation. The results of mathematical gradient descent were used as a reference in evaluating the performance of the computational approach. For this comparison, standard (nonadapting) rate-model neurons were used for both approaches. The only difference was the gradient calculation: the mathematical approach used the derivative at a point in weight space, while the computational approach used the slope for a step change in weight space. Theoretically, the results of the computational approach should match those of the mathematical approach, as the step size is reduced but floating-point accuracy formed a lower limit to usable step sizes. A systematic search for an optimal step size yielded a computational approach that faithfully reproduced the results of mathematical gradient descent. The computational approach was then used for supervised learning of both connection weights and intrinsic properties of rate-model neurons to convert a tonic input into a phasic-tonic output pattern. Learning produced biologically realistic connectivity that essentially used a monosynaptic connection from the tonic input neuron to an output neuron with strong frequency adaptation as compared to a complex network when using nonadapting neurons. Thus, more biologically realistic connectivity was achieved by implementing rate-model neurons with more realistic intrinsic properties. Our computational approach could be applied to learning of other neuron properties.

Interpolation and extrapolation in human behavior and neural networks.

Unlike most artificial systems, the brain is able to face situations that it has not learned or even encountered before. This ability is not in general echoed by the properties of most neural networks. Here, we show that neural computation based on least-square error learning between populations of intensity-coded neurons can explain interpolation and extrapolation capacities of the nervous system in sensorimotor and cognitive tasks. We present simulations for function learning experiments, auditory-visual behavior, and visuomotor transformations. The results suggest that induction in human behavior, be it sensorimotor or cognitive, could arise from a common neural associative mechanism.

Computing with populations of monotonically tuned neurons.

The parametric variation in neuronal discharge according to the values of sensory or motor variables strongly influences the collective behavior of neuronal populations. A multitude of studies on the populations of broadly tuned neurons (e.g., cosine tuning) have led to such well-known computational principles as population coding, noise suppression, and line attractors. Much less is known about the properties of populations of monotonically tuned neurons. In this letter, we show that there exists an efficient weakly biased linear estimator for monotonic populations and that neural processing based on linear collective computation and least-square error learning in populations of intensity-coded neurons has specific generalization capacities.

Reliability of spike timing is a general property of spiking model neurons.

The responses of neurons to time-varying injected currents are reproducible on a trial-by-trial basis in vitro, but when a constant current is injected, small variances in interspike intervals across trials add up, eventually leading to a high variance in spike timing. It is unclear whether this difference is due to the nature of the input currents or the intrinsic properties of the neurons. Neuron responses can fail to be reproducible in two ways: dynamical noise can accumulate over time and lead to a desynchronization over trials, or several stable responses can exist, depending on the initial condition. Here we show, through simulations and theoretical considerations, that for a general class of spiking neuron models, which includes, in particular, the leaky integrate-and-fire model as well as nonlinear spiking models, aperiodic currents, contrary to periodic currents, induce reproducible responses, which are stable under noise, change in initial conditions and deterministic perturbations of the input. We provide a theoretical explanation for aperiodic currents that cross the threshold.