Spinal-like regulator facilitates control of a two-degree-of-freedom wrist

An alpha- to gamma-motoneurone collateral can mitigate velocity-dependent stretch reflexes during voluntary movement: A computational study

The primary motor cortex does not uniquely or directly produce alpha motoneurone (α-MN) drive to muscles during voluntary movement. Rather, α-MN drive emerges from the synthesis and competition among excitatory and inhibitory inputs from multiple descending tracts, spinal interneurons, sensory inputs, and proprioceptive afferents. One such fundamental input is velocity-dependent stretch reflexes in lengthening muscles, which should be inhibited to enable voluntary movement. It remains an open question, however, the extent to which unmodulated stretch reflexes disrupt voluntary movement, and whether and how they are inhibited in limbs with numerous multi-articular muscles. We used a computational model of a Rhesus Macaque arm to simulate movements with feedforward α-MN commands only, and with added velocity-dependent stretch reflex feedback. We found that velocity-dependent stretch reflex caused movement-specific, typically large and variable disruptions to arm movements. These disruptions were greatly reduced when modulating velocity-dependent stretch reflex feedback (i) as per the commonly proposed (but yet to be clarified) idealized alpha-gamma (α-γ) co-activation or (ii) an alternative α-MN collateral projection to homonymous γ-MNs. We conclude that such α-MN collaterals are a physiologically tenable, but previously unrecognized, propriospinal circuit in the mammalian fusimotor system. These collaterals could still collaborate with α-γ co-activation, and the few skeletofusimotor fibers (β-MNs) in mammals, to create a flexible fusimotor ecosystem to enable voluntary movement. By locally and automatically regulating the highly nonlinear neuro-musculo-skeletal mechanics of the limb, these collaterals could be a critical low-level enabler of learning, adaptation, and performance via higher-level brainstem, cerebellar and cortical mechanisms.

Inverting a model of neuromuscular control to estimate descending activation patterns that generate fast-reaching movements

Reaching movements generally show smooth kinematic profiles that are invariant across varying movement speeds even as interaction torques and muscle properties vary nonlinearly with speed. How the brain brings about these invariant profiles is an open question. We developed an analytical inverse dynamics method to estimate descending activation patterns directly from observed joint angle trajectories based on a simple model of the stretch reflex, and of muscle and biomechanical dynamics. We estimated descending activation patterns for experimental data from eight different planar two-joint movements performed at two movement times (fast: 400 ms; slow: 800 ms). The temporal structure of descending activation differed qualitatively across speeds, consistent with the idea that the nervous system uses an internal model to generate anticipatory torques during fast movement. This temporal structure also depended on the cocontraction level of antagonistic muscle groups. Comparing estimated muscle activation and descending activation revealed the contribution of the stretch reflex to movement generation that was found to set in after about 20% of movement time.NEW & NOTEWORTHY By estimating descending activation patterns directly from observed movement kinematics based on a model of the dynamics of the stretch reflex, of muscle force generation, and of the biomechanics of the limb, we observed how brain signals must be temporally structured to enable fast movement.

The spinal cord facilitates cerebellar upper limb motor learning and control; inputs from neuromusculoskeletal simulation

Complex interactions between brain regions and the spinal cord (SC) govern body motion, which is ultimately driven by muscle activation. Motor planning or learning are mainly conducted at higher brain regions, whilst the SC acts as a brain-muscle gateway and as a motor control centre providing fast reflexes and muscle activity regulation. Thus, higher brain areas need to cope with the SC as an inherent and evolutionary older part of the body dynamics. Here, we address the question of how SC dynamics affects motor learning within the cerebellum; in particular, does the SC facilitate cerebellar motor learning or constitute a biological constraint? We provide an exploratory framework by integrating biologically plausible cerebellar and SC computational models in a musculoskeletal upper limb control loop. The cerebellar model, equipped with the main form of cerebellar plasticity, provides motor adaptation; whilst the SC model implements stretch reflex and reciprocal inhibition between antagonist muscles. The resulting spino-cerebellar model is tested performing a set of upper limb motor tasks, including external perturbation studies. A cerebellar model, lacking the implemented SC model and directly controlling the simulated muscles, was also tested in the same. The performances of the spino-cerebellar and cerebellar models were then compared, thus allowing directly addressing the SC influence on cerebellar motor adaptation and learning, and on handling external motor perturbations. Performance was assessed in both joint and muscle space, and compared with kinematic and EMG recordings from healthy participants. The differences in cerebellar synaptic adaptation between both models were also studied. We conclude that the SC facilitates cerebellar motor learning; when the SC circuits are in the loop, faster convergence in motor learning is achieved with simpler cerebellar synaptic weight distributions. The SC is also found to improve robustness against external perturbations, by better reproducing and modulating muscle cocontraction patterns.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

Numerical instability of Hill-type muscle models

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

Developing Intelligent Robots that Grasp Affordance

Humans and robots operating in unstructured environments both need to classify objects through haptic exploration and use them in various tasks, but currently they differ greatly in their strategies for acquiring such capabilities. This review explores nascent technologies that promise more convergence. A novel form of artificial intelligence classifies objects according to sensory percepts during active exploration and decides on efficient sequences of exploratory actions to identify objects. Representing objects according to the collective experience of manipulating them provides a substrate for discovering causality and affordances. Such concepts that generalize beyond explicit training experiences are an important aspect of human intelligence that has eluded robots. For robots to acquire such knowledge, they will need an extended period of active exploration and manipulation similar to that employed by infants. The efficacy, efficiency and safety of such behaviors depends on achieving smooth transitions between movements that change quickly from exploratory to executive to reflexive. Animals achieve such smoothness by using a hierarchical control scheme that is fundamentally different from those of conventional robotics. The lowest level of that hierarchy, the spinal cord, starts to self-organize during spontaneous movements in the fetus. This allows its connectivity to reflect the mechanics of the musculoskeletal plant, a bio-inspired process that could be used to adapt spinal-like middleware for robots. Implementation of these extended and essential stages of fetal and infant development is impractical, however, for mechatronic hardware that does not heal and replace itself like biological tissues. Instead such development can now be accomplished in silico and then cloned into physical robots, a strategy that could transcend human performance.

In-silico neuro musculoskeletal model reproduces the movement types obtained by spinal micro stimulation

BACKGROUND AND OBJECTIVES

Virtual patients and physiologies allow experimentation, design, and early-stage clinical trials in-silico. Virtual patient technology for human movement systems that encompasses musculoskeleton and its neural control are few and far in between. Our major goal is to create a neuro- musculoskeletal upper limb in-silico model, which is modular in architecture and generates movement as an emergent phenomenon out of a multiscale co-simulation of spinal cord neural control and musculoskeletal dynamics.

METHODS

The model is developed on the NEUROiD movement simulation platform that enables a co-simulation of popular neural simulator NEURON and the musculoskeletal simulator OpenSim. We further characterized and demonstrated the use of this model in generating a range of commonly observed upper limb movements by means of a spatio-temporal stimulation pattern delivered to the cervical spinal cord.

RESULTS

We were able to characterize the model based on proprioception (Ia, Ib and II fibers), afferent conduction delay and inital postures of the musculoskeletal system. A smooth movement was achieved in all the considered experiments. The generated movements in all degrees of freedom were reproduced in accordance with the previous experimental studies.

CONCLUSION

In this work, design and development of the upper limb model was described in a modular fashion, while reusing existing models and modules. We believe this work enables a first and small step towards an in-silico paradigms for understanding upper limb movement, disease pathology, medication, and rehabilitation.

A Model for Self-Organization of Sensorimotor Function: Spinal Interneuronal Integration

Control of musculoskeletal systems depends on integration of voluntary commands and somatosensory feedback in the complex neural circuits of the spinal cord. Particular connectivity patterns have been identified experimentally, and it has been suggested that these may result from the wide variety of transcriptional types that have been observed in spinal interneurons. We ask instead whether the details of these connectivity patterns (and perhaps many others) can arise as a consequence of Hebbian adaptation during early development. We constructed an anatomically simplified model plant system with realistic muscles and sensors and connected it to a recurrent, random neuronal network consisting of both excitatory and inhibitory neurons endowed with Hebbian learning rules. We then generated a wide set of randomized muscle twitches typical of those described during fetal development and allowed the network to learn. Multiple simulations consistently resulted in diverse and stable patterns of activity and connectivity that included subsets of the interneurons that were similar to 'archetypical' interneurons described in the literature. We also found that such learning led to an increased degree of cooperativity between interneurons when performing larger limb movements on which it had not been trained. Hebbian learning gives rise to rich sets of diverse interneurons whose connectivity reflects the mechanical properties of the plant. At least some of the transcriptomic diversity may reflect the effects of this process rather than the cause of the connectivity. Such a learning process seems better suited to respond to the musculoskeletal mutations that underlie the evolution of new species.

Diversified physiological sensory input connectivity questions the existence of distinct classes of spinal interneurons

The spinal cord is engaged in all forms of motor performance but its functions are far from understood. Because network connectivity defines function, we explored the connectivity of muscular, tendon, and tactile sensory inputs among a wide population of spinal interneurons in the lower cervical segments. Using low noise intracellular whole cell recordings in the decerebrated, non-anesthetized cat in vivo, we could define mono-, di-, and trisynaptic inputs as well as the weights of each input. Whereas each neuron had a highly specific input, and each indirect input could moreover be explained by inputs in other recorded neurons, we unexpectedly also found the input connectivity of the spinal interneuron population to form a continuum. Our data hence contrasts with the currently widespread notion of distinct classes of interneurons. We argue that this suggested diversified physiological connectivity, which likely requires a major component of circuitry learning, implies a more flexible functionality.

A differential Hebbian framework for biologically-plausible motor control

In this paper we explore a neural control architecture that is both biologically plausible, and capable of fully autonomous learning. It consists of feedback controllers that learn to achieve a desired state by selecting the errors that should drive them. This selection happens through a family of differential Hebbian learning rules that, through interaction with the environment, can learn to control systems where the error responds monotonically to the control signal. We next show that in a more general case, neural reinforcement learning can be coupled with a feedback controller to reduce errors that arise non-monotonically from the control signal. The use of feedback control can reduce the complexity of the reinforcement learning problem, because only a desired value must be learned, with the controller handling the details of how it is reached. This makes the function to be learned simpler, potentially allowing learning of more complex actions. We use simple examples to illustrate our approach, and discuss how it could be extended to hierarchical architectures.

Integrating Non-spiking Interneurons in Spiking Neural Networks

Researchers working with neural networks have historically focused on either non-spiking neurons tractable for running on computers or more biologically plausible spiking neurons typically requiring special hardware. However, in nature homogeneous networks of neurons do not exist. Instead, spiking and non-spiking neurons cooperate, each bringing a different set of advantages. A well-researched biological example of such a mixed network is a sensorimotor pathway, responsible for mapping sensory inputs to behavioral changes. This type of pathway is also well-researched in robotics where it is applied to achieve closed-loop operation of legged robots by adapting amplitude, frequency, and phase of the motor output. In this paper we investigate how spiking and non-spiking neurons can be combined to create a sensorimotor neuron pathway capable of shaping network output based on analog input. We propose sub-threshold operation of an existing spiking neuron model to create a non-spiking neuron able to interpret analog information and communicate with spiking neurons. The validity of this methodology is confirmed through a simulation of a closed-loop amplitude regulating network inspired by the internal feedback loops found in insects for posturing. Additionally, we show that non-spiking neurons can effectively manipulate post-synaptic spiking neurons in an event-based architecture. The ability to work with mixed networks provides an opportunity for researchers to investigate new network architectures for adaptive controllers, potentially improving locomotion strategies of legged robots.

Learning to use Muscles

The human musculoskeletal system is highly complex mechanically. Its neural control must deal successfully with this complexity to perform the diverse, efficient, robust and usually graceful behaviors of which humans are capable. Most of those behaviors might be performed by many different subsets of its myriad possible states, so how does the nervous system decide which subset to use? One solution that has received much attention over the past 50 years would be for the nervous system to be fundamentally limited in the patterns of muscle activation that it can access, a concept known as muscle synergies or movement primitives. Another solution, based on engineering control methodology, is for the nervous system to compute the single optimal pattern of muscle activation for each task according to a cost function. This review points out why neither appears to be the solution used by humans. There is a third solution that is based on trial-and-error learning, recall and interpolation of sensorimotor programs that are good-enough rather than limited or optimal. The solution set acquired by an individual during the protracted development of motor skills starting in infancy forms the basis of motor habits, which are inherently low-dimensional. Such habits give rise to muscle usage patterns that are consistent with synergies but do not reflect fundamental limitations of the nervous system and can be shaped by training or disability. This habit-based strategy provides a robust substrate for the control of new musculoskeletal structures during evolution as well as for efficient learning, athletic training and rehabilitation therapy.

Model and experiments to optimize co-adaptation in a simplified myoelectric control system

OBJECTIVE

To compensate for a limb lost in an amputation, myoelectric prostheses use surface electromyography (EMG) from the remaining muscles to control the prosthesis. Despite considerable progress, myoelectric controls remain markedly different from the way we normally control movements, and require intense user adaptation. To overcome this, our goal is to explore concurrent machine co-adaptation techniques that are developed in the field of brain-machine interface, and that are beginning to be used in myoelectric controls.

APPROACH

We combined a simplified myoelectric control with a perturbation for which human adaptation is well characterized and modeled, in order to explore co-adaptation settings in a principled manner.

RESULTS

First, we reproduced results obtained in a classical visuomotor rotation paradigm in our simplified myoelectric context, where we rotate the muscle pulling vectors used to reconstruct wrist force from EMG. Then, a model of human adaptation in response to directional error was used to simulate various co-adaptation settings, where perturbations and machine co-adaptation are both applied on muscle pulling vectors. These simulations established that a relatively low gain of machine co-adaptation that minimizes final errors generates slow and incomplete adaptation, while higher gains increase adaptation rate but also errors by amplifying noise. After experimental verification on real subjects, we tested a variable gain that cumulates the advantages of both, and implemented it with directionally tuned neurons similar to those used to model human adaptation. This enables machine co-adaptation to locally improve myoelectric control, and to absorb more challenging perturbations.

SIGNIFICANCE

The simplified context used here enabled to explore co-adaptation settings in both simulations and experiments, and to raise important considerations such as the need for a variable gain encoded locally. The benefits and limits of extending this approach to more complex and functional myoelectric contexts are discussed.

Focal Vibration Stretches Muscle Fibers by Producing Muscle Waves

Focal vibration is an effective intervention for the management of spasticity. However, its neuromechanical effects, particularly how tonic vibration reflex is induced explicitly, remain implicit. In this paper, we utilize a high-speed camera and a method of image processing to quantify the muscle vibration rigorously and disclose the neuromechanical mechanism of focal vibration. The vibration of 75 Hz is applied on the muscle belly of the biceps brachii and muscle responses are captured by a high-speed camera in profile. The muscle silhouettes are identified by the Canny edge detector to represent the stretch of muscle fibers, and the consistency between the muscle stretch and profile deformation has been confirmed by the magnetic resonance imaging in advance. Oscillations of muscle points discretized by pixels are identified by the fast Fourier transformation, respectively, and results demonstrate that focal vibration stretches muscle by producing muscle waves. Specifically, each point vibrates harmonically, and, given the linear phase modulation with transverse position, the muscle vibration propagates as traveling waves. The propagation of muscle waves is associated with muscle stretch, whose frequency is the same with the vibrator due to the curved baseline, and thus induces the tonic vibration reflex via spinal circuits.

On the Relationship Between Muscle Synergies and Redundant Degrees of Freedom in Musculoskeletal Systems

It has been suggested that the human nervous system controls motions in the task (or operational) space. However, little attention has been given to the separation of the control of the task-related and task-irrelevant degrees of freedom. Aim: We investigate how muscle synergies may be used to separately control the task-related and redundant degrees of freedom in a computational model. Approach: We generalize an existing motor control model, and assume that the task and redundant spaces have orthogonal basis vectors. This assumption originates from observations that the human nervous system tightly controls the task-related variables, and leaves the rest uncontrolled. In other words, controlling the variables in one space does not affect the other space; thus, the actuations must be orthogonal in the two spaces. We implemented this assumption in the model by selecting muscle synergies that produce force vectors with orthogonal directions in the task and redundant spaces. Findings: Our experimental results show that the orthogonality assumption performs well in reconstructing the muscle activities from the measured kinematics/dynamics in the task and redundant spaces. Specifically, we found that approximately 70% of the variation in the measured muscle activity can be captured with the orthogonality assumption, while allowing efficient separation of the control in the two spaces. Implications: The developed motor control model is a viable tool in real-time simulations of musculoskeletal systems, as well as model-based control of bio-mechatronic systems, where a computationally efficient representation of the human motion controller is needed.

Modularity speeds up motor learning by overcoming mechanical bias in musculoskeletal geometry

We can easily learn and perform a variety of movements that fundamentally require complex neuromuscular control. Many empirical findings have demonstrated that a wide range of complex muscle activation patterns could be well captured by the combination of a few functional modules, the so-called muscle synergies. Modularity represented by muscle synergies would simplify the control of a redundant neuromuscular system. However, how the reduction of neuromuscular redundancy through a modular controller contributes to sensorimotor learning remains unclear. To clarify such roles, we constructed a simple neural network model of the motor control system that included three intermediate layers representing neurons in the primary motor cortex, spinal interneurons organized into modules and motoneurons controlling upper-arm muscles. After a model learning period to generate the desired shoulder and/or elbow joint torques, we compared the adaptation to a novel rotational perturbation between modular and non-modular models. A series of simulations demonstrated that the modules reduced the effect of the bias in the distribution of muscle pulling directions, as well as in the distribution of torques associated with individual cortical neurons, which led to a more rapid adaptation to multi-directional force generation. These results suggest that modularity is crucial not only for reducing musculoskeletal redundancy but also for overcoming mechanical bias due to the musculoskeletal geometry allowing for faster adaptation to certain external environments.

Feasibility Theory Reconciles and Informs Alternative Approaches to Neuromuscular Control

We present Feasibility Theory, a conceptual and computational framework to unify today's theories of neuromuscular control. We begin by describing how the musculoskeletal anatomy of the limb, the need to control individual tendons, and the physics of a motor task uniquely specify the family of all valid muscle activations that accomplish it (its ‘feasible activation space’). For our example of producing static force with a finger driven by seven muscles, computational geometry characterizes—in a complete way—the structure of feasible activation spaces as 3-dimensional polytopes embedded in 7-D. The feasible activation space for a given task is the landscape where all neuromuscular learning, control, and performance must occur. This approach unifies current theories of neuromuscular control because the structure of feasible activation spaces can be separately approximated as either low-dimensional basis functions (synergies), high-dimensional joint probability distributions (Bayesian priors), or fitness landscapes (to optimize cost functions).

Long-latency reflexes for inter-effector coordination reflect a continuous state feedback controller

Successful performance in many everyday tasks requires compensating unexpected mechanical disturbance to our limbs and body. The long-latency reflex plays an important role in this process because it is the fastest response to integrate sensory information across several effectors, like when linking the elbow and shoulder or the arm and body. Despite the dozens of studies on inter-effector long-latency reflexes, there has not been a comprehensive treatment of how these reveal the basic control organization that sets constraints on any candidate model of neural feedback control such as optimal feedback control. We considered three contrasting ways that controllers can be organized: multiple independent controllers vs. a multiple-input multiple-output (MIMO) controller, a continuous feedback controller vs. an intermittent feedback controller, and a direct MIMO controller vs. a state feedback controller. Following a primer on control theory and review of the relevant evidence, we conclude that continuous state feedback control best describes the organization of inter-effector coordination by the long-latency reflex.

Real-time slacking as a default mode of grip force control: implications for force minimization and personal grip force variation

During trial-to-trial movement adaptation, the motor system systematically reduces extraneous muscle forces when kinematic errors experienced on previous movements are small, a phenomenon termed "slacking." There is also growing evidence that the motor system slacks continuously (i.e., in real-time) during arm movement or grip force control, but the initiation of this slacking is not well-characterized, obfuscating its physiological cause. Here, we addressed this issue by asking participants ( n = 32) to track discrete force targets presented visually using isometric grip force, then applying a brief, subtle error-clamp to that visual feedback on random trials. Participants reduced their force in an exponential fashion, on these error-clamp trials, except when the target force was <10% maximum voluntary contraction (MVC). This force drift began <250 ms after the onset of the error-clamp, consistent with slacking being an ongoing process unmasked immediately after the motor system finished reacting to the last veridical feedback. Above 10% MVC, the slacking rate increased linearly with grip force magnitude. Grip force variation was approximately 50-100% higher with veridical feedback, largely due to heightened signal power at ~1 Hz, the band of visuomotor feedback control. Finally, the slacking rate measured for each participant during error-clamp trials correlated with their force variation during control trials. That is, participants who slacked more had greater force variation. These results suggest that real-time slacking continuously reduces grip force until visual error prompts correction. Whereas such slacking is suited for force minimization, it may also account for ~30% of the variability in personal grip force variation. NEW & NOTEWORTHY We provide evidence that a form of slacking continuously conditions real-time grip force production. This slacking is well-suited to promote efficiency but is expected to increase force variation by triggering additional feedback corrections. Moreover, we show that the rate at which a person slacks is substantially correlated with the variation of their grip force. In combination, at the neurophysiological level, our results suggest slacking is caused by one or more relatively smooth neural adaptations.

Systems Analysis of Human Visuo-Myoelectric Control Facilitated by Anodal Transcranial Direct Current Stimulation in Healthy Humans

Induction of neuroplasticity by transcranial direct current stimulation (tDCS) applied to the primary motor cortex facilitates motor learning of the upper extremities in healthy humans. The impact of tDCS on lower limb functions has not been studied extensively so far. In this study, we applied a system identification approach to investigate the impact of anodal transcranial direct current stimulation of the leg area of the motor cortex via the human visuo-myoelectric controller. The visuo-myoelectric reaching task (VMT) involves ballistic muscle contraction after a visual cue. We applied a black box approach using a linear ARX (Auto-regressive with eXogenous input) model for a visuomotor myoelectric reaching task. We found that a 20th order finite impulse response (FIR) model captured the TARGET (single input)—CURSOR (single output) dynamics during a VMT. The 20th order FIR model was investigated based on gain/phase margin analysis, which showed a significant (p < 0.01) effect of anodal tDCS on the gain margin of the VMT system. Also, response latency and the corticomuscular coherence (CMC) time delay were affected (p < 0.05) by anodal tDCS when compared to sham tDCS. Furthermore, gray box simulation results from a Simplified Spinal-Like Controller (SSLC) model demonstrated that the input-output function for motor evoked potentials (MEP) played an essential role in increasing muscle activation levels and response time improvement post-tDCS when compared to pre-tDCS baseline performance. This computational approach can be used to simulate the behavior of the neuromuscular controller during VMT to elucidate the effects of adjuvant treatment with tDCS.

Cardinal features of involuntary force variability can arise from the closed-loop control of viscoelastic afferented muscles

Involuntary force variability below 15 Hz arises from, and is influenced by, many factors including descending neural drive, proprioceptive feedback, and mechanical properties of muscles and tendons. However, their potential interactions that give rise to the well-structured spectrum of involuntary force variability are not well understood due to a lack of experimental techniques. Here, we investigated the generation, modulation, and interactions among different sources of force variability using a physiologically-grounded closed-loop simulation of an afferented muscle model. The closed-loop simulation included a musculotendon model, muscle spindle, Golgi tendon organ (GTO), and a tracking controller which enabled target-guided force tracking. We demonstrate that closed-loop control of an afferented musculotendon suffices to replicate and explain surprisingly many cardinal features of involuntary force variability. Specifically, we present 1) a potential origin of low-frequency force variability associated with co-modulation of motor unit firing rates (i.e.,‘common drive’), 2) an in-depth characterization of how proprioceptive feedback pathways suffice to generate 5-12 Hz physiological tremor, and 3) evidence that modulation of those feedback pathways (i.e., presynaptic inhibition of Ia and Ib afferents, and spindle sensitivity via fusimotor drive) influence the full spectrum of force variability. These results highlight the previously underestimated importance of closed-loop neuromechanical interactions in explaining involuntary force variability during voluntary ‘isometric’ force control. Furthermore, these results provide the basis for a unifying theory that relates spinal circuitry to various manifestations of altered involuntary force variability in fatigue, aging and neurological disease.

Involuntary fluctuations in muscle force are an unavoidable consequence of human motor control and underlie movement execution errors. Amplification and distortion of involuntary force variability are common phenomena found in various neurological conditions and in fatigue. However, the underlying mechanisms for this are often unclear. We investigated the generation and modulation of involuntary force variability arising from different sources, as well as their interactions. We used a closed-loop simulation which included a physiologically-grounded model of an afferented musculotendon and an error-controller. We show that interactions among neural noise, musculotendon mechanics, proprioceptive feedback, and error correction are critical components of force control, and by taking these into account, our model was able to both replicate and explain many cardinal features of involuntary force variability previously reported experimentally. Also, our results suggest previously unrecognized pathways through which force variability may be altered in fatigue and in certain neurological diseases. Finally, we emphasize the potential for important clinical and scientific information to be extracted from relatively simple, non-invasive measurements of force.

A multi-joint model of quiet, upright stance accounts for the "uncontrolled manifold" structure of joint variance

The upright body in quiet stance is usually modeled as a single-link inverted pendulum. This agrees with most of the relevant sensory organs being at the far end of the pendulum, i.e., the eyes and the vestibular system in the head. Movement of the body in quiet stance has often been explained in terms of the "ankle strategy," where most movement is generated by the ankle musculature, while more proximal muscle groups are only rarely activated for faster movements or in response to perturbations, for instance, by flexing at the hips in what has been called the "hip strategy." Recent empirical evidence, however, shows that instead of being negligible in quiet stance, the movement in the knee and hip joints is even larger on average than the movement in the ankle joints (J Neurophysiol 97:3024-3035, 2007). Moreover, there is a strong pattern of covariation between movements in the ankle, knee and hip joints in a way that most of the observed movements leave the anterior-posterior position of the whole-body center of mass (CoM) invariant, i.e., only change the configuration of the different body parts around the CoM, instead of moving the body as a whole. It is unknown, however, where this covariation between joint angles during quiet stance originates from. In this paper, we aim to answer this question using a comprehensive model of the biomechanical, muscular and neural dynamics of a quietly standing human. We explore four different possible feedback laws for the control of this multi-link pendulum in upright stance that map sensory data to motor commands. We perform simulation studies to compare the generated inter-joint covariance patterns with experimental data. We find that control laws that actively coordinate muscle activation between the different joints generate correct variance patterns, while control laws that control each joint separately do not. Different specific forms of this coordination are compatible with the data.

Physiological tremor increases when skeletal muscle is shortened: implications for fusimotor control

KEY POINTS

In tonic, isometric, plantarflexion contractions, physiological tremor increases as the ankle joint becomes plantarflexed. Modulation of physiological tremor as a function of muscle stretch differs from that of the stretch reflex amplitude. Amplitude of physiological tremor may be altered as a function of reflex pathway gains. Healthy humans likely increase their γ-static fusimotor drive when muscles shorten. Quantification of physiological tremor by manipulation of joint angle may be a useful experimental probe of afferent gains and/or the integrity of automatic fusimotor control.

ABSTRACT

The involuntary force fluctuations associated with physiological (as distinct from pathological) tremor are an unavoidable component of human motor control. While the origins of physiological tremor are known to depend on muscle afferentation, it is possible that the mechanical properties of muscle-tendon systems also affect its generation, amplification and maintenance. In this paper, we investigated the dependence of physiological tremor on muscle length in healthy individuals. We measured physiological tremor during tonic, isometric plantarflexion torque at 30% of maximum at three ankle angles. The amplitude of physiological tremor increased as calf muscles shortened in contrast to the stretch reflex whose amplitude decreases as muscle shortens. We used a published closed-loop simulation model of afferented muscle to explore the mechanisms responsible for this behaviour. We demonstrate that changing muscle lengths does not suffice to explain our experimental findings. Rather, the model consistently required the modulation of  γ-static fusimotor drive to produce increases in physiological tremor with muscle shortening - while successfully replicating the concomitant reduction in stretch reflex amplitude. This need to control γ-static fusimotor drive explicitly as a function of muscle length has important implications. First, it permits the amplitudes of physiological tremor and stretch reflex to be decoupled. Second, it postulates neuromechanical interactions that require length-dependent γ drive modulation to be independent from α drive to the parent muscle. Lastly, it suggests that physiological tremor can be used as a simple, non-invasive measure of the afferent mechanisms underlying healthy motor function, and their disruption in neurological conditions.

Transfer of dynamic motor skills acquired during isometric training to free motion

Recent studies have explored the prospects of learning to move without moving, by displaying virtual arm movement related to exerted force. However, it has yet to be tested whether learning the dynamics of moving can transfer to the corresponding movement. Here we present a series of experiments that investigate this isometric training paradigm. Subjects were asked to hold a handle and generate forces as their arms were constrained to a static position. A precise simulation of reaching was used to make a graphic rendering of an arm moving realistically in response to the measured interaction forces and simulated environmental forces. Such graphic rendering was displayed on a horizontal display that blocked their view to their actual (statically constrained) arm and encouraged them to believe they were moving. We studied adaptation of horizontal, planar, goal-directed arm movements in a velocity-dependent force field. Our results show that individuals can learn to compensate for such a force field in a virtual environment and transfer their new skills to the actual free motion condition, with performance comparable to practice while moving. Such nonmoving techniques should impact various training conditions when moving may not be possible.NEW & NOTEWORTHY This study provided early evidence supporting that training movement skills without moving is possible. In contrast to previous studies, our study involves 1) exploiting cross-modal sensory interactions between vision and proprioception in a motionless setting to teach motor skills that could be transferable to a corresponding physical task, and 2) evaluates the movement skill of controlling muscle-generated forces to execute arm movements in the presence of external forces that were only virtually present during training.

Neuromorphic meets neuromechanics, part II: the role of fusimotor drive

OBJECTIVE

We studied the fundamentals of muscle afferentation by building a Neuro-mechano-morphic system actuating a cadaveric finger. This system is a faithful implementation of the stretch reflex circuitry. It allowed the systematic exploration of the effects of different fusimotor drives to the muscle spindle on the closed-loop stretch reflex response.

APPROACH

As in Part I of this work, sensory neurons conveyed proprioceptive information from muscle spindles (with static and dynamic fusimotor drive) to populations of α-motor neurons (with recruitment and rate coding properties). The motor commands were transformed into tendon forces by a Hill-type muscle model (with activation-contraction dynamics) via brushless DC motors. Two independent afferented muscles emulated the forces of flexor digitorum profundus and the extensor indicis proprius muscles, forming an antagonist pair at the metacarpophalangeal joint of a cadaveric index finger. We measured the physical response to repetitions of bi-directional ramp-and-hold rotational perturbations for 81 combinations of static and dynamic fusimotor drives, across four ramp velocities, and three levels of constant cortical drive to the α-motor neuron pool.

MAIN RESULTS

We found that this system produced responses compatible with the physiological literature. Fusimotor and cortical drives had nonlinear effects on the reflex forces. In particular, only cortical drive affected the sensitivity of reflex forces to static fusimotor drive. In contrast, both static fusimotor and cortical drives reduced the sensitivity to dynamic fusimotor drive. Interestingly, realistic signal-dependent motor noise emerged naturally in our system without having been explicitly modeled.

SIGNIFICANCE

We demonstrate that these fundamental features of spinal afferentation sufficed to produce muscle function. As such, our Neuro-mechano-morphic system is a viable platform to study the spinal mechanisms for healthy muscle function-and its pathologies such as dystonia and spasticity. In addition, it is a working prototype of a robust biomorphic controller for compliant robotic limbs and exoskeletons.

Emergence of gamma motor activity in an artificial neural network model of the corticospinal system

Muscle spindle discharge during active movement is a function of mechanical and neural parameters. Muscle length changes (and their derivatives) represent its primary mechanical, fusimotor drive its neural component. However, neither the action nor the function of fusimotor and in particular of γ-drive, have been clearly established, since γ-motor activity during voluntary, non-locomotor movements remains largely unknown. Here, using a computational approach, we explored whether γ-drive emerges in an artificial neural network model of the corticospinal system linked to a biomechanical antagonist wrist simulator. The wrist simulator included length-sensitive and γ-drive-dependent type Ia and type II muscle spindle activity. Network activity and connectivity were derived by a gradient descent algorithm to generate reciprocal, known target α-motor unit activity during wrist flexion-extension (F/E) movements. Two tasks were simulated: an alternating F/E task and a slow F/E tracking task. Emergence of γ-motor activity in the alternating F/E network was a function of α-motor unit drive: if muscle afferent (together with supraspinal) input was required for driving α-motor units, then γ-drive emerged in the form of α-γ coactivation, as predicted by empirical studies. In the slow F/E tracking network, γ-drive emerged in the form of α-γ dissociation and provided critical, bidirectional muscle afferent activity to the cortical network, containing known bidirectional target units. The model thus demonstrates the complementary aspects of spindle output and hence γ-drive: i) muscle spindle activity as a driving force of α-motor unit activity, and ii) afferent activity providing continuous sensory information, both of which crucially depend on γ-drive.

Long-latency reflexes of elbow and shoulder muscles suggest reciprocal excitation of flexors, reciprocal excitation of extensors, and reciprocal inhibition between flexors and extensors

Postural corrections of the upper limb are required in tasks ranging from handling an umbrella in the changing wind to securing a wriggling baby. One complication in this process is the mechanical interaction between the different segments of the arm where torque applied at one joint induces motion at multiple joints. Previous studies have shown the long-latency reflexes of shoulder muscles (50-100 ms after a limb perturbation) account for these mechanical interactions by integrating information about motion of both the shoulder and elbow. It is less clear whether long-latency reflexes of elbow muscles exhibit a similar capability and what is the relation between the responses of shoulder and elbow muscles. The present study utilized joint-based loads tailored to the subjects' arm dynamics to induce well-controlled displacements of their shoulder and elbow. Our results demonstrate that the long-latency reflexes of shoulder and elbow muscles integrate motion from both joints: the shoulder and elbow flexors respond to extension at both joints, whereas the shoulder and elbow extensors respond to flexion at both joints. This general pattern accounts for the inherent flexion-extension coupling of the two joints arising from the arm's intersegmental dynamics and is consistent with spindle-based reciprocal excitation of shoulder and elbow flexors, reciprocal excitation of shoulder and elbow extensors, and across-joint inhibition between the flexors and extensors.

Suboptimal Muscle Synergy Activation Patterns Generalize their Motor Function across Postures

We used a musculoskeletal model to investigate the possible biomechanical and neural bases of using consistent muscle synergy patterns to produce functional motor outputs across different biomechanical conditions, which we define as generalizability. Experimental studies in cats demonstrate that the same muscle synergies are used during reactive postural responses at widely varying configurations, producing similarly-oriented endpoint force vectors with respect to the limb axis. However, whether generalizability across postures arises due to similar biomechanical properties or to neural selection of a particular muscle activation pattern has not been explicitly tested. Here, we used a detailed cat hindlimb model to explore the set of feasible muscle activation patterns that produce experimental synergy force vectors at a target posture, and tested their generalizability by applying them to different test postures. We used three methods to select candidate muscle activation patterns: (1) randomly-selected feasible muscle activation patterns, (2) optimal muscle activation patterns minimizing muscle effort at a given posture, and (3) generalizable muscle activation patterns that explicitly minimized deviations from experimentally-identified synergy force vectors across all postures. Generalizability was measured by the deviation between the simulated force direction of the candidate muscle activation pattern and the experimental synergy force vectors at the test postures. Force angle deviations were the greatest for the randomly selected feasible muscle activation patterns (e.g., >100°), intermediate for effort-wise optimal muscle activation patterns (e.g., ~20°), and smallest for generalizable muscle activation patterns (e.g., <5°). Generalizable muscle activation patterns were suboptimal in terms of effort, often exceeding 50% of the maximum possible effort (cf. ~5% in minimum-effort muscle activation patterns). The feasible muscle activation ranges of individual muscles associated with producing a specific synergy force vector was reduced by ~45% when generalizability requirements were imposed. Muscles recruited in the generalizable muscle activation patterns had less sensitive torque-producing characteristics to changes in postures. We conclude that generalization of function across postures does not arise from limb biomechanics or a single optimality criterion. Muscle synergies may reflect acquired motor solutions globally tuned for generalizability across biomechanical contexts, facilitating rapid motor adaptation.

Primary motor cortex neurons classified in a postural task predict muscle activation patterns in a reaching task

Primary motor cortex (M1) activity correlates with many motor variables, making it difficult to demonstrate how it participates in motor control. We developed a two-stage process to separate the process of classifying the motor field of M1 neurons from the process of predicting the spatiotemporal patterns of its motor field during reaching. We tested our approach with a neural network model that controlled a two-joint arm to show the statistical relationship between network connectivity and neural activity across different motor tasks. In rhesus monkeys, M1 neurons classified by this method showed preferred reaching directions similar to their associated muscle groups. Importantly, the neural population signals predicted the spatiotemporal dynamics of their associated muscle groups, although a subgroup of atypical neurons reversed their directional preference, suggesting a selective role in antagonist control. These results highlight that M1 provides important details on the spatiotemporal patterns of muscle activity during motor skills such as reaching.

Enhanced crosslimb transfer of force-field learning for dynamics that are identical in extrinsic and joint-based coordinates for both limbs

Humans are able to adapt their motor commands to make accurate movements in novel sensorimotor environments, such as when wielding tools that alter limb dynamics. However, it is unclear to what extent sensorimotor representations, obtained through experience with one limb, are available to the opposite, untrained limb and in which form they are available. Here, we compared crosslimb transfer of force-field compensation after participants adapted to a velocity-dependent curl field, oriented either in the sagittal or the transverse plane. Due to the mirror symmetry of the limbs, the force field had identical effects for both limbs in joint and extrinsic coordinates in the sagittal plane but conflicting joint-based effects in the transverse plane. The degree of force-field compensation exhibited by the opposite arm in probe trials immediately after initial learning was significantly greater after sagittal (26 ± 5%) than transverse plane adaptation (9 ± 4%; P < 0.001), irrespective of whether participants learned initially with the left or the right arm or via abrupt or gradual exposure to the force field. Thus transfer was impaired when the orientation of imposed dynamics conflicted in intrinsic coordinates for the two limbs. The data reveal that neural representations of novel dynamics are only partially available to the opposite limb, since transfer is incomplete even when force-field perturbation is spatially compatible for the two limbs, according to both intrinsic and extrinsic coordinates.

Goal-dependent modulation of the long-latency stretch response at the shoulder, elbow, and wrist

Many studies have demonstrated that muscle activity 50-100 ms after a mechanical perturbation (i.e., the long-latency stretch response) can be modulated in a manner that reflects voluntary motor control. These previous studies typically assessed modulation of the long-latency stretch response from individual muscles rather than how this response is concurrently modulated across multiple muscles. Here we investigated such concurrent modulation by having participants execute goal-directed reaches to visual targets after mechanical perturbations of the shoulder, elbow, or wrist while measuring activity from six muscles that articulate these joints. We found that shoulder, elbow, and wrist muscles displayed goal-dependent modulation of the long-latency stretch response, that the relative magnitude of participants' goal-dependent activity was similar across muscles, that the temporal onset of goal-dependent muscle activity was not reliably different across the three joints, and that shoulder muscles displayed goal-dependent activity appropriate for counteracting intersegmental dynamics. We also observed that the long-latency stretch response of wrist muscles displayed goal-dependent modulation after elbow perturbations and that the long-latency stretch response of elbow muscles displayed goal-dependent modulation after wrist perturbations. This pattern likely arises because motion at either joint could bring the hand to the visual target and suggests that the nervous system rapidly exploits such simple kinematic redundancy when processing sensory feedback to support goal-directed actions.

A model-based approach to predict muscle synergies using optimization: application to feedback control

This paper presents a new model-based method to define muscle synergies. Unlike the conventional factorization approach, which extracts synergies from electromyographic data, the proposed method employs a biomechanical model and formally defines the synergies as the solution of an optimal control problem. As a result, the number of required synergies is directly related to the dimensions of the operational space. The estimated synergies are posture-dependent, which correlate well with the results of standard factorization methods. Two examples are used to showcase this method: a two-dimensional forearm model, and a three-dimensional driver arm model. It has been shown here that the synergies need to be task-specific (i.e., they are defined for the specific operational spaces: the elbow angle and the steering wheel angle in the two systems). This functional definition of synergies results in a low-dimensional control space, in which every force in the operational space is accurately created by a unique combination of synergies. As such, there is no need for extra criteria (e.g., minimizing effort) in the process of motion control. This approach is motivated by the need for fast and bio-plausible feedback control of musculoskeletal systems, and can have important implications in engineering, motor control, and biomechanics.

Efferent Feedback in a Spinal-Like Controller: Reaching With Perturbations

We use simulations of a controller that adopts a spinal-like network topology for goal-oriented reaching and assess its sensitivity to the dynamics of internal elements that allow context-independent performance. Such internal elements are often referred to as inverse or forward models of the periphery dynamics, depending on the proposed controller theory. Here, the "models" are used in a forward implementation, and we evaluate how the controller's performance would be affected by the nature of the model. For each point-to-point reaching motion experiment, we use forms of internal "efference models" (e.g., full mathematical representations of peripheral dynamics, simple spindle feedback, etc.) driven by motor reafference, then compare hand trajectories and hand path speeds in the presence or absence of external perturbations. It is demonstrated that a simple velocity-based model reduced the effects of dynamic perturbations by as much as 66%. In addition, the 2D hand trajectories varied from a biological reference by only 0.05 cm. Thus, the controller facilitated biological like motions while providing response to dynamic events which are omitted in earlier biomimetic controllers. This research suggests that these spinal-like systems are robust and tunable via gain-fields without the need of context dependent pre-planning.

Major remaining gaps in models of sensorimotor systems

Experimental descriptions of the anatomy and physiology of individual components of sensorimotor systems have revealed substantial complexity, making it difficult to intuit how complete systems might work. This has led to increasing efforts to develop and employ mathematical models to study the emergent properties of such systems. Conversely, the development of such models tends to reveal shortcomings in the experimental database upon which models must be constructed and validated. In both cases models are most useful when they point up discrepancies between what we think we know and possibilities that we may have overlooked. This overview considers those components of complete sensorimotor systems that currently appear to be potentially important but poorly understood. These are generally omitted completely from modeled systems or buried in implicit assumptions that underlie the design of the model.

Spinal circuits for motor learning

Studies of motor learning have largely focussed on the cerebellum, and have provided key concepts about neural circuits required. However, other parts of the nervous system are involved in learning, as demonstrated by the capacity to 'train' spinal circuits to produce locomotion following spinal cord injury. While somatosensory feedback is necessary for spinal motor learning, feed forward circuits within the spinal cord must also contribute. In fact, motoneurons themselves could act as comparators that integrate feed forward and feedback inputs, and thus contribute to motor learning. Application of cerebellar-derived principles to spinal circuitry leads to testable predictions of spinal organization required for motor learning.

An adaptive spinal-like controller: tunable biomimetic behavior for a robotic limb

Background

Spinal-like regulators have recently been shown to support complex behavioral patterns during volitional goal-oriented reaching paradigms. We use an interpretation of the adaptive spinal-like controller as inspiration for the development of a controller for a robotic limb. It will be demonstrated that a simulated robot arm with linear actuators can achieve biological-like limb movements. In addition, it will be shown that programmability in the regulator enables independent spatial and temporal changes to be defined for movement tasks, downstream of central commands using sensory stimuli. The adaptive spinal-like controller is the first to demonstrate such behavior for complex motor behaviors in multi-joint limb movements.

Methods

The controller is evaluated using a simulated robotic apparatus and three goal-oriented reaching paradigms: 1) shaping of trajectory profiles during reaching; 2) sensitivity of trajectories to sudden perturbations; 3) reaching to a moving target. The experiments were designed to highlight complex motor tasks that are omitted in earlier studies, and important for the development of improved artificial limb control.

Results

In all three cases the controller was able to reach the targets without a priori planning of end-point or segmental motor trajectories. Instead, trajectory spatio-temporal dynamics evolve from properties of the controller architecture using the spatial error (vector distance to goal). Results show that curvature amplitude in hand trajectory paths are reduced by as much as 98% using simple gain scaling techniques, while adaptive network behavior allows the regulator to successfully adapt to perturbations and track a moving target. An important observation for this study is that all motions resemble human-like movements with non-linear muscles and complex joint mechanics.

Conclusions

The controller shows that it can adapt to various behavioral contexts which are not included in previous biomimetic studies. The research supplements an earlier study by examining the tunability of the spinal-like controller for complex reaching tasks. This work is a step toward building more robust controllers for powered artificial limbs.

Spinal mechanisms may provide a combination of intermittent and continuous control of human posture: predictions from a biologically based neuromusculoskeletal model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.

The control of upright stance is a challenging task since the objective is to maintain the equilibrium of an intrinsically unstable biomechanical system. Somatosensory information is used by the central nervous system to modulate muscle contraction, which prevents the body from falling. While the visual and vestibular systems also provide important additional sensory information, a human being with only somatosensory inputs is able to maintain an upright stance. In this study, we used a biologically-based large-scale neuromusculoskeletal model driven only by somatosensory feedback to investigate human postural control from a neurophysiological point of view. No neural structures above the spinal cord were included in the model. The results showed that the model based on a spinal control of posture can reproduce several neuromechanical outcomes previously reported in the literature, including an intermittent muscle activation. Since this intermittent muscular recruitment is an emergent property of this spinal-like controller, we argue that the so-called intermittent control of upright stance might be produced by an interplay between spinal cord properties and modulated sensory inflow.

Spinal circuits can accommodate interaction torques during multijoint limb movements

The dynamic interaction of limb segments during movements that involve multiple joints creates torques in one joint due to motion about another. Evidence shows that such interaction torques are taken into account during the planning or control of movement in humans. Two alternative hypotheses could explain the compensation of these dynamic torques. One involves the use of internal models to centrally compute predicted interaction torques and their explicit compensation through anticipatory adjustment of descending motor commands. The alternative, based on the equilibrium-point hypothesis, claims that descending signals can be simple and related to the desired movement kinematics only, while spinal feedback mechanisms are responsible for the appropriate creation and coordination of dynamic muscle forces. Partial supporting evidence exists in each case. However, until now no model has explicitly shown, in the case of the second hypothesis, whether peripheral feedback is really sufficient on its own for coordinating the motion of several joints while at the same time accommodating intersegmental interaction torques. Here we propose a minimal computational model to examine this question. Using a biomechanics simulation of a two-joint arm controlled by spinal neural circuitry, we show for the first time that it is indeed possible for the neuromusculoskeletal system to transform simple descending control signals into muscle activation patterns that accommodate interaction forces depending on their direction and magnitude. This is achieved without the aid of any central predictive signal. Even though the model makes various simplifications and abstractions compared to the complexities involved in the control of human arm movements, the finding lends plausibility to the hypothesis that some multijoint movements can in principle be controlled even in the absence of internal models of intersegmental dynamics or learned compensatory motor signals.

Beyond muscles stiffness: importance of state-estimation to account for very fast motor corrections

Feedback delays are a major challenge for any controlled process, and yet we are able to easily control limb movements with speed and grace. A popular hypothesis suggests that the brain largely mitigates the impact of feedback delays (∼50 ms) by regulating the limb intrinsic visco-elastic properties (or impedance) with muscle co-contraction, which generates forces proportional to changes in joint angle and velocity with zero delay. Although attractive, this hypothesis is often based on estimates of limb impedance that include neural feedback, and therefore describe the entire motor system. In addition, this approach does not systematically take into account that muscles exhibit high intrinsic impedance only for small perturbations (short-range impedance). As a consequence, it remains unclear how the nervous system handles large perturbations, as well as disturbances encountered during movement when short-range impedance cannot contribute. We address this issue by comparing feedback responses to load pulses applied to the elbow of human subjects with theoretical simulations. After validating the model parameters, we show that the ability of humans to generate fast and accurate corrective movements is compatible with a control strategy based on state estimation. We also highlight the merits of delay-uncompensated robust control, which can mitigate the impact of internal model errors, but at the cost of slowing feedback corrections. We speculate that the puzzling observation of presynaptic inhibition of peripheral afferents in the spinal cord at movement onset helps to counter the destabilizing transition from high muscle impedance during posture to low muscle impedance during movement.

Simulating spinal border cells and cerebellar granule cells under locomotion--a case study of spinocerebellar information processing

The spinocerebellar systems are essential for the brain in the performance of coordinated movements, but our knowledge about the spinocerebellar interactions is very limited. Recently, several crucial pieces of information have been acquired for the spinal border cell (SBC) component of the ventral spinocerebellar tract (VSCT), as well as the effects of SBC mossy fiber activation in granule cells of the cerebellar cortex. SBCs receive monosynaptic input from the reticulospinal tract (RST), which is an important driving system under locomotion, and disynaptic inhibition from Ib muscle afferents. The patterns of activity of RST neurons and Ib afferents under locomotion are known. The activity of VSCT neurons under fictive locomotion, i.e. without sensory feedback, is also known, but there is little information on how these neurons behave under actual locomotion and for cerebellar granule cells receiving SBC input this is completely unknown. But the available information makes it possible to simulate the interactions between the spinal and cerebellar neuronal circuitries with a relatively large set of biological constraints. Using a model of the various neuronal elements and the network they compose, we simulated the modulation of the SBCs and their target granule cells under locomotion and hence generated testable predictions of their general pattern of modulation under this condition. This particular system offers a unique opportunity to simulate these interactions with a limited number of assumptions, which helps making the model biologically plausible. Similar principles of information processing may be expected to apply to all spinocerebellar systems.

From spontaneous motor activity to coordinated behaviour: a developmental model

In mammals, the developmental path that links the primary behaviours observed during foetal stages to the full fledged behaviours observed in adults is still beyond our understanding. Often theories of motor control try to deal with the process of incremental learning in an abstract and modular way without establishing any correspondence with the mammalian developmental stages. In this paper, we propose a computational model that links three distinct behaviours which appear at three different stages of development. In order of appearance, these behaviours are: spontaneous motor activity (SMA), reflexes, and coordinated behaviours, such as locomotion. The goal of our model is to address in silico four hypotheses that are currently hard to verify in vivo: First, the hypothesis that spinal reflex circuits can be self-organized from the sensor and motor activity induced by SMA. Second, the hypothesis that supraspinal systems can modulate reflex circuits to achieve coordinated behaviour. Third, the hypothesis that, since SMA is observed in an organism throughout its entire lifetime, it provides a mechanism suitable to maintain the reflex circuits aligned with the musculoskeletal system, and thus adapt to changes in body morphology. And fourth, the hypothesis that by changing the modulation of the reflex circuits over time, one can switch between different coordinated behaviours. Our model is tested in a simulated musculoskeletal leg actuated by six muscles arranged in a number of different ways. Hopping is used as a case study of coordinated behaviour. Our results show that reflex circuits can be self-organized from SMA, and that, once these circuits are in place, they can be modulated to achieve coordinated behaviour. In addition, our results show that our model can naturally adapt to different morphological changes and perform behavioural transitions.

An Augmented Two-Layer Model Captures Nonlinear Analog Spatial Integration Effects in Pyramidal Neuron Dendrites

In pursuit of the goal to understand and eventually reproduce the diverse functions of the brain, a key challenge lies in reverse engineering the peculiar biology-based "technology" that underlies the brain's remarkable ability to process and store information. The basic building block of the nervous system is the nerve cell, or "neuron," yet after more than 100 years of neurophysiological study and 60 years of modeling, the information processing functions of individual neurons, and the parameters that allow them to engage in so many different types of computation (sensory, motor, mnemonic, executive, etc.) remain poorly understood. In this paper, we review both historical and recent findings that have led to our current understanding of the analog spatial processing capabilities of dendrites, the major input structures of neurons, with a focus on the principal cell type of the neocortex and hippocampus, the pyramidal neuron (PN). We encapsulate our current understanding of PN dendritic integration in an abstract layered model whose spatially sensitive branch-subunits compute multidimensional sigmoidal functions. Unlike the 1-D sigmoids found in conventional neural network models, multidimensional sigmoids allow the cell to implement a rich spectrum of nonlinear modulation effects directly within their dendritic trees.

Quantification of dexterity as the dynamical regulation of instabilities: comparisons across gender, age, and disease

Dexterous manipulation depends on using the fingertips to stabilize unstable objects. The Strength-Dexterity paradigm consists of asking subjects to compress a slender and compliant spring prone to buckling. The maximal level of compression [requiring low fingertip forces <300 grams force (gf)] quantifies the neural control capability to dynamically regulate fingertip force vectors and motions for a dynamic manipulation task. We found that finger dexterity is significantly affected by age (p = 0.017) and gender (p = 0.021) in 147 healthy individuals (66F, 81M, 20-88 years). We then measured finger dexterity in 42 hands of patients following treatment for osteoarthritis of the base of the thumb (CMC OA, 33F, 65.8 ± 9.7 years), and 31 hands from patients being treated for Parkinson's disease (PD, 6F, 10M, 67.68 ± 8.5 years). Importantly, we found no differences in finger compression force among patients or controls. However, we did find stronger age-related declines in performance in the patients with PD (slope -2.7 gf/year, p = 0.002) than in those with CMC OA (slope -1.4 gf/year, p = 0.015), than in controls (slope -0.86 gf/year). In addition, the temporal variability of forces during spring compression shows clearly different dynamics in the clinical populations compared to the controls (p < 0.001). Lastly, we compared dexterity across extremities. We found stronger age (p = 0.005) and gender (p = 0.002) effects of leg compression force in 188 healthy subjects who compressed a larger spring with the foot of an isolated leg (73F, 115M, 14-92 years). In 81 subjects who performed the tests with all four limbs separately, we found finger and leg compression force to be significantly correlated (females ρ = 0.529, p = 0.004; males ρ = 0.403, p = 0.003; 28F, 53M, 20-85 years), but surprisingly found no differences between dominant and non-dominant limbs. These results have important clinical implications, and suggest the existence - and compel the investigation - of systemic versus limb-specific mechanisms for dexterity.

Bayesian action&perception: representing the world in the brain

Theories of perception seek to explain how sensory data are processed to identify previously experienced objects, but they usually do not consider the decisions and effort that goes into acquiring the sensory data. Identification of objects according to their tactile properties requires active exploratory movements. The sensory data thereby obtained depend on the details of those movements, which human subjects change rapidly and seemingly capriciously. Bayesian Exploration is an algorithm that uses prior experience to decide which next exploratory movement should provide the most useful data to disambiguate the most likely possibilities. In previous studies, a simple robot equipped with a biomimetic tactile sensor and operated according to Bayesian Exploration performed in a manner similar to and actually better than humans on a texture identification task. Expanding on this, "Bayesian Action&Perception" refers to the construction and querying of an associative memory of previously experienced entities containing both sensory data and the motor programs that elicited them. We hypothesize that this memory can be queried (i) to identify useful next exploratory movements during identification of an unknown entity ("action for perception") or (ii) to characterize whether an unknown entity is fit for purpose ("perception for action") or (iii) to recall what actions might be feasible for a known entity (Gibsonian affordance). The biomimetic design of this mechatronic system may provide insights into the neuronal basis of biological action and perception.

A Simplified Spinal-Like Controller Facilitates Muscle Synergies and Robust Reaching Motions

We develop an adaptive controller for multi-joint, multi-muscle arm movements based on simplified spinal-like circuits found in the periphery, muscle synergies, and interpretations of gain-field projections from reach related neurons in the Superior Colliculus. The resulting innovation provides a highly robust sensory based controller that can be adapted to systems which require multi-muscle co-ordination. It provides human-like responses during perturbations elicited either internally or by the environment and for simple point-to-point reaching. We simulate limb motion and EMGs in Simulink using Virtual Muscle models and a variety of paradigms, including motion with external perturbations, and varying levels of antagonist muscle co-contractions. The results show that the system can exhibit smooth coordinated motions, without explicit kinematic or dynamic planning even in the presence of perturbations. In addition, we show by varying the level of muscle co-contractions from 0% to 40%, that the effects of external perturbations on joint trajectories can be reduced by up to 42%. The improved controller design is novel providing robust behavior during dynamic events and an automatic adaptive response from sensory-integration.

An adaptive filter model of cerebellar zone C3 as a basis for safe limb control?

The review asks how the adaptive filter model of the cerebellum might be relevant to experimental work on zone C3, one of the most extensively studied regions of cerebellar cortex. As far as features of the cerebellar microcircuit are concerned, the model appears to fit very well with electrophysiological discoveries concerning the importance of molecular layer interneurons and their plasticity, the significance of long-term potentiation and the striking number of silent parallel fibre synapses. Regarding external connectivity and functionality, a key feature of the adaptive filter model is its use of the decorrelation algorithm, which renders it uniquely suited to problems of sensory noise cancellation. However, this capacity can be extended to the avoidance of sensory interference, by appropriate movements of, for example, the eyes in the vestibulo-ocular reflex. Avoidance becomes particularly important when painful signals are involved, and as the climbing fibre input to zone C3 is extremely responsive to nociceptive stimuli, it is proposed that one function of this zone is the avoidance of pain by, for example, adjusting movements of the body to avoid self-harm. This hypothesis appears consistent with evidence from humans and animals concerning the role of the intermediate cerebellum in classically conditioned withdrawal reflexes, but further experiments focusing on conditioned avoidance are required to test the hypothesis more stringently. The proposed architecture may also be useful for automatic self-adjusting damage avoidance in robots, an important consideration for next generation 'soft' robots designed to interact with people.