Stabilisation of walking by intrinsic muscle properties revealed in a three-dimensional muscle-driven simulation

A fundamental question in movement science is how humans perform stable movements in the presence of disturbances such as contact with objects. It remains unclear how the nervous system, with delayed responses to disturbances, maintains the stability of complex movements. We hypothesised that intrinsic muscle properties (i.e. the force–length–velocity properties of muscle fibres and tendon elasticity) may help stabilise human walking by responding instantaneously to a disturbance and providing forces that help maintain the movement trajectory. To investigate this issue, we generated a 3D muscle-driven simulation of walking and analysed the changes in the simulation's motion when a disturbance was applied to models with and without intrinsic muscle properties. Removing the intrinsic properties reduced the stability; this was true when the disturbing force was applied at a variety of times and in different directions. Thus, intrinsic muscle properties play a unique role in stabilising walking, complementing the delayed response of the central nervous system.     

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.     

The discontinuous nature of motor execution

Human movement control requires adequate coordination of different movements, which is particularly important when different motor tasks are simultaneously executed by the same effector(s) (e.g. a muscle or a joint). The process of movement execution involves a series of highly nonlinear elements; for instance, a motor unit of a muscle produces force only in the direction of muscle shortening, thus representing a threshold operator that transforms the bipolar (i.e. excitatory or inhibitory) information at its spinal input into a purely unipolar signal (i.e. muscle force). This tripartite research report addresses the contribution of the nonlinearity of neuromuscular elements to the coordination of different motor tasks simultaneously executed by the same limb. In this first part of the series, a new hypothesis for such a single-muscle multiple-task coordination is presented which suggests an essentially threshold-linear coordination mechanism. Control signals generated by the central nervous system for each individual movement independently and feedback information from peripheral receptors are linearly superimposed. This compound control/feedback signal is processed by a nonlinear limiter element reflecting the discontinuous properties of the muscle and its reflex circuitry. It is shown that threshold-linear interaction of descending commands and afferent feedback information can lead to complex interdependent patterns of compound motor action. This includes the possibility of gating (i.e. the ability of one movement pattern to constrain or even impede the execution of another pattern) and of delayed response initiation when simultaneously performing more than one voluntary motor task. A theoretical analysis of the threshold-linear coordination mechanism and an extensive experimental validation of the model is provided in part II and part III of the report. Received: 6 October 1998 / Accepted in revised form: 2 June 1999     

Disturbance induces the contrasting evolution of reinforcement and dispersiveness in directed and random movers

Spatial models commonly assume that dispersal rates are constant across individuals and environments and that movement directions are unbiased. These random-movement assumptions are inadequate to capture the range of dispersal behaviors revealed in diverse case studies. We examine an alternative assumption of directed movement, in which dispersal is a conditional and directional response by individuals to varying environmental conditions. Specifically, we assume individuals bias their movements to climb spatial fitness gradients. We compare the consequences of random and directed movement for local adaptation, the evolution of dispersal, and the reinforcement process. The implications of each movement strategy depend on the nature of environmental disturbance, and we examine the outcomes for undisturbed environments and with uncorrelated and autocorrelated disturbances. Both movement strategies offer advantages over sedentary life histories by allowing colonization of suitable habitats. However, random movement eventually becomes costly in stable environments because it inhibits local adaptation. In contrast, directed movement accelerates local adaptation. In disturbed environments, random movement offers bet-spreading advantages by distributing offspring across habitats. Despite being a more targeted strategy, an intermediate amount of directed movement provides similar bet-spreading benefits. These fitness consequences have implications for the evolution of dispersal. Dispersiveness is lost by random movers in undisturbed environments, is maintained in polymorphism with infrequent disturbances, and evolves when disturbances are uncorrelated. Directed movement becomes selectively neutral in the absence of disturbance, evolves when disturbances are autocorrelated, and is maintained in polymorphism with uncorrelated disturbances. Disturbance also determines the outcome of the reinforcement process for each strategy. For example, directed movers show no progress toward reinforcement in undisturbed environments, evolve random mating with uncorrelated disturbances, and can evolve assortative mating in infrequently disturbed environments.     

Impedance characteristics of a neuromusculoskeletal model of the human arm II. Movement control

The modulation of neuromusculoskeletal impedance during movements is analysed using a motor control model of the human arm. The motor control system combines feedback and feedforward control and both control modes are determined in one optimization process. In the model, the stiffness varies at the double movement frequency for 2-Hz oscillatory elbow movements and has high values at the movement reversals. During goal-directed two-degrees-of-freedom arm movements, the stiffness is decreased during the movement and may be increased in the initial and final phases, depending on the movement velocity. The stiffness has a considerable curl during the movement, as was also observed in experimental data. The dynamic stiffness patterns of the model can be explained basically by the α−γ coactivation scheme where feedback gains covary with motor control signals. In addition to the modulation of the gain factors, it is argued that the variation of the intrinsic stiffness has a considerable effect on movement control, especially during fast movements. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

A mathematical modeling study of inter-segmental coordination during stick insect walking

The biomechanical conditions for walking in the stick insect require a modeling approach that is based on the control of pairs of antagonistic motoneuron (MN) pools for each leg joint by independent central pattern generators (CPGs). Each CPG controls a pair of antagonistic MN pools. Furthermore, specific sensory feedback signals play an important role in the control of single leg movement and in the generation of inter-leg coordination or the interplay between both tasks. Currently, however, no mathematical model exists that provides a theoretical approach to understanding the generation of coordinated locomotion in such a multi-legged locomotor system. In the present study, I created such a theoretical model for the stick insect walking system, which describes the MN activity of a single forward stepping middle leg and helps to explain the neuronal mechanisms underlying coordinating information transfer between ipsilateral legs. In this model, CPGs that belong to the same leg, as well as those belonging to different legs, are connected by specific sensory feedback pathways that convey information about movements and forces generated during locomotion. The model emphasizes the importance of sensory feedback, which is used by the central nervous system to enhance weak excitatory and inhibitory synaptic connections from front to rear between the three thorax-coxa-joint CPGs. Thereby the sensory feedback activates caudal pattern generation networks and helps to coordinate leg movements by generating in-phase and out-of-phase thoracic MN activity.     

An equilibrium-point model of electromyographic patterns during single-joint movements based on experimentally reconstructed control signals

The purpose of this work has been to develop a model of electromyographic (EMG) patterns during single-joint movements based on a version of the equilibrium-point hypothesis, a method for experimental reconstruction of the joint compliant characteristics, the dual-strategy hypothesis, and a kinematic model of movement trajectory. EMG patterns are considered emergent properties of hypothetical control patterns that are equally affected by the control signals and peripheral feedback reflecting actual movement trajectory. A computer model generated the EMG patterns based on simulated movement kinematics and hypothetical control signals derived from the reconstructed joint compliant characteristics. The model predictions have been compared to published recordings of movement kinematics and EMG patterns in a variety of movement conditions, including movements over different distances, at different speeds, against different-known inertial loads, and in conditions of possible unexpected decrease in the inertial load. Changes in task parameters within the model led to simulated EMG patterns qualitatively similar to the experimentally recorded EMG patterns. The model's predictive power compares it favourably to the existing models of the EMG patterns.     

Cortical Factor Feedback Model for Cellular Locomotion and Cytofission

Eukaryotic cells can move spontaneously without being guided by external cues. For such spontaneous movements, a variety of different modes have been observed, including the amoeboid-like locomotion with protrusion of multiple pseudopods, the keratocyte-like locomotion with a widely spread lamellipodium, cell division with two daughter cells crawling in opposite directions, and fragmentations of a cell to multiple pieces. Mutagenesis studies have revealed that cells exhibit these modes depending on which genes are deficient, suggesting that seemingly different modes are the manifestation of a common mechanism to regulate cell motion. In this paper, we propose a hypothesis that the positive feedback mechanism working through the inhomogeneous distribution of regulatory proteins underlies this variety of cell locomotion and cytofission. In this hypothesis, a set of regulatory proteins, which we call cortical factors, suppress actin polymerization. These suppressing factors are diluted at the extending front and accumulated at the retracting rear of cell, which establishes a cellular polarity and enhances the cell motility, leading to the further accumulation of cortical factors at the rear. Stochastic simulation of cell movement shows that the positive feedback mechanism of cortical factors stabilizes or destabilizes modes of movement and determines the cell migration pattern. The model predicts that the pattern is selected by changing the rate of formation of the actin-filament network or the threshold to initiate the network formation.     

The contribution of muscle properties in the control of explosive movements

Explosive movements such as throwing, kicking, and jumping are characterized by high velocity and short movement time. Due to the fact that latencies of neural feedback loops are long in comparison to movement times, correction of deviations cannot be achieved on the basis of neural feedback. In other words, the control signals must be largely preprogrammed. Furthermore, in many explosive movements the skeletal system is mechanically analogous to an inverted pendulum; in such a system, disturbances tend to be amplified as time proceeds. It is difficult to understand how an inverted-pendulum-like system can be controlled on the basis of some form of open loop control (albeit during a finite period of time only). To investigate if actuator properties, specifically the force-length-velocity relationship of muscle, reduce the control problem associated with explosive movement tasks such as human vertical jumping, a direct dynamics modeling and simulation approach was adopted. In order to identify the role of muscle properties, two types of open loop control signals were applied: STIM(t), representing the stimulation of muscles, and MOM(t), representing net joint moments. In case of STIM control, muscle properties influence the joint moments exerted on the skeleton; in case of MOM control, these moments are directly prescribed. By applying perturbations and comparing the deviations from a reference movement for both types of control, the reduction of the effect of disturbances due to muscle properties was calculated. It was found that the system is very sensitive to perturbations in case of MOM control; the sensitivity to perturbations is markedly less in case of STIM control. It was concluded that muscle properties constitute a peripheral feedback system that has the advantage of zero time delay. This feedback system reduces the effect of perturbations during human vertical jumping to such a degree that when perturbations are not too large, the task may be performed successfully without any adaptation of the muscle stimulation pattern.     

The use of an internal representation in fast goal-directed movements: a modelling approach

This study investigates the role of the human central nervous system (CNS) in the control of fast goaldirected movements. The main problem is that the latencies inherent in the transmission of physiological signals cause a delayed feedback of sensory information. Therefore, the muscle command signals cannot be explained by a simple servo-loop, so a more sophisticated control structure is required. Our hypothesis is that the CNS employs an internal representation of the controlled system in order to circumvent the drawbacks of the physiological loop delay. To test this hypothesis a mathematical model based on an internal representation and an internal state feedback has been developed. Computer simulations of double-step stimuli (control behaviour), tendon vibration and torque disturbances (disturbance behaviour) and load perturbations (adaptation behaviour) proved to agree remarkably well with experimental observations. The proposed control model can explain the open-loop and closed-loop aspects of human motor control. Hence, the use of an internal representation in generating the muscle command signals is very plausible.     

A mechanomolecular model for the movement of chromosomes during mitosis driven by a minimal kinetochore bicyclic cascade

During mitosis chromosomes use a complex network of dynamic microtubules to find the cell equator in preparation for division signals. The roles of cellular chemical signals in mechanisms driving mitotic chromosomal movements are not well understood. In this paper we propose a mathematical model of this process which incorporates a molecular scale model of kinetochore-microtubule interactions into a negative feedback loop between spindle forces and local kinetochore biochemical reactions. This system allows kinetochore biochemical reactions to control and coordinate chromosome movement thus providing a direct connection between mechanical signals and mitosis chemical species. Our feedback control model can recreate chromosome movement from prometaphase to anaphase in good agreement with experimental data.     

Multi-scale regulated plant community dynamics: mechanisms and implications

Plant competition is not a direct interaction, but operates via environmental feedback loops, which interconnect population densities and environmental regulating variables. It is suggested that due to scale dependent elements of these feedback loops, competition may occur eventually on very different scales, necessitating a cross-scale extension of plant competition theory. After introducing the concept of cross-scale competition, we incorporate its elements into a metacommunity model and study its implications on community organization. It is found that both the equilibrium community composition, regarding coexisting functional types, and its stability depend on scale dependent attributes of environmental feedback loops and disturbance regimes. We argue that plant communities are likely to exhibit properties, which are in line with the hierarchical ecosystem concept. Environmental feedback loops on different scales act as distinct organizational levels, what can be affected by disturbances of corresponding spatial extent.     

The reach-to-grasp movement in children with autism spectrum disorder

Autism is associated with a wide and complex array of neurobehavioural symptoms. Examination of the motor system offers a particularly appealing method for studying autism by providing information about this syndrome that is relatively immune to experimental influence. In this article, we considered the relationship between possible movement disturbance and symptoms of autism and introduced an experimental model that may be useful for rehabilitation and diagnostic purposes: the reach-to-grasp movement. Research is reviewed that characterizes kinematically the reach-to-grasp movement in children with autism compared with age-matched 'controls'. Unlike the age-matched children, autistic children showed differences in movement planning and execution, supporting the view that movement disturbances may play a part in the phenomenon of autism.     

Quantization of human motions and learning of accurate movements

This paper presents a mathematical model for the learning of accurate human arm movements. Its main features are that the movement is the superposition of smooth submovements, the intrinsic deviation of arm movements is considered, visual and kinesthetic feedback are integrated in the motion control, and the movement duration and accuracy are optimized with practice. This model is consistent with the jerky arm movements of infants, and may explain how the adult motion behavior emerges from the infant behavior. Comparison with measurements of adult movements shows that the kinematics of accurate movements are well predicted by the model. Received: 15 May 1997 / Accepted 5 December 1997     

Disruption of successive specialized movements in a chain conditioned reflex after extirpation of individual fields of the prefrontal cortex in baboons

After extirpation of the field 9 and 47 disturbances of a chain instrumental reflex appear in monkeys as a fragmentation of successive acts and simplification of the forms of manipulation with experimental instruments. Disturbances of movement forms are stable. This fact to some extent is modelling human frontal pathology which is manifested in inability to perform a series of successive movements with switching over to different forms. Extirpation of the field 10 elicits disturbances of successive act only in the initial period and further the chain reflex is fully restored. Locomotor hyperactivity dominates in the behaviour. Author's initial conclusion is confirmed that the field 10 does not participate in formation and manifestation of temporal connections and has regulating influence on the organization of complex animals' behaviour.     

Assessing the Perception of Trunk Movements in Military Personnel with Chronic Non-Specific Low Back Pain Using a Virtual Mirror

Chronic pain, including chronic non-specific low back pain (CNSLBP), is often associated with body perception disturbances, but these have generally been assessed under static conditions. The objective of this study was to use a “virtual mirror” that scaled visual movement feedback to assess body perception during active movement in military personnel with CNSLBP (n = 15) as compared to military healthy control subjects (n = 15). Subjects performed a trunk flexion task while sitting and standing in front of a large screen displaying a full-body virtual mirror-image (avatar) in real-time. Avatar movements were scaled to appear greater, identical, or smaller than the subjects’ actual movements. A total of 126 trials with 11 different scaling factors were pseudo-randomized across 6 blocks. After each trial, subjects had to decide whether the avatar’s movements were “greater” or “smaller” than their own movements. Based on this two-alternative forced choice paradigm, a psychophysical curve was fitted to the data for each subject, and several metrics were derived from this curve. In addition, task adherence (kinematics) and virtual reality immersion were assessed. Groups displayed a similar ability to discriminate between different levels of movement scaling. Still, subjects with CNSLBP showed an abnormal performance and tended to overestimate their own movements (a right-shifted psychophysical curve). Subjects showed adequate task adherence, and on average virtual reality immersion was reported to be very good. In conclusion, these results extend previous work in patients with CNSLBP, and denote an important relationship between body perception, movement and pain. As such, the assessment of body perception during active movement can offer new avenues for understanding and managing body perception disturbances and abnormal movement patterns in patients with pain.     

Visual feedback is not necessary for the learning of novel dynamics

Background

When learning to perform a novel sensorimotor task, humans integrate multi-modal sensory feedback such as vision and proprioception in order to make the appropriate adjustments to successfully complete the task. Sensory feedback is used both during movement to control and correct the current movement, and to update the feed-forward motor command for subsequent movements. Previous work has shown that adaptation to stable dynamics is possible without visual feedback. However, it is not clear to what degree visual information during movement contributes to this learning or whether it is essential to the development of an internal model or impedance controller.

Methodology/Principle Findings

We examined the effects of the removal of visual feedback during movement on the learning of both stable and unstable dynamics in comparison with the case when both vision and proprioception are available. Subjects were able to learn to make smooth movements in both types of novel dynamics after learning with or without visual feedback. By examining the endpoint stiffness and force after learning it could be shown that subjects adapted to both types of dynamics in the same way whether they were provided with visual feedback of their trajectory or not. The main effects of visual feedback were to increase the success rate of movements, slightly straighten the path, and significantly reduce variability near the end of the movement.

Conclusions/Significance

These findings suggest that visual feedback of the hand during movement is not necessary for the adaptation to either stable or unstable novel dynamics. Instead vision appears to be used to fine-tune corrections of hand trajectory at the end of reaching movements.     

Changes in the amplitude and direction of goal-directed hand movements in the lack of visual information

The goal of the present investigation was to determine the precision of goal-directed hand movements in the lack of visual information. The movement amplitude and direction was examined under different experimental conditions. Subjects were ten female and ten male university students. The motor test was drawing 10 cm long straight line and 24 cm long zigzag line in four different experimental conditions. 1) The drawing with open eyes was followed immediately with drawing with closed eyes. 2) The drawing was executed from memory in the lack of visual information. 3) Drawing with restricted amplitude or direction. 4) Drawing with verbal feedback. The errors of the target distance and the lateral deviations from the target were different under the different experimental conditions. The largest errors and underestimation of the target distance occurred in drawing horizontal straight line with closed eyes. No statistically significant gender differences were found. It is concluded that the practice, adjustment of single movement parameter to the target, and the verbal feedback assist better the accuracy of unseen goal-directed hand movement than the recent visual memory.     

Modeling and Analysis of a Density-Dependent Stochastic Integral Projection Model for a Disturbance Specialist Plant and Its Seed Bank

In many plant species dormant seeds can persist in the soil for one to several years. The formation of these seed banks is especially important for disturbance specialist plants, as seeds of these species germinate only in disturbed soil. Seed movement caused by disturbances affects the survival and germination probability of seeds in the seed bank, which subsequently affect population dynamics. In this paper, we develop a stochastic integral projection model for a general disturbance specialist plant-seed bank population that takes into account both the frequency and intensity of random disturbances, as well as vertical seed movement and density-dependent seedling establishment. We show that the probability measures associated with the plant-seed bank population converge weakly to a unique measure, independent of initial population. We also show that the population either persists with probability one or goes extinct with probability one, and provides a sharp criteria for this dichotomy. We apply our results to an example motivated by wild sunflower (Helianthus annuus) populations, and explore how the presence or absence of a “storage effect” impacts how a population responds to different disturbance scenarios.     

Hedging Your Bets: Intermediate Movements as Optimal Behavior in the Context of an Incomplete Decision

Existing theories of movement planning suggest that it takes time to select and prepare the actions required to achieve a given goal. These theories often appeal to circumstances where planning apparently goes awry. For instance, if reaction times are forced to be very low, movement trajectories are often directed between two potential targets. These intermediate movements are generally interpreted as errors of movement planning, arising either from planning being incomplete or from parallel movement plans interfering with one another. Here we present an alternative view: that intermediate movements reflect uncertainty about movement goals. We show how intermediate movements are predicted by an optimal feedback control model that incorporates an ongoing decision about movement goals. According to this view, intermediate movements reflect an exploitation of compatibility between goals. Consequently, reducing the compatibility between goals should reduce the incidence of intermediate movements. In human subjects, we varied the compatibility between potential movement goals in two distinct ways: by varying the spatial separation between targets and by introducing a virtual barrier constraining trajectories to the target and penalizing intermediate movements. In both cases we found that decreasing goal compatibility led to a decreasing incidence of intermediate movements. Our results and theory suggest a more integrated view of decision-making and movement planning in which the primary bottleneck to generating a movement is deciding upon task goals. Determining how to move to achieve a given goal is rapid and automatic.