Perturbation-dependent selection of postural feedback gain and its scaling

In this study we examined whether the selection of postural feedback gain and its scaling is dependent on perturbation type. We compare forward pushes applied to the back of a standing subject to previous work on responses to support translation. As was done in the previous work, we quantified the subject's response in terms of perturbation-dependent feedback gains. Seven healthy young subjects (25±3 yr) experienced five different magnitudes of forward push applied by a 1.25 m-long pendulum falling from the height of 1.4m toward the center of mass of the subject's torso. The loads on the pendulum ranged from 2 to 10 kg. Impulsive force, ground reaction forces and joint kinematics were measured, and joint torques were calculated from inverse dynamics. A full-state feedback control model was used to quantify the empirical data, and the feedback gains that minimized the fitting error between the data and model simulation were identified. As in previously published feedback gains for support translation trials, gradual gain scaling with push perturbation magnitude was consistently observed, but a different feedback gain set was obtained. The results imply that the nervous system may be aware of body dynamics being subjected to various perturbation types and may select perturbation-dependent postural feedback gains that satisfy postural stability and feasible joint torque constraints.     

Effects of reflex delays on postural control during unstable seated balance

Patients with low-back pain (LBP) exhibit longer trunk muscle reflex latencies and poorer postural control than healthy individuals. We hypothesized that balance during a simulated postural control task would become impaired when the delays exhibited by LBP patients were incorporated into neuromuscular control. The task chosen for this investigation was seated balancing, which emphasizes trunk muscles’ contribution in postural control. This task was modeled in Simulink? as a fourth order linearized dynamic system with feedback delays. Optimization (minimizing error between experimental and model data) of state variables was used to determine neuromuscular control parameters. Experimental data were obtained from 7 subjects during 5 perturbation trials while balancing on the seat with eyes closed. Model accuracy, reflecting the ability of the model to capture the dynamics of seated balance, was correlated with seated balance performance (r=0.91, p<0.001). To minimize the risk of erroneous findings from inaccurate modeling, only the best five balancers’ data were used for hypothesis testing. In these five subjects, feedback delays in modeled neuromuscular control were increased to determine their effect on task stability, trunk displacement and trunk moment. Simulations showed that longer delays found in LBP, in general, did not produce unstable balancing, but did result in increased trunk displacement (p<0.001) and trunk moment (p=0.001). This impairment in neuromuscular control in chronic LBP patients could possibly exacerbate their condition by increasing tissue strain (more spinal displacement) and stress (more spinal loading).     

Modeling human postural sway using an intermittent control and hemodynamic perturbations

Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1–0.7 Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.     

A robotic device for understanding neuromechanical interactions during standing balance control

Postural stability in standing balance results from the mechanics of body dynamics as well as active neural feedback control processes. Even when an animal or human has multiple legs on the ground, active neural regulation of balance is required. When the postural configuration, or stance, changes, such as when the feet are placed further apart, the mechanical stability of the organism changes, but the degree to which this alters the demands on neural feedback control for postural stability is unknown. We developed a robotic system that mimics the neuromechanical postural control system of a cat in response to lateral perturbations. This simple robotic system allows us to study the interactions between various parameters that contribute to postural stability and cannot be independently varied in biological systems. The robot is a 'planar', two-legged device that maintains compliant balance control in a variety of stance widths when subject to perturbations of the support surface, and in this sense reveals principles of lateral balance control that are also applicable to bipeds. Here we demonstrate that independent variations in either stance width or delayed neural feedback gains can have profound and often surprisingly detrimental effects on the postural stability of the system. Moreover, we show through experimentation and analysis that changing stance width alters fundamental mechanical relationships important in standing balance control and requires a coordinated adjustment of delayed feedback control to maintain postural stability.     

A single muscle's multifunctional control potential of body dynamics for postural control and running

A neuromechanical approach to control requires understanding how mechanics alters the potential of neural feedback to control body dynamics. Here, we rewrite activation of individual motor units of a behaving animal to mimic the effects of neural feedback without concomitant changes in other muscles. We target a putative control muscle in the cockroach, Blaberus discoidalis (L.), and simultaneously capture limb and body dynamics through high-speed videography and a micro-accelerometer backpack. We test four neuromechanical control hypotheses. We supported the hypothesis that mechanics linearly translates neural feedback into accelerations and rotations during static postural control. However, during running, the same neural feedback produced a nonlinear acceleration control potential restricted to the vertical plane. Using this, we reject the hypothesis from previous work that this muscle acts primarily to absorb energy from the body. The conversion of the control potential is paralleled by nonlinear changes in limb kinematics, supporting the hypothesis that significant mechanical feedback filters the graded neural feedback for running control. Finally, we insert the same neural feedback signal but at different phases in the dynamics. In this context, mechanical feedback enables turning by changing the timing and direction of the accelerations produced by the graded neural feedback.     

Comparing internal models of the dynamics of the visual environment

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion.We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.     

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior–posterior and medial–lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were < 8%, and those for most statistical mechanics measures were ～3–66%. On the basis these results, the proposed 3D balance control model appears to have the ability to accurately simulate 3D postural sway behaviours.     

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior-posterior and medial-lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were 相似文献   

Identification of the nonlinear state-space dynamics of the action-perception cycle for visually induced postural sway

Human subjects standing in a sinusoidally moving visual environment display postural sway with characteristic dynamical properties. We analyzed the spatiotemporal properties of this sway in an experiment in which the frequency of the visual motion was varied. We found a constant gain near 1, which implies that the sway motion matches the spatial parameters of the visual motion for a large range of frequencies. A linear dynamical model with constant parameters was compared quantitatively with the data. Its failure to describe correctly the spatiotemporal properties of the system led us to consider adaptive and nonlinear models. To differentiate between possible alternative structures we directly fitted nonlinear differential equations to the sway and visual motion trajectories on a trial-by-trial basis. We found that the eigenfrequency of the fitted model adapts strongly to the visual motion frequency. The damping coefficient decreases with increasing frequency. This indicates that the system destabilizes its postural state in the inertial frame. This leads to a faster internal dynamics which is capable of synchronizing posture with fast-moving visual environments. Using an algorithm which allows the identification of essentially nonlinear terms of the dynamics we found small nonlinear contributions. These nonlinearities are not consistent with a limit-cycle dynamics, accounting for the robustness of the amplitude of postural sway against frequency variations. We interpret our results in terms of active generation of postural sway specified by sensory information. We derive also a number of conclusions for a behavior-oriented analysis of the postural system.     

Nonlinear control of HIV-1 infection with a singular perturbation model

Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value.     

Modeling the Dynamics of Sensory Reweighting

Reweighting sensory information adaptively is considered critical for flexible postural control, but little is known of the time scale of the reweighting process. We analyzed the transient dynamics of sensory reweighting in a previously published nonlinear adaptive model of sensory integration in the human postural control system. The model’s dynamics of adaptation were tested in response to abrupt changes in the amplitude of the motion of the visual surround. In addition to qualitatively reproducing the correct asymptotic response to such changes in visual amplitude, as previously found, the model qualitatively reproduced the asymmetric transient response elucidated in recent experiments (Oie et al. in Gait Posture 2005). In particular, the model adapts at an initially rapid rate to a switch from low to high amplitude visual motion, but at an initially slower rate upon the return to low amplitude motion. The observed temporal asymmetry has potential functional value. Rapid downweighting of a visual stimulus that suddenly increases is necessary to prevent loss of upright equilibrium. A visual stimulus that decreases in amplitude does not pose a threat to upright balance, allowing for slower upweighting without functional consequence.     

Cross-correlation between EMG and center of gravity during quiet stance: theory and simulations

Several signal processing tools have been employed in the experimental study of the postural control system in humans. Among them, the cross-correlation function has been used to analyze the time relationship between signals such as the electromyogram and the horizontal projection of the center of gravity. The common finding is that the electromyogram precedes the biomechanical signal, a result that has been interpreted in different ways, for example, the existence of feedforward control or the preponderance of a velocity feedback. It is shown here, analytically and by simulation, that the cross-correlation function is depedent in a complicated way on system parameters and on noise spectra. Results similar to those found experimentally, e.g., electromyiogram preceding the biomechanical signal may be obtained in a postural control model without any feedforward control and without any velocity feedback. Therefore, correct interpretations of experimentally obtained cross-correlation functions may require additional information about the system. The results extend to other biomedical applications where two signals from a closed loop system are cross-correlated.     

Neural model of the genetic network

Many cell control processes consist of networks of interacting elements that affect the state of each other over time. Such an arrangement resembles the principles of artificial neural networks, in which the state of a particular node depends on the combination of the states of other neurons. The lambda bacteriophage lysis/lysogeny decision circuit can be represented by such a network. It is used here as a model for testing the validity of a neural approach to the analysis of genetic networks. The model considers multigenic regulation including positive and negative feedback. It is used to simulate the dynamics of the lambda phage regulatory system; the results are compared with experimental observation. The comparison proves that the neural network model describes behavior of the system in full agreement with experiments; moreover, it predicts its function in experimentally inaccessible situations and explains the experimental observations. The application of the principles of neural networks to the cell control system leads to conclusions about the stability and redundancy of genetic networks and the cell functionality. Reverse engineering of the biochemical pathways from proteomics and DNA micro array data using the suggested neural network model is discussed.     

Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics

Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations.     

Oscillations and multiple steady states in a cyclic gene model with repression

In this paper we study the cyclic gene model with repression considered by H. T. Banks and J. M. Mahaffy. Roughly, the model describes a biochemical feedback loop consisting of an integer number G of single gene reaction sequences in series. The model leads to a system of functional differential equations. We show that there is a qualitative difference in the dynamics between even and odd G if the feedback repression is sufficiently large. For even G, multiple stable steady states can coexist while for odd G, periodic orbits exist.This research was supported in part by the Air Force Office of Scientific Research under Contract #AFOSR-84-0376 and by the US Army Research Office under Contract #DAAG29-84-K-0082     

Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson’s Disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson’s disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson’s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson’s disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.     

A structurally optimal control model for predicting and analyzing human postural coordination

This paper proposes a closed-loop optimal control model predicting changes between in-phase and anti-phase postural coordination during standing and related supra-postural activities. The model allows the evaluation of the influence of body dynamics and balance constraints onto the adoption of postural coordination. This model minimizes the instantaneous norm of the joint torques with a controller in the head space, in contrast with classical linear optimal models used in the postural literature and defined in joint space. The balance constraint is addressed with an adaptive ankle torque saturation. Numerical simulations showed that the model was able to predict changes between in-phase and anti-phase postural coordination modes and other non-linear transient dynamics phenomena.     

Analysis and implementation of a neural extended Kalman filter for target tracking

Having a better motion model in the state estimator is one way to improve target tracking performance. Since the motion model of the target is not known a priori, either robust modeling techniques or adaptive modeling techniques are required. The neural extended Kalman filter is a technique that learns unmodeled dynamics while performing state estimation in the feedback loop of a control system. This coupled system performs the standard estimation of the states of the plant while estimating a function to approximate the difference between the given state-coupling function model and the behavior of the true plant dynamics. At each sample step, this new model is added to the existing model to improve the state estimate. The neural extended Kalman filter has also been investigated as a target tracking estimation routine. Implementation issues for this adaptive modeling technique, including neural network training parameters, were investigated and an analysis was made of the quality of performance that the technique can have for tracking maneuvering targets.     

Postural maintenance during movement: Simulations of a two joint model

Voluntary movements of the upper body are accompanied by anticipatory postural adjustments to the lower body in a standing subject. The long-standing hypothesis is that these anticipatory adjustments serve to counteract the perturbation to the body's center of gravity caused by the voluntary arm movement. This paper presents model simulations investigating the possible roles of anticipatory postural activity that accompanies a rapid, upward arm swing. The model encorporates two (idealized) antagonistic muscle pairs controlling the movements of a double-joint system, with a shoulder joint between the arm and stiff body links, and an ankle joint between the stiff body-leg segment and the ground. Each muscle is represented by a nonlinear viscoelastic element and also includes proprioceptive feedback. Four inputs to the model define the motor control signals for muscle force generation in both the arm and the postural muscle pairs. The neurological component of the model describes consequences of alternate strategies for cocontractions, stretch reflex activity, and anticipatory and synchronous postural activities (or combinations thereof). Simulations with this model show that: (1) none of the postural maintenance schemes considered in these simulations (including varying anticipation) could suppress the initial backward thrust on the body link; (2) the more important destabilizing perturbation is a subsequent forward sway that, left uncountered by postural activity, would eventually leave the body to fall flat on its face; and (3) anticipatory silencing of the postural extensor followed by a brief period of extensor activation (descending control) and synchronous reflex activity (feedback control) appears to be the most likely postural stabilizing strategy that inhibits the continuous forward sway and is consistent with the experimental evidence.