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 mathematical model for insulin kinetics and its application to protein-deficient (malnutrition-related) diabetes mellitus (PDDM)

A nonlinear mathematical model which incorporates both beta-cell kinetics and a glucose-insulin feedback system is proposed for describing the time variations of plasma glucose and insulin levels. Numerical simulations show that this model is consistent with experimental observations on normal groups. An analysis of the changes in the solutions with variations in the parameters showed that a decrease in a single parameter gave results consistent with experimental findings in protein-deficient (malnutrition-related) diabetes mellitus (PDDM). The model predicts that it is the function and not the number of beta cells which is reduced in PDDM.     

A note on the reafference principle

Two alternative circuits to realize the reafference principle are considered and quantitatively analyzed. Both are combinations of a conventional control loop with negative feedback and linear transfer functions, as well as of an efference copy branch. The feedback control loop compensates for passive movements of the body or of its parts, and generates active movements, whenever the set point differs from zero. The efference copy branch should eliminate sensory messages to higher brain centres during active body movements and, thus, mediate perceptual stability. In one of the combinations, discussed also briefly by Mittelstaedt (1971), the efference copy branch interacts with and thus modifies the properties of the feedback loop. The performance of this circuit is very sensitive to variations of the system parameters and, therefore, requires precise adjustment. When the transfer function of the efference copy branch exactly matches that of the feedback loop and its gain amounts to 1, this circuit performs as a control loop with an integrator in the negative feedback branch: there is no steady state control error. However, for certain parameter combination the circuit becomes unstable. In the alternative circuit proposed here, the efference copy branch does not interfere with the feedback loop. It is robust against parameter variations. The transient properties of both circuits are described under simplified assumptions regarding the linear transfer functions in the different branches.     

A method of studying variations in the common center of gravity (stabilometry)

A procedure to study variations of the common human centre of gravity (stabilometry) permits using a principle of a biological feedback. It is achieved by application of a device to study the nervous system. A procedure is recommended to be widely used in applied physiology.     

Learning combined feedback and feedforward control of a musculoskeletal system

The goal of this paper is the learning of neuromuscular control, given the following necessary conditions: (1) time delays in the control loop, (2) non-linear muscle characteristics, (3) learning of feedforward and feedback control, (4) possibility of feedback gain modulation during a task. A control system and learning methodology that satisfy those conditions is given. The control system contains a neural network, comprising both feedforward and feedback control. The learning method is backpropagation through time with an explicit sensitivity model. Results will be given for a one degree of freedom arm with two muscles. Good control results are achieved which compare well with experimental data. Analysis of the controller shows that significant differences in controller characteristics are found if the loop delays are neglected. During a control task the system shows feedback gain modulation, similar to experimentally found reflex gain modulation during rapid voluntary contraction. If only limited feedback information is available to the controller the system learns to co-contract the antagonistic muscle pair. In this way joint stiffness increases and stable control is more easily maintained. Received: 7 November 1995 / Accepted in revised form: 13 February 1996     

Optimal control mode of a biochemical feedback system

An optimal feedback system for constant-value control of biochemical reaction system was investigated by computer simulations. A feedback system containing a cyclic enzyme system where two enzyme types share a substrate in a cyclic manner, was found to be the most reliable one. This feedback system has a capability to keep the stationary value of the end product at a desired level against not only exogenous substrate supply but also endogenous parametric disturbances. The cyclic enzyme system installed as a control element of this feedback system played the role of comparator in this feedback system. The control mode of this feedback system was in good agreement with that of a system established by means of optimization technique based on the maximum principle. Also bang - bang control could be performed in this biochemical feedback system as well as in electrical one.     

A Symbolic Model for the Regulation by Bone Metabolism of the Blood Calcium Level in Rats

The control by bone metabolism of the blood calcium level in young rats may be described in terms of a regulator-type system. The model presented here comprises a feedback loop involving only a proportional control in thyroparathyroidectomized, and a combination of proportional and integral controls in normal animals. It accounts for the variations observed when the system was subjected to a variety of experimental constraints. The implications, limitations, and possible extensions of the model are discussed.     

Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species.     

An investigation of the mechanisms of eye movement control

Summary Feedback mechanisms exist in all the periferal sense organs including the eye, which acts as a highly efficient position control servo system. Histological studies so far have not revealed the precise circuitry of the eye movement control system but some information about it can be obtained by a study of the sources of feedback. Existing theories have considered three types of feedback originating in the oculomotor tract, in the proprioceptive fibres of the extrinsic eye muscles and from retinal image displacement. In the present experiments an optical arrangement has been used to vary or eliminate the amount of information available from retinal image motion, and the response of the eye to simple harmonic displacement of a target has been recorded. The response curves of gain (eyeball movement divided by target motion) against frequency indicate that the system is lion linear when the image falls in the retinal region which is insensitive to position. Outside this area, retinal image position is used as negative feedback but the information from the oculomotor tract must be regenerative. There is also evidence for feedback proportional to the first derivative of eyeball position and this function is ascribed to the proprioceptive signals; this form of feedback appears to saturate for large amplitude movements, thus avoiding heavy damping of the flick movements.A schematic eye movement control system having the same characteristics as the eye is proposed. The transfer function of this system indicates that it should be unstable if the sign of the retinal image feedback loop is reversed. Experiments with this form of feedback show that steady fixation is impossible and the eye performs a pendular nystagmus.     

Robustness analysis of biochemical network models

Biological systems that have been experimentally verified to be robust to significant changes in their environments require mathematical models that are themselves robust. In this context, a necessary condition for model robustness is that the model dynamics should not be sensitive to small variations in the model's parameters. Robustness analysis problems of this type have been extensively studied in the field of robust control theory and have been found to be very difficult to solve in general. The authors describe how some tools from robust control theory and nonlinear optimisation can be used to analyse the robustness of a recently proposed model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium cells. The network model, which consists of a system of seven coupled nonlinear differential equations, accurately reproduces the spontaneous oscillations in cAMP observed during the early development of D. discoideum. The analysis by the authors reveals, however, that very small variations in the model parameters can effectively destroy the required oscillatory dynamics. A biological interpretation of the analysis results is that correct functioning of a particular positive feedback loop in the proposed model is crucial to maintaining the required oscillatory dynamics.     

Feedback control architecture and the bacterial chemotaxis network

Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance.     

Stabilizing feedback of a nonlinear process involving uncertain data

A nonlinear control system describing the process of continuous methane fermentation is considered. Assuming that the parameters of the model are not exactly known but bounded within intervals, the set of optimal static points according to a practical criterion is computed. A continuous feedback control is proposed, which asymptotically stabilizes the dynamic system towards this set. Numerical results are also reported.     

Information processing organs,mathematical mappings and self-organizing systems

A self-organizing system, which may be biological or man-made, adjusts itself in response to inputs from the surroundings. The input information is processed and transformed, so as to guide the system in accordance with a desired final state. The visual nervous system is considered, to illustrate some possible transformations or mappings, which may be employed by self-organizing systems. The mappings given as examples are linear, but there is evidence also for nonlinear mappings to explain the action of biological systems. The successive stages of adjustment in a self-organizing system can be treated as a feedback control process. Mathematically, feedback control of linear as well as nonlinear systems can be handled by using the principle of contraction mapping. The kind of control considered is flexible in the sense that a desired state of the system as a whole can be achieved through a variety of states of the individual parts. This leads to such questions as equivalence and classification which are also discussed in this paper.     

Quantifying the relative contributions of divisive and subtractive feedback to rhythm generation

Biological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes: divisive (decreases the gain of the positive feedback loop) and subtractive (increases the input threshold) that both contribute to slowly move the system between the high- and low-activity states. Can we determine the relative contribution of each type of negative feedback process to the rhythmic activity? Does one dominate? Do they control the active and silent phase equally? To answer these questions we use a neural network model with excitatory coupling, regulated by synaptic depression (divisive) and cellular adaptation (subtractive feedback). We first attempt to apply standard experimental methodologies: either passive observation to correlate the variations of a variable of interest to system behavior, or deletion of a component to establish whether a component is critical for the system. We find that these two strategies can lead to contradictory conclusions, and at best their interpretive power is limited. We instead develop a computational measure of the contribution of a process, by evaluating the sensitivity of the active (high activity) and silent (low activity) phase durations to the time constant of the process. The measure shows that both processes control the active phase, in proportion to their speed and relative weight. However, only the subtractive process plays a major role in setting the duration of the silent phase. This computational method can be used to analyze the role of negative feedback processes in a wide range of biological rhythms.     

Evaluation of a generalized model of human postural dynamics and control in the sagittal plane

A two-step identification method is used to evaluate a generalized model of human postural control in the sagittal plane. Postural dynamics are represented as a planar open-chain linkage system supported by a triangular foot. The control mechanism is modeled as a state feedback element in which the torque acting at a given link is an arbitrary function of the state variables — angles and angular velocities. To validate the approach, six normal subjects underwent two series of experiments. The first series were used to determine an appropriate model of the system dynamics. The second series were used to estimate the parameters of the feedback model. A computer simulation of the complete system shows that the model predictions closely match the observed responses. These results suggest that the proposed model provides a useful framework for analysis of postural control mechanisms.This work was supported by the National Institutes of Health under Grant NS 21363     

Neuronal mechanisms of voice control are affected by implicit expectancy of externally triggered perturbations in auditory feedback

Accurate vocal production relies on several factors including sensory feedback and the ability to predict future challenges to the control processes. Repetitive patterns of perturbations in sensory feedback by themselves elicit implicit expectations in the vocal control system regarding the timing, quality and direction of perturbations. In the present study, the predictability of voice pitch-shifted auditory feedback was experimentally manipulated. A block of trials where all pitch-shift stimuli were upward, and therefore predictable was contrasted against an unpredictable block of trials in which the stimulus direction was randomized between upward and downward pitch-shifts. It was found that predictable perturbations in voice auditory feedback led to a reduction in the proportion of compensatory vocal responses, which might be indicative of a reduction in vocal control. The predictable perturbations also led to a reduction in the magnitude of the N1 component of cortical Event Related Potentials (ERP) that was associated with the reflexive compensations to the perturbations. We hypothesize that formation of expectancy in our study is accompanied by involuntary allocation of attentional resources occurring as a result of habituation or learning, that in turn trigger limited and controlled exploration-related motor variability in the vocal control system.     

Feedback in physiological systems: An application of feedback analysis and stochastic models to neurophysiology

In the human, the antagonistic, extensor-flexor system of the leg is an example of a common type of neurophysiological feedback system. After a brief introduction to the neuroanatomy and physiology of this feedback system, the paper formulates transfer functions from temporal response data available in the literature. A feedback stability analysis, based on the extension of Nyquist's stability criteria to multiple-loop systems and utilizing flow-graph techniques, demonstrates the stable behavior of the system. Expressions are given relating the sensitivity of the system to variations in muscle response and Golgi tendon organ (tension receptor) response. By considering the events taking place at synapses and end-plates during “isometric tension-small knee angle excursion” conditions as stationary stochastic processes, an external “noise” input to the system is given, whose spectrum is derived from the statistics of a shot-process representation of these events. The paper concludes with some correlations between the analytical results and clinical syndromes.     

The nature of the cell cycle and the control of cell proliferation

It is generally accepted that cells contain numerous negative feedback control systems which are frequently invoked for their ability to maintain homeostasis. There is no reason to believe that the replicating cell is an exception yet paradoxically it is a highly dynamic entity in that the levels of constituents vary with time. The inconsistency between theory and observation is easily resolvable if (a) the events of the cell cycle reflect the oscillatory behaviour of certain of the regulatory processes, and, (b) proliferation control is exerted via transitions between periodic and aperiodic (or damped periodic) states as the result of changes in the values of the parameters determining the behaviour of the system. This concept is briefly discussed in relation to: the wide variety of agents that can affect replication; the existence of distinct non-proliferative states; the continuous control of proliferation rate; variations in the sensitivity toward cell cycle inhibitory agents; senescence; the ‘loss’ of control of cell division in cancer.     

Optimal feedback control to describe multiple representations of primary motor cortex neurons

Primary motor cortex (M1) neurons are tuned in response to several parameters related to motor control, and it was recently reported that M1 is important in feedback control. However, it remains unclear how M1 neurons encode information to control the musculoskeletal system. In this study, we examined the underlying computational mechanisms of M1 based on optimal feedback control (OFC) theory, which is a plausible hypothesis for neuromotor control. We modelled an isometric torque production task that required joint torque to be regulated and maintained at desired levels in a musculoskeletal system physically constrained by muscles, which act by pulling rather than pushing. Then, a feedback controller was computed using an optimisation approach under the constraint. In the presence of neuromotor noise, known as signal-dependent noise, the sensory feedback gain is tuned to an extrinsic motor output, such as the hand force, like a population response of M1 neurons. Moreover, a distribution of the preferred directions (PDs) of M1 neurons can be predicted via feedback gain. Therefore, we suggest that neural activity in M1 is optimised for the musculoskeletal system. Furthermore, if the feedback controller is represented in M1, OFC can describe multiple representations of M1, including not only the distribution of PDs but also the response of the neuronal population.