Stabilizing PID controllers for a single-link biomechanical model with position, velocity, and force feedback

In this paper we address the problem of PID stabilization of a single-link inverted pendulum-based biomechanical model with force feedback, two levels of position and velocity feedback, and with delays in all the feedback loops. The novelty of the proposed model lies in its physiological relevance, whereby both small and medium latency sensory feedbacks from muscle spindle (MS), and force feedback from Golgi tendon organ (GTO) are included in the formulation. The biomechanical model also includes active and passive viscoelastic feedback from Hill-type muscle model and a second-order low-pass function for muscle activation. The central nervous system (CNS) regulation of postural movement is represented by a proportional-integral-derivative (PID) controller. Padé approximation of delay terms is employed to arrive at an overall rational transfer function of the biomechanical model. The Hermite-Biehler theorem is then used to derive stability results, leading to the existence of stabilizing PID controllers. An algorithm for selection of stabilizing feedback gains is developed using the linear matrix inequality (LMI) approach.     

Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov' stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

Support surface related changes in feedforward and feedback control of standing posture

The aim of the study was to investigate the effect of different support surfaces on feedforward and feedback components of postural control. Nine healthy subjects were exposed to external perturbations applied to their shoulders while standing on a rigid platform, foam, and wobble board with eyes open or closed.Electrical activity of nine trunk and leg muscles and displacements of the center of pressure were recorded and analyzed during the time frames typical of feedforward and feedback postural adjustments. Feedforward control of posture was characterized by earlier activation of anterior muscles when the subjects stood on foam compared to a wobble board or a firm surface. In addition, the magnitude of feedforward muscle activity was the largest when the foam was used. During the feedback control, anterior muscles were activated prior to posterior muscles irrespective of the nature of surface. Moreover, the largest muscle activity was seen when the supporting surface was foam. Maximum CoP displacement occurred when subjects were standing on a rigid surface.Altering support surface affects both feedforward and feedback components of postural control. This information should be taken into consideration in planning rehabilitation interventions geared towards improvement of balance.     

Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov's stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

Feedback regulation of EGFR signalling: decision making by early and delayed loops

Human-made information relay systems invariably incorporate central regulatory components, which are mirrored in biological systems by dense feedback and feedforward loops. This type of system control is exemplified by positive and negative feedback loops (for example, receptor endocytosis and dephosphorylation) that enable growth factors and receptor Tyr kinases of the epidermal growth factor receptor (EGFR)/ERBB family to regulate cellular function. Recent studies show that the collection of feedback regulatory loops can perform computational tasks - such as decoding ligand specificity, transforming graded input signals into a digital output and regulating response kinetics. Aberrant signal processing and feedback regulation can lead to defects associated with pathologies such as cancer.     

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.     

A simulation study to examine the use of cross-correlation as an estimate of surface EMG cross talk.

Cross-correlation between surface electromyogram (EMG) signals is commonly used as a means of quantifying EMG cross talk during voluntary activation. To examine the reliability of this method, the relationship between cross talk and the cross-correlation between surface EMG signals was examined by using model simulation. The simulation results illustrate an increase in cross talk with increasing subcutaneous fat thickness. The results also indicate that the cross-correlation function decays more rapidly with increasing distance from the active fibers than cross talk, which was defined as the normalized EMG amplitude during activation of a single muscle. The influence of common drive and short-term motor unit synchronization on the cross-correlation between surface EMG signals was also examined. While common drive did not alter the maximum value of the cross-correlation function, the correlation increased with increasing motor unit synchronization. It is concluded that cross-correlation analysis is not a suitable means of quantifying cross talk or of distinguishing between cross talk and coactivation during voluntary contraction. Furthermore, it is possible that a high correlation between surface EMG signals may reflect an association between motor unit firing times, for example due to motor unit synchronization.     

Gait Initiation in Children with Rett Syndrome

Rett syndrome is an X-linked neurodevelopmental condition mainly characterized by loss of spoken language and a regression of purposeful hand use, with the development of distinctive hand stereotypies, and gait abnormalities. Gait initiation is the transition from quiet stance to steady-state condition of walking. The associated motor program seems to be centrally mediated and includes preparatory adjustments prior to any apparent voluntary movement of the lower limbs. Anticipatory postural adjustments contribute to postural stability and to create the propulsive forces necessary to reach steady-state gait at a predefined velocity and may be indicative of the effectiveness of the feedforward control of gait. In this study, we examined anticipatory postural adjustments associated with gait initiation in eleven girls with Rett syndrome and ten healthy subjects. Muscle activity (tibialis anterior and soleus muscles), ground reaction forces and body kinematic were recorded. Children with Rett syndrome showed a distinctive impairment in temporal organization of all phases of the anticipatory postural adjustments. The lack of appropriate temporal scaling resulted in a diminished impulse to move forward, documented by an impairment in several parameters describing the efficiency of gait start: length and velocity of the first step, magnitude and orientation of centre of pressure-centre of mass vector at the instant of (swing-)toe off. These findings were related to an abnormal muscular activation pattern mainly characterized by a disruption of the synergistic activity of antagonistic pairs of postural muscles. This study showed that girls with Rett syndrome lack accurate tuning of feedforward control of gait.     

Description and validation of an ECG removal procedure for EMGdi power spectrum analysis

We describe a cross-correlation procedure for removing contaminating electrocardiogram (ECG) complexes from the diaphragmatic electromyogram (EMGdi). First, the operator selects ECG templates from the EMGdi signal during expiratory intervals. Second, these templates are used to locate ECG complexes occurring during inspiratory EMGdi activity. Third, at the point of maximum correlation between the template and these ECG complexes, the template is adjusted in size and offset to "match" the ECG complex, and adjustments are determined by the linear regression coefficients. Finally, the modified template is subtracted from the EMGdi signal. To evaluate our method, we compared the power spectral density (PSD) obtained from processing EMGdi signals by our method with those obtained from the EMGdi signal in which ECG complexes had been removed by gating. Our results indicate that PSD obtained by these two different methods shows no statistically significant differences with respect to the following features: centroid frequency, median frequency, total power, standard deviation, skewness, and kurtosis.     

Computational Modeling of Orientation Tuning Dynamics in Monkey Primary Visual Cortex

In the primate visual pathway, orientation tuning of neurons is first observed in the primary visual cortex. The LGN cells that comprise the thalamic input to V1 are not orientation tuned, but some V1 neurons are quite selective. Two main classes of theoretical models have been offered to explain orientation selectivity: feedforward models, in which inputs from spatially aligned LGN cells are summed together by one cortical neuron; and feedback models, in which an initial weak orientation bias due to convergent LGN input is sharpened and amplified by intracortical feedback. Recent data on the dynamics of orientation tuning, obtained by a cross-correlation technique, may help to distinguish between these classes of models. To test this possibility, we simulated the measurement of orientation tuning dynamics on various receptive field models, including a simple Hubel-Wiesel type feedforward model: a linear spatiotemporal filter followed by an integrate-and-fire spike generator. The computational study reveals that simple feedforward models may account for some aspects of the experimental data but fail to explain many salient features of orientation tuning dynamics in V1 cells. A simple feedback model of interacting cells is also considered. This model is successful in explaining the appearance of Mexican-hat orientation profiles, but other features of the data continue to be unexplained.     

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     

Motor unit recruitment strategies investigated by surface EMG variables.

During isometric contractions of increasing strength, motor units (MUs) are recruited by the central nervous system in an orderly manner starting with the smallest, with muscle fibers that usually show the lowest conduction velocity (CV). Theory predicts that the higher the velocity of propagation of the action potential, the higher the power at high frequencies of the detected surface signal. These considerations suggest that the power spectral density of the surface detected electromyogram (EMG) signal may give indications about the MU recruitment process. The purpose of this paper is to investigate the potential and limitations of spectral analysis of the surface EMG signal as a technique for the investigation of muscle force control. The study is based on a simulation approach and on an experimental investigation of the properties of surface EMG signals detected from the biceps brachii during isometric linearly increasing torque contractions. Both simulation and experimental data indicate that volume conductor properties play an important role as confounding factors that may mask any relation between EMG spectral variables and estimated CV as a size principle parameter during ramp contractions. The correlation between spectral variables and CV is thus significantly lower when the MU pool is not stable than during constant-torque isometric contractions. Our results do not support the establishment of a general relationship between spectral EMG variables and torque or recruitment strategy.     

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.     

Feedback enhances feedforward figure-ground segmentation by changing firing mode

In the visual cortex, feedback projections are conjectured to be crucial in figure-ground segregation. However, the precise function of feedback herein is unclear. Here we tested a hypothetical model of reentrant feedback. We used a previous developed 2-layered feedforward spiking network that is able to segregate figure from ground and included feedback connections. Our computer model data show that without feedback, neurons respond with regular low-frequency (～9 Hz) bursting to a figure-ground stimulus. After including feedback the firing pattern changed into a regular (tonic) spiking pattern. In this state, we found an extra enhancement of figure responses and a further suppression of background responses resulting in a stronger figure-ground signal. Such push-pull effect was confirmed by comparing the figure-ground responses with the responses to a homogenous texture. We propose that feedback controls figure-ground segregation by influencing the neural firing patterns of feedforward projecting neurons.     

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     

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.     

Contextual cues are not unique for motor learning: Task-dependant switching of feedback controllers

The separation of distinct motor memories by contextual cues is a well known and well studied phenomenon of feedforward human motor control. However, there is no clear evidence of such context-induced separation in feedback control. Here we test both experimentally and computationally if context-dependent switching of feedback controllers is possible in the human motor system. Specifically, we probe visuomotor feedback responses of our human participants in two different tasks—stop and hit—and under two different schedules. The first, blocked schedule, is used to measure the behaviour of stop and hit controllers in isolation, showing that it can only be described by two independent controllers with two different sets of control gains. The second, mixed schedule, is then used to compare how such behaviour evolves when participants regularly switch from one task to the other. Our results support our hypothesis that there is contextual switching of feedback controllers, further extending the accumulating evidence of shared features between feedforward and feedback control.     

Secretory process regularity monitors neuroendocrine feedback and feedforward signaling strength in humans

The present experiments examine the neuroregulatory hypothesis that the degree of sample-by-sample regularity of hormone output by an interlinked hypothalamopituitary target-organ system monitors the strength of feedback and/or feedforward signaling. To test this postulate and assess its generality, we implemented a total of nine thematically complementary perturbation experiments. In particular, we altered feedback or feedforward signaling selectively in two distinct neuroendocrine systems; namely, the growth hormone (GH) insulin-like growth factor type I (IGF-I) and the luteinizing hormone-testosterone axes. Four experimental paradigms comprised preferential reduction vs. enhancement of IGF-I or testosterone feedback signal strength; and, conversely, five others entailed selective attenuation vs. augmentation of GH-releasing hormone and gonadotropin-releasing hormone feedforward signal intensity. In these independent interventions, quantitation of subordinate (nonpulsatile) secretory pattern reproducibility via the approximate entropy statistic unmasked salient changes (P values typically <10(-3)) in the conditional regularity of serial hormone output with high consistency (96-100%). In particular, approximate entropy quantified degradation of secretory subpattern orderliness under either muted feedback restraint or heightened feedforward drive. Assuming valid interpretation of the biological constraints imposed, these experimental observations coincide with earlier reductionist mathematical predictions, wherein increased irregularity of coupled parameter output mirrors attenuated feedback and/or augmented feedforward coupling within an integrative system.     

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.