A Sensitivity Analysis of an Inverted Pendulum Balance Control Model

The role of torque feedback in standing balance

It has been proposed that sensory force/pressure cues are integrated within a positive feedback mechanism, which accounts for the slow dynamics of human standing behavior and helps align the body with gravity. However, experimental evidence of this mechanism remains scarce. This study tested predictions of a positive torque feedback mechanism for standing balance, specifically that differences between a "reference" torque and actual torque are self-amplified, causing the system to generate additional torque. Seventeen healthy young adults were positioned in an apparatus that permitted normal sway at the ankle until a brake on the apparatus was applied, discreetly "locking" body movement during stance. Once locked, a platform positioned under the apparatus remained in place (0 mm) or slowly translated backward (3 mm or 6 mm), tilting subjects forward. Postural behavior was characterized by two distinct responses: the center of pressure (COP) offset (i.e., change in COP elicited by the surface translation) and the COP drift (i.e., change in COP during the sustained tilt). Model simulations were performed using a linear balance control model containing torque feedback to provide a conceptual basis for the interpretation of experimental results. Holding the body in sustained tilt positions resulted in COP drifting behavior, reflecting attempts of the balance control system to restore an upright position through increases in plantar flexor torque. In line with predictions of positive torque feedback, larger COP offsets led to faster increases in COP over time. These findings provide experimental support for a positive torque feedback mechanism involved in the control of standing balance.NEW & NOTEWORTHY Using model simulations and a novel experimental approach, we tested behavioral predictions of a sensory torque feedback mechanism involved in the control of upright standing. Torque feedback is thought to reduce the effort required to stand and play a functional role in slowly aligning the body with gravity. Our results provide experimental evidence of a torque feedback mechanism and offer new and valuable insights into the sensorimotor control of human balance.

Posturographic Standards for Optimal Control of Human Standing Posture

Static posturography is a simple non-invasive technique commonly used in contemporary labs and clinics to quantify the central nervous system adaptive mechanisms involved in the control of posture and balance. Its diagnostic value, however, is quite limited due to the lack of posturographic standards for stable posture. To solve this problem, in this research, we aimed to establish reference values for the stable human posture using our novel parameters of static posturography including the sway anteroposterior directional index (DIAP), the mediolateral directional index (DIML), the stability vector amplitude (SVamp), and the stability vector azimuth (SVaz). Towards this end, in a population of young (mean age 22 yrs), healthy able-bodied volunteers (50 males and 50 females), trajectories of postural sway, based upon the center-of-pressure (COP), were assessed. The experiment consisted of ten 60s trials that were carried out 5 times while subjects were standing quietly on the force plate with eyes open (EO test) and 5 times with eyes closed (EC test). Results showed that in young healthy subjects, regardless of gender, the basic variables of COP remained at the following levels: SVamp = 9.2 ± 1.6 mm/s, SVaz = 0.9 ± 0.1 rad, and directional indices DIAP = 0.7 ± 0.05, DIML = 0.56 ± 0.06. Some of the measures were sensitive to visual input (EC trials) and showed a weak to moderate correlation with anthropometric features. These measures can be recommended as reference values that characterize the most stable erect posture.

Optimal controllers resembling postural sway during upright stance

The human postural control system can maintain our balance in an upright stance. A simplified control model that can mimic the mechanisms of this complex system and adapt to the changes due to aging and injuries is a significant problem that can be used in clinical applications. While the Intermittent Proportional Derivative (IPD) is commonly used as a postural sway model in the upright stance, it does not consider the predictability and adaptability behavior of the human postural control system and the physical limitations of the human musculoskeletal system. In this article, we studied the methods based on optimization algorithms that can mimic the performance of the postural sway controller in the upright stance. First, we compared three optimal methods (Model Predictive Control (MPC), COP-Based Controller (COP-BC) and Momentum-Based Controller (MBC)) in simulation by considering a feedback structure of the dynamic of the skeletal body as a double link inverted pendulum while taking into account sensory noise and neurological time delay. Second, we evaluated the validity of these methods by the postural sway data of ten subjects in quiet stance trials. The results revealed that the optimal methods could mimic the postural sway with higher accuracy and less energy consumption in the joints compared to the IPD method. Among optimal approaches, COP-BC and MPC show promising results to mimic the human postural sway. The choice of controller weights and parameters is a trade-off between the consumption of energy in the joints and the prediction accuracy. Therefore, the capability and (dis)advantage of each method reviewed in this article can navigate the usage of each controller in different applications of postural sway, from clinical assessments to robotic applications.

Change in task conditions leads to changes in intermittency in intermittent feedback control employed by CNS in control of human stance

Event-driven intermittent feedback control is a form of feedback control in which the corrective control action is only initiated intermittently when the variables of interest exceed certain threshold criteria. It has been reported in the literature that the CNS uses an event-driven intermittent control strategy to stabilize the human upright posture. However, whether the threshold criteria may change under different postural task conditions is not yet well understood. We employ a numerical study with inverted pendulum models and an experimental study with 51 young healthy individuals (13 females and 38 males; age: 27.8 ± 6.5 years) with stabilogram-diffusion, temporal and spectral analysis applied to COP (Center of Pressure) trajectories measured from these experiments to examine this aspect. The present study provides compelling evidence that inducing a natural arm swing during quiet stance appears to lead to higher sensory dead zone in neuronal control reflecting higher intermittency thresholds in active feedback control and a corresponding lower sensory dependence. Beyond the obvious scientific interest in understanding this aspect of how CNS controls the standing posture, an investigation of the said control strategy may subsequently help uncover insights about how control of quiet stance degrades with age and in diseased conditions. Additionally, such an understanding will also be of interest to the humanoid robotics community as it may lead to insights leading to improving control strategies for posture control in robots.

Response to perturbation during quiet standing resembles delayed state feedback optimized for performance and robustness

Postural sway is a result of a complex action–reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the response to large enough perturbations during quiet standing such that the resulting responses can clearly be distinguished from the local postural sway. Measurements show that typical responses very closely resemble those of a critically damped oscillator. The recovery dynamics are modelled by an inverted pendulum subject to delayed state feedback and is described in the space of the control parameters. We hypothesize that the control gains are tuned such that (H1) the response is at the border of oscillatory and nonoscillatory motion similarly to the critically damped oscillator; (H2) the response is the fastest possible; (H3) the response is a result of a combined optimization of fast response and robustness to sensory perturbations. Parameter fitting shows that H1 and H3 are accepted while H2 is rejected. Thus, the responses of human postural balance to “large” perturbations matches a delayed feedback mechanism that is optimized for a combination of performance and robustness.

Rolling balance board of adjustable geometry as a tool to assess balancing skill and to estimate reaction time delay

The relation between balancing performance and reaction time is investigated for human subjects balancing on rolling balance board of adjustable physical parameters: adjustable rolling radius R and adjustable board elevation h. A well-defined measure of balancing performance is whether a subject can or cannot balance on balance board with a given geometry (R, h). The balancing ability is linked to the stabilizability of the underlying two-degree-of-freedom mechanical model subject to a delayed proportional-derivative feedback control. Although different sensory perceptions involve different reaction times at different hierarchical feedback loops, their effect is modelled as a single lumped reaction time delay. Stabilizability is investigated in terms of the time delay in the mechanical model: if the delay is larger than a critical value (critical delay), then no stabilizing feedback control exists. Series of balancing trials by 15 human subjects show that it is more difficult to balance on balance board configuration associated with smaller critical delay, than on balance boards associated with larger critical delay. Experiments verify the feature of the mechanical model that a change in the rolling radius R results in larger change in the difficulty of the task than the same change in the board elevation h does. The rolling balance board characterized by the two well-defined parameters R and h can therefore be a useful device to assess human balancing skill and to estimate the corresponding lumped reaction time delay.

The effects of sensory quantization and control torque saturation on human balance control

The effect of reaction delay, temporal sampling, sensory quantization, and control torque saturation is investigated numerically for a single-degree-of-freedom model of postural sway with respect to stability, stabilizability, and control effort. It is known that reaction delay has a destabilizing effect on the balancing process: the later one reacts to a perturbation, the larger the possibility of falling. If the delay is larger than a critical value, then stabilization is not even possible. In contrast, numerical analysis showed that quantization and control torque saturation have a stabilizing effect: the region of stabilizing control gains is greater than that of the linear model. Control torque saturation allows the application of larger control gains without overcontrol while sensory quantization plays a role of a kind of filter when sensory noise is present. These beneficial effects are reflected in the energy demand of the control process. On the other hand, neither control torque saturation nor sensory quantization improves stabilizability properties. In particular, the critical delay cannot be increased by adding saturation and/or sensory quantization.

Revisiting the Instrumented Romberg Test: Can Today's Technology Offer a Risk-of-Fall Screening Device for Senior Citizens? An Experience-Based Approach

Risk of fall (ROF) is a worldwide major concern for its prevalence and consequent dramatic outcomes in the elderly population. The growing age-related risk appears to be associated with increasing motor, sensory, and cognitive problems in the elderly population. There is a consensus on the need to screen for these balance dysfunctions, but the available methods are largely based on subjectively assessed performances. The instrumented Romberg test using a force plate represents a validated assessment process for the evaluation of balance performances. The purpose of this study is to propose an innovative instrumental method to identify balance deficits, assess their severity, and give an automated indication of the most likely etiology. The proposed new method was applied to the instrumented Romberg test, using force plate data recorded in a cohort of 551 females aged >65 participating in adapted physical activity courses. The method allowed us to identify 145 dysfunctional subjects and to determine the likely origin of their deficit: 21 central, 5 vestibular, 9 visual, 59 proprioceptive (musculoskeletal etiology), and 51 functional. Based on the preliminary findings of the study, this test could be an efficient and cost-effective mass screening tool for identifying subjects at risk of fall, since the procedure proves to be rapid, non-invasive, and apparently devoid of any contraindications.

Postural instability via a loss of intermittent control in elderly and patients with Parkinson's disease: A model-based and data-driven approach

Postural instability is one of the major symptoms of Parkinson's disease. Here, we assimilated a model of intermittent delay feedback control during quiet standing into postural sway data from healthy young and elderly individuals as well as patients with Parkinson's disease to elucidate the possible mechanisms of instability. Specifically, we estimated the joint probability distribution of a set of parameters in the model using the Bayesian parameter inference such that the model with the inferred parameters can best-fit sway data for each individual. It was expected that the parameter values for three populations would distribute differently in the parameter space depending on their balance capability. Because the intermittent control model is parameterized by a parameter associated with the degree of intermittency in the control, it can represent not only the intermittent model but also the traditional continuous control model with no intermittency. We showed that the inferred parameter values for the three groups of individuals are classified into two major groups in the parameter space: one represents the intermittent control mostly for healthy people and patients with mild postural symptoms and the other the continuous control mostly for some elderly and patients with severe postural symptoms. The results of this study may be interpreted by postulating that increased postural instability in most Parkinson's patients and some elderly persons might be characterized as a dynamical disease.

Human motor control: Is a subject-specific quantitative assessment of its multiple characteristics possible? A demonstrative application on children motor development

In synergy with the musculoskeletal system, motor control is responsible of motor performance, determining joint kinematics and kinetics as related to task and environmental constraints. Multiple metrics have been proposed to quantify motor control from kinematic measures of motion, each index quantifying a different specific aspect, but the characterization of motor control as related to a specific subject or population during the execution of a specific task is still missing. In the present work, the performance of a novel approach for quantitative parametrization of motor control is tested over 86 primary school children: 36 I grade, 50 II grade; 40 females, 46 males. Children were assessed performing natural and tandem gait using 3 inertial measurement units, and gait variability, regularity, and complexity indexes were calculated from gait temporal parameters and trunk acceleration. Standard Test of Motor Competence and Developmental Coordination Disorder Questionnaire were used to assess reference motor competence. The proposed set of parameters allowed to discriminate the level of motor competence as related to age and standardised scales, while differences related to sex resulted negligible. The proposed method can effectively integrate musculoskeletal dynamic models, allowing the parametric characterization of motor control of specific subjects and/or populations.

Optimal time-varying postural control in a single-link neuromechanical model with feedback latencies

Maintaining balance during quiet standing is a challenging task for the neural control mechanisms due to the inherent instabilities involved in the task. The feedback latencies and the lowpass characteristics of skeletal muscle add to the difficulty of regulating postural dynamics in real-time. Inverted-pendulum (IP) type robotic models have served as a popular paradigm to investigate control of postural balance. In this study, an in-depth neuromechanical postural control model is developed from physiological principles. The model comprises a single-segment IP robotic model, Hill-type muscle model, and proprioceptive feedback from the muscle spindle (MS) and golgi tendon organ (GTO). An optimal proportional-integral-derivative (PID) controller is proposed to realize effective postural control amid latencies in sensory feedback. The neural commands for postural stabilization are generated by a time-varying PID controller, tuned using linear quadratic regulator (LQR) principles. Computer simulations are used to assess the efficacy of the tuned PID-LQR controller. Sensitivity analysis of the controlled system shows a delay tolerance of 300ms. Preliminary empirical data in support of the mathematical model were obtained from perturbation experiments. The model response to perturbation torque, measured in terms of the center of mass (COM) excursion in the anterior-posterior (AP) direction, displays a high degree of correlation with the empirical data ([Formula: see text]).

Reductions in body sway responses to a rhythmic support surface tilt perturbation can be caused by other mechanisms than prediction

Studies investigating balance control often use external perturbations to probe the system. These perturbations can be administered as randomized, pseudo-randomized, or predictable sequences. As predictability of a given perturbation can affect balance performance, the way those perturbations are constructed may affect the results of the experiments. In the present study, we hypothesized that subjects are able to adapt to short, rhythmic support surface tilt stimuli, but not to long pseudo-random stimuli. 19 subjects were standing with eyes closed on a servo-controlled platform tilting about the ankle joint axis. Pre and post to the learning intervention, pseudo-random tilt sequences were applied. For the learning phase, a rhythmic and easy-to-memorize 8-s long sequence was applied 75 times, where subjects were instructed to stand as still as possible. Body kinematics were measured and whole body center of mass sway was analyzed. Results showed reduced sway and less forward lean of the body across the learning phase. The sway reductions were similar for stimulus and non-stimulus frequencies. Surprisingly, for the pseudo-random sequences, comparable changes were found from pre- to post-tests. In summary, results confirmed that considerable adaptations exist when exposing subjects to an 8-s long rhythmic perturbation. No indications of predictions of the learning tilt sequence were found, since similar changes were also observed in response to pseudo-random sequences. We conclude that changes in body sway responses following 75 repetitions of an 8-s long rhythmic tilt sequence are due to adaptations in the dynamics of the control mechanism (presumably stiffness).

Acting together, destabilizing influences can stabilize human balance

The causes of falling in the elderly are multi-factorial. Three factors that influence balance stability are the time delay, a sensory dead zone and the maximum ankle torque that can be generated by muscular contraction. Here, the effects of these contributions are evaluated in the context of a model of an inverted pendulum stabilized by time-delayed proportional-derivative (PD) feedback. The effect of the sensory dead zone is to produce a hybrid type of control in which the PD feedback is switched ON or OFF depending on whether or not the controlled variable is larger or smaller than the detection threshold, Π. It is shown that, as Π increases, the region in the plane of control parameters where the balance time (BT) is greater than 60 s is increased slightly. However, when maximum ankle torque is also limited, there is a dramatic increase in the parameter region associated with BTs greater than 60 s. This increase is due to the effects of a torque limitation on over-control associated with bang-bang type switching controllers. These observations show that acting together influences, which are typically thought to destabilize balance, can actually stabilize balance. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Implementation of a Central Sensorimotor Integration Test for Characterization of Human Balance Control During Stance

Balance during stance is regulated by active control mechanisms that continuously estimate body motion, via a "sensory integration" mechanism, and generate corrective actions, via a "sensory-to-motor transformation" mechanism. The balance control system can be modeled as a closed-loop feedback control system for which appropriate system identification methods are available to separately quantify the sensory integration and sensory-to-motor components of the system. A detailed, functionally meaningful characterization of balance control mechanisms has potential to improve clinical assessment and to provide useful tools for answering clinical research questions. However, many researchers and clinicians do not have the background to develop systems and methods appropriate for performing identification of balance control mechanisms. The purpose of this report is to provide detailed information on how to perform what we refer to as "central sensorimotor integration" (CSMI) tests on a commercially available balance test device (SMART EquiTest CRS, Natus Medical Inc, Seattle WA) and then to appropriately analyze and interpret results obtained from these tests. We describe methods to (1) generate pseudorandom stimuli that apply cyclically-repeated rotations of the stance surface and/or visual surround (2) measure and calibrate center-of-mass (CoM) body sway, (3) calculate frequency response functions (FRFs) that quantify the dynamic characteristics of stimulus-evoked CoM sway, (4) estimate balance control parameters that quantify sensory integration by measuring the relative contribution of different sensory systems to balance control (i.e., sensory weights), and (5) estimate balance control parameters that quantify sensory-to-motor transformation properties (i.e., feedback time delay and neural controller stiffness and damping parameters). Additionally, we present CSMI test results from 40 subjects (age range 21-59 years) with normal sensory function, 2 subjects with results illustrating deviations from normal balance function, and we summarize results from previous studies in subjects with vestibular deficits. A bootstrap analysis was used to characterize confidence limits on parameters from CSMI tests and to determine how test duration affected the confidence with which parameters can be measured. Finally, example results are presented that illustrate how various sensory and central balance deficits are revealed by CSMI testing.

Microchaos in human postural balance: Sensory dead zones and sampled time-delayed feedback

Models for the stabilization of an inverted pendulum figure prominently in studies of human balance control. Surprisingly, fluctuations in measures related to the vertical displacement angle for quietly standing adults with eyes closed exhibit chaos. Here we show that small-amplitude chaotic fluctuations ("microchaos") can be generated by the interplay between three essential components of human neural balance control, namely time-delayed feedback, a sensory dead zone, and frequency-dependent encoding of force. When the sampling frequency of the force encoding is decreased, the sensitivity of the balance control to changes in the initial conditions increases. The sampled, time-delayed nature of the balance control may provide insights into why falls are more common in the very young and the elderly.