Balancing with reflex delay

Torque modulation mechanism of the knee joint during balance recovery

Exploring the torque modulation mechanisms of human joints is critical for analyzing the human balance control system and developing natural human-machine interactions for balance support. However, the knee joint is often overlooked in biomechanical models because of its limited range of motion during balance recovery. This poses a challenge in establishing mathematical models for the knee joint's torque modulation mechanisms using computer simulations based on the inverted pendulum model. This study aims to provide a simplified linear feedback model inspired by sensorimotor transformation theory to reveal the torque modulation mechanism of the knee joint. The model was validated using data from experiments involving support-surface translation perturbations. The goodness-of-fit metrics of the model, including R2 values and root mean square errors (RMSE), demonstrated strong explanatory power (R2 ranged from 0.77 to 0.90) and low error (RMSE ranging from 0.035 to 0.072) across different perturbation magnitudes and directions. Through pooling samples across various perturbation conditions and conducting multiple fits, this model revealed that knee torque is modulated using a direction-specific strategy with adaptable feedback gains. These results suggest that the proposed simplified linear model can be used to develop assistive systems and retrieve insights on balance recovery mechanisms.

Associative anticipatory learning and control of the cerebellar cortex based on the spike-timing-dependent plasticity of the parallel fiber-Purkinje cell synapses

Time delays are inevitable in the neural processing of sensorimotor systems; small delays can cause severe damage to movement accuracy and stability. It is strongly suggested that the cerebellum compensates for delays in neural signal processing and performs predictive control. Neural computational theories have explored concepts of the internal models of control objects-believed to avoid delays by providing internal feedback information-although there has been no clear relevance to neural processing. The timing-dependent plasticity of parallel fiber-Purkinje cell synapses is well known. The long-term depression of the synapse is observed when parallel fiber activation precedes climbing fiber activation within -50-300 ms, and is the greatest within 50-200 ms. This paper presents a theory that this temporal difference of 50-200 ms is the basis for an associative anticipation of as many milliseconds. Associative learning can theoretically connect an input signal to a desired signal; therefore, a 50-200 ms earlier input signal can be connected to a desired output signal through temporary asymmetric plasticity. After learning is completed, an input signal generates a desired output signal that appears 50-200 ms later. For the associative learning of temporally continuous signals, this study integrates the universal function approximation capability of the cerebellar cortex model and temporally asymmetric synaptic plasticity to create the theory of associative anticipatory learning of the cerebellum. The effective motor control of this learning is demonstrated by adaptively stabilizing an inverted pendulum with a delay similar to that done by humans.

Slacklining: A narrative review on the origins, neuromechanical models and therapeutic use

Slacklining, the neuromechanical action of balance retention on a tightened band, is achieved through self-learned strategies combining dynamic stability with optimal energy expenditure. Published slacklining literature is recent and limited, including for neuromechanical control strategy models. This paper explores slacklining's definitions and origins to provide background that facilitates understanding its evolution and progressive incorporation into both prehabilitation and rehabilitation. Existing explanatory slacklining models are considered, their application to balance and stability, and knowledge-gaps highlighted. Current slacklining models predominantly derive from human quiet-standing and frontal plane movement on stable surfaces. These provide a multi-tiered context of the unique and complex neuro-motoric requirements for slacklining's multiple applications, but are not sufficiently comprehensive. This consequently leaves an incomplete understanding of how slacklining is achieved, in relation to multi-directional instability and complex multi-dimensional human movement and behavior. This paper highlights the knowledge-gaps and sets a foundation for the required explanatory control mechanisms that evolve and expand a more detailed model of multi-dimensional slacklining and human functional movement. Such a model facilitates a more complete understanding of existing performance and rehabilitation applications that opens the potential for future applications into broader areas of movement in diverse fields including prostheses, automation and machine-learning related to movement phenotypes.

Slacklining: An explanatory multi-dimensional model considering classical mechanics, biopsychosocial health and time

This paper aims to overcome slacklining's limited formulated explanatory models. Slacklining is an activity with increasing recreational use, but also has progressive adoption into prehabilitation and rehabilitation. Slacklining is achieved through self-learned strategies that optimize energy expenditure without conceding dynamic stability, during the neuromechanical action of balance retention on a tightened band. Evolved from rope-walking or 'Funambulus', slacklining has an extensive history, yet limited and only recent published research, particularly for clinical interventions and in-depth hypothesized multi-dimensional models describing the neuromechanical control strategies. These 'knowledge-gaps' can be overcome by providing an, explanatory model, that evolves and progresses existing standards, and explains the broader circumstances of slacklining's use. This model details the individual's capacity to employ control strategies that achieve stability, functional movement and progressive technical ability. The model considers contributing entities derived from: Self-learned control of movement patterns; subjected to classical mechanical forces governed by Newton's physical laws; influenced by biopsychosocial health factors; and within time's multi-faceted perspectives, including as a quantified unit and as a spatial and cortical experience. Consequently, specific patient and situational uses may be initiated within the framework of evidence based medicine that ensures a multi-tiered context of slacklining applications in movement, balance and stability. Further research is required to investigate and mathematically define this proposed model and potentially enable an improved understanding of human functional movement. This will include its application in other diverse constructed and mechanical applications in varied environments, automation levels, robotics, mechatronics and artificial-intelligence factors, including machine learning related to movement phenotypes and applications.

The influence of parametric and external noise in act-and-wait control with delayed feedback

We apply several novel semi-analytic approaches for characterizing and calculating the effects of noise in a system with act-and-wait control. For concrete illustration, we apply these to a canonical balance model for an inverted pendulum to study the combined effect of delay and noise within the act-and-wait setting. While the act-and-wait control facilitates strong stabilization through deadbeat control, a comparison of different models with continuous vs. discrete updating of the control strategy in the active period illustrates how delays combined with the imprecise application of the control can seriously degrade the performance. We give several novel analyses of a generalized act-and-wait control strategy, allowing flexibility in the updating of the control strategy, in order to understand the sensitivities to delays and random fluctuations. In both the deterministic and stochastic settings, we give analytical and semi-analytical results that characterize and quantify the dynamics of the system. These results include the size and shape of stability regions, densities for the critical eigenvalues that capture the rate of reaching the desired stable equilibrium, and amplification factors for sustained fluctuations in the context of external noise. They also provide the dependence of these quantities on the length of the delay and the active period. In particular, we see that the combined influence of delay, parametric error, or external noise and on-off control can qualitatively change the dynamics, thus reducing the robustness of the control strategy. We also capture the dependence on how frequently the control is updated, allowing an interpolation between continuous and frequent updating. In addition to providing insights for these specific models, the methods we propose are generalizable to other settings with noise, delay, and on-off control, where analytical techniques are otherwise severely scarce.

Changes in balance coordination and transfer to an unlearned balance task after slackline training: a self-organizing map analysis

How humans maintain balance and change postural control due to age, injury, immobility or training is one of the basic questions in motor control. One of the problems in understanding postural control is the large set of degrees of freedom in the human motor system. Therefore, a self-organizing map (SOM), a type of artificial neural network, was used in the present study to extract and visualize information about high-dimensional balance strategies before and after a 6-week slackline training intervention. Thirteen subjects performed a flamingo and slackline balance task before and after the training while full body kinematics were measured. Range of motion, velocity and frequency of the center of mass and joint angles from the pelvis, trunk and lower leg (45 variables) were calculated and subsequently analyzed with an SOM. Subjects increased their standing time significantly on the flamingo (average +2.93 s, Cohen's d = 1.04) and slackline (+9.55 s, d = 3.28) tasks, but the effect size was more than three times larger in the slackline. The SOM analysis, followed by a k-means clustering and marginal homogeneity test, showed that the balance coordination pattern was significantly different between pre- and post-test for the slackline task only (χ ² = 82.247; p < 0.001). The shift in balance coordination on the slackline could be characterized by an increase in range of motion and a decrease in velocity and frequency in nearly all degrees of freedom simultaneously. The observation of low transfer of coordination strategies to the flamingo task adds further evidence for the task-specificity principle of balance training, meaning that slackline training alone will be insufficient to increase postural control in other challenging situations.

Learning an intermittent control strategy for postural balancing using an EMG-based human-computer interface

It has been considered that the brain stabilizes unstable body dynamics by regulating co-activation levels of antagonist muscles. Here we critically reexamined this established theory of impedance control in a postural balancing task using a novel EMG-based human-computer interface, in which subjects were asked to balance a virtual inverted pendulum using visual feedback information on the pendulum's position. The pendulum was actuated by a pair of antagonist joint torques determined in real-time by activations of the corresponding pair of antagonist ankle muscles of subjects standing upright. This motor-task raises a frustrated environment; a large feedback time delay in the sensorimotor loop, as a source of instability, might favor adopting the non-reactive, preprogrammed impedance control, but the ankle muscles are relatively hard to co-activate, which hinders subjects from adopting the impedance control. This study aimed at discovering how experimental subjects resolved this frustrated environment through motor learning. One third of subjects adapted to the balancing task in a way of the impedance-like control. It was remarkable, however, that the majority of subjects did not adopt the impedance control. Instead, they acquired a smart and energetically efficient strategy, in which two muscles were inactivated simultaneously at a sequence of optimal timings, leading to intermittent appearance of periods of time during which the pendulum was not actively actuated. Characterizations of muscle inactivations and the pendulum¡Çs sway showed that the strategy adopted by those subjects was a type of intermittent control that utilizes a stable manifold of saddle-type unstable upright equilibrium that appeared in the state space of the pendulum when the active actuation was turned off.

Balancing on tightropes and slacklines

Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.

Stability in a frontal plane model of balance requires coupled changes to postural configuration and neural feedback control

Postural stability depends on interactions between the musculoskeletal system and neural control mechanisms. We present a frontal plane model stabilized by delayed feedback to analyze the effects of altered stance width on postural responses to perturbations. We hypothesized that changing stance width alters the mechanical dynamics of the body and limits the range of delayed feedback gains that produce stable postural behaviors. Surprisingly, mechanical stability was found to decrease as stance width increased due to decreased effective inertia. Furthermore, due to sensorimotor delays and increased leverage of hip joint torque on center-of-mass motion, the magnitudes of the stabilizing delayed feedback gains decreased as stance width increased. Moreover, the ranges of the stable feedback gains were nonoverlapping across different stance widths such that using a single neural feedback control strategy at both narrow and wide stances could lead to instability. The set of stable feedback gains was further reduced by constraints on foot lift-off and perturbation magnitude. Simulations were fit to experimentally measured kinematics, and the identified feedback gains corroborated model predictions. In addition, analytical gain margin of the linearized system was found to predict step transitions without the need for simulation. In conclusion, this model offers a method to dissociate the complex interactions between postural configuration, delayed sensorimotor feedback, and nonlinear foot lift-off constraints. The model demonstrates that stability at wide stances can only be achieved if delayed neural feedback gains decrease. This model may be useful in explaining both expected and paradoxical changes in stance width in healthy and neurologically impaired individuals.

Human strategies in balancing an inverted pendulum with time delay

The strategy of human manual control is investigated in balancing an inverted pendulum under time-delay constraints. Experiments show that as the task becomes more difficult due to the increase in time delay, the human operator adopts a more discrete-like strategy. Interpretation of the discrete-control mechanism is provided by relating the observed human responses with a human-performance model.

The time-delayed inverted pendulum: implications for human balance control

The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: (1) mechanical inverted time-delayed pendulum, (2) stick balancing at the fingertip, and (3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is for the time delay to make a corrective movement, tau(n), be greater than a critical delay tau(c) that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty of controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations ("noise") suggest that neural control for the upright position likely resembles an adaptive-type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when theta exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.

Balancing with positive feedback: the case for discontinuous control

Experimental observations indicate that positive feedback plays an important role for maintaining human balance in the upright position. This observation is used to motivate an investigation of a simple switch-like controller for postural sway in which corrective movements are made only when the vertical displacement angle exceeds a certain threshold. This mechanism is shown to be consistent with the experimentally observed variations in the two-point correlation for human postural sway. Analysis of first-passage times for this model suggests that this control strategy may slow escape by taking advantage of two intrinsic properties of a stochastic unstable first-order delay differential equation: (i) time delay and (ii) the possibility that the dynamics can be 'temporarily confined' near the origin.

Delay effects in the human sensory system during balancing

Mechanical models of human self-balancing often use the Newtonian equations of inverted pendula. While these mathematical models are precise enough on the mechanical side, the ways humans balance themselves are still quite unexplored on the control side. Time delays in the sensory and motoric neural pathways give essential limitations to the stabilization of the human body as a multiple inverted pendulum. The sensory systems supporting each other provide the necessary signals for these control tasks; but the more complicated the system is, the larger delay is introduced. Human ageing as well as our actual physical and mental state affects the time delays in the neural system, and the mechanical structure of the human body also changes in a large range during our lives. The human balancing organ, the labyrinth, and the vision system essentially adapted to these relatively large time delays and parameter regions occurring during balancing. The analytical study of the simplified large-scale time-delayed models of balancing provides a Newtonian insight into the functioning of these organs that may also serve as a basis to support theories and hypotheses on balancing and vision.

On-off intermittency in a human balancing task

Motion analysis in three dimensions demonstrate that the fluctuations in the vertical displacement angle of a stick balanced at the fingertip obey a scaling law characteristic of on-off intermittency and that >98% of the corrective movements occur fast compared to the measured time delay. These experimental observations are reproduced by a model for an inverted pendulum with time-delayed feedback in which parametric noise forces a control parameter across a particular stability boundary. Our observations suggest that parametric noise is an essential, but up until now underemphasized, component of the neural control of balance.