Optimization model predictions for postural coordination modes

Biomechanical optimization and reinforcement learning provide insight into transition from ankle to hip strategy in human postural control

Human postural control strategies, categorized as ankle or hip strategies, adapt to varying perturbation magnitudes and support surface sizes. While numerous studies have characterized these strategies, few have explored the underlying mechanisms driving the transition from ankle to hip strategy. This study investigated whether postural strategy transitions can be explained through an optimization mechanism incorporating biomechanical constraints. We analyzed postural strategy changes in human responses to backward perturbations and developed a reinforcement learning (RL)-based optimization model. The biomechanical constraint was defined as the center of pressure (CoP) range limitation to the metatarsal joint. The control objective function featured a novel CoP constraint penalty, complemented by terms for upright posture recovery and control effort minimization. The RL-based optimization model successfully reproduced the ankle-to-hip strategy transition observed in human postural responses. With increasing perturbation magnitude, the model demonstrated a pattern of limited ankle torque coupled with increased hip joint kinematics, closely aligning with observed human postural adaptations. These results suggest that the adaptive nature of human postural strategy transitions can be understood within an optimization framework incorporating biomechanical constraints. Additionally, this study supports the use of RL models, capable of implementing nonlinear optimization, as a valuable tool for comprehensively analyzing diverse adaptive characteristics in human movement.

Self-organizing neural network for reproducing human postural mode alternation through deep reinforcement learning

A self-organized phenomenon in postural coordination is essential for understanding the auto-switching mechanism of in-phase and anti-phase postural coordination modes during standing and related supra-postural activities. Previously, a model-based approach was proposed to reproduce such self-organized phenomenon. However, if we set this problem including the process of how we establish the internal predictive model in our central nervous system, the learning process is critical to be considered for establishing a neural network for managing adaptive postural control. Particularly when body characteristics may change due to growth or aging or are initially unknown for infants, a learning capability can improve the hyper-adaptivity of human motor control for maintaining postural stability and saving energy in daily living. This study attempted to generate a self-organizing neural network that can adaptively coordinate the postural mode without assuming a prior body model regarding body dynamics and kinematics. Postural coordination modes are reproduced in head-target tracking tasks through a deep reinforcement learning algorithm. The transitions between the postural coordination types, i.e. in-phase and anti-phase coordination modes, could be reproduced by changing the task condition of the head tracking target, by changing the frequencies of the moving target. These modes are considered emergent phenomena existing in human head tracking tasks. Various evaluation indices, such as correlation, and relative phase of hip and ankle joint, are analyzed to verify the self-organizing neural network performance to produce the postural coordination transition between the in-phase and anti-phase modes. In addition, after learning, the neural network can also adapt to continuous task condition changes and even to unlearned body mass conditions keeping consistent in-phase and anti-phase mode alternation.

Reliability and robustness of optimization properties for stabilization of the upright stance as determined using posturography

Diagnostic value of static posturography depends on its methodological features, measurement properties, and on computational methods that extract meaningful information from the postural sway i.e. the center-of-pressure (CoP) displacements. In this study, we assessed the reliability and robustness of the postural system based on the optimization properties of the CoP signal: descending, local and global stability, and convergence. For the analysis, we used CoP data from 146 participants (104 [71%] female, age 46 ± 23 years, body mass index 23.6 ± 3.4 kg/m²) recorded while standing quietly on a foam surface without visual input. Reliability was estimated using the intraclass correlation coefficient from a single (ICC_2,1) and averaged (ICC_2,3) measurements. Robustness was assessed through main and interaction effects for the signal duration (60, 30 s), sampling frequency (100, 50 Hz), and lowpass filtering cutoff frequency (10, 5 Hz). The observed reliability depended on the use of average or single measurements as it was excellent for the stability property (ICC_2,k ≥ 0.772); excellent-to-acceptable (ICC_2,3 ≥ 0.540) or excellent-to-unacceptable (ICC_2,1 ≥ 0.281) for the descending property; and excellent-to-unacceptable (ICC_2,3 > 0.295; ICC_2,1 > 0.122) for the convergence property. Robustness analysis showed large main effects of signal duration (ω² ≤ 0.834, p < 0.001), sampling frequency (ω² ≤ 0.526, p < 0.001), and the lowpass filter cutoff frequency (ω² ≤ 0.523, p < 0.001) on the optimization properties; but all two-way and three-way effects varied from medium to trivial. Reliability is thus excellent to acceptable for deriving the descending, stability, and convergence properties from the average of three measurements. Those optimization properties are robust to the interaction but not the main effects of methodological sources of variation of posturography.

Evidence for subjective values guiding posture and movement coordination in a free-endpoint whole-body reaching task

When moving, humans must overcome intrinsic (body centered) and extrinsic (target-related) redundancy, requiring decisions when selecting one motor solution among several potential ones. During classical reaching studies the position of a salient target determines where the participant should reach, constraining the associated motor decisions. We aimed at investigating implicit variables guiding action selection when faced with the complexity of human-environment interaction. Subjects had to perform whole body reaching movements towards a uniform surface. We observed little variation in the self-chosen motor strategy across repeated trials while movements were variable across subjects being on a continuum from a pure 'knee flexion' associated with a downward center of mass (CoM) displacement to an 'ankle dorsi-flexion' associated with an upward CoM displacement. Two optimality criteria replicated these two strategies: a mix between mechanical energy expenditure and joint smoothness and a minimization of the amount of torques. Our results illustrate the presence of idiosyncratic values guiding posture and movement coordination that can be combined in a flexible manner as a function of context and subject. A first value accounts for the reach efficiency of the movement at the price of selecting possibly unstable postures. The other predicts stable dynamic equilibrium but requires larger energy expenditure and jerk.

Trajectory of human movement during sit to stand: a new modeling approach based on movement decomposition and multi-phase cost function

The purpose of this work is to develop a computational model to describe the task of sit to stand (STS). STS is an important movement skill which is frequently performed in human daily activities, but has rarely been studied from the perspective of optimization principles. In this study, we compared the recorded trajectories of STS with the trajectories generated by several conventional optimization-based models (i.e., minimum torque, minimum torque change and kinetic energy cost models) and also with the trajectories produced by a novel multi-phase cost model (MPCM). In the MPCM, we suggested that any complex task, such as STS, is decomposable into successive motion phases, so that each phase requires a distinct strategy to be performed. In this way, we proposed a multi-phase cost function to describe the STS task. The results revealed that the conventional optimization-based models failed to correctly predict the invariable features of STS, such as hip flexion and ankle dorsiflexion movements. However, the MPCM not only predicted the general features of STS with a sufficient accuracy, but also showed a potential flexibility to distinguish between the movement strategies from one subject to the other. According to the results, it seems plausible to hypothesize that the central nervous system might apply different strategies when planning different phases of a complex task. The application areas of the proposed model could be generating optimized trajectories of STS for clinical applications (such as functional electrical stimulation) or providing clinical and engineering insights to develop more efficient rehabilitation devices and protocols.

Impact of Functional Electrical Stimulation of Lower Limbs during Sitting Pivot Transfer Motion for Paraplegic People

Individuals with Spinal Cord Injury (SCI), perform Sitting Pivot Transfer (SPT) motion around fifteen times a day using upper extremities. It can lead to upper limbs pain and often shoulder complications. In this paper, we investigate the influence of Functional Electrical Stimulation (FES) on SPT motion of a paraplegic person. First, we proposed to develop a dynamic optimization method in order to predict SPT motion of an able-bodied subject. This approach has been validated by comparing the computed SPT trajectories with the ones measured during the experiment with an able-bodied subject. Then, we used the optimization tool to analyze the influence of FES on the SPT maneuver of paraplegic persons. Our results suggest that FES can decrease arm participation during the transfer motion of a paraplegic person.

OPTIMIZATION-BASED DYNAMIC PREDICTION OF HUMAN POSTURAL RESPONSE UNDER TILTING OF BASE OF SUPPORT

The purpose of this paper is to study formulations and computational procedures for prediction of natural human response to tilting of its base of support. The human skeletal structure is modeled as a five-segment, four-degree-of-freedom mechanical system standing on sinusoidally driven tilting platform in the sagittal plane. The problem is formulated based on predictive dynamics method that leads to an optimization problem. The joint torque square is included in the performance measure and the dynamic stability is achieved by satisfying the vertical forces criterion. The constrained nonlinear optimization problem is solved using an algorithm based on the sequential quadratic programming (SQP) approach. The results which are joint trajectories and torques are characterized in terms of two main types of movement strategies observed in humans, namely, the ankle and hip strategies. Moreover, the effect of arms on the stability of the model is studied. The results obtained with the formulation are validated with the experimental data. Simulation results demonstrate the effectiveness of the proposed formulation in prediction of natural motion of human in response to tilting of the base plate.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423-453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem.

Active Control of Bias for the Control of Posture and Movement

Posture and movement are fundamental, intermixed components of motor coordination. Current approaches consider either that 1) movement is an active, anticipatory process and posture is a passive feedback process or 2) movement and posture result from a common passive process. In both cases, the presence of a passive component renders control scarcely robust and stable in the face of transmission delays and low feedback gains. Here we show in a model that posture and movement could result from the same active process: an optimal feedback control that drives the body from its estimated state to its goal in a given (planning) time by acting through muscles on the insertion position (bias) of compliant linkages (tendons). Computer simulations show that iteration of this process in the presence of noise indifferently produces realistic postural sway, fast goal-directed movements, and natural transitions between posture and movement.

Changes in preferred postural patterns following stroke during intentional ankle/hip coordination

We compared the spatio-temporal postural organization between stroke patients and healthy controls in a bipedal standing task where participants had to intentionally produce two specific ankle/hip coordination patterns: in-phase and anti-phase. The pattern to reproduce was visually represented by a ankle-hip Lissajous figure, and a real-time biofeedback displayed the current coordination sur-imposed to the expected coordination. Contrary to the healthy participants who were successful at reproducing the two patterns, stroke patients were unable to produce the in-phase pattern. In addition, when the anti-phase pattern was required, a reduction of stability was observed for the stroke group. The impairment of postural capacities following stroke was thus accompanied by a disappearance of one of the two preferred patterns found in healthy participants, a result that have consequences for understanding the etiology of postural pattern formation and the elaboration of rehabilitation programs.

Neuromechanical tuning of nonlinear postural control dynamics

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

A balance control model of quiet upright stance based on an optimal control strategy

Models of balance control can aid in understanding the mechanisms by which humans maintain balance. A balance control model of quiet upright stance based on an optimal control strategy is presented here. In this model, the human body was represented by a simple single-segment inverted pendulum during upright stance, and the neural controller was assumed to be an optimal controller that generates ankle control torques according to a certain performance criterion. This performance criterion was defined by several physical quantities relevant to sway. In order to accurately simulate existing experimental data, an optimization procedure was used to specify the set of model parameters to minimize the scalar error between experimental and simulated sway measures. Thirty-two independent simulations were performed for both younger and older adults. The model's capabilities, in terms of reflecting sway behaviors and identifying aging effects, were then analyzed based on the simulation results. The model was able to accurately predict center-of-pressure-based sway measures, and identify potential changes in balance control mechanisms caused by aging. Correlations between sway measures and model parameters are also discussed.

On Perturbation and Pattern Coexistence in Postural Coordination Dynamics

In studies of postural control, investigators have used either experimentally induced perturbations to stance or unperturbed stance. The distinction between perturbed and unperturbed stance has gained renewed importance in the context of inphase and antiphase coordination of the hips and ankles. Several contributions have replicated the findings published over the past decade, suggesting the possibility of a unified view of postural control. However, any proposed unified view depends on how so called perturbed and unperturbed are defined. The authors argue that, to date, there is no explicit and general definition of those terms. The main reason is that all perturbations are relative and depend on appropriate frames of reference for perception and action. Arguments about empirical or theoretical unification of perturbed and unperturbed stance are premature.

Effects of plantar flexor muscle fatigue induced by electromyostimulation on postural coordination

The aim of the present study was to investigate the influence of a modification of an intrinsic capacity (plantar flexor strength) on the implementation of in-phase and anti-phase mode of coordination. Analysis of hip and ankle relative phases during fore-aft tracking task was done before and after an electromyostimulation fatigue protocol on the soleus muscles. Results showed participants used exclusively in-phase and anti-phase modes of coordination, with a sudden switch from one to the other with target frequency increase. Regarding tracking tasks, fatigue induces a decrease of performance for lower frequencies, and a significant decrease of switch frequency (-0.08 Hz) for each subject. In conclusion, changes in mode of coordination implementation suggest that the in-phase mode implementation is highly linked to the strength production capacity at the ankle joint.

Postural coordination modes and transition: dynamical explanations

While research to date has been successful in quantifying postural behaviour, this paper examines the causes of transition between postural coordination mode using dynamical variables and, by inference, efficient control strategies underlying postural behaviour. To this end, six subjects in bipedal stance were instructed to maintain a constant distance between their head and a visual target that oscillated along the line of sight. Within sessions, participants were exposed to gradual changes in increasing target motion frequency. Kinematic results showed a sudden transition between in-phase and anti-phase postural coordination modes in visual target tracking. The dynamical analysis pointed out that (1) the center of pressure (CoP) position parameter is a crucial parameter in the determination of the adopted coordination mode, (2) the change occurred in response to limits bordered by the system: the interaction between equilibrium constraints (A/P displacements of CoP), physiological limits (net joint moments) support the emergence of different postural behaviours and, (3) finally, the anti-phase mode presents a better distribution of muscular moment between hip and ankle joints and is more effective to achieve high frequency oscillations with limited CoP displacements.