Direct estimation of the parameters of a delayed, intermittent activation feedback model of postural sway during quiet standing

Time-delay estimation in biomechanical stability: a scoping review

Despite its high-level of robustness and versatility, the human sensorimotor control system regularly encounters and manages various noises, non-linearities, uncertainties, redundancies, and delays. These delays, which are critical to biomechanical stability, occur in various parts of the system and include sensory, signal transmission, CNS processing, as well as muscle activation delays. Despite the relevance of accurate estimation and prediction of the various time delays, the current literature reflects major discrepancy with regards to existing prediction and estimation methods. This scoping review was conducted with the aim of characterizing and categorizing various approaches for estimation of physiological time delays based on PRISMA guidelines. Five data bases (EMBASE, PubMed, Scopus, IEEE and Web of Science) were consulted between the years of 2000 and 2022, with a combination of four related categories of keywords. Scientific articles estimating at least one physiological time delay, experimentally or through simulations, were included. Eventually, 46 articles were identified and analyzed with 20 quantification and 16 qualification questions by two separate reviewers. Overall, the reviewed studies, experimental and analytical, employing both linear and non-linear models, reflected heterogeneity in the definition of time delay and demonstrated high variability in experimental protocols as well as the estimation of delay values. Most of the summarized articles were classified in the high-quality category, where multiple sound analytical approaches, including optimization, regression, Kalman filter and neural network in time domain or frequency domain were used. Importantly, more than 50% of the reviewed articles did not clearly define the nature of the estimated delays. This review presents and summarizes these issues and calls for a standardization of future scientific works for estimation of physiological time-delay.

Sensorimotor Time Delay Estimation by EMG Signal Processing in People Living with Spinal Cord Injury

Neuro mechanical time delay is inevitable in the sensorimotor control of the body due to sensory, transmission, signal processing and muscle activation delays. In essence, time delay reduces stabilization efficiency, leading to system instability (e.g., falls). For this reason, estimation of time delay in patients such as people living with spinal cord injury (SCI) can help therapists and biomechanics to design more appropriate exercise or assistive technologies in the rehabilitation procedure. In this study, we aim to estimate the muscle onset activation in SCI people by four strategies on EMG data. Seven complete SCI individuals participated in this study, and they maintained their stability during seated balance after a mechanical perturbation exerting at the level of the third thoracic vertebra between the scapulas. EMG activity of eight upper limb muscles were recorded during the stability. Two strategies based on the simple filtering (first strategy) approach and TKEO technique (second strategy) in the time domain and two other approaches of cepstral analysis (third strategy) and power spectrum (fourth strategy) in the time-frequency domain were performed in order to estimate the muscle onset. The results demonstrated that the TKEO technique could efficiently remove the electrocardiogram (ECG) and motion artifacts compared with the simple classical filtering approach. However, the first and second strategies failed to find muscle onset in several trials, which shows the weakness of these two strategies. The time-frequency techniques (cepstral analysis and power spectrum) estimated longer activation onset compared with the other two strategies in the time domain, which we associate with lower-frequency movement in the maintaining of sitting stability. In addition, no correlation was found for the muscle activation sequence nor for the estimated delay value, which is most likely caused by motion redundancy and different stabilization strategies in each participant. The estimated time delay can be used in developing a sensory motor control model of the body. It not only can help therapists and biomechanics to understand the underlying mechanisms of body, but also can be useful in developing assistive technologies based on their stability mechanism.

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.

Ankle muscle fatigability impairs body sway for more than 24 h

This study aimed to investigate if the impairing in postural control, induced by ankle fatiguing exercise, remains after 24/48 h in young adults. Center of Pressure (CoP) was assessed in 16 participants (23 ± 3 years old) before, immediately after an ankle fatigability induction protocol (FI) and after 24 or 48 h of recovery using two 60-s trials with eyes open (EO) and closed (EC). The FI consisted of performing the ankle plantar flexion and dorsiflexion movement repeatedly (0.5 Hz). Ankle muscle fatigability increased CoP anterior-posterior (AP - p < 0.02) and medial-lateral (ML - p < 0.009) root mean square (RMS), and AP (p < 0.01) mean velocity immediately after compared to before FI. These effects remained after 24/48 h of recovery: higher CoP AP (p < 0.03) and ML (p < 0.009) RMS. No significant effects for detrend fluctuation analysis and entropy analysis among periods of postural evaluations was found. Fatigue*visual condition interaction revealed an increased AP median frequency (p < 0.001) during EC compared to EO only immediately after FI. Young adults' body sway remains impaired until 48 h, but not the postural control adaptability and complexity. Visual information may not attenuate the late deleterious ankle muscle fatigability effects. Individuals should be cautious during balance tasks and exercise after fatiguing exercise in the next 24/48 h, therefore avoiding unbalances and falls.

Center of pressure plausibility for the double-link human stance model under the intermittent control paradigm

Despite human balance maintenance in quiet conditions could seem a trivial motor task, it is not. Recently, the human stance was described through a double link inverted pendulum (DIP) actively controlled at the ankle with an intermittent proportional (P) and derivative (D) control actions based on the sway of a virtual inverted pendulum (VIP) that links the ankle joint with the DIP center of mass. Such description, encompassing both the mechanical model and the intermittent control policy, was referred as the DIP/VIP human stance model, and it showed physiologically plausible kinematic patterns. In this study a mathematical formalization of the Center of pressure (COP) for a DIP structure was developed. Then, it was used in conjunction with an intermittently controlled DIP/VIP model to assess its kinetic plausibility. Three descriptors commonly employed in posturography were selected among six based on their capability to discriminate between young (Y) and elderly (O) adults groups. Then, they were applied to assess whether variations of the P-D parameters affect the synthetic COP. The results showed that DIP/VIP model can reproduce COP trajectories, showing characteristics similar to the Y and O groups. Moreover, it was observed that both P and D parameters increased passing from Y to O, indicating that the COP obtained from the DIP/VIP model is able to highlight differences in balance control between groups. The study hence promote the use of DIP/VIP in posturography, where inferential techniques can be applied to characterize neural control.

A review of center of pressure (COP) variables to quantify standing balance in elderly people: Algorithms and open-access code

Postural control is often quantified by recording the trajectory of the center of pressure (COP)-also called stabilogram-during human quiet standing. This quantification has many important applications, such as the early detection of balance degradation to prevent falls, a crucial task whose relevance increases with the aging of the population. Due to the complexity of the quantification process, the analyses of sway patterns have been performed empirically using a number of variables, such as ellipse confidence area or mean velocity. This study reviews and compares a wide range of state-of-the-art variables that are used to assess the risk of fall in elderly from a stabilogram. When appropriate, we discuss the hypothesis and mathematical assumptions that underlie these variables, and we propose a reproducible method to compute each of them. Additionally, we provide a statistical description of their behavior on two datasets recorded in two elderly populations and with different protocols, to hint at typical values of these variables. First, the balance of 133 elderly individuals, including 32 fallers, was measured on a relatively inexpensive, portable force platform (Wii Balance Board, Nintendo) with a 25-s open-eyes protocol. Second, the recordings of 76 elderly individuals, from an open access database commonly used to test static balance analyses, were used to compute the values of the variables on 60-s eyes-open recordings with a research laboratory standard force platform.

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.

Hierarchical Biometrical Genetic Analysis of Longitudinal Dynamics

For many phenotypes, individual scores are obtained as the parameter estimates of person-level models fit to intensive repeated measures from physiological sensors or experience sampling studies. Biometrical genetic analysis of such phenotypes is often done in a 2-step sequence: first the phenotypic parameters are estimated for each individual, then classical twin modeling is used to partition their variance. This study demonstrates deficiencies in accuracy and statistical power of the two-step approach to estimate genetic signals and advocates for the use of hierarchical models to overcome both problems. Simulations are used to demonstrate the benefits to accuracy and statistical power from a hierarchical modeling approach. A model of heart rate fluctuations was applied to experimental data from twin pairs recorded in independent trials. Results of the data application reveal moderate but uncorrelated heritabilities for two parameters of heart rate: oscillation frequency and damping ratio. By merging biometrical genetic analysis with process models, hierarchical mixed-effects modeling has potential to assist with discovery and extraction of novel phenotypes from within-person data and to validate theoretical models of within-person processes.

Dynamic Systems, Contextual Influences, and Multiple Timescales: Emotion Regulation as a Resilience Resource

We need to understand how psychosocial resources develop, identify the influences that threaten their maintenance, detect the circumstances under which these resources are used, and elucidate the factors that support and promote their growth. Three important components to studying the development of resilience include its dynamic nature, context, and timescale of measurement. Dynamic systems (DS) approaches focus on physiological and psychological structures underling the development of resilience by explicitly mapping parameters of change onto their corresponding aspects of functioning. Previous research has captured emotion regulation within individuals, across traits, and in close personal relationships to show how these methods depict dynamic regulation/resilience resources and their influence on outcomes of interest. The use of multi-time scaled data informs how daily emotion regulation is disrupted in the context of stress to produce dysregulation and disease later in the life course. This approach can also reveal how resilience resources counteract these adverse processes and allow others to thrive and be well. Researchers must not only explore short-term variation in constructs of interest, but also explore how these shorter-term fluctuations contribute to longer-term changes. The confluence of DS, contextual influences, and multiple timescales provides an important set of tools to better understand development.

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.

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.