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

Abstract

Human postural sway during quiet standing has been characterized as a proportional-integral-derivative controller with intermittent activation. In the model, patterns of sway result from both instantaneous, passive, mechanical resistance and delayed, intermittent resistance signaled by the central nervous system. A Kalman-Filter framework was designed to directly estimate from experimental data the parameters of the model’s stochastic delay differential equations with discrete dynamic switching conditions. Simulations showed that all parameters could be estimated over a variety of possible data-generating configurations with varying degrees of bias and variance depending on their empirical identification. Applications to experimental data reveal distributions of each parameter that correspond well to previous findings, suggesting that many useful, physiological measures may be extracted from sway data. Individuals varied in degree and type of deviation from theoretical expectations, ranging from harmonic oscillation to non-equilibrium Langevin dynamics.

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

“…Further possible control concepts are acceleration feedback 32 , 56 , predictor feedback 39 , 43 or an event-driven combination of ankle and ankle–hip strategies 25 , just to mention a few. An advantage of the delayed PD feedback model is that while it is widely used in the literature 26 , 31 , 33 , 47 , 50 , it accounts with the two most important features of neural motor control: (1) actuation is performed based on perceived sensory signals; and (2) there is a reaction time delay between sensory perception and action.…”

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

“…Of course, other types of control concepts may also apply, for instance, intermittent feedback [10,13,20], acceleration feedback [7,8], predictor feedback [16] or hierarchical control [38,39]. An advantage of delayed PD feedback model is that while it is widely used in the literature [5,6,9,17,18,27] it can be described with a small number of parameters. In the case of the two-degree-of-freedom model of balancing on a balance board, the control model involves only five parameters: the four control gains and the feedback delay.…”

“…Since the model of the human body and the operation of the CNS involve many uncertain parameters, it is advantageous to consider tasks associated with low-degree-of-freedom mechanical models with well-defined physical properties. For instance, stick balancing [4,6,11,16], ankle strategy during quiet standing [5,9,15,17,18] and ball and beam balancing [19] are often modelled as a single inverted pendulum system, while ankle-hip strategy during quiet standing [20,21] and standing on a balance board [22][23][24] are modelled as a generalized double inverted pendulum.…”

Response to Perturbation During Quiet Standing Matches Delayed State Feedback With Precisely Tuned Control Gains

“…It shall be mentioned that other than delayed PD feedback is also a possible concept to describe the stabilization process. Several ideas are available in the literature, such as intermittent feedback where intermittency can be either a control logic [25][26][27][28]56 or an inherent consequence of the sensory system 20,30 , acceleration feedback 33,57 or predictor feedback 40,44 , just to mention a few. An advantage of the delayed PD feedback model is that while it is widely used in the literature 27,32,34,48,51 , it accounts with the two most important features of neural motor control: (1) actuation is performed based on perceived sensory signals; and (2) there is a reaction time delay between sensory perception and action.…”

“…The dynamics of human postural sway during quiet standing with eyes closed is very complex and has been described in terms of stochastic and even chaotic motions 21,22 . The underlying mathematical model can be either an inherently stochastic process 23,24 or a deterministic nonlinear feedback mechanism governed by some kind of intermittent control [25][26][27][28] or their combinations [29][30][31] . One of the simplest physiological mechanisms for generating a chaotic motion is the interplay between a time-delayed, sampled data system and a sensory dead zone, i.e., corrective actions take place only when the sensory inputs exceed some threshold values 22 .…”