Table1_What is the contribution of voluntary and reflex processes to sensorimotor control of balance?.docx

The contribution to balance of spinal and transcortical processes including the long-latency reflex is well known. The control of balance has been modelled previously as a continuous, state feedback controller representing, long-latency reflexes. However, the contribution of slower, variable delay processes has not been quantified. Compared with fixed delay processes (spinal, transcortical), we hypothesize that variable delay processes provide the largest contribution to balance and are sensitive to historical context as well as current states. Twenty-two healthy participants used a myoelectric control signal from their leg muscles to maintain balance of their own body while strapped to an actuated, inverted pendulum. We study the myoelectric control signal (u) in relation to the independent disturbance (d) comprising paired, discrete perturbations of varying inter-stimulus-interval (ISI). We fit the closed loop response, u from d, using one linear and two non-linear non-parametric (many parameter) models. Model M1 (ARX) is a generalized, high-order linear-time-invariant (LTI) process with fixed delay. Model M1 is equivalent to any parametric, closed-loop, continuous, linear-time-invariant (LTI), state feedback model. Model M2, a single non-linear process (fixed delay, time-varying amplitude), adds an optimized response amplitude to each stimulus. Model M3, two non-linear processes (one fixed delay, one variable delay, each of time-varying amplitude), add a second process of optimized delay and optimized response amplitude to each stimulus. At short ISI, the myoelectric control signals deviated systematically both from the fixed delay LTI process (M1), and also from the fixed delay, time-varying amplitude process (M2) and not from the two-process model (M3). Analysis of M3 (all fixed delay and variable delay response amplitudes) showed the variable (compared with fixed) delay process 1) made the largest contribution to the response, 2) exhibited refractoriness (increased delay related to short ISI) and 3) was sensitive to stimulus history (stimulus direction 2 relative to stimulus 1). For this whole-body balance task and for these impulsive stimuli, non-linear processes at variable delay are central to control of balance. Compared with fixed delay processes (spinal, transcortical), variable delay processes provided the largest contribution to balance and were sensitive to historical context as well as current states.

包括长潜伏期反射（long-latency reflex）在内的脊髓与经皮层过程对姿势平衡的调控作用已广为人知。此前已有研究将姿势平衡调控建模为表征长潜伏期反射的连续状态反馈控制器。然而，动作更为缓慢的可变延迟过程对平衡的调控贡献尚未被量化。相较于固定延迟过程（脊髓、经皮层过程），我们提出如下假设：可变延迟过程对姿势平衡的调控贡献最大，且其既受当前状态影响，也与历史情境相关。22名健康受试者被固定于驱动式倒立摆装置上，通过腿部肌肉产生的肌电控制信号（myoelectric control signal）维持自身身体平衡。本研究聚焦肌电控制信号（u）与独立扰动（d）之间的关联，其中独立扰动由刺激间隔（inter-stimulus-interval, ISI）各异的成对离散扰动构成。我们采用1种线性模型与2种非线性非参数（多参数）模型，对独立扰动d到肌电控制信号u的闭环响应进行拟合。模型M1（ARX）是一类带有固定延迟的广义高阶线性时不变（linear-time-invariant, LTI）过程，其等价于任意参数化的闭环连续线性时不变状态反馈模型。模型M2为单非线性过程（固定延迟、时变振幅），可为每个刺激添加经优化的响应振幅。模型M3包含两个非线性过程（一个固定延迟、一个可变延迟，二者均为时变振幅），可为每个刺激额外添加一个经优化延迟与经优化响应振幅的过程。当刺激间隔较短时，肌电控制信号与固定延迟线性时不变过程（M1）以及固定延迟时变振幅过程（M2）均呈现系统性偏离，但与双过程模型（M3）的拟合结果一致。对模型M3（包含所有固定延迟与可变延迟的响应振幅）的分析结果显示：相较于固定延迟过程，可变延迟过程1）对响应的贡献最大；2）呈现不应期特性（即刺激间隔较短时延迟增加）；3）受刺激历史影响显著（如第二个刺激的方向与第一个刺激存在关联时）。针对该全身平衡任务与这类脉冲式刺激而言，可变延迟的非线性过程是平衡调控的核心机制。相较于固定延迟过程（脊髓、经皮层过程），可变延迟过程对姿势平衡的调控贡献最大，且既受当前状态影响，也与历史情境相关。