Guarín Diego L, Kearney Robert E
Biomedical Engineering Department, McGill UniversityMontréal, QC, Canada.
Front Comput Neurosci. 2017 Jun 9;11:51. doi: 10.3389/fncom.2017.00051. eCollection 2017.
Dynamic joint stiffness determines the relation between joint position and torque, and plays a vital role in the control of posture and movement. Dynamic joint stiffness can be quantified during quasi-stationary conditions using disturbance experiments, where small position perturbations are applied to the joint and the torque response is recorded. Dynamic joint stiffness is composed of intrinsic and reflex mechanisms that act and change together, so that nonlinear, mathematical models and specialized system identification techniques are necessary to estimate their relative contributions to overall joint stiffness. Quasi-stationary experiments have demonstrated that dynamic joint stiffness is heavily modulated by joint position and voluntary torque. Consequently, during movement, when joint position and torque change rapidly, dynamic joint stiffness will be Time-Varying (TV). This paper introduces a new method to quantify the TV intrinsic and reflex components of dynamic joint stiffness during movement. The algorithm combines ensemble and deterministic approaches for estimation of TV systems; and uses a TV, parallel-cascade, nonlinear system identification technique to separate overall dynamic joint stiffness into intrinsic and reflex components from position and torque records. Simulation studies of a stiffness model, whose parameters varied with time as is expected during walking, demonstrated that the new algorithm accurately tracked the changes in dynamic joint stiffness using as little as 40 gait cycles. The method was also used to estimate the intrinsic and reflex dynamic ankle stiffness from an experiment with a healthy subject during which ankle movements were imposed while the subject maintained a constant muscle contraction. The method identified TV stiffness model parameters that predicted the measured torque very well, accounting for more than 95% of its variance. Moreover, both intrinsic and reflex dynamic stiffness were heavily modulated through the movement in a manner that could not be predicted from quasi-stationary experiments. The new method provides the tool needed to explore the role of dynamic stiffness in the control of movement.
动态关节刚度决定了关节位置与扭矩之间的关系，在姿势和运动控制中起着至关重要的作用。在准静态条件下，可以通过干扰实验来量化动态关节刚度，即对关节施加小的位置扰动并记录扭矩响应。动态关节刚度由共同作用和变化的内在机制与反射机制组成，因此需要非线性数学模型和专门的系统识别技术来估计它们对整体关节刚度的相对贡献。准静态实验表明，动态关节刚度受关节位置和自主扭矩的强烈调节。因此，在运动过程中，当关节位置和扭矩快速变化时，动态关节刚度将随时间变化（时变）。本文介绍了一种新方法，用于量化运动过程中动态关节刚度的时变内在和反射成分。该算法结合了整体和确定性方法来估计时变系统；并使用时变、并行级联、非线性系统识别技术，从位置和扭矩记录中将整体动态关节刚度分离为内在和反射成分。对一个刚度模型的仿真研究表明，其参数在行走过程中随时间变化，结果表明新算法仅使用40个步态周期就能准确跟踪动态关节刚度的变化。该方法还被用于从一名健康受试者的实验中估计踝关节的内在和反射动态刚度，实验过程中受试者保持肌肉持续收缩的同时踝关节进行运动。该方法识别出的时变刚度模型参数能够很好地预测测量到的扭矩，解释了其方差的95%以上。此外，内在和反射动态刚度在整个运动过程中都受到强烈调节，这种调节方式无法从准静态实验中预测。新方法提供了探索动态刚度在运动控制中作用所需的工具。
