Abstract
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.
Highlights
The role of the short-latency stretch reflex during movement remains controversial (Dietz et al, 1979; Sinkjaer et al, 1996; Zehr and Stein, 1999)
We have introduced methods to estimate intrinsic and stretch reflex mechanisms using the parallel-cascade model structure during TV conditions; these methods require very large data sets for parameter estimation, which severely limits their application (Giesbrecht et al, 2006; Ludvig et al, 2011; Guarin and Kearney, 2012, 2015b); or make the strong assumption that there is a static-nonlinear relation between the parallel-cascade model parameters and joint position or torque (Sobhani Tehrani et al, 2013; Jalaleddini et al, 2015)
This paper presents a new model parameterization and identification algorithm for the accurate estimation of the intrinsic and stretch reflex components of dynamic joint stiffness during movement
Summary
The role of the short-latency stretch reflex during movement remains controversial (Dietz et al, 1979; Sinkjaer et al, 1996; Zehr and Stein, 1999). EMG is often used to study the functional role of reflexes (Dietz et al, 1979; Stein and Capaday, 1988; Zehr and Stein, 1999; Burdet et al, 2013). The relation between EMG and joint torque is influenced by muscle length and contraction velocity, so that is difficult to estimate the mechanical contributions of stretch reflex from EMG alone (Toft et al, 1991; Stein and Kearney, 1995; Kearney et al, 1999). The functional relevance of these H-reflex studies is not completely clear
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