Linear parameter varying identification of ankle joint intrinsic stiffness during imposed walking movements.
The time-varying stiffness dynamics of the human ankle joint were identified during a large stretch imposed upon the active triceps surae muscles. Small stochastic position perturbations were superimposed upon many repetitions of the larger movement and an ensemble time-varying identification technique was then used to characterize the relationship between the small perturbation and the torque it evoked at each sample in time throughout the movement. This technique was found to provide an excellent description of the ankle stiffness dynamics throughout this movement, with the identified stiffness impulse response functions accounting for more than 80% of the torque variance at all times. The average low-frequency stiffness values (K low) derived from the stiffness impulse responses at each sample in time are believed to reflect primarily the instantaneous elastic properties of active crossbridges. These properties, which reflect the contractile state of the muscles more directly than force or torque measurements, have not been obtained previously from an intact muscle-joint system. We found that stiffness actually increased during the later portion of the large imposed stretch, indicating the triceps surae muscles did not yield significantly, and that the post-stretch steady-state stiffness level was approximately 60% higher than prior to the stretch. Reflex activity evoked by the large stretch did not produce a detectable change in K low, even though this activity did produce a clear twitch-like response in joint torque beginning approximately 60 ms following stretch onset. A second-order mechanical model was found to provide an adequate characterization of stiffness dynamics for steady-state periods before and well after the imposed movement, but it could not adequately describe the observed changes in stiffness dynamics during the movement itself. However, the variation of model parameters indicated that the torque evoked by the stochastic displacement was predominantly elastic in nature. The stiffness behavior during stretch observed here for the intact human ankle joint is largely consistent with previous studies performed in isolated muscle preparations.