Time-Varying Ankle Mechanical Impedance During Human Locomotion

Abstract

In human locomotion, we continuously modulate joint mechanical impedance of the lower limb (hip, knee, and ankle) either voluntarily or reflexively to accommodate environmental changes and maintain stable interaction. Ankle mechanical impedance plays a pivotal role at the interface between the neuro-mechanical system and the physical world. This paper reports, for the first time, a characterization of human ankle mechanical impedance in two degrees-of-freedom simultaneously as it varies with time during walking. Ensemble-based linear time-varying system identification methods implemented with a wearable ankle robot, Anklebot, enabled reliable estimation of ankle mechanical impedance from the pre-swing phase through the entire swing phase to the early-stance phase. This included heel-strike and toe-off, key events in the transition from the swing to stance phase or vice versa. Time-varying ankle mechanical impedance was accurately approximated by a second order model consisting of inertia, viscosity, and stiffness in both inversion-eversion and dorsiflexion-plantarflexion directions, as observed in our previous steady-state dynamic studies. We found that viscosity and stiffness of the ankle significantly decreased at the end of the stance phase before toe-off, remained relatively constant across the swing phase, and increased around heel-strike. Closer investigation around heel-strike revealed that viscosity and stiffness in both planes increased before heel-strike occurred. This finding is important evidence of "pretuning" by the central nervous system. In addition, viscosity and stiffness were greater in the sagittal plane than in the frontal plane across all subgait phases, except the early stance phase. Comparison with previous studies and implications for clinical study of neurologically impaired patients are provided.

Multivariable Dynamic Ankle Mechanical Impedance With Active Muscles

“…One weakness of this method is that a single estimate of impedance is made at one position at a time, requiring multiple separate measurements to characterize impedance over a wide ROM. The use of LTI system identification is another limitation, but this method can be extended to time-varying system identification [42], [43] or nonlinear system identification while retaining the current experimental setup using a wearable ankle robot actuating multiple DOFs. On the other hand, in the static studies [20], [21], a precise vector field describing a nonlinear torque-angle relationship at the ankle was identified, from which local stiffness can be calculated at any point in the displacement field over a wide ROM.…”

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

“…Then, an unperturbed trajectory, consisting of the angle of the ankle joint during walking, with a duration of 2 s, was applied; this trajectory was extracted from Lee and Hogan (2015). The trajectory was repeated periodically 30 times; the trial was repeated twice to obtain a total of 60 cycles.…”

“…Several studies have characterized dynamic joint stiffness during TV conditions by modeling the intrinsic and reflex response together using a single linear model (Bennett et al, 1992; MacNeil et al, 1992; Kirsch and Kearney, 1997; Rouse et al, 2014; Lee and Hogan, 2015). These type of models cannot provide any information regarding the modulation of reflex mechanisms and likely overestimate the contribution of intrinsic mechanisms to the overall dynamic joint stiffness.…”

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

“…The segmentation is not always trivial and often requires the TV behavior to be very slow. Ensemble-based methods (MacNeil et al, 1992; Kirsch et al, 1993; Ludvig et al, 2011; Lee and Hogan, 2015) are effective but require many trials with identical TV behavior, which is hard to achieve in many experimental conditions. Moreover, repeating the same task many times may result in fatigue and affect the reliability of estimates.…”