Subspace Methods for Identification of Human Ankle Joint Stiffness

• Published in: IEEE transactions on biomedical engineering Vol. 58; no. 11; pp. 3039 - 3048
• Main Authors: Zhao, Y., Westwick, D. T., Kearney, R. E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Ankle dynamics; Ankle Joint - physiology; Applied sciences; Biomechanical Phenomena - physiology; Computer Simulation; Detection, estimation, filtering, equalization, prediction; Estimation; Exact sciences and technology; Hammerstein system identification; Humans; Information, signal and communications theory; Joints; Low pass filters; Models, Biological; Monte Carlo Method; Muscle, Skeletal - physiology; Noise; parallel-cascade structure; Predictive models; Range of Motion, Articular - physiology; Reflexes; Signal and communications theory; Signal, noise; Signal-To-Noise Ratio; Studies; subspace method; Telecommunications and information theory; Torque; Torque measurement; Ankle; Human; Hammerstein system identification; Ankle joint; Hammerstein equation; Subspace method; Stiffness; parallel-cascade structure; System identification; Ankle dynamics; Biomedical engineering
• ISSN: 0018-9294; 1558-2531; 1558-2531
• DOI: 10.1109/TBME.2010.2092430

Joint stiffness, the dynamic relationship between the angular position of a joint and the torque acting about it, describes the dynamic, mechanical behavior of a joint during posture and movement. Joint stiffness arises from both intrinsic and reflex mechanisms, but the torques due to these mechanisms cannot be measured separately experimentally, since they appear and change together. Therefore, the direct estimation of the intrinsic and reflex stiffnesses is difficult. In this paper, we present a new, two-step procedure to estimate the intrinsic and reflex components of ankle stiffness. In the first step, a discrete-time, subspace-based method is used to estimate a state-space model for overall stiffness from the measured overall torque and then predict the intrinsic and reflex torques. In the second step, continuous-time models for the intrinsic and reflex stiffnesses are estimated from the predicted intrinsic and reflex torques. Simulations and experimental results demonstrate that the algorithm estimates the intrinsic and reflex stiffnesses accurately. The new subspace-based algorithm has three advantages over previous algorithms: 1) It does not require iteration, and therefore, will always converge to an optimal solution; 2) it provides better estimates for data with high noise or short sample lengths; and 3) it provides much more accurate results for data acquired under the closed-loop conditions, that prevail when subjects interact with compliant loads.