A Subspace Approach to the Structural Decomposition and Identification of Ankle Joint Dynamic Stiffness

Objective: The purpose of this paper is to present a structural decomposition subspace (SDSS) method for decomposition of the joint torque to intrinsic, reflexive, and voluntary torques and identification of joint dynamic stiffness. Methods: First, it formulates a novel state-space representation for the joint dynamic stiffness modeled by a parallel-cascade structure with a concise parameter set that provides a direct link between the state-space representation matrices and the parallel-cascade parameters. Second, it presents a subspace method for the identification of the new state-space model that involves two steps: 1) the decomposition of the intrinsic and reflex pathways and 2) the identification of an impulse response model of the intrinsic pathway and a Hammerstein model of the reflex pathway. Results: Extensive simulation studies demonstrate that SDSS has significant performance advantages over some other methods. Thus, SDSS was more robust under high noise conditions, converging where others failed; it was more accurate, giving estimates with lower bias and random errors. The method also worked well in practice and yielded high-quality estimates of intrinsic and reflex stiffnesses when applied to experimental data at three muscle activation levels. Conclusion: The simulation and experimental results demonstrate that SDSS accurately decomposes the intrinsic and reflex torques and provides accurate estimates of physiologically meaningful parameters. Significance: SDSS will be a valuable tool for studying joint stiffness under functionally important conditions. It has important clinical implications for the diagnosis, assessment, objective quantification, and monitoring of neuromuscular diseases that change the muscle tone.