System Identification of Postural Tremor in Wrist Flexion-Extension and Radial-Ulnar Deviation

• Main Author: Ward, Sydney Bryanna
• Format: Others
• Published: BYU ScholarsArchive 2021
• Subjects: system identification; parameter estimation; tremor; neuromusculoskeletal; wrist; Mechanical Engineering
• Online Access: https://scholarsarchive.byu.edu/etd/9306; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=10315&context=etd

Generic simulations of tremor propagation through the upper limb have been achieved using a previously developed postural tremor model, but this model had not yet been compared with experimental data or utilized for subject-specific studies. This work addressed these two issues, which are important for optimizing peripheral tremor suppression techniques. For tractability, we focused on a subsystem of the upper limb: the isolated wrist, including the four prime wrist muscles (extensor carpi ulnaris, flexor carpi ulnaris, extensor carpi radialis, and flexor carpi radialis) and the two degrees of freedom of the wrist (flexion-extension and radial-ulnar deviation). Muscle excitation and joint displacement signals were collected while subjects with Essential Tremor resisted gravity. System identification was implemented for three subjects who experienced significant tremor using two approaches: 1. Generic linear time-invariant (LTI) models, including autoregressive-exogenous (ARX) and state-space forms, were identified from the experimental data, and characteristics including model order and modal parameters were compared with the previously developed postural tremor model; 2. Subject-specific parameters for the previously developed postural tremor model were directly estimated from experimental data using nonlinear least-squares optimization combined with regularization. The identified LTI models fit the experimental data well, with coefficients of determination of 0.74 ± 0.18 and 0.83 ± 0.13 for ARX and state-space forms, respectively. The optimal model orders identified from the experimental data (4.8 ± 1.9 and 6.4 ± 1.9) were slightly lower than the orders of the ARX and state-space forms of the previously developed model (6 and 8). For each subject, at least one pair of identified complex poles aligned with the complex poles of the previously developed model, whereas the identified real poles were assumed to represent drift in the data rather than characteristics of the system. Subject-specific parameter estimates reduced the sum of squared-error (SSE) between the measured and predicted joint displacement signals to be between 10% and 50% of the SSE using generic literature parameters. The predicted joint displacements maintained high coherence at the tremor frequency for flexion-extension (0.90 ± 0.10), which experienced the most tremor. We successfully applied multiple system identification techniques to identify tremor propagation models using only tremorogenic muscle activity as the input. These techniques identified model order, poles, and subject-specific model parameters, and indicate that tremor propagation at the wrist is well approximated by an LTI model.