Simultaneous and nonlinear identification of mechanical and reflex properties of human elbow joint muscles

Li Qun Zhang*, William Zev Rymer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


The naturally coexisting intrinsic mechanical and reflex properties of the human elbow joint were identified simultaneously using nonlinear, time-delay, continuous-time, and dynamic models. Angular random perturbations of small amplitude and low bandwidth were applied to the joint using a computer-controlled servomotor, while the subject maintained various levels of mean background muscle torque. Joint neuromuscular dynamics were identified from the measured elbow angle and torque. Stretch reflexes were modeled nonlinearly with both dynamic and static reflex gains. A continuous-time system identification method was developed to estimate parameters of the nonlinear models directly from sampled data while retaining realistic physical or physiological interpretations. Results from six subjects showed that dynamic stretch reflex gains, joint stiffness, and viscosity generally increased with mean background muscle torque; and that dynamic stretch reflex gain was higher during muscle stretch than that during muscle shortening. More importantly, the study provided realistic simultaneous estimates of the relative contributions of intrinsic mechanical and reflex actions to net joint torque. In particular, reflexively-mediated stiffness generated a significant portion of the total joint stiffness and the percentage varied systematically with background muscle torque.

Original languageEnglish (US)
Pages (from-to)1192-1209
Number of pages18
JournalIEEE Transactions on Biomedical Engineering
Issue number12
StatePublished - 1997


  • Identification
  • Intrinsic stiffness
  • Neuromuscular control
  • Reflex

ASJC Scopus subject areas

  • Biomedical Engineering

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