Multivariable dynamic ankle mechanical impedance with relaxed muscles

Hyunglae Lee, Hermano Igo Krebs, Neville Hogan

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Neurological or biomechanical disorders may distort ankle mechanical impedance and thereby impair locomotor function. This paper presents a quantitative characterization of multivariable ankle mechanical impedance of young healthy subjects when their muscles were relaxed, to serve as a baseline to compare with pathophysiological ankle properties of biomechanically and/or neurologically impaired patients. Measurements using a highly backdrivable wearable ankle robot combined with multi-input multi-output stochastic system identification methods enabled reliable characterization of ankle mechanical impedance in two degrees-of-freedom (DOFs) simultaneously, the sagittal and frontal planes. The characterization included important ankle properties unavailable from single DOF studies: coupling between DOFs and anisotropy as a function of frequency. Ankle impedance in joint coordinates showed responses largely consistent with a second-order system consisting of inertia, viscosity, and stiffness in both seated (knee flexed) and standing (knee straightened) postures. Stiffness in the sagittal plane was greater than in the frontal plane and furthermore, was greater when standing than when seated, most likely due to the stretch of bi-articular muscles (medial and lateral gastrocnemius). Very low off-diagonal partial coherences implied negligible coupling between dorsiflexion-plantarflexion and inversion-eversion. The directions of principal axes were tilted slightly counterclockwise from the original joint coordinates. The directional variation (anisotropy) of ankle impedance in the 2-D space formed by rotations in the sagittal and frontal planes exhibited a characteristic 'peanut' shape, weak in inversion-eversion over a wide range of frequencies from the stiffness dominated region up to the inertia dominated region. Implications for the assessment of neurological and biomechanical impairments are discussed.

Original languageEnglish (US)
Article number6778753
Pages (from-to)1104-1114
Number of pages11
JournalIEEE Transactions on Neural Systems and Rehabilitation Engineering
Issue number6
StatePublished - Nov 1 2014
Externally publishedYes


  • Ankle joint
  • ankle joint stiffness
  • ankle stiffness
  • human ankle
  • impedance structure
  • multivariable impedance
  • multivariable stiffness
  • stiffness anisotropy

ASJC Scopus subject areas

  • Internal Medicine
  • Neuroscience(all)
  • Biomedical Engineering


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