Ankle Joint Intrinsic Dynamics is More Complex than a Mass-Spring-Damper Model

Tehrani, Ehsan Sobhani; Jalaleddini, Kian; Kearney, Robert E.

doi:10.1109/tnsre.2017.2679722

Cited by 33 publications

(12 citation statements)

References 33 publications

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“…This is consistent with recent evidence that joint mechanical properties are more complex than second order (Sobhani Tehrani et al, 2017). …”

Section: Experimental Studysupporting

confidence: 93%

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Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Guarín

Kearney

2017

Front. Comput. Neurosci.

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Dynamic joint stiffness determines the relation between joint position and torque, and plays a vital role in the control of posture and movement. Dynamic joint stiffness can be quantified during quasi-stationary conditions using disturbance experiments, where small position perturbations are applied to the joint and the torque response is recorded. Dynamic joint stiffness is composed of intrinsic and reflex mechanisms that act and change together, so that nonlinear, mathematical models and specialized system identification techniques are necessary to estimate their relative contributions to overall joint stiffness. Quasi-stationary experiments have demonstrated that dynamic joint stiffness is heavily modulated by joint position and voluntary torque. Consequently, during movement, when joint position and torque change rapidly, dynamic joint stiffness will be Time-Varying (TV). This paper introduces a new method to quantify the TV intrinsic and reflex components of dynamic joint stiffness during movement. The algorithm combines ensemble and deterministic approaches for estimation of TV systems; and uses a TV, parallel-cascade, nonlinear system identification technique to separate overall dynamic joint stiffness into intrinsic and reflex components from position and torque records. Simulation studies of a stiffness model, whose parameters varied with time as is expected during walking, demonstrated that the new algorithm accurately tracked the changes in dynamic joint stiffness using as little as 40 gait cycles. The method was also used to estimate the intrinsic and reflex dynamic ankle stiffness from an experiment with a healthy subject during which ankle movements were imposed while the subject maintained a constant muscle contraction. The method identified TV stiffness model parameters that predicted the measured torque very well, accounting for more than 95% of its variance. Moreover, both intrinsic and reflex dynamic stiffness were heavily modulated through the movement in a manner that could not be predicted from quasi-stationary experiments. The new method provides the tool needed to explore the role of dynamic stiffness in the control of movement.

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“…This is consistent with recent evidence that joint mechanical properties are more complex than second order (Sobhani Tehrani et al, 2017). …”

Section: Experimental Studysupporting

confidence: 93%

“…However, recent experimental evidence suggests that the intrinsic dynamics stiffness is more complex than second-order (Sobhani Tehrani et al, 2017). Therefore, we choose to describe intrinsic stiffness with the TV, non-parametric model…”

Section: Model Formulation and Parameter Identificationmentioning

confidence: 99%

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Guarín

Kearney

2017

Front. Comput. Neurosci.

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“…These results indicate that contribution of reflex stiffness is highest at low contractions and decreases as contraction level increase, whereas, intrinsic stiffness monotonically increases with contraction level. Note that we did not attempt to parameterize the LPV IRFs for the intrinsic pathway as a second-order system because: (1) intrinsic dynamics may be more complex than the I,B,K model as demonstrated recently in Sobhani et al (2017) (2) the fitting procedure would involve non-linear minimization that would introduce an additional source of error.…”

Section: Discussionmentioning

confidence: 99%

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

Golkar

Tehrani

Kearney

2017

Front. Comput. Neurosci.

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Dynamic joint stiffness is a dynamic, nonlinear relationship between the position of a joint and the torque acting about it, which can be used to describe the biomechanics of the joint and associated limb(s). This paper models and quantifies changes in ankle dynamic stiffness and its individual elements, intrinsic and reflex stiffness, in healthy human subjects during isometric, time-varying (TV) contractions of the ankle plantarflexor muscles. A subspace, linear parameter varying, parallel-cascade (LPV-PC) algorithm was used to identify the model from measured input position perturbations and output torque data using voluntary torque as the LPV scheduling variable (SV). Monte-Carlo simulations demonstrated that the algorithm is accurate, precise, and robust to colored measurement noise. The algorithm was then used to examine stiffness changes associated with TV isometric contractions. The SV was estimated from the Soleus EMG using a Hammerstein model of EMG-torque dynamics identified from unperturbed trials. The LPV-PC algorithm identified (i) a non-parametric LPV impulse response function (LPV IRF) for intrinsic stiffness and (ii) a LPV-Hammerstein model for reflex stiffness consisting of a LPV static nonlinearity followed by a time-invariant state-space model of reflex dynamics. The results demonstrated that: (a) intrinsic stiffness, in particular ankle elasticity, increased significantly and monotonically with activation level; (b) the gain of the reflex pathway increased from rest to around 10–20% of subject's MVC and then declined; and (c) the reflex dynamics were second order. These findings suggest that in healthy human ankle, reflex stiffness contributes most at low muscle contraction levels, whereas, intrinsic contributions monotonically increase with activation level.

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“…To reduce this elongated torque response, the control scheme of the actuator should be revised. Another discrepancy between simulation and experiment is the sim-plified 2nd-order model used for the intrinsic pathway, while evidence exists that a more complex model is required [14].…”

Section: Validation Of Identification Algorithmmentioning

confidence: 99%

Validation of Online Intrinsic and Reflexive Joint Impedance Estimates Using Correlation with EMG Measurements

Veld

Schouten

Kooij

et al. 2018

2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob)

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Biofeedback of online system identification estimates of intrinsic and reflexive joint impedance can be used by able-bodied subjects to voluntarily modulate their reflexive impedance independent of the intrinsic contribution. Similar to EMG-based paradigms, this could potentially be used to reduce muscle hyperreflexia in people with spasticity by facilitating spinal neuroplasticity. However, it remains unanswered if spastic participants are able to use this specific feedback to modulate their reflexes. We show, while subjects were free to co-contract, that the system identification measures have a large linear association with independently measured and processed EMG measures. The impedance estimates were obtained using an existing algorithm with incremental improvements to increase general applicability and decrease bias on the identified parameters in both simulation an experimental data. The correlation with EMG-based measures demonstrates the validity of the use of joint impedance measures within a training paradigm to reduce hyperreflexia. This could potentially improve participant comfort, increase applicability across joints, target hyperreflexia at joint level and generate faster training effects.

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Ankle Joint Intrinsic Dynamics is More Complex than a Mass-Spring-Damper Model

Cited by 33 publications

References 33 publications

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

Validation of Online Intrinsic and Reflexive Joint Impedance Estimates Using Correlation with EMG Measurements

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