Dynamics of human ankle stiffness: Variation with mean ankle torque

doi:10.1016/0021-9290(82)90089-6

Journal of Biomechanics

Volume 15, Issue 10, 1982, Pages 747-752

https://doi.org/10.1016/0021-9290(82)90089-6 Get rights and content

Abstract

The left foot of five human subjects was rotated in a fixed stochastic pattern about a constant ankle angle and the forces opposing these perturbations were measured. The dynamic stiffness transfer functions relating ankle angular position to ankle torque were calculated. Stiffness gain was flat at low frequencies, had a resonant valley at intermediate frequencies and rose at about 40 dB/decade at high frequencies. The low frequency gain and resonant frequency increased progressively with increases in tonic muscular activity. The dynamic stiffness of the ankle was well described by a linear, under-damped, second-order transfer function having inertial, viscous and elastic terms. Estimates of the inertial parameter were independent of the level of muscle activity whereas the viscous and elastic parameters increased with increases in mean torque level.

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Cited by (254)

Reliability and minimal detectable change of stiffness and other mechanical properties of the ankle joint in standing and walking
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Ankle joint stiffness and viscosity are fundamental mechanical descriptions that govern the movement of the body and impact an individual’s walking ability. Hence, these internal properties of a joint have been increasingly used to evaluate the effects of pathology (e.g., stroke) and in the design and control of robotic and prosthetic devices. However, the reliability of these measurements is currently unclear, which is important for translation to clinical use.
Can we reliably measure the mechanical impedance parameters of the ankle while standing and walking?
Eighteen able-bodied individuals volunteered to be tested on two different days separated by at least 24 h. Participants received several small random ankle dorsiflexion perturbations while standing and during the stance phase of walking using a custom-designed robotic platform. Three-dimensional motion capture cameras and a 6-component force plate were used to quantify ankle joint motions and torque responses during normal and perturbed conditions. Ankle mechanical impedance was quantified by computing participant-specific ensemble averages of changes in ankle angle and torque due to perturbation and fitting a second-order parametric model consisting of stiffness, viscosity, and inertia. The test-retest reliability of each parameter was assessed using intraclass correlation coefficients (ICCs). We also computed the minimal detectable change (MDC) for each impedance parameter to establish the smallest amount of change that falls outside the measurement error of the instrument.
In standing, the reliability of stiffness, viscosity, and inertia was good to excellent (ICCs=0.67–0.91). During walking, the reliability of stiffness and viscosity was good to excellent (ICCs=0.74–0.84) while that of inertia was fair to good (ICCs=0.47–0.68). The MDC for a single subject ranged from 20%− 65% of the measurement mean but was higher (>100%) for inertia during walking.
Results indicate that dynamic measures of ankle joint impedance were generally reliable and could serve as an adjunct clinical tool for evaluating gait impairments.
Frontal plane ankle stiffness increases with weight-bearing
2021, Journal of Biomechanics
Citation Excerpt :
This sensitivity of stiffness to muscle activation is consistent with previous studies of ankle stiffness. In the sagittal plane of the ankle, muscle activity in the LG, MG, and SOL can increase the stiffness by an order of magnitude relative to passive conditions (Hunter and Kearney, 1982). However, these muscles act mainly in the sagittal plane and have small moment arms in the frontal plane (McCullough et al., 2011).
Ankle sprains are among the most common musculoskeletal injuries. They are not isolated innocuous injuries as 30–40% of people who sprain their ankles develop chronic ankle instability. Ankle instability is typically assessed under passive unloaded conditions, ignoring any potential contribution of joint loading or muscle activation to the maintenance of ankle stability. Thus, the relevance of unloaded ankle stability assessments to the evaluation of impairments in chronic ankle instability or the prediction of future ankle sprains is questionable. Ankle impedance, which quantifies the resistance to an imposed rotation, has often been used to quantify ankle stability. However, few studies have investigated impedance in the frontal plane where sprains occur, and none have systematically investigated the effect of weight-bearing on ankle impedance. The objective of this study was to determine whether weight-bearing affects frontal plane ankle impedance. We had subjects systematically alter the weight on the tested ankle, while imposed frontal plane rotations were applied to estimate the impedance. We found that ankle stiffness, the static component of impedance, increased proportionally with the weight on the ankle. This increase in stiffness was due to a combination of the increase loading on the joint and the increase in muscle activation that occurs during weight-bearing. Finally, we found that men had a greater stiffness than women over the majority of the weight-bearing range. These results highlight the importance of clinically assessing ankle stability during weight-bearing conditions to better determine the impairments in chronic ankle instability and identify those at risk for ankle sprains.
Quantitative comparison of time-varying system identification methods to describe human joint impedance
2021, Annual Reviews in Control
Accurate and swift tuning of joint impedance is crucial to perform movement and interaction with our environment. Time-varying system identification enables quantification of joint impedance during movement. Many methods have been developed over the years, each with their own mathematical approach and underlying assumptions. Yet, for the identification of joint impedance, a systematic comparison revealing each method's unique strengths and weaknesses, is lacking. Here, we propose a quantitative framework to compare these methods.
The framework is used to review five time-varying system identification methods using both simulated data and experimental data. These methods included three time-domain methods: ensemble, short data segment, and basis impulse response function; and two frequency-domain methods: ensemble spectral, and kernel-based regression. In the simulation study, joint stiffness – the static component of impedance – was simulated as a square wave to mimic the most extreme case of time-varying behavior. The identification results were compared based on the (1) variance accounted for (VAF), (2) bias, (3) random, and (4) total estimation error with respect to the simulated joint stiffness; and (5) rise time between two stiffness levels. In the experimental study, human ankle joint impedance was identified. Identification performance was compared using the variability in estimating joint stiffness – representative of the random error – and VAF.
The performance metrics revealed distinct identification properties for each method. Therefore, researchers must make a well-justified decision which method is most appropriate for their application. The combination of simulation and experimental work with extensive performance quantification creates a framework for quantitative assessment of newly developed time-varying system identification methods.
Task-dependent modulation of multi-dimensional human ankle stiffness
2020, Powered Prostheses: Design, Control, and Clinical Applications
While recent research on controlling an ankle joint of the lower extremity robots that mimic intact human ankle stiffness has gained much attention, this approach is still limited by the fact that modulation of human ankle stiffness is not fully understood yet. This chapter presents a series of our recent efforts to quantify two-dimensional ankle stiffness during various motor tasks including seated, standing, and walking tasks. Robotic devices capable of actuating 2 DOF (degrees-of-freedom) of the ankle, in particular, dorsiflexion-plantarflexion in the sagittal plane and inversion-eversion in the frontal plane, in combination with system identification methods, allowed us to reliably quantify two-dimensional ankle stiffness during static and dynamic tasks that involve a wide range of muscle activation patterns. Our studies have demonstrated that human ankle stiffness modulates in a task-dependent manner, but it is consistently greater in the sagittal plane than in the frontal plane. The studies have also confirmed that quantification results in one specific task cannot be directly translated to explain ankle stiffness modulation in other tasks, emphasizing the importance of quantification over various motor tasks. Ultimately, integration of findings observed from a wide range of tasks will allow us to construct a universal ankle stiffness model that better explains task-dependent modulation of multi-dimensional ankle stiffness and provides more reliable information to robotic controllers.
The 2-DOF mechanical impedance of the human ankle during poses of the stance phase
2020, Powered Prostheses: Design, Control, and Clinical Applications
The mechanical impedance of the human ankle is vital for the human interactions with the environment for many activities of daily living (ADL), and its accurate characterization is necessary for the development of ankle-foot prostheses that mimic the unimpaired ankle behavior. This work reports the methods and the results of the ankle impedance identification of healthy subjects standing in poses resembling stages of the gait cycle. The resulting impedance was similar to functional experiments where the subjects are walking. Finally, to validate the proposed method, artificial subjects were numerically simulated, and their impedance was evaluated, to assess the accuracy of the proposed method.
Non-linear properties of the Achilles tendon determine ankle impedance over a broad range of activations in humans
2023, Journal of Experimental Biology
Regulating ankle mechanics is essential for controlled interactions with the environment and rejecting unexpected disturbances. Ankle mechanics can be quantified by impedance, the dynamic relationship between an imposed displacement and the torque generated in response. Ankle impedance in the sagittal plane depends strongly on the triceps surae and Achilles tendon, but their relative contributions remain unknown. It is commonly assumed that ankle impedance is controlled by changing muscle activation and, thereby, muscle impedance, but this ignores that tendon impedance also changes with activation-induced loading. Thus, we sought to determine the relative contributions from the triceps surae and Achilles tendon during conditions relevant to postural control. We used a novel technique that combines B-mode ultrasound imaging with joint-level perturbations to quantify ankle, muscle and tendon impedance simultaneously across activation levels from 0% to 30% of maximum voluntary contraction. We found that muscle and tendon stiffness, the static component of impedance, increased with voluntary plantarflexion contractions, but that muscle stiffness exceeded tendon stiffness at very low loads (21±7 N). Above these loads, corresponding to 1.3% of maximal strength for an average participant in our study, ankle stiffness was determined predominately by Achilles tendon stiffness. At approximately 20% MVC for an average participant, ankle stiffness was 4 times more sensitive to changes in tendon stiffness than to changes in muscle stiffness. We provide the first empirical evidence demonstrating that the nervous system, through changes in muscle activations, leverages the non-linear properties of the Achilles tendon to increase ankle stiffness during postural conditions.

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View full text

Dynamics of human ankle stiffness: Variation with mean ankle torque

Abstract

Brain Res.

J. Biomechanics

J. Biomechanics

Studies in postural control systems. Part 1: torque disturbance input

IEEE Trans. Systems Man Cybernet

Oscillation of the human ankle joint in response to applied sinusoidal torque on the foot

J. Physiol., Lond.

Compliance of the human ankle

Trans. Am. Soc. mech. Engrs

Dynamic characteristics of stretch reflex using force inputs

J. Neurophysiol.

Evidence that the human jaw stretch reflex increases the resistance of the mandible to small displacements

J. Physiol., Lond.

Regulatory actions of human stretch reflex

J. Neurophysiol.

Intended arm movements in response to externally produced arm displacements in man

Tension responses to sudden length change in stimulated frog muscle fibres near slack length

J. Physiol., Lond.

The relation between stiffness and filament overlap in stimulated frog muscle fibres

J. Physiol., Lond.

Response to sudden torques about ankle in man: myotatic reflex

J. Neurophysiol.