Multivariable dynamic ankle mechanical impedance with relaxed muscles

Design and Validation of Soft Sliding Structure with Adjustable Stiffness for Ankle Sprain Prevention

This study presents the design and validation of a soft sliding stiffness structure with a soft-rigid layer sliding mechanism. It aims to mitigate ankle sprains and address the progression of chronic ankle instability by providing stiffness support. The soft-rigid layer sliding mechanism of the structure is designed to achieve a wide range of stiffness while maintaining a compact form factor. The structure incorporates rigid retainer pieces within each layer, which allows for sliding within a hollow cuboid structure and enables modulation of stiffness. An analytical model is presented to investigate the variations in stiffness resulting from the different sliding states. The stiffness characteristics of the structure were validated through both bench tests and human subject tests. The gradual sliding of the structure's layer resulted in an increase in stiffness, aligning with the analytical model's predictions. At the most rigid stage (0% alignment), the stiffness exhibited a significant increase of 111.1% compared to the most flexible stage (100% alignment). Additionally, the human subject testing demonstrated a stiffness increase of up to 93.8%. These results underscore the potential applicability of the soft sliding structure in ankle support applications.

Introduction to a Twin Dual-Axis Robotic Platform for Studies of Lower Limb Biomechanics

This paper presents a twin dual-axis robotic platform system which is designed for the characterization of postural balance under various environmental conditions and quantification of bilateral ankle mechanics in 2 degrees-of-freedom (DOF) during standing and walking. Methods: Validation experiments were conducted to evaluate performance of the system: 1) to apply accurate position perturbations under different loading conditions; 2) to simulate a range of stiffness-defined mechanical environments; and 3) to reliably quantify the joint impedance of mechanical systems. In addition, several human experiments were performed to demonstrate the system's applicability for various lower limb biomechanics studies. The first two experiments quantified postural balance on a compliance-controlled surface (passive perturbations) and under oscillatory perturbations with various frequencies and amplitudes (active perturbations). The second two experiments quantified bilateral ankle mechanics, specifically, ankle impedance in 2-DOF during standing and walking. The validation experiments showed high accuracy of the platform system to apply position perturbations, simulate a range of mechanical environments, and quantify the joint impedance. Results of the human experiments further demonstrated that the platform system is sensitive enough to detect differences in postural balance control under challenging environmental conditions as well as bilateral differences in 2-DOF ankle mechanics. This robotic platform system will allow us to better understand lower limb biomechanics during functional tasks, while also providing invaluable knowledge for the design and control of many robotic systems including robotic exoskeletons, prostheses and robot-assisted balance training programs. Clinical and Translational Impact Statement- Our robotic platform system serves as a tool to better understand the biomechanics of both healthy and neurologically impaired individuals and to develop assistive robotics and rehabilitation training programs using this information.

Biomarkers for rhythmic and discrete dynamic primitives in locomotion

Rehabilitation can promote brain plasticity and improve motor control after central nervous system injuries. Our working model is that motor control is encoded using dynamic primitives: submovements, oscillations, and mechanical impedances. We hypothesize that therapies focusing on these primitives can achieve greater motor recovery. At the observational level, these primitives lead to discrete and rhythmic movements. Here, we propose two novel biomarkers to evaluate rhythmic and discrete movements in gait based on the feet forward position: the smoothness of their relative position, using the mean-squared jerk ratio (MSJR), to assess rhythmicity; and the angle between principal components of consecutive trajectories (dPCA), to detect discrete movements amidst rhythmic motion. We applied these methods to kinematic data collected with healthy individuals during experiments employing the MIT-Skywalker: level-ground walking at five speeds, with and without imposed ankle stiffness; walking at constant speed on ascending, descending, and laterally tilted slopes; and performing sidesteps. We found a decrease in MSJR as speed increases, related to increased rhythmicity, even with imposed stiffness. Rhythmicity seems unaffected by the terrain perturbations imposed. Finally, dPCA successfully detects sidesteps, discrete events amidst rhythmic movement. These biomarkers appear to accurately assess rhythmic and discrete movements during walking and can potentially improve clinical evaluation and rehabilitation of neurological patients.

Multivariable passive ankle impedance in stroke patients: A preliminary study

Multivariable ankle mechanical impedance was estimated in four stroke survivors, in coupled dorsi- plantarflexion and inversion-eversion. We applied external torque perturbation with an ankle robot and used multi-input, multi-output stochastic system identification methods to estimate impedance, in both paretic and nonparetic limbs. Subjects were instructed to remain at rest throughout the four trials performed on each leg. Impedance projected onto the directions of maximum and minimum stiffness was fit to a 2nd order linear model, including inertia, viscosity and stiffness. For most trials, stiffness and damping in dorsi-plantarflexion are increased on the paretic side. However, for two subjects, overall impedance is not increased in the absence of sustained involuntary tonic contraction, registering values comparable to the non-paretic side. Thus, we speculate that the intrinsic properties of the paretic ankle remained unaffected at the evaluated pose. Spasticity (hyperflexive stretch reflex) would have systematically increased stiffness and damping, even in the absence of involuntary contraction. Hence, we speculate that these two subjects did not exhibit spasticity, while the remaining two subjects did, since impedance was increased, with no involuntary tonic muscle contraction. Regarding inversion-eversion, impedance in this direction remained unaffected by stroke. We evaluated two volunteers before and after the application of botulinum toxin. Surprisingly, ankle stiffness was not reduced, but anisotropy was normalized.

A Configurable Architecture for Two Degree-of-Freedom Variable Stiffness Actuators to Match the Compliant Behavior of Human Joints

Living beings modulate the impedance of their joints to interact proficiently, robustly, and safely with the environment. These observations inspired the design of soft articulated robots with the development of Variable Impedance and Variable Stiffness Actuators. However, designing them remains a challenging task due to their mechanical complexity, encumbrance, and weight, but also due to the different specifications that the wide range of applications requires. For instance, as prostheses or parts of humanoid systems, there is currently a need for multi-degree-of-freedom joints that have abilities similar to those of human articulations. Toward this goal, we propose a new compact and configurable design for a two-degree-of-freedom variable stiffness joint that can match the passive behavior of a human wrist and ankle. Using only three motors, this joint can control its equilibrium orientation around two perpendicular axes and its overall stiffness as a one-dimensional parameter, like the co-contraction of human muscles. The kinematic architecture builds upon a state-of-the-art rigid parallel mechanism with the addition of nonlinear elastic elements to allow the control of the stiffness. The mechanical parameters of the proposed system can be optimized to match desired passive compliant behaviors and to fit various applications (e.g., prosthetic wrists or ankles, artificial wrists, etc.). After describing the joint structure, we detail the kinetostatic analysis to derive the compliant behavior as a function of the design parameters and to prove the variable stiffness ability of the system. Besides, we provide sets of design parameters to match the passive compliance of either a human wrist or ankle. Moreover, to show the versatility of the proposed joint architecture and as guidelines for the future designer, we describe the influence of the main design parameters on the system stiffness characteristic and show the potential of the design for more complex applications.

Sex Differences in Human Ankle Stiffness During Standing Balance

The purpose of this study is to quantify sex differences in 2-dimensional (2D) ankle stiffness during upright standing balance and investigate the mechanisms for the differences. A dual-axis robotic platform, capable of perturbing the ankle and measuring the corresponding ankle torques in both the sagittal and frontal planes, was used to reliably quantify the 2D ankle stiffness while healthy young human subjects perform a range of standing balance tasks, specifically, ankle muscle co-contraction tasks, weight-bearing tasks, and ankle torque generation tasks. In all task conditions and in both planes of ankle motion, ankle stiffness in males was consistently greater than that in females. Among all 26 experimental conditions, all but 2 conditions in the frontal plane showed statistically significant sex differences. Further investigation on the normalized ankle stiffness, scaled by weight times height, suggests that while sex differences in ankle stiffness in the sagittal plane could be explained by sex differences in anthropometric factors as well as neuromuscular factors, the differences in the frontal plane are mostly explained by anthropometric factors. This study also demonstrates that the sex differences in the sagittal plane were significantly higher as compared to those in the frontal plane. The results in this study will provide a foundation for not only characterizing sex differences in ankle stiffness during locomotion, but also investigating sex differences in lower body stability and risk of ankle injury.

Quantification and Modeling of Ankle Stiffness During Standing Balance

OBJECTIVE

This study investigates the factors contributing to the modulation of ankle stiffness during standing balance and evaluates the reliability of linear stiffness models.

METHODS

A dual-axis robotic platform and a visual feedback display were used to quantify ankle stiffness in both the sagittal and frontal planes while subjects controlled different levels of ankle muscle co-contraction, center-of-pressure (CoP), and loading on the ankle.

RESULTS

Results of 40 subjects demonstrated that ankle stiffness in the sagittal plane linearly increased with the increasing level of these three factors. The linear model relating the change in these factors from the baseline measurements during quiet standing to the change in weight normalized ankle stiffness resulted in high reliability (R² = 0.83). Ankle stiffness in the frontal plane increased with the increasing ankle muscle co-contraction and ankle loading, but the linearity was less obvious. It also exhibited a clear nonlinear trend when CoP was shifted mediolaterally. Consequently, the reliability of the linear model was low for ankle stiffness in the frontal plane (R² = 0.37).

CONCLUSION

During standing balance, ankle stiffness in the sagittal plane could be well explained by a linear model if ankle muscle activation, CoP, and ankle loading were collectively considered. However, the linear model cannot capture highly variable and nonlinear ankle stiffness characteristics in the frontal plane.

SIGNIFICANCE

The outcomes of this study could benefit the development of lower-extremity robots and their controllers. Furthermore, the ankle stiffness models could be used as a baseline in developing patient-specific ankle rehabilitation protocols.

Multi-Directional Ankle Impedance During Standing Postures

In this study, we estimated the multi-directional ankle mechanical impedance in two degrees-of-freedom (DOF) during standing, and determined how the stiffness, damping, and inertia vary with ankle angle and ankle torque at different postures. Fifteen subjects stood on a vibrating instrumented platform in four stationary postures, while subjected to pulse train perturbations in both the sagittal and frontal planes of motion. The four stationary postures were selected to resemble stages within the stance phase of the gait cycle: including post-heel-strike during the loading response, mid-stance, post-mid-stance, and just before the heel rises from the ground in terminal-stance phase. In general, the ankle stiffness and damping increased in all directions as the foot COP moved forward, and more torque is generated in plantarflexion. Interestingly, the multi-directional ankle impedance during standing showed a similar shape and major tilt axes to the results of non-loaded scenarios. However, there were notable differences in the impedance amplitude when the ankle was not under bodyweight loading. Last, the stiffness during standing had similar amplitudes ranges to the time-varying ankle stiffness during the stance phase of dynamic walking estimated in previous studies. These results have implications on the design of new, less physically intense, biomechanics experiments aimed at people with neuromuscular disorders or other physical impairments who cannot complete a standard gait test.

A Clustering-Based Approach to Identify Joint Impedance During Walking

Mechanical impedance, which changes with posture and muscle activations, characterizes how the central nervous system regulates the interaction with the environment. Traditional approaches to impedance estimation, based on averaging of movement kinetics, requires a large number of trials and may introduce bias to the estimation due to the high variability in a repeated or periodic movement. Here, we introduce a data-driven modeling technique to estimate joint impedance considering the large gait variability. The proposed method can be used to estimate impedance in both the stance and swing phases of walking. A 2-pass clustering approach is used to extract groups of unperturbed gait data and estimate candidate baselines. Then patterns of perturbed data are matched with the most similar unperturbed baseline. The kinematic and torque deviations from the baselines are regressed locally to compute joint impedance at different gait phases. Simulations using the trajectory data of a subject's gait at different speeds demonstrate a more accurate estimation of ankle stiffness and damping with the proposed clustering-based method when compared with two methods: i) using average unperturbed baselines, and ii) matching shifted and scaled average unperturbed velocity baselines. Furthermore, the proposed method requires fewer trials than methods based on average unperturbed baselines. The experimental results on human hip impedance estimation show the feasibility of clustering-based technique and verifies that it reduces the estimation variability.

Quantifying Age-Related Differences of Ankle Mechanical Properties Using a Robotic Device

A deep analysis of ankle mechanical properties is a fundamental step in the design of an exoskeleton, especially if it is to be suitable for both adults and children. This study aims at assessing age-related differences of ankle properties using pediAnklebot. To achieve this aim, we enrolled 16 young adults and 10 children in an experimental protocol that consisted of the evaluation of ankle mechanical impedance and kinematic performance. Ankle impedance was measured by imposing stochastic torque perturbations in dorsi-plantarflexion and inversion-eversion directions. Kinematic performance was assessed by asking participants to perform a goaldirected task. Magnitude and anisotropy of impedance were computed using a multipleinput multiple-output system. Kinematic performance was quantified by computing indices of accuracy, smoothness, and timing. Adults showed greater magnitude of ankle impedance in both directions and for all frequencies, while the anisotropy was higher in children. By analyzing kinematics, children performed movements with lower accuracy and higher smoothness, while no differences were found for the duration of the movement. In addition, adults showed a greater ability to stop the movement when hitting the target. These findings can be useful to a proper development of robotic devices, as well as for implementation of specific training programs.

Activation-Dependent Changes in Soleus Length-Tension Behavior Augment Ankle Joint Quasi-Stiffness

The triceps surae muscle-tendon units are important in governing walking performance, acting to regulate mechanical behavior of the ankle through interaction between active muscle and passive elastic structures. Ankle joint quasi-stiffness (the slope of the relation between ankle moment and ankle rotation, k_A) is a useful aggregate measure of this mechanical behavior. However, the role of muscle activation and length-tension behavior in augmenting k_A remains unclear. In this study, 10 subjects completed eccentric isokinetic contractions at rest and at 2 soleus activation levels (25% and 75% isometric voluntary contraction) prescribed using electromyographic biofeedback. Ultrasound imaging quantified activation-dependent modulation of soleus muscle length-tension behavior and its role in augmenting k_A. The authors found that soleus muscle stiffness (k_M) and k_A exhibit nonlinear relations with muscle activation and both were more sensitive to the onset of activation than to subsequent increases in activation. Our findings also suggest that k_A can be modulated via activation through changes in soleus muscle length-tension behavior. However, this modulation is more complex than previously appreciated-reflecting interaction between active muscle and passive elastic tissues. Our findings may have implications for understanding normal and pathological ankle joint function and the design of impedance-based prostheses.

A novel protocol to evaluate ankle movements during reaching tasks using pediAnklebot

The aim of the study is to design a novel protocol to characterize the ankle movements during dorsal and plantar flexion reaching tasks using the pediAnklebot. Five healthy children were instructed to control a pointer and hit targets appearing on the monitor, by moving their ankle alternatively up and down. The protocol consisted of 60 targets, 30 up and 30 down, reachable via dorsiflexion and plantarflexion movements, respectively. Ankle angular displacements and torques were gathered by encoders and load cells embedded in the robot. Ankle motor performance was evaluated by means of kinematic, submovements and dynamic indices. Results suggest that (i) plantarflexion movements are faster and more accurate than the dorsiflexion ones, but children are able to perform with a higher level of smoothness the latter ones; (ii) children are able to stop the ankle movement more easily at the end of dorsiflexion rather than plantarflexion; (iii) the central nervous system plans plantarflexion and dorsiflexion movements with the same efficiency; (iv) children apply different torque levels during the two motor tasks and they cannot balance the inversion and eversion moments during dorsiflexion. These findings provide an important starting point for the assessment of a reference baseline of motor indices for the ankle joint.

Summary of Human Ankle Mechanical Impedance During Walking

The human ankle joint plays a critical role during walking and understanding the biomechanical factors that govern ankle behavior and provides fundamental insight into normal and pathologically altered gait. Previous researchers have comprehensively studied ankle joint kinetics and kinematics during many biomechanical tasks, including locomotion; however, only recently have researchers been able to quantify how the mechanical impedance of the ankle varies during walking. The mechanical impedance describes the dynamic relationship between the joint position and the joint torque during perturbation, and is often represented in terms of stiffness, damping, and inertia. The purpose of this short communication is to unify the results of the first two studies measuring ankle mechanical impedance in the sagittal plane during walking, where each study investigated differing regions of the gait cycle. Rouse et al. measured ankle impedance from late loading response to terminal stance, where Lee et al. quantified ankle impedance from pre-swing to early loading response. While stiffness component of impedance increases significantly as the stance phase of walking progressed, the change in damping during the gait cycle is much less than the changes observed in stiffness. In addition, both stiffness and damping remained low during the swing phase of walking. Future work will focus on quantifying impedance during the “push off” region of stance phase, as well as measurement of these properties in the coronal plane.

A Subspace Approach to the Structural Decomposition and Identification of Ankle Joint Dynamic Stiffness

OBJECTIVE

The purpose of this paper is to present a structural decomposition subspace (SDSS) method for decomposition of the joint torque to intrinsic, reflexive, and voluntary torques and identification of joint dynamic stiffness.

METHODS

First, it formulates a novel state-space representation for the joint dynamic stiffness modeled by a parallel-cascade structure with a concise parameter set that provides a direct link between the state-space representation matrices and the parallel-cascade parameters. Second, it presents a subspace method for the identification of the new state-space model that involves two steps: 1) the decomposition of the intrinsic and reflex pathways and 2) the identification of an impulse response model of the intrinsic pathway and a Hammerstein model of the reflex pathway.

RESULTS

Extensive simulation studies demonstrate that SDSS has significant performance advantages over some other methods. Thus, SDSS was more robust under high noise conditions, converging where others failed; it was more accurate, giving estimates with lower bias and random errors. The method also worked well in practice and yielded high-quality estimates of intrinsic and reflex stiffnesses when applied to experimental data at three muscle activation levels.

CONCLUSION

The simulation and experimental results demonstrate that SDSS accurately decomposes the intrinsic and reflex torques and provides accurate estimates of physiologically meaningful parameters.

SIGNIFICANCE

SDSS will be a valuable tool for studying joint stiffness under functionally important conditions. It has important clinical implications for the diagnosis, assessment, objective quantification, and monitoring of neuromuscular diseases that change the muscle tone.

Energetic Passivity of the Human Ankle Joint

Understanding the passive or nonpassive behavior of the neuromuscular system is important to design and control robots that physically interact with humans, since it provides quantitative information to secure coupled stability while maximizing performance. This has become more important than ever apace with the increasing demand for robotic technologies in neurorehabilitation. This paper presents a quantitative characterization of passive and nonpassive behavior of the ankle of young healthy subjects, which provides a baseline for future studies in persons with neurological impairments and information for future developments of rehabilitation robots, such as exoskeletal devices and powered prostheses. Measurements using a wearable ankle robot actuating 2 degrees-of-freedom of the ankle combined with curl analysis and passivity analysis enabled characterization of both quasi-static and steady-state dynamic behavior of the ankle, unavailable from single DOF studies. Despite active neuromuscular control over a wide range of muscle activation, in young healthy subjects passive or dissipative ankle behavior predominated.

Mechanical Impedance of the Non-loaded Lower Leg with Relaxed Muscles in the Transverse Plane

This paper describes the protocols and results of the experiments for the estimation of the mechanical impedance of the humans' lower leg in the External-Internal direction in the transverse plane under non-load bearing condition and with relaxed muscles. The objectives of the estimation of the lower leg's mechanical impedance are to facilitate the design of passive and active prostheses with mechanical characteristics similar to the humans' lower leg, and to define a reference that can be compared to the values from the patients suffering from spasticity. The experiments were performed with 10 unimpaired male subjects using a lower extremity rehabilitation robot (Anklebot, Interactive Motion Technologies, Inc.) capable of applying torque perturbations to the foot. The subjects were in a seated position, and the Anklebot recorded the applied torques and the resulting angular movement of the lower leg. In this configuration, the recorded dynamics are due mainly to the rotations of the ankle's talocrural and the subtalar joints, and any contribution of the tibiofibular joints and knee joint. The dynamic mechanical impedance of the lower leg was estimated in the frequency domain with an average coherence of 0.92 within the frequency range of 0-30 Hz, showing a linear correlation between the displacement and the torques within this frequency range under the conditions of the experiment. The mean magnitude of the stiffness of the lower leg (the impedance magnitude averaged in the range of 0-1 Hz) was determined as 4.9 ± 0.74 Nm/rad. The direct estimation of the quasi-static stiffness of the lower leg results in the mean value of 5.8 ± 0.81 Nm/rad. An analysis of variance shows that the estimated values for the stiffness from the two experiments are not statistically different.

Multivariable dynamic ankle mechanical impedance with active muscles

Multivariable dynamic ankle mechanical impedance in two coupled degrees-of-freedom (DOFs) was quantified when muscles were active. Measurements were performed at five different target activation levels of tibialis anterior and soleus, from 10% to 30% of maximum voluntary contraction (MVC) with increments of 5% MVC. Interestingly, several ankle behaviors characterized in our previous study of the relaxed ankle were observed with muscles active: ankle mechanical impedance in joint coordinates showed responses largely consistent with a second-order system consisting of inertia, viscosity, and stiffness; stiffness was greater in the sagittal plane than in the frontal plane at all activation conditions for all subjects; and the coupling between dorsiflexion-plantarflexion and inversion-eversion was small-the two DOF measurements were well explained by a strictly diagonal impedance matrix. In general, ankle stiffness increased linearly with muscle activation in all directions in the 2-D space formed by the sagittal and frontal planes, but more in the sagittal than in the frontal plane, resulting in an accentuated "peanut shape." This characterization of young healthy subjects' ankle mechanical impedance with active muscles will serve as a baseline to investigate pathophysiological ankle behaviors of biomechanically and/or neurologically impaired patients.