Elbow impedance during goal-directed movements

System identification: a feasible, reliable and valid way to quantify upper limb motor impairments

BACKGROUND

Upper limb impairments in a hemiparetic arm are clinically quantified by well-established clinical scales, known to suffer poor validity, reliability, and sensitivity. Alternatively, robotics can assess motor impairments by characterizing joint dynamics through system identification. In this study, we establish the merits of quantifying abnormal synergy, spasticity, and changes in joint viscoelasticity using system identification, evaluating (1) feasibility and quality of parametric estimates, (2) test-retest reliability, (3) differences between healthy controls and patients with upper limb impairments, and (4) construct validity.

METHODS

Forty-five healthy controls, twenty-nine stroke patients, and twenty cerebral palsy patients participated. Participants were seated with the affected arm immobilized in the Shoulder-Elbow-Perturbator (SEP). The SEP is a one-degree-of-freedom perturbator that enables applying torque perturbations to the elbow while providing varying amounts of weight support to the human arm. Participants performed either a 'do not intervene' or a resist task. Elbow joint admittance was quantified and used to extract elbow viscosity and stiffness. Fifty-four of the participants performed two sessions to establish the test-retest reliability of the parameters. Construct validity was assessed by correlating system identification parameters to parameters extracted using a SEP protocol that objectifies current clinical scales (Re-Arm protocol).

RESULTS

Feasibility was confirmed by all participants successfully completing the study protocol within ~ 25 min without reporting pain or burden. The parametric estimates were good with a variance-accounted-for of ~ 80%. A fair to excellent test-retest reliability was found ([Formula: see text]) for patients, except for elbow stiffness with full weight support ([Formula: see text]). Compared to healthy controls, patients had a higher elbow viscosity and stiffness during the 'do not intervene' task and lower viscosity and stiffness during the resist task. Construct validity was confirmed by a significant (all [Formula: see text]) but weak to moderate ([Formula: see text]) correlation with parameters from the Re-Arm protocol.

CONCLUSIONS

This work demonstrates that system identification is feasible and reliable for quantifying upper limb motor impairments. Validity was confirmed by differences between patients and controls and correlations with other measurements, but further work is required to optimize the experimental protocol and establish clinical value.

Validation of Methods for Estimation of Knee Joint Mechanical Impedance During Locomotion Using a Torque-Controllable Knee Exoskeleton

The mechanical impedance of the joints of the leg governs the body's response to external disturbances, and its regulation is essential for the completion of tasks of daily life. However, it is still unclear how this quantity is regulated at the knee during dynamic tasks. In this work, we introduce a method to estimate the mechanical impedance of spring-mass systems using a torque-controllable exoskeleton with the intention of extending these methods to characterize the mechanical impedance of the human knee during locomotion. We characterize system bandwidth and intrinsic impedance and present a perturbation-based methodology to identify the mechanical impedance of known spring-mass systems. Our approach was able to obtain accurate estimates of stiffness and inertia, with errors under 3% and ∼13-16%, respectively. This work provides a qualitative and quantitative foundation that will enable accurate estimates of knee joint impedance during locomotion in future works.

sEMG-Based Natural Control Interface for a Variable Stiffness Transradial Hand Prosthesis

We propose, implement, and evaluate a natural human-machine control interface for a variable stiffness transradial hand prosthesis that achieves tele-impedance control through surface electromyography (sEMG) signals. This interface, together with variable stiffness actuation (VSA), enables an amputee to modulate the impedance of the prosthetic limb to properly match the requirements of a task while performing activities of daily living (ADL). Both the desired position and stiffness references are estimated through sEMG signals and used to control the VSA hand prosthesis. In particular, regulation of hand impedance is managed through the impedance measurements of the intact upper arm; this control takes place naturally and automatically as the amputee interacts with the environment, while the position of the hand prosthesis is regulated intentionally by the amputee through the estimated position of the shoulder. The proposed approach is advantageous since the impedance regulation takes place naturally without requiring amputees' attention and diminishing their functional capability. Consequently, the proposed interface is easy to use, does not require long training periods or interferes with the control of intact body segments. This control approach is evaluated through human subject experiments conducted over able volunteers where adequate estimation of references and independent control of position and stiffness are demonstrated.

Linear Predictive Coding for Acute Stress Prediction from Computer Mouse Movements

Prior work demonstrated the potential of using the Linear Predictive Coding (LPC) filter to approximate muscle stiffness and damping from computer mouse movements to predict acute stress levels of users. Theoretically, muscle stiffness and damping in the arm can be estimated using a mass-spring-damper (MSD) biomechanical model. However, the damping frequency (i.e., stiffness) and damping ratio values derived using LPC were not yet compared with those from a theoretical MSD model. This work demonstrates that the damping frequency and damping ratio from LPC are significantly correlated with those from an MSD model, thus confirming the validity of using LPC to infer muscle stiffness and damping. We also compare the stress level binary classification performance using the values from LPC and MSD with each other and with neural network-based baselines. We found comparable performance across all conditions demonstrating LPC and MSD model-based stress prediction efficacy, especially for longer mouse trajectories.Clinical relevance- This work demonstrates the validity of the LPC filter to approximate muscle stiffness and damping and predict acute stress from computer mouse movements.

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.

Effects of model inaccuracies on reaching movements with intermittent control

Background and objectives

Human motor control (HMC) has been hypothesized to involve state estimation, prediction and feedback control to overcome noise, delays and disturbances. However, the nature of communication between these processes, and, in particular, whether it is continuous or intermittent, is still an open issue. Depending on the nature of communication, the resulting control is referred to as continuous control (CC) or intermittent control (IC). While standard HMC theories are based on CC, IC has been argued to be more viable since it reduces computational and communication burden and agrees better with some experimental results. However, to be a feasible model for HMC, IC has to cope well with inaccurately modeled plants, which are common in daily life, as when lifting lighter than expected loads. While IC may involve event-driven triggering, it is generally assumed that refractory mechanisms in HMC set a lower limit on the interval between triggers. Hence, we focus on periodic IC, which addresses this lower limit and also facilitates analysis.

Theoretical methods and results

Theoretical stability criteria are derived for CC and IC of inaccurately modeled linear time-invariant systems with and without delays. Considering a simple muscle-actuated hand model with inaccurately modeled load, both CC and IC remain stable over most of the investigated range, and may become unstable only when the actual load is much smaller than expected, usually smaller than the minimum set by the actual mass of the forearm and hand. Neither CC nor IC is consistently superior to the other in terms of the range of loads over which the system remains stable.

Numerical methods and results

Numerical simulations of time-delayed reaching movements are presented and analyzed to evaluate the effects of model inaccuracies when the control and observer gains are time-dependent, as is assumed to occur in HMC. Both IC and CC agree qualitatively with previously published experimental results with inaccurately modeled plants. Thus, our study suggests that IC copes well with inaccurately modeled plants and is indeed a viable model for HMC.

Passive Elbow Movement Assistant (PEMA): A portable exoskeleton to compensate angle-dependent tone profile of the elbow joint post-stroke

Significant impairments in upper extremity function are commonly observed after neurological injuries such as stroke. While the efficacy of robotic training has been demonstrated, the use of these devices is confined to the laboratory setting due to its complexity and power requirements. In this study, we developed a passive, portable device (Portable Elbow Movement Assistant; PEMA) that can provide assistance during elbow movements of stroke survivors. The geometric properties of the device were designed to allow morphological changes in the elastic components during movements, so that the assistance produced by the elastic component counteract the angle-dependent flexor hypertonia commonly observed in stroke survivors. A mathematical model for the proposed design was first developed to characterize the assistance provided by the device. The capacity of the device was then tested in a pilot testing with four healthy subjects, for whom a custom device to simulate elbow flexor hypertonia (providing an increased resistance for the extended posture) was implemented. The proposed device was found to effectively counteract the angle-dependent flexion moment, produced by the hypertonia simulator, as a significant decrease was observed in the slope of the angle-activation relationship (movement phase) and activation level (hold phase) of the triceps brachii muscle. The assistance did not affect the activation of the antagonist muscle (biceps brachii), indicating an independent modulation of the agonist and antagonist muscles resulted from the assistance.

Altered Neural Control Reduces Shear Forces and Ankle Impedance on a Slippery Surface

OBJECTIVE

This study investigated the consequences of reduced ankle muscle activity on slippery surfaces. We hypothesized that reduced activation would reduce shear forces and ankle impedance to improve contact and reduce slip potential.

METHODS

Data were collected from unimpaired adults walking across non-slippery and slippery walkways. Set within the walkway was a robotic platform with an embedded force plate for collecting shear forces and estimating the mechanical impedance of the ankle; impedance was characterized by a model with stiffness, damping, and inertia.

RESULTS

We found a significant reduction in shear force due to reduced muscle activity in late mid-stance. We found no significant difference in stiffness between the surfaces. However, the muscle activation changes that contributed to shear force modulation occurred in late mid-stance, where reliable impedance estimates could not be made due to the foot leaving the measurement platform. When impedance could be measured, we found that a change in muscle activity predicted a change in stiffness, providing indirect estimates that stiffness was likely reduced later in stance.

CONCLUSION

These results suggest that reduced muscle activity on slippery surfaces serves to reduce shear forces, and possibly also stiffness, during late mid-stance.

SIGNIFICANCE

These results have implications for identifying and training likely fallers, and possibly for designing prosthetic systems that help prevent falls when walking across different terrains.

Simulation of variable impedance as an intervention for upper extremity motor exploration

Current methods in robot-assisted therapy are limited in providing predictions of the effectiveness of interventions. Our approach focuses on how robotic interaction can impact the distribution of movements expressed in the arm. Using data from a previous study with stroke survivors (n=10), we performed simulations to examine how changes in hand endpoint impedance would alter exploratory motion. We present methods for designing a custom training intervention, by relating the desired change in acceleration covariance in planar motion with a corresponding change in inertia matrix. We first characterized motor exploration in terms of overall covariance in acceleration, and secondly as covariance that varies with position in the workspace. Using a forward dynamics simulation of the hand endpoint impedance, we found that the variable change in endpoint inertia resulted in better recovery of acceleration covariance compared to the fixed change in inertia method. These results could significantly impact rehabilitation firstly in terms of design principles for altering coordination patterns through direct assistance. Furthermore, our work might serve to improve therapy by facilitating access to repeated practice of independent joint motion.

Position and stiffness modulation of a wrist haptic device using myoelectric interface

Modulation of stiffness provides a great deal of advantage in the way humans interact with the environment, and is very important in successfully performing activities of daily living. In the context of human-machine interactions, stiffness control could provide a safer interaction, especially when dealing with unpredictable environment. In this paper we propose a user-modulated stiffness and position control for the wrist flexion/extension degree of freedom while physically coupled to a haptic device. A virtual position tracking experiment in a varying external force field is designed in order to test the performance of the control strategy with and without co-contraction techniques. Tracking accuracy and smoothness of motion indicate better performance when subjects use co-contraction techniques, and the difference in the two types of experiment is also statistically significant.

Evaluation of speed-accuracy trade-off in a computer task in individuals with cerebral palsy: a cross-sectional study

BACKGROUND

Individuals with Cerebral Palsy (CP) present with sensorimotor dysfunction which make the control and execution of movements difficult. This study aimed to verify the speed-accuracy trade-off in individuals with CP.

METHODS

Forty eight individuals with CP and 48 with typical development (TD) were evaluated (32 females and 64 males with a mean age of 15.02 ± 6.37 years: minimum 7 and maximum 30 years). Participants performed the "Fitts' Reciprocal Aiming Task v.1.0 (Horizontal)" on a computer with different sizes and distance targets, composed by progressive indices of difficulty (IDs): ID2, ID4a and ID4b.

RESULTS

There were no statistical differences between the groups in relation to the slope of the curve (b1) and dispersion of the movement time (r²). However, the intercept (b0) values presented significant differences (F(1.95) = 11.3; p = .001]), with greater movement time in the CP group compared to the TD group. It means that for individuals with CP, regardless of index difficulty, found the task more difficult than for TD participants. Considering CP and TD groups, speed-accuracy trade-off was found when using different indices of difficulty (ID2 and ID4). However, when the same index of difficulty was used with a larger target and longer distance (ID4a) or with a narrow target and shorter distance (ID4b), only individuals with CP had more difficulty performing the tasks involving smaller targets. Marginally significant inverse correlations were identified between the values of b1 and age (r = -0.119, p = .052) and between r² and Gross Motor Function Classification System (r = -0.280, p = .054), which did not occur with the Manual Ability Classification System.

CONCLUSION

We conclude that the individuals with CP presented greater difficulty when the target was smaller and demanded more accuracy, and less difficulty when the task demanded speed. It is suggested that treatments should target tasks with accuracy demands, that could help in daily life tasks, since it is an element that is generally not considered by professionals during therapy.

TRIAL REGISTRATION

ClinicalTrials.gov, NCT03002285 , retrospectively registered on 20 Dec 2016.

Mechanisms contributing to reduced knee stiffness during movement

The ability to modulate the mechanical properties of our limbs contributes to our ability to interact with the physical world in a consistent and predictable manner. An individual joint's contributions to whole limb mechanics can be quantified by its joint impedance, which characterizes the torque generated about a joint in response to external perturbations of position. A number of studies have estimated joint impedance during movement and have shown that it can be much lower than it is during posture. However, the mechanisms contributing to these differences remain unknown partly because conditions known to affect impedance, including muscle activation and joint angles, have not been carefully controlled across studies. The goal of this study was to contrast knee impedance during continuous volitional movements with that during maintained postures spanning a similar range of joint angles and muscle activations and to explore physiological mechanisms likely to contribute to the observed differences. We found that knee impedance was substantially lower during movement than during matched postural tasks, even for matched muscle activations. At times, the impedance during movement was even lower than that measured during isometric tasks with no volitional muscle activity. These decreases in impedance could be attributed in part to reduced stretch reflexes during movement and to an effect of movement itself on reducing knee impedance.

Motor Control Performance During Rapid Voluntary Movements of Elbow and Knee

Knowledge of motor control differences during rapid goal-directed movements of the upper and lower limbs could be useful in improving rehabilitation protocols. The authors investigated performance and control differences between elbow and knee joints and between different contraction types (concentric vs. eccentric) during rapid movements under externally applied load. There were no significant differences in performance and control with respect to joint (elbow vs. knee) but the performance during concentric contractions was better than eccentric for both the joints. The findings indicate that despite anatomical and functional differences, the CNS is finely tuned for both the joints to maximize the efficiency of movement during a dynamic environment, but there are differences in control strategies between the 2 contraction types.

Critical damping conditions for third order muscle models: implications for force control

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semi-infinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.

Handedness can be explained by a serial hybrid control scheme

Our previous studies on healthy individuals and stroke patients led us to propose that the dominant and nondominant arms are specialized for distinct motor control processes. We hypothesize that the dominant arm is specialized for predictive control of limb dynamics, and the nondominant arm is specialized for impedance control. We previously introduced a hybrid control scheme to explain lateralization of single-joint elbow movements. In this paper we apply a similar computational framework to explore interlimb differences in multi-joint reaching movements: the movements of both arms are initiated using predictive control mechanisms, and terminated using impedance mechanisms. Four parameters characterize predictive mechanisms, four parameters characterize impedance mechanisms, and the ninth parameter describes the instant of switch between the two modes of control. Based on our hypothesis of motor lateralization, we predict an early switch to impedance control for the nondominant arm, but a late switch, near the end of motion, for the dominant arm. We fit our model to multi-joint reaching movements of each arm, made in the horizontal plane. Our results reveal that the more curved trajectories of the nondominant arm are characterized by an early switch to impedance mechanisms, in the initial phase of motion near peak velocity. In contrast, the trajectories of the dominant arm were best fit, when the switch to impedance mechanisms occurred late in the deceleration phase of motion. These results support a model of motor lateralization in which the dominant controller is specialized for predictive control of task dynamics, while the nondominant arm is specialized for impedance control mechanisms. For the first time, we are able to operationally define handedness expressed during multi-joint movements by applying a computational control model.

Motor inhibition affects the speed but not accuracy of aimed limb movements in an insect

When reaching toward a target, human subjects use slower movements to achieve higher accuracy, and this can be accompanied by increased limb impedance (stiffness, viscosity) that stabilizes movements against motor noise and external perturbation. In arthropods, the activity of common inhibitory motor neurons influences limb impedance, so we hypothesized that this might provide a mechanism for speed and accuracy control of aimed movements in insects. We recorded simultaneously from excitatory leg motor neurons and from an identified common inhibitory motor neuron (CI1) in locusts that performed natural aimed scratching movements. We related limb movement kinematics to recorded motor activity and demonstrate that imposed alterations in the activity of CI1 influenced these kinematics. We manipulated the activity of CI1 by injecting depolarizing or hyperpolarizing current or killing the cell using laser photoablation. Naturally higher levels of inhibitory activity accompanied faster movements. Experimentally biasing the firing rate downward, or stopping firing completely, led to slower movements mediated by changes at several joints of the limb. Despite this, we found no effect on overall movement accuracy. We conclude that inhibitory modulation of joint stiffness has effects across most of the working range of the insect limb, with a pronounced effect on the overall velocity of natural movements independent of their accuracy. Passive joint forces that are greatest at extreme joint angles may enhance accuracy and are not affected by motor inhibition.

Task-dependent impedance and implications for upper-limb prosthesis control

Modern-day prosthetic limbs are currently unable to imitate the versatile interaction behaviors of real human arms. Although humans can vary the impedance of their arms, commercially available prosthetic limbs have impedance properties that cannot be directly controlled by users. We investigate the hypothesis that user-selectable prosthesis impedance properties could improve the user’s ability to interact effectively with a variety of environments. We report the results of a series of human subject studies exploring this hypothesis using either a virtual prosthesis or a robot arm as a prosthesis proxy. We observed human performance with different stiffness and damping levels in the prosthesis proxy in two one-degree-of-freedom tasks: (1) a force minimization task and (2) a trajectory tracking task. The virtual prosthesis studies focus on human performance in an ideal simulated system to avoid limitations of a physical implementation, whereas the robot arm study focuses on performance changes that result from limitations of physical robotic hardware. The virtual prosthesis results showed that task-dependent impedance can improve user performance and that users can evaluate the effects of changing impedance. The robot arm results showed similar performance benefits of task-dependent impedance in a physical robotic system. These studies identified areas in which non-ideal characteristics of the physical system limited users’ performance; most notably, the physical system could not achieve the low damping levels that helped subjects reduce contact forces in the virtual prosthesis studies. Thus, we identify some design considerations for prostheses with user-selectable impedance that can achieve useful impedance ranges for improving user performance.

The dynamic effect of muscle activation on knee stiffness

Adapting limb mechanics in a task and environment dependent manner is one component of human motor control. Joint mechanics have been extensively studied under static postural conditions, but less so under time-varying movement conditions. The limited studies that have investigated joint mechanics during movement, have found a drop in joint stiffness during movement, however the source of this decrease in stiffness remains unknown. Here in this paper we investigate whether time-varying muscle activation, which occurs during volitional movement, can lead to the drop in stiffness seen during movement. We found that under time-varying isometric conditions stiffness dropped when subjects transitioned from extension to flexion and vice-versa, a phenomenon that could not be explained by simply superimposing extension and flexion contractions. These findings suggest that dynamics of muscle activation may be responsible for the complex pattern of stiffness changes seen during simple movements. Furthermore, these results imply that EMG-based estimates of stiffness, which work well for steady-state postural conditions, will need to be augmented to account for the highly non-linear relationship between muscle activation and stiffness before they can also be used to estimate stiffness during dynamic contractions.

Development of a mechatronic platform and validation of methods for estimating ankle stiffness during the stance phase of walking

The mechanical properties of human joints (i.e., impedance) are constantly modulated to precisely govern human interaction with the environment. The estimation of these properties requires the displacement of the joint from its intended motion and a subsequent analysis to determine the relationship between the imposed perturbation and the resultant joint torque. There has been much investigation into the estimation of upper-extremity joint impedance during dynamic activities, yet the estimation of ankle impedance during walking has remained a challenge. This estimation is important for understanding how the mechanical properties of the human ankle are modulated during locomotion, and how those properties can be replicated in artificial prostheses designed to restore natural movement control. Here, we introduce a mechatronic platform designed to address the challenge of estimating the stiffness component of ankle impedance during walking, where stiffness denotes the static component of impedance. The system consists of a single degree of freedom mechatronic platform that is capable of perturbing the ankle during the stance phase of walking and measuring the response torque. Additionally, we estimate the platform's intrinsic inertial impedance using parallel linear filters and present a set of methods for estimating the impedance of the ankle from walking data. The methods were validated by comparing the experimentally determined estimates for the stiffness of a prosthetic foot to those measured from an independent testing machine. The parallel filters accurately estimated the mechatronic platform's inertial impedance, accounting for 96% of the variance, when averaged across channels and trials. Furthermore, our measurement system was found to yield reliable estimates of stiffness, which had an average error of only 5.4% (standard deviation: 0.7%) when measured at three time points within the stance phase of locomotion, and compared to the independently determined stiffness values of the prosthetic foot. The mechatronic system and methods proposed in this study are capable of accurately estimating ankle stiffness during the foot-flat region of stance phase. Future work will focus on the implementation of this validated system in estimating human ankle impedance during the stance phase of walking.

Linear parameter varying identification of ankle joint intrinsic stiffness during imposed walking movements

This paper describes a novel model structure and identification method for the time-varying, intrinsic stiffness of human ankle joint during imposed walking (IW) movements. The model structure is based on the superposition of a large signal, linear, time-invariant (LTI) model and a small signal linear-parameter varying (LPV) model. The methodology is based on a two-step algorithm; the LTI model is first estimated using data from an unperturbed IW trial. Then, the LPV model is identified using data from a perturbed IW trial with the output predictions of the LTI model removed from the measured torque. Experimental results demonstrate that the method accurately tracks the continuous-time variation of normal ankle intrinsic stiffness when the joint position changes during the IW movement. Intrinsic stiffness gain decreases from full plantarflexion to near the mid-point of plantarflexion and then increases substantially as the ankle is dosriflexed.

Joint impedance decreases during movement initiation

The mechanical properties of the joint influence how we interact with our environment and hence are important in the control of both posture and movement. Many studies have investigated how the mechanical properties-specifically the impedance-of different joints vary with different postural tasks. However, studies on how joint impedance varies with movement remain limited. The few studies that have investigated how impedance varies with movement have found that impedance is lower during movement than during posture. In this study we investigated how impedance changed as people transitioned from a postural task to a movement task. We found that subjects' joint impedances decreased at the initiation of movement, prior to increasing at the cessation of movement. This decrease in impedance occurred even though the subjects' torque and EMG levels increased. These findings suggest that during movement the central nervous system may control joint impedance independently of muscle activation.

System identification of physiological systems using short data segments

System identification of physiological systems poses unique challenges, especially when the structure of the system under study is uncertain. Nonparametric techniques can be useful for identifying system structure, but these typically assume stationarity and require large amounts of data. Both of these requirements are often not easily obtained in the study of physiological systems. Ensemble methods for time-varying nonparametric estimation have been developed to address the issue of stationarity, but these require an amount of data that can be prohibitive for many experimental systems. To address this issue, we developed a novel algorithm that uses multiple short data segments. Using simulation studies, we showed that this algorithm produces system estimates with lower variability than previous methods when limited data are present. Furthermore, we showed that the new algorithm generates time-varying system estimates with lower total error than an ensemble method. Thus, this algorithm is well suited for the identification of physiological systems that vary with time or from which only short segments of stationary data can be collected.

Biomechanical constraints on the feedforward regulation of endpoint stiffness

Although many daily tasks tend to destabilize arm posture, it is still possible to have stable interactions with the environment by regulating the multijoint mechanics of the arm in a task-appropriate manner. For postural tasks, this regulation involves the appropriate control of endpoint stiffness, which represents the stiffness of the arm at the hand. Although experimental studies have been used to evaluate endpoint stiffness control, including the orientation of maximal stiffness, the underlying neural strategies remain unknown. Specifically, the relative importance of feedforward and feedback mechanisms has yet to be determined due to the difficulty separately identifying the contributions of these mechanisms in human experiments. This study used a previously validated three-dimensional musculoskeletal model of the arm to quantify the degree to which the orientation of maximal endpoint stiffness could be changed using only steady-state muscle activations, used to represent feedforward motor commands. Our hypothesis was that the feedforward control of endpoint stiffness orientation would be significantly constrained by the biomechanical properties of the musculoskeletal system. Our results supported this hypothesis, demonstrating substantial biomechanical constraints on the ability to regulate endpoint stiffness throughout the workspace. The ability to regulate stiffness orientation was further constrained by additional task requirements, such as the need to support the arm against gravity or exert forces on the environment. Together, these results bound the degree to which slowly varying feedforward motor commands can be used to regulate the orientation of maximum arm stiffness and provide a context for better understanding conditions in which feedback control may be needed.

Measuring multi-joint stiffness during single movements: numerical validation of a novel time-frequency approach

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

An EMG-Based Control for an Upper-Limb Power-Assist Exoskeleton Robot

Many kinds of power-assist robots have been developed in order to assist self-rehabilitation and/or daily life motions of physically weak persons. Several kinds of control methods have been proposed to control the power-assist robots according to user's motion intention. In this paper, an electromyogram (EMG)-based impedance control method for an upper-limb power-assist exoskeleton robot is proposed to control the robot in accordance with the user's motion intention. The proposed method is simple, easy to design, humanlike, and adaptable to any user. A neurofuzzy matrix modifier is applied to make the controller adaptable to any users. Not only the characteristics of EMG signals but also the characteristics of human body are taken into account in the proposed method. The effectiveness of the proposed method was evaluated by the experiments.

Design and validation of a platform robot for determination of ankle impedance during ambulation

In order to provide natural, biomimetic control to recently developed powered ankle prostheses, we must characterize the impedance of the ankle during ambulation tasks. To this end, a platform robot was developed that can apply an angular perturbation to the ankle during ambulation and simultaneously acquire ground reaction force data. In this study, we detail the design of the platform robot and characterize the impedance of the ankle during quiet standing. Subjects were perturbed by a 3° dorsiflexive ramp perturbation with a length of 150 ms. The impedance was defined parametrically, using a second order model to map joint angle to the torque response. The torque was determined using the inverted pendulum assumption, and impedance was identified by the least squares best estimate, yielding an average damping coefficient of 0.03 ± 0.01 Nms/° and an average stiffness coefficient of 3.1 ± 1.2 Nm/°. The estimates obtained by the proposed platform robot compare favorably to those published in the literature. Future work will investigate the impedance of the ankle during ambulation for powered prosthesis controller development.

Motor lateralization is characterized by a serial hybrid control scheme

Our previous studies of limb coordination in healthy right- and left-handers led to the development of a theoretical model of motor lateralization, dynamic dominance, which was recently supported by studies in patients with unilateral stroke. One of our most robust findings was on single-joint movements in young healthy subjects [Sainburg and Schaefer (2004) J Neurophysiol 92:1374-1383]. In this study, subjects made elbow joint reaching movements toward four targets of different amplitudes with each arm. Although both arms achieved equivalent task performance, each did so through different strategies. The dominant arm strategy scaled peak acceleration with peak velocity and movement extent, while the nondominant strategy adjusted acceleration duration to achieve the different velocities and distances. We now propose that these observed interlimb differences can be explained using a serial hybrid controller in which movements are initiated using predictive control and terminated using impedance control. Further, we propose that the two arms should differ in the relative time that control switches from the predictive to the impedance mechanisms. We present a mathematical formulation of our hybrid controller and then test the plausibility of this control paradigm by investigating how well our model can explain interlimb differences in experimental data. Our findings confirm that the model predicts early shifts between controllers for left arm movements, which rely on impedance control mechanisms, and late shifts for right arm movements, which rely on predictive control mechanisms. This is the first computational model of motor lateralization and is consistent with our theoretical model that emerged from empirical findings. It represents a first step in consolidating our theoretical understanding of motor lateralization into an operational model of control.

In vivo dynamics of the musculoskeletal system cannot be adequately described using a stiffness-damping-inertia model

BACKGROUND

Visco-elastic properties of the (neuro-)musculoskeletal system play a fundamental role in the control of posture and movement. Often, these properties are described and identified using stiffness-damping-inertia (KBI) models. In such an approach, perturbations are applied to the (neuro-)musculoskeletal system and subsequently KBI-model parameters are optimized to obtain a best fit between simulated and experimentally observed responses. Problems with this approach may arise because a KBI-model neglects critical aspects of the real musculoskeletal system.

METHODOLOGY/PRINCIPAL FINDINGS

The purpose of this study was to analyze the relation between the musculoskeletal properties and the stiffness and damping estimated using a KBI-model, to analyze how this relation is affected by the nature of the perturbation and to assess the sensitivity of the estimated stiffness and damping to measurement errors. Our analyses show that the estimated stiffness and damping using KBI-models do not resemble any of the dynamical parameters of the underlying system, not even when the responses are very accurately fitted by the KBI-model. Furthermore, the stiffness and damping depend non-linearly on all the dynamical parameters of the underlying system, influenced by the nature of the perturbation and the time interval over which the KBI-model is optimized. Moreover, our analyses predict a very high sensitivity of estimated parameters to measurement errors.

CONCLUSIONS/SIGNIFICANCE

The results of this study suggest that the usage of stiffness-damping-inertia models to investigate the dynamical properties of the musculoskeletal system under control by the CNS should be reconsidered.

The effects of gender, level of co-contraction, and initial angle on elbow extensor muscle stiffness and damping under a step increase in elbow flexion moment

Flexion buckling of an arm under the large ground reaction loads associated with arresting a fall to the ground increases the risk for head and thorax injuries. Yet, the factors that determine the arm buckling load remain poorly understood. We tested the hypothesis in 18 healthy young adults that neither gender, triceps co-contraction level (i.e., 25, 50, or 75% MVC) nor elbow angle would affect the rotational stiffness and damping resistance to step changes in elbow flexion loading. Data on the step response were gathered using optoelectronic markers (150 Hz) and myoelectric activity measurements (2 kHz), and an inverse dynamics analysis was used to estimate elbow extensor stiffness and damping coefficients. A repeated-measures analysis of variance showed that gender (p = 0.032), elbow flexion angle and co-contraction level (both p < 0.001) affected stiffness, but only the latter affected the damping coefficient (p = 0.035). At 25° of initial elbow flexion angle and maximum co-contraction, female stiffness and damping coefficients were 18 and 30% less, respectively, than male values after normalization by body height and weight. We conclude that the maximum extensor rotational stiffness and damping at the elbow is lower in women than in men of the same body size, and varies with triceps co-contraction level and initial elbow angle.

A new time-frequency approach to estimate single joint upper limb impedance

This paper proposes a new technique to estimate single joint impedance during postural tasks. The method is based on a reassigned spectrogram and can track the frequency modulation of biomechanical system after perturbations. Compared to the existing techniques, this procedure successfully estimated rapidly time varying impedance parameters in a faster and equally accurate way. For this reason it can be an optimum tool to easily estimate limb impedance of stroke patients, before, during, and after robot therapy sessions, without interfering with the delivered treatment.

Effects of Human Arm Impedance on Dynamics Learning and Generalization

Previous studies have demonstrated anisotropic patterns of hand impedance under static conditions and during movement. Here we show that the pattern of kinematic error observed in studies of dynamics learning is associated with this anisotropic impedance pattern. We also show that the magnitude of kinematic error associated with this anisotropy dictates the amount of motor learning and, consequently, the extent to which dynamics learning generalizes. Subjects were trained to reach to visual targets while holding a robotic device that applied forces during movement. On infrequent trials, the load was removed and the resulting kinematic error was measured. We found a strong correlation between the pattern of kinematic error and the anisotropic pattern of hand stiffness. In a second experiment subjects were trained under force-field conditions to move in two directions: one in which the dynamic perturbation was in the direction of maximum arm impedance and the associated kinematic error was low and another in which the perturbation was in the direction of low impedance where kinematic error was high. Generalization of learning was assessed in a reference direction that lay intermediate to the two training directions. We found that transfer of learning was greater when training occurred in the direction associated with the larger kinematic error. This suggests that the anisotropic patterns of impedance and kinematic error determine the magnitude of dynamics learning and the extent to which it generalizes.

Stability and Variability: Indicators for Passive Stability and Active Control in a Rhythmic Task

Using a rhythmic task where human subjects bounced a ball with a handheld racket, fine-grained analyses of stability and variability extricated contributions from open-loop control, noise strength, and active error compensation. Based on stability analyses of a stochastic-deterministic model of the task—a surface contacting the ball by periodic movements—open-loop or dynamic stability was assessed by the acceleration of the racket at contact. Autocovariance analyses of model and data were further used to gauge the contributions of open-loop stability and noise strength. Variability and regression analyses estimated active error compensation. Empirical results demonstrated that experienced actors exploited open-loop stability more than novices, had lower noise strength, and applied more active error compensations. By manipulating the model parameter coefficient of restitution, task stability was varied and showed that actors graded these three components as a function of task stability. It is concluded that actors tune into task stability when stability is high but use more active compensation when stability is reduced. Implications for the neural underpinnings for passive stability and active control are discussed. Further, results showed that stability and variability are not simply the inverse of each other but contain more quantitative information when combined with model analyses.

User-modulated impedance control of a prosthetic elbow in unconstrained, perturbed motion

Humans use the agonist-antagonist structure of their muscles to simultaneously determine both the motion and the stiffness of their joints. Designing this feature into an artificial limb may prove advantageous. To evaluate the performance of an artificial limb capable of modulating its impedance, we have created a compact series elastic actuator that has the same size and similar weight as commercially available electric prosthetic elbows. The inherent compliance in series elastic actuators ensure their safety to the user, even at high speeds, while creating a high-fidelity force actuator ideally suited for impedance control. This paper describes three serial studies that build on each other. The first study presents modeling of the actuator to ensure stability in the range of impedance modulation and empirically tests the actuator to validate its ability to modulate impedance. The actuator is found to be stable and accurate over a wide range of impedances. In the second study, four subjects are tested in a preliminary experiment to answer basic questions necessary to implement user-modulated impedance control. Findings include the superiority of velocity control over position control as the underlying motion paradigm and the preference for high stiffness and non-negative inertia. Based on the findings of the second study, the third study evaluates the performance of 15 able-bodied subjects for two tasks, using five different impedance paradigms. Impedance modulation, speed, and error were compared across paradigms. The results indicate that subjects do not actively modulate impedance if it is near a preferred baseline. Fixed impedance and viscosity modulation provide the most accurate control.

Equilibrium point control cannot be refuted by experimental reconstruction of equilibrium point trajectories

In the literature, it has been hotly debated whether the brain uses internal models or equilibrium point (EP) control to generate arm movements. EP control involves specification of EP trajectories, time series of arm configurations in which internal forces and external forces are in equilibrium; if the arm is not in a specified EP, it is driven toward this EP by muscle forces arising due to central drive, reflexes, and muscle mechanics. EP control has been refuted by researchers claiming that EP trajectories underlying movements of subjects were complex. These researchers used an approach that involves applying force perturbations during movements of subjects and fitting a mass-spring-damper model to the kinematic responses, and then reconstructing the EP trajectory using the estimated stiffness, damping, and measured kinematics. In this study, we examined the validity of this approach using an EP-controlled musculoskeletal model of the arm. We used the latter model to simulate unperturbed and perturbed maximally fast movements and optimized the parameter values of a mass-spring-damper model to make it reproduce as best as possible the kinematic responses. It was shown that estimated stiffness not only depended on the "true" stiffness of the musculoskeletal model but on all of its dynamical parameters. Furthermore it was shown that reconstructed EP trajectories were in agreement with those presented in the literature but did not resemble the simple EP trajectories that had been used to generate the movement of the model. It was concluded that the refutation of EP control on the basis of results obtained with mass-spring-damper models was unjust.

A model of open-loop control of equilibrium position and stiffness of the human elbow joint

According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the alpha-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (K (ilf)). For this purpose, a model of the upper and lower arm was constructed, equipped with Hill-type muscles. At a constant neural input, the isometric force of the contractile element of the muscles depended on both the myofilamentary overlap and the effect of sarcomere length on the sensitivity of myofilaments to [Ca2+] (LDCS). The musculoskeletal model, for which the parameters were chosen carefully on the basis of physiological literature, captured the salient isometric properties of the muscles spanning the elbow joint. It was found that stable open-loop EPs could be achieved over the whole range of motion of the elbow joint and that K (ilf), which ranged from 18 to 42 N m.rad(-1), could be independently controlled. In the model, LDCS contributed substantially to K (ilf) (up to 25 N m.rad(-1)) and caused K (ilf) to peak at a sub-maximal level of co-contraction.

Threshold control of arm posture and movement adaptation to load

We addressed the fundamental questions of which variables underlie the control of arm movement and how they are stored in motor memory, reproduced and modified in the process of adaptation to changing load conditions. Such variables are defined differently in two major theories of motor control (internal models and threshold control). To resolve the controversy, these theories were tested (experiment 1) based on their ability to explain why active movement away from a stable posture is not opposed by stabilizing mechanisms (the posture-movement problem). The internal model theory suggests that the system counteracts the opposing forces by increasing the muscle activity in proportion to the distance from the initial posture (position-dependent EMG control). In contrast, threshold control fully excludes these opposing forces by shifting muscle activation thresholds and thus resetting the stabilizing mechanisms to a new posture. Subjects were sitting, holding the vertical handle of a double-joint manipulandum with their right hand and were facing a computer screen on which the handle and target to be reached were displayed. In response to an auditory signal, subjects quickly moved the handle from an initial position to one of two (frontal and sagittal) targets. No load was applied during the movement but in separate trials, a brief perturbation was applied to the handle by torque motors controlling the manipulandum. Perturbations were applied prior to or 3 s after movement offset, in the latter case in one of eight directions. The EMG activity of the majority of the seven recorded muscles was at zero level before movement onset and returned to zero level after movement offset. Those muscles that remained active before or after the movement could be made silent whereas previously silent muscles could be activated after a small passive displacement (several millimeters) elicited by perturbations in appropriate directions. Results showed that the activation thresholds of motoneurons of arm muscles were reset from the initial to a final position and that EMG activity was not position-dependent. These results were inconsistent with the internal model theory but confirmed the threshold control theory. Then the ability of threshold control theory to explain rapid movement adaptation to a position-dependent load was investigated (experiment 2 and 3). Subjects produced fast movement to the frontal target with and without a position-dependent load applied to the handle. Trials were organized in blocks alternating between the load and no-load condition (20 blocks in total, with randomly chosen number of five to ten trials in each). Subjects were instructed "do not correct" in experiment 2 and "correct" movement errors during the trial in experiment 3. Five threshold arm configurations underlying the movement production and adaptation were identified. When instructed "do not correct", movement precision was fully restored on average after two trials. No significant improvement was observed as the experiment progressed despite the fact that the same load condition was repeated after one block of trials. Thus, in each block, the adaptation was made anew, implying that subjects relied on short-term memory and could not recall the threshold arm configurations they specified to accurately reach the same target in the same load condition in previous blocks. When instructed to "correct" within each trial, precision was restored faster, on average after one trial. Major aspects of the production and adaptation of arm movement (including the kinematics, movement errors, instruction-dependent behavior, and absence of position-related EMG activity) are explained in terms of threshold control.

Postural fluctuations during pointing from a unilateral or bilateral stance

An experiment was conducted to compare the effects of bilateral and unilateral stance on postural fluctuations and intralimb coordination during active balance control. Fifteen participants stood bilaterally and unilaterally while conducting a pointing task with an outstretched arm. Excursion of center of foot pressure (CoP) and limb movements were recorded with a force plate and eight dual-axis accelerometers, respectively. Compared to bilateral stance, unilateral stance resulted in wider CoP trajectories and greater postural fluctuations, especially in the lower limbs. The limb-dependent postural fluctuations during unilateral stance were associated with an increased coupling between the upper limb segments and a decreased coupling between the segments of the stance leg. Unilateral stance further resulted in greater regularity and spectral changes in postural fluctuations of the trunk and lower limb due to increased central oscillations (8-15 Hz). The observed structural differences in postural fluctuations between unilateral and bilateral stance strongly suggested that the postural control system modulates joint stiffness in a stance-dependent manner. Probably, in unilateral stance, attentive control was shifted to the stance leg at the expense of increasing arm stiffness to reduce movement redundancy.

Intrinsic musculoskeletal properties stabilize wiping movements in the spinalized frog

The mechanical stability properties of hindlimb-hindlimb wiping movements of the spinalized frog were examined. One hindlimb, the wiping limb, was implanted with 12 electromyographic (EMG) electrodes and attached to a robot that both recorded its trajectory and applied brief force perturbations. Cutaneous electrical stimulation was applied to the other hindlimb, the target limb, to evoke the hindlimb-hindlimb wiping reflex. Kinematic and EMG data from both unperturbed trials and trials in which a phasic perturbation was applied were collected from each spinalized frog. In the perturbed behaviors, we found that the initially large displacement attributable to the perturbation was compensated such that the final position was statistically indistinguishable from the unperturbed final position in all of the frogs, thus indicating the dynamic stability of these movements. This stability was robust to the range of perturbation amplitudes and nominal kinematic variation observed in this study. In addition, we investigated the extent to which intrinsic viscoelastic properties of the limb and proprioceptive feedback play a role in stabilizing the movements. No significant changes were seen in the EMGs after the perturbation. Furthermore, deafferentation of the wiping limb did not significantly affect the stability of the wiping reflex. Thus, we found that the intrinsic viscoelastic properties of the hindlimb conferred robust stability properties to the hindlimb-hindlimb wiping behavior. This stability mechanism may simplify the control required by the frog spinal motor systems to produce successful movements in an unpredictable and varying environment.

Is equilibrium point control feasible for fast goal-directed single-joint movements?

Several types of equilibrium point (EP) controllers have been proposed for the control of posture and movement. EP controllers are appealing from a computational perspective because they do not require solving the "inverse dynamic problem" (i.e., computation of the torques required to move a system along a desired trajectory). It has been argued that EP controllers are not capable of controlling fast single-joint movements. To refute this statement, several extensions have been proposed, although these have been tested using models in which only the tendon compliance, force-length-velocity relation, and mechanical interaction between tendon and contractile element were not adequately represented. In the present study, fast elbow-joint movements were measured and an attempt was made to reproduce these using a realistic musculoskeletal model of the human arm. Three types of EP controllers were evaluated: an open-loop alpha-controller, a closed-loop lambda-controller, and a hybrid open- and closed-loop controller. For each controller we considered a continuous version and a version in which the control signals were sent out intermittently. Only the intermittent hybrid EP controller was capable of generating movements that were as fast as those of the subjects. As a result of the nonlinear muscle properties, the hybrid EP controller requires a more detailed representation of static muscle properties than generally assumed in the context of EP control. In sum, this study shows that fast single-joint movements can be realized without explicitly solving the inverse dynamics problem, but in a less straightforward manner than implied by proponents of conventional EP controllers.

Impedance is modulated to meet accuracy demands during goal-directed arm movements

The neuromuscular system is inherently noisy and joint impedance may serve to filter this noise. In the present experiment, we investigated whether individuals modulate joint impedance to meet spatial accuracy demands. Twelve subjects were instructed to make rapid, time constrained, elbow extensions to three differently sized targets. Some trials (20 out of 140 for each target, randomly assigned) were perturbed mechanically at 75% of movement amplitude. Inertia, damping and stiffness were estimated from the torque and angle deviation signal using a forward simulation and optimization routine. Increases in endpoint accuracy were not always reflected in a decrease in trajectory variability. Only in the final quarter of the trajectory the variability decreased as target width decreased. Stiffness estimates increased significantly with accuracy constraints. Damping estimates only increased for perturbations that were initially directed against the movement direction. We concluded that joint impedance modulation is one of the strategies used by the neuromuscular system to generate accurate movements, at least during the final part of the movement.

Testing hypotheses and the advancement of science: recent attempts to falsify the equilibrium point hypothesis

Criticisms of the equilibrium point (EP) hypothesis have recently appeared that are based on misunderstandings of some of its central notions. Starting from such interpretations of the hypothesis, incorrect predictions are made and tested. When the incorrect predictions prove false, the hypothesis is claimed to be falsified. In particular, the hypothesis has been rejected based on the wrong assumptions that it conflicts with empirically defined joint stiffness values or that it is incompatible with violations of equifinality under certain velocity-dependent perturbations. Typically, such attempts use notions describing the control of movements of artificial systems in place of physiologically relevant ones. While appreciating constructive criticisms of the EP hypothesis, we feel that incorrect interpretations have to be clarified by reiterating what the EP hypothesis does and does not predict. We conclude that the recent claims of falsifying the EP hypothesis and the calls for its replacement by EMG-force control hypothesis are unsubstantiated. The EP hypothesis goes far beyond the EMG-force control view. In particular, the former offers a resolution for the famous posture-movement paradox while the latter fails to resolve it.