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Appropriate regulation of joint impedance is required to successfully navigate our environment. Joint impedance is strongly dependent upon the mechanical properties of the muscles and tendons spanning it. While the impedance of the joint has been well characterized, methods to determine the individual contribution from the muscles and tendons are limited. This is a crucial gap as muscle and tendon impedance can be selectively altered by aging, pathology, or injury. Therefore, we developed an innovative in vivo method that allows for the simultaneous quantification of joint, muscle, and tendon impedance. Stochastic perturbations of ankle angle were applied while a B-mode ultrasound was used to image the displacement of the medial gastrocnemius muscle-tendon junction. Non-parametric system identification was used to quantify ankle impedance and the frequency response function between ankle rotations and muscle-tendon junction displacements. The latter represents, when scaled by Achilles tendon moment arm, the ratio between the net musculotendon impedance and the impedance of the muscle, a relationship we refer to as the impedance ratio. Muscle and tendon impedance can be calculated from these experimental estimates. The ability to simultaneously quantify joint, muscle, and tendon impedance will provide a clearer understanding their respective roles in our ability to navigate our environment, and how changes in those roles may contribute to functional impairments.

Falls initiated by slipping are a major cause for concern for lower-limb amputees, due to their lacking the distal musculature that aids in avoiding the initiation of a slip. It has been previously demonstrated that able-bodied individuals can interact safely with slippery surfaces by adapting limb kinematics and altering muscle activity to minimize slipping. Newly developed prosthetic devices have the potential to restore specific gait modes to the user, such as walking on a slippery surface, if only more was known about how the mechanical properties should be regulated in each mode. As a first step towards understanding the mechanics relevant to slip prevention, this study sought to quantify lower-limb muscle activity during steady state walking on a range of slippery surfaces. A specific goal was to quantify how people walk on moderately slippery surfaces that pose a hazard, but are more likely to be found on an everyday basis than some of the surfaces previously studied. Our results showed a significant trend (p

Functional electrical stimulation can be used to reanimate paralyzed muscles, thereby restoring movement following spinal cord injury (SCI). Developing FES controllers for complex tasks involving multiple muscles and kinematic degrees of freedom remains formidable, partly due to the challenges associated with developing robust models for control. Here we demonstrate the utility of incorporating a data-driven semi-parametric model into an FES controller. A subject-specific model was estimated from experimental data collected from a single subject with a high-level SCI and an implanted FES neuroprosthesis. The model was used as part of a feedforward controller of arm kinematics. This system performed well for regions of the workspace where sufficient muscle strength was available. It could be used to predict the additional assistance needed when FES-generated strength was not available. These results demonstrate a first step towards developing a feedforward FES controller that could be used as part of a feedback system for restoring arm control or for a cooperative system combining FES with lightweight robotics for augmentation.

We present a method to experimentally identify the inverse dynamics of a human arm. We drive a person’s hand with a robot along smooth reaching trajectories while measuring the motion of the shoulder and elbow joints and the force required to move the hand. We fit a model that predicts the shoulder and elbow joint torques required to achieve a desired arm motion. This torque can be supplied by functional electrical stimulation of muscles to control the arm of a person paralyzed by spinal cord injury. Errors in predictions of the joint torques for a subject without spinal cord injury were less than 20% of the maximum torques observed in the identification experiments. In most cases a semiparametric Gaussian process model predicted joint torques with equal or less error than a nonparametric Gaussian process model or a parametric model.

In this paper we present a method to stimulate multiple muscles in a human arm to perform interaction tasks, using an implanted Functional Electrical Stimulation (FES) neuroprosthesis. The unstable effect arising from interaction tasks is considered, and the arm stability is directly treated as one of the control objectives in the controller design. By ex- ploiting the kinematic and muscular redundancy of the system, we can control the interaction force and the arm's stiffness property simultaneously, thus ensuring the stable execution of interaction tasks. A representative example of such interaction tasks, namely the "pushing with a stick" task, is simulated. It is found that using our proposed controller, as compared to a previously developed feedforward FES controller that does not consider arm stiffness or stability, the stability of the arm is guaranteed while the task of force control is correctly achieved.

Handedness has been proposed as a laterality of motor control specialization: the dominant limb specializes in controlling limb trajectory using feed-forward mechanisms, while the non-dominant limb is specialized for position control, reliant largely upon feedback mechanisms. Experimental motor control research has tended to use the dominant arm, which could bias our understanding of control toward dominant-sided mechanisms. To determine if this is the case for our work on rapid motor responses, we here investigate the effect of laterality on long-latency reflexes, which are a rapid feedback response to perturbations of limb posture. Our results confirm previous work showing that environmental instabilities increase long-latency reflex gain, but we did not observe any difference between the dominant and non-dominant arm. Both arms displayed similar reflex responses during a stabilizing postural task, despite the proposed advantage of the non-dominant side for position feedback control. This suggests that the lateralized specialization of motor control is confined to different cortical pathways than those involved in this reflex response.

Following tendon transfer of the biceps to triceps after cervical spinal cord injuries (SCI), individuals must learn to activate the transferred biceps muscle to extend the elbow. Corticomotor excitability of the transferred biceps may play a role in post-operative elbow extension strength. In this study, we evaluated whether corticomotor excitability of the transferred biceps is related to an individuals' ability to extend the elbow, and whether posture and muscle length affects corticomotor excitability after SCI and tendon transfer similarly to the nonimpaired biceps. Corticomotor excitability was assessed in twelve nonimpaired arms and six arms of individuals with SCI and biceps-to-triceps transfer using transcranial magnetic stimulation (TMS) delivered at rest. Maximum isometric elbow extensor moments were recorded in transferred arms and the fiber length of the transferred biceps was estimated using a musculoskeletal model. Across the SCI subjects, corticomotor excitability of the transferred biceps increased with elbow extension strength. Thus, rehabilitation to increase excitability may enhance strength. Excitability of the transferred biceps was not related to fiber length suggesting that similar to nonimpaired subjects, posture-dependent changes in biceps excitability are primarily centrally modulated after SCI. All nonimpaired biceps were most excitable in a posture in the horizontal plane with the forearm fully supinated. The proportion of transferred biceps in which excitability was highest in this posture differed from the nonimpaired group. Therefore, rehabilitation after tendon transfer may be most beneficial if training postures are tailored to account for changes in biceps excitability.

One approach to designing robotic prostheses that interact with the environment in a naturally compliant fashion is to design them with mechanical properties that replicate the functions of an intact limb. Limb and joint mechanics can be quantified using estimates of impedance, a measure that can also be regulated in robotic systems using feedback control. Numerous studies have quantified the impedance of intact joints under static postural conditions. However, the few studies that have quantified impedance during movement have shown that it differs drastically from estimates obtained during static postural conditions. Specifically, the static component of impedance, known as stiffness, is substantially lower during movement control than during postural control. This difference has important implications for designing biomimetic prostheses and other robotic systems, though the factors contributing to the differences between posture and movement and the extent of these differences under different movement conditions are not yet known. In this paper, we systematically explore how human knee stiffness is affected by the kinematic and mechanical variables that constantly vary during movement. To do so we used a non-parametric system identification algorithm that makes few assumptions on the structure of the system or the relationship of the system to these changing kinematic and mechanical variables. We found that stiffness did not correlate with the net joint torque, as occurs during postural conditions, but rather with computed active muscle torque. Furthermore, we found that externally imposed movements during passive conditions cause a drop in joint stiffness, implying that at least some of the observed results are due to changes in intrinsic muscle or joint mechanics rather than altered neural control.

Trajectory decoding from neural signals may be useful for the restoration of reach to paralyzed arms through functional electrical stimulation or the control of robotic arms or computer interfaces. Electromyograms (EMGs) are a popular non-invasive choice of signal source for neuroprosthetic interfaces but continuous trajectory control is challenging, especially when the set of muscles that can be recorded from is limited. One reason for this difficulty is that many applications provide only visual feedback to the users. In addition to motor impairments, spinal cord injury (SCI) may alter or eliminate sensation in the arm below the level of injury. We tested an EMG-controlled robot-assisted reaching task, in which the arm was moved in congruence with the output of the decoder, in 5 individuals with cervical SCI and 5 healthy controls. We also evaluated remote control of the robot, where the congruent sensory feedback at the arm was removed. We found a significant drop in performance without feedback at the arm that was larger for the individuals with SCI. Despite their sensory impairments, moving their arms as part of the task enabled functional control of reach that was impossible without the additional sensory information.

Functional electrical stimulation (FES) can be used to restore movement control following paralysis. For complex multijoint systems, it is becoming increasingly apparent that closed-loop controllers are needed. Designing a closed-loop control system is easiest when the open-loop system is stable. In this study we developed a computational model to assess the open-loop stability of FES-control systems. We used the model to examine the open-loop stability of the human arm throughout its reachable workspace. For each simulated position of the hand we examined the stability of the arm, assuming that a minimal pattern of muscle activation was used to support the arm against gravity. Only muscles available to an existing FES user were considered. We found that with this reduced muscle set, the stability of the arm was severely compromised. We also demonstrated that muscle co-contraction can be an effective method to improve the stability for many postures.

For rehabilitative devices to restore functional movement to paralyzed individuals, user intent must be determined from signals that remain under voluntary control. Tracking eye movements is a natural way to learn about an intended reach target and, when combined with just a small set of electromyograms (EMGs) in a probabilistic mixture model, can reliably generate accurate trajectories even when the target information is uncertain. To experimentally assess the effectiveness of our algorithm in closed-loop control, we developed a robotic system to simulate a reaching neuroprosthetic. Incorporating target information by tracking subjects' gaze greatly improved performance when the set of EMGs was most limited. In addition we found that online performance was better than predicted by the offline accuracy of the training data. By enhancing the trajectory model with target information the decoder relied less on neural control signals, reducing the burden on the user.

There are numerous approaches to estimating the dynamics of time-varying systems. Ensemble approaches are especially suited for estimating time-varying biological systems as they require no assumptions about the time-varying behavior of the system being estimated. In this paper we evaluate the ability of non-parametric ensemble methods to estimate time-varying changes in the underlying parameters of a dynamic system. Using simulated data we determined that the estimated static gain of the system was filtered by the dynamics of the system. Furthermore, when the underlying parameters of the system changed in a step-wise fashion, the parameters estimated from the identified non-parametric impulse or frequency response functions did not match the simulated model parameters for a time corresponding to the transient response of the simulated system. These findings show that a system with time-varying parameters cannot be represented by a series of impulse or frequency responses characterized by parameters that match the values and time course of the underlying system. Thus, underlying system parameters cannot be inferred directly from non-parametric time-varying estimates, as they can be in a time-invariant case. These results have important implications for understanding the parametric variations associated with time-varying systems that are best studied using non-parametric approaches, such as many biological systems.

We present a method for controlling a neuroprosthesis for a paralyzed human arm using functional electrical stimulation (FES). The subject has surgically implanted electrodes for stimulating muscles in her shoulder and arm. Using input/output data, a model is identified that describes the mapping from muscle stimulations to the endpoint force measured at the subject's hand. To compute the muscle stimulations given a target endpoint force the model is inverted. Because the system is redundant, we compute the inverse by minimizing muscle activations and use this inverse for feedforward control. This is the first published demonstration with a human subject with a high spinal cord injury of an FES controller that treats the arm with shoulder and elbow as a multiple-input multiple-output system and can achieve arbitrary goals.

Trajectory-based models that incorporate target position information have been shown to accurately decode reaching movements from bio-control signals, such as muscle (EMG) and cortical activity (neural spikes). One major hurdle in implementing such models for neuroprosthetic control is that they are inherently designed to decode single reaches from a position of origin to a specific target. Gaze direction can be used to identify appropriate targets, however information regarding movement intent is needed to determine when a reach is meant to begin and when it has been completed. We used linear discriminant analysis to classify limb states into movement classes based on recorded EMG from a sparse set of shoulder muscles. We then used the detected state transitions to update target information in a mixture of Kalman filters that incorporated target position explicitly in the state, and used EMG activity to decode arm movements. Updating the target position initiated movement along new trajectories, allowing a sequence of appropriately timed single reaches to be decoded in series and enabling highly accurate continuous control.

Knee joint impedance varies substantially during physiological gait. Quantifying this modulation is critical for the design of transfemoral prostheses that aim to mimic physiological limb behavior. Conventional methods for quantifying joint impedance typically involve perturbing the joint in a controlled manner, and describing impedance as the dynamic relationship between applied perturbations and corresponding joint torques. These experimental techniques, however, are difficult to apply during locomotion without impeding natural movements. In this paper, we propose a method to estimate the elastic component of knee joint impedance that depends on muscle activation, often referred to as active knee stiffness. The method estimates stiffness using a musculoskeletal model of the leg and a model for activation-dependent short-range muscle stiffness. Muscle forces are estimated from measurements including limb kinematics, kinetics and muscle electromyograms. For isometric validation, we compare model estimates to measurements involving joint perturbations; measured stiffness is 17% lower than model estimates for extension, and 42% lower for flexion torques. We show that sensitivity of stiffness estimates to common approaches for estimating muscle force is small in isometric conditions. We also make initial estimates of how knee stiffness is modulated during gait, illustrating how this approach may be used to obtain parameters relevant to the design of transfemoral prostheses. © 2011 IEEE.

Joint stiffness is often represented by a parallel cascade model. The present study proposes a new approach to identify the parameters of such model structures from nonlinear frequency response functions. At first, a harmonic probing technique is used to derive the linear and higher-order frequency response functions (called the generalized frequency response functions (GFRFs)) of systems represented by parallel cascade models. The computation of the GFRFs is a recursive procedure where each lower order GFRF contains no effects from higher order terms. Thus the parameter estimation problem can be formulated in a linear least squares framework where the parameters corresponding to nonlinearities of different orders can be estimated independently, beginning with first order and then building up to include the nonlinear terms using the weighted complex orthogonal estimator, which is a modified version of the standard orthogonal least squares, that accommodates complex data. Simulation results are included to demonstrate that the proposed method can successfully estimate the parameters of the system under the effects of significant levels of noise.

The present study proposes a new approach to identify the parameters of both continuous and discrete time Hammerstein systems in frequency domain. A harmonic probing technique is used to derive the linear and higher-order frequency response functions (called the generalized frequency response functions (GFRF)) of both discrete and continuous-time Hammerstein models. The computation of the n-th order generalized frequency response functions (GFRF) is a recursive procedure where each lower order GFRF contains no effects from higher order terms. Thus the parameter estimation problem can be formulated in a linear least squares framework where the parameters corresponding to nonlinearities of different orders can be estimated independently, beginning with first order and then building up to include the nonlinear terms using the weighted complex orthogonal estimator, which is a modified version of the standard orthogonal least squares, to accommodate complex data. Simulation results are included to demonstrate that the proposed method can successfully estimate the parameters of the system under the effects of significant levels of noise.

The dynamics of sway during quiet stance have often been approximated by the movement of an unstable inverted pendulum. Controlling this unstable load requires the nervous system to balance the reliance on feed-forward volitional activation and feedback mechanisms such as stretch reflexes. It has been demonstrated that reflex excitability is heightened when postural stability is threatened by destabilizing forces in the environment. However, the relationship between postural stability, volitional activation, and stretch reflex excitability remains unclear. We addressed this question by characterizing feed-forward and feedback activation strategies during balance of a simulated inverted pendulum. We hypothesized that feed-forward co-contraction and stretch reflex amplitude would scale together as the external support provided by the environment was reduced. Electromyographic (EMG) responses in 5 muscles of the lower limb were used to characterize co-contraction patterns and stretch reflex amplitude as subjects stabilized the simulated loads. Our results revealed that co-contraction magnitude did indeed scale with increasingly destabilizing torques; however reflex amplitude was attenuated as stability was reduced. These findings suggest that the contribution of feedback mechanisms to postural stability depends on both the level of stability provided by the environment and how the environment influences the pattern of volitional activation.

The purpose of this study was to develop an animal model to evaluate the efficacy of a brain machine interface (BMI) to control a neuroprosthesis intended to restore hand function via functional neuromuscular stimulation (FNS). We have implemented the system in a single primate, whose limb could be temporarily paralyzed by a reversible peripheral nerve block Recordings from the primary motor cortex were obtained from a 100-electrode array in the intact monkey, and used to predict the activity of a variety of wrist and hand muscles. These predictions were calculated in real-time, and used as inputs to a 4 channel neuromuscular stimulator for electrically activating the paralyzed muscles. Here we demonstrate that the BMI can be used to restore voluntary control of wrist flexion following muscle paralysis.

The purpose of this study was to develop an animal model for evaluating the efficacy of a brain machine interface (BMI) for controlling functional neuromuscular stimulation (FNS). We have implemented such a system in a single primate. Our experimental model includes a 100-electrode implanted micro-array for recording intracortical signals, a reversible peripheral nerve block for temporarily paralyzing wrist and hand muscles, and a neuromuscular stimulator for electrically activating the paralyzed muscles. To date, we have evaluated the efficacy of each of these components and demonstrated how the BMI can be used to restore voluntary control of wrist flexion following muscle paralysis

The strategy the central nervous system utilizes to produce movements in the face of multiple degrees of freedom available has been a subject of study for the past few years. Of the possible mechanisms, the muscle synergies-stereotypical coordinated patterns of muscle activity elicited by dedicated networks have been suggested to be the building blocks. Based on this hypothesis, several algorithms have been proposed to discern these synergies from the recorded electromyographic signals (EMG). In the proposed model, the synergies are treated as filters (IRFs) that take as input any arbitrary non-negative signal. That is, the EMG is seen as a convolution mixture of synergies and corresponding inputs.

We are investigating whether repetitive training, such as that used during rehabilitation interventions, can induce short term plasticity in the motor pathways controlling the proximal muscles of the human upper-limb. A ballistic, planar whole limb extension training routine has been employed in this study. This study uses transcranial magnetic stimulation (TMS) to quantify user-dependent plasticity in proximal and distal muscles throughout the upper-limb. Previous studies have shown consistent training induced plasticity in distal upper-limb muscles and proximal muscles with altered somatosensory input. This study demonstrates that whole limb motions can generate short term plastic effects in proximal upper-limb muscles, though results have not been consistent.

This study assessed the ability of the Hill model to predict muscle force for both electrically stimulated and naturally activated cat soleus muscle. Our results indicate that Hill model errors increase with increases in muscle velocity and decrease with increases in motor unit firing rates. For a given muscle velocity, errors were largest in for the range of firing frequencies most relevant for naturally activated muscle. During large muscle displacements, average Hill model errors often were greater than 100%.

It has been difficult to determine the functional role of stretch reflexes because of the difficulty in separating the reflex response from the passive and intrinsic properties of a joint. We have developed a method which uses the delay inherent in this reflex pathway to separate the reflex contribution from the other dynamical properties of the human ankle. Preliminary results indicate that the stretch reflexes have a significant effect on joint dynamics in the 3-15Hz range.

We have developed an algorithm for selecting an optimal set of inputs for use in linear multiple-input, single-output system identification processes. The algorithm provides a decomposition of the system output such that each component is uniquely attributable to a specific input This reduces the complexity of the estimation problem by optimally selecting inputs according to the uniqueness of their output contribution and is useful in when subsets of the inputs are highly correlated or do not contribute significantly to the system output. The algorithm was evaluated on experimental data consisting of up to 40 simultaneously recorded motor cortical signals and peripheral electromyograms (EMGs) from four upper limb muscles in a freely moving primate. It was used to select the optimal motor cortical signals for predicting each of the EMGs and significantly reduced the number of inputs needed to generate accurate EMG predictions. For example, although physiological recordings from up to 40 different neuronal signals were available, the input selection algorithm reduced this 10 neuronal signals that made significant contributions to the recorded EMGs

Several nonparametric system identification techniques have been used to estimate the dynamic joint stiffness of the human elbow. Most studies involved a very stiff environment, but some studies have also shown that stiffness is modified in response to environmental compliance. However, using the same identification technique used under very stiff conditions to do identification under compliant conditions leads to a biased estimate. This is due to the presence of feedback in the latter. In this paper, we use a nonparametric identification algorithm to demonstrate this problem. We then show how instrumental variables can be employed to obtain an unbiased estimate of the same. Both simulations as well as experimental data are used to this effect.

Discretization of dynamic stiffness models is shown to produce an a-causal impulse response. Expressions are derived for discrete-time impulse responses of first-and second-order derivatives. Enforcing periodicity gives rise to anti-causal components in these models. These models are used to describe the anti-causal components in identified stiffness models.

Understanding how stretch sensitive reflexes contribute to the coordination of whole arm posture and movement is best understood in the context of multijoint pertunrbations. However, it is difficult to assess the mechanisms contributing to reflex activity during such unconstrained tasks due to the uncertainties associated with estimating the relative importance of biomechanical and neural coupling between muscles. This study combines experimental and modeling approaches to investigate whether there is significant, neurally-mediated coupling between the muscles of the upper limb. Our data suggest that heteronymous pathways link the actions of muscles spanning multiple joints in the human arm and that these pathways contribute significantly to the reflex responses to perturbations of whole limb posture.

An analysis of activity of primary motor cortex (Ml) and muscle activity in the form of EMGs suggests that Ml contains a large amount of muscle related information. The simultaneous activity of a population of Ml neurons was recorded using a multi-electrode, intracortical array while recording arm muscle EMGs from a rhesus monkey during a multi-target, reaching task. Using multiple-input system identification techniques, linear, non-parametric filters relating the firing rates of the neuronal signals to the muscle EMGs were estimated. These filters were able to reconstruct and predict EMG signals directly from the recorded neuronal tiring rates with a high level of accuracy. Initial cross-validations of the filters suggest that the relationships between Ml and muscles contain time and task dependencies as the quality of the predictions drop for longer time periods between filter estimation and EMG prediction and for cross-validations that involve movements to individual targets. Further tests involving more data sets and cross-validations are necessary to determine more precisely the temporal and task-specific stability of these filters. This will greatly increase our knowledge of how arm movement and muscle activity is encoded in the brain and offer practical applications in the harvesting of neural control signals.

Successful task completion requires strength to counter external forces acting on a limb and stability to maintain limb posture. However, these simultaneous requirements can be at odds with each other as reaction forces directed towards the joints can interact with limb geometry to reduce limb stability. Net stability is due to these external force effects combined with the stability provided by muscles resisting those forces. The goal of this study was to quantify the contributions of cat hindlimb muscles to the 3D force generation and stability properties of the entire limb. Our hypothesis is that anti-gravity extensors must be co-activated with flexors to counter the destabilizing effects of the ground reaction forces directed towards the joints. Data were collected during three experimental conditions: passive, electrical stimulation of the triceps surae on its own, and in conjunction with the hamstrings. We found that the hamstrings muscle group, a leg extensor, destabilized hindlimb posture. These instabilities could be countered by simultaneous co-contraction of the triceps surae muscle group, which had a net ground reaction force in flexion direction. These initial results support our hypothesis that muscles generating downward forces (leg extensors) decrease limb stability.

Extracellular recordings of 43 spinal interneurons were performed in the decerebrate cat while its hindlimb was manipulated in 3 dimensional space with a 6-degree of freedom robotic arm. Internal/external rotations, toe in/toe out and flexion/extension movements were performed about the ankle joint. Peripheral nerve stimulation was used to categorize cells by field potential threshold into gr Ila and gr II types. 80% (16/20) of the gr la cells showed firing frequency changes to less than half of the rotations imposed by the robot and only 20% to more than half. 39% (9/23) of the gr II cells showed responses to less than half of the imposed movements and 61% (14/23) of the gr II cells responded to more than half of the imposed movements.

This study examined the hypothesis that muscles operating in the normal physiological state act as independent actuators. This hypothesis was tested by measuring the nonlinearities associated with three-dimensional (3D) moment and stiffness summation for three muscle groups crossing the cat ankle joint. Our results indicate that the nonlinearities associated with joint moment and stiffness summation are small (

Effects of shoulder stability on endpoint stiffness were investigated with a method that separates elbow and shoulder rotational contributions from shoulder translational contributions to endpoint stiffness.

Tetraplegia resulting from cervical spinal cord injury typically leaves the muscles paralyzed, with the resulting loss extension function. Elbow extension is for many daily activities, important in the rehabilitation of the spinal cord injured individual. This paper compares the widely used surgical transfer of the posterior deltoid muscle, which restores voluntary control over elbow extension, to a technique based on functional neuromuscular stimulation (FNS) of the triceps muscles. Both methods were found to restore a modest level of elbow extension. The posterior deltoid transfer produced variable results and the resulting elbow extension moments were strongly dependent on shoulder position.

Understanding the dynamic response of the human arm to external perturbations is critical for understanding the neural and mechanical factors contributing to postural arm stability and for predicting stability during interactions with the external environment. One means of describing arm dynamics is by estimating the dynamic endpoint stiffness (DES). This paper introduces an efficient nonparametric approach for estimating DES, and uses this technique to characterize changes in DES under different endpoint loading conditions.