Cross-correlation time-frequency analysis for multiple EMG signals in Parkinson's disease: a wavelet approach

Using a wavelet analysis approach, it is possible to investigate better the transient and intermittent behavior of multiple electromyographic (EMG) signals during ballistic movements in Parkinsonian patients. In particular, a wavelet cross-correlation analysis on surface signals of two different shoulder muscles allows us to evidence the related unsteady and synchronization characteristics. With a suitable global parameter extracted from local wavelet power spectra, it is possible to accurately classify the subjects in terms of a reliable statistic and to study the temporal evolution of the Parkinson's disease level. Moreover, a local intermittency measure appears as a new promising index to distinguish the low-frequency behavior from normal subjects to Parkinsonian patients.     

Compensation for interaction torques during single- and multijoint limb movement

During multijoint limb movements such as reaching, rotational forces arise at one joint due to the motions of limb segments about other joints. We report the results of three experiments in which we assessed the extent to which control signals to muscles are adjusted to counteract these "interaction torques." Human subjects performed single- and multijoint pointing movements involving shoulder and elbow motion, and movement parameters related to the magnitude and direction of interaction torques were manipulated systematically. We examined electromyographic (EMG) activity of shoulder and elbow muscles and, specifically, the relationship between EMG activity and joint interaction torque. A first set of experiments examined single-joint movements. During both single-joint elbow (experiment 1) and shoulder (experiment 2) movements, phasic EMG activity was observed in muscles spanning the stationary joint (shoulder muscles in experiment 1 and elbow muscles in experiment 2). This muscle activity preceded movement and varied in amplitude with the magnitude of upcoming interaction torque (the load resulting from motion of the nonstationary limb segment). In a third experiment, subjects performed multijoint movements involving simultaneous motion at the shoulder and elbow. Movement amplitude and velocity at one joint were held constant, while the direction of movement about the other joint was varied. When the direction of elbow motion was varied (flexion vs. extension) and shoulder kinematics were held constant, EMG activity in shoulder muscles varied depending on the direction of elbow motion (and hence the sign of the interaction torque arising at the shoulder). Similarly, EMG activity in elbow muscles varied depending on the direction of shoulder motion for movements in which elbow kinematics were held constant. The results from all three experiments support the idea that central control signals to muscles are adjusted, in a predictive manner, to compensate for interaction torques-loads arising at one joint that depend on motion about other joints.     

Relating biceps EMG to elbow kinematics during self-paced arm flexions

Repetitive reaching movements to a fixed target can be generally characterized by bell-shaped velocity profiles and sigmoidal trajectories with variable morphologies across multiple repetitions. A neuromuscular correspondence of these kinematic variations has thus far eluded electromyographic (EMG) analysis. We recorded EMG and elbow kinematics from fourteen healthy individuals performing repetitive, self-paced, isolated elbow flexions, with their arms supported against gravity. The global kinematic pattern of each flexion was classified as either sigmoidal (S) or non-sigmoidal (NS), based on goodness of fit with analytical curves. Ten of the fourteen subjects generated an approximately equal number of S and NS types (383 movement cycles). Trajectories of the other four subjects were not classifiable or did not vary sufficiently and were excluded from subsequent analysis. A post hoc predictor of trajectory type was derived by testing linear support vector machines trained with a strategically selected 3-feature sub-space of the early phase of enveloped biceps EMG during a leave-one-out cross-validation paradigm. Results showed that EMG features predicted kinematic morphology with sensitivity and specificity both exceeding 80%. The high predictive accuracy suggests neuromotor signals coding for subtle variations in elbow kinematics during self-paced, unloaded motions, can be deciphered from the biceps EMG.     

Premovement silence of EMG activity prior to movement in Parkinson patients.

Premovement silence (PMS) of tonic agonist electromyographic activity (EMG) preceding a maximum effort elbow extension was studied in eight bradykinetic Parkinson patients. The occurrence and duration of PMS have been shown to be significantly correlated with peak acceleration of movement in normal subjects. To determine if inability to silence the EMG prior to the initial agonist burst may contribute to bradykinesia of Parkinson's disease, patients maintained elbow extension against a tonic load on triceps, and in response to a tone performed a maximum effort elbow extension. All eight patients showed some trials (mean = 30%) with PMS. However, neither the incidence of PMS nor its duration were significantly correlated with mean peak acceleration. A significant correlation was found between the incidence of abnormal initial agonist bursts, called "segmented bursts," and mean peak acceleration. We conclude that ability to silence the agonist muscle prior to movement is not strongly associated with bradykinesia in Parkinson's disease.     

Independent coactivation of shoulder and elbow muscles

 The aim of this study was to examine the possibility of independent muscle coactivation at the shoulder and elbow. Subjects performed rapid point-to-point movements in a horizontal plane from different initial limb configurations to a single target. EMG activity was measured from flexor and extensor muscles acting at the shoulder (pectoralis clavicular head and posterior deltoid) and elbow (biceps long head and triceps lateral head) and flexor and extensor muscles acting at both joints (biceps short head and triceps long head). Muscle coactivation was assessed by measuring tonic levels of electromyographic (EMG) activity after limb position stabilized following the end of the movements. It was observed that tonic EMG levels following movements to the same target varied as a function of the amplitude of shoulder and elbow motion. Moreover, for the movements tested here, the coactivation of shoulder and elbow muscles was found to be independent – tonic EMG activity of shoulder muscles increased in proportion to shoulder movement, but was unrelated to elbow motion, whereas elbow and double-joint muscle coactivation varied with the amplitude of elbow movement and were not correlated with shoulder motion. In addition, tonic EMG levels were higher for movements in which the shoulder and elbow rotated in the same direction than for those in which the joints rotated in opposite directions. In this respect, muscle coactivation may reflect a simple strategy to compensate for forces introduced by multijoint limb dynamics. Received: 7 July 1998 / Accepted: 28 July 1998     

Isometric torque-angle relationship and movement-related activity of human elbow flexors: implications for the equilibrium-point hypothesis

Since the moment arms for the elbow-flexor muscles are longest at intermediate positions of the elbow and shorter at the extremes of the range of motion, it was expected that the elbow torque would also show a peak at an intermediate angle provided the activity of the flexor muscles remained constant. We measured the isometric elbow torque at different elbow angles while the subject attempted to keep constant the electromyographic activity (EMG) of the brachioradialis muscle. The torque-angle relationship thus obtained exhibited a peak, as expected, but the shape of the relationship varied widely among subjects. This was due in part to differences in the variation of the biceps brachii EMG with elbow angle among the different subjects. The implications of these observations for the equilibrium-point hypothesis of movement were investigated as follows. The subject performed elbow movements in the presence of an external torque (which tended to extend the elbow joint) provided by a weight-and-pulley arrangement. We found in the case of flexion movements that invariably there was a transient increase in flexor EMG, as would seem necessary for initiating the movement. However, the steady-state EMG after the movement could be greater or less than the pre-movement EMG. Specifically, the least flexor EMG was required for equilibrium in the intermediate range of elbow angles, compared to the extremes of the range of motion. The EMG-angle relationship, however, varied with the muscle and the subject. The observation that the directions of change in the transient and the steady-state EMG are independent of each other militates against the generality of the equilibrium-point hypothesis. However, a form of the hypothesis which includes the effects of the stretch reflex is not contradicted by this observation.     

Coordination of grip and load forces during vertical point-to-point movements with a grasped object in Parkinson's disease

Thirteen patients with Parkinson's disease and 13 age-matched control subjects performed vertical point-to-point arm movements with an instrumented object, starting and ending with the object being held stationary. All Parkinsonian patients were tested on medication. Parkinsonian patients retained all aspects of predictive grip force control. Compared with healthy controls, they generated similar static grip forces during stationary holding and similar force ratios between maximum grip and load force, reflecting effective grip force adjustments in relation to movement-induced inertial loads. Grip and load force maximums coincided very closely, indicating that temporal aspects of predictive grip force regulation were also unaffected. However, Parkinsonian subjects showed additional oscillations in acceleration and grip force due to tremor and produced significantly slower arm accelerations due to bradykinesia. The results suggest that Parkinson's disease does not significantly impair the anticipation of movement-induced load fluctuations during voluntary arm movements with a grasped object performed on medication.     

Spontaneous blinks of Parkinson's disease patients evaluated by EMG and EOG

In a study of spontaneous blinks, both electromyographic (EMG) activities from m. orbicularis oculi which is responsible for initiating closure of the eyelid and electro-oculogram (EOG) of vertical direction to the movement of the eyelid were measured in ten patients with Parkinson's disease and in thirty normal subjects. The aim of this study was to evaluate the generative mechanism of the spontaneous blinks by comparison of both the EMG and the EOG waveforms in the patients with Parkinson's disease and those in the normal subjects. The mean duration and the amplitude of both the EMG and the EOG were evaluated by the averaging of ten waveforms for the spontaneous blinks. The time lag between the onset of the generation of the EMG and the onset of the EOG signal was analyzed. The mean duration of the EMG and the mean amplitude of both the EMG and the EOG in the patients with Parkinson's disease were shorter and smaller than those in the normal subjects by the significant level of 1%, respectively. There was no difference of the time lag between the subject groups. These results suggest that the function of m. orbicularis oculi for the spontaneous blinks is reduced in patients with Parkinson's disease, because the motoneurones of the facial nucleus innervating the m. orbicularis oculi becomes hypoactive due to abnormal output of basal ganglia.     

Shoulder and elbow muscle activity in goal-directed arm movements

 This research examined the electromyographic (EMG) activity of shoulder and elbow muscles during reaching movements of the upper limb. Subjects performed goal-directed arm movements in the horizontal plane. Movements which varied in amplitude, speed, and direction were performed in different sections of the workspace. EMG activity was recorded from the pectoralis major, posterior deltoid, biceps brachii short head, brachioradialis, triceps brachii long head, and triceps brachii lateral head; motion recordings were obtained with an optoelectric system. The analysis focused on the magnitude and timing of opposing muscle groups at the shoulder and elbow joints. For hand movements within any given direction of the workspace direction, kinematic manipulations changed agonist and antagonist EMG magnitude and intermuscle timing in a manner consistent with previous single-joint findings. To produce reaching movements in different directions and areas of the workspace, shoulder and elbow agonist EMG magnitude increased for those hand motions which required higher angular velocities, while the timing between opposing muscle groups at each joint was invariant. Received: 11 January 1996 / Accepted: 24 February 1997     

MUAP extraction and classification based on wavelet transform and ICA for EMG decomposition

We have developed an effective technique for extracting and classifying motor unit action potentials (MUAPs) for electromyography (EMG) signal decomposition. This technique is based on single-channel and short periodȁ9s real recordings from normal subjects and artificially generated recordings. This EMG signal decomposition technique has several distinctive characteristics compared with the former decomposition methods: (1) it bandpass filters the EMG signal through wavelet filter and utilizes threshold estimation calculated in wavelet transform for noise reduction in EMG signals to detect MUAPs before amplitude single threshold filtering; (2) it removes the power interference component from EMG recordings by combining independent component analysis (ICA) and wavelet filtering method together; (3) the similarity measure for MUAP clustering is based on the variance of the error normalized with the sum of RMS values for segments; (4) it finally uses ICA method to subtract all accurately classified MUAP spikes from original EMG signals. The technique of our EMG signal decomposition is fast and robust, which has been evaluated through synthetic EMG signals and real EMG signals.     

Coordination of multiple muscles in two degree of freedom elbow movements

The present study quantifies electromyographic (EMG) magnitude, timing, and duration in one and two degree of freedom elbow movements involving combinations of flexion-extension and pronation-supination. The aim is to understand the organization of commands subserving motion in individual and multiple degrees of freedom. The muscles tested in this study fell into two categories with respect to agonist burst magnitude: those whose burst magnitude varied with motion in a second degree of freedom at the elbow, and those whose burst magnitude depended on motion in one degree of freedom only. In multiarticular muscles contributing to motion in two degrees of freedom at the elbow, we found that the magnitude of the agonist burst was greatest for movements in which a muscle acted as agonist in both degrees of freedom. The burst magnitudes for one degree of freedom movements were, in turn, greater than for movements in which the muscle was agonist in one degree of freedom and antagonist in the other. It was also found that, for movements in which a muscle acted as agonist in two degrees of freedom, the burst magnitude was, in the majority of cases, not different from the sum of the burst magnitudes in the component movements. When differences occurred, the burst magnitude for the combined movement was greater than the sum of the components. Other measures of EMG activity such as burst onset time and duration were not found to vary in a systematic manner with motion in these two degrees of freedom. It was also seen that several muscles which produced motion in one degree of freedom at the elbow, including triceps brachii (long head), triceps brachii (lateral head), and pronator quadratus displayed first agonist bursts whose magnitude did not vary with motion in a second degree of freedom. However, for the monoarticular elbow flexors brachialis and brachioradialis, agonist burst magnitude was affected by pronation or supination. Lastly, it was observed that during elbow movements in which muscles acted as agonist in one degree of freedom and antagonist in the other, the muscle activity often displayed both agonist and antagonist components in the same movement. It was found that, for pronator teres and biceps brachii, the timing of the bursts was such that there was activity in these muscles concurrent with activity in both pure agonists and pure antagonists. The empirical summation of EMG burst magnitudes and the presence in a single muscle of both agonist and antagonist bursts within a movement suggest that central commands associated with motion in individual degrees of freedom at the elbow may be superimposed to produce elbow movements in two degrees of freedom.     

Movement and electromyographic disorders associated with cerebellar dysmetria

The objective of these experiments was to determine whether dysmetric elbow flexions, which occurred during cerebellar dysfunction, had the same kinematic and electromyographic characteristics as movements of the same amplitude and velocity performed under normal conditions. Reversible cerebellar lesions were produced by cooling through two probes implanted on either side of the dentate nucleus in five Cebus albifrons monkeys. Normal, fast, and accurate elbow flexions had single-peaked velocities and a bi- or triphasic EMG pattern in agonist and antagonist muscles. During cerebellar dysfunction movements became ataxic. Ataxic movements were classified into two categories: those with oscillations (tremor) during the movement and those without oscillations. A terminal tremor occurred after both types of movements. Oscillations during movements were more likely to occur when a constant force loaded the antagonist. Addition of mass to the handle attenuated or abolished the oscillations. Movements with oscillations reached the target with increased variability of end position, whereas movements without oscillations were often hypermetric. The movement parameters and EMG patterns associated with flexions without oscillations during the movement were studied in detail. A characteristic of these movements was that the acceleration and deceleration phases were asymmetric. Compared with control movements of the same peak velocity, they had smaller magnitudes of acceleration and larger magnitudes of deceleration. The large deceleration was abnormal because it initiated the terminal tremor. The disorder in acceleration was associated with agonist EMG activity that was less abrupt in onset, smaller in magnitude, and more prolonged in duration. The disorder in deceleration was associated with delayed onset of phasic antagonist EMG activity. The results show that hypermetric arm movements without oscillations have different properties than those of normal movements of similar velocity and amplitude. Thus it is unlikely that dysmetria results from inappropriate selection or triggering of an otherwise normal motor program. We conclude that normal function of the cerebellum is necessary for the generation of agonist and antagonist muscle activity that is both of the appropriate magnitude and timing to control the dynamic phase of arm movements.     

Adjustments of fast goal-directed movements in response to an unexpected inertial load

Summary Subjects made fast goal-directed elbow flexion movements against an inertial load. Target distance was 8 or 16 cm, randomly chosen. To exert a force in the direction of the movement subjects had to activate flexors of both shoulder and elbow, but shoulder flexors did not change appreciably in length during the movement. In 20% of the trials the inertial load was increased or decreased without knowledge of the subjects. Until 90–110 ms after the onset of the agonist muscle activity (about 65–85 ms after the start of movement) EMG activity was very similar in all conditions tested. The changes that occured in the EMG from that moment on were effectively a later cessation of the agonist activity and a later start of the antagonist activity if the load was increased unexpectedly. If the load was reduced unexpectedly, the agonist activity ceased earlier and the antagonist activity began earlier. The latency at which EMGs started to change was the same for muscles around shoulder and elbow, for agonists and antagonists and for both distances. All adjustments had the same latency (37 ms) relative to the point where the angular velocity of the elbow in the unexpectedly loaded movements differed by 0.6 rad/s from the expected value. We discuss why simple reflex- or servo-mechanisms cannot account for the measured EMG changes. We conclude that appropriate adjustments of motor programmes for fast goal-directed arm movements start within 40 ms of the detection of misjudgment of load.     

独立分量分析和小波熵在动作模式分类中的应用

在表面肌电信号(electromyography,EMG)中,各类动作的识别是一个重要研究方向.本文采用独立分量分析independent component analysis,ICA)对肌电信号进行处理,消除各动作信号之间的相互线性耦合叠加,并采用信号的小波熵作为特征向量进行模式识别.试验表明,在对信号进行先期ICA处理以后,动作模式的识别效果较好.此方法也可应用于其他生理信号的识别分类.     

EMG responses to an unexpected load in fast movements are delayed with an increase in the expected movement time

When moving an object, the motor system estimates the dynamic properties of the object and then controls the movement using a combination of predictive feedforward control and proprioceptive feedback. In this study, we examined how the feedforward and proprioceptive feedback processes depend on the expected movement task. Subjects made fast elbow flexion movements from an initial position to a target. The experimental protocol included movements made over a short and a long distance against an expected light or heavy inertial load. In each task in a few randomly chosen trials, a motor applied an unexpected viscous load that produced a velocity error, defined as the difference between the expected and unexpected velocities, and electromyographic (EMG) responses. The EMG responses appeared not earlier than 170-250 ms from the agonist EMG onset. Our main finding is that the onset of the EMG responses was correlated with the expected time of peak velocity, which increased for longer distances and larger loads. An analysis of the latency of the EMG responses with respect to the velocity error suggested that the EMG responses were due to segmental reflexes. We conclude that segmental reflex gains are centrally modulated with the time course dependent on the expected movement task. According to this view, the control of fast point-to-point movement is feedforward from the agonist EMG onset until the expected time of peak velocity after which the segmental reflex feedback is briefly facilitated.     

Viscosity of the elbow flexor muscles during maximal eccentric and concentric actions

The aim of the present study was to estimate the damping coefficient (B factor) of the elbow flexor muscles during both eccentric and concentric muscle actions. We used a muscle model consisting of a viscous damper associated in parallel with a contractile component, both in series with an elastic component. The viscous damper allowed the concentric loss and the eccentric gain of force to be modelled. Eight volunteer subjects performed maximal eccentric and concentric elbow movements on an isokinetic dynamometer at angular velocities of 0.52, 1.04 and 2.09 rad·s^–1. Torques at an elbow joint angle of 90° were recorded. Electromyogram (EMG) signals from the belly of the right elbow flexor and from the long head of the triceps brachia muscles were recorded using two pairs of bipolar surface electrodes. The root mean square (rms) of the EMG was determined. Eccentric and concentric rms were not significantly different (P>0.05). The B factor was higher in the concentric than in the eccentric conditions (P<0.05), and, whatever the muscle action type it decreased as the velocity increased. These results indicated that the concentric loss and the eccentric gain of force were attributable to the behaviour of the contractile machinery. Furthermore, whatever the exact cause of loss and gain of tension, our study showed that the total effect can be modelled by the viscous damper of a three-component muscle model.     

Proportional myoelectric control of a virtual object to investigate human efferent control

We used proportional myoelectric control of a one-dimensional virtual object to investigate differences in efferent control between the proximal and distal muscles of the upper limbs. Eleven subjects placed one of their upper limbs in a brace that restricted movement while we recorded electromyography (EMG) signals from elbow flexors/extensors or wrist flexors/extensors during isometric contractions. By activating their muscles, subjects applied virtual forces to a virtual object using a real-time computer interface. The magnitudes of these forces were proportional to EMG amplitudes. Subjects used this proportional EMG control to move the virtual object through two tracking tasks, one with a static target and one with a moving target (i.e., a sine wave). We hypothesized that subjects would have better control over the virtual object using their distal muscles rather than using their proximal muscles because humans typically use more distal joints to perform fine motor tasks. The results indicated that there was no difference in subjects ability to control virtual object movements when using either upper arm muscles or forearm muscles. These results suggest that differences in control accuracy between elbow joint movements and wrist joint movements are more likely to be a result of motor practice, proprioceptive feedback or joint mechanics rather than inherent differences in efferent control.     

Vertical,horizontal, and torsional eye movement responses to head roll in the squirrel monkey

Based on studies using direct observation methods, type I motility, the first motility pattern to emerge in chick embryos, is characterized as random, uncoordinated movement. Yet, electromyographic (EMG) studies indicate that leg muscles are recruited in orderly patterns of alternating flexor and extensor activity during type I motility. It has been suggested that this apparent paradox may be attributable to perturbations arising during movement in ovo under buoyant conditions. It is also possible that direct observation methods are insufficient to detect the extent of coordination between body parts during type I motility. To address the apparent discrepancy between random features reported in observational studies and reliable features reported in EMG studies, embryos were video recorded continuously for 60 min at embryonic day 9 and criteria were established to obtain homogeneous samples of motility for kinematic analysis of synchronous wing and leg movements. Limited to a single camera attached to a stereomicroscope, methods were developed to correct for out-of-plane movements of the ipsilateral wing and leg. Also, amniotic fluid was extracted from the egg in some recordings to test the possibility that movement under buoyant conditions may mask coordinated movement. Extended sequences of activity were digitized and analyzed. Results indicated that within a limb (wing or leg), direction and timing of excursions at adjacent joints covaried and limb excursions were characterized by reliable patterns of alternating flexion and extension consistent with EMG studies. Concurrent elbow and ankle excursions for ipsilateral wing and leg movements also shared common spatiotemporal features: the onset of excursions at the beginning of an activity sequence were closely timed, ankle excursions preceded elbow excursions; the number of movement cycles and duration of movement cycles were similar; ankle and elbow excursions closely covaried in 33% of cycles in control embryos; and activity sequences ended with abrupt, synchronous excursions of the elbow and ankle. Reduction in buoyancy increased the spatiotemporal covariation of shoulder and elbow excursions, but had no effect on leg movements — possibly because the leg remained more submerged than the wing. Collectively, results suggest that type I motility at embryonic day 9 is characterized by reliable features indicative of intralimb and interlimb coordination and the effect can be enhanced by a reduction in buoyancy. Thus, the apparent paradox between findings in observational and EMG studies may be attributable to both the effects of perturbations arising under buoyant conditions in ovo and the limitations of observational methods in earlier studies.     

Recognition of the physiological actions of the triphasic EMG pattern by a dynamic recurrent neural network

Triphasic electromyographic (EMG) patterns with a sequence of activity in agonist (AG1), antagonist (ANT) and again in agonist (AG2) muscles are characteristic of ballistic movements. They have been studied in terms of rectangular pulse-width or pulse-height modulation. In order to take into account the complexity of the EMG signal within the bursts, we used a dynamic recurrent neural network (DRNN) for the identification of this pattern in subjects performing fast elbow flexion movements. Biceps and triceps EMGs were fed to all 35 fully-connected hidden units of the DRNN for mapping onto elbow angular acceleration signals. DRNN training was supervised, involving learning rule adaptations of synaptic weights and time constants of each unit. We demonstrated that the DRNN is able to perfectly reproduce the acceleration profile of the ballistic movements. Then we tested the physiological plausibility of all the networks that reached an error level below 0.001 by selectively increasing the amplitude of each burst of the triphasic pattern and evaluating the effects on the simulated accelerating profile. Nineteen percent of these simulations reproduced the physiological action classically attributed to the 3 EMG bursts: AG1 increase showed an increase of the first accelerating pulse, ANT an increase of the braking pulse and AG2 an increase of the clamping pulse. These networks also recognized the physiological function of the time interval between AG1 and ANT, reproducing the linear relationship between time interval and movement amplitude. This task-dynamics recognition has implications for the development of DRNN as diagnostic tools and prosthetic controllers.     

Signal-dependent wavelets for electromyogram classification

In the study, an efficient method to perform supervised classification of surface electromyogram (EMG) signals is proposed. The method is based on the choice of a relevant representation space and its optimisation with respect to a training set. As EMG signals are the summation of compact-support waveforms (the motor unit action potentials), a natural tool for their representation is the discrete dyadic wavelet transform. The feature space was thus built from the marginals of a discrete wavelet decomposition. The mother wavelet was designed to minimise the probability of classification error estimated on the learning set (supervised classification). As a representative example, the method was applied to simulate surface EMG signals generated by motor units with different degrees of short-term synchronisation. The proposed approach was able to distinguish surface EMG signals with degrees of synchronisation that differed by 10%, with a misclassification rate of 8%. The performance of a spectral-based classification (error rate approximately 33%) and of the classification with Daubechies wavelet (21%) was significantly poorer than with the proposed wavelet optimisation. The method can be used for a number of different application fields of surface EMG classification, as the feature space is adapted to the characteristics of the signal that discriminate between classes. An erratum to this article is available at .