The Journal of Neurophysiology Vol. 80 No. 4 October 1998, pp. 1787-1799
Copyright ©1998 by the American Physiological Society

Intermittency in Preplanned Elbow Movements Persists in the Absence of Visual Feedback

Joseph A. Doeringer¹ and Neville Hogan^{1, 2}

Departments of ¹ Mechanical Engineering and ² Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

	ABSTRACT

Abstract Introduction Methods Results Discussion References

Doeringer, Joseph A. and Neville Hogan. Intermittency in preplanned elbow movements persists in the absence of visual feedback. J. Neurophysiol. 80: 1787-1799, 1998. It has been observed for nearly 100 years that visually guided human movements appear to be composed of submovements, intermittently executed overlapping segments. This paper presents experiments to investigate the pervasiveness of movement intermittency and, in particular, whether it is exclusively due to visual feedback. With and without visual feedback, human subjects were asked to 1) move with constant velocity and 2) draw elliptical figures on a phase-plane display (showing velocity vs. position) that required cyclic movements at different frequencies. In both tasks, we found that removal of visual feedback did not significantly change movement intermittency. Subjects were unable to generate movements at constant speed. In addition, subjects moved less smoothly when drawing slower phase-plane ellipses. Furthermore, elliptical phase-plane figures were not always drawn at the frequency suggested by the center of the display. Instead, subjects moved more slowly than the tall (fast) ellipse displays suggested, and faster than the wide (slow) displays suggested. These results show that 1) movement intermittency is not exclusively due to visual feedback and 2) may in fact be a fundamental feature of movement behavior.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

A comprehensive explanation of how humans generate arm movement remains elusive. One of the key elements missing is an explanation of how movement is planned. We know from both common experience and well-known experiments (Woodworth 1899) that movements can be corrected (i.e., movement plans can be modified) in midmovement; it is not necessary to completely stop the limb and start all over again from a different fixed position (Henis 1991; van Sonderen et al. 1989). It is also well-known that humans, when pointing to a small fixed visual target, tend to slow their limbs as they approach the target (Meyer et al. 1990 provide an excellent review of the literature). When the target is very small, the velocity profile becomes multipeaked; the human appears to make "submovements" in an attempt to home in on the target; this is true in both single degree of freedom (DOF) (Meyer et al. 1990) and multi DOF cases (Milner 1992; Milner and Ijaz 1990). When the target moves unpredictably, humans also seem to execute multiple submovements; the arm moves in quick, intermittent, jerks and lags the target, even as the target moves slowly and smoothly (Bekey 1962; Bekey and Neal 1968; Miall et al. 1993; Navas and Stark 1968; Neilson et al. 1988; Poulton 1974; Wolpert et al. 1992). When the target waveform is simple and predictable, human movement smooths out considerably (relative to the unpredictable case), and much of the lag is removed (Miall 1996). Interestingly, nonhuman primates do not seem to exhibit this change; they appear unable to learn the predictability of the tracking signal and track it with the same characteristics as an unpredictable signal (Miall et al. 1986).

When humans trace curves in a plane (on, say, a desk), it has been observed that subjects have difficulty drawing lines of constant curvature. Instead, curves produced by humans generally have distinct peaks in curvature. Flash and Hogan (1985) investigated a mathematical model that successfully described unconstrained point-to-point movements as optimizing a kinematic measure of movement smoothness (Hogan 1984). They found that it could be adapted to reproduce the apparent nonsmoothness of curved movements by adding the constraint that the limb pass through an intermediate via point. The tangential velocity along a curved trajectory tends to dip at the same points where the curvature peaks, as if the movement plan for these "complex" movements is a concatenation of simpler straight movements (Abend et al. 1982; Viviani and Terzuolo 1980). Supporting this idea is the observation that humans prefer to generate straight line movements in visual space even under strong visual and mechanical perturbations (Flanagan and Rao 1995; Shadmehr and Mussa-Ivaldi 1994; Wolpert et al. 1995). It has been argued that the multipeaked velocity traces are an artifact of limited actuator force on an inertial mechanism. However, Massey et al. (1992) observed the effect when humans operate an isometric joystick (so the limb does not actually move).

We shall refer in this paper to the nonsmooth nature of human movement as "movement intermittency." A survey of the literature did not reveal any consensus on a rigorous quantitative definition of "movement intermittency," and we do not propose one here. Instead, we use the term to describe variability of movement kinematics that is not attributable to either the task or the biomechanics of the musculoskeletal system. This working definition does not imply any mechanism for the kinematic variability.

Movement intermittency could be due to fundamental features of the neuromuscular system. It could be a result of a movement planner that can only construct simple movements and must approximate complex movements.¹ A second possible origin is noise in the neuromuscular circuitry, and there may be other sources (McRuer 1980; Pew 1974). Unfortunately, we do not even know whether movement intermittency is a robust observation. It is known that movement intermittency occurs when the limbs are driven by unpredictable visual tracking error, but it is not at all clear under what other conditions the phenomenon might appear. Movements smooth out significantly when target tracking inputs are predictable, but the amount of this smoothing has not been addressed quantitatively in the literature. The reason this question is important is that a large subset of human movements are not guided visually, but rather executed from memory or through other forms of feedback. For example, when a human reaches for a coffee cup while reading a newspaper, the person plans and executes the movement via a combination of memory of the coffee cup location and proprioceptive/tactile feedback. Visual guidance and feedback are not required, although a quick look at movement end is often useful to avoid spilling the beverage. In pilot instruction, "cockpit familiarization" exercises are commonly and successfully used to train students to reach accurately for controls without looking at them. Humans can generate slow, complex movements with relative ease; visual feedback generally increases performance but is not strictly required (for example, it appears to be relatively easy to write on a blackboard with eyes closed).

The issue can be visualized by imagining an "intermittency source" within the neuromotor system as illustrated in Fig. 1. In this figure, an intermittency source is nothing more than a point in the system where movement becomes nonsmooth; it could be an effective location where noise is coupled in, or perhaps a place where a sparse representation (submovements) is employed. The important question is where the source is located, and Fig. 1 shows three possibilities.

View larger version (39K): [in this window] [in a new window]   FIG. 1. Three possible locations for an "intermittency generator." A: generator is in the feedback path. B: it is in the forward path. C: generator is in the forward path but can be bypassed.

One possible location is the visual feedback path (Fig. 1A); if intermittency is a result of visual error corrections, we would expect human movement to smooth out significantly when visual feedback was removed from all visual feedback tasks (including those where the feedback is not strictly necessary). Another possibility is the forward path (Fig. 1B); perhaps movement intermittency occurs in all arm motions, because it is fundamentally linked with how humans plan movement. (Note that we are not establishing whether the source is inside or outside the feedback loop, only that it cannot be bypassed.) If this idea is taken further, a third possibility is that movement intermittency is a sort of low effort movement execution mode (e.g., simple movements being downloaded as needed) that can be turned off or superseded when smooth movement is required (Fig. 1C).

View larger version (90K): [in this window] [in a new window]   FIG. 2. Elbow measurement chair. Subjects sit with their right forearms secured inside the wrist splint. The medial epicondyle of the elbow rests in the thermoplastic bowl above the encoder.

To test these ideas, one must be careful about the paradigm, because many tasks change fundamentally when visual feedback is removed. It is necessary to provide a task where this is not the case; where a movement with some complexity is demanded yet remains fully defined when visual feedback is removed. For example: pursuit tracking is a well-known paradigm in which both a target and a limb representative cursor are displayed, and the subject is asked to minimize the error between target and cursor. Unfortunately, if the target motion is unpredictable, one cannot simply hide the representative cursor temporarily to break the feedback loop; because the error signal is now invisible, the subject must now invent a new task that does not require an error signal. An example of such a substituted task would be to try to move in the same direction as the cursor at a convenient speed. Although pursuit tracking has been studied extensively, it is for this reason unsuitable for testing the role of visual feedback in movement intermittency.

A better paradigm would be something analogous to drawing unusual shapes (with well-defined basic features) on a blackboard. Visual feedback helps in this case, but lack of it does not change the definition of the task, unless one is trying to very accurately trace the shapes.

View larger version (38K): [in this window] [in a new window]   FIG. 3. Raw results of the constant velocity task for 1 subject. Elbow velocity is plotted vs. time. Each row of panels corresponds to a task speed. The 2 columns of panels show visual and blind results, respectively. Vertical lines denote boundaries of the "attempt zone"; see text for further details.

View larger version (25K): [in this window] [in a new window]   FIG. 4. A: means ± SD of elbow velocity inside the attempt zone for 1 subject. *, vision trials; , blind trials. B: SD vs. mean for 4 subjects. *, vision trials; , blind trials. The 2 lines in each plot correspond to linear least-squares fit and average slope of the displayed points.

To test the third intermittency hypothesis mentioned above, that the phenomenon can be overcome if necessary, implies that the experimental subject must somehow be penalized for moving intermittently; the subject must be made aware of the phenomenon. This could be accomplished by a display that somehow indicated movement smoothness to the subject.

We chose to investigate the above questions in the context of one-DOF elbow movements. Using a high-performance angle sensor, we were able to directly display both the position and the velocity of the elbow directly to the subject in real time, with a delay² of <18 ms; significantly smaller than the smallest visual reaction time of ~150 ms (Deecke et al. 1969). This gave us the opportunity not only to provide visual feedback to the subject, but also to penalize the intermittency phenomenon.

Our first experiment examined constant-velocity elbow movements, which have been studied extensively in prior work. Nagaoka and Tanaka (1981) used a constant-velocity visual pursuit tracking task to examine patients with deep sensory disturbance. Beppu et al. (1984, 1987) used a similar paradigm to compare patients with cerebellar motor disorders to unimpaired controls. Nelson (1983) showed that a violinist can make reasonably constant velocity strokes during bowing. Finally, Cooke and Brown (1990) used a constant-velocity paradigm to better understand the well-known triphasic electromyographic (EMG) pattern of muscle activation. The relation of these studies to our work is addressed in the DISCUSSION.

	METHODS

Abstract Introduction Methods Results Discussion References

Subjects

Ten subjects participated in this experiment. Subjects were recruited from the local graduate student pool; all were male, all were in good health, and they ranged from 22 to 28 yr of age. All were right handed, because the experimental apparatus could only be used with the right arm.

View larger version (38K): [in this window] [in a new window]   FIG. 5. Normalized histograms of the normalized elbow velocity (divided by the mean) inside the attempt zone. The upright histograms correspond to vision trials, the inverted to blind trials. Each row of plots corresponds to a task speed. The 2 columns represent 2 different subjects.

Equipment

The equipment used for this experiment consisted of a special elbow measurement chair (see Fig. 2). This was a standard metal office chair with some modifications: a large piece of milled aluminum replaced the back, and connected to this was a rigid "arm extension" designed to support the right arm in the horizontal plane. A forearm support, consisting of a commercially available wrist splint (Orthomerica Newport wrist/hand orthosis) attached to a lightweight aluminum tube, was hinged to the arm extension via precision ball bearings. We estimated the inertia of the forearm support by approximating the forearm tube and wrist orthotic as ideal tubes, and we estimated the inertia of the subjects' forearms (including hands) by using formulas from Dempster's cadaver studies (Miller and Nelson 1973; Plagenhoef 1971). Because the wrist splint was adjustable to accommodate the different forearm lengths of the subjects, the moment of inertia of the forearm support varied somewhat; its mean value was ~0.0251 kg·m², and the mean value of the subjects' forearms was ~0.0631 kg·m². We deliberately made the forearm support as light as possible, because we wanted to see the natural behavior of the limb (rather than the behavior of the limb coupled to a significant inertia). The fact that the inertia was ~40% of the natural forearm was mostly due to the wrist orthotic being positioned near the endpoint of the limb.

On top of the shaft joining the forearm support to the arm extension was a small thermoplastic bowl, designed to cradle the medial epicondyle. Because the axis of elbow rotation does not deviate significantly from the line connecting the lateral and medial epicondyles (Shiba et al. 1988), the thermoplastic bowl served to keep the axis of the elbow aligned with the axis of the measurement mechanism.

The forearm support was connected to the shaft of a high-precision incremental optical encoder/interpolater set (Gurley Precision Instruments encoder No. 8335-11250-CBQA, interpolator No. HR2-80QA-BRD). This instrument provided a position resolution of 0.0004° per count. The encoder was connected to a set of counters that were in turn connected to a digital input/output card inside a Pentium computer running the QNX real-time operating system. The computer controlled the recording of the data as well as the display, which was a 17-in. monitor (311 × 238 mm measured) running at 1,280 × 1,024 resolution ~75 cm from a subject's eyes. All experiments were recorded at 100 Hz; the display was refreshed at 76 Hz by the computer's video card.

During the experiments, the subject's entire body below the neck (including the right arm) was occluded from view by an adjustable cover designed to fit over the front of the chair.

Protocol

The protocol of this experiment took place in two stages, with each stage consisting of 3 groups of 30 trials.

In the first stage, subjects attempted to extend their elbows at constant velocity. The display was similar to that of an oscilloscope; the horizontal axis was time, and the vertical axis was elbow velocity. Velocity was estimated using the simple finite difference algorithm in which v_i is the current position, x_i and x_i1 are the current and last recorded position, respectively, and t is the time between samples (the reciprocal of the sampling frequency). This estimate of elbow velocity is computationally simple and minimum delay; it lags the elbow position by only one-half sample (5 ms). In all cases, the height of the screen represented 120°/s, and the width of the screen was 10 s; we kept the same dependence between arm and display for each trial group because we wanted to minimize unnecessary relearning of the relationship. The three groups of trials in the first experiment stage corresponded to different target velocities, represented by a horizontal line on the display. The first group of 30 trials corresponded to 40°/s, the second was 20°/s, and the third was 10°/s. The groups were always presented in this order because we believed that faster target velocities were easier, and we wanted any learning to take place as fast as possible. For each group of 30 trials, 7 of them (the 2nd, last, and 5 randomly selected) were blind; subjects could see the horizontal target line, but not the trace corresponding to their own elbow velocity. Again, subjects were prevented from viewing their arms by a cover.

The specific instructions to the subjects in the first set of experiments were as follows:

Starting from about here (demonstrate), I want you to attempt to extend your elbow at constant speed. On the screen you will see a trace that represents the extension velocity of the elbow, as well as a target horizontal line. Try to match your elbow velocity to this line. On some trials, the trace won't be visible; you won't be able to see how your arm is moving. When this happens, continue to try to move at the same constant velocity as before.

In the second stage of the experiments, subjects were presented with a display of the "phase-plane" of their elbow; the horizontal axis was position (45° per screen), and the vertical axis was velocity (144°/s per screen). Again, we kept the same dependence between arm and display for each trial group because we wanted to minimize unnecessary relearning of the relationship. In this experiment, the target elbow behavior was indicated by a region of the phase-plane; this region was a doughnut shape formed from two ellipses displayed on the screen. These regions suggest sinusoidal elbow behavior, with the nonzero width of the doughnut shape allowing a range of amplitudes and frequencies. This display is actually quite intuitive after a trial or two, and subjects had no difficulty understanding the goal of the task. The three groups of trials were differentiated by the shapes of their target regions; the first group corresponded to a tall thin region (fast, small-amplitude sinusoid), the second to a circular region, and the third to a wide region (slow, large-amplitude sinusoid). Again, the groups were always presented to the subjects in this order because we believed that it was easiest to stay within the tall thin regions, and we wanted any learning to take place as fast as possible. All of the target regions took equal amounts of display screen area. For each group of 30 trials, 7 of them (the 2nd, last, and 5 randomly selected) were blind; subjects could see the doughnut-shaped target region, but not the trace corresponding to their own elbow.

In the second set of experiments, the instructions to the subjects were as follows:

On the screen in front of you, you will see a small box whose up/down position will depend on your elbow velocity, and whose left/right position will depend on your elbow position. I want you to move your elbow back and forth like this (demonstrate) so that this crosshair moves through a closed round path. On the screen you will see guidelines; I want you to try to stay within those guidelines. On some trials, the small box won't be visible; you won't be able to see how your arm is moving. When this happens, continue to try and move within the guidelines even though you cannot see the small box.

	RESULTS

Abstract Introduction Methods Results Discussion References

Constant velocity

Figure 3 shows some raw results of the constant-velocity tracking task. Note that these graphs (without numbers) were basically what the subjects could see on the display when feedback was provided; these data have not been filtered or postprocessed in any way. Even when subjects were given direct information about the intermittent nature of their elbow movements, they appeared unable to smooth their movements to resemble the target line. The vertical lines in Fig. 3 represent the borders of the "attempt zone" (the region where subjects actually attempted to generate constant elbow velocity). The borders of this region were estimated by taking ³/₄ of the height of the first and last velocity peaks whose height was greater than ¹/₂ of the target velocity.

View larger version (25K): [in this window] [in a new window]   FIG. 6. A: fast Fourier transforms (FFTs) and Kolmogorov-Smirnov significance levels plotted vs. frequency for the constant-velocity task. Each row corresponds to a different task speed. The FFT graphs plot mean ± SD for each frequency; the actual mean is omitted for clarity. , vision trials; ···, blind trials. B: average Kolmogorov-Smirnov significance levels across all frequencies for each subject in the constant-velocity task.

Figure 4A shows typical means and standard deviations within the attempt zone versus trial. It appears that the standard deviation of the blind trials is greater than that of the vision trials, which at face value might be expected; one might think that the visual display of intermittent behavior may induce subjects to move more smoothly. However, one must note also that the mean of the blind trials is also higher; Fig. 4B shows that the standard deviation of the velocity is correlated with the mean. This correlation suggests that a reasonable performance measure for the constant-velocity task is the ratio of mean to standard deviation (the reciprocal of what is sometimes called the "coefficient of variation"), with a higher ratio indicative of better performance.

View larger version (58K): [in this window] [in a new window]   FIG. 7. Raw phase-plane task data for 1 subject. The thick lines correspond to the target region boundaries, thin traces correspond to the subject's elbow position/velocity. Each row of plots corresponds to a different phase-plane shape. The left 2 columns of plots correspond to vision trials; the right 2 columns to blind trials. Phase-plane drawings (what the subject saw in the vision condition) are shown alongside plots of elbow velocity vs. time.

To compare blind and vision trials, we divided velocity by the mean velocity inside the attempt zone and looked at histograms of normalized velocity sample points. Figure 5 shows these distributions. To compare the variance of the vision versus the blind velocities, we conducted an F test with the number of DOFs estimated by the length of the total sequence (all trials strung together) divided by the estimated autocorrelation interval. The idea was to find the time separation of sample points such that their covariance is essentially zero. If, as the F test assumes, the samples were normally distributed, they may be considered statistically independent when their correlation is zero. We refer the reader to Bendat and Piersol (1986) and Papoulis (1991) for basic texts in stochastic process analysis.

We first estimated the shape of the autocovariance function for all trials as where K is the autocovariance function, i is the trial number, N_i is the number of points in that trial, _i is the velocity signal (with mean subtracted), and t_m,i is the midpoint time of the ith attempt zone.

We then estimated the correlation time as These estimators are recommended by Dziech (1993). At the 5% significance level, the F test results were such that one subject was different in only the fast case, one subject in only the medium case, and one subject in only the slow case. In addition, one subject was different in both the medium and slow cases. These results are summarized in Table 1. By this measure, in almost all cases, blind and vision trials were not statistically distinguishable.

As a further comparison, we examined the frequency content of the blind and vision trials. This was performed by removing the mean of the constant velocity data inside the attempt zone, windowing the data with a Hamming window (to reduce transient effects), and taking fast Fourier transforms (FFTs). The FFT magnitudes were then limited to the range of 0-8 Hz, and divided by the mean FFT magnitude in this range to normalize the FFT shape. Because the signals in the attempt zone are all of different lengths, the FFT points are all in slightly different frequency locations, and so, to compare blind and vision trials, the FFT points were collected in bins 0.3 Hz wide. Some sample FFTs can be seen in Fig. 6A.

The blind and vision FFT magnitudes were then compared bin by bin using the Kolmogorov-Smirnov statistical test (Press et al. 1992). The null hypothesis of this test is that the two data sets are drawn from identical distributions; one calculates a statistic based on the maximum distance between the estimated cumulative distribution functions. If, in every frequency bin, the two data sets were always drawn from the same distribution, we would expect to see a uniform distribution of significance levels from the test,³ and so looking at all the bins together we would expect to see an average significance level of 0.5. If they were different, we would expect to see an average significance level close to zero. Figure 6A, right column, shows significance levels across frequencies for one subject, and Fig. 6B shows average significance levels for all subjects. The FFT magnitudes across frequencies appear to be very similar, and the average significance levels, although not equal to 0.5, are not close to zero. Thus the distributions are statistically similar.

View larger version (31K): [in this window] [in a new window]   FIG. 8. Plots of amplitude vs. frequency for the phase-plane task (1 subject). Shapes define allowable ranges of amplitudes and frequencies for a particular task, and the dots (vision trials) and plus signs (blind trials) indicate the amplitudes and frequencies chosen by the subject. Left plots: position amplitude vs. frequency. Right plots: velocity amplitude vs. frequency.

View larger version (35K): [in this window] [in a new window]   FIG. 9. Normalized histograms of the velocity intermittency in the phase-plane task. The upright histograms correspond to vision trials, the inverted to blind trials. The 2 columns represent 2 different subjects.

Phase-plane figures

Figure 7 shows some raw results of the phase-plane task. Note again that the phase-plane graphs (without numbers) were basically what the subjects could see on the display when feedback was provided; these data have not been filtered or postprocessed in any way. From the figure it is apparent that as the ellipses get wider the subject seems to move less smoothly.

In this experiment, an elliptical shape in the phase-plane corresponds to a sinusoidal time response; the ratio of height to width corresponds to frequency, and the width itself corresponds to amplitude. One can therefore think of this phase-plane task as requiring the subjects to move their elbows over a range of frequencies (corresponding to the different width to height ratios inside the "doughnut") as well as over a range of amplitudes. This can be illustrated by a closed shape on a graph of amplitude versus frequency, as depicted in Fig. 8.

If a subject solves the task by generating an elliptical shape in the phase-plane, the arm must move in a sinusoidal fashion, and the characteristics of this sinusoid must fit inside the shape of Fig. 8.

Frequencies other than those of the primary sinusoid, and particularly frequencies that are outside the shape in Fig. 8, hinder performance of the task, as they increase the "spread" of the points as the signal moves around the doughnut shape.

We estimated both the frequency and the amplitude of the primary sinusoid by looking at the peaks/troughs in the position record; the reciprocal of 2 times the average peak-trough horizontal distance yields a reasonable estimate of frequency, and ¹/₂ of the average peak-trough vertical distance yields a reasonable estimate of amplitude. The individual points in Fig. 8 show how a typical subject falls into the regions defined by the task. Note that, in the tall ellipse task (corresponding to a fast sinusoid), most points lie to the left of the "optimum frequency" (corresponding to a sinusoid in the exact center of the doughnut shape). In the circular task, the points are on both sides of the optimum frequency. In the wide ellipse task, most points are to the right of the optimum frequency. These observations suggest that humans may have a preferred "cadence"; a range of frequencies that is both upper and lower bounded.

In the constant velocity task, the elbow velocity generally fluctuated around the constant target velocity; we were able to analyze the fluctuations directly by subtracting the mean. In the phase-plane task, we can analyze the "fluctuations" (frequencies outside of the allowable region) simply by filtering them out. Because we were most interested in high-frequency intermittency artifact, we simply low-pass filtered the velocity signals up to the maximum allowable frequency. The specific filters used were Kaiser window based, type I low-pass filters (Oppenheim and Schafer 1989) such that the passband was zero to the maximum frequency of the task, the stop band was always 1 Hz above the passband to infinity, and the maximum magnitude error in either the stop or the passband was 0.001. Subtracting the low-pass underlying signal from the original signal reveals the high-frequency "extra" signal (the signal we would have gotten by high-frequency filtering).

In a manner similar to the constant-velocity analysis, we can investigate the fluctuations in the phase-plane task. Figure 9 shows sample histograms of the velocity error signal once the allowable frequencies have been filtered out. To compare the variance of the vision versus the blind signals, we again used an F test similar to that used in the constant-velocity task above. These histograms were not normalized in any way, but similarity between blind and vision trials is still evident. At the 5% significance level, the F test results are such that two subjects were different in only the circular case, and one subject in only the wide case. In addition, two subjects were different in both the tall and round cases, and two subjects in both the round and wide cases. The results are summarized in Table 2; even though the signals are not normalized in any way, in the majority of cases vision and blind trials are statistically similar.

Testing the relative frequency contribution in the phase-plane task is easier than in the constant-velocity task because the trials are all the same length. After a reaction time, all subjects were attempting to accomplish the task for the same length of time; there was no need to bin frequencies because the FFT points occurred at identical frequencies. Figure 10 is analogous to Fig. 6; the same processing was done to calculate FFT magnitudes, and the blind and vision magnitudes were compared frequency by frequency using the Kolmogorov-Smirnov test. Note that the primary peaks in the FFT plots result from the sinusoidal motion of the elbow tracing around the ellipse shape. Significance level averages for each subject can be seen in Fig. 10B. As in the constant-velocity task, The FFT magnitudes across frequencies appear to be very similar. The average significance levels are not equal to 0.5 but are not close to zero; the distributions are statistically similar.

View larger version (28K): [in this window] [in a new window]   FIG. 10. A: FFTs and Kolmogorov-Smirnov significance levels plotted vs. frequency for the phase-plane task. Each row corresponds to a different phase-plane shape. The FFT graphs plot mean ± SD for each frequency; the actual mean is omitted. , vision trials; ···, blind trials; missing points indicate that the mean minus SD was negative at that frequency and could not be graphed on a log plot. Note that the primary peaks result from the sinusoidal motion of the elbow tracing around the ellipse shape. B: average Kolmogorov-Smirnov significance levels across all frequencies for each subject in the phase-plane task.

	DISCUSSION

Abstract Introduction Methods Results Discussion References

The most important result presented here is that humans appear to have difficulty moving their elbows smoothly, regardless of the presence of visual feedback. Could the movement intermittency be a quirk of our methods? Certainly it is not a signal processing artifact; the unprocessed data were quite clean, and consequently no noise removal processing was necessary. Our arm measurement mechanism was constructed with very low friction ABEC 7 ball and roller bearings, and no significant resistance or stiction was detectable by the subject. In designing our apparatus, we reasoned that to best reflect natural movement behavior it should minimally impede the arm, and so we also attempted to make it as light as possible. We can use the performance measures calculated in both experiments to test for learning; the results can be seen in Fig. 11. Note that the performance measures remained essentially constant over the course of the trials; if any learning did take place, it occurred quickly (which was the intent of the authors). We cannot assume that subjects achieved the final performance plateau of smooth movement ability; we can only conclude that moving smoothly is a difficult task insofar as it is not learned in 180 attempts over ~90 min.

View larger version (65K): [in this window] [in a new window]   FIG. 11. Performance measures for all subjects vs. trial for both the constant-velocity task (left column) and phase-plane task (right column). The constant-velocity performance measure is the ratio of SD to mean (the coefficient of variation), and the performance measure for the phase-plane task is the SD of the error signal (allowable frequencies filtered out). Plots are offset on the y-axis according to subject number; the bottom trace in each plot is not offset.

How was nonsmooth the movement in our experiments? Figure 4B implies that the standard deviation of the fluctuations was approximately one-fourth of the elbow velocity. These fluctuations are not small; for example, if automobile speed were controlled with this imprecision, regulating to a speed limit of 80 km/h would result in speeds between 20 and 140 km/h (±3). Yet perhaps it is not surprising, if we consider that constant velocity may be an "unnatural" task; muscles are activated by trains of impulses, and perhaps this type of input constrains the types of velocity profiles the nervous system can generate.

There are few tasks humans perform that strictly require a constant velocity, and the few tasks that do generally require some sort of special technique. For example, the compound slide on a conventional metal cutting lathe is unpowered; when an operator cuts a tapered shape he must turn the handle manually. Because a nonuniform handle speed results in a nonuniform part finish, machinist textbooks recommend turning the handle using a special two-handed technique that requires practice to master (Walker 1993).

Not only were movements nonsmooth, but they were also similar to each other in both the vision and nonvision cases. The amplitude distributions of the fluctuations were visually similar, and a reasonable statistical test failed to disprove their similarity in the majority of cases. It is important to note here that the statistical test chosen was likely conservative. Because the fluctuations exhibit smoothness, there is always some correlation between points no matter how far apart they are, and the F test is based on points that are completely uncorrelated. We tried to estimate the duration at which points were reasonably uncorrelated, but this is just measuring when the correlation drops below a particular threshold. In the phase-plane case, the test is even more conservative because there was no straightforward way to normalize the data (as there was in the constant-velocity case). Hence we would expect to find more statistical disagreement between vision and blind trials in the phase-plane experiments. This was in fact the case, but in the majority of the phase-plane experiments, the test still failed to prove that the variances were different.

Of course, examination of the fluctuation amplitude alone does not demonstrate that the signals are similar; two sine waves with identical amplitudes and differing frequencies will share the same amplitude distribution. One must also examine frequency content. There were some unexpected features of the constant-velocity frequency spectra, in fact. Most of the constant-velocity spectra seemed to possess single frequency peaks at ~1-2 Hz, and in some of the subjects this peak seemed to shift according to the speed of the task (faster velocities had higher frequency peaks). The covariance function estimates used to estimate correlation times (not shown) looked like sinc functions [sin(x)/x], which is also indicative of periodicity in the constant-velocity data.

In the phase-plane data, the dominant frequency of the data did not generally correspond to the middle of the tracking shape, which actually makes the task more difficult because a subject has less room for error near the edges of the shape. This indicates that subjects had preferences for a particular range of frequencies. Subjects always generated frequencies that were biased in the direction of the circular shape (the medium condition), which could lead one to believe that the subjects were somehow reacting to the display and not the task; would this bias disappear if all displays were scaled to be circular? This is unlikely, because subjects continued to be biased toward the circular shape frequencies even when the display was turned off.

As the phase-plane shape became wider, subjects had greater difficulty making elliptical shapes and instead began to produce intermittent movement patterns (see Fig. 7). We might expect, of course, for subjects to be upper bounded in the frequencies they can generate, but a lower bound is not so obvious. This lower bound in frequency generation is likely related to the difficulty of producing constant velocity.

It is important to note that these observations of frequency preference (particularly the lower bound) would probably not have been apparent from a traditional pursuit tracking task. If subjects had been position tracking the sine waves, they would likely not have been as aware of their intermittent behavior, because they would not have seen the distinct velocity fluctuations. Unlike a pursuit task, the phase-plane display gives subjects a choice of frequencies to make; subjects choose an appropriate sinusoid frequency given the additional constraint of making their movements smooth enough to fit inside the annulus shape.

By testing at each frequency and looking at the average Kolmogorov-Smirnov significance across frequencies, we found that the average significance level was usually between 0.2 and 0.4 (see Figs. 6B and 10B). If the signals were in fact statistically identical (the null hypothesis was true for every frequency), we would expect the average significance level to be 0.5, but if the null hypothesis was false, we would expect the average significance level to be very close to zero. The average significance levels reported in this study are neither close to 0 nor equal to 0.5, which implies that the null hypothesis probably was true for most frequencies, but that there were some outlier points (possibly related to initial learning or other confounding factors).

Could our choice of display have induced the velocity fluctuations? We chose to display velocity to the subject because we wanted the subjects to be as aware as possible of their intermittent behavior; Fig. 12, when compared with Fig. 3, indicates that subjects would probably not have been aware of their intermittency had they not been shown the velocity signals; position plots of the sinusoid data (not shown) are similar in this respect. But perhaps our display gave too much information, compelling subjects to make additional unnecessary corrections. This is unlikely because the intermittent behavior was preserved even when the display was turned off.

View larger version (32K): [in this window] [in a new window]   FIG. 12. Raw results of the constant-velocity task, plotted as position instead of velocity. Elbow position is plotted vs. time. Each row of panels corresponds to a task speed. The 2 columns of panels show visual and blind results, respectively. These plots represent the exact same trials of Fig. 3; note that the traces are much smoother. Vertical lines denote boundaries of the "attempt zone"; see text for further details.

Are our results any more intermittent than past studies of constant velocity? Nagaoka and Tanaka (1981) used a constant-velocity visual pursuit tracking task to examine patients with deep sensory disturbance but unfortunately did not plot velocity data. Beppu et al. (1984, 1987) used a similar paradigm to compare patients with cerebellar motor disorders to unimpaired controls. The movements of the patients were much more intermittent than those of the controls, with frequent complete stops and starts, but the appearance of the velocity records of the control subjects (Beppu et al. 1984, Fig. 2; Beppu et al. 1987, Fig. 1) are roughly similar to those presented in this paper.

Beppu et al. (1984) did not estimate velocity variance directly. Instead, they quantified movement intermittency by calculating what they called the "Movement Arrest Period Ratio" (MAP ratio). The idea is to measure the amount of time spent below a velocity threshold as a percentage of total constant velocity time; the authors calculated ranges of MAP ratios (for several subjects and experiments) for velocity thresholds of 20, 40, 60, and 80% of target velocity. For example, if the velocity oscillates around the target velocity symmetrically, then we would expect the MAP to be 50% at a threshold of 100% of the target velocity (see Beppu et al. 1984, Fig. 9). By assuming symmetry and taking the limits of MAP ratios in the range, we can estimate a probability mass function of velocity, and from this we can estimate velocity standard deviation. From the numbers given in Beppu et al.'s (1984) Fig. 9 (constant velocity of 7.5°/s), the standard deviation calculated from the estimated probability mass function is between 20.6 and 36.3% of the target velocity, which agrees with our results (see Fig. 4B).

In Beppu et al. (1987), movement intermittency is calculated through a parameter called the "Weaving Ratio," in which the authors calculate the length of the velocity trace (vs. time) and normalize it by the length of the ideal straight line. Unfortunately, this number does not translate in a straightforward manner to velocity variance. However, the study of Beppu et al. (1987) used the same apparatus as Beppu et al. (1984), and so one may assume the results are not radically different.

Nelson (1983) showed that a violinist can make reasonably constant velocity strokes during bowing, but did not characterize the variance of the velocity fluctuations. This task is a highly multijointed movement moving against significant friction; it is also a highly trained skill that many humans cannot achieve, and it may in addition require auditory and skeletal vibration feedback (because violins are normally pressed against the musician's chin). Nelson's work is therefore quite dissimilar to that of the current study, and so comparisons are not straightforward to make.

The study of Cooke and Brown (1990) is similar to this one in two respects: subjects were instructed to produce constant velocity, and they did so with the aid of a phase-plane display of a target template: a single line indicating the desired trajectory. Cooke and Brown used much faster velocities than those used in the present study; ~67-167°/s (as opposed to 10-40°/s in the present study). Consequently, constant-velocity durations were quite short in the Cooke and Brown paper, ranging only up to 800 ms. Cooke and Brown did not quantify the velocity fluctuations of their subjects (the intent of the paper was to study the triphasic EMG pattern during uncommon movement trajectories), but certain nonaveraged trajectories in the paper (Fig. 3, for example) look similar to this paper's Fig. 3 except that the time axis has been expanded. Cooke and Brown did not quantify the inertia of their manipulandum, which could significantly affect the degree of their subjects' velocity variance. They also did not constrain their subjects' wrists; our pilot experiments suggested that subjects may be able to move more smoothly when they can recruit more joints, although this idea needs more rigorous testing.

What could be the source of the intermittency in our data? Could the intermittency be a mild form of tremor? The term tremor is derived from the Latin tremere, meaning simply "to tremble." Tremor is most often classified according to the behaviors under which it occurs, regardless of the underlying mechanisms (Findley 1988). The diagnostic label essential tremor refers to the most common type of tremor, which generally manifests itself as mild sinusoidal oscillations, particularly of the outstretched arms, while maintaining posture. Because of the benign nature of the condition, there have been few well-documented pathological studies. It is well agreed on, however, that the frequencies of essential tremor are significantly higher than those observed in this study, ranging from 6 to 12 Hz (Findley 1987).

Vallbo and Wessberg (1993) studied constant-speed tracking movements of single fingers and found dominant frequencies between 8 and 10 Hz, although lower frequencies were sometimes seen in particular subjects during visual feedback conditions. The 8- to 10-Hz cycles were often separated by periods of zero velocity and were observed in position holding as well as during movement. In a later study (Wessberg and Vallbo 1996), these authors concluded that stretch reflex activity could not account for the discontinuous finger movements. We did not observe any significant intermittency in the region of 8-10 Hz in our elbow measurements, but this does not necessarily mean that our observations are unrelated to those of Vallbo and Wessberg, because the finger and forearm have such different system characteristics; both inertial properties and relevant muscle stiffnesses are different. In addition, the neural system might deliberately control the fingers at faster time scales, and neural noise might be filtered differently through the finger system.

Slow arm tremor, closer to the movement intermittency observed in this study, is induced by cerebellar damage; tremor frequencies of 4-5 Hz are commonly observed (Findley 1988). It is believed that cerebellar tremor may actually be a series of movement corrections, because local cooling of the cerebellum disrupts the agonist/antagonist muscle timing, resulting in endpoint errors and subsequent movement corrections (Hore and Flament 1986). The cerebellum also plays a large role in turning trains of corrective movements into learned movements. Gilbert and Thach (1977) demonstrated that climbing fiber activity is highly correlated to unexpected load changes. Further support comes from Gellman et al. (1985), who showed that unexpected cutaneous or proprioceptive perturbations triggered activity in the inferior olive. Perhaps the intermittency observed in this study is a result of an incomplete blending of movement corrections by the cerebellum.

If the intermittency is due to incomplete blending, that implies that it stems from the structure of the limb controller (as opposed to some type of noise disturbance). One possibility is that the intermittency is caused by multiple preprogrammed point-to-point movements being either superimposed or replacing each other (Henis 1991). This is an attractive idea, because it unifies the classical tracking and accurate pointing results under a common model. Perhaps humans can only make short, open loop movements; long slow movements, regardless of whether feedback is employed, must somehow be pieced together from these shorter submovements (Milner and Ijaz 1990). Another possibility is that the muscle inputs must somehow be cyclic, because of the intermittent nature of cell firing and the cyclic nature of interneuron reverberating circuits (Pearson 1976). For example, spinal cord interneurons allow cats to walk on a moving treadmill even if the lower thoracic cord is transected, isolating the circuitry that controls the hindlimbs from descending signals (Grillner and Shik 1973).

Our experiment rules out completely that intermittency is due to noise or delays in the visual feedback loop. Of course, noise or delays in the visual feedback loop may amplify the problem (Weir et al. 1989), but movement intermittency cannot be solely a result of visual feedback. This experiment does not completely rule out delays or noise in the haptic feedback loop as an intermittency source, but previous studies of subjects with peripheral sensory loss have revealed intermittent movement behavior that is qualitatively similar to that of unimpaired subjects (Ghez et al. 1995; Gordon et al. 1995; Miall 1996).

Our experiment demonstrates that intermittency is not an additive noise process at the output of the system. Because of the correlation between velocity amplitude and noise amplitude (see Fig. 4B), any signal fluctuations must somehow be coupled into the signal at the input, before they get through the system to be turned into elbow velocity. The velocity fluctuations are not caused, for example, by a fixed-force level of random muscle twitching, but they might be caused by a fixed level of neural noise further upstream or by a submovement limb controller as described above. Whatever the source of the movement intermittency, it is either a direct result of the way movement is planned, or it is a handicap for which the movement planner must explicitly compensate. Experimental distinction of noise models versus controller structure models is deferred for future work.

It is important to recognize that this study only looked at unconstrained motion tasks; constrained limb motion was not examined. Indeed, the primary function of limbs is to interact mechanically with one's surroundings, a skill at which humans are remarkably adept. If movement intermittency is a necessary attribute of human limb manipulation, then it is only natural to assume that humans either minimize intermittency's negative effects or somehow exploit it to better interact mechanically with the outside world. An understanding of exactly how this is accomplished would be an important contribution to the field.

	ACKNOWLEDGEMENTS

  This research was performed in the Eric P. and Evelyn E. Newman Laboratory for Biomechanics and Human Rehabilitation at Massachusetts Institute of Technology and was supported by National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant AR-40029.

	FOOTNOTES

²   The delay imposed by a finite difference filter (¹/₂ sample) plus the maximum delay of one display frame. See METHODS.

¹   If this planner could be identified and accurately characterized, the model would prove quite valuable for telerobotics, rehabilitation, and several other applications.

³   For example, if the FFT magnitude data points are drawn from identical distributions at every frequency, we would expect to see significance levels below 0.1 10% of the time, below 0.5 50% of the time, and below 0.9 90% of the time (therefore above 0.9 10% of the time). In other words, we would expect a uniform distribution of significance levels from the tests (Drake 1967).

  Address for reprint requests: J. A. Doeringer, Dept. of Mechanical Engineering, MIT, Rm. 3-147, 77 Massachusetts Ave., Cambridge, MA 02139.

  Received 28 January 1998; accepted in final form 23 June 1998.

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