Chapter 11 Learning a dynamic limb synergy

Motor Control and Sensory Motor Integration: Issues and Directions D.J. Glencross and J.P. Pier (Editors) 9 1995 Elsevier Science B.V. All fights reserved.

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Chapter 11

LEARNING A DYNAMIC LIMB SYNERGY

Nicholas O'Dwyer Peter Neilson

Cerebral Palsy Research Unit, Institute of Neurological Sciences, The Prince Henry Hospital and School of Electrical Engineering, University of New South Wales, Sydney, Australia

Dynamic and non-dynamic bimanual synergies were studied during pursuit tracking of a common visual target by both hands. Subjects were required to track a target with two response cursors simultaneously. The target moved in the centre of a computer screen, while the response cursors were located at either side of the target and controlled via a joystick with either hand. The target moved irregularly in amplitude and speed, with a frequency bandwidth up to 2Hz. The tracking system was contrived in two ways so as to produce either dynamic or non-dynamic synergies between the hands. Six subjects practised tracking where the joystick-cursor relation was a straighO~orward, non-dynamic, scalar relation, identical for the left and right joysticks. This meant that, in order to track the target, the left and right hands simply had to be moved in synergy in an identical fashion, with only one virtual degree of freedom of movement. This was a scalar, non-dynamic synergy. Another six subjects practised a novel task where the right joystick input was first linearly filtered (first-order, low-pass) before driving the response cursor. This meant that, in order to track the target together, the left and right hands had to be moved with different amplitudes and out of phase with each other, but still in synergy. The relative amplitude and timing of the limbs in this synergy were required to vary with the frequency of the movement, so that this was a dynamic synergy. The results showed that the subjects accomplished both non-dynamic and dynamic inter-limb synergies. In the former case, the hands were coupled as expected in a simple, one-to-one relation. In the latter case, the hands were coupled in a dynamic, linear relation, although the specific characteristics of this relation deviated from those required for full compensation for the effect of the filter on the joystick. The degree of inter-limb coupling did not differ between the non-dynamic and dynamic synergies and was high (87-91%)for both, indicating little independent activity between the limbs in either case. Furthermore, the demands of forming the inter-limb synergies, either non-dynamic or dynamic, interfered only minimally with tracking performance, since only minor differences were observed between single-handed and bimanual tracking.

1.

INTRODUCTION

Studies of bimanual coordination may be divided into three broad categories on the basis of the dependence or independence of the amplitude and timing of the movements in the limbs. The first category includes tasks where the limbs execute movements with independent timing,

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such as in piano playing or tapping different rhythms with each hand. A primary focus of studies in this category has been the constraints on achieving independence between the limbs, owing to the tendency for the limbs to interfere or become synchronised (e.g., Kelso & DeGuzman, 1992; Klapp, 1979; Peters, 1985; Shaffer, 1981; Swinnen, Walter, Beirinckx and Meugens, 1991). The second category includes tasks where the limbs execute movements with the same timing (though the limbs may be either 'in phase' or 'out of phase') and amplitude (e.g., Kelso, 1984; Schmidt, Zelaznik, Hawkins, Frank & Quinn, 1979; Turvey, Schmidt & Beek, 1993).

These studies have focused on the nature of the inter-limb

dependence when the limbs move with similar amplitude and timing, such as moving opposite wrists or fingers rhythmically together. The third category includes tasks where the limbs execute movements with independent amplitude but where independent timing has not been critical to successful task performance (e.g., Kelso, Southard & Goodman, 1979; Marteniuk, MacKenzie & Baba, 1984; Sherwood, 1989). This has been the case, for example, in twohanded aiming to targets at different distances. In the first category, the movements in different limbs were, or strove to be, independent or mathematically uncorrelated. def'mition, uncorrelated.

Rhythmical movements of different frequencies are, by

For the movements to be uncorrelated, their temporo-spatial

trajectories must be quite different.

Everyday examples in this category include the

cooperative limb movements in doing up buttons or using a knife and fork.

In such

movements the two hands perform different actions but in order to work cooperatively, their timing must coincide at crucial moments.

Movements in this category exemplify the

suggestion of Kelso and DeGuzman (1992) that "coordination holds only at some points in the signal "trajectories" of the individual components: in between, trajectories may vary spatially (e.g., characteristic amplitudes) and temporally (e.g., characteristic periods and frequency content)". Similar considerations apply to the coordination between respiratory, laryngeal, pharyngeal, velar and articulatory movements during speech. In both the second and third categories, the movements were dependent or mathematically correlated. This means that the trajectories of the movements must be quite similar. Everyday examples here include clapping the hands together, catching a ball in both hands and turning the steering wheel of a car. It is precisely by virtue of the correlation between the movements in different limbs that these actions can be said to involve synergies between the limbs.

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The correlation or dependency between limbs or limb segments reduces the effective degrees of fw.exlom to be controlled. In studies of synergies to date, however,

despite

differences

in

amplitude between the limbs, the interlimb relation invariably has been a scalar one, without dynamics in the relation per

I

I

Figure 1. Illustration of signals related in a linear,

dynamicway.

se. (this is not to deny dynamics in the movements of the limbs themselves, but only in the

relation between the limbs). A non-dynamic synergy is one where the limbs have a constant phase relation. This may be 'in phase' or 'out of phase', but the important point is that the phase relation is constant. Furthermore, the gain or relative amplitude between the limbs is also constant in the same way. A dynamic relation, on the other hand, is one where both the gain and phase between the limbs vary as a continuous function of the frequency. (Frequency is directly related to speed as long as the amplitude remains constant). In other words, both the spatial and temporal aspects of the limb trajectories vary. A specific example is illustrated in Figure 1. It can be seen that the signals differ both in amplitude and timing, with the thick trace being both smaller and smoother than the thin trace and lagging it in time. In spite of these spatial and temporal differences, the signals are in fact perfectly linearly correlated - the thin trace represents the input and the thick trace the output of a first-order, low-pass digital f'llter. However, a linear regression analysis of the signals (actually 1 minute in duration, of which only 4.4 seconds are shown here) shows a coefficient of variation (r ~) of only 0.57. On the other hand, a cross-correlational and spectral analysis (Bendat & Piersol, 1966; McRuer & Krendel, 1959;

Neilson, 1972), which computes the best-fit linear dynamic relation

between the signals, accounts for 98% of their variance. The importance of dynamic relations cannot be overemphasised because they are ubiquitous in movement control. One of the most obvious examples is the relation between muscle tensions and joint movements, where the inertial load of the limbs on muscles introduces important dynamics. The relation between the firing of a motor neuron pool and the resulting muscle tension is also a dynamic relation, akin to a low-pass filter (Partridge, 1965). In our interactions with the external environment, examples abound of diverse dynamic

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relations. Consider the relations between rotation of the steering wheel of a car or a ship and the resultant changes in direction of motion; or the change in load on the ann in using a teaspoon compared with a serving spoon; or the effect of one hand holding an object which is manipulated by the free hand. This latter is an example of bimanual coordination where the relation between the limbs involves dynamics due to the additional inertial load on one limb. Since dynamic relations occur so commonly in controlling and coordinating movement, it follows that the human central nervous system (CNS) must be able to learn to cope with new dynamic relations. It is with such learning that this chapter is concerned. We describe two experiments on bimanual coordination, one involving a non-dynamic and one a dynamic relation between the limbs. The first experiment involves movements that are identical in amplitude and timing in each hand, whereas the second involves movements that are dissimilar in amplitude and timing in each hand. However, in both studies the hand movements are required to remain linearly correlated (dependent).

The former involves a simple, non-

dynamic (zero-order) relation between the limbs, while the latter involves a dynamic (firstorder), though still linear, relation. The particular dynamic relation to be studied here means that the hands move in phase and with equal amplitude for very slow movements and move out of phase and with differing amplitudes for faster movements - this in a task that involves a mixture of slow and fast movements. Our main aim is to observe how our subjects adapt to this unfamiliar inter-limb relation. An additional feature of the experiments to be described here is that they involve arrhythmic movements, whereas many studies in this area have involved rhythmic movements.

We

examine continuous, irregular movements during pursuit tracking of a visual target. In this task, the characteristics of the movements required of the subject are determined by the characteristics of the target signal. These can be controlled in advance by the experimenter. By using irregular movements, the predictability of the task is greatly reduced and the complexity of the movement waveforms is increased. These features are characteristic of many everyday tasks such as visually fixating irregularly moving objects or maintaining upright posture in a moving vehicle. Additionally, tracking is an externally-paced task, so that the time to respond is limited and this imposes a greater processing load on the subject. Again, this feature applies to many everyday tasks such as driving a car or catching a ball

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2. T R A C K I N G S E T U P

The tracking setup is illustrated in Figure 2. The target cursor is the bar in the middle of the screen. There are two response cursors, one on either side. The target moves irregularly in the vertical plane only. The left and fight response cursors are controlled by the joysticks shown on the left and fight, respectively. Forward rotation of the joystick sends the response cursor up the screen and backward rotation brings it down. The subjects were required to keep both response cursors aligned with the target cursor. This meant that they had to move both joysticks (and both hands) together.

Figure 2. Schematic diagram of tracking setup for both experiments. The target (hatched bar) was red and both response cursors (solid bars) were blue. The screen background colour was pale green. The angular excursion of the joysticks was approximately + 30~ We were interested in the coordination between the two hands in this tracking task, but we also needed to compare two-handed tracking with single-handed tracking.

Therefore, the

general procedure was that subjects performed an initial series of two-handed and one-handed (both left and fight) tests, then practised on the two-handed test only and finally repeated the initial series of two-handed and one-handed tests. All tests were continuous pursuit tracking of one-minute duration.

Practice consisted of 10 one-minute tests per day for 13 days,

performed over a period of two months, giving a total of 130 minutes of distributed practice. Two experirnents were carded out - the first with a simple relation between the hands and the second with a dynamic relation between the hands.

294

N. O'Dwyer & P. Neilson The movement of the target was driven by signals generated in advance by the

experimenters.

Computer-generated pseudo-random numbers were filtered (2*d-order,

Butterworth) at 1Hz to produce signals that were irregular and contained a mixture of slow and fast changes. Two 'test' target signals and one 'practice' target signal were produced in this way. The frequency spectra of the targets showed substantial power up to almost 2Hz and low-level power up to about 3Hz (see Figure 8). The sampling and display rate of the target and response cursors was 40Is.

3. EXPERIMENT 1

3.1 Subjects Six adult volunteers aged 22-33 years (mean=26.5) participated. There were three males and three females and all were right-handed. All were university students or graduates and had no musculoskeletal or uncorrected visual problems or any known neurological disease. All subjects were fully informed of the procedures before data collection was undertaken.

3.2 Procedure The purpose of this first experiment was primarily to provide baseline performance against which the results of Experiment 2 could be assessed. On the first day the subjects performed three types of tracking test: (i)

two-handed tracking (L+R),

(ii) single-handed tracking with the right hand (R), ('tii) single-handed tracking with the left hand (L). For the two-handed tests, the response cursors were independent, so that rotation of the left joystick moved only the left cursor and rotation of the right joystick moved only the right cursor. For the single-handed tests, the response cursors were linked together so that rotation of one joystick moved both the left and right cursors. In this way the visual display was as similar as possible for the two-handed and single-handed tests. Following an initial one-minute familiarisation test (L+R) using the 'practice' target, the subjects performed each of the three tests - L+R, R and L - using the two 'test' targets, to give a total of six tests. The order of the tests was counterbalanced across the group in order to minimise possible sequence effects. On the subsequent 13 days (spread over two months)

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they practised only the two-handed (L+R) test using the 'practice' target. On the final day, each subject repeated the test sequence that they had performed on the first day.

3.3 Analysis of Tracdking Performance Five sets of analysis were required. The relation between the target and response signals was analysed for each of the single-handed tests. Similarly, the relation between the target and the left response and the target and the right response was analysed for the two-handed tests. In addition, for the two-handed tests, the relation between the left and right response was analysed. Thus, the two-handed tests required three sets of analysis. Table 1 illustrates the analysis sets and the notation employed (in parentheses). Since neither the target nor response signals contained frequency power above about 4Hz, the sampling rate was reduced to 10Hz (ie, still greater than twice the maximum frequency in the signals) for these analyses.

Table 1. Tracking analyses

(L)

Single -Handed (R)

Target-Left

Two-Handed (L+R) Target-Left (L/L+R)

(L) Target-Right (R)

Target-Right (R/L+R) Left-Right (L-R)

An overall measure of tracking performance was provided by the root mean square (RMS) value of the error between the target and response signals (McRuer and Krendel, 1959). In addition, cross-correlational and spectral analysis was carded out on the five signal-pairs indicated in Table 1. This analysis illuminates aspects of tracking performance that cannot be assessed via conventional measures of error alone. It is based on the waveform similarity between the target and response and therefore it measures both amplitude and timing aspects of performance. The degree of waveform similarity (ie, correlation) between the target and response is quantified by the coherence for each frequency, the magnitude of the correlated response relative to the target is quantified by the gain for each frequency and the time lag of the correlated response behind the target is quantified by the phase for each frequency. It

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should be noted that the coherence measures the variance of the response that is correlated with the target at each frequency as a proportion of the subject's total response at that frequency. The overall coherence quantifies the degree of correlation between target and response over all frequencies and is analogous to the coefficient of determination (r 2) in a regression analysis. For ideal tracking, the response waveform would be an exact replica of the target waveform; hence, for all frequencies, the coherence would be 100%, the gain would be unity and the phase lag zero. In actual tracking, of course, the response never exactly matches the target, but instead lags behind and reproduces the target waveform only in a 'noisy' fashion. Repeated measures analyses of variance were subsequently applied to all of the above measures in order to test for significant differences (i) before and after practice, (ii) between one-handed and two-handed tracking and (iii) between the left and right hand. In addition, using frequency as a fourth factor in the analyses of variance, we tested the pattern of variation across frequency of the coherence, gain and phase measures.

3.4 Results

The results will be presented in two sections: (i) left- right coordination and (ii) left and right hand performance in tracking the target.

3.4.1 Left-Right Coordination The degree of coupling between the left and right hand in two-handed tracking is quantified by the coherence versus frequency, shown in Figure 3. Also shown for comparison is the coherence of either hand with the target. It can be seen that following practice there was an overall increase in left-fight, target-left and target-fight coherence (F[1,5]=7.16, p<0.05), as well as a change in the variation of coherence with frequency (F[5,25]=2.64, p<0.05), the latter due to a greater increase in coherence at the higher frequencies.

The

increase in coherence of each hand with the target shows that the subjects were tracking the target better after practice than before, while the increase in left-right coherence shows that the two hands were more tightly coupled after practice. In fact the coupling between the hands after practice accounted for 91% of the variance of their movements. Moreover, the coherence between the hands was signifcanfly greater than the coherence of either hand with the target (F[2,10]=20.69, p<0.001).

Furthermore, as reflected in a significant interaction

between the three coherences and frequency (F[10,50]=7.47, p<0.001), the coherence

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Learning a Dynamic Limb Synergy

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The changes with practice were not significant here

(F[1,5]<2.74, p_>0.16). The average left-fight gain approached unity, indicating that the fight and left hand movements were very similar in amplitude.

Similarly, the average left-fight

phase approached zero, indicating that the fight and left hand movements were very closely locked in phase with each other. Furthermore, with the exception of the left-fight gain at 0.1Hz only, the gain (F[4,20]=0.46, p--0.77) and phase (F[5,25]--0.11, p--0.99) values did not

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vary significantly with frequency, so that the coupling between the hands was essentially a non-dynamic (zero order) one.

3.4.2

Left Hand and Right Hand Tracking Performance (L, R, IJL+R, R/L+R)

Performance of both one-handed and two-handed tracking improved following practice of two-handed tracking. Tracking error decreased for all tracking conditions (L, R, IJL+R and R/L+R), though the changes were not significant (F[ 1,5]--4.58, p=0.09). However, the overall coherence (Figure 5) increased significantly (F[1,5]=8.72, p<0.05), so that on average about 80% of the subjects' response movements were linearly correlated with the target after practice. It can be seen that following practice of the two-handed condition, performance was similar for the left hand and fight hand in both one-handed and two-handed tracking. 100 g5 "-"

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one-handed (L, R) and two-handed (L/L+R, R/L+R) tracking. The gain of the target to response relation quantifies the amplitude of the response with respect to the target. Following practice the gain (Figure 6A) did not differ significantly between the left and fight hand (F[1,5]=0.04, p----0.85) nor between one-handed and twohanded tracking (F[1,5]-2.98, p--O.15). The shape of the gain versus frequency curves is typical for tracking these kinds of target signals. We have described previously how this particular shape can be attributed in large measure to prediction of the target signals and so it will not be considered further here (Neilson, Neilson and O'Dwyer, 1993 and this volume). It can be seen that this shape was similar for all conditions (L, R, LtL+R and R/L+R), except at the highest frequency (1.1Hz), but the absence of any significant interactions with frequency showed that this difference was not significant.

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respect to the target. As with the gain, the phase following practice (Figure 6B) did not differ significantly between the left and right hands (F[1,5]--0.07, p--0.80). However, unlike the gain, the phase did differ, for both hands, between one-handed and two-handed tracking, as shown both by a main effect (F[1,5]=11.86, p<0.025) and in the interaction of phase with frequency (F[5,25]=10.18, p<0.001). The small difference (about 10~ at 1Hz) means that the response of either hand lagged on average about 28ms more behind the target during twohanded compared to one-handed tracking.

3.5 Discussion The main finding of this study was that, following just over two hours of distributed practice at two-handed tracking with a simple synergy between the hands (L+R), performance of one-handed and two-handed tracking was very similar for both hands. Initial small (nonsignificant) differences between the left and fight hand (in these fight-handed subjects) and between one- and two-handed tasks had largely disappeared after practice. The one important remaining difference was the small increase (about 28ms) in tracking time delay in two-handed compared with one-handed tracking. This difference may reflect an extra processing load on

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the CNS when the two hands are required to perform together in a simple synergy compared with single-handed performance. It may reasonably be questioned whether in the two-handed task the left and right hands were not really working together in a synergy but rather were working independently to track a common target. The coherence between the hands might thus have been induced simply by their similar behaviour in following the common target. Against this view, however, is the finding that the coherence between the hands was significantly greater than the coherence of either hand with the target. This showed that the left and right hands were making movements that were correlated with each other but not correlated with the target. In other words, they were making correlated tracking errors. This was especially apparent at higher frequencies where tracking errors increase but the coupling between the hands was maintained.

The

nature of this coupling was shown (by the gain and phase curves) to be a simple, non-dynamic (zero order) relation.

4. EXPERIMENT 2

4.1 Subjects Six right-handed, male volunteers aged 22-37 years (mean=27.3) participated. As with Experiment 1, all were university students or graduates and the inclusion and exclusion criteria were as before.

All were fully informed of the procedures before data collection was

undertaken.

4.2 Setup The tracking setup was the same as before except that now we wished to induce a dynamic synergy between the hands. In order to achieve this we introduced a low-pass filter between the right joystick and the fight screen cursor.

This meant that the deflection of the fight

response cursor on the screen was now the filtered fight joystick rotation. The effect of the filter on the relation between the left and fight screen cursors can be seen in Figure 7, where the thin lines show the excursion of the response cursors on the tracking screen and the thick lines show the corresponding sequence of joystick rotations (and hence movements of the hands).

Consider the situation where both hands move in perfect

synchrony, as illustrated in the top part of the figure. On the left side, the hand and screen cursor move identically in a one-to-one relation. On the fight side, the hand moves in perfect

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Learning a Dynamic Limb Synergy

synchrony with the left, but the cursor movement, due to the f'dter, is smaller and smoother and is also lagged in time. This smoothing is greater for faster (higher frequency) movements, such that the fastest movements are virtually eliminated. Thus, the hands move identically on both sides but the screen cursors do not. The relation between the two hands is a simple oneto-one synergy, while the relation between the cursors is the dynamic, linear relation of the falter. 1

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The scenario in the top part of Figure 7 applies where the subject makes absolutely no compensation for the effect of the f'dter - the hands move identically on both sides but the screen cursors move differently. However, the tracking task requires the subject to make both screen cursors move identically in order to track their common target. To achieve this, the

~rhe e q u a t i o n for t h e filter (digital, first-order, e x p o n e n t i a l l y - w e i g h t e d , m o v i n g a v e r a g e ) is as f o l l o w s : y, = a u , + (1-a)y,. I

w h e r e u, = t h e i n p u t to t h e filter a t t i m e t, y, = t h e o u t p u t of t h e filter at t i m e t a n d Y,-I = t h e o u t p u t of t h e filter a t t i m e t-l; a 6= 0 . 1 1 7 6 ) is t h e p a r a m e t e r t h a t sets t h e t i m e c o n s t a n t of t h e filter.

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hands must move differently. In order to overcome the filter effects and make the fight response cursor behave as though there was no filter present, the subject must compensate by making considerably larger and faster hand movements on the fight, as illustrated in the bottom part of the figure. This shows the situation if the subject compensates fully for the effect of the filter. If this can be achieved, then the left and fight cursors will have a simple one-to-one relation but the left and fight hands will have a dynamic linear relation.

This

dynamic relation will be the inverse of the low-pass filter. In other words, instead of moving in a simple synergy as in Experiment 1, the hands will be moving in a dynamic synergy. It is important to point out that the degree of coupling between the hands and the nature of the coupling are in principle quite independent and need to be considered separately. Thus, in both scenarios illustrated in the Figure 7, the left and fight hands are still perfectly coupled (ie, left-fight coherence = 1), regardless of the degree of compensation for the filter. In the case of no filter compensation, however, the left-fight synergy is a scalar, one-to-one relation, whereas in the case of full compensation, the synergy is a dynamic relation. Furthermore, this distinction between degree and nature of coupling still applies if partial rather than full compensation occurs, which as will be,seen, turns out to be the case in the present experiment. Figure 8 shows the characteristics of the filter in the frequency domain. The gain and phase of the filter are plotted above the spectrum of the target waveform, so that the effects of the filter over the target bandwidth may be appreciated. At 1Hz, the gain of the filter is about 0.6 and the phase lag is about 47 ~. In order to compensate for the filter at this frequency, therefore, the subject needs to produce hand movements at 1.7 (= 1+0.6) times the normal amplitude and with 130ms (= [47+360]x1000) lead.

4.3 Procedure

The design and procedure were similar to Experiment 1 but now there were five measurements: (i)

two-handed tracking (L+R)

(ii)

two-handed tracking with the joystick filter on the fight hand (L+RF)

(iii) single-handed tracking with the fight hand (R) (iv) single-handed tracking with the fight hand and the joystick filter (RF) (v)

single-handed tracking with the left hand (L).

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As before, for the two-handed tests, the response cursors were independent, so that rotation of the left joystick moved only the left cursor and rotation of the fight joystick moved only the fight cursor; for all single-handed tests, the response cursors were linked together so that rotation of one joystick moved both the left and fight cursors.

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On the final day, eachsubject repeated the test sequence that they had

performed on the first day.

4.4 Analysis of Tracking Performance Nine sets of analyses were required, as illustrated in Table 2. The relation between the target and response signals was analysed for each of the single-handed tests. Similarly, the

304

N. O'Dwyer & P. NeUson

relation between the target and the left response and the target and the fight response was analysed for the two-handed tests. In addition, the relation between the left and fight response signals was analysed for the two-handed tests. Thus, the two-handed tests required three sets of analysis each.

Table 2. Tracking analyses

(L)

Single-Handed (R)

Two-Handed (RF)

Target-Left

(L) Target-Right (R)

Target-Right (RF)

(L+R)

(L+RF)

Target-Left (L/L+R)

Target-Left (IL+RF)

Target- Right (R/L+R)

Target-Right (R/L+RF)

Left-Right (L-R)

Left-Right (L-RF)

4.5 Results

Traces of the target, left cursor and fight cursor for the two-handed tracking conditions are shown in Figure 9. Before practice, without the filter (L+R), both cursors show typical tracking responses to this type of target - they reproduce the target waveform with a lag due to reaction time delay (ie, phase lag > 0) and with added 'noise' or deviations from the target waveform (ie, coherence < 1). It can also be seen that, even on this first day of tracking, the left and fight cursors are well synchronised in time, as was found in Experiment 1, but less well matched in amplitude. The equivalent traces for tracking with the falter (L+RF) before practice show that the left cursor is similar in amplitude and timing to the case without the filter, but the deviations from the target waveform are different. With regard to the fight cursor, the major differences due to the filter are, not surprisingly, that the response lags further behind the target and is generally reduced in amplitude. Hence, the left and fight responses are quite clearly different. The equivalent traces after practice are also shown in Figure 9. Without the filter (L+R), it can be seen that, again as was found in Experiment 1, the left and fight cursors are very tightly synchronised and are now well matched in amplitude. With the filter in place (L+RF), the left and fight cursors are now also tightly synchronised and closely matched in amplitude. However, the fight cursor still lags the target more than the left, though the gap clearly has

305

Learning a Dynamic Limb Synergy

been narrowed as a result of practice. It is also evident that both without and with the falter, the tracking responses are superior after practice since they reproduce the target waveform more accurately (ie, with less noise). Before Practice

After Practice

t

L+R

- Target

~

Left Cursor

Right Cursor

, 1 sec

,

Figure 9. Left and right response to same target segment during two-handed tracking without (L+R) and with (L+RF) the filter on the right hand, before and after practice. Signals are 4.4 seconds in duration and were selected from subject whose performancewas close to the group mean. For ease of presentation, the quantitative results will be organised into four sections: (i) left-right coordination, (ii) left hand tracking performance, ('tii) right hand tracking performance and (iv) right hand compared with left hand performance.

4.5.1

Left-Right Coordination

The overall coherence between the left and right hands, which quantifies the degree of coupling between them in two-handed tracking, is shown in Figure 10. It can be seen that, even before practice, the hands were highly coupled.

The coupling increased significantly

(F[ 1,5]=10.25, p<0.025) with practice for both conditions (L+R, L+RF), so that on average it accounted for 87% of the variance of the movements of the hands. The comparable figure for two-handed tracking (L+R) in Experiment 1 was 91%. Despite the fact that only the filter condition was practised, there was no significant difference in the coupling between the hands with and without the filter (F[1,5]=1.30, p=0.31). The difference before practice was not significant (F[1,5]--0.99, p=0.37) and the two conditions were virtually identical after practice.

306

N. O'Dwyer & P. Neilson

The variation across frequency of

100

the coherence between the hands is

-0-

95

shown after practice in Figure 11. The coherence is lowest at the lowest ID

frequencies, rises to

L+R

]

9-o-. L+RF]

90

a plateau for O

intermediate frequencies and drops off

__o 85

slightly at the highest frequencies. The

>~ O 80

coherence between the left and right o

hands can be compared in this figure

75

with the coherence of either hand with

Before Praclice

After Praclice

Figure 10. Overall coherence

left and right hand during two-handed tracking without and with the f'flter on the right hand.

the target. For the two hands in the t w o

of

conditions (L+R, L+RF), the correlation with the target accounted for 72-77% of the total variance of their movements and there was no significant difference between the left and right hands (F[1,5]=0.18, p=0.69) nor between tracking without and with the f'dter (F[1,5]=3.79, p=0.11).

However, as in Experiment 1

(Figure 3), it can be seen that the coherence between the two hands is both greater overall than the coherence of either hand with the target (F[2,10]=23.60, p<0.001) and also varies differently with frequency (F[14,70]=10.87, p<0.001).

This is especially apparent at the

higher frequencies. 100

Oo.,..,O.-.-..-~,~

90

(D 0 ~" ~D L r

/

0" .

.

.

.

.

' ' 0 .... ~

,,o......,o.......o,,

.... 0

.r . . . . . . . . . .

~.

f

f

80

-o

tO

70

60

Q

.1

--o..

T-R

9- o - . .

L-R

.3 .5 .7 .9 111 113 115 Hz L+R

9 9

91

t 121

.3

.5

.7

.9

1.1 1 . 3 1 . 5 M z

L+RF

Figure 11. Coherence versus frequencyof target and left hand (T-L), target and right hand (T-R) and left and right hand (L-R), after practice, during two-handed tracking without (L+R) and with (L+RF) the filter on the right hand.

307

Learning a Dynamic Limb Synergy

Of equal importance to the degree of coupling between the hands is the nature of their coupling, that is, their relative amplitude and timing as quantified by the gain and phase relations, respectively. Before practice the average gain of the right hand relative to the left hand during two- handed tracking without the f'flter (L+R) was about 0.8 for all frequencies, as shown in Figure 12. This means that, on average, the movements of the right hand were only 0.8 the amplitude of the movements of the left hand. With the f'flter in place (L+RF), however, the movements of the right hand increased so that they were larger in amplitude than the left hand for all but the lowest frequency. The relative amplitude increased with frequency up to 0.7Hz and thereafter declined slightly. This indicates partial compensation for the attenuation of the filter even on the first day of tracking. Actually, the f'dter has been slightly over-compensated at the lower frequencies and significantly under-compensated at the higher frequencies, as can be seen by comparison with the curve in Figure 12 representing the gain necessary for full compensation for the filter. 2.2

1.8

c- 1.6 (.~

.

.

.

.

.

.

.

2.2

.

--o- Before Practice

2

"'Q- After Practice

1.8

i

1.6

o...-(rl, 9 ,."-o..,,i 3 -,o"

9.0... Full Compensation

1.4

1.4

1.2

1.2 .,.El d I'I'P t,

~

0.8

i

b L+R

""o

1

OO

0.8

/

13

1'3 's.z L+RF

Figure 12. Left hand-right hand gain versus frequency, before and after practice, during two-handed tracking without (L+R) and with (L+RF) the filter. Also shown is the left-rightgain that would have been observedhad the filter been fully compensated. After practice, further compensation f o r the filter has occurred, extending to higher frequencies, but it still falls short of the ideal beyond 1.1Hz. Furthermore, during tracking without the filter (L+R), it can be seen that there is an after-effect of practice with the f'dter (L+RF), whereby the gain of the right hand has increased relative to the left at the highest frequencies (Figure 12).

This increase occurred at those frequencies where the greatest

increase with practice occurred for tracking with the f'dter. The change in the gain versus

308

N. O'Dwyer & P. Neilson

frequency curves with practice was significant (F[7,35]=10.40, p<0.001), as was the difference between tracking without and with the f'dter (F[7,35]=34.67, p<0.001). The phase of the fight hand relative to the left is shown in Figure 13. Before practice, in tracking without the f'dter (L+R) the two hands were virtually in phase on average for all frequencies. With the f'dter in place (L+RF) the fight hand led the left by up to 10~ at the lower frequencies but this lead gradually switched to a lag of about 10~ as the frequency increased. This phase relation fell far short of that required for full compensation for the fdter, also shown in Figure 13.

60 50

40 30 .c:

Q.

.

.

.

.

.

.

60

...^"".......o" ......o

- o - - Before Practice 9- o - After

9..o-..

50

p .......~""

40

Practice Full Compensation

~e w~

30

2O

i

20 .13,...13.-

10

.13

-10 .

.i

.3

.

.5

.

,f

"El,

10

~

.

.7

.

.9

.

1.1 1.3 1.5 I-Iz

L+R

-10 .

.1

,

.3

,

.5

,

.7

,

.9

,

,

,

1.1 1.3 1.5 Hz

L+RF

Figure 13. Left hand-right hand phase versus frequency, before and after practice, during two-handed tracking without (L+R) and with (L+RF) the f'flter. Also shown is the left-right phase that would have been observed had the filter been fully compensated. After practice, clear compensation for the falter had occurred, so that the fight hand led the left at all frequencies. However, the compensation fell short of the ideal at all but the lowest frequencies. Again, during tracking without the fdter (L+R), it can be seen that there was an after-effect of practice with the fdter (L+RF), so that the fight hand now led the left by about 15o, similar to the amount of actual compensation (10o-20 ~ for the fdter achieved with practice. As with the gain, the change in the phase versus frequency curves with practice was significant (F[7,35]=8.03, p<0.001), as was the difference between tracking without and with the f'dter (F[7,35]=151.40, p<0.001). In addition to these changes in left-fight coordination, it was necessary to evaluate the tracking performance of each hand and any changes with practice. For this, it was necessary to analyse the relation of the left and fight response cursors to the target.

309

Learning a Dynamic Limb Synergy 4.5.2

Left Hand Tracking Performance (L, L/L+R, L/L+RF)

The mean after

tracking error

practice

for

the

before and left

120 .-o- L

hand

-'~"

conditions is shown in Figure 14. The

,_ 110

error reduced significantly with practice

t~ o9 ~ 100

for

all

conditions

p<0.01).

(F[1,5]=18.33,

L/L+R

9"~"" L/L+RF 8~1,Q

Moreover, it is clear that

performance was similar for the three conditions after practice. Indeed, apart

90 Before Practice

After Practice

Figure 14. Root mean square (RMS) error for the left hand from the improvement with practice, the during single-handedwaeking (L) and two-handed tracking without the filter (I.JL+R) and with the filter (L/L+RF) o n most important finding for left hand was the right hand. that, after practice, performance was apparently unaffected by what the right hand was doing.

4.5.3

Right Hand Tracking Performance (R, RF, R/L+R, R/L+RF)

The mean tracking error before and after practice for the right hand conditions is shown in Figure 15. The error reduced significantly with practice for all conditions (F[1,5)=26.59, p<0.01).

Although there was greater improvement for the two conditions with the filter

present (F[ 1,5)=13.64, p<0.025), performance was still superior without the filter because the effect of the filter was not fully compensated.

120 1 Hand .-o-.

2 Hands

110 01.. L

W

rr

1 O0

i1

90 Before Practice No filter (R,

After Practice R/L+R)

Before Practice Filter (RF,

After Practice R/L+RF)

Figure 15. Root mean square (RMS) tracking error for the right hand, before and after practice, during singlehanded (R) and two-handed (R/L+R) tracking, without and with the filter on the right hand.

310

N. O'Dwyer & P. Neilson

In light of the finding that left hand tracking performance was apparently unaffected by what the fight hand was doing, it was of interest here whether fight hand performance was similarly unaffected by what the left hand was doing (ie, whether the left hand was tracking or not). With no filter present (R, R/L+R) this was indeed true. This can be seen in the error scores in Figure 15 and it was also reflected in the gain and phase functions. With the filter present, however, a difference in performance between the one-handed and two-handed tasks (RF, R/L+RF) was apparent in the gain and phase functions (though not in the error scores in Figure 15).

Specifically, as illustrated in Figures 16A and 16B, the gain was lower

(F[7,35]=4.58, p<0.01) and the phase lag longer (F([7,35]=3.48, p<0.01) at the higher frequencies in the two-handed compared with the one-handed task when the filter was present. What this means is that there was greater compensation for the filter if only one hand was tracking rather than two, the difference being apparent at the higher frequencies only.

0.9

--o---El--

1 Hand 2 Hands

A

I s

o

0.8 0.7 0.6 0.5 0.4

.~ .& .s .~, .b 1'1 ~ i a l : ~ z

.1 .3 .; .7 .; 1"1 1:3 115

Hz

0

B

-20 -40 -60 -80

/-

a.

-1 O 0 -120 -140 -160

b

.1 .; .; .7 No

Filter

"1 1 : 3 (R, R/L_+R) .9

1

1:5

HZ

.3

.5

Filter

.7

(RF,

.9

1.1

1.31.5

Hz

R/L+RF)

Figure 16. Target to response gain (A) and phase 03) versus frequency for the right hand, after practice, during one-handed and two-handed tracking, without and with the filter.

4.5.4

Right Hand vs Left Hand Tracking Performance (L/R, L+R, L+RF)

The mean tracking error did not differ overall between the left and fight hands (F[1,5]=2.95, p=0.15) in this group of fight-handed subjects. For tracking without the filter, the initial difference in means for both one-handed and two-handed tracking (Figure 17) was

311

Learning a Dynamic Limb Synergy

not significant (F[1,5]=2.82, p---0.15) and their performance was virtually identical following practice. Whenever the filter was present on the right hand, of course, its performance was significantly poorer than on the left both before and after practice, as shown by a significant interaction (F[2,10]=53.04, p<0.001) between the hands and the three tracking conditions (L/R, L+R, L+RF). (The RF condition was excluded from this comparison since there was no corresponding condition for the left hand).

120 n # #

--o--

Left Hand

--~--

Right Hand

110 0 L..

LU

[]

--o #

0o

:~ 1 0 0 rr o

o

o

o

o

o

.d

# #

El

#

90 i

i

i

L, FI L+FI L+RF Before Practice

i

L, FI

i

i

L+FI L+RF After Practice

Figure 17. Root mean square (RMS) tracking error for the left and right hand, before and after practice, during single-handed tracking (L, R), two-handedtracking without the filter (L+R) and two-handed tracking with the filter on the right hand (L+RF).

4.6 Discussion As in Experiment 1, the high coherence (87%) between the hands in the two-handed tasks and the fact that this was higher than the coherence of either hand with the target, provides strong evidence that the hands were working together in a synergy.

Again, the coupling

between the hands was seen to be maintained even for the highest frequencies of movement. Furthermore, this was true regardless of whether the filter was in place for the right hand. However, it is the nature of the synergy that is of most interest here. Before practice, in the task without the filter (L+R), it is clear from the gain and phase relations between the hands that the synergy was a simple, non-dynamic one. In contrast, in the task with the filter (L+RF), the synergy was a dynamic one. After practice, at low frequencies the amplitude of the movement was similar in the two hands, but as the frequency increased, the amplitude of movement of the fight hand increased to 1.6 times that of the left and remained at about this level for the highest frequencies. The fight hand also had a phase lead ahead of the left for all

312

N. O'Dwyer & P. Neilson

frequencies, with a maximum lead of about 20 ~ at 0.5Hz. Furthermore, the after-effect of learning this dynamic synergy was apparent at the higher frequencies in the task without the filter. The subjects in this study exhibited a dynamic synergy between the hands, but the characteristics of this synergy deviated from what was required for full filter compensation. The amplitude characteristics of the fight hand movements showed good compensation up to about 1.1Hz, while the phase characteristics showed good compensation only up to 0.3Hz. Partial compensation was obtained beyond these frequencies.

It is not surprising that

compensation occurred in this low to high frequency pattern, since tracking in general becomes increasingly difficult with increasing frequency. Furthermore, the more complete amplitude (gain) compared to timing (phase) compensation is consistent with other studies of inter-limb coordination which show that it is easier to vary the amplitude of movement in two limbs than their timing (eg., Kelso et al., 1979; Schmidt et al., 1979; Swinnen et al., 1991). Indeed, in the present study, considerable amplitude differentiation (and thus, filter gain compensation) was evident even on the first day, whereas the liming differentiation (and thus, filter phase compensation) was small. It is possible that more complete compensation for the falter, and thus closer approximation to the expected inter-limb synergy, might be achieved with more extended practice, especially under less artificial conditions than those which necessarily obtained in the present laboratory study.

Coordinated movements may require many thousands or even

millions of repetitions in order to be perfected (Kottke, Halpem, Easton, Ozel and BurriU, 1978) and this level of repetition is difficult to accomplish in a laboratory. Thus, in subjects who have experienced extensive practice at a task, such as highly trained musicians and percussionists, it appears that a degree of temporal differentiation between limbs can be achieved (Shaffer, 1981). It is important to point out, however, that in the present study the amplitude and timing of the two hands were not required to be statistically independent, as is the case in producing different rhythms with each hand; rather, the hands were required to be statistically dependent, but with their amplitude and timing dynamically related. (The inter-limb coherence of 87% showed that the requirement of statistical dependence was largely achieved). This distinction between statistical independence between signals and a dynamic relation between them is an important one that may not be generally appreciated. In both cases the signal waveforms

313

Learning a Dynamic Limb Synergy

appear different on visual inspection, but in the former they are uncorrelated whereas in the latter they are correlated. An alternative view of the incomplete filter compensation is that it is due to an adaptive optimal control strategy that incorporates a compromise between tracking accuracy and the demand for muscular energy. A similar compromise has been incorporated into other optimal control models of movement (e.g., Agarwal, Logsdon, Corcos & Gottlieb, 1993; Hasan, 1986; Hogan, 1984; Meyer, Abrams, Komblum, Wright & Smith, 1988). In other words, the subject sacrifices filter compensation and thus, tracking accuracy, in order to reduce the muscular energy that would otherwise be necessary (the extent of this requirement can be appreciated from the illustration in Figure 7 of the magnitude and velocity of hand movements necessary for full filter compensation). We have elaborated this hypothesis in some detail and argued that the accuracy-energy compromise is equivalent to the well-known speed-accuracy tradeoff underlying Fitts' law (Neilson, Neilson & O'Dwyer, this volume). In support of this view, in other experiments with various filters we have observed incomplete filter compensation even with single-handed tracking (Sriharan, Neilson & O'Dwyer, 1995). It should be noted also that this alternative view of the incomplete filter compensation is not incompatible with the earlier explanation in terms of insufficient practice. The optimal control strategy would be adapted for the existing level of skill in a task, so as to limit the expenditure of energy. However, as skill increases during the course of practice at a new task, the expenditure of energy would be expected to decrease (Sparrow, 1983). Therefore, the energy-accuracy trade-off could be adapted in line with this hypothesised reduced energy demand to enable greater accuracy at the task.

5. CONCLUSION

In both experiments, tracking performance improved for all conditions following practice, despite the fact that only one tracking condition was practiced.

This improvement can

presumably be attributed to a general increase in skills that contribute to tracking performance, such as more proficient control of the joysticks and more accurate statistical prediction of the target signals (see Neilson et al., 1993). Both experiments demonstrated small but significant differences in performance between single-handed and two-handed tracking. In Experiment 1 the difference was a small increase in tracking time delay in two-handed tracking (L+R) compared with one-handed tracking (L,

314 R).

N. O'Dwyer & P. Neilson

Interestingly, this difference was not reproduced in the equivalent conditions in

Experiment 2, perhaps due to confounding effects of the filter on the subjects' tracking phase lag. However, a difference was found in the extent of compensation for the filter in twohanded (L+RF) compared with single-handed (RF) tracking, the gain and phase functions (Figure 16) showing less high frequency filter compensation in the two-handed condition. As noted earlier, these differences likely reflect the cost in extra processing for a two-handed compared with a single-handed motor task.

However, it must be emphasised that the

differences observed were minor, such that they were not reflected in the tracking error scores and actually, the performance of each hand was surprisingly insensitive to activity in the other hand. Consequently, it would appear that the information processing demands of forming the inter-limb synergies, whether non-dynamic or dynamic, interfered only minimally with ongoing tracking performance. The degree of coupling between the hands in two-handed tracking was very high, even before practice. In Experiment 1, the average overall coherence between the hands was 88% before practice, rising to 91% after practice. In Experiment 2, the average coherences were 80% (L+R) and 76% (L+RF) before practice, both rising to 87% after practice. Nevertheless, since the coupling was not perfect, this meant that there was still some independent activity in each hand. Conceivably, this lack of perfect coupling was due simply to 'noise' in the motor output that was independent in each hand. Schmidt et al. (1979), for example, reported that spatial (though not timing) errors in a two-handed aiming task were largely independent. Alternatively, however, it is possible that the independence between the hands was real. In the tracking situation each hand-joystick system comprised one degree of freedom and the task required the subjects to reduce these two degrees of freedom to a single virtual degree of freedom system. It is not unlikely that in the course of the one-minute tracking tests, the hands may have intermittently reverted to their independent 'ground' state, briefly moving out of synergy; or alternatively, they may have moved briefly between the dynamic and the nondynamic synergy. With improved skill at the task, however, such time-varying behaviour would be expected to diminish, consistent with the observed increase in coherence between the hands after practice. This suggestion of time-varying behaviour has an important bearing on the techniques employed to analyse the tracking performance. The cross-correlational and spectral analysis employed is often described as the 'quasi-linear approach'. This is because it involves the application of highly developed linear theory to study behaviour that is not strictly linear. To

315

Learning a Dynamic Limb Synergy

use this approach is not to deny nonlinear behaviour (such as time variation) but to characterise the subject's linear behaviour and thereby separate it from the remainder of the subject's output. This remainder that is not accountable by the linear analysis is often known as the 'remnant'. Since it is well known that there is 'noise' in human motor output (e.g., Hatze, 1979; Kim, Carlton & Newell, 1990; Meyer, Smith & Wright, 1982; Schmidt et al., 1979), the remnant may consist entirely of noise that is unrelated (either linearly or nonlinearly) to the (target) input.

However, it may also contain a component that has a

nonlinear relation with the input. In the present studies, the subjects' response had a high average coherence with the target (about 80% after practice in Experiment 1 and about 75% in Experiment 2), so that a linear analysis seems entirely justified and any nonlinear component in the subjects' response was necessarily minor (it will be recalled that coherence measures the proportion of variance accounted for by the linear relation).

In the case of the relation

between the hands, of course, the coherences were even higher and the remnant component was almost negligible. Finally, it may be noted that the requirement of the task in these studies was for a strictly linear response - the two hands were required to be linearly coupled and each hand was required to linearly follow the target.

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Optimized movement trajectories and joint stiffness in unperturbed,

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