Human Movement North-Holland

83

Science 11 (1992) 83-100

Timing and sequencing of human arm trajectories: Normal and abnormal motor behaviour * T. Flash a, E. Henis ‘IThe Wewmnn Institute of

a, R. Inzelberg

’ and A.D.

Korczyn

‘,’

Science, Rehooot, Israel h Tel AG Medral Center, Tel Aviv, Israel ’ Tel Aoiu Unwersrty, Ramat AVIV, Israel

Abstract

Flash. T.. E. Henis, R. Inzelberg and A.D. Korczyn, 1992. Timing and sequencing of human trajectories: Normal and abnormal motor behavior. Human Movement Science 11, 83-100.

arm

Using the dynamic optimization approach to the description of arm trajectories, the present paper examines trajectory planning principles underlying the generation of sequential arm movements in neurologically normal and Parkinsonian subjects. The paper discusses a possible scheme for sequence generation involving the superposition of temporally overlapping trajectory units. Evidence for the feasibility of this scheme is drawn from a recent study of arm tracking responses to double-step stimuli. The paper also discusses a possible criterion according to which basic strokes can be identified, and it examines to what extent the difficulties that Parkinson’s disease patients have in generating motor sequences emerge from their inability to preplan a simple stroke or movement chunk as a single unit.

Introduction

This paper is concerned with the planning and timing upper limb movements. It has often been suggested that motor tasks, such as handwriting or drawing, the motor not internally represent all possible letters or figural forms

of sequential in sequential system need but may use,

* This research was partially supported by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. T. Flash is an Incumbent of the Corinne S. Koshland Career Development Chair. Requests for reprints should be sent to T. Flash, Dept. of Applied Mathematical & Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel.

0167.9457/92/$05.00

0 1992 - Elsevier Science

Publishers

B.V. All rights reserved

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instead, a limited set of basic primitives or strokes that can then be concatenated to form more complicated movements (e.g., Morass0 and Mussa-Ivaldi 1982; Edelman and Flash 1987; Soechting and Terzuolo 1987a, 1987b; Lacquaniti 1989). This paper addresses several fundamental issues which are closely related to this view of motor sequences by drawing upon the results and conclusions of several recent studies dealing with sequential arm movement generation in both neurologitally normal subjects and Parkinson’s disease patients. Our key questions are the following: What is the nature of the underlying elemental movement segments of strokes? On the basis of what criteria can these segments be identified? How are these strokes joined together to form the entire motor sequence? A motor unit or a stroke can be viewed as a relatively simple movement, for which the whole trajectory is preplanned in advance. The timing of individual portions of such unit are expected to be dictated by the rule or principle according to which the entire unit trajectory is planned and not to be independently specified. Movement segments or strokes have often been identified by detecting abrupt changes or discontinuities in certain movement parameters, such as movement curvature and tangential velocity, in the coefficient relating these two variables to each other (as in the two-third power law, Viviani and Cenzato 1985; Soechting and Terzuolo 1987a), or in the plane of motion (Soechting and Terzuolo 1987b). In all the studies cited above, the underlying sub-units were assumed to be discrete and to follow each other in time. Consecutive strokes were then hypothesized to be smoothly joined together by satisfying certain continuity constraints on position, velocity, or higher order derivatives of position with respect to time. In this paper we summarize recent results which indicate that the basic motor units need not follow each other in time, or be directly detectable from the motor output. Rather, the segments might be planned in parallel and overlap in time. Such trajectory units might then be superimposed to generate the observed movement pattern. The idea that more complex motor behaviors are constructed from the superposition of simpler movements has been suggested in the context of speech (Saltzman and Munhall 1989) locomotion (Flashner et al. 1988) and both single-joint (Adamovitch and Feldman 1984) and complex arm trajectories (Morass0 and Mussa-Ivaldi 1982). However, the elementary building blocks cannot be easily identified in these

T. Flash et al. / Human am trajectories

85

tasks. Here, evidence for the existence and superposition of elemental units, i.e., units whose kinematic form is invariant under changes in the temporal and spatial scales of the movement, is drawn from a recent study of arm trajectory modification using the double-step target displacement paradigm (Henis and Flash 1989; Flash and Henis 1991). In that study the basic units were found to have the same kinematic form as that of simple unconstrained point-to-point movements, i.e., straight hand paths with bell-shaped velocity profiles. Clearly, not all basic motor units are that simple. How are we to define a basic stroke in handwriting or drawing movements, for example? To what extent is the ability to preplan simple strokes an emergent property of the intact central nervous system? In this paper, these issues are examined, based on the analysis of simple curved and obstacle-avoidance movements in both neurologically healthy subjects and Parkinson’s disease patients (Flash and Hogan 1985; Flash et al. 1990a). Previously, the kinematic and temporal characteristics of curved and obstacle-avoidance movements and of movements passing through spatially fixed intermediate visual targets (‘ via-points’) were accounted for by a model which suggests that hand jerk is globally minimized over the entire trajectory (Flash and Hogan 1985). Those results have therefore suggested that for such movement chunks the whole trajectory is preplanned in advance. That model was further applied to the analysis of similar movements in Parkinsonian patients (Flash et al. 1990a). The basal ganglia seem to play an important role in motor sequence generation as demonstrated by the major difficulties that Parkinson’s disease (PD) patients have in generating sequential motor tasks. Such difficulties might be attributed to the inability of PD patients both to accurately specify the trajectory plans for individual motor units and to automatically run the entire sequence, switching from one motor program to another (Marsden 1984). The deficits in automatically running a sequence were demonstrated in studies dealing either with sequences of predefined sets of independently programmed motor acts or of distinct movements as in a finger tapping task (Benecke et al. 1987; Stelmach et al. 1987). Here, therefore, we summarize the main results from a study aimed at investigating the ability of PD patients to preplan the entire trajectory for simple strokes, i.e., continuous curved movements through intermediate spatially fixed visual targets (Flash et al. 1990a). We also briefly discuss

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the possibility that deficits in motor switching abilities in PD may reflect underlying impairments in the patients’ ability to plan in parallel and/or to superimpose consecutive strokes.

The superposition of elemental trajectory plans Earlier monkey and human studies have demonstrated that aimed arm movements can be elicited in quick succession, without appreciable delays in responding to the target displacement, beyond the normal reaction time (Gottsdanker 1967; Megaw 1974; Georgopoulos et al. 1981; Soechting and Lacquaniti 1983; Gielen et al. 1984; Van Sonderen et al. 1988; Barrett and Glencross 1988). Many previous studies aimed at elucidating the mechanisms governing the switch from one arm movement to another have focused on the analysis of the observed reaction and movement times. Relatively few studies, however, have attempted to account for the kinematic details of the recorded arm trajectories. Those details are needed to evaluate the model proposed here. Obtaining the kinematic results was the objective of a recent study involving the use of the double-step target displacement paradigm (Flash and Henis 1991). The results of that study are summerized below. Human horizontal planar movements were recorded at a rate of 100 samples per second with a spatial resolution of 0.025 mm by means of a digitizing table controlled by a computer. The experiments were performed in a darkened room, eliminating any visual feedback from the moving limb. The hand was constrained to move in the horizontal plane, at the level of the subject’s shoulder. No specific instructions were given to the subject about movement speed, end-point accuracy, or the type of trajectory to be generated. Light-emitting diodes installed beneath the table served as the visual targets. In a typical trial the hand was initially at rest at a location A specified by an illuminated light emitting diode (LED). The target was then displaced once (to one of two equally probable positions B) (control condition, probability 0.4) (ISI), to or was shifted again, following an inter-stimulus-interval another one of two equally probable locations C (probability 0.3 for each). Various amplitudes and directions of target displacements were used and the two target displacement steps were either in the same or

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opposite directions, or obliquely oriented with respect to each other. The values of IS1 ranged between 50 and 700 msec. One plausible strategy for trajectory modification may involve aborting the rest of the initially planned trajectory and replacing it by a new movement, between the location of the hand at the amendment time, and the final target position. For the two movement parts to be smoothly joined together, information about the kinematic state of the hand at the amendment time must be available to the system. For ISIS shorter than the reaction time to the first target displacement step, since the planning of the amendment process must begin before movement initiation, such information cannot be derived from kinesthetic or visual feedback. Even when the target location is changed during movement time, given the delays in processing kinesthetic and visual information, the role of peripherally based information in the planning of the amendment process is questionable. The information about the kinematic state of the hand at the amendment time might be derived from efference copies of past motor commands, but as discussed by Glencross and Barrett (1989), an accurate prediction of the limb position on the basis of efference copies is unlikely. Here we summarize evidence, however, that the systme may use an alternative, simpler modification scheme, as follows. Instead of aborting the rest of the initial trajectory plan, the initial plan continues unmodified until its intended completion and is vectorially summed with a second, timeshifted point-to-point hand trajectory plan for moving between the first and second target locations. Both trajectory units start and end at rest and each trajectory is separately planned regardless of the other (Flash and Henis 1991). Because the amplitudes of the vectorially added first and second trajectory units are assumed to be equal to those of the corresponding target displacement steps, when both elemental motions are completed, the final target will always be reached, independent of the amendment time. Analysis Our kinematic analysis of the modified movements was based on the minimum-jerk model of hand trajectories which was shown to account successfully for the kinematic features of planar horizontal reaching movements (Flash and Hogan 1985). As proposed by that model, a major objective of motor coordination is to generate maximally smooth.

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T. Flash et al. / Human m-m trajectories

hand trajectories. Equating this objective with the minimization of integrated hand jerk (rate of change of acceleration), the point-to-point trajectories, predicted by that model, were described by the following fifth order polynomials: x(f)

=x, + (xr-

x,)(10r3

=_y, + (yr-y,)(10r3

y(r)

- 15r4 + 6r5), - 15r4 + 6r5)

t

where r = -. tf

(1)

In (1) (x,, v,) and (xf, yr) are, respectively, the x and y position coordinates of the initial and final target locations and t, is the movement duration. Although movement duration might be affected by different central and peripheral factors including practice (Gottlieb et al. 1989) and the mechanical state of the muscles, several previous studies (Morass0 1981; Flash and Hogan 1985) have shown that point-to-point hand trajectories are invariant under translation, rotation, amplitude and time scaling. Hence, in our work (Henis and Flash 1989; Flash and Henis 1991) no a priori assumption was made with respect to the durations of the superimposed trajectory plans. Instead, we tested whether the modified movements, whatever their durations might be, may emerge from the vectorial summation of two point-to-point trajectories, each having the same kinematic form as that of an unconstrained point-to-point movement (i.e., obeying eq. (1)). The amplitudes of the initial and added elemental trajectories were assumed to be equal to those of the corresponding target displacement steps (i.e., AB and BC). This hypothesis was tested on the basis of the following analysis of each individual measured movement:

(4 Time scaled velocity

(b)

profiles corresponding to a point-to-point minimum jerk (control) trajectory between targets A and B (i.e., eq. (1)) were superimposed on the initial part of the movement. These served as the first motion unit. Visually inspecting the velocity profiles of the modified movements, the time of the first detectable deviation of the measured speed profile from that of the first motion unit (t,) was determined. From this time on, the position components of the modified movement were assumed to be represented by the algebraic sum-

cc>

89

T. Flash et al. / Human arm trajectories

mation of the position components of the initial unmodified trajectory unit with the corresponding position components of an added trajectory unit. In view of the minimum-jerk model, the latter were described by general fifth-order polynomials. Hence, the expression used to describe the x-component of the added motion units was:

x(t) = (XC - x,)(a,T3+a,T4+a,Ts),

whereT=G.

f

s

(2)

In (2), (xc - xs) is the x component of the displacement vector

(4

between target position B and the final hand location C, and tf is the duration of the entire modified movement. Both xc and tf were derived from the data. The expression for y(t) was analogous to eq. (2). At t,, the trajectories described by eq. (2) have zero positions, velocities and accelerations. Thereafter, since a3, a4 and a5 are unspecified coefficients, these trajectories may have many possible kinematic forms. To determine which specific polynomial among this entire family, when added to the initial trajectory, can best describe the entire modified movement following t,, the values of u3, a4 and a5 for both the x and y components were determined using a least-squares best-fit method based on the position error between the simulated and measured data points.

Results For the modified motions, the analysis showed that point-to-point minimum-jerk trajectories (see eq. (1)) between the first and second targets provided the best fit for the added (second) trajectory units. This was also confirmed on the basis of statistical tests (Flash and Henis 1991). Thus, the modified movements were found to result from the vectorial summation of the initial unmodified trajectories with point-to-point trajectories between the first and second target locations that have the same kinmatic form as that of simple point-to-point movements. The recorded hand paths and velocity profiles for all target configurations and all ISI’s were successfully accounted for. Fig. 1 shows two examples of measured modified movements, the corresponding trajectories predicted by the superposition scheme, and the superimposed

--v .\ .I

02 00

-\

:1_

1

lcloms

.\,

\

\

\

“.. _.

Fig. 1. Typical examples of measured modified movements (IS1 = 50 msec) and movements resulting from the superposition scheme. The intial hand positions and the first and second target locations are marked by A, B and C, respectively. Hand paths are shown in the top panels. The x and ,r components of velocity, V, and I’,, respectively, are shown in the two bottom panels. Measured trajectories are marked by solid lines, superimposed initial and added trajectory units by alternating dots and dashes and their vectorial sums by dashed lines. The added trajectories in the top panels are shown to begin at the locations corresponding to the modification times. (Reprinted from Flash. T. and E. Henis. 1991. Arm trajectory modification during reaching towards visual targets. Journal of Cognitive Science 3, 220-230, with permission of MIT Press Journals. Article copyrights MIT.)

trajectory units. The exact kinematic details of any modified movement were found to depend on the specific durations of the superimposed trajectory units and on the time delay between their initiation. The alternative strategy for trajectory modification which involves aborting the rest of the initial response and replacing it by a new trajectory plan was also mathematically modeled (Flash and Henis 1991). However, the velocity profiles predicted by this scheme showed substantially larger deviations from the measured movements than in the case of the superpostion scheme. Statistical comparison tests were then used to evaluate the successes of the two schemes (superposition versus abort) in accounting for the observed behavior. The sum of squares of the

T. Flash et al. / Human

arm trajectories

91

differences between the measured and simulated velocity profiles, normalized by the sum of squares of the measured velocities, was used as a numerical estimate of the degree of fit of the simulated to the measured movements. Using Student’s t-test, the hypothesis that the differences between the numerical estimates obtained for the abort-replan scheme and the ones obtained for the superposition scheme are due to chance was rejected, at the 0.001 level. Thus, for the range of ISIS and target displacement amplitudes considered here, the superposition scheme was found to be significantly more successful in accounting for the measured data than the alternative abort-replan strategy.

Sequential movements jects

in neurologically normal and Parkinsonian

sub-

In a previous study dealing with the generation of simple curved and obstacle avoidance movements it has been shown that the whole trajectory of such movements is preplanned, i.e., these movements are not composed of independently planned segments. Moreover, the durations of consecutive portions of these trajectories were found to obey the isochrony principle (see below) and not to be independently specified (Flash and Hogan 1985). Based on these results it was concluded that not every detectable inflection point in the hand path or valley in the tangential velocity profile should be regarded as an indication of a new segment (Flash and Hogan 1985). Hence, our primary interest in the study summarized below was to determine whether Parkinsonians programmed such simple curved movements in a similar way to control subjects. Six PD patients at stages II or III on the Hoehn and Yahr scale (Hoehn and Yahr 1967) and six age-matched control subjects were studied. Subject movements were recorded using a digitizing table. The patients were 24 hours off drugs. The experiment was performed in darkness, i.e. when the subject was unable to see the moving limb but could see the targets. Two different paradigms were used in that study. In the first paradigm, planar horizontal point-to-point movements were recorded. In the second paradigm, the subject was instructed to generate a smooth continuous movement from one target to another through an intermediate target. The intermediate target was lit throughout the movement and was located either closer to the initial or final positions,

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T. Flash et al. / Human mm trajectories

or midway between them. No instructions were given to the subject about movement speed or end-point accuracy. The experimental paradigms used are similar to the ones used in Flash and Hogan (1985). Further experimental details can be found in that paper and in Flash et al. (1990a). Analysis Previously, in applying the minimum-jerk model to the description of curved movements, the minimum-jerk cost function was augmented by the via-point constraints which force the trajectory to pass through some specified intermediate location (Flash and Hogan 1985). The resulting hand movement turned out to be of the form:

x(t) =

c

ant"

+p,(t -

tl):_

(3)

n=O

The expression for y(t) is analogous to the expression for x(t). The coefficients p, and a, (n = 0, 1,. . . ,5) in (3) are chosen to satisfy the boundary conditions on hand position, velocity and acceleration at the onset and termination of the movement, the via-point position constraint and additional requirements resulting from the wish to globally minimize the hand jerk, integrated over the entire movement duration (see in Flash and Hogan 1985). In expression (3), tf is the total movement duration and (t - ti) + is defined as follows:

(4 Here t, is the time of passage through the via-point, obtained together with the coefficients a, (n = 0, 1,. . . ,5), and p, by solving the minimization problem. In predicting the minimum-jerk trajectories for a prescribed set of initial, intermediate and final targets, the kinematic form of the entire curved trajectory is dictated by all three target locations. Thus, the velocity of the first movement portion, for example, depends also on the final target position and not only on the initial and via-point locations. The trajectories, predicted by the model, usually consisted of

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93

two low-curvature segments connected by a high curvature one. At points of high curvature the tangential velocity was reduced. Deriving the minimum-jerk trajectories for different sets of initial, intermediate and final targets, it was found that for the optimal trajectories the durations of the movement portions before and after the via-point are roughly equal, except for cases that the via-point is very close to either one of the two end-points. This phenomenon, i.e., the finding that different movement portions have nearly the same duration independently of their extent, will be referred to as the isochrony principle (Viviani and Terzuolo 1982). All the above predictions of the minimum-jerk model were corroborated by the movements recorded from control subjects. The success of the model in accounting for the kinematic features of these movements may therefore suggest that in neurologically healthy subjects the movement trajectory for such simple strokes is globally preplanned. Consequently, the model-predicted trajectories were used in developing a measure for the assessment of the patients’ performance (Flash et al. 1990a). Deriving movement duration and the location of the via-point, as the point of maximum curvature, from each individual measured movement, the corresponding minimum-jerk trajectories were simulated. For both control subjects and patients, a numerical estimate of the degree of fit between the measured and simulated movements was then obtained by calculating the normalized correlation indices for several measured data time sequences (see Edelman and Flash 1987) with their simulated counterparts. These time sequences included the x and y components of the position and velocity profiles. For each subject, each of the four correlation indices (two for the x and y position components and two for the corresponding velocity components) were then averaged over all curved movements generated by that subject. Then, for each subject group (controls and Parkinsonians), mean correlation indices and standard deviations were calculated over the individual means of all the subjects belonging to that group and statistical analysis, using the Student’s t-test, was then performed. Results Typical measured hand paths and velocity profiles for curved movements generated by control subjects and Parkinsonian patients are displayed in fig. 2 and compared with the corresponding simulated

94

T. Flash et al. / Human arm trajectortes

mxsec

IOGW Fig. 2. Typical examples of measured (solid lines) curved hand paths (P), tangential velocity profiles (V,) and the x-components of velocity (V,) and the corresponding model-predicted trajectories (dashed lines) for (a) control subjects, (b) Parkinsonian patients. The movements displayed in the upper and lower parts of both (a) and (b) were recorded in trials in which the intermediate target was located either closer to the initial target or closer to the final target, respectively.

movements. Notice, that the while the patients’ velocity These abnormalities include multiple small velocity peaks

patients’ hand paths appear rather normal profiles show substantial abnormalities. the lack of smoothness and the presence of or occasionally a velocity plateau indicat-

95

T. Flash et al. / Human arm trajectories

0.6

;/;”

/-I

r

0.5 .= 0.4

++

_---p-

P

0.3

I

I

I

0.2

I

I

I

0.6

0.4

I

I

0.8

dl dl +dz

Fig. 3. Measured

t,/(t, + t2) values versus d,/(d, nian patients.

+ d,) values for control subjects See text for the definition of t,, t2, d, and d,

and Parkinso-

ing an almost constant movement speed. Moreover, the patients tended to pause at the points of maximum curvature. Such pauses were not present in the movements of control subjects. Regarding the correlation indices, the mean value of the correlation index for the x component of position was as high for Parkinsonians as for controls (0.961 5 0.021 versus 0.947 f 0.024). The mean correlation index for the y component of position was lower in Parkinsonians than in controls (0.824 + 0.115 versus 0.945 f 0.017, p < 0.05). For the x component of velocity the correlation indices for patients and controls were quite low with no significant difference (0.535 * 0.191 versus 0.519 + 0.209) but for the y component of velocity the mean correlation index was significantly lower: 0.685 f 0.128 for Parkinsonians versus 0.867 f 0.032 for control subjects ( p < 0.05). Another prominent characteristic of the patient’s behavior was the deviation from the isochrony principle. This is illustrated in fig. 3 where we have plotted the values of t,/( t, + t2) derived from control and Parkinsonian movements against the values of d,/(d, + d2). The durations t, and t, relate to the movement durations of the two trajectory portions between the initial hand position and the via-point and between the via-point and the final target, respectively. The distances d, and d, relate to the distances between the same two pairs of targets along the straight line connecting the initial and final targets. Thus, while in control subjects t,/(t, + t2) was roughly constant and equal to 0.5, for the patients’ data the values of tl/( t, + t2) covaried with the values of d,/(d, + d2).

96

T. Flash et al. / Human orin trqectories

Discussion Here we have presented evidence in support of the notion that the observed motor output emerges from the superposition of temporally overlapping elementary trajectory plans. Since the initial response is programmed to have the amplitude of the first target displacement step, the system need not rely on efference copies in amending ongoing movements. Barrett and Glencross (1988) reached a similar conclusion. However, they suggested that location programming, as offered by the spring-mass model, is relied upon to bring the hand to the final target without recourse to knowledge about starting position. Bizzi et al. (1984) have shown, however, that the system programs the entire time-course of the equilibrium point and not merely the final position. Hence, as discussed in Flash and Henis (1991), we have suggested that the system vectorially sums two temporally overlapping trajectory plans and that the combined trajectory is executed on the basis of the principles of the equilibrium trajectory control scheme (Hogan 1985; Flash 1987). The validity of a somewhat different superposition hypothesis has already been tested by Massey et al. (1986) in the context of the double-target displacement paradigm. These authors assumed that the superimposed trajectories have the same durations as the control pointto-point movements separately performed by the same subject in response to the two separate target displacement steps (i.e., AB and BC). Since these authors found that the peak velocity attained on the way to the second target was generally much higher (up to threefold) than during the corresponding control movement (see also in Georgopoulos et al. 1981), the simulated motions obtained by superimposing average, measured control movements did not reproduce the observed modified movements. Hence, these authors concluded that trajectory modification does not involve the superposition of temporally overlapping point-to-point movements. Instead, they suggested a different trajectory modification strategy involving the application of large forces to brake the first movement, if needed, and the implementation of a new movement as fast as possible. In our study, no a priori assumption with respect to the durations of the superimposed trajectory units was made. Instead, we tested whether the underlying units may have the same kinematic form, even if not the same duration, as point-to-point control movements. The durations of

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91

the superimposed units were inferred from our kinematic analysis of the measured modified movements and were found not to be much different from those of the corresponding control movements (Flash and Henis 1991). While the reasons for the differences between the observations of Massey et al. (1986) and ours, regarding movement durations, are not clear, our findings and the lack of appreciable delays in responding to successive stimuli (e.g., Georgopoulos et al. 1981) may indicate the presence of parallel planning and superposition of consecutive movement units. In the second study considered here, we examined what trajectory planning principles underlie the generation of simple curved strokes. With respect to the trajectories of Parkinsonian patients, we found that the hand paths retained a normal morphology but the velocity profiles displayed several abnormalities. Thus, the movements were performed in the correct sequence and direction but with improper relative timing. As predicted by the minimum-jerk model, the hand should slow down but not pause at maximum curvature points. While this prediction was corroborated by the data obtained from age-matched control subjects, contrary to the model predictions, the patients tended to pause at maximum curvature points. This, thereforee, may indicate that the patients were unable to plan the entire movement as a whole, but decomposed it into its constituent parts. We found that in control subjects the durations of the motion portions (before and after the via-point) are nearly equal as predicted by the minimum-jerk model. This behaviour of the measured and predicted movements is consistent with the observed differences in the heights of the two velocity peaks on either side of the velocity valley because, if the hand travels along both movement segments in roughly the same time, then the velocity amplitude for the longer movement should be higher. By contrast, in Parkinsonian patients the movement durations of the two trajectory portions monotonically increased with their extent. This deviation of the patients’ performance from the isochrony principle merits special attention. It has been suggested that the characteristic bradykinesia seen in PD patients may reflect underlying deficits in their ability to adequately scale movement speed with movement size (DeLong et al. 1986; Berardelli et al. 1986). In previous studies, dealing with discrete movements in PD patients, it has been shown that the movement time covaried with movement amplitude

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T Flash et al. / Human arm trqectories

(e.g., Flowers 1976). Hence, the deviation from the isochrony principle, found in PD patients, might be yet another manifestation of the bradykinesia in PD. Still, if in Parkinsonian subjects the curved trajectory was to be planned as a single unit, one would have expected the velocity amplitude for the longer movement portion to be higher than for the shorter movement portion, with both being scaled down in proportion to the increase in movement duration. Thus, both the pauses at the maximum curvature points and the deviations of the movement from the isochrony principle indicate that the detailed contents of the simple movement strokes examined here are abnormally specified in PD. Finally, with respect to the mechanisms that govern the generation of general motor sequences, here we have identified motor units that were planned based on the motion end-points and in the case of curved strokes, also on the basis of some intermediate, externally or internally specified, via-point. Thus, the interanl representations of curved, handwriting, and drawing trajectories may consist of chains of such straight and curved segments. While we have discussed the superposition of temporally overlapping units in the case of the target switching task, extending this idea to the planning of predefined movement sequences, we may argue that in this case too, the observed motor output may result from the parallel planning and superposition of temporally overlapping elemental segments or strokes. In a similar vain, Morass0 and Mussa-Ivaldi (1982) have suggested that the smoothness of handwriting and drawing movements may result from the partial time overlap and superposition of consecutive hidden strokes. What are the implications of this notion for the motor impairments in sequence generation in Parkinson’s disease? Marsden (1984) has suggested that the inability of PD patients to automatically execute motor plans results from difficulties in switching from one motor program to another. The multiple inputs from all areas of the cerebral cortex into the striatum provide moment-to-moment information about the external environment and the aims of the subject (Marsden 1984). Such inputs might be processed by the basal ganglia and relayed to other cortical areas in order to adjust the form and sequence of motor programs by switching from one motor program to another. Recently, we began investigating arm trajectory modification in PD using the double step-target displacement paradigm (Flash et al. 1990b). Our preliminary results have demonstrated that in contrast to age-matched

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trajectories

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control subjects, hardly any movement was normally modified in PD patients. Instead, the hand moved all the way to the first target, occasionally pausing there, before moving to the second target. In some of the patients and for some target configurations, weird loops and return movements were observed when responding to the target switch. These preliminary observations may suggest that both the difficulties in sequence generation and in trajectory modification in PD may reflect underlying deficits in the ability of Parkinsonians to plan in parallel and/or to superimpose the elemental hidden strokes.

References Adamovitch. S.V. and A.G. Feldman, 1984. Regulation of the parameters of motor trajectories. Biofizika 29, 306-309 (English translation: 338-342). Barrett, C.N. and D.J. Glencross, 1988. The double step analysis of rapid manual aiming movements. The Quarterly Journal of Experimental Psychology 40A, 299-322. Benecke, R., J.C. Rothwell, J.P.R. Dick, B.L. Day, and C.D. Marsden, 1987. Disturbance of sequential movements in patients with Parkinson’s disease. Brain 110, 361-379. Berardelli, A., J.P.R. Dick, J.C. Rothwell, B.L. Day and C.D. Marsden, 1986. Scaling of the size of the first agonist EMG burst during rapid wrist movements in patients with Parkinson’s disease. Journal of Neurology Neurosurgery and Psychiatry 49. 127331279. Bizzi, E.. N. Accornero, W. Chapple and N. Hogan, 1984. Posture control and traJectory formation during arm movement. Journal of Neuroscience 4, 2738-2744. DeLong. M.R., G.E. Alexander, S.J. Mitchell and R.T. Richardson. 1986. The contribution of basal ganglia to limb control. Prog. in Brain Research 64, 161-174. Edelman. S. and T. Flash, 1987. A model of handwriting. Biological Cybernetics 57, 25-36. Flash. T., 1987. The control of hand equilibrium trajectories in multijoint arm movements. Biological Cybernetica 57, 2577274. Flash, T. and E. Henis, 1991. Arm trajectory modification during reaching towards visual targets. Journal of Cognitive Neuroscience 3. 220-230. Flash, T. and N. Hogan, 1985. The coordination of arm movements: An experimentally confirmed mathematical model. Journal of Neuroscience 7, 1688-1703. Flash. T.. R. Inzelberg and A.D. Korczyn, 1990a. ‘Quantitative methods for the assessment of motor performance in Parkinson’s disease’. In: CF. Rose (ed.), Methodological problems of clinical trials in Parkinson’s disease. New York: Demos (in press). Flash, T., R. Inzelberg and A.D. Korczyn, 1990b. Switching abilities in Parkinson’s disease. Movement Disorders 5 (suppl. 1) 21. Flashner. H., A. Beuter and A. Arabyan. 1988. Fitting mathematical functions to joint kinematics during stepping: Implications for motor control. Biological Cybernetics 58, 91-99. Flowers K.A., 1976. Visual ‘closed-loop’ and ‘open-loop’ characteristics of voluntary movements in patients with Parkinsonism and intention tremor. Brain 99. 2699310. Georgopoulos, A.P., J.F. Kalaska and J.T. Massey, 1981. Spatial trajectories and reaction times of aimed movements: Effects of practice, uncertainty and change in target location, Journal of Neurophysiology 46. 7255743.

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