Pflfigers Archiv

Pfl/igers Arch. 377, 15-23 (1978)

EuropeanJournal of Physiology 9 by Springer-Verlag 1978

Pursuit Eye Movements and their Neural Control in the Monkey Rolf Eckmiller* and Manfred Mackeben Institut fiir Physiologicder Freien UniversiffttBerlin, Fachbereich I, Arnimallee22, D-1000 Berlin 33, and Smith-Kettlewell Institute of Visual Sciences, 2232 Webster Street, San Francisco, California 94115, U.S.A.

Abstract. 1. Single units in the 3. and 6. nerve nuclei were recorded, together with the stimulus and eye movements in trained macaques during pursuit eye movements. 2. The relationship between the impulse rate of an oculomotor motoneuron and the corresponding eye movements can be described by a first order differential equation only, if distinctions are made between the modes of the oculomotor system (e.g., fixation or pursuit) and between the agonist phase and the antagonist phase of the corresponding eye muscle. 3. The trained monkeys showed a frequency response during pursuit eye movements, which was comparable to that of humans and which clearly indicates the existence of a predictor mechanism. 4. After sudden stimulus disappearance in the pursuit anode, both the neural impulse rate and the eye movement performed smooth changes for more than ls. These slow post-pursuit eye movements were related to the time course before stimulus disappearance. 5. Our findings lead to the hypothesis, that pursuit eye movements in primates, if elicited by small moving visual stimuli, are generated by means of a feedback system consisting of a predictor mechanism, the parameters of which are continuously corrected by an updating process in the afferent visual system. Key words: Oculomotor motoneurons - Primates Pursuit eye movements - Predictor mechanism Frequency response.

Introduction Smooth eye movements can be elicited in a large number of ways in primates, e.g. : by vestibular stimuli, 9 * New address: Institut fiJr Allgemeine Biologie, Abteilung Biokybernetik, Universit[itDiisseldorf, UniversitS.tsstrage1, D-4000 Dtisseldorf 1, Federal Republic of Germany

by visual stimulation of various foveal or extrafoveal parts of the retina, or even without such stimuli in total darkness (Cheng and Outerbridge, 1975; Gauthier and Hofferer, 1976; Grfisser and Behrens, 1978; Morgan et al., 1976; Rashbass, 1961; Robinson, 1965; Skavenski and Robinson, 1973; Trincker et al., 1961 ; Westheimer, 1954; Yasui and Young, 1975). The performance of monkeys during visually induced pursuit eye movements (PEM) has led to some controversy in the literature. Fuchs (1967) found his trained monkeys to be unable to exhibit predictive tracking (Westheimer, 1954) comparable to humans. More recently, however, Barmack (1970) could show that monkeys in his experiments clearly were capable of predictive tracking. The recent literature gives a very incomplete picture concerning the neurophysiology of PEM in monkeys (Eckmiller, 1975, 1978; Keller, 1974; Lynch et al., 1977; Miles and Fuller, 1975; Robinson, 1970; Robinson and Keller, 1972; Sparks and Sides, 1974). In this paper, we will present data from both untrained and trained monkeys who performed PEM, which were elicited exclusively by small slowly moving visual stimuli. These data for the first time show the frequency response of single oculomotor motoneurons, together with the frequency response of the overall oculomotor system. Also, the single unit activity and the corresponding eye movements are discussed for periodic stimulus movements, non-periodic movements, and after sudden stimulus disappearance.

Methods This study incorporates data from 6 male monkeys (5 macaca fascicularis and 1 macaca arctoides) and single unit recordingswere obtained from 4 of them (2 trained and 2 untrained). Four monkeyswereinitiallytrained in their cages to press a bar, whenevera dimlylit small stationary lamp outsidethe cageincreased

0031-6768/78/0377/0015/$1.80

16 its intensity for a short time (test stimulus). For pressing the bar within a certain time after the test stimulus, the monkey was rewarded by a small quantity of water released by a magnetic valve. When this task had been learned with a very low rate of error (after about 4 weeks), the training was continued daily in the primate chair for another 2 weeks. In this situation, a small light spot (initially 24 min of arc, but later 8 or 4 min of arc) was projected onto a cylindrical screen in a distance of 1.5 m. The monkey was light adapted and learned to pursue this light spot, which was barely visible on the screen. The light spot movement in the horizontal plane was generated by means of a function generator and a mirror galvanometer close to the monkey's head. Both phases of the training procedure were controlled by an automatic trainer in microprocessor technology designed by the authors and built in the electronics workshop of the Institute of Physiology in Berlin. This automatic trainer not only determines the periodic or non-periodic occurrence of test stimuli, but also counts two types of errors and two reward parameters which allow a good evaluation of the monkey's performance. Following this training period, a headgear for the attachment of the head to the upper portion of the primate chair and a lucite chamber (2 cm in diameter) were implanted over a trephine hole in the vertex of the skull. Horizontal eye movements were measured in 4 of the monkeys as DC electro-oculograms (N-temporally) with skin electrodes (Beckman or Hellige). In the other 2 monkeys, small Ag/AgC1 electrodes (In Vivo Metrics Systems, Healdsburg, California) were implanted into the bone of the outer canti of the orbits and between both eyes. With these implanted EOG-electrodes, the horizontal eye movements of both eyes could be recorded independently with very small drift (typically less than 1 degree per min). The eye movements were calibrated by means of the small light spot which the monkey was trained to fixate or to pursue. This calibration was based on the assumption that the monkey pursued the light spot in the low frequency range (0.1-0.4 Hz) with good accuracy (position errors between stimulus and eye position less than 1 degree), if the pursuit eye movements were not interrupted by correctional saccades over several cycles. Microelectrodes (tungsten coated with Isonel 31 varnish) were placed in the nuclei of the 3. and 6. nerves by means of a 3-coordinate stereotaxic manipulator. The time functions of single unit activity, stimulus movement, as well as a superimposed signal for the trainer status were recorded on instrumentation tape (Bell and Howell : VR 3200 or Ampex: SP 300) and in parallel on a jet ink writer (Siemens: Mingograf 800). Both recording systems had a cut-off frequency above 1 kHz. Although the neurons, which are considered here, were not identified by antidromic stimulation, they are assumed to represent oculomotor motoneurons and will be referred to as such on the basis of the following criteria: the background activity at the recording site and the fact that the recorded neurons or neighboring neurons with similar features could occasionally be identified as cells, when they produced injury discharges due to cell damage by the electrode tip. The steady state impulse rate during fixation was tightly correlated with eye position in the direction of action of the corresponding extraocular muscle. During saccades the impulse rate showed the typical dynamic increases in the on-direction and decreases in the off-direction (Robinson, 1970). It can, however, not be ruled out that some of these neurons were in fact intranuclear interneurons with activity patterns similar to those of motoneurons. For further analysis, the impulse trains of single neurons were converted in real time into time functions of the instantaneous impulse rate IR(t) by means of a digitally operating device (MOMIRA-meter) which provides a signal for each impulse interval with an amplitude proportional to 1/interval (Eckmiller and Petsch, 1975). The error is 1 imp./s over the whole range of 0-1000 imp./s. The data analysis was performed by graphical means on the Mingograf read-outs.

Pfltigers Arch. 377 (1978)

Results

A. Fixation Versus Pursuit Eye Movements T h e g e n e r a l l y a c c e p t e d f i n d i n g t h a t in the alert m o n k e y all o c u l o m o t o r m o t o n e u r o n s are to s o m e e x t e n t c o r r e l a t e d w i t h d i f f e r e n t m o d e s o f the o c u l o m o t o r c o n t r o l s y s t e m (e.g. ; s a c c a d e s p l u s f i x a t i o n o r p u r s u i t eye m o v e m e n t s ) led to t h e h y p o t h e s i s t h a t t h e r e l a t i o n s h i p b e t w e e n the n e u r a l i m p u l s e r a t e I R , eye p o s i t i o n O , a n d eye v e l o c i t y ~) c a n a l w a y s be d e s c r i b e d b y o n e d i f f e r e n tial e q u a t i o n ( R o b i n s o n , 1970; R o b i n s o n a n d K e l l e r , 1972): IR = K(O-O0)

+ RO

w i t h : K, R, O o as c o n s t a n t s . M o r e r e c e n t l y , h o w e v e r , it c o u l d be s h o w n t h a t this hypothesis does not account for the following new findings: 1. D u r i n g f i x a t i o n , t h e r e exist t w o l i n e a r c h a r a c t e r istics f o r I R v e r s u s O b e c a u s e o f the static hysteresis ( E c k m i l l e r , 1974), w h i c h was c o n f i r m e d l a t e r to h o l d also f o r t h e h u m a n o c u l o m o t o r s y s t e m ( C o l l i n s et al., 1975). 2. C h a n g e s f r o m f i x a t i o n to v i s u a l t r a c k i n g m o v e m e n t s l e a d t o c h a n g e s in t h e I R - l e v e l at a g i v e n v a l u e f o r O ( E c k m i l l e r , 1975). I n this s t u d y t h o s e f i n d i n g s w e r e c o n f i r m e d in 17 motoneurons of 2 untrained monkeys who performed s p o n t a n e o u s eye m o v e m e n t s a n d o c c a s i o n a l l y p u r s u e d s m a l l o b j e c t s o f i n t e r e s t in the h o r i z o n t a l p l a n e at a d i s t a n c e o f I m. A t y p i c a l e x a m p l e is s h o w n in Fig. 1 f o r a m o t o n e u r o n in t h e 3. n e r v e n u c l e u s . T h e t w o d o t t e d lines d e m o n s t r a t e the static hysteresis d u r i n g f i x a t i o n w i t h ( § v a l u e s c o r r e s p o n d i n g to p o s i t i o n s r e a c h e d a f t e r an I R - i n c r e a s e a n d ( - ) v a l u e s to p o s i t i o n s r e a c h e d after an IR-decrease. These fixation data were recorded i m m e d i a t e l y b e f o r e a n d a f t e r a p e r i o d o f a b o u t 10 s, d u r i n g w h i c h the m o n k e y p u r s u e d a s l o w l y m o v i n g s m a l l object. T h e filled s q u a r e s w h i c h a r e c o n n e c t e d w i t h e a c h o t h e r to f o r m a " d y n a m i c c h a r a c t e r i s t i c " , are v a l u e s t h a t w e r e m e a s u r e d e v e r y 100 m s d u r i n g a p a r t o f this t r a c k i n g e p i s o d e f r o m a b o u t 20 d e g r e e s left to a b o u t 20 d e g r e e s r i g h t a n d b a c k . T h i s d y n a m i c c h a r a c teristic is s i g n i f i c a n t l y shifted t o w a r d s a h i g h e r I R - l e v e l r e l a t i v e to the p a i r o f static c h a r a c t e r i s t i c s d u r i n g f i x a t i o n . F o r m o s t m o t o n e u r o n s , s u c h a c h a n g e in t h e m o d e o f the o c u l o m o t o r s y s t e m f r o m s a c c a d e s p l u s f i x a t i o n to p u r s u i t led to a shift t o w a r d s h i g h e r I R values, w h e r e a s f o r a f e w m o t o n e u r o n s t h e o p p o s i t e was f o u n d . I n o r d e r to u n d e r l i n e this I R - s h i f t d u r i n g p u r s u i t eye m o v e m e n t s , we m e a s u r e d all v a l u e s w i t h ~) = 0 f o r the t r a c k i n g e p i s o d e u s e d f o r Fig. 1. T h e v a l u e s c o r r e s p o n d i n g to ~) -- 0, w h i c h are the m a x i m a a n d m i n i m a o f the eye m o v e m e n t t i m e course, are p l o t t e d as o p e n t r i a n g l e s a n d c o n n e c t e d b y the c o r r e s p o n d i n g

R. Eckmiller and M. Mackeben: Pursuit Eye Movements and their Neural Control FA6"~- O24-224

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Fig. 1. Shift of the characteristic between eye position O and impulse rate IR of an oculomotor neuron from the fixation mode to the pursuit mode. The two static characteristics for fixation values reached by an IR-increase(+) or IR-decrease(--) showthe finding of static hysteresis. These values were all taken at least 200 ms after the end of the preceding saccade. The filled squares and interconnecting lines show one episode of a horizontal pursuit eye movement with consecutive values taken every 100ms. The arrows on this dynamic characteristic indicate, that the eyeswerefirst movingto the right and then back to the left. The open triangles are values for the eye position maxima and minima (~) = 0) during the whole pursuit phase. Note the shift of their regression line (dot-slashed) relative to the pair of static characteristics. Eye position values OR(increasingto the right) are given in relative units (E); they cover a range of about _+ 20 degrees around the primary position. Instantaneous impulse rate IR is givenin impulsesper s. The neuron was recordedin the oculomotor nuclear complex (N.n. III.) on the left side. Eye movements were measured with two bitemporallyplaced surfaceelectrodes as electrooculograms

regression line. This line (which one could call the static characteristic for the pursuit mode) is clearly shifted towards higher impulse rates in parallel to the pair of static characteristics for the fixation mode.

B. Agonist - Versus Antagonist Phase of Oculomotor Unit Activity Our findings show that it is necessary to distinguish between an agonist phase (IR-increase) and an antagonist phase 0R-decrease) of oculomotor unit activity according to the momentary function of the corresponding eye muscle. This distinction was already indicated by the finding of static hysteresis in the fixation mode (Fig. I). During pursuit eye movements, however, this distinction becomes imperative, if one wants to unravel the different position (O) and velocity (6)) components of the neural command signals available at the motoneuron level. Seven motoneurons of the 2 untrained monkeys were arbitrarily chosen for a quantitative analysis of this question during pursuit. Figure2 shows diagrams for I R versus 0 taken from pursuit movement records of two representative oculomotor motoneurons. As described elsewhere

17

(Robinson, 1970), we measured the O-values and the corresponding IR-values at those times when the eye movement time course passed a given constant eye position O = C. In case of the left diagram, values were plotted for comparison for two different values O = C~ and C2. The values on the ordinate for 0 = 0 (open triangles) are particularly exact because they were taken from the corresponding regression lines for 6) = 0 for each motoneuron as described in Fig. 1. The (+) and (-) values on the ordinate (at O = C in the right diagram and O = C2 in the left diagram) were taken from the static characteristics for these neurons as a reminder of the shift in the IR-level between the fixation and pursuit mode. The regression lines for the agonist- and antagonist phase are plotted as dashed lines. Two main findings are shown in these diagrams: 1. The slopes of the characteristics are different for positive velocities 6) (i. e. : agonist phase) in comparison to negative velocities. 2. There are motoneurons with a steeper slope in the agonist phase and others with a steeper slope in the antagonist phase. U p o n evaluation of single unit recordings from 2 trained monkeys, it became evident that there often was an asymmetry between the slopes of the IR-increase during one half of the sinusoid and the IR-decrease during the other half of the sinusoid (Eckmiller,/978). In different motoneurons the steeper slope occurred on either half of the sinusoid. This asymmetry, which remained constant for any given motoneuron, probably reflects the findings shown in Fig. 2.

C. Dependence of Oculomotor Function on Movement Frequency The data in this section refer exclusively to the 4 monkeys that were trained to pursue a sinusoidally moving light spot (see methods). Figure 3 shows simultaneous recordings of the stimulus movement, the instantaneous impulse rate IR(t) of a motoneuron and the horizontal electro-oculogram of the right eye. Parts (a) and (b) show recordings for two different movement frequencies. The record in part (c), however, demonstrates, that the monkey can pursue the stimulus, even if it moves with a non-periodic time function consisting of continuous, but unpredictable changes of the stimulus velocity. The monkeys used in these experiments showed this ability without previous experience with non-periodic stimulus movements. This figure, which represents similar recordings from more than 30 motoneurons in the 3. and 6. nerve nuclei of 2 monkeys, shall demonstrate the following findings: 1. For periodic and non-periodic stimulus movements the phase difference between stimulus and eye movement is very small.

18

Pfliigers Arch. 377 (1978)

024-224

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Fig.3. Correlation o f stimulus-, impulse rate-, and eye movement time functions during periodic and non-periodic pursuit eye movements. The stimulus was a light spot with a diameter o f 4 min o f arc. Recording site: right abducens nucleus. Eye movements o f this trained monkey were recorded with implanted EOG-electrodes on both sides of the right eye. Responses to sinusoidal stimulus movements in sections a and b. Responses to continuous non-periodic velocity changes of the stimulus in section c

R. Eckmiller and M. Mackeben: Pursuit Eye Movements and their Neural Control Gain (d B)

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Fig.4. Frequency response of the overall pursuit system [Gain 0r) in the top diagram and phase ~b(/) in the bottom diagram] and of the maximumimpulserate IRr~.x(middlediagrams). Note the monotonic increase of IRma~and its phase relation to the maximum stimulus position (second diagram from the bottom) with increasing frequency. Eye movement recordings with bitemporal surface electrodes; localization of this motoneuron with on-direction to the left was the oculomotor nuclear complex on the right side

Fig. 5. Frequency response of the overall pursuit system [Gain (/) in the top diagram and phase ~(f) in the bottom diagram] and of the maximumimpulserate IRma x (middlediagrams). Note the monotonic increase of IRm.x and its phase relation to the maximum stimulus position with increasing frequency as in Fig.4. Eye movement recordings with implanted EOG-electrodeson both sides of the right eye; localization of this motoneuron was the right abducens nucleus

2. Periodic and non-periodic velocity changes in the stimulus time course are correlated with continuous, rather than discrete velocity changes in the single unit activity IR(/) and in the eye movement. 3. The m a x i m u m of IR(t) always occurs before the m a x i m u m eye position and it increases with stimulus frequency (Fig. 3 a, b). For a quantitative analysis of the pursuit system, we plotted the frequency response as Bode plot (Milsum, 1966; Stark, 1968) for the overall system with the stimulus as input and the eye movement as output several times for each of the 4 monkeys (total number: 14 Bode plots). In a slightly different manner, one part of the pursuit system with the stimulus as input and the impulse rates of single motoneurons as output was analyzed (frequency characteristics for 7 neurons from 2 monkeys) and added to the corresponding Bode plots. Figures 4 and 5 show such diagrams as typical examples for two different monkeys (FA 8, SF 2*). Each value in these diagrams represents the mean of three measurements. The dashed lines represent non-mathematical, estimated fittings of the data. In both cases, the gain

(dB) (20 log eye movement amplitude/stimulus amplitude) and the corresponding phase relationship for the overall system were plotted as a function of movement frequency as top and b o t t o m diagram. The stimulus always moved only in the horizontal plane at a distance of 1.5 m from 10 degrees right to 10 degrees left. The two diagrams in the middle show the m a x i m u m impulse rate IRmax and the phase difference q~ between IRmax and the m a x i m u m stimulus position as a function of frequency. The main findings demonstrated in these diagrams, are listed below: 4. Although the monkeys showed inter-individual and day to day differences in their pursuit performance of the overall system, the average phase error is negligible for frequencies up to at least 0.8 (Hz) and the gain stays within + 1.0 (dB) for frequencies up to at least 1.0 (Hz). 5. With increasing frequency IRm~X shows first a monotonic increase and then a significant decrease above 1 (Hz) when the gain of the overall system drops. The slope and absolute values of this characteristic can

20

Pflfigers Arch. 377 (1978)

t

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Fig.6. The response of the impulse rate of an oculomotor motoneuron and the corresponding eye movement in the pursuit mode after sudden disappearance of the moving light spot. Disappearance time: 800 ms. Top trace: stimulus movement; second trace from the top: impulse rate IR in impulses per s of the motoneuron, located in the right abducens nucleus; third trace from the top: horizontal eye movement of the right eye measured with implanted EOG-electrodes; bottom trace: light intensity of the stimulus, with the step indicating stimulus disappearance. Sections a, b and c were recorded during sinusoidal stimulus movement at 1.0 Hz (a + b) or 0.4 Hz (c). In d, the stimulus performed non-periodic changes of velocity. Note that with higher stimulus frequencies, even reversals of the direction of stimulus movement are anticipated (a, b and d), after which the eye position slowly approaches a steady value. Also note the increasing deviation from the correct course with time in c, which is compensated for by a correctional saccade, occurring only 350 ms after stimulus reappearance. The arrows in Fig. 6 a and b indicate that during PPEM, the relation between O and IR can deviate from normal (as given by the mathematical description)

differ considerably between different motoneurons (compare Figs. 4 and 5). 6. The phase lead (b of IRmax relative to the maximum stimulus position increases monotonically with frequency. The slope and absolute values of this characteristic can differ considerably between different motoneurons (compare Figs. 4 and 5).

D. Smooth Eye Movements after Sudden Stimulus Disappearance For any hypothesis concerning a possible predictor mechanism in the pursuit system, one needs to know, how the eyes continue to move when during PEM the moving light spot suddenly disappears. In Fig. 6, four typical exampIes for such cases were assembled. They refer to two different sinusoidal movement frequencies (Fig.6a, b and c) and to one

record of unpredictable stimulus movement (Fig.6d). The main findings can be listed as follows: 1. When the moving stimulus disappears for more than 300-500ms, the eyes are unable to continue PEM after stimulus reappearance without correctional saccades. Similar responses were obtained from all 4 trained monkeys. 2. Very often, both the motoneuron activity IR(t) and the eye perform smooth changes for more than 1 s after stimulus disappearance. We call these movements: slow post-pursuit eye movements (PPEM). 3. The smooth changes oflR(t) and PPEM are very often related to the time course before stimulus disappearance in a characteristic way: (1) the error between the correct values (if the stimulus had not disappeared) and the real values gradually increases; (2) the real values gradually diminish their changes with time and approach various final positions; (3) changes in direc-

R. Eckmfllerand M. Mackeben:Pursuit Eye Movementsand their Neural Control tion of eye movement are often performed after stimulus disappearance, in an apparent attempt to simulate the previous stimulus time course; (4) in various cases, the IR time course during PPEM showed significant deviations from its normal relationship to eye position and eye velocity as marked by arrows in Fig. 6a and b.

Discussion

Our findings presented in Fig. 1 and 2 strongly suggest that the mathematical description of the relationship between the impulse rate of an oculomotor motoneuron and the corresponding eye movement by means of one first-order differential equation holds (Robinson, 1970), but only with some important restrictions. We have shown that this relationship changes for different modes of the oculomotor system (e. g. : fixation or pursuit). Even at a given mode, one has to distinguish between the agonist phase and the antagonist phase. Therefore, we propose for a more adequate mathematical description a pair of equations for each mode of the oculomotor system. For the pursuit mode (O o = a constant eye position: IR+l, = K+p (O - O0) + R+l, 0 for the agonist

21

Pola and Robinson (1978) reported that certain pause units have similar features. One possible interpretation of Keller's finding is that these pre-motor neurons receive a position signal and a velocity signal which, however, is directionally selective. The motoneurons could then superimpose the output from ipsilateral and contralateral pre-motor neurons with a signalinversion (e. g. : by an inhibitory interneuron) in one of the pathways (Eckmiller, 1978). The frequency response of the pursuit system of our trained monkeys is quite comparable with that of humans (Drischel, 1958; St. Cyr and Fender, 1969; Stinderhauf, 1960). Our monkeys could not reproduce the much weaker performance of those measured by Fuchs (1967). This is of some importance because it allows us more easily to draw comparisons between the neural control mechanisms of pursuit eye movements in experimental non-human primates and humans. The frequency characteristic of IRm~x of single motoneurons, as demonstrated in Figs.4 and 5, supports the differential equation mentioned above, which assumes the superposition of a position component and a velocity component. If we assume for the sake of simplicity that O ( t ) is identical with the sinusoidal stimulus movement and K+p = K_p = I~,, R+I, = R - i , = Ri,, it follows: IR(t) = K I, A sin 2 ~ f t - K I, 0 o + R I, A 2rcfcos 2 ~ f t

phase, and IR_l, = K-i, ( 0 - 0 o ) + R - i , 0 for the antagonist phase. It appears that eye movements in monkeys can be performed with changing IR levels (muscle tones) in different modes and even in the same mode, but different levels of alertness (Eckmiller and Mackeben, 1976; Henn and Cohen, 1973). This is not surprising in the light of the present knowledge of other striated muscles and their neural control (Granit, 1970; Matthews, 1972). The finding of different slopes (Fig. 2) in the characteristics for IR versus O for the agonist phase (R +l,) and the antagonist phase (R_l,) requires particular attention. It is possible that these slopes differ, because each single motoneuron receives its velocity component (R 0 in the equation) for movements in opposite directions from two different pre-motor sources. Such premotor neurons, which code the eye velocity, but are directionally selective, have been found recently (Eckmiller and Mackeben, 1978b) in the monkey brainstem. Keller (1974) found that some eye position coded neurons in the pontine reticular formation of alert monkeys showed an IR-increase (positive velocity component) during pursuit eye movements in the agonist phase, but no IR-change (no negative velocity component) in the antagonist phase. More recently,

with: A = movement amplitude; O ( t ) = A sin 2 ~ f t ; O ( t ) = A 2~zfcos 2 ~ z f t . The maximum of the velocity component (P~, A 2re f) increases with the frequency f. This is in agreement with our findings (Figs.4 and 5) that IRm,x increased with increasing f and that the phase lead of IRmax relative to the maximum of the stimulus movement S(t) = A sin 2re f t also increased monotonically with increasing frequency. The decrease of IRm,x at the upper end of the investigated frequency range shows that the corresponding drop in the gain of the overall system is closely correlated with the neural command signal. Therefore, this gain reduction cannot be exclusively attributed to the mechanical properties of the orbit plant (Robinson, 1965). In his classical paper concerning pursuit eye movements in humans, Westheimer (1954) coined the term prediction (or anticipation) for a mechanism, that allows the oculomotor system to keep a visual stimulus, which moved with a periodic or otherwise predictable time function, on the fovea. The need for such a postulate clearly arises from the fact that humans, as well as our trained monkeys (Figs. 3, 4 and 5), show virtually no phase difference between the stimulus and the projection of the fovea on the screen during sinusoidal movement frequencies up to at least 0.8 (Hz).

22 Various authors since then have tried to describe the basic features of such a predictor mechanism (Dallos and Jones, 1963 ; Michael and Jones, 1966; Young and Stark, 1963; see also Stark, 1968). More recently, St. Cyr and Fender (1969 b) concluded from their findings, that it would be more reasonable to replace such a rather complicated predictor by time delays. Our own findings (Figs. 3 and 6) confirm the existence of a predictor mechanism in monkeys [in agreement with Barmack (1970), but in contradiction to Fuchs (1967)], and they allow to ascribe some basic features to it. Pursuit of a sinusoidally moving stimulus requires instantaneous smooth changes in eye position and velocity. Astoundingly, our monkeys, having been trained only for sinusoidal (i.e. : periodical) movements, continued to pursue the small light spot equally precisely, when the time function was changed from a constant frequency [typically 0.5 (Hz)] to instantaneously changing frequencies without any transient deficiencies in performance (see Fig. 3). This fact led us to the following hypothesis: a) If the oculomotor system is in the pursuit mode, and b) if the movement velocities are in the range of about + 50 degrees per s and c) if the velocity changes are in the range of only _+ 250 degrees per s 2 [these figures correspond to proper pursuit of a light spot moving at frequencies up to 0.8 (Hz) with an amplitude of 10 degrees], d) then, the accuracy of PEM does not depend on the movement time function of the stimulus. Consequently, we assume that the pursuit system uses a second mechanism in addition to prediction of the future time course of the stimulus from its past time course (this would always be wrong in case of instantaneous frequency-changes; Fig. 3 c) to avoid large phase differences between eye and stimulus. Therefore, we postulate a continuous updating process utilizing a "pursuit area" around the center of the fovea (Eckmiller and Mackeben, 1978a), within which the stimulus projection moves during PEM. These relative movements of the stimulus projection during PEM may be similar to miniature eye movements during fixation (Steinman et al., 1973). However, we assume that the image of the small light spot moves into the opposite portion of the pursuit area, when the stimulus movement shifts from acceleration to deceleration or vice versa. Whenever this image crosses the border of the pursuit area towards peripheral parts of the retina, correctional saccades occur. If the stimulus reaches receptive fields in the periphery of the pursuit area, their response is transformed within the afferent visual system into a control signal for a change in eye movement velocity, in order to bring the stimulus back to the center of the fovea.

Pflfigers Arch. 377 (1978) If PEM were indeed generated by means of a feedback system consisting of a predictor mechanism, the parameters of which are continuously corrected by the updating process using the position error within the pursuit area, then it would be desirable to separate the predictor from the updating component. Such a separation occurs, if during PEM the stimulus suddenly disappears. In this situation (see Results, Section D), the slow post-pursuit eye movements (PPEM) are determined only by the predictor mechanism without additional updating. It can be seen in Fig. 6 that the oculomotor system stays in the pursuit mode for more than 1 s after stimulus disappearance. Such a behavior could be very useful in the natural environment of primates where moving objects (e. g. : a fellow monkey) are pursued, although they may sometimes be disguised by stationary objects (e.g. : trees). But during PPEM, the predictor mechanism leads to a continuous decrease in eye velocity, and thus increase in position error, which is particularly obvious in the recording in Fig. 6 c. The amplitude of the first saccade, which occurred about 350ms after stimulus reappearance, shows the difference between predicted and real stimulus position. The record in Fig. 6 d underlines the fact that the predictor mechanism also functions in case of nonperiodic instantaneous frequency changes in the stimulus movement. PPEM also occur in humans (v. Noorden and Mackensen, 1962). It remains to be shown, how the afferent visual system manages to create control signals for the PEM velocity (Eckmiller and Mackeben, 1978b) on the basis of position errors in the pursuit area. Such a neural mechanism would require that the position of the stimulus projection on the pursuit area (which is assumed to be concentric around the center of the fovea) determines the direction and size of the velocity signal by the angle and absolute value of the vector from tlle foveal center to the stimulus position.

Acknowledgements. This investigation was supported in part by Grant No. Ec 43/4 awarded by the Deutsche Forschungsgemeinschaft, by Grant Nos. 5 R01 EY01474and 5 P30 EY01186, awarded by the National Institute of Health, and by the Smith-Kettlewell Eye Research Foundation. The authors wish to thank Mr. Petsch and Mr. Nietert (Freie Universit~tBerlin)for the constructionof the automatic trainer in microprocessortechnology.

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Received May 5, 1978