Saccadic responses evoked by presentation of visual and ... - Research

The superior colliculus (SC) is very likely involved in the central processing of sensory information for visual and auditory saccade generation (Sparks and.
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Exp Brain Res (1982) 47:417-427

9 Springer-Verlag 1982

Saccadic Responses Evoked by Presentation of Visual and Auditory Targets* D. Zambarbieri 1, R. Schmid 1, G. Magenes 1, and C. Prablanc 2 1 Istituto di Informatiea e Sistemistica, Universit& di Pavia, Strada Nuova 106 C, 1-27100 Pavia, Italy 2 Laboratoire de Neuropsychologie Exp6rimentale, Unit6 94 - INSERM, 16, Avenue du Doyen L6pine, F-69500 Bron, France

Summary. Saccadic eye movements evoked by the presentation of visual and auditory targets were examined and compared. Differences were found either in the pattern of the saccadic response and in the characteristics of single saccades of the same amplitude. The longer latency and the higher percentage of multiple saccade responses in the auditory case were attributed to a more complex central processing, whereas the longer duration and the lower peak velocity of the saccades to auditory targets were attributed to reduced performances of the execution mechanism in the absence of vision. Key words: Saccades - Audio-ocular responses Fixation - Sound localization

Introduction Saccades are fixation eye movements which need a position reference signal to be made available within the CNS. A reference signal can be reconstructed from sensory information about external targets or can be internally generated without sensory afference as for voluntary saccades in darkness. In the case of saccades evoked by target presentation three different processes should be accomplished: acquisition of sensory information, central reconstruction of target position, and execution. Central processing is strictly related to the type of sensory information provided to the subject, and therefore to the sensory system involved in the acquisition process. Spatial information reaches sensory organs with a superimposed noise. The characteristics of this noise will depend on how information * Supported by CNR (Italy) and by INSERM (France) Offprint requests to: D. Zambarbieri (address see above)

is coded with respect to the detecting mechanisms. Transduction will also contribute to noise in a specific way. The final result is that spatial information is made available within the CNS with some degree of uncertainty. The level of uncertainty is strictly related to the sensory channel through which information is received. Since spatial information can be presented in different ways, central processing will also assume different characteristics. Whatever the processing, the goal is always that of producing an appropriate oculomotor command to the execution mechanisms. To avoid errors causing the eyes to go back and forth wasting a lot of energy, an oculomotor command is likely to be generated only when a given level of reliability is reached in the central reconstruction of target position. The neural mechanisms involved in the execution process seem to be the same for all types of saccadic eye movements (Ron et al. 1972). Nevertheless, their performances can vary in relation to the state of the subject (alertness or drowsiness) and to the environmental situation (light or darkness) (Becker and Fuchs 1969; Ron et al. 1972; K6rner 1975; Jfirgens et al. 1981). How much does the morphology of the oculomotor response evoked by a target presentation and the characteristics of individual saccades depend on the type, quality, and quantity of sensory information provided to the subject? A way to investigate this point is to compare the saccadic responses evoked by the presentation of visual and auditory targets in the same experimental conditions. Such a comparison in man was first made by Zahn et al. (1978). Surprisingly, no multiple saccade responses (a primary saccade followed by corrective secondary saccades) were reported by these authors and comparison was based only on primary saccade characteristics (latency, accuracy, and peak velocity). The short duration of target presentation considered 0014-4819/82/0047/0417/$ 2.20

418

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

in t h e s t u d y b y Z a h n e t al. (1978) c o u l d h a v e b e e n one of the reasons for the absence of corrective s a c c a d e s at l e a s t in t h e a u d i t o r y case. S i n c e t h e p a t t e r n o f t h e s a c c a d i c r e s p o n s e is l i k e l y t o b e m u c h m o r e r e l a t e d to c e n t r a l p r o c e s s i n g t h a n single s a c c a d e p a r a m e t e r s , it w a s w o r t h r e p e a t i n g t h e study under experimental conditions giving second a r y s a c c a d e s t h e o p p o r t u n i t y o f o c c u r r i n g . I n this way the comparison between visually and acoustically e v o k e d s a c c a d i c r e s p o n s e s c o u l d h a v e b e e n extended by examining the frequency of single and multiple saccade responses and by considering primary a n d s e c o n d a r y s a c c a d e s s e p a r a t e l y .

Material and Methods Six subjects with normal auditory, visual, and ocular motor functions were examined. Tests were performed in a quasianechoic room obtained by covering the walls by glass wool panels. Subjects were seated in total darkness at the center of a circular frame 1.2 m in diameter. Their head was restrained by both a chin rest and a bite board. Visual and auditory targets were placed on the frame at 0, 5, 10, 15, 20, and 30 deg right and left of the subject's sagittal plane. The central visual target was a green light emitting diode (LED) with an intensity of 64 cd/m2, whereas the peripheral visual targets were red LEDs with an intensity of 148 cd/m2. The auditory targets were 5 cm diameter loudspeakers fed with a square wave signal at 7 Hz which produced pulses interspaeed by about 66 ms. Sound pressure at the subject's ear level was of 60 dB. The parameters of the auditory stimulus were chosen after a previous study in which different auditory stimuli (pure tones, noise, pulses, and bursts) were compared (Zambarbieri 1978). Comparison was based on the accuracy of the saccadic responses following the presentation of the different types of auditory targets. By using pulses at 15 Hz a fixation error of less than 3 deg for target eccentricity between 0 and 30 deg was observed. Intersubject variability was also found to be smaller with pulses at 15 Hz than with other types of auditory stimuli. Three experimental conditions were considered in the present study.

Condition A (Visually Evoked Responses) After calibration of eye movement, the central light was first presented to give the subject a reference point for keeping his eyes in the central position. After a short period of time varying randomly between 3 and 5 s, the central light was switched off and a new light was presented for 2 s in a lateral position. In each session this procedure was repeated in such a way that each lateral light appeared three times within a random sequence. Each subject participated in two sessions separated by at least 1 day

localized and fixed after 1 s from its presentation. As for condition A, each subject participated in two sessions. In each session auditory targets were presented in a random sequence, and each lateral position was considered three times. Subject's task in both conditions A and B was to move his eyes from the position of the central light to the position of the lateral target (visual or auditory) and to fixate the target as accurately as possible.

Condition C (Simple Reaction Times) The simple reaction time (RT) to the presentation of eccentric visual and auditory targets was measured using a key-pressing device opening an electric circuit at the release of subject's pressure on a small sprung lever. Subjects were asked to release the key-pressing device as quickly as possible after stimulus presentation. The modality of target presentation was the same as in conditions A and B, with the only difference that the central light was not switched off at the presentation of a lateral visual or auditory target. The preliminary fixation of the central light was still necessary in order to guarantee that visual targets appeared with the desired eccentricities. On the other hand, care had to be taken to avoid that measured reaction times were those following the disappearance of the central light and not those related to the appearance of the lateral targets. The same use of the central light was made also in the experiments with auditory targets to obtain comparable experimental conditions. All the experiments were carried on under the control of a PDP 8 computer (Echallier et al. 1978). Eye movements were recorded by means of an optoelectronic device. The left eye was illuminated by infra-red sources on both nasal and temporal sides. The image of the eye was projected through a lens on two phototransistors arrays mounted in a differential mode. This set-up allowed the measurement of the border position between iris and sclera without drift (Mass6 1971). Accuracy in the measurement of eye position was of +20' over the full range. Eye movements were analyzed by means of an interactive program implemented on a Laben 70 minicomputer (Cabiati and Pastormerlo 1979). Latency, amplitude, duration, and peak velocity were computed for primary and secondary saceades as shown schematically in Fig. 1. Owing to their high predictability, recentering saccades were not considered in this analysis. In responses evoked by auditory targets, only saccades executed within the period of sound presentation (1 s) were considered. Response accuracy was appreciated by computing the difference between eye position at the end of sound presentation and eye position during the later fixation of the light presented at the same place as the previous sound source. For the sake of brevity, we shall refer to the patterns of eye movement following the presentation of visual and auditory targets as "visual" or "auditory responses", respectively. In what follows, we shall also use the subscripts "V" and "A" to distinguish whether the parameters defined in Fig. 1 refer to a visual or to an auditory response.

Results Condition B (Auditory Evoked Responses) As in condition A, after calibration of eye movement, the central light was first presented. When this light was turned off, a loudspeaker was switched on in a lateral position. After 1 s of sound presentation, the light placed in the same lateral position as the active loudspeaker was also presented for an additional second. This procedure aimed at provoking a visually elicited corrective saccade whenever the source of sound was not correctly

Statistical analysis w a s first m a d e s e p a r a t e l y f o r e a c h s u b j e c t . S i n c e t h e t r e n d s o f d a t a w e r e f o u n d to b e s i m i l a r f o r all s u b j e c t s w i t h t h e s a m e statistical differences between visual and auditory responses, subjects were then considered altogether. When u s e f u l to a p p r e c i a t e i n t r a s u b j e c t a n d i n t e r s u b j e c t variations, results referring to both one subject (the

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

419

secondary saccade

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9 Auditory responses o Visual responses

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primary or main saecade

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Fig. 1. Definition of saccade parameters. Upper trace: eye position; middle trace: eye velocity; lower trace: stimulus onset. A: amplitude; D: duration; Vp: peak velocity; T: latency. Subscripts 1 and 2 indicate whether these parameters refer to a primary or a secondary saccade. Saccade duration is computed as the time during which eye velocity stays greater than a given threshold value

POSITION

(deg)

Fig. 2. Simple reaction time of key releasing responses to visual and auditory stimuli versus target position. Vertical bars indicate 1 SD. Dashed lines represent the average values of visual and auditory RT (262 and 221 ms, respectively)

lOO

0., "0

same throughout the paper) and to the population of subjects will be reported.

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For each subject and for each target position simple RT to the visual stimulus was greater than that to the auditory stimulus. Both RTs did not vary significantly in relation to target eccentricity. The average difference between RTs of visual and auditory key realising responses was of about 40 ms. The same average difference was reported by Woodworth and Schlosberg (1955). Mean values and standard deviations (SD) for the population of subjects vs. target position are given in Fig. 2. The mean values represented by dashed lines were 262 ms for visual responses and 221 ms for auditory responses.

Pattern of the Eye Movement The presentation of a target (visual or auditory) was followed by a response composed either by only one

I.L. O

20

.N

TARGET

POSITION

(deg)

Fig. 3. Percentage of single saccade responses vs. target position

saccade (single saccade response) or by a main (primary) saccade followed by one or more secondary saccades (multiple saccade response). The percentage of single saccade responses decreased with target eccentricity. The decrease was greater for visual than for auditory responses. At the smaller eccentricities visual responses were normally com-

420

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

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100

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10

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0

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I

0

POSITION

10

I

t

20

30

(deg)

Fig. 4A, B. Latency (T1) of primary saccades vs. target position. A Mean values and SD for one subject. B Mean values and SD for the population of subjects

Visual

X /

responses

Auditory

X

"P1, ,,, i

20

responses

20

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lo

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0

0

100

200

300

LATENCY T2 Fig. S. Histograms of secondary saccades latency distributions of the two populations P1 and P2

i 400

l 500

(ms) (T2).

C 0

100

200

300

LATENCY

400

500

T2 (ms)

Dashed lines on the histograms of visual responses represent the best fit normal

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

posed by only one saccade, whereas auditory responses were often composed by at least two saccades. At the larger eccentricities, the percentage of single saccade responses was greater in the auditory than in the visual case. Figure 3 gives the percentage of single saccade responses vs. target position for the whole population of subjects. The presence of a third saccade in multiple visual responses was rare. At the end of these responses the eyes were right on the target. In contrast, auditory responses could be made of more than two saccades and the final eye position generally underestimated that of the target. When the auditory target was presented near the midline (i.e., 5 deg right or left) there could be no response at all or a response with the primary saccade in the wrong direction. Auditory responses were also observed with a primary saccade in one direction followed by a second saccade in the opposite direction and by a third saccade in the direction of the first one. This pattern was never found in visual responses.

421

Table 1. Statistical parameters of secondary saccade latency. Two populations (P1 and P2) of visual secondary saecades were distinguished, whereas auditory saecades were considered as belonging to only one population Visual

Percentage Average latency S.D.

Auditory

P1

P2

onepopulation

77 133.6 22.8

23 237.5 29

100 204.9 131.4

O CORREC11HYPOM. HYPERM X Y. Z

w

0

VISUAL

55.6

/-3.7

03

I-

AUDITORY

13.8

75./,

10.8

_I

0_

#J

jJ

S~j

# fJ

30

w#

S~

jj f~Jl#l~

< /

UJ

C~
rr < Z; nO_

,,..,,,..6" l ,.,,,6 T ,,5"" T

9 Auditory responses responses

o Visual

0 0

10

TARGET

20

POSITION

30

(deg)

Fig. 6. Mean values and SD of primary saccade amplitude versus target position for the population of subjects. Table inserted in figure gives the percentage of correct, hypometric, and hypermetric primary saccades

tinct populations could be recognized. The average value and SD of the latency of auditory secondary saccades considered as belonging to only one population is given in the last column of Table 1. The average latency of P2 visual saccades was almost the same as that of primary visual saccades. In contrast, the average latency of P1 visual saccades was significantly shorter. Due to the broad distribution of auditory secondary saccade latency, its average value is not meaningful.

Precision Precision was first examined in terms of primary saccade amplitude vs. target position. The results are

422

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

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Z

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0 0

10

20

TARGET

' 30

0

i

0

POSITION

10

20

30

(deg)

Fig. 7A, B. Final eye position in auditory responses vs. target position. A Mean values and SD for one subject computed from single and multiple saccade responses. B Mean values and standard deviations for the population of subjects. For all target positions but 5 deg mean values and SD were computed separately for single and multiple saccade responses, and for the full set of auditory responses (single + multiple). The number of multiple saccade responses to a 5 deg target presentation was so small that no statistical parameters could be computed from them

given in Fig. 6 for the whole population of subjects. For all target positions, the average amplitude of primary saccades was greater in visual than in auditory responses. Most primary saccades to visual targets placed near the midline (5 and 10 deg) drove the eyes right on the target, whereas the average relative precision of primary saccades to 30 deg targets was reduced to 83%. The relative precision of primary auditory saccades in terms of both average values and standard deviations was almost constant (68% and 23%, respectively) for all target positions except for 5 deg for which a much greater relative standard deviation was observed. The Table inserted in Fig. 6 gives the percentage of correct, hypometric and hypermetric primary saccades in visual and auditory responses. Correct primary saccades, defined as saccades driving the eyes right on the target with a precision greater than 1 deg, were much more frequent in visual than in auditory responses. Most uncorrect primary saccades were hypometric both in visual and auditory responses. The percentage of hypermetric primary saccades was negligible in the visual case and reached about 10% in the auditory case. All the uncorrect primary visual saccades were followed by secondary saccades, whereas only 57% of the hypometric and

38% of the hypermetric primary auditory saccades were followed by secondary saccades. The precision of auditory responses was then examined in terms of the total eye displacement at the end of the presentation of the auditory targets. The results are given for one subject in Fig. 7A and for the whole population of subjects in Fig. 7B. Most of the responses were hypometric, and no correlation was found between precision and target eccentricity. The average final error computed from the auditory responses of all subjects was of less than 3 deg for all the examined target positions. No significant difference in the precision of single and multiple saccade responses was noted.

Amplitude-Duration Relationship The amplitude-duration characteristic was first examined separately for primary and secondary saccades and for each subject. 9 no difference was found among subjects and between the two classes of saccades, the experimental data were considered altogether. Distinction was made only between visual and auditory saccades. For both, data could accurately be fitted by a linear function of the type

D. Zambarbieri et al.: SaccadicResponses Evoked by Presentation of Visual and Auditory Targets

A

B

Subject J.V.

150

150

D:3.9A+22.4(r~.92) E

a

423

(Auditory

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./

D= 3.4A+24.2 (r2=.95)

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(Visual responses)

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20

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AMPLITUDE

I

0

A

10

D= 2.7A §23.4 (r2=.96)

(Visual responses)

I

20

I

30

(deg)

Fig. 8A, B. Amplitude-durationcharacteristics for visual (dashed lines) and auditory (continuous lines) saccades. The relevant best fit

equations and the regression coefficientsr2are also indicated. A Results from one subject. B Results from the population of subjects

D = a + b A , where D and A are saccade duration and amplitude, respectively. The regression lines for one subject are shown in Fig. 8A, whereas the results for the population of subjects are reported in Fig. 8B. The correlation coefficient r 2 was greater than 0.9 for all subjects and for both visual and auditory saccades. The two diagrams in Fig. 8B present the same intercept with the duration axis, but a different slope. For the same amplitude, auditory saccades displayed a longer duration than visual saccades. This difference tended to disappear as saccade amplitude approached zero. This feature was common to all the examined subjects.

Amplitude-PeakVelocityRelationship Amplitude-peak velocity data were fitted by using the function

%=

A a + BA

where Vp and A are saccade peak velocity and amplitude, respectively. The fitting function was chosen according to the considerations reported in the Appendix.

Primary and secondary saccades were considered as only one population. The best fitting curves for one subject are shown in Fig. 9A, whereas the results for the whole population of subjects are reported in Fig. 9B. The major differences occurred for the largest saccades, and the peak velocity of auditory saccades was always smaller than that of visual saccades of the same amplitude.

Discussion

The experimental results reported in this paper indicate significant differences in saccadic responses evoked by the presentation of visual and auditory targets. Differences were observed in the pattern of responses, in their precision, and in the characteristics of individual saccades. In order to interprete these differences we should make reference to the current theories on how saccades are commanded and executed. As far as saccade command is concerned, there are basically two lines of hypothesis, which assume a retinotopic and a craniotopic (or spatial) saccade organization, respectively. In the retinotopic hypothesis, the neural command to the execution mechanism is: make a saccade of a given amplitude in a

424

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

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Sensory information

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Fig. 10. Model of the saccadic system. target position relative to the head; OEH:eye position in the head; OEH:efference copy of OzH; PG: pulse generator; NI: central neural integrator; K: gain

given direction. In the craniotopic hypothesis the command is: drive the eyes to a given position in the orbit. The retinotopic hypothesis is the simplest to explain saccades evoked by the presentation of visual targets since the retina directly provides the signal required by the execution mechanism (i.e., target position relative to the eyes). Nevertheless, there are

experimental results which seem to indicate that saccades are craniotopically and not retinotopically organized. Some of these results have been reviewed by Robinson in 1975. More recently, further evidence was given by Mays and Sparks (1980) As far as saccade execution is concerned, an accurate description of this process has been given by

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

Robinson (1975). Saccades are executed through the action of a neural pulse generator placed in the brainstem. Since the accuracy of saccades of the same amplitude was found to be largely independent of their duration and peak velocity (Zee et al. 1976; Jtirgens et al. 1981), the existence of a local feedback has been assumed (Zee et al. 1976; Berthoz 1981; Jiirgens et al. 1981). The pulse generator is switched off only when the intended final eye position is reached. Under the assumption that saccades are spatially organized, the model in Fig. 10 can be proposed. A central reconstructor receives sensory information and efference copy signals of eye, head, and body positions relative to their supporting platforms. It reconstructs an absolute representation of external and internal space, and it sends appropriate reference signals to the different motor systems. In particular, a reference signal representing the estimated target position relative to the head is sent to the execution mechanism of the saccadic system. A corollary discharge pathway from the output of a central neural integrator (NI) provides the local feedback required to switch off the pulse generator (PG). Whatever the sensory system involved in the perception process, it is reasonable to assume that information on target position reaches the central reconstructor affected by some uncertainty. The degree of uncertainty will depend on the characteristics of both the incoming sensory signals and the detecting and transducing mechanisms. The greater the uncertainty, the longer the processing time needed to obtain an accurate estimate of target position is. The results on simple RT indicate that the detection time is shorter for auditory than for visual stimuli. In both cases, it is almost independent of stimulus position. Then, the observed greater latency of auditory with respect to visual saccadic responses in subjects asked to respond as accurately as possible has to be attributed to differences in the processing time. It should also be inferred that the degree of uncertainty associated to auditory spatial information is not only greater than that affecting visual spatial information, but it is also dependent on stimulus position with respect to the head. As a matter of fact, when the source of sound is placed near the midline, both phase and amplitude differences at the level of the subject's ears are very small and the estimate of absolute values could consequently be more difficult. The longer time needed for processing auditory spatial information would reverse the relationship observed between RTs of auditory and visual responses. In monkeys trained to reach visual and

425

auditory targets only within +5 deg and therefore in a more "reflexive way", the latency of auditory saccadic responses was found to be shorter than that of visual responses (Whittington et al. 1981). A greater uncertainty in the acquisition of spatial information by the auditory system does not necessarily imply that the accuracy of auditory saccadic responses results much worse than that of visual responses. Actually, it is not. An average final error of about 3 deg was observed at all target positions. Only the processing time would be different. The exponential decrease of the latency of auditory responses with target eccentricity would be perfectly consistent with the hypothesis of an higher level of uncertainty for the smaller eccentricities and with the observed constant precision of the overall response. The greater accuracy of primary saccades and the higher percentage of single saccade responses in the visual case can also be related to the fact that the uncertainty in the acquisition of target position is smaller for visual than for auditory targets. A more formal description of central processing in saccade generation has been developed in a stochastic model that will be published elsewhere (Schmid et al. 1982). Results of computer simulation will also be presented and compared with the results reported in this paper. A last comment is needed for the amplitude-duration and amplitude-peak velocity characteristics of saccades to visual and auditory targets. For the same amplitude, the latter displayed a longer duration and a smaller peak velocity. Since the execution mechanism is likely to be the same, the observed difference can probably be related to a lower level of the pulse generator activity. It has been shown that the decrease of pulse amplitude produces a longer duration and a smaller peak velocity of saccades (Robinson 1975). As for the anatomic localization of the central reconstructor, it is likely that its functions are actually distributed among several anatomical structures. The superior colliculus (SC) is very likely involved in the central processing of sensory information for visual and auditory saccade generation (Sparks and Mays 1982). Both the visual and the auditory space are represented in this structure (Cynader and Berman 1972; Gordon 1973; Drager and Hubel 1975, 1976; Pollack and Hickey 1979). Moreover, electrical stimulation of SC has been proved to evoke saccadic responses (Robinson 1972; Schiller and Stryker 1972). Nevertheless, SC is certainly not the only structure in which central processing occurs as proved by the fact that saccades are preserved after SC lesions (Pasik et al. 1966; Wurtz and Goldberg 1972; Mohler and Wurtz 1977; Schiller et al. 1980). Visual saccades are abolished only if combined

426

D. Zambarbieri et al.: Saccadic Responses Evoked by Presentation of Visual and Auditory Targets

lesions of S C a n d visual c o r t e x ( M o h l e r a n d W u r t z 1977) o r o f S C a n d f r o n t a l e y e - f i e l d (Schiller et al. 1980) a r e p r o d u c e d .

Appendix T h e r e l a t i o n s h i p b e t w e e n a v e r a g e (Vm) a n d p e a k (Vp) s a c c a d e v e l o c i t y can b e w r i t t e n as V m = "~Vp w h e r e t h e coefficient y was r e p o r t e d to b e t h e s a m e (y = 0.6) for all t y p e s of s a c c a d e s a n d for all s a c c a d e a m p l i t u d e ( B a l o h et al. 1975). Since Vm =1000

A D

w h e r e A is in d e g , D in m s a n d Vm in deg/s, a n d D=a+bA, the e x p e c t e d r e l a t i o n s h i p b e t w e e n Vp a n d A is Vp = -

1000 A A 7 a+b-------A- a + [ 3 ~

where a = 10-~a

(1)

a n d ~ = 1 0 ~ b.

W h e n f u n c t i o n (1) was u s e d to fit t h e e x p e r i m e n t a l d a t a o b t a i n e d f r o m t h e visual a n d t h e a u d i t o r y r e s p o n s e s of t h e w h o l e p o p u l a t i o n o f s u b j e c t s , a c o r r e l a t i o n coefficient of 0.96 a n d 0.91, r e s p e c t i v e l y , was f o u n d b e t w e e n e x p e r i m e n t a l a n d t h e o r e t i c a l values u n d e r b e s t fit c o n d i t i o n s . T h e ratios a / a a n d B/b, w h i c h a r e b o t h e x p e c t e d to give an e s t i m a t e of t h e s a m e p a r a p e t e r y = Win/Up, w e r e c o m p u t e d f r o m t h e b e s t fit o f a m p l i t u d e d u r a t i o n a n d a m p l i t u d e - p e a k v e l o c i t y d a t a . It was f o u n d to b e a / a = 0.75 10 -3 a n d 13/b = 0.6 10 -3 for b o t h visual a n d a u d i t o r y saccades. T h e o b s e r v e d difference might i n d i c a t e t h a t y = 0.6 is o n l y an a v e r a g e value, a n d small v a r i a t i o n s o f y in r e l a t i o n to s a c c a d e a m p l i t u d e can a c t u a l l y occur.

Acknowledgement. The authors wish to tank Prof. M. Jeannerod for helpful suggestions and criticism.

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