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The effect of stimulus velocity on human torsional eye movements
Vision RCJ. Vol.
10. pp. 781-784.
Pcrgamon
Press
1970.
Printed
in Great
Britain.
LETTER TO THE EDITORS
THE EFFECT OF STIMULUS VELOCITY ON HUMAN TORSIONAL EYE MOVEMENTS’ (Received 26 Nocember
1969; in revised form 11 February
1970)
IT WAS reported in a previous publication (KERTESZ and JONES,1969) that an eye undergoes torsional movement about the line of sight when it monocularIy hates the center of a rotating sectored disc while the other eye is occluded. At the onset of the stimuhts, i.e. when thedisc begins to rotate,theeye rotates in the samedirection as thedisc (“on”response). When the stimulus is turned off, i.e. when the disc is stopped, the eye rotates back toward its resting position (“off” response). Objective measurements of “on” and “off” responses indicated that the magnitude of the torsional responses is proportional to the number of retinal receptors exposed to the moving boundaries contained in the rotating sectored disc, and is a function of the linear velocity with which the moving boundaries cut across retinal receptors. The oculomotor system responsible for mediating the response can be divided into two components: the sensory system and the motor system. The sensory system, consisting of retinal receptors and higher order sensory neurones, is responsible for the detection of the stimulus. The motor system, consisting of the extraocular muscles and the eyeball, executes the response. These two sub-systems are interconnected via neural pathways. The nature of the response (a slow rotational eye movement whose amplitude is a function of stimulus velocity) suggests that the functional dependence of response amplitude on stimulus velocity is due to the velocity selectivity of sensory neurons. In this paper, the torsional response of the eyes to a stimulus moving across the retina with uniform velocity will be deduced, using a linear model, from experimentally recorded torsional eye movements elicited by a rotating sectored annuIus containing a narrow range of linear velocities. The deduced torsional response of the eyes as a function of the uniform velocity with which the stimulus is assumed to move across retina1 receptors will provide a more accurate representation of the velocity selectivity of visual sensory neurons involved in the detection of motion. EXPERIMENTAL
RESULTS
The functional dependence of eye rotations on the range of linear velocities contained in the stimulus was demonstrated as follows. The stimulus consisted of a rotating sectored annulus (23-l cm outside dia. and 15.24 cm inside dia.) made up of 15 black and 15 white equal sectors that was viewed from a distance of 43.18 cm. The range of linear velocities 1This paper was supported in part by Research Grant B-02165 from the Institute of Neurological Diseases and Blindness, National Institutes of Health, Public Health Service. I wish to thank Professor RICHARDW. JONES for his advice and counsel he had so generously given during the course of these experiments. 781
LETTER TO THE EDITORS
782
present in the stimulus for a given speed of rotation of the annulus was restricted. The ratio of maximum to minimum linear velocity contained in the stimulus was 1.51. Rotational movements of the subject’s right eye about the line of sight were measured in response to the counter clockwise (CC%‘) rotation of the annulus at various speeds. A detailed description of the experimental protocol has appeared in KERTESZand JONES(1969). The results of this experiment are shown in Fig. 1. The data shown in Fig. 1 exhibits a peak. The annulus rotating at approximately 17 rev/min, corresponding to an average drift velocity of 21.9 deg of arc/set, evoked the maximum response. It is informative to compare the torsional response of the eyes to a rotating sectored disc with the response obtained when the range of linear velocities present in the stimulus for a given speed of rotation of the disc was restricted by presenting only an annular portion of the disc. KERIBZ and JONES(1969) observed that the angular rotation of the eyes induced by the rotating sectored disc is fairly constant over the speed range of 2-28 rev/mm. However,
‘2 r
0 On response
7
CCW I 0
rev/min
velocity,
I 30 deg
response
onnulus
I 20
I IO Av. stimulus
of
x Calculated
of
I 40
arc/set
Fro. 1. Rotational response of the fight eye to a sectored amulus (30 sectors, 15.24 cm and 23.1 cm annulus dia.) rotating in a CCW direction as seen by the eye vs. rcv/min of annulus. Vertical bars about each data point represent f I standard deviation. The average spatial frequency of the stimulus was O-194 c/deg.
when only an annular portion of the rotating sectored disc is presented to the subject, the torsional response of the eyes is peaked as is shown in Fig. 1. This seems to indicate that the response is a function of the range of linear velocities contained in the stimulus. It is reasonable to assume that the eye rotation produced by the rotating sectors would be even more sharply peaked than is shown in Fig. 1, if it were possible to reduce the spread of linear velocities present in the stimulus below the value of 1.51 given above, that is, the response of sensory neurons to rotating contours drifting across the retina with uniform velocities is even more sharply peaked than the response shown in Fig. 1. The broadening of the curve is attributed to the presence of a finite range of linear velocities in the stimulus at a given speed of rotation of the annulus. Attempts to obtain responses using narrower annuli were unsuccessful, presumably due to the inadequacy of the number of receptors stimulated. Some features of the response as a function of stimulus velocity can be deduced from Fig. 1. Since the data shown in Fig. 1 peaks, and has its axis of symmetry at approximately 17 rev/min corresponding to an average drift velocity of 2 1.9 deg of arc/set and decreases to a small value outside the range of 4-30 rev/mm, therefore, the response as a function of
LEAR TOTHEEDITORS
783
stimulus velocity should also peak and be symmetrical about an axis located at 21.9 deg of arc/set and fall off at both high and low velocities. A Gaussian distribution with its mean equal to 21.9 deg of arc/set satisfies all of the above requirements. The suggestion that the rotational response of the eyes is proportional to the number of retinal receptors exposed to the moving boundaries contained in the stimulus and that spatial summation of receptor responses takes place, as was concluded by KERTESZand JONES(1969) leads one to consider a linear model as a first approximation. The annulus used in the experiments was considered to have been made up of 16 nonoverlapping subannuli. It was assumed that every point in a subannulus moved with the velocity given by the product of the speed of rotation of the annulus and the mean radius of the subannulus, so that a given rev/mm the rotating contours of the annulus were assumed to move with 16 different velocities. Each experimentally obtained response plotted in Fig. 1 was assumed to be the sum of 16 separate components. Let R(p) denote an experimentally obtained response (deg) to the annulus used in the above experiment rotating with p rev/min and r(u() the response, in deg, of a trio of retinal receptors (the minimum number required to detect a curved track across the retina in order to generate a torsional response) to a grating drifting across the retina with velocity v,(m/sec), then : R(p) = C i? b&J i-1
(1)
and r(q) = e
-1/2(q-1.63)/d2
(2)
where P= speed of rotation of the annulus b, = the number of receptor trios covered by the i-th subannulus
as calculated from OS~ERG’S (1935) results v, = linear velocity (in m/set) of every point contained in the i-th subannulus when the entire annulus is rotating at p rev/mm. Note, that l-63 mjsec = 21.9 deg of arc/set for the 30 sectored annulus of 19.17 cm mean dia. a= a parameter to be varied (in m/set). C= a constant calculated for every value of a to yield the least mean squared error.
The values of C and a were empirically determined to yield the smallest error. This error is defined as the sum of the squareddifferences between the calculated and observed responses for each experimental observation shown in Fig. 1. The procedure utilized to determine the values of C and a is as follows. First, a was assigned a value 2.54 x 10S2 and r(v&s were computed at points corresponding to each experimental observation. A corresponding value of C was then calculated to yield the smallest error. The value of a was subsequently increased in steps of 2.54 x 10m2 up to 1.143. The above calculations were repeated for each new value of a. The value of a (0.889 m/set = 1l-9439 deg of arc/set) which yielded the smallest error was then selected. The resulting response as a function of stimulus velocity is shown in Fig. 2.
784
LErrEzRTO ‘I-HEEDITORS
Av.
FIG. 2. Non&i&
velocity,
deg
of arc/set
roFational response of the ri&t eye (as predicted by the linear model} to a stimulus moving across the retina with a uniform velocity.
The calculated responses to the rotating annulus used in the experiment, based on the response as a function of stimulus velocity of Fig. 2, are shown as x’s on Fig. 1. While the representation of the response as a function of stimulus velocity as shown in Fig. 2 is not unique the calculated responses, to a rotating annulus, based on it agree quite well with the experimentally observed responses. WATANABEet al. (1968) measured contrast sensitivity functions, reciprocal of threshold contrast, in humans for a drifting grating target whose luminance was sinusoidally modulated with a spatial frequency& (c/deg of arc) in the horizontal dimension (perpendicular to the bars) as a function of drift velocity. It should be noted that Watanabe’s gratings were drifting linearly as opposed to the rotating grating used in the present experiments. Their results also exhibit definite peaks and the drift velocity associated with the peak is shown to be a function of the spatial frequency of the stimulus. For a target whose spatial frequency was O-174 c/deg of arc, the peak occurred at a drift velocity of approximately 15 deg of arc/set. The response shown in Fig. 1 and 2 peaks at an average velocity of 21.9 deg of arc/ set and the spatial frequency of the stimulus was O-194 c/deg of arc. ANDREWE. KER’I-ESZ W. H. Booth Computing Center, Calfimia Institute of Technology, Pasua’ena,Calfomia 91109, U.S.A. REFERENCES Kuwsz, A. E. aad JOPUS, R. W. (1969). The dfect of angular velocity of stimulus on humau torsional eye
movanatta. VZrkw~ J?u. 9,995-998. Osrramaa. G. (1935). Topograpy of the layer of rods and u)aes in the human zetina Acru Oplrtkl. Sqppi.6. WATANABE et uI. (1968). Spatial sine-wave resm of the humanvisualsystem.VLrlon Rrs. 8, 12454263.
10. pp. 781-784.
Pcrgamon
Press
1970.
Printed
in Great
Britain.
LETTER TO THE EDITORS
THE EFFECT OF STIMULUS VELOCITY ON HUMAN TORSIONAL EYE MOVEMENTS’ (Received 26 Nocember
1969; in revised form 11 February
1970)
IT WAS reported in a previous publication (KERTESZ and JONES,1969) that an eye undergoes torsional movement about the line of sight when it monocularIy hates the center of a rotating sectored disc while the other eye is occluded. At the onset of the stimuhts, i.e. when thedisc begins to rotate,theeye rotates in the samedirection as thedisc (“on”response). When the stimulus is turned off, i.e. when the disc is stopped, the eye rotates back toward its resting position (“off” response). Objective measurements of “on” and “off” responses indicated that the magnitude of the torsional responses is proportional to the number of retinal receptors exposed to the moving boundaries contained in the rotating sectored disc, and is a function of the linear velocity with which the moving boundaries cut across retinal receptors. The oculomotor system responsible for mediating the response can be divided into two components: the sensory system and the motor system. The sensory system, consisting of retinal receptors and higher order sensory neurones, is responsible for the detection of the stimulus. The motor system, consisting of the extraocular muscles and the eyeball, executes the response. These two sub-systems are interconnected via neural pathways. The nature of the response (a slow rotational eye movement whose amplitude is a function of stimulus velocity) suggests that the functional dependence of response amplitude on stimulus velocity is due to the velocity selectivity of sensory neurons. In this paper, the torsional response of the eyes to a stimulus moving across the retina with uniform velocity will be deduced, using a linear model, from experimentally recorded torsional eye movements elicited by a rotating sectored annuIus containing a narrow range of linear velocities. The deduced torsional response of the eyes as a function of the uniform velocity with which the stimulus is assumed to move across retina1 receptors will provide a more accurate representation of the velocity selectivity of visual sensory neurons involved in the detection of motion. EXPERIMENTAL
RESULTS
The functional dependence of eye rotations on the range of linear velocities contained in the stimulus was demonstrated as follows. The stimulus consisted of a rotating sectored annulus (23-l cm outside dia. and 15.24 cm inside dia.) made up of 15 black and 15 white equal sectors that was viewed from a distance of 43.18 cm. The range of linear velocities 1This paper was supported in part by Research Grant B-02165 from the Institute of Neurological Diseases and Blindness, National Institutes of Health, Public Health Service. I wish to thank Professor RICHARDW. JONES for his advice and counsel he had so generously given during the course of these experiments. 781
LETTER TO THE EDITORS
782
present in the stimulus for a given speed of rotation of the annulus was restricted. The ratio of maximum to minimum linear velocity contained in the stimulus was 1.51. Rotational movements of the subject’s right eye about the line of sight were measured in response to the counter clockwise (CC%‘) rotation of the annulus at various speeds. A detailed description of the experimental protocol has appeared in KERTESZand JONES(1969). The results of this experiment are shown in Fig. 1. The data shown in Fig. 1 exhibits a peak. The annulus rotating at approximately 17 rev/min, corresponding to an average drift velocity of 21.9 deg of arc/set, evoked the maximum response. It is informative to compare the torsional response of the eyes to a rotating sectored disc with the response obtained when the range of linear velocities present in the stimulus for a given speed of rotation of the disc was restricted by presenting only an annular portion of the disc. KERIBZ and JONES(1969) observed that the angular rotation of the eyes induced by the rotating sectored disc is fairly constant over the speed range of 2-28 rev/mm. However,
‘2 r
0 On response
7
CCW I 0
rev/min
velocity,
I 30 deg
response
onnulus
I 20
I IO Av. stimulus
of
x Calculated
of
I 40
arc/set
Fro. 1. Rotational response of the fight eye to a sectored amulus (30 sectors, 15.24 cm and 23.1 cm annulus dia.) rotating in a CCW direction as seen by the eye vs. rcv/min of annulus. Vertical bars about each data point represent f I standard deviation. The average spatial frequency of the stimulus was O-194 c/deg.
when only an annular portion of the rotating sectored disc is presented to the subject, the torsional response of the eyes is peaked as is shown in Fig. 1. This seems to indicate that the response is a function of the range of linear velocities contained in the stimulus. It is reasonable to assume that the eye rotation produced by the rotating sectors would be even more sharply peaked than is shown in Fig. 1, if it were possible to reduce the spread of linear velocities present in the stimulus below the value of 1.51 given above, that is, the response of sensory neurons to rotating contours drifting across the retina with uniform velocities is even more sharply peaked than the response shown in Fig. 1. The broadening of the curve is attributed to the presence of a finite range of linear velocities in the stimulus at a given speed of rotation of the annulus. Attempts to obtain responses using narrower annuli were unsuccessful, presumably due to the inadequacy of the number of receptors stimulated. Some features of the response as a function of stimulus velocity can be deduced from Fig. 1. Since the data shown in Fig. 1 peaks, and has its axis of symmetry at approximately 17 rev/min corresponding to an average drift velocity of 2 1.9 deg of arc/set and decreases to a small value outside the range of 4-30 rev/mm, therefore, the response as a function of
LEAR TOTHEEDITORS
783
stimulus velocity should also peak and be symmetrical about an axis located at 21.9 deg of arc/set and fall off at both high and low velocities. A Gaussian distribution with its mean equal to 21.9 deg of arc/set satisfies all of the above requirements. The suggestion that the rotational response of the eyes is proportional to the number of retinal receptors exposed to the moving boundaries contained in the stimulus and that spatial summation of receptor responses takes place, as was concluded by KERTESZand JONES(1969) leads one to consider a linear model as a first approximation. The annulus used in the experiments was considered to have been made up of 16 nonoverlapping subannuli. It was assumed that every point in a subannulus moved with the velocity given by the product of the speed of rotation of the annulus and the mean radius of the subannulus, so that a given rev/mm the rotating contours of the annulus were assumed to move with 16 different velocities. Each experimentally obtained response plotted in Fig. 1 was assumed to be the sum of 16 separate components. Let R(p) denote an experimentally obtained response (deg) to the annulus used in the above experiment rotating with p rev/min and r(u() the response, in deg, of a trio of retinal receptors (the minimum number required to detect a curved track across the retina in order to generate a torsional response) to a grating drifting across the retina with velocity v,(m/sec), then : R(p) = C i? b&J i-1
(1)
and r(q) = e
-1/2(q-1.63)/d2
(2)
where P= speed of rotation of the annulus b, = the number of receptor trios covered by the i-th subannulus
as calculated from OS~ERG’S (1935) results v, = linear velocity (in m/set) of every point contained in the i-th subannulus when the entire annulus is rotating at p rev/mm. Note, that l-63 mjsec = 21.9 deg of arc/set for the 30 sectored annulus of 19.17 cm mean dia. a= a parameter to be varied (in m/set). C= a constant calculated for every value of a to yield the least mean squared error.
The values of C and a were empirically determined to yield the smallest error. This error is defined as the sum of the squareddifferences between the calculated and observed responses for each experimental observation shown in Fig. 1. The procedure utilized to determine the values of C and a is as follows. First, a was assigned a value 2.54 x 10S2 and r(v&s were computed at points corresponding to each experimental observation. A corresponding value of C was then calculated to yield the smallest error. The value of a was subsequently increased in steps of 2.54 x 10m2 up to 1.143. The above calculations were repeated for each new value of a. The value of a (0.889 m/set = 1l-9439 deg of arc/set) which yielded the smallest error was then selected. The resulting response as a function of stimulus velocity is shown in Fig. 2.
784
LErrEzRTO ‘I-HEEDITORS
Av.
FIG. 2. Non&i&
velocity,
deg
of arc/set
roFational response of the ri&t eye (as predicted by the linear model} to a stimulus moving across the retina with a uniform velocity.
The calculated responses to the rotating annulus used in the experiment, based on the response as a function of stimulus velocity of Fig. 2, are shown as x’s on Fig. 1. While the representation of the response as a function of stimulus velocity as shown in Fig. 2 is not unique the calculated responses, to a rotating annulus, based on it agree quite well with the experimentally observed responses. WATANABEet al. (1968) measured contrast sensitivity functions, reciprocal of threshold contrast, in humans for a drifting grating target whose luminance was sinusoidally modulated with a spatial frequency& (c/deg of arc) in the horizontal dimension (perpendicular to the bars) as a function of drift velocity. It should be noted that Watanabe’s gratings were drifting linearly as opposed to the rotating grating used in the present experiments. Their results also exhibit definite peaks and the drift velocity associated with the peak is shown to be a function of the spatial frequency of the stimulus. For a target whose spatial frequency was O-174 c/deg of arc, the peak occurred at a drift velocity of approximately 15 deg of arc/set. The response shown in Fig. 1 and 2 peaks at an average velocity of 21.9 deg of arc/ set and the spatial frequency of the stimulus was O-194 c/deg of arc. ANDREWE. KER’I-ESZ W. H. Booth Computing Center, Calfimia Institute of Technology, Pasua’ena,Calfomia 91109, U.S.A. REFERENCES Kuwsz, A. E. aad JOPUS, R. W. (1969). The dfect of angular velocity of stimulus on humau torsional eye
movanatta. VZrkw~ J?u. 9,995-998. Osrramaa. G. (1935). Topograpy of the layer of rods and u)aes in the human zetina Acru Oplrtkl. Sqppi.6. WATANABE et uI. (1968). Spatial sine-wave resm of the humanvisualsystem.VLrlon Rrs. 8, 12454263.