Biol. Cybernetics 19, 211--215 (1975) @ by Springer-Verlag 1975
On the Characteristic of Nonlinear Spatial Summation Observed in the Lateral Geniculate Cells of Cats N o b o r u Sugie, Shigeru Yamane, Shinji Karl, and Masaaki Yoshimura Bionics Research Section, Electrotechnical Laboratory, Nagatacho, Chiyodako, Tokyo, Japan Received: December 10, 1974
Abstract The spatial summation characteristic in the receptive fields of cat lateral geniculate cells were investigated. First, the central area of the receptive field was determined using a spot of light. Then the response of the cell were obtained using disc-shaped stimuli of various radii located in the middle point of the receptive field center. When the radius was increased gradually, the response tended to increase, at first, until it reached a peak value and began to decrease thereafter. The radius where the peak response took place was generally less than that of the receptive field center. Furthermore, this radius decreased when the intensity of the stimulus light was increased. These neurophysiological findings could be simulated by a model. The model consists of two parts. The first part receives the input from the photoreceptors. It is of homogeneous structure with shunting inhibition. The second part receives the input from the first part. The structure is characterized by the conventional center-surround type lateral interaction.
I. Introduction As a model of retinal ganglion or lateral geniculate cell of the cat, the linear spatial summation characteristic is often assumed (Enroth-Cugell and Robson, 1966). However, there are several neurophysiological studies reporting the nonlinearity in spatial summation. The Y cells due to Enroth-Cugell and Robson (1966) exhibit considerable nonlinearity. Biittner and Grusser (1968) stimulated retinal ganglion cells with one or two spots of light located in the central area of the receptive fields. Let the response to a spot A be R a. Similarly the response to another spot B is designated by R 8. Then the response to a pair of spots A and B can be approximated by the following experimental formula
Stone and Fabian (1968) conducted experiments similar to those by Btittner and Gfiisser and similar results were obtained. They argued that this characteristic may be ascribed to intrinsic properties (e.g. refractoriness) of ganglion cells. Instead of two light spots, Freund and Grtinewalt (1969) employed a family of discs with various radii, each of which was located in the middle point of the receptive field center. It was found that the responses increased with the increase in disc size until some point but was saturated or began to decrease beyond it. The minimal radius of the disc giving the maximal response was found to be considerably smaller than that of the receptive field center. The same kind of experiment was carried out regarding the lateral geniculate cells of the cat yielding similar results (Freund et al., 1969). In the present article, neurophysiological investigations of the spatial summation characteristic of lateral geniculate cells were described first. The receptive fields were studied with a family of discshaped stimuli, the maximum radius of which exceeded that of the receptive field center. Various intensities of stimuli were employed to study the nonlinearity in more detail than the studies by Freund and Gfiinewald (1969). In the second part of this article, the experimental observations were simulated with a model consisting of two stages, characterized by homogeneous shunting inhibition and center-surround type linear summation, respectively. The model may reflect the nonlinear characteristic as well as the centersurround antagonism.
RAB = a(RA + RB) + b,
II. Neurophysiological Studies where a and b are constants. As the model underlying this finding, Bfittner and Grfisser proposed two types of models. One is a model incorporating subtractive inhibition and the other is a model with shunting inhibition. In either case, the horizontal cell is assumed to be inhibitory.
II. 1. Methods The cat, 2.5~4.5 kg weight, was first anesthetized with N 2 0 / O 2 (3l/1) mixed gas containing 4% Fluothane (2-bromo-2 chloro-1, 1, 1-trifluroethane). After cannulation of trachea, the level of anesthesia was
212
maintained with the gas containing Fluothane (2%). One ml of Penicillin (3 x 104 i.u.) was injected intramuscularly. The wounds were infiltrated with surface anesthetic (lidocaine hydrochloride) and the rectal temperature was kept at 38-t- 1~ by a blanket heater. After surgical procedures, the cat's head was fixed to a Bishop type stereotaxic apparatus (Takahashi) which left the visual field free. To prevent eye movement, a mixed solution of gallamine triethiodide (6mg/kg per hour) and d-tubocurarine (1 mg/kg per hour) diluted with Ringer's solution was continuously injected through the intravenous cannula during the experiment under artificial respiration by a pump (R-50, Aika). Now the anesthesia was maintained with N 2 0 / O z (1/1) by the closed method. The pupils were dilated by applying tropicamid and phenylepherine chloride (Midorin P, Santen Chemical). In order to keep the cornea wet, a few drops of hydroxyethyl cellulose (Opetea, Senju Chemical) were applied to the eyes which were covered with contact lenses. A pair of contact lenses with artificial pupils were selected from a family of lenses prepared in 1/8 diopter steps, so that the screen (translucent type, hung 171 cm apart from cat's eyes) was conjugated with the retina using the projection method (Yamane et al., 1971). Single unit discharges were recorded from lateral genieulate cells through a resin coated tungsten microelectrode. The impulses were fed into a computer (NEAC-3100, NEC) for data processing. The visual stimuli were presented on the screen through a computer-controlled projector. The approximate size of the receptive field were determined first in the conventional way. The spatial organization was examined by exploring sequentially the post-stimulus-time histograms (PSTH) of the on- and off-response to a light spot (10 rain in diameter) at each point ofa 9 x 9 matrix around the approximate center of the receptive field. Thus, the middle point of the receptive field center as well as the diameter can be determined. After that the spot was replaced by a family of disc-shaped light stimuli, 10-310min in diameter. These stimuli were turned on and off iteratively at the middle point of the respective field center to examine the spatial summation characteristic. As discussed by Freund and Grtinewald (1969), cares were taken in this experiment with regard to the effect of stray light and the sharpness of the retinal image, lest the results should be contaminated by undesirable effects. 11.2. Results
The receptive fields of seven on-center units from three cats were studied in detail. As for off-center units,
ON-CENTER
\ \
~
8
J
60
40 /
1. Isoresponse contour m a p of an on-center unit
pps
ON - C E N T E R B.G. 6.2 ed/m2
200
150 LIJ U3 Z O
...."~%~190
INTENSITY oo
..".....
a. 100
c dl rn'
60
.... "
40
u')
U..l n."
50 ....
20
I0
20
30
40 rain
D ISTANCE Fig. 2. One-dimensional response profiles of an on-center unit through the middle point of the receptive field center at various levels of stimulus light intensity
sufficiently reliable results could not be obtained. In Fig. 1 is shown the isoresponse contour map of a typical receptive field center of an on-center unit. The map was obtained with a light spot turned on and off sequentially at each point of a 9 x 9 matrix. The numerical values denote the averaged peak pulse rates (pulses per second). The background illumination was 1 cd/m 2. The stimulus intensity was 440 cd/m 2. The spontaneous discharge rate was 29 pulses per second.
213 pps
ta
Ik_1 Ik
RFC I
150
~20
ON-CENTER
Ik+I
Stimulus
(B.G. 8.0cd/m a)
INTENSITY
zl00 O I]_ ffl w
0
60
120 DISC
180 DIAMETER
240
300
diffused
/
(rain)
Fig. 3. Response characteristic of an on-center unit to a family of disc-shaped stimuli of various light intensities. RFC denotes the diameter of receptive field center determined with a spot stimulus
From the isoresponse contour map, the middle point of the receptive field center was determined. Since the map consists of approximately circular contours, it may be permitted to represent the response characteristic by one dimensional response profile along the straight line passing through the middle point of the receptive field center. In Fig. 2 are shown several response profiles from an on-center unit, each of which was obtained at a constant stimulus light intensity ranging from 6.2 to 190 cd/m z, while the background light intensity was kept at 6.2 cd/m 2. It can be noted that the radius (about 30 min) of the receptive field center tended to increase only a little bit with increasing stimulus light intensity. In Fig. 3 are shown the responses of an on-center unit to a family of disc-shaped light stimuli of various light intensities. The background illumination was kept at 8 cd/m 2. RFC in it denotes the diameter of the receptive field center determined with spot stimuli. It can be seen that the diameter where the peak of the response curve in Fig. 3 took place was dependent on the stimulus light intensity. That is, the diameter where the peak of the response curve took place got smaller, when the stimulus light intensity was increased. If the spatial summation characteristic is linear, the diameter where the peak of the response curve took place should be equal to RFC independent of stimulus intensity. This nonlinear summation can be explained by as, suming the co-existence of shunting inhibition (Furman, 1965) along with conventional linear lateral inhibition (Enroth-Cugell and Robson, 1966).
Fig. 4. Layer of forward shunting inhibition. Small open and dosed circles denote excitatory and inhibitory synapses, respectively
retina is responsible for the nonlinear spatial summation. This summation may be validated by Freund and Grtinewald's studies. It is assumed further that the retina is of one dimension for simplicity. The model consists of two layers. The organization of the first layer is shown in Fig. 4. This layer is responsible for nonlinear spatial summation. The receptor Rk responds to the stimulus I t. For simplicity, it is assumed that the response R k= Ik.
The neuron Uk receives an excitatory input from Ik and inhibitory inputs from the receptors in the neighborhood of Rk. The inhibition is of forward shunting type. Thus the relation is represented in the following way. Rk
Uk-- 1 -}- 2 hkjRj J
where hjk'S are weighting coefficients and j~: k. In computer simulation, hjk'S were derived from the following formula hk(k +j) = a exp {
(0. lj) 2 2So2 }.
111.3. Outline o f M o d e l
Though the neurophysiological studies were conducted on lateral geniculate cells, it is assumed that the
(2)
In simulation, the following values were used a = 0.5642 1/2s~ = 0.04
IIL S i m u l a t i o n S t u d i e s
(1)
(3)
-- 100=
On the Characteristic of Nonlinear Spatial Summation Observed in the Lateral Geniculate Cells of Cats N o b o r u Sugie, Shigeru Yamane, Shinji Karl, and Masaaki Yoshimura Bionics Research Section, Electrotechnical Laboratory, Nagatacho, Chiyodako, Tokyo, Japan Received: December 10, 1974
Abstract The spatial summation characteristic in the receptive fields of cat lateral geniculate cells were investigated. First, the central area of the receptive field was determined using a spot of light. Then the response of the cell were obtained using disc-shaped stimuli of various radii located in the middle point of the receptive field center. When the radius was increased gradually, the response tended to increase, at first, until it reached a peak value and began to decrease thereafter. The radius where the peak response took place was generally less than that of the receptive field center. Furthermore, this radius decreased when the intensity of the stimulus light was increased. These neurophysiological findings could be simulated by a model. The model consists of two parts. The first part receives the input from the photoreceptors. It is of homogeneous structure with shunting inhibition. The second part receives the input from the first part. The structure is characterized by the conventional center-surround type lateral interaction.
I. Introduction As a model of retinal ganglion or lateral geniculate cell of the cat, the linear spatial summation characteristic is often assumed (Enroth-Cugell and Robson, 1966). However, there are several neurophysiological studies reporting the nonlinearity in spatial summation. The Y cells due to Enroth-Cugell and Robson (1966) exhibit considerable nonlinearity. Biittner and Grusser (1968) stimulated retinal ganglion cells with one or two spots of light located in the central area of the receptive fields. Let the response to a spot A be R a. Similarly the response to another spot B is designated by R 8. Then the response to a pair of spots A and B can be approximated by the following experimental formula
Stone and Fabian (1968) conducted experiments similar to those by Btittner and Gfiisser and similar results were obtained. They argued that this characteristic may be ascribed to intrinsic properties (e.g. refractoriness) of ganglion cells. Instead of two light spots, Freund and Grtinewalt (1969) employed a family of discs with various radii, each of which was located in the middle point of the receptive field center. It was found that the responses increased with the increase in disc size until some point but was saturated or began to decrease beyond it. The minimal radius of the disc giving the maximal response was found to be considerably smaller than that of the receptive field center. The same kind of experiment was carried out regarding the lateral geniculate cells of the cat yielding similar results (Freund et al., 1969). In the present article, neurophysiological investigations of the spatial summation characteristic of lateral geniculate cells were described first. The receptive fields were studied with a family of discshaped stimuli, the maximum radius of which exceeded that of the receptive field center. Various intensities of stimuli were employed to study the nonlinearity in more detail than the studies by Freund and Gfiinewald (1969). In the second part of this article, the experimental observations were simulated with a model consisting of two stages, characterized by homogeneous shunting inhibition and center-surround type linear summation, respectively. The model may reflect the nonlinear characteristic as well as the centersurround antagonism.
RAB = a(RA + RB) + b,
II. Neurophysiological Studies where a and b are constants. As the model underlying this finding, Bfittner and Grfisser proposed two types of models. One is a model incorporating subtractive inhibition and the other is a model with shunting inhibition. In either case, the horizontal cell is assumed to be inhibitory.
II. 1. Methods The cat, 2.5~4.5 kg weight, was first anesthetized with N 2 0 / O 2 (3l/1) mixed gas containing 4% Fluothane (2-bromo-2 chloro-1, 1, 1-trifluroethane). After cannulation of trachea, the level of anesthesia was
212
maintained with the gas containing Fluothane (2%). One ml of Penicillin (3 x 104 i.u.) was injected intramuscularly. The wounds were infiltrated with surface anesthetic (lidocaine hydrochloride) and the rectal temperature was kept at 38-t- 1~ by a blanket heater. After surgical procedures, the cat's head was fixed to a Bishop type stereotaxic apparatus (Takahashi) which left the visual field free. To prevent eye movement, a mixed solution of gallamine triethiodide (6mg/kg per hour) and d-tubocurarine (1 mg/kg per hour) diluted with Ringer's solution was continuously injected through the intravenous cannula during the experiment under artificial respiration by a pump (R-50, Aika). Now the anesthesia was maintained with N 2 0 / O z (1/1) by the closed method. The pupils were dilated by applying tropicamid and phenylepherine chloride (Midorin P, Santen Chemical). In order to keep the cornea wet, a few drops of hydroxyethyl cellulose (Opetea, Senju Chemical) were applied to the eyes which were covered with contact lenses. A pair of contact lenses with artificial pupils were selected from a family of lenses prepared in 1/8 diopter steps, so that the screen (translucent type, hung 171 cm apart from cat's eyes) was conjugated with the retina using the projection method (Yamane et al., 1971). Single unit discharges were recorded from lateral genieulate cells through a resin coated tungsten microelectrode. The impulses were fed into a computer (NEAC-3100, NEC) for data processing. The visual stimuli were presented on the screen through a computer-controlled projector. The approximate size of the receptive field were determined first in the conventional way. The spatial organization was examined by exploring sequentially the post-stimulus-time histograms (PSTH) of the on- and off-response to a light spot (10 rain in diameter) at each point ofa 9 x 9 matrix around the approximate center of the receptive field. Thus, the middle point of the receptive field center as well as the diameter can be determined. After that the spot was replaced by a family of disc-shaped light stimuli, 10-310min in diameter. These stimuli were turned on and off iteratively at the middle point of the respective field center to examine the spatial summation characteristic. As discussed by Freund and Grtinewald (1969), cares were taken in this experiment with regard to the effect of stray light and the sharpness of the retinal image, lest the results should be contaminated by undesirable effects. 11.2. Results
The receptive fields of seven on-center units from three cats were studied in detail. As for off-center units,
ON-CENTER
\ \
~
8
J
60
40 /
1. Isoresponse contour m a p of an on-center unit
pps
ON - C E N T E R B.G. 6.2 ed/m2
200
150 LIJ U3 Z O
...."~%~190
INTENSITY oo
..".....
a. 100
c dl rn'
60
.... "
40
u')
U..l n."
50 ....
20
I0
20
30
40 rain
D ISTANCE Fig. 2. One-dimensional response profiles of an on-center unit through the middle point of the receptive field center at various levels of stimulus light intensity
sufficiently reliable results could not be obtained. In Fig. 1 is shown the isoresponse contour map of a typical receptive field center of an on-center unit. The map was obtained with a light spot turned on and off sequentially at each point of a 9 x 9 matrix. The numerical values denote the averaged peak pulse rates (pulses per second). The background illumination was 1 cd/m 2. The stimulus intensity was 440 cd/m 2. The spontaneous discharge rate was 29 pulses per second.
213 pps
ta
Ik_1 Ik
RFC I
150
~20
ON-CENTER
Ik+I
Stimulus
(B.G. 8.0cd/m a)
INTENSITY
zl00 O I]_ ffl w
0
60
120 DISC
180 DIAMETER
240
300
diffused
/
(rain)
Fig. 3. Response characteristic of an on-center unit to a family of disc-shaped stimuli of various light intensities. RFC denotes the diameter of receptive field center determined with a spot stimulus
From the isoresponse contour map, the middle point of the receptive field center was determined. Since the map consists of approximately circular contours, it may be permitted to represent the response characteristic by one dimensional response profile along the straight line passing through the middle point of the receptive field center. In Fig. 2 are shown several response profiles from an on-center unit, each of which was obtained at a constant stimulus light intensity ranging from 6.2 to 190 cd/m z, while the background light intensity was kept at 6.2 cd/m 2. It can be noted that the radius (about 30 min) of the receptive field center tended to increase only a little bit with increasing stimulus light intensity. In Fig. 3 are shown the responses of an on-center unit to a family of disc-shaped light stimuli of various light intensities. The background illumination was kept at 8 cd/m 2. RFC in it denotes the diameter of the receptive field center determined with spot stimuli. It can be seen that the diameter where the peak of the response curve in Fig. 3 took place was dependent on the stimulus light intensity. That is, the diameter where the peak of the response curve took place got smaller, when the stimulus light intensity was increased. If the spatial summation characteristic is linear, the diameter where the peak of the response curve took place should be equal to RFC independent of stimulus intensity. This nonlinear summation can be explained by as, suming the co-existence of shunting inhibition (Furman, 1965) along with conventional linear lateral inhibition (Enroth-Cugell and Robson, 1966).
Fig. 4. Layer of forward shunting inhibition. Small open and dosed circles denote excitatory and inhibitory synapses, respectively
retina is responsible for the nonlinear spatial summation. This summation may be validated by Freund and Grtinewald's studies. It is assumed further that the retina is of one dimension for simplicity. The model consists of two layers. The organization of the first layer is shown in Fig. 4. This layer is responsible for nonlinear spatial summation. The receptor Rk responds to the stimulus I t. For simplicity, it is assumed that the response R k= Ik.
The neuron Uk receives an excitatory input from Ik and inhibitory inputs from the receptors in the neighborhood of Rk. The inhibition is of forward shunting type. Thus the relation is represented in the following way. Rk
Uk-- 1 -}- 2 hkjRj J
where hjk'S are weighting coefficients and j~: k. In computer simulation, hjk'S were derived from the following formula hk(k +j) = a exp {
(0. lj) 2 2So2 }.
111.3. Outline o f M o d e l
Though the neurophysiological studies were conducted on lateral geniculate cells, it is assumed that the
(2)
In simulation, the following values were used a = 0.5642 1/2s~ = 0.04
IIL S i m u l a t i o n S t u d i e s
(1)
(3)
-- 100=
