IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-22, NO. 4, JULY 1975 ACKNOWLEDGMENT
The authors wish to thank B. A. Saunders and G. T. Manning [9] from the Department of Anesthesiology and S. J. Purves from the Department of Electroencephalography at the Vancouver General Hospital for their cooperation and assistance. The [101 help provided by M. E. Koombes of the Department of Electri- [111 cal Engineering of the University of British Columbia is gratefully acknowledged. [12]
REFERENCES [1] F. A. Gibbs, E. L. Gibbs, and W. G. Lennox, "Effect on the electroencephalogram of certain drugs which influence nervous activity," Arch. Intern. Med., vol. 60, pp. 154-166, July 1937. [2] M. A. Rubin and H. Freeman, "Brain potential changes in man during cyclopropane anesthesia," J. Neurophysiol., vol. 3, pp. 33-42, Jan. 1940. [3] R. F. Courtin, R. G. Bickford, and A. Faulkoner, Jr., "The classification and significance of electroencephalographic patterns produced by nitrous oxide-ether anesthesia during surgical operations," Proc. Staff Meet. Mayo Clin., vol. 25, pp. 197-206, 1950. [4] D. K. Kiersay, R. G. Bickford, and A. Faulkoner, Jr., "Electroencephalographic patterns produced by thiopental sodium during surgical operations: Description and classification," Br. J. Anesth., vol. 23, pp. 14 1-152, 195 1. [5] A. Faulkoner, Jr., "Correlation of concentration of ether in arterial blood with electroencephalographic patterns during etheroxygen and during nitrous oxide, oxygen and ether anesthesia of human surgical patients," Anesthesiology, vol. 13, pp. 361-369, July 1952. [6] S. Possati, A. Faulkoner, Jr., R. G. Bickford, et al., "Electroencephalographic patterns during anesthesia with cyclopropane: Correlation with coricentrations in arterial blood," Anesth. Analg. (Cleve.), vol. 32, pp. 130-135, 1953. [71 D. L. Clark and B. S. Rosner, "Neurophysiological effects of general anesthetics: The electroencephalogram and sensory evoked responses in man," Anesthesiology, vol. 38, pp. 564-582, June 1973. [8] J. T. Martin, A. Faulkoner, Jr., and R. G. Bickford, "Electro-
[131 [14] [15]
[161 [17]
[181 [19]
[20] [211 [22]
[23]
305
encephalography in anesthesiology," Anesthesiology, vol. 20, pp. 359-376, May 1959. V. L. Brechner, R. D. Walter, and J. B. Dillon, Practical Electroencephalography for the Anesthesiologist. Springfield: Thomas, 1962. J. Volavka, M. Matousek, S. Feldstein et al., "The reliability of EEG assessment," EEG-EMG, in press. E. A. Gain and S. G. Paletz, "An attempt to correlate the clinical signs of fluothane anesthesia with the electroencephalographic levels," Can. Anaesth. Soc. J., vol. 4, pp. 289-294, July 1957. S. J. Galla, A. K. Olmedo, H. E. Kretchmer, et al., "Correlation of EEG patterns with arterial concentrations and clinical signs during halothane anesthesia," Anesthesiology, vol. 23, pp. 147-148, Jan. 1962. E. Lowenstein, "Morphine 'anesthesia'-a perspective," Anesthesiology, vol. 35, pp. 563-565, Dec. 1971. L. Kanal and B. Chandrasekaran, "On dimensionality and sample size in statistical pattern classification," Patt. Recog., vol. 3, pp. 225-234, Oct. 1971. R. 0. Duda and P. E. Hart, Pattern Classification and Scene Analysis. New York: Wiley, 1973. I. J. Good, The Estimation ofProbabilities, Research Monograph 30. Cambridge, Mass.: M.I.T. Press, 1965. G. T. Toussaint and P. M. Sharpe, "An efficient method for estimating the probability of misclassification applied to a problem in medical diagnosis," Comput. Biol. Med., in press. G. Nagy, "State- of the art in pattern recognition," Proc. IEEE, vol. 56, pp. 836-862, May 1968. J. R. Cox, Jr., F. M. Nolle, and R. M. Arthur, "Digital analysis of the electroencephalogram, the blood pressure wave and the electrocardiogram," Proc. IEEE, vol. 60, pp. 1137-1164, Oct. 1972. B. Kleiner, H. Fluhler, P. J. Huber, and G. Dumermuth, "Spectral analysis of the electroencephalogram," Comp. Progr. Biomed., vol. 1, pp. 183-197, 1970. G. Dumermuth, W. Waltz, G. Scollo-Lavizzari, et al., "Spectral analysis of EEG activity in different sleep stages in normal adults," Europ. Neurol., vol. 7, pp. 265-296, July 1972. N. R. Burch, "Period analysis of the EEG on a general-purpose digital computer," Ann. N. Y. Acad. Sci., vol. 115, pp. 827-843, 1964. G. Dumermuth, P. J. Huber, B. Kleiner and T. Gasser, "Numerical analysis of electroencephalographic data," IEEE Trans. Audio Electroacoust., vol. AU-18, pp. 404-411, December 1970.
Electronic Simulation of the Vertebrate Retina ROLF ECKMILLER
-Abstract-An electronic analog model of a section of the vertebrate retina has been constructed. It is structured in 5 layers of cells corresponding to the structure of the natural retina, whereby the function and connections of the single cell models can be varied. While signal processing occurs in the first four layers by evaluating several timedependent slow potentials as positive or negative, impulse rate tine functions are emitted from the ganglion cells at the retina output. Various neural networks as inputs for the 25 Ganglion cells can be realized by using various patchboard connections. Several examples for
Manuscript received January 31, 1974; revised August 27, 1974. This work was supported by a grant from the Stiftung Volkswagenwerk. The author is with the Freie Universitat Berlin, Physiologisches Institut, Fachbereich 1-Vorklinik, 1 Berlin 33, Arnimallee 22, Germany.
simulation results are presented which closely fit comparable neurophysiological findings.
INTRODUCTION T HE function of the vertebrate retina has received attention from many scientists in various fields ranging from ophthalmnology via neurophysiology to biomathematics and engineering. The neural network of the human retina, for example, with about 120 million photoreceptors and about 1.2 million ganglion cells at the output layer participates in various tasks, e.g., pattern recognition, color, motion, and depth perception. This encouraged several approaches to simulate parts
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25 Horizontal Cells
25Amacrine Cells
Fig. 1. Block diagram of the retina model. The patchboards are indicated by the cell contacts which they include, i.e., r,j - rails for the output contacts of receptors 1 to 115. The patchboards for 25 centers and 25 peripheries correspond to passive summing networks (see text). The Add-Subtract-Synapses are operational amplifiers with differential inputs to simulate neural contacts (synapses).
of the retina [71, [10], [16]. These were computer as well as hardware simulations with a rather limited reference to the neurophysiological and histological data [ 1 ] - [3], [91, [ 11][15], [18] - [20] of the various vertebrate retinas. In order to interpret these extensive data (literature) new working hypotheses are constantly being developed. These hypotheses can be tested by the model [4] -[6] which is presented here. In contrast with simulations using large digital computers, the function of this electronic model that is structured as a kind of special purpose analog computer is evident and clearly arranged since it consists of artificial neurons with variable parameters capable of being connected in various combinations. THE ELECTRONIC MODEL For the model-design of a part of the vertebrate retina, the
operating range of the photoreceptors was limited to one decimal. All types of information processing, which in reality are either electrochemical or thermodynamic, were simulated by means of electronic components. All voltage time funcUs- + 10 V. The tions vary within a range of -10 V simulated nerve impulses have an impulse width of 1 msec. The model consists of 5 different types of nerve cell simulation circuits. There are 115 photoreceptors, 25 horizontal cells, 115 bipolar cells, 25 amacrine cells and 25 ganglion cells. The inputs and outputs of these neurons can be connected via patchboards (Fig. 1). The photoreceptor outer segments are simulated by cylindrical phototransistors with a light sensitive area of 2 mm in diameter. They are arranged together in maximal package density in a moveable head (Fig. 2) and are connected with the inner segments via a flexible cable. The bipolar cell models can, in principle, sum up to 7 receptor outputs. Each bipolar cell has an input for shunting inhibition [8]. The 25 horizontal cell models have connections with neighboring horizontals so that an input signal of one cell can spread laterally. The inputs and outputs are conducted to patchboards. Each horizontal cell has 7 inputs. The neural nets with a receptive field (RF) [1 ] as input surface and one single ganglion cell as output are circumscribed in the neurophysiological literature as "functional organization of receptive fields." These neural nets for which the term perceptive units (PU) is used in the model, are prepared by connections of the bipolar cell outputs with 25 passive summing networks for RF-centers and 25 networks for RF-peripheries. They represent a number of con...
Fig. 2. The entire model. The upper four and lower two frames hold power supplies and printed circuit cards. In the middle is an oscilloscope for the simultaneous demonstration of up to four signal functions. Below are five speakers with selectors to make the impulse activity of some ganglion cells audible. The rest of the front panel is covered with various patchboards and knobs for threshold and slope of the voltage-to-impulse rate converters in the ganglion cells. The light-sensitive area of the 115 phototransistors is moveable and connected with the other part of the receptor circuits via a flexible cable (on the table).
nections between bipolar cells and ganglion cells. A light stimulus to the center, i.e., to the inner area of a receptive field, elicits a response that is opposite to that elicited by the same light stimulus to the field periphery. Accordingly one differentiates between On-fields, where excitation increases when the center is stimulated and decreases when the periphery is stimulated, and Off-fields, where the opposite occurs [11]. In addition to this prepared possibility for the form of receptive fields with 7 center receptors and 30 surrounding periphery receptors (see also Fig. 8) other combinations can be chosen by means of the patchboards (Fig. 2). The 25 amacrine cells are connected similarly as the horizontals to each other. These inputs and outputs are conducted to patchboards. The threshold and steepness of the voltage-toimpulse rate converter of the ganglion cells may be varied by
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ECKMILLER: VERTEBRATE RETINA SIMULATION
means of potentiometers in the front panel. Finally the ganglion cell outputs are conducted to a patchboard and in parallel to loudspeakers. FUNCTION OF THE DIFFERENT CELL MODELS Photoreceptors show non-linear behavior at high input amplitudes [181 . This feature is qualitatively simulated with the circuit shown in Fig. 3. The response of this receptor circuit Photoreceptor to rectangular light stimulus time functions with various amjUrLV] E:?ia plitudes shows the increasing asymmetry between the transient at "light on" and "light off" for increasing stimulus amplitudes. The bipolar cell models evaluate the output signals from photoreceptors and horizontal cells. With a summer up to 7 receptor outputs can be summed after multiplication with a 0,2 0,4 0,6 0,8 1,0 72 t [sec Q2 0,4 0,6 0,8 1,0 i2 tf[sc weighting factor wi = 1/7. In the configuration described here Fig. 3. Circuit photoreceptor of a together with response curves for one receptor is attached to one bipolar with wi = 1. The simurectangular stimulations of the stimulus luminosity at various amplilation circuit and the output signals for rectangular light tudes. Letters a-d relate corresponding curves. stimuli presented on a preceding receptor circuit are given in -lo [v] Fig. 4. If Ub(t) is inverted by means of a synapse circuit (explained later), an Off-bipolar cell is obtained. 25,u [ ~ 10k 10k The existence of On- and Off-bipolar cells was demonstrated 50 68k~~~~~~~~~33 in neurophysiological experiments [19], [20] and is very 12-5 t likely to form the basis of antagonistically organized perceptive units with On-centers or Off-centers [5]. For the simulation of shunting inhibition [8] of bipolar cells by horizontal 'E [Ix] cells a simple circuit was developed. In principle an inhibitory Inhibition Input d signal causes a reduction of an excitatory signal by means of 76 0~~~~~0 ( shunting (amplitude reduction with a shunting resistor) prior to the excitatory synapse. Here the shunt is represented by LUbV -u the channel resistor of a field effect transistor (FET) which is 1L controlled by the inhibitory voltage. A FET channel resistance is approximately inversely proportional to the gate-source 6la~~~~~~~~~~~~~~~ voltage UGS for small drain-source voltages UDS. For the amplified resulting output voltage U, the following equation is q20,4 0,6 0,8 1,012 tJ q2o,40,6Qo,e02 1,4 1,6 1,8 2.0 valid: Fig. 4. Electronic circuit of a bipolar cell together with a comparison 6d
~~~~~~~0k
JB-
6_
Ua
=11+ h
-UH
U
with: U = excitatory input UH = inhibitory input h = inhibitory constant.
Horizontal cells (Fig. 5) sum up the output signals from several receptors after multiplication with a weighting factor wi = 1/7 as well as the output signals from immediate neighboring horizontals which are also weighted wi = 1/7. This is to make sure that on the one hand signals can travel with a spatial decrement in the layer of the horizontal cells, and on the other hand they do not reach self-oscillation because of the positive feedback from the neighboring horizontals. The horizontal outputs can be connected with the shunting inhibition inputs of single bipolar cells via patchboards. The simulation circuits form a bandpass with lower and upper break frequencies of 1 and 10 Hz, respectively. (Recently another alternative circuit was developed with lowpass properties and an upper break frequency at 20 Hz. The transfer properties of natural horizontals are still unknown in detail.) Between the layers of the bipolar cells and the ganglion cells
of stimulus and response curves for a receptor and a bipolar cell in series. Because of the bandpass properties of the bipolar cell the dccomponent gets suppressed.
1k
100)Ok
68k~~~~
25J
l0
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0
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~~~~51k
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Fig. 5. Simulation circuit of a horizontal cell (early version) or amacrine cell. The gain is set to V = 1 by means of the 50 k potentiometer to avoid self-oscillations of these cell layers.
there are the amacrine cells with varying numbers in the retinas of various vertebrates. As the horizontal cells they form a cell layer in which signals can travel with a spatial decrement to match the histological findings and to simulate lateral inhibition [8]. In this model they sum up the output signals from several bipolars and from the immediate neighboring amacrines after multiplication with a weighting factor
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1975
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lmsec
Inhibition Input -
Mono - Flop
Voltage- Impulserate-Converter
-
Threshold, .to[v
Fig. 6. Circuit of a ganglion cell. It consists of three parts. On the left is a circuit similar to the bipolar cell model except for an additional inverter which can be connected with the switch S. The following voltage-to-frequency converter is then modulated by the resulting voltage time function. Its converter characteristic can be shifted with the "threshold" potentiometer and turned with the "steepness" potentiometer. On the right is a mono vibrator which generates 1 msec pulses at a rate determined by the converter.
1/7. Their outputs can be connected with the shunting inhibition inputs of single ganglion cells or with one of the synapse circuits ASS (explained later) for the simulation of signal inversion or postsynaptic inhibition. The simulation circuit is similar to that shown in Fig. 5. In the vertebrate retina the last cell layer consists of ganglion cells. They convert the signal processing results of their perceptive units into impulse rate time functions, whereas the other retinal neurons operate with slow voltage time functions. These impulse trains are then conducted on nerve fibers to the next stage in the visual system. As known from histological findings [1], [3] each ganglion cell evaluates the output signals of bipolar cells and amacrines. In the model the summing point of each ganglion cell is conducted directly to the patchboard to sum bipolar outputs via passive summing networks or even via amacrines. An internal inverting amplifier for the inversion of the simulated membrane potential time function from depolarization (decreasing negative voltage) into hyperpolarization (increasing negative voltage) and vice versa is accessible by a switch S (Fig. 6) on the printed card. This is to simulate the possibility that all synapses on the ganglion cell are inverted. The entire simulation circuit (Fig. 6) is structured in the input part where continuous voltage time functions are evaluated as positive or negative with the possibility of shunting inhibition, and the output part which simulates that part of a nerve cell (axon hillock) where the signal conversion (modified after [17] ) into an impulse train occurs. At this phase in the development of the model this circuit is designed to perform a highly precise linear conversion rather than to fit the neurophysiological properties of natural neurons. The steepness as well as the range of operation of the converter are adjustable. Given a sinusoidal input signal Ug,e a shift of the operation range leads to a change in the impulse train (Fig. 7). This feature is to simulate various thresholds which can occur in ganglion cells.
wi
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Fig. 7. Comparison of input voltage Uge, membrane potential UM and impulse train of a ganglion cell for two values of the adjustable resting membrane potential UMO (threshold-potentiometer). It can be seen that impulses occur only at the positive half of the sine wave if UMO is shifted to 0 V.
indicate that intraretinal synapses often have signal inverting properties. Accordingly by use of the (-)-input a depolarizing signal is inverted into a hyperpolarizing one and vice versa. The difference between the signals occurring at the two inputs occurs currently at the output and represents the intracellular voltage of the neuron to which it belongs. The Add-SubtractSynapses can be used as part of horizontals, bipolars and amacrines, and mainly of ganglion cells via the patchboards.
SIMULATION OF DIFFERENT PERCEPTIVE UNITS (PU) Perceptive units as neural networks with receptive fields as input surface and single neurons at the output consist of various neurons. In the retina [5] their output neurons are the ganglion cells whereas a perceptive unit of a principal cell in the lateral geniculate body (the next major stage of the afferent visual pathway) will evaluate the output signals of several ganglion cells. Fig. 8 indicates the light sensitive area of the photoreceptor outer segments and their participation in the various receptive For an economical simulation of various synapses in the fields. The numbers 1 to 25 mark the receptors in the middle retina, the circuit for the general Add-Subtract-Synapse was of the 25 receptive fields which represent the input areas of designed on the basis of an operational amplifier with (+)- and the 25 perceptive units prepared by the passive summing net(-)-input. Each of these 25 circuits simulates synapses of works. Not only the RF-peripheries but also the RF-centers single neurons. Neurophysiological measurements [19], [20] are overlapping. Only the receptor in the middle of each field
ECKMILLER: VERTEBRATE RETINA SIMULATION
Fig. 8. Diagram of the distribution of 25 receptive fields over the surface of 115 photoreceptors. The numbers 1 to 25 designate the central receptors of the receptive fields. The field center belonging to the perceptive unit PU 13 is checkered and the field periphery indicated with horizontal lines. The arrangement implies that even the field centers overlap. In the model the surface area of the 115 phototransistors is 21 mm X 24 mm (see Fig. 2).
belongs to one center alone. Each of the 25 fields functions as the receiving surface for one of the 25 ganglion cells. If the horizontal and amacrine cells are used, there is an additional spreading of the signals within the cell layers which is indicated by histological and neurophysiological findings [ 1 ], [19]. Thus quite asymmetrical fields can be set for single ganglion cells. Furthermore, by inhibition of bipolar cells, symmetrical or asymmetrical perceptive units can be simulated already in the layer of the bipolar cells which respond antagonistically to the stimulation of certain receptors. Amacrine cells can also have antagonistic receptive fields [19]. This finding can be simulated as well. In view of the large number of possible perceptive units for bipolar cells, amacrines and ganglion cells, it is expedient to prepare 25 units for the ganglion cells by wiring the 50 passive summing networks which were described above. This enables the user of the model to arrange perceptive units of ganglion cells wi-th only very few plug-in connections. Since the bipolar cell models are connected 1: 1 to the receptors, Fig. 8 is also valid for the bipolar cell output level. PROPERTIES OF THE ENTIRE MODEL Since the model was designed for a partial interpretation of the extensive biological data (see Introduction), its functional properties should fit those of real neuronal networks in the retina as close as possible. Three examples for simulation results are presented here to demonstrate the power and flexibility of the model. Some further results are reported elsewhere [4] -[6]. First a methodological remark: the reciprocal values of the time intervals between two consecutive impulses will be referred to as the instantaneous impulse rate IR and ,designated by the dimension: impulses per second. A) Excitability-distribution of a perceptive unit PU with On-center: The stimulus was a light spot as large as the receptive field center which was switched on and off every second periodically and placed at various locations within the receptive field RF 13. In this case the PU consisted of ganglion cell
309
G 13 which evaluated the responses of the 7 receptors belonging to the center Z 13 and the 30 receptors belonging to the periphery P 13 via the corresponding bipolar cells, the passive summing networks for Z 13 and P 13 and the Add-SubtractSynapse 1. The spontaneous impulse rate IRo was adjusted to 20 impulses per second. The maximum impulse rate IRmax is defined here as the average value of the highest impulse rates for three stimulus periods. Fig. 9 shows the impulse rate difference values IRmax - IRo for the various stimulus locations given by the coordinates x and y. The excitability condition inverts if the stimulus location changes from a center position into a periphery position in that the maximum impulse rate is reached at "light on" in the center and at "light off' in the periphery. Values of IRmax - IRo at "light on" imply a strong impulse rate decrease at "light off' (see also Fig. 4) and vice versa. This antagonistic behavior of perceptive units in the retina is one of its fundamental features which was described by various authors [9], [11], [15]. In the model the opposite possibility, namely Off-fields, as well as various degrees of antagonism, can be achieved by simply changing the connections between the summed center and periphery signals and the inputs of the Add-Subtract-Synapses as well as by potentiometer changes in the ganglion cell circuit. Note that the antagonistic behavior in the simulation is achieved by evaluating all signal channels from the field center as positive and those from the periphery as negative. This is contradictory to the hypothesis that the well known antagonism is reached by the difference of two dome-shaped functions, a narrow and positive one for the center and a broad and negative one for the periphery [15]. B) Responses of a simulated On-neuron to moving stimuli: The PU with ganglion cell G13 at the output was structured as in example A). A disk of light on a dark background or dark disk on a light background was moved across the receptive field RF 13 at two velocities back and forth. The disk had the size of the RF-center (Fig. 10). Especially at the lower velocity two features are significant: 1) the response time functions for stimulation with light and dark disk are roughly inverse; 2) the response to a stimulus reaching the periphery from outside the field is weaker than for reaching the periphery again from the center. These two features have been found also in neurophysiological experiments (Fig. 11) where a light and a dark stimulus was moved across the receptive field of an On-neuron in the cat's retina [14]. The asymmetry of the response curve can be explained (for the simulation at least) as follows. Light on the periphery of an On-field elicits first a signal decrease and the following removal of the light stimulus elicits a signal increase. This increase coincides more or less with that elicited by the moving stimulus now reaching the field center. Finally when the stimulus leaves the center and reaches the periphery on the other side of the RF, a superposed signal decrease occurs, one from the periphery just reached and the other from the center which was just left. The inverted mechanism accounts for the inverted asymmetry in the response curve of the ganglion cell for the dark stimulus. It should be noted here that the same measurements on a simulated Off-neuron gave the same results with exchanged stimuli. In other words, the Off-neuron re-
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1975
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at light ON'
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Fig. 9. Excitability-distribution for an On-neuron. The spontaneous impulse rate IRo was adjusted to 20 (Imp/sec). The light stimulus was a disk of center size which was presented periodically at various locations given by the coordinates x and y (see the schematic map in the upper left). The connections at ganglion cell G 13 and the stimulus time course are given in the upper right. The curve for measurements along the median y = 0 mm is drawn with enhanced lines to demonstrate the typical antagonistic behavior of center and periphery. 10 A
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Dark Point Fig. 10. Impulse rate time functions of a simulated retinal perceptive unit PU 13 with an On-center to moving light (a), (b) or dark (c), (d) disks at two velocities over the receptive field. The stimulus had the size of the field center. The top traces give the movement time functions of the disks. The responses for left and right movements differ slightly (as in nature) because of various inhomogeneities in the various signal channals. The instantaneous impulse rate IR (Imp/sec) is superimposed for 10 consecutive trails. For the computer evaluation the dot of each rate value was set in the middle of the corresponding interval, which meets the special conditions of the voltage to impulse rate converter. Note that the single dots for the IR values lie precisely on a common curve. The movement velocities are given in relative values v' (DE/sec) where 1 DE = 12 mm = average diameter of a simulated receptive field.
1 4 3 2 0 Fig. 11. Response of two ganglion cells in the cat retina to moving light stimuli back and forth over their receptive fields (modified after [14]). Each response histogram was compiled from 30 repetitions whereby the occurring impulses were counted into consecutive time bins of 16 msec. (a) Response of an On-neuron to a light stimulus. (b) Response of an On-neuron to a dark stimulus. Dimension of the ordinate scale: impulses per second.
sponded to a light stimulus as the On-neuron to a dark one and vice versa. This is also in agreement with comparable
neurophysiological findings [ 14]. C) Simulation of the velocity function of class-2 neurons in
the frog retina: A detailed report is given elsewhere [6]. In order to interpret quantitative fmdings on the velocity function of certain classes of neurons in the frog retina [9] a simulation was attempted with the model. In Fig. 12 an example of the results is given. As reported for the movement sensitive
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ECKMILLER: VERTEBRATE RETINA SIMULATION
AcKNOWLEDGMENT The author wishes to thank Dr. 0. -J. Griisser, Professor of physiology at the Physiologisches Institut, Freie Universitat Berlin, for continuous valuable support of this project.
R I Imp/sec)
REFERENCES
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Fig. 12. Simulation of the relationship between the average impulse rate R and the stimulus angular velocity v for class-2 neurons in the frog retina. The slope m gives the exponent of the power function. Open and filled circles and crosses give the values for three different measuring cycles. At high stimulus velocities the ganglion cell stops generating impulses (in agreement to neurophysiological findings) and leads therefore to an abrupt drop of the curve.
class-2
neurons 9, the course of the average impulse rate R the angular velocity v of the light stimulus follows a function, then reaches a plateau for higher angular velocities which is then abruptly interrupted because at about 100 degrees per second these neurons stop generating impulses. Following the simplest hypothesis, receptors were connected directly to a ganglion cell in the model. The outputs of 7 center receptors were summed at the positive input and the outputs of the surrounding 30 periphery receptors were summed at the negative input of an Add-SubtractSynapse which functionally belongs to the ganglion cell membrane. The spontaneous impulse rate IRo was adjusted to .9 impulses per second. The exponent of the power function was .76 in the simulation which closely fits the reported value of .7 in the frog retina 9.
versus power
SUMMARY This paper describes the design and some applications of an electronic analog model of the vertebrate retina. Various parameters of the 315 discrete neuronal simulation circuits, as well as their interconnections, can be changed in order to simulate various retinal functions. It is shown that various neurophysiological findings, e.g., the antagonistic receptive field organization, the response patterns of retinal ganglion cells to moving stimuli, as well as the relationship between impulse rate and stimulus velocity for class-2 neurons in the frog retina, can be simulated very precisely. These results support certain working hypotheses concerning the function of the vertebrate retina.
[1] Ramon y Cajal, "Die Retina der Wirbeltiere," ubers. von Greeff, J. F. Bergmann, Wiesbaden 1890. [2] 0. Creutzfeldt and B. Sakmann, "Neurophysiology of vision," Ann. Rev. Physiol., vol. 31, pp. 499-544, 1969. [31 J. Dowling, "Synaptic organization of the frog retina: An electron microscopic analysis comparing the retinas of frogs and primates," Proc. Roy. Soc., (London), Ser. B, vol. 170, pp. 205227, 1968. [4] R. Eckmiller, "Electronic analog models of the retina and the visual system," in: Pattern Recognition in Biological and Technical Systems, Grusser and Klinke, eds., Springer, Berlin 1971. [5] R. Eckmiller, "Electronic simulation of retinal receptive fieldin vertebrates," in: Biocybernetics IV, Drischel and Dettma eds., Fischer, Jena 1972. [6] R. Eckmiller and 0. -J. Grusser, "Simulation of the sual function of movement detecting neurons," Bibl. opthal., vol. 82, pp. 274-279, Karger, Basel 1972. [7] K. Fukushima, "Visual feature extraction by- a multilayered network of analog threshold elements," IEEE Trans. Syst. Sc. Cyb., vol. SSC-5, pp. 322-333, 1969. [81 G. G. Furman, "Comparison of models for subtractive and shunting lateral inhibition in receptor-neurons fields," Kybernetik, vol. 2, pp. 257-274, 1965. [91 0. -J. Grusser and U. Grusser-Cornehls, "Neurophysiologie des Bewegungssehens," Rev. Physiol., vol. 61, pp. 178-265, 1969. [10] M. B. Herscher and T. P. Kelley, "Functional electronic model of the frog retina," IEEE Trans. Mil. El., vol. MIL-7, pp. 98-103, April 1963. [11] S. W. Kuffler, "Discharge patterns and functional organization of mammalian retina," J. Neurophysiol., vol. 16, pp. 37-68, 1953. [12] Th. Meikle and J. Sprague, "The neural organization of the visual pathways in the cat," Intern. Rev. Neurobiol., vol. 6, pp. 149189, 1964. [13] S. Polyak, "The vertebrate visual system," University of Chicago Press, 1957. [14] R. W. Rodieck and J. Stone, "Response of cat retinal ganglion cells to moving visual patterns," J. Neurophysiol., vol. 28, pp. 819-832, 1965. [15] R. W. Rodieck and J. Stone, "Analysis of receptive fields of cat retinal ganglion cells," J. Neurophysiol., vol. 28, 833-849, 1965. [16] R. G. Runge, M. Uemura, and S. S. Viglione, "Electronic synthesis of avian retina," IEEE Trans. Bio-Med. Eng., vol. BME-15, 138151, 1968. [17] K. C. Smith and A. Sedra, "Simple wideband voltage-to-frequency converter," Electronic Eng., vol. 40, pp. 140-143, 1968. [18] R. H. Steinberg, "High-intensity effects on slow potentials and ganglion cell activity in the area centralis of cat retina," Vision Res., vol. 9, pp. 333-350, 1969. [19] F. Werblin and J. Dowling, "Organization of the retina of the mudpuppy, Necturus maculosus. II. Intracellular recordings," J. Neurophysiol., vol. 32, pp. 339-355, 1969. [20] F. Werblin, "Response of retinal cells to moving spots: Intracellular recordings in Necturus maculosus," J. Neurophysiol., vol. 33, pp. 342-350, 1970.
The authors wish to thank B. A. Saunders and G. T. Manning [9] from the Department of Anesthesiology and S. J. Purves from the Department of Electroencephalography at the Vancouver General Hospital for their cooperation and assistance. The [101 help provided by M. E. Koombes of the Department of Electri- [111 cal Engineering of the University of British Columbia is gratefully acknowledged. [12]
REFERENCES [1] F. A. Gibbs, E. L. Gibbs, and W. G. Lennox, "Effect on the electroencephalogram of certain drugs which influence nervous activity," Arch. Intern. Med., vol. 60, pp. 154-166, July 1937. [2] M. A. Rubin and H. Freeman, "Brain potential changes in man during cyclopropane anesthesia," J. Neurophysiol., vol. 3, pp. 33-42, Jan. 1940. [3] R. F. Courtin, R. G. Bickford, and A. Faulkoner, Jr., "The classification and significance of electroencephalographic patterns produced by nitrous oxide-ether anesthesia during surgical operations," Proc. Staff Meet. Mayo Clin., vol. 25, pp. 197-206, 1950. [4] D. K. Kiersay, R. G. Bickford, and A. Faulkoner, Jr., "Electroencephalographic patterns produced by thiopental sodium during surgical operations: Description and classification," Br. J. Anesth., vol. 23, pp. 14 1-152, 195 1. [5] A. Faulkoner, Jr., "Correlation of concentration of ether in arterial blood with electroencephalographic patterns during etheroxygen and during nitrous oxide, oxygen and ether anesthesia of human surgical patients," Anesthesiology, vol. 13, pp. 361-369, July 1952. [6] S. Possati, A. Faulkoner, Jr., R. G. Bickford, et al., "Electroencephalographic patterns during anesthesia with cyclopropane: Correlation with coricentrations in arterial blood," Anesth. Analg. (Cleve.), vol. 32, pp. 130-135, 1953. [71 D. L. Clark and B. S. Rosner, "Neurophysiological effects of general anesthetics: The electroencephalogram and sensory evoked responses in man," Anesthesiology, vol. 38, pp. 564-582, June 1973. [8] J. T. Martin, A. Faulkoner, Jr., and R. G. Bickford, "Electro-
[131 [14] [15]
[161 [17]
[181 [19]
[20] [211 [22]
[23]
305
encephalography in anesthesiology," Anesthesiology, vol. 20, pp. 359-376, May 1959. V. L. Brechner, R. D. Walter, and J. B. Dillon, Practical Electroencephalography for the Anesthesiologist. Springfield: Thomas, 1962. J. Volavka, M. Matousek, S. Feldstein et al., "The reliability of EEG assessment," EEG-EMG, in press. E. A. Gain and S. G. Paletz, "An attempt to correlate the clinical signs of fluothane anesthesia with the electroencephalographic levels," Can. Anaesth. Soc. J., vol. 4, pp. 289-294, July 1957. S. J. Galla, A. K. Olmedo, H. E. Kretchmer, et al., "Correlation of EEG patterns with arterial concentrations and clinical signs during halothane anesthesia," Anesthesiology, vol. 23, pp. 147-148, Jan. 1962. E. Lowenstein, "Morphine 'anesthesia'-a perspective," Anesthesiology, vol. 35, pp. 563-565, Dec. 1971. L. Kanal and B. Chandrasekaran, "On dimensionality and sample size in statistical pattern classification," Patt. Recog., vol. 3, pp. 225-234, Oct. 1971. R. 0. Duda and P. E. Hart, Pattern Classification and Scene Analysis. New York: Wiley, 1973. I. J. Good, The Estimation ofProbabilities, Research Monograph 30. Cambridge, Mass.: M.I.T. Press, 1965. G. T. Toussaint and P. M. Sharpe, "An efficient method for estimating the probability of misclassification applied to a problem in medical diagnosis," Comput. Biol. Med., in press. G. Nagy, "State- of the art in pattern recognition," Proc. IEEE, vol. 56, pp. 836-862, May 1968. J. R. Cox, Jr., F. M. Nolle, and R. M. Arthur, "Digital analysis of the electroencephalogram, the blood pressure wave and the electrocardiogram," Proc. IEEE, vol. 60, pp. 1137-1164, Oct. 1972. B. Kleiner, H. Fluhler, P. J. Huber, and G. Dumermuth, "Spectral analysis of the electroencephalogram," Comp. Progr. Biomed., vol. 1, pp. 183-197, 1970. G. Dumermuth, W. Waltz, G. Scollo-Lavizzari, et al., "Spectral analysis of EEG activity in different sleep stages in normal adults," Europ. Neurol., vol. 7, pp. 265-296, July 1972. N. R. Burch, "Period analysis of the EEG on a general-purpose digital computer," Ann. N. Y. Acad. Sci., vol. 115, pp. 827-843, 1964. G. Dumermuth, P. J. Huber, B. Kleiner and T. Gasser, "Numerical analysis of electroencephalographic data," IEEE Trans. Audio Electroacoust., vol. AU-18, pp. 404-411, December 1970.
Electronic Simulation of the Vertebrate Retina ROLF ECKMILLER
-Abstract-An electronic analog model of a section of the vertebrate retina has been constructed. It is structured in 5 layers of cells corresponding to the structure of the natural retina, whereby the function and connections of the single cell models can be varied. While signal processing occurs in the first four layers by evaluating several timedependent slow potentials as positive or negative, impulse rate tine functions are emitted from the ganglion cells at the retina output. Various neural networks as inputs for the 25 Ganglion cells can be realized by using various patchboard connections. Several examples for
Manuscript received January 31, 1974; revised August 27, 1974. This work was supported by a grant from the Stiftung Volkswagenwerk. The author is with the Freie Universitat Berlin, Physiologisches Institut, Fachbereich 1-Vorklinik, 1 Berlin 33, Arnimallee 22, Germany.
simulation results are presented which closely fit comparable neurophysiological findings.
INTRODUCTION T HE function of the vertebrate retina has received attention from many scientists in various fields ranging from ophthalmnology via neurophysiology to biomathematics and engineering. The neural network of the human retina, for example, with about 120 million photoreceptors and about 1.2 million ganglion cells at the output layer participates in various tasks, e.g., pattern recognition, color, motion, and depth perception. This encouraged several approaches to simulate parts
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25 Horizontal Cells
25Amacrine Cells
Fig. 1. Block diagram of the retina model. The patchboards are indicated by the cell contacts which they include, i.e., r,j - rails for the output contacts of receptors 1 to 115. The patchboards for 25 centers and 25 peripheries correspond to passive summing networks (see text). The Add-Subtract-Synapses are operational amplifiers with differential inputs to simulate neural contacts (synapses).
of the retina [71, [10], [16]. These were computer as well as hardware simulations with a rather limited reference to the neurophysiological and histological data [ 1 ] - [3], [91, [ 11][15], [18] - [20] of the various vertebrate retinas. In order to interpret these extensive data (literature) new working hypotheses are constantly being developed. These hypotheses can be tested by the model [4] -[6] which is presented here. In contrast with simulations using large digital computers, the function of this electronic model that is structured as a kind of special purpose analog computer is evident and clearly arranged since it consists of artificial neurons with variable parameters capable of being connected in various combinations. THE ELECTRONIC MODEL For the model-design of a part of the vertebrate retina, the
operating range of the photoreceptors was limited to one decimal. All types of information processing, which in reality are either electrochemical or thermodynamic, were simulated by means of electronic components. All voltage time funcUs- + 10 V. The tions vary within a range of -10 V simulated nerve impulses have an impulse width of 1 msec. The model consists of 5 different types of nerve cell simulation circuits. There are 115 photoreceptors, 25 horizontal cells, 115 bipolar cells, 25 amacrine cells and 25 ganglion cells. The inputs and outputs of these neurons can be connected via patchboards (Fig. 1). The photoreceptor outer segments are simulated by cylindrical phototransistors with a light sensitive area of 2 mm in diameter. They are arranged together in maximal package density in a moveable head (Fig. 2) and are connected with the inner segments via a flexible cable. The bipolar cell models can, in principle, sum up to 7 receptor outputs. Each bipolar cell has an input for shunting inhibition [8]. The 25 horizontal cell models have connections with neighboring horizontals so that an input signal of one cell can spread laterally. The inputs and outputs are conducted to patchboards. Each horizontal cell has 7 inputs. The neural nets with a receptive field (RF) [1 ] as input surface and one single ganglion cell as output are circumscribed in the neurophysiological literature as "functional organization of receptive fields." These neural nets for which the term perceptive units (PU) is used in the model, are prepared by connections of the bipolar cell outputs with 25 passive summing networks for RF-centers and 25 networks for RF-peripheries. They represent a number of con...
Fig. 2. The entire model. The upper four and lower two frames hold power supplies and printed circuit cards. In the middle is an oscilloscope for the simultaneous demonstration of up to four signal functions. Below are five speakers with selectors to make the impulse activity of some ganglion cells audible. The rest of the front panel is covered with various patchboards and knobs for threshold and slope of the voltage-to-impulse rate converters in the ganglion cells. The light-sensitive area of the 115 phototransistors is moveable and connected with the other part of the receptor circuits via a flexible cable (on the table).
nections between bipolar cells and ganglion cells. A light stimulus to the center, i.e., to the inner area of a receptive field, elicits a response that is opposite to that elicited by the same light stimulus to the field periphery. Accordingly one differentiates between On-fields, where excitation increases when the center is stimulated and decreases when the periphery is stimulated, and Off-fields, where the opposite occurs [11]. In addition to this prepared possibility for the form of receptive fields with 7 center receptors and 30 surrounding periphery receptors (see also Fig. 8) other combinations can be chosen by means of the patchboards (Fig. 2). The 25 amacrine cells are connected similarly as the horizontals to each other. These inputs and outputs are conducted to patchboards. The threshold and steepness of the voltage-toimpulse rate converter of the ganglion cells may be varied by
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ECKMILLER: VERTEBRATE RETINA SIMULATION
means of potentiometers in the front panel. Finally the ganglion cell outputs are conducted to a patchboard and in parallel to loudspeakers. FUNCTION OF THE DIFFERENT CELL MODELS Photoreceptors show non-linear behavior at high input amplitudes [181 . This feature is qualitatively simulated with the circuit shown in Fig. 3. The response of this receptor circuit Photoreceptor to rectangular light stimulus time functions with various amjUrLV] E:?ia plitudes shows the increasing asymmetry between the transient at "light on" and "light off" for increasing stimulus amplitudes. The bipolar cell models evaluate the output signals from photoreceptors and horizontal cells. With a summer up to 7 receptor outputs can be summed after multiplication with a 0,2 0,4 0,6 0,8 1,0 72 t [sec Q2 0,4 0,6 0,8 1,0 i2 tf[sc weighting factor wi = 1/7. In the configuration described here Fig. 3. Circuit photoreceptor of a together with response curves for one receptor is attached to one bipolar with wi = 1. The simurectangular stimulations of the stimulus luminosity at various amplilation circuit and the output signals for rectangular light tudes. Letters a-d relate corresponding curves. stimuli presented on a preceding receptor circuit are given in -lo [v] Fig. 4. If Ub(t) is inverted by means of a synapse circuit (explained later), an Off-bipolar cell is obtained. 25,u [ ~ 10k 10k The existence of On- and Off-bipolar cells was demonstrated 50 68k~~~~~~~~~33 in neurophysiological experiments [19], [20] and is very 12-5 t likely to form the basis of antagonistically organized perceptive units with On-centers or Off-centers [5]. For the simulation of shunting inhibition [8] of bipolar cells by horizontal 'E [Ix] cells a simple circuit was developed. In principle an inhibitory Inhibition Input d signal causes a reduction of an excitatory signal by means of 76 0~~~~~0 ( shunting (amplitude reduction with a shunting resistor) prior to the excitatory synapse. Here the shunt is represented by LUbV -u the channel resistor of a field effect transistor (FET) which is 1L controlled by the inhibitory voltage. A FET channel resistance is approximately inversely proportional to the gate-source 6la~~~~~~~~~~~~~~~ voltage UGS for small drain-source voltages UDS. For the amplified resulting output voltage U, the following equation is q20,4 0,6 0,8 1,012 tJ q2o,40,6Qo,e02 1,4 1,6 1,8 2.0 valid: Fig. 4. Electronic circuit of a bipolar cell together with a comparison 6d
~~~~~~~0k
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-UH
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with: U = excitatory input UH = inhibitory input h = inhibitory constant.
Horizontal cells (Fig. 5) sum up the output signals from several receptors after multiplication with a weighting factor wi = 1/7 as well as the output signals from immediate neighboring horizontals which are also weighted wi = 1/7. This is to make sure that on the one hand signals can travel with a spatial decrement in the layer of the horizontal cells, and on the other hand they do not reach self-oscillation because of the positive feedback from the neighboring horizontals. The horizontal outputs can be connected with the shunting inhibition inputs of single bipolar cells via patchboards. The simulation circuits form a bandpass with lower and upper break frequencies of 1 and 10 Hz, respectively. (Recently another alternative circuit was developed with lowpass properties and an upper break frequency at 20 Hz. The transfer properties of natural horizontals are still unknown in detail.) Between the layers of the bipolar cells and the ganglion cells
of stimulus and response curves for a receptor and a bipolar cell in series. Because of the bandpass properties of the bipolar cell the dccomponent gets suppressed.
1k
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Fig. 5. Simulation circuit of a horizontal cell (early version) or amacrine cell. The gain is set to V = 1 by means of the 50 k potentiometer to avoid self-oscillations of these cell layers.
there are the amacrine cells with varying numbers in the retinas of various vertebrates. As the horizontal cells they form a cell layer in which signals can travel with a spatial decrement to match the histological findings and to simulate lateral inhibition [8]. In this model they sum up the output signals from several bipolars and from the immediate neighboring amacrines after multiplication with a weighting factor
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1975
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lmsec
Inhibition Input -
Mono - Flop
Voltage- Impulserate-Converter
-
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Fig. 6. Circuit of a ganglion cell. It consists of three parts. On the left is a circuit similar to the bipolar cell model except for an additional inverter which can be connected with the switch S. The following voltage-to-frequency converter is then modulated by the resulting voltage time function. Its converter characteristic can be shifted with the "threshold" potentiometer and turned with the "steepness" potentiometer. On the right is a mono vibrator which generates 1 msec pulses at a rate determined by the converter.
1/7. Their outputs can be connected with the shunting inhibition inputs of single ganglion cells or with one of the synapse circuits ASS (explained later) for the simulation of signal inversion or postsynaptic inhibition. The simulation circuit is similar to that shown in Fig. 5. In the vertebrate retina the last cell layer consists of ganglion cells. They convert the signal processing results of their perceptive units into impulse rate time functions, whereas the other retinal neurons operate with slow voltage time functions. These impulse trains are then conducted on nerve fibers to the next stage in the visual system. As known from histological findings [1], [3] each ganglion cell evaluates the output signals of bipolar cells and amacrines. In the model the summing point of each ganglion cell is conducted directly to the patchboard to sum bipolar outputs via passive summing networks or even via amacrines. An internal inverting amplifier for the inversion of the simulated membrane potential time function from depolarization (decreasing negative voltage) into hyperpolarization (increasing negative voltage) and vice versa is accessible by a switch S (Fig. 6) on the printed card. This is to simulate the possibility that all synapses on the ganglion cell are inverted. The entire simulation circuit (Fig. 6) is structured in the input part where continuous voltage time functions are evaluated as positive or negative with the possibility of shunting inhibition, and the output part which simulates that part of a nerve cell (axon hillock) where the signal conversion (modified after [17] ) into an impulse train occurs. At this phase in the development of the model this circuit is designed to perform a highly precise linear conversion rather than to fit the neurophysiological properties of natural neurons. The steepness as well as the range of operation of the converter are adjustable. Given a sinusoidal input signal Ug,e a shift of the operation range leads to a change in the impulse train (Fig. 7). This feature is to simulate various thresholds which can occur in ganglion cells.
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indicate that intraretinal synapses often have signal inverting properties. Accordingly by use of the (-)-input a depolarizing signal is inverted into a hyperpolarizing one and vice versa. The difference between the signals occurring at the two inputs occurs currently at the output and represents the intracellular voltage of the neuron to which it belongs. The Add-SubtractSynapses can be used as part of horizontals, bipolars and amacrines, and mainly of ganglion cells via the patchboards.
SIMULATION OF DIFFERENT PERCEPTIVE UNITS (PU) Perceptive units as neural networks with receptive fields as input surface and single neurons at the output consist of various neurons. In the retina [5] their output neurons are the ganglion cells whereas a perceptive unit of a principal cell in the lateral geniculate body (the next major stage of the afferent visual pathway) will evaluate the output signals of several ganglion cells. Fig. 8 indicates the light sensitive area of the photoreceptor outer segments and their participation in the various receptive For an economical simulation of various synapses in the fields. The numbers 1 to 25 mark the receptors in the middle retina, the circuit for the general Add-Subtract-Synapse was of the 25 receptive fields which represent the input areas of designed on the basis of an operational amplifier with (+)- and the 25 perceptive units prepared by the passive summing net(-)-input. Each of these 25 circuits simulates synapses of works. Not only the RF-peripheries but also the RF-centers single neurons. Neurophysiological measurements [19], [20] are overlapping. Only the receptor in the middle of each field
ECKMILLER: VERTEBRATE RETINA SIMULATION
Fig. 8. Diagram of the distribution of 25 receptive fields over the surface of 115 photoreceptors. The numbers 1 to 25 designate the central receptors of the receptive fields. The field center belonging to the perceptive unit PU 13 is checkered and the field periphery indicated with horizontal lines. The arrangement implies that even the field centers overlap. In the model the surface area of the 115 phototransistors is 21 mm X 24 mm (see Fig. 2).
belongs to one center alone. Each of the 25 fields functions as the receiving surface for one of the 25 ganglion cells. If the horizontal and amacrine cells are used, there is an additional spreading of the signals within the cell layers which is indicated by histological and neurophysiological findings [ 1 ], [19]. Thus quite asymmetrical fields can be set for single ganglion cells. Furthermore, by inhibition of bipolar cells, symmetrical or asymmetrical perceptive units can be simulated already in the layer of the bipolar cells which respond antagonistically to the stimulation of certain receptors. Amacrine cells can also have antagonistic receptive fields [19]. This finding can be simulated as well. In view of the large number of possible perceptive units for bipolar cells, amacrines and ganglion cells, it is expedient to prepare 25 units for the ganglion cells by wiring the 50 passive summing networks which were described above. This enables the user of the model to arrange perceptive units of ganglion cells wi-th only very few plug-in connections. Since the bipolar cell models are connected 1: 1 to the receptors, Fig. 8 is also valid for the bipolar cell output level. PROPERTIES OF THE ENTIRE MODEL Since the model was designed for a partial interpretation of the extensive biological data (see Introduction), its functional properties should fit those of real neuronal networks in the retina as close as possible. Three examples for simulation results are presented here to demonstrate the power and flexibility of the model. Some further results are reported elsewhere [4] -[6]. First a methodological remark: the reciprocal values of the time intervals between two consecutive impulses will be referred to as the instantaneous impulse rate IR and ,designated by the dimension: impulses per second. A) Excitability-distribution of a perceptive unit PU with On-center: The stimulus was a light spot as large as the receptive field center which was switched on and off every second periodically and placed at various locations within the receptive field RF 13. In this case the PU consisted of ganglion cell
309
G 13 which evaluated the responses of the 7 receptors belonging to the center Z 13 and the 30 receptors belonging to the periphery P 13 via the corresponding bipolar cells, the passive summing networks for Z 13 and P 13 and the Add-SubtractSynapse 1. The spontaneous impulse rate IRo was adjusted to 20 impulses per second. The maximum impulse rate IRmax is defined here as the average value of the highest impulse rates for three stimulus periods. Fig. 9 shows the impulse rate difference values IRmax - IRo for the various stimulus locations given by the coordinates x and y. The excitability condition inverts if the stimulus location changes from a center position into a periphery position in that the maximum impulse rate is reached at "light on" in the center and at "light off' in the periphery. Values of IRmax - IRo at "light on" imply a strong impulse rate decrease at "light off' (see also Fig. 4) and vice versa. This antagonistic behavior of perceptive units in the retina is one of its fundamental features which was described by various authors [9], [11], [15]. In the model the opposite possibility, namely Off-fields, as well as various degrees of antagonism, can be achieved by simply changing the connections between the summed center and periphery signals and the inputs of the Add-Subtract-Synapses as well as by potentiometer changes in the ganglion cell circuit. Note that the antagonistic behavior in the simulation is achieved by evaluating all signal channels from the field center as positive and those from the periphery as negative. This is contradictory to the hypothesis that the well known antagonism is reached by the difference of two dome-shaped functions, a narrow and positive one for the center and a broad and negative one for the periphery [15]. B) Responses of a simulated On-neuron to moving stimuli: The PU with ganglion cell G13 at the output was structured as in example A). A disk of light on a dark background or dark disk on a light background was moved across the receptive field RF 13 at two velocities back and forth. The disk had the size of the RF-center (Fig. 10). Especially at the lower velocity two features are significant: 1) the response time functions for stimulation with light and dark disk are roughly inverse; 2) the response to a stimulus reaching the periphery from outside the field is weaker than for reaching the periphery again from the center. These two features have been found also in neurophysiological experiments (Fig. 11) where a light and a dark stimulus was moved across the receptive field of an On-neuron in the cat's retina [14]. The asymmetry of the response curve can be explained (for the simulation at least) as follows. Light on the periphery of an On-field elicits first a signal decrease and the following removal of the light stimulus elicits a signal increase. This increase coincides more or less with that elicited by the moving stimulus now reaching the field center. Finally when the stimulus leaves the center and reaches the periphery on the other side of the RF, a superposed signal decrease occurs, one from the periphery just reached and the other from the center which was just left. The inverted mechanism accounts for the inverted asymmetry in the response curve of the ganglion cell for the dark stimulus. It should be noted here that the same measurements on a simulated Off-neuron gave the same results with exchanged stimuli. In other words, the Off-neuron re-
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1975
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Dark Point Fig. 10. Impulse rate time functions of a simulated retinal perceptive unit PU 13 with an On-center to moving light (a), (b) or dark (c), (d) disks at two velocities over the receptive field. The stimulus had the size of the field center. The top traces give the movement time functions of the disks. The responses for left and right movements differ slightly (as in nature) because of various inhomogeneities in the various signal channals. The instantaneous impulse rate IR (Imp/sec) is superimposed for 10 consecutive trails. For the computer evaluation the dot of each rate value was set in the middle of the corresponding interval, which meets the special conditions of the voltage to impulse rate converter. Note that the single dots for the IR values lie precisely on a common curve. The movement velocities are given in relative values v' (DE/sec) where 1 DE = 12 mm = average diameter of a simulated receptive field.
1 4 3 2 0 Fig. 11. Response of two ganglion cells in the cat retina to moving light stimuli back and forth over their receptive fields (modified after [14]). Each response histogram was compiled from 30 repetitions whereby the occurring impulses were counted into consecutive time bins of 16 msec. (a) Response of an On-neuron to a light stimulus. (b) Response of an On-neuron to a dark stimulus. Dimension of the ordinate scale: impulses per second.
sponded to a light stimulus as the On-neuron to a dark one and vice versa. This is also in agreement with comparable
neurophysiological findings [ 14]. C) Simulation of the velocity function of class-2 neurons in
the frog retina: A detailed report is given elsewhere [6]. In order to interpret quantitative fmdings on the velocity function of certain classes of neurons in the frog retina [9] a simulation was attempted with the model. In Fig. 12 an example of the results is given. As reported for the movement sensitive
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ECKMILLER: VERTEBRATE RETINA SIMULATION
AcKNOWLEDGMENT The author wishes to thank Dr. 0. -J. Griisser, Professor of physiology at the Physiologisches Institut, Freie Universitat Berlin, for continuous valuable support of this project.
R I Imp/sec)
REFERENCES
*01
.'
*05 *1
I
*5
'-1 l
-
5
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Fig. 12. Simulation of the relationship between the average impulse rate R and the stimulus angular velocity v for class-2 neurons in the frog retina. The slope m gives the exponent of the power function. Open and filled circles and crosses give the values for three different measuring cycles. At high stimulus velocities the ganglion cell stops generating impulses (in agreement to neurophysiological findings) and leads therefore to an abrupt drop of the curve.
class-2
neurons 9, the course of the average impulse rate R the angular velocity v of the light stimulus follows a function, then reaches a plateau for higher angular velocities which is then abruptly interrupted because at about 100 degrees per second these neurons stop generating impulses. Following the simplest hypothesis, receptors were connected directly to a ganglion cell in the model. The outputs of 7 center receptors were summed at the positive input and the outputs of the surrounding 30 periphery receptors were summed at the negative input of an Add-SubtractSynapse which functionally belongs to the ganglion cell membrane. The spontaneous impulse rate IRo was adjusted to .9 impulses per second. The exponent of the power function was .76 in the simulation which closely fits the reported value of .7 in the frog retina 9.
versus power
SUMMARY This paper describes the design and some applications of an electronic analog model of the vertebrate retina. Various parameters of the 315 discrete neuronal simulation circuits, as well as their interconnections, can be changed in order to simulate various retinal functions. It is shown that various neurophysiological findings, e.g., the antagonistic receptive field organization, the response patterns of retinal ganglion cells to moving stimuli, as well as the relationship between impulse rate and stimulus velocity for class-2 neurons in the frog retina, can be simulated very precisely. These results support certain working hypotheses concerning the function of the vertebrate retina.
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