10 Circuit Designs That Model the Properties Kareem A. Zaghloul,

10 Circuit Designs That Model the Properties Kareem A. Zaghloul,
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10
Circuit Designs That Model the Properties
of the Outer and Inner Retina
Kareem A. Zaghloul, MD, PhD and Kwabena Boahen, PhD
CONTENTS
SILICON MODELS
OUTER RETINA
INNER RETINA
SILICON CHIP LAYOUT
SILICON RETINA RESPONSES
CONCLUSIONS
REFERENCES
SILICON MODELS
One goal of understanding neural systems is to develop prosthetic devices that can
someday be used to replace lesioned neural tissue. For such prosthesis to be practical,
the device must perform these computations as efficiently as, and at a physical scale
comparable with the lesioned network, and should adapt its properties over time, independent of external control. The approach to design a successful prosthesis that faithfully replicates the computations performed by a neural circuit is based on a detailed
understanding of that circuit’s anatomic connections and functional computations.
The retina, one of the best studied neural systems is a complex piece of biological
wetware designed to signal the onset or offset of visual stimuli in a sustained or transient fashion (1). To encode its signals into spike patterns for transmission to higher
processing centers, the retina has evolved intricate neuronal circuits that capture information, efficiently contained within natural scenes (2). This visual preprocessing, realized by the retina, occurs in two stages, the outer retina and the inner retina. Each local
retinal microcircuit plays a specific role in the retina’s function, and neurophysiologists
have extracted a wealth of data characterizing how its constituent cell types contribute
to visual processing. These physiological functions can be replicated in artificial systems
by emulating their underlying synaptic interactions.
From: Ophthalmology Research: Visual Prosthesis and Ophthalmic Devices: New Hope in Sight
Edited by: J. Tombran-Tink, C. Barnstable, and J. F. Rizzo © Humana Press Inc., Totowa, NJ
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Present attempts to engineer a viable retinal prosthesis have focused on the significant problem of efficient electrical stimulation of neurons along the visual pathway
(3,4). Microelectrode arrays, implanted epiretinally or subretinally, evoke phosphenes
in patients with visual loss (because of outer retinal degeneration) by relying on electrical stimulation of the remaining retinal cells to dictate firing patterns (5,6). Whereas
the epiretinal approach relies on an external camera to capture visual information and
on an external processor to recreate retinal computation, subretinal devices use photodiodes embedded in the electrode array to locally transduce light into stimulating current. Cortical visual prostheses address disease processes affecting structures
postsynaptic to the outer retina (7,8). They are similar to epiretinal prostheses in that
they also depend on external devices to capture and process visual information, but
they must fully recreate thalamic function as well as retinal function.
Whereas the emphasis on electrical stimulation technology is important in addressing the difficult problem of interfacing with the nervous system, a fully implantable
retinal prosthesis would ideally capture all of the functions performed by the mammalian retina in one autonomous device. These neural computations can be performed
at an energy efficiency and physical scale comparable with biology by morphing neural
circuits into electronic circuits (9). Micron-sized transistors function as excitatory or
inhibitory synapses or as gap junctions, thereby recreating the synaptic organization of
the retina at a similar physical scale. The time-scale and energy dissipation can be
matched as well by operating these transistors in the subthreshold region, where they
conduct nanoamperes or even picoamperes, just like small populations of ion channels
do. Furthermore, as millions of transistors can be fabricated on a thumb-nail-sized
piece of silicon using very large scale integration technology, this neuromorphic
approach offers a fully implantable solution for neural prostheses. This implementation
efficiency is translated to a higher ability to explore model parameters to further understand the underlying biological system and, by communicating with other neuromorphic chips, a higher ability to replicate more complicated neural systems.
The first effort to morph the retina into silicon, though widely acclaimed, suffered
from several shortcomings. First, only outer retina circuitry was morphed: the cones,
horizontal cells (HC), and bipolar cells (BC) (10). Second, a logarithmic photoreceptor
(cf., cone) was used to capture a wide intensity range, but this degraded the signal-tonoise ratio by attenuating large amplitudes (i.e., signal) whereas leaving small amplitudes (i.e., noise) unchanged. Third, the spatiotemporal average (cf., HC) was
subtracted to obtain contrast (cf., bipolar signal) or more precisely, the logarithm of
contrast, but this made the signal-to-noise ratio even worse. Subsequent efforts (11)
overcame these limitations by modulating synaptic strengths locally to control sensitivity,
and by including the cone-to-cone gap junctions to attenuate noise. But they still omitted
the inner retina, which contains upwards of 44 cell types (12).
The most recent effort to model retinal processing in silicon incorporated outer
retina circuitry as well as bipolar and amacrine cell interactions in the inner retina
(13). This outer retina circuit took the difference between the photoreceptor signal and
its spatiotemporal average, computed by a network of coupled lateral elements HCs,
through negative (inhibitory) feedback. Cone-coupling in this model attenuated highfrequency noise to realize a spatial bandpass filter and dynamic range was extended
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by implementing local automatic gain control. Furthermore, this model used HC activity to boost cone to HC excitation (13), which eliminated the luminance-dependent
receptive-field expansion and temporal instability that plagued previous efforts to modulate synaptic strengths locally (14). This gain boosting mechanism has some physiological basis as glutamate release from cones is modulated by HC hemichannels (15),
and may be enhanced further by HC autofeedback (16). The outer retina design adopts
this approach.
The bipolar and amacrine cell interactions, introduced by this earlier design, represented a model for inner retina processing that much like the circuit discussed here,
attempted to capture temporal adaptation through adjustment of amacrine cell feedback
inhibition. However, this earlier design did not include the retina’s complementary
push-pull architecture (1). Hence, at low frequency stimulation, baseline direct current
(DC) levels tended to rise, and thus, modulation of the feedback loop gain was not realized as intended (13). Furthermore, this previous implementation did not replicate
synaptic interactions at the ganglion cell level, and thus, did not faithfully capture the
behavior of the retina’s major output pathways.
A silicon retina has been developed modeled on neural circuitry in both the outer
and inner retina that addresses the design flaws in earlier designs (13) and extends them
to include ganglion-cell level synaptic interactions. The model is based on the functional architecture of the mammalian retina and on physiological studies that have characterized the computations performed by the retina. By capturing both outer and inner
retina circuitry using single-transistor synapses, the silicon retina, which was built,
passes only an intermediate range of frequencies. It attenuates redundant low spatiotemporal frequencies and rejects noisy high frequencies, much like the retina does.
And by modulating the strengths of its single-transistor synapses locally, the device
adapts to luminance and to contrast. It responds faster, but more transiently as contrast
increases, much like the retina does. This contrast gain control arises from a new inner
retina circuit design that assigns specific roles to anatomically identified microcircuits
in the mammalian retina.
This silicon retina outputs spike trains that capture the behavior of ON- and OFFcenter (17) versions of wide-field transient and narrow-field sustained ganglion cells
(GC) (18), which provide ninety percent of the primate retina’s optic nerve fibers
(19). And, more significant for a prosthetic application, these are the four major
types that project through thalamus, to primary visual cortex. Furthermore, the silicon circuit is constructed at a scale comparable with the human retina and uses
under a tenth of a watt, thereby satisfying the requirements of a fully implantable
prosthesis.
This chapter describes the silicon implementation of the outer and inner retina circuits. It is organized as follows: In outer retina section, the outer retina model and its
silicon implementation are presented. In inner retina section, the novel model for the
inner retina and its silicon implementation are presented. In silicon chip layout section,
the architecture of the silicon chip layout is presented. In silicon retina response
section, the responses of the silicon retina to physiological stimuli are described and
are compared with those of the mammalian retina. Finally, conclusion section concludes the article.
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OUTER RETINA
The model for outer retinal circuitry is based on identified synaptic interactions and
local microcircuits previously described in the literature, obtained using histological
and physiological techniques. After constructing this model of the outer retina’s synaptic connections, it is used as a blueprint with which the silicon retina is assembled.
Modeling the Outer Retina
The model for the outer retina (Fig. 1A) is designed to realize luminance adaptation
by adjusting synaptic strengths locally. Photocurrents from the cone outer segments
(CO) in the model drive a network of cone terminals, which subsequently, excite a
network of HCs. Because they are coupled through gap junctions, these HCs compute
the local average intensity in the model. This signal is used to modulate cone-to-cone
coupling strength as well as the cone’s membrane conductance (shunting inhibition).
Using the local intensity signal to adjust these two synaptic strengths makes the cone
terminal’s sensitivity inversely proportional to luminance, whereas preventing the
changes in spatial frequency tuning that plagued previous attempts at light adaptation
(11). To compensate for the resulting signal attenuation at the cone terminal, the HC’s
local intensity signal is also used to modulate the cone-to-HC synaptic strength. This
autofeedback mechanism, whereby the HC regulates its own input, is similar to that
found in the retina (15,16).
From the synaptic interactions, the block diagram was derived for the outer retina
shown in Fig. 1B by modeling both the cone and HC networks as spatial lowpass filters. The system level equations can be derived that describe how CO activity determines HC and cone terminal activity, represented by ihc and ict, respectively, from this
block diagram. These equations, reproduced from ref. 13 are as follows:



i
A
 co
ihc (ρ) = 
 l 2 ρ2 + 1 l 2 ρ2 + 1 + A  B
h
 c
B
(
)(
)



i
lh2 ρ2 + 1
 co
ict (ρ) = 
A
 l 2 ρ2 + 1 l 2 ρ2 + 1 +  B
h
 c
B
(
(
)(
)
)
where ico represents CO activity, excited by photocurrents, lc and lh are the cone- and
horizontal-network space-constants, respectively, B is the attenuation from the CO to
the cone terminal, A is the amplification from cone terminal to HC, and ρ is spatial frequency. HCs have stronger coupling in the model (i.e., lh is larger than lc), causing their
spatial lowpass filter to attenuate lower spatial frequencies. Thus, HCs lowpass filter
the signal whereas cone terminals bandpass filter it, as shown in Fig. 1C, contributing
to the GCs’ spatial frequency tuning (20).
To realize local automatic gain control in the model, HC activity is set proportional
to intensity and this activity is used to modulate CO to cone terminal attenuation,
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Fig. 1. Modeling the outer retina. (A) Neural circuit: cone terminals (CT) receive a signal
that is proportional to incident light intensity from the cone outer segment (CO) and from neighboring cones, through gap junctions, and excite horizontal cells (HC). HCs spread their input
laterally through gap junctions, provide shunting inhibition onto CT, and modulate cone coupling and cone excitation. (B) System diagram: signals travel from the CO to the cone
terminal (CT) and on to the HC network, which provides negative feedback. Both cone terminals and HCs form networks, connected through gap junctions that are governed by their respective space constants, lc and lh. Excitation of HCs by cone terminals is modulated by the HCs,
which also modulate the attenuation from the CO to the cone terminal together with modulation
of cone gap junctions to keep lc constant. These compensatory interactions realize local automatic gain control in the cone terminal and keep receptive field size invariant.
(C) Frequency responses: both HCs and cone terminals (CT) lowpass filter input signals, but
because of the HC network’s larger space constant, HC inhibition eliminates low frequency signals, yielding a spatially bandpass response in the cone terminal. (D) Outer retina circuitry. A
phototransistor draws current through an nMOS transistor whose source is tied to Vc, decreases
in which represent increased cone terminal activity, and whose gate is tied to Vh, increases in
which represent increased HC activity. This transistor passes a current proportional to the product of cone terminal and HC activity, thus, modeling shunting inhibition from HCs to cones. In
addition, this current, mirrored through pMOS transistors, dumps charge on the HC node, Vh,
modeling cone terminal excitation of the HCs, and its modulation by HCs. VL, a global bias set
externally sets the mean level of Vc. Vhh, another external, bias sets the strength of the HC gap
junctions. The strength of those between cones are modulated locally by Vh (30).
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B, by changing cone-to-cone conductance. This modulation adapts cone sensitivity to
different light intensities (14). Furthermore, to overcome the expansion in receptivefield size that this modulation caused in earlier designs, HC modulation of cone gapjunctions is complemented with HC modulation of cone leakage conductance, through
shunting inhibition, making lc independent of luminance. The change in loop-gain with
HC modulation of cone excitation was also compensated by keeping A, the amplification from cone terminal to HC, proportional to B, thus, fixing the peak spatial frequency
of cone terminal response (21).
Cone terminal activity in the model is primarily determined by spatial contrast, saturates when increasing signal fluctuations cause this ratio to become large, and is
entirely independent of absolute luminance. From the outer retina model’s system equations, how the silicon model’s cone terminal activity depends on its cone and horizontal space constants and on contrast (21) was derived:
iCT =
2r
c
r + 2 − 1 / r + 2c
where iCT represents cone terminal activity and c represents stimulus contrast; r = lh/lc
is the ratio of the HC space constant to the cone space constant. This behavior is remarkably similar to the mammalian retina. Physiologists have found that cone responses as
a function of contrast—intensity of light stimulation relative to a background—are
described by a simple equation:
V =
IVm
I+σ
where V is the peak amplitude of the cone response produced by a given level of stimulating light intensity, I. Vm is the maximum response and σ is the background intensity. The response reaches half of the maximum when I = σ (22). This adaptive behavior
is preserved across five decades of background intensities. Cone responses obtained
from the model, where c corresponds to I/σ, behave similarly when lh is comparable
with lc (21).
Morphing the Outer Retina Into Silicon
The retinal models were morphed into a silicon chip by replacing each synapse or
gap-junction in the model with a transistor. One of its terminals is connected to the
presynaptic node, another to the postsynaptic node, and a third to the modulatory node.
By permuting these assignments, excitation, inhibition, and conduction are realized, all
of which are under modulatory control.
Modulation was implemented by exploiting the exponential I(V) relationship of the
MOS (metal-oxide-semiconductor) transistor. In the subthreshold regime, the current
from the drain terminal to the source terminal is the superposition of a forward component that decreases exponentially with the source voltage (Vs) and a reverse component
that decreases similarly with the drain voltage (Vd); both components increase exponentially with the gate voltage (Vg). That is, Ids = IoeκVg(e−Vs − e−Vd) where κ ≈ 0.7 is a nonideality factor; voltages are in units of UT = 25 mV, at 25°C. This equation describes the
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n-type device; voltage and current signs are reversed for a p-type (23). Hence, the transistor converts voltage to current exponentially and converts current back to voltage logarithmically. By adding a voltage offset representing the log of the modulation factor,
the current can be multiplied by a constant, thereby modulating the synaptic strength.
Synaptic strengths are modulated locally, within the chip, except for a small number of
biases globally controlled by the user. Current-mirrors are added to reverse the direction
of current when necessary.
Morphing the model for the outer retina yielded the electronic circuit shown in
Fig. 1D. Omitting adaptation in the phototransduction cascade, photocurrents linearly proportional to luminance discharge the cone terminal node, Vc, which is
defined as an increase in cone terminal activity. This drop in Vc produces a current
that excites the HC network through an nMOS transistor followed by a pMOS
current-mirror. This excitatory current is modulated by HC activity, represented by
Vh, and increases as Vh increases to realize autofeedback. But this increased current
also releases more charge on to Vc, thereby realizing horizontal-cell inhibition of
cone terminal activity. Thus, a single transistor implements two distinct synaptic
interactions, one excitatory, the other inhibitory. Cone nodes are electrically coupled
to their six nearest neighbors through nMOS transistors whose gates are controlled
locally by HCs, implementing the model of cone gap-junction modulation. HCs also
communicate with one another, through pMOS transistors, but this coupling is controlled by an externally applied voltage (Vhh).
Cone terminals in the model drive two types of BCs that rectify the cone signal into
ON and OFF channels, thus, reproducing the complementary signaling scheme found in
the mammalian retina (17). the cone signal using push–pull pMOS current mirrors is
rectified, not shown here, but described in detail in (21). Briefly, the current generated
by cone terminal activity is compared with a reference current set at the mean.
Subtracting these currents by mirroring them on to one another removes the baseline;
the difference drives the ON bipolar cell if it is positive and drives the OFF bipolar cell if
it is negative (21). Thus, the bipolar circuitry divides signals into ON and OFF channels.
INNER RETINA
Adopting the same approach, that was taken with the outer retina, the model for the
inner retina is based on identified synaptic interactions and local microcircuits previously described in the literature, obtained using histological and physiological techniques. After constructing this model of the inner retina’s synaptic connections, it is
used as a blueprint with which the silicon retina is assembled.
Modeling the Inner Retina
The model of the inner retina, which realizes lowpass and highpass temporal filtering, adapts temporal dynamics to input frequency and to contrast, and drives ganglion
cell responses, is shown in Fig. 2A. BCs from the outer retina excite amacrine cells
with either narrow or wide fields. To ensure that only the ON or OFF channel is active
at any time, bipolar and amacrine cells receive inhibition from the complementary
channel in the model, similar to vertical inhibition found between the inner-plexiform
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Fig. 2. Inner retina model and circuit. (A) Inner retina synaptic interactions: ON and OFF
bipolar cells (BC) relay cone signals to ganglion cells (GC), and excite narrow- and wide-field
amacrine cells (NA, WA). Narrow-field amacrine cells inhibit BC, wide-field amacrine cells,
and transient GCs; their inhibition onto wide-field amacrine cells is shunting. Wide-field
amacrine cells modulate narrow-field amacrine cell presynaptic inhibition and spread their signals laterally through gap junctions. BC also excite local interneurons that inhibit complementary bipolar cell and narrow-field amacrine cells. Four types of GCs signal the onset or offset
of visual stimuli in a sustained (OnS, OffS) or transient (OnT, OffT) fashion. (B) System diagram:
narrow-field amacrine cell (NA) signals represent a lowpass filtered version of bipolar terminal
(BT) signals and provide negative feedback on to the bipolar cell (BC). The wide-field amacrine
cell (WA) network modulates the gain of NA feedback (X). WA receives full-wave rectified
excitation from BT and full-wave rectified inhibition from modulated NA (double arrows). BT
drives sustained GCs directly whereas the difference between BT and NA drives transient ganglion cells (GCt). (C) Numerical solution to inner retina model with a unit step input of 1V.
Traces show 1 s of ON cell responses for BC, BT, NA, GCt, and WA. Outer retina time constant, τo, is 96 ms; τna is 1 s. (D) Wide field amacrine cell modulation: bipolar terminal (BT)
activity (Ibt) excites a network of wide-field amacrine cells (WA) through a current mirror; it
also excites the narrow-field amacrine cell (NA, excitation circuitry not shown). Wide-field
amacrine cell activity modulates the strength of narrow-field amacrine cell feedback inhibition
on to the bipolar terminal, subtracting a current wIna from the bipolar cell’s excitatory input Ibc.
The same current is also subtracted from the wide-field amacrine cell’s excitatory input, Ibt,
thereby inhibiting it. Vbq controls the quiescent current supplied to the inner retina by the
bipolar terminal and Vaa controls the extent of gap-junction coupling in the wide-field amacrine
cell network (30).
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layer’s ON or OFF laminae (24). The signal is made at the bipolar cell’s terminal more
transient (highpass filtered) than its cone input by applying sustained (lowpass filtered)
inhibition from the narrow-field amacrine-cell (25). The bipolar cell terminal in the
model also excites two types of GCs, which is called transient and sustained. In transient GCs, feedforward inhibition from the narrow-field amacrine cells cancels residual
sustained excitation from the bipolar terminal, similar to the synaptic complex found in
mammalian retina (26).
Contrast gain control in the inner retina model is determined by the modulatory
effects of wide-field amacrine cell activity. Wide-field amacrine cell activity represents the local measure of contrast, weighed on neighboring spatial locations. These
cells are excited by both ON and OFF BCs and inhibited by both ON and OFF narrowfield amacrine cells in the model, similar to ON–OFF amacrine cells found in the
retina (27), and are coupled together through gap-junctions to form a wide-field
amacrine cell network. By modulating their own inhibitory inputs as well as narrowfield amacrine cell inhibition at bipolar terminals, the wide-field amacrine cells
compute temporal contrast. That is, their activity reflects the ratio between contrast
fluctuations (highpass signal) and average contrast (lowpass signal). As this
temporal contrast increases, their modulatory activity increases, the net effect of
which is to make the GCs respond more quickly and more transiently. There is also
an overall decrease in sensitivity because of the less sustained nature of the response.
This adaptation captures properties of contrast gain control in the mammalian
retina (21,28).
From the synaptic interactions of Fig. 2A, the block diagram was derived for the
inner retina, shown in Fig. 2B, by modeling the narrow-field amacrine cell as a lowpass filter. Responses of the different inner retina cell types in this model to a step
input are shown in Fig. 2C. Bipolar cell activity is a low-pass filtered version of light
input to the outer retina. Increase in bipolar cell activity causes an increase at the
bipolar terminal and slower increase in the narrow-field amacrine cell. The difference
between bipolar terminal activity and gain-modulated narrow-field amacrine cell
activity determines wide-field amacrine cell activity, which, in turn, sets the gain of
narrow-field amacrine cell feedback inhibition on to the bipolar terminal and on
to the wide-field amacrine cell. Thus, after a step input, bipolar terminal activity
initially rises, but narrow-field amacrine cell inhibition, setting in later, attenuates
this rise until bipolar terminal activity is equaled by gain-modulated narrow-field
amacrine cell activity. Wide-field amacrine cell activity rises above its baseline value
of unity at both onset and offset, driven by full-wave rectified input from ON and OFF
bipolar terminals. The bipolar terminal drives the sustained ganglion cell, which
responds for the duration of the step, whereas the difference between bipolar terminal
and narrow-field amacrine cell activity drives the transient ganglion cell, which
decays to zero.
From the block diagram in Fig. 2B, the system level equations can be derived for
narrow-field amacrine and bipolar cell acitivity with the help of the Laplace transform:
τ s +ε
gε
ibc , ibt = A
ibc
ina =
τ As + 1
τ As + 1
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where g is the gain of the excitation from the bipolar terminal to the narrow-field
amacrine cell, and where
τ A ≡ ετ na , ε ≡
1
1 + wg
τna is the time constant of the narrow-field amacrine cell and w represents wide-field
amacrine cell activity, which determines feedback strength. From the equations, it can
be seen that the bipolar terminal highpass filters and the narrow-field amacrine cell
lowpass filters the bipolar cell signal; they have the same corner frequency, 1/τA. This
closed-loop time-constant, τA, depends on the loop gain wg, and therefore on wide-field
amacrine cell activity. For example, stimulating the inner retina with a high frequency
would provide more bipolar terminal excitation (highpass response) than narrow-field
amacrine cell inhibition (lowpass response) to the wide-field amacrine cell network.
Wide-field amacrine cell activity, and hence w, would subsequently rise, reducing the
closed-loop time-constant τA, until the corner frequency 1/τA reaches a point where
bipolar terminal excitation equaled narrow-field amacrine cell inhibition. This drop in
τA, accompanied by a similar drop in ε, will also reduce overall sensitivity and advance
the phase of the response.
The system behavior governed by these equations is remarkably similar to the contrast gain control model proposed by Victor (29), which accounts for the compression
of retinal responses in amplitude and in time with increasing contrast. Victor proposed
a model for the inner retina whose highpass filter’s time-constant, TS, is determined by
a “neural measure of contrast,” c. The governing equation is:
Ts =
TO
1+
c
c1/ 2
This model’s time-constant depends on contrast in the same way that the model’s
time constant depends on wide-field amacrine cell activity, where Victor’s TO is similar
to the τna and where Victor’s ratio c/c1/2 is represented by how much wide-field
amacrine cell activity increases above its value at DC in the model. As this activity is
sensitive to temporal contrast (21), it is proposed that wide-field amacrine cells are the
anatomical substrate that computes Victor’s neural measure of contrast.
In the model, the loop gain wg is set by the local temporal contrast. Wide-field
amacrine cell activity reflects inputs from bipolar terminals and narrow-field amacrine
cells weighted across spatial locations, so these pooled excitatory and inhibitory inputs
should balance when the system is properly adapted:
w b ina b = b ibt b + isurr
⇒ w = ( b ibt b + isurr )/ b ina b
where isurr is defined as the gap-junction current, resulting from spatial differences in
wide-field amacrine cell activity w. bibtb and binab are full-wave rectified versions of
ibt and ina, computed by summing ON and OFF signals. If all different phases are pooled
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spatially, these full-wave rectified signals will not fluctuate and will be proportional to
amplitude. And if isurr, is ignored w will simply be |ibt|/|ina|, yielding a temporal measure
of contrast, because it is the ratio of a temporal difference (highpass signal, ibt) and a
temporal average (lowpass signal, ina). At DC, this ratio is equal to 1/g; hence the loop
gain is unity and the DC gain from the bipolar cell to its terminal is ε = 1/2.
Ganglion cell responses in the inner retina model are derived from the bipolar terminal and narrow-field amacrine cell signals. Specifically, bipolar terminal signals directly
excite both sustained and transient types of GCs, but transient cells receive feedforward
narrow-field amacrine cell inhibition as well. The system equations determining sustained and transient ganglion cell responses (GCs and GCt), derived from the equations
above, as a function of the input to the inner retina, ibc, are as follows:
iGCs =
jτ Aω + ε
ibc
jτ Aω + 1
iGCt =
jτ Aω + ε(1 − g )
ibc
jτ Aω + 1
where ω is temporal frequency (and j = √–1). When bipolar terminal to narrow-field
amacrine cell excitation has unity gain (g = 1), feedforward inhibition causes a purely
high-pass (transient) response in the transient ganglion cell whereas the sustained ganglion cell retains a low-pass (sustained) component. With a small loop-gain, wg, the DC
gain, ε, approaches 1/2 and the bipolar terminal and sustained ganglion cell response
becomes all-pass. However, as the loop gain increases, ε decreases and the response
becomes highpass. The change in ε with loop gain is matched in both bipolar terminals
and narrow-field amacrine cells, and so taking the difference between these two signals
always cancels the sustained component in the transient ganglion cell (21). Thus, the
transient ganglion cell produces a purely highpass response irrespective of the system’s
loop gain.
Morphing the Inner Retina Into Silicon
The model for the inner retina is implemented in part by the electronic circuit shown
in Fig. 2D. Wide-field amacrine cell modulation of narrow-field amacrine cell inhibition is realized by applying voltages representing wide- and narrow-field amacrine
activity to a transistor’s source and gate terminals, respectively. This transistor drains
current from the node that represents bipolar terminal activity, implementing presynaptic inhibition by the narrow-field amacrine cell. It also sources current onto the node
that represents wide-field amacrine activity, charging up that voltage, Vwa. This increase
corresponds to inhibition of wide-field amacrine activity since, as Vwa increases, the
strength of narrow-field amacrine inhibition (w) decreases. Conversely, as Vwa
decreases, the strength of this inhibition increases. A pMOS transistor and a currentmirror realize excitation of the wide-field amacrine by the bipolar terminal. Wide-field
amacrine cell nodes are coupled to one another through nMOS transistors gated by Vaa.
The circuit diagram of Fig. 2D represents only one of the inner retina circuit’s complementary halves and does not show bipolar terminal to narrow-field amacrine excitation, lowpass filtering in the narrow-field amacrine cell, or push-pull inhibition. In the
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complete circuit, ON and OFF signals from bipolar cell circuitry drive either half of the
inner retina circuit. Excitatory current from the bipolar terminal excites the narrowfield amacrine cell node on one side of the circuit whereas also inhibiting the narrowfield amacrine cell node on the complementary side, thus, realizing push-pull inhibition.
To realize linear lowpass filtering, these inputs are divided by the sum of ON and OFF
narrow-field amacrine cell activity, which compensates for the exponential voltagecurrent relationship in the subthreshold regime (30). ON and OFF bipolar terminal and
narrow-field amacrine cell signals converge on to the wide-field amacrine cell network,
implementing full-wave rectification. Finally, signals from the bipolar terminal and
narrow-field amacrine cells are used to drive ON and OFF transient and sustained GCs.
Because analog signals cannot be relayed over long distances, retinal GCs use spikes
to communicate with central structures. Similarly, each ganglion cell in the chip array
converts the current it receives from the inner retina circuit to spikes. The spike generating circuit (not shown) exhibits spike-rate adaptation through Ca++ activated K+ channel analogs, modeled with a current-mirror integrator (31).
SILICON CHIP LAYOUT
In the mammalian retina, cone signals converge on to BCs (1), which makes the
receptive field center Gaussian-like (32). To implement signal convergence in the
model, chip BCs connect the outputs from a central phototransistor and its six nearest
neighbors (hexagonally tiled) to one inner retina circuit, as shown in Fig. 3A. Each of
the outer retina circuits actually produces two output currents. A central photoreceptor
drives the bipolar cell with both of these outputs while photoreceptors at the six vertices divide these outputs between their two nearest BCs. For symmetry, a similar architecture is implemented for the reference current (see ref. 21).
Transient GCs in the mammalian retina pool their inputs from a larger region than
sustained GCs. This difference is maintained in the chip by pooling inner retina signals
in the same way that outer retina signals are pooled. Thus, each transient ganglion cell
receives input from a central inner retina circuit and its six nearest neighbors, as shown
in Fig. 3A. This central circuit excites its ganglion cell with both copies of its transient
output whereas those at the six vertices divide their outputs between their two nearest
transient GCs. As inner retina circuits are tiled at one-quarter the density of the phototransistors that provide their input, this results in a larger receptive field for each ganglion cell than for each bipolar cell. All GCs tile hexagonally, but the transient ones tile
more sparsely than the sustained ones. This architecture gives transient GCs a larger
receptive field, as found in cat Y-GCs. It also accounts for transient GCs’ nonlinear subunits (20) since all the rectified bipolar cell signals can never sum to zero, at any one
moment, in response to a sinusoidal grating. Conversely, if the cells were linear, a
contrast-reversing grating exactly centered on the cell’s receptive field would not modulate the cell’s response as decreases in dark regions would exactly cancel out increases
in light regions.
The chip design was fabricated in a 0.35 µm minimum feature-size process with its
cell mosaics tiled at a scale similar to the mammalian retina (Fig. 3B). Phototransistors
are tiled triangularly 40 µm apart; this spacing is only about two and a half times that
of human cones at 5 mm nasal eccentricity (33). The phototransistors are only 10 µm
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Fig. 3. Chip layout. (A) Functional architecture: signals from a central photoreceptor (not
shown) and its six neighbors (CO) are pooled to provide synaptic input to each bipolar cell
(BC). Each bipolar cell generates a rectified output, either ON or OFF that drives a local inner
plexiform layer (IPL) circuit. Sustained GCs (OffS), which have a dendritic field diameter of
80 µm, receive input from a single local IPL circuit. Transient GCs (OffT), however, receive
signals from a central IPL circuit (not shown) and its six neighbors, and hence, their dendritic
field is 240 µm wide. (B) Chip design and human photoreceptor mosaic: each pixel with 38
transistors on average has a phototransistor (P), outer plexiform (synaptic) layer circuitry, bipolar cells, and IPL circuitry. Spike-generating GC are found in five out of eight pixels; the remaining three contain a narrow field amacrine (NA) cell membrane capacitor. Inset: Tangential view
of human cone (large) and rod (small) mosaic at 5 mm eccentricity, plotted at the same scale
(reproduced from refs. 30, 33).
on a side, leaving ample space for postsynaptic circuitry, which is interspersed between
them. This spacing is necessary because, unlike neural tissue, silicon microfabrication
technology cannot produce three-dimensional structures.
One pixel—the basic element that is tiled to create the silicon retina—contains a
phototransistor, outer retina circuitry, a pair of BCs, and one-quarter of the inner retina
circuit. Hence, 2 × 2- and 4 × 4-pixel blocks are needed to generate a complementary
pair of sustained and transient outputs, respectively. Because transient GCs occur at a
quarter resolution, not every pixel contains ganglion cell circuitry. Three out of every
eight pixels instead contain a large capacitor that gives the narrow-field amacrine cell
its long time-constant. A spike generating circuit in the remaining five pixels converts
GC inputs into spikes that are sent off chip. The 3.5 × 3.3 mm2 silicon die has 5760
phototransistors at a density of 722/mm2 and 3600 GCs at a density of 461/mm2—tiled
in 2 × 48 × 30 and 2 × 24 × 15 mosaics of sustained and transient ON and OFF GCs.
Because of wiring limitations, each ganglion cell output off chip cannot be communicated directly. Instead, an asynchronous, arbitered, multiplexer are used to read spikes
out from the silicon neurons (34). Each ganglion cell interfaces with digital circuitry
that communicates the occurrence of a spike to the row and each column arbiters. The
arbiters select one row and one column at a time, and an encoder outputs their
addresses. Row and column addresses are communicated serially off chip. The spike
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activity of all 3600 GCs can be represented with just seven bits using this address-event
representation. By noting the address of each event generated by the chip, Ganglion
cell location and type can be decoded in the array. In a future prosthetic application,
such a scheme would be unnecessary as each ganglion cell’s local spiking circuit could
drive a local micro-electrode to stimulate adjacent neural tissue.
SILICON RETINA RESPONSES
To gauge the validity of the outer and inner retina models and to verify their ability
to recreate retinal function, the responses of the silicon retina are compared with those
of the mammalian retina. Specifically, the silicon retina’s responses were recorded to
different spatial and temporal frequencies, to different luminances, and to different contrasts and these responses were compared with physiological measurements available
in the literature.
Spatiotemporal Filtering
The silicon retina’s GCs respond to a restricted band of spatiotemporal frequencies,
with transient cells displaying nonlinear spatial summation. In response to a drifting
sinusoidal grating, spike trains from GCs of the same type differ significantly because
of the cumulative effect of variability between transistors (CV = 20–25% for currents
in identically sized and biased transistors). It was possible to obtain results that match
physiological data by averaging responses from all cells in a given column, much as
physiologists average several trials from the same cell.
The results reveal that at low temporal frequencies, both low and high spatial frequencies are attenuated in our silicon chip. However, sustained cells respond to a higher
range of frequencies, as expected from their smaller receptive fields (Fig. 4A,B). Spatial
frequency responses of ganglion cell activity (Fig. 4b) were fit with a balanced differenceof-Gaussians, an empirical model for retinal GCs (35). Briefly, the frequency profile of
a one-dimensional zero-mean inhibitory Gaussian was computed, with standard deviation σInh and unit area, subtracted from a one-dimensional zero-mean excitatory
Gaussian, with standard deviation σExc and unit area. This frequency response was
compared with the data and was optimized σExc and σInh to give the best fit.
When the phase of a contrast-reversing sinusoidal grating was varied, frequency
doubling in transient cells was observed (Fig. 4C,D). This nonlinear summation is the
fundamental distinction between narrow- and wide-field mammalian GCs (20,36,37)
and arises because the bipolar cell signals are rectified before they are summed (20).
Sustained cells in the silicon retina retain bandpass spatial filtering at all temporal frequencies (Fig. 5A,B). This pattern of spatiotemporal filtering matches the mammalian
retina, except for a resonance found at very high temporal frequencies (38). In the silicon retina, fast wide-field amacrine-cell modulation augments slow horizontal-cell inhibition to suppress low spatial frequencies, irrespective of whether they are presented at
high or low temporal frequencies. And the optics and the cone–cone gap-junctions blur
high spatial frequencies, also irrespective of temporal frequency. As a result, the sustained cells pass a restricted band of spatial frequencies at all temporal frequencies.
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Fig. 4. Spatial filtering and nonlinear summation: (A) Varying spatial frequency: responses
to 7.5 Hz horizontally drifting sinusoids with three different spatial frequencies. The responses
are the strongest at an intermediate frequency, except for OnT cells, which showed an anomalous preference for low frequencies (see Fig. 2A for color code). (B) Spatial frequency tuning:
OffT and OffS amplitudes are plotted for all spatial frequencies tested; they both peaked at
0.164 cpd, but OffS cells pass a higher range of frequencies. Solid lines are the best fit of a balanced difference-of-Gaussian model (OffT: σExc/σInh = 0.20; OffS: σExc/σInh = 0.15) (35). (C)
Varying spatial phase: responses to a 5 Hz 0.33 cpd contrast-reversing grating at four different
spatial phases. Transient cells (yellow and blue) show frequency doubled responses at 15° and
195°. (D) Null Test: amplitudes of the second Fourier component (F2) of OffT and OffS
responses are plotted for all phases tested. The sustained cells’ F2 response disappeared at certain phases, but it could not be nulled in the transient cells. Fluctuations in F2 amplitude arise
from uneven spatial sampling in the silicon retina (30).
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Fig. 5. Temporal filtering: (A) Varying temporal frequency: responses to 0.22 cpd horizontally drifting sinusoids at three different temporal
frequencies. The response is the strongest at an intermediate frequency for transient cells (yellow and blue), whereas sustained cell (red and
green) responses decline monotonically. (B) Sustained-cell temporal frequency tuning: responses of OffS and cat ON-center X-cells to low,
medium, and high spatial-frequency sinusoidal gratings drifting horizontally at different temporal frequencies (see legend in C). Both pass all
temporal frequencies less than 10 Hz, except at low spatial frequencies. However, the cat data display a high-frequency resonance (Cat data are
reproduced from ref. 38). The ordinate here and in c represents responsivity, which is the amplitude of the fundamental Fourier component
divided by the stimulus contrast. (C) Transient-cell temporal frequency tuning: same as in B but for OffT cells and cat ON-center Y-cells. Both
pass a restricted band of temporal frequencies at all spatial frequencies less than 0.33 cpd. (D) Responses to a face: in the static image (top), only
sustained GCs respond. Reconstruction of the image from their activity (middle) demonstrates fidelity of retinal encoding. In the moving image
(bottom), transient GCs respond as well, highlighting moving edges. The velocity of the image was approx 26.96°/s. The mean spike rate was 19
spikes/cell/s (30).
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On the other hand, the silicon retina’s transient cells retain bandpass temporal filtering at all spatial frequencies (Fig. 5A,C). This pattern also matches the mammalian
retina, except for the high-frequency resonance (38). In the silicon retina, focussed narrow-field amacrine-cell inhibition augments diffuse horizontal-cell inhibition to suppress low temporal frequencies, irrespective of whether they are presented at high or
low spatial frequencies. And the cone membrane’s capacitance smears high temporal
frequencies, also irrespective of spatial frequency. As a result, the transient cells pass a
restricted band of temporal frequencies at all spatial frequencies.
The overall effect of spatiotemporal filtering is the best illustrated by natural stimuli
(Fig. 5D). Bandpass spatial filtering in sustained GCs enhances edges in the static
image. During rapid motion, bandpass temporal filtering in transient GCs captures this
information with surprisingly little blurring. To confirm that the chip encodes visual
information, the natural stimulus was reconstructed from the sustained ganglion cell
spike activity. The visual image was reconstructed from the spikes by convolving ON
and OFF sustained ganglion cell spike output with the same difference-of-Gaussian
model, whose excitatory and inhibitory standard deviations were determined by the fit
to the ganglion cell spatial frequency responses (σExc and σInh, Fig. 4B). The outputs of
this convolution were passed through a temporal low-pass filter with a time constant of
22.7 ms, computing a new frame every 20 ms. The difference between images obtained
from ON and OFF spikes was taken, and was displayed on a gray-scale, with ON and
OFF activity corresponding to bright and dark pixels, respectively. Activity from transient GCs did not enhance the resolution of the reconstructed image and was not
included. Passing spike output through this simple spatiotemporal filter produces an
image that is easily recognizable, even with only 30 × 48 pixels and just 0.4
spikes/cell/frame. This result suggests that cortical structures receiving input from such
a visual prostheses can extract useful visual information from the silicon retina’s neural
code through simple linear filtering.
Light and Contrast Adaptation
The silicon retina’s GCs adapt to mean luminance and encode stimulus contrast (Fig. 6).
They maintain contrast sensitivity during at least one and a half decades of mean luminance. This intensity range was limited on the low end by leakage currents; the transistors
pass a few pico-amps even when their gate voltage is zero. And it was limited on the
high end by the projector (could not exceed 200 cd/m2) in the experimental set-up and
by stray photocurrents (light-induced leakage currents) in the silicon chip. To obtain the
results presented here, the effect of these photocurrents was compensated by changing
two externally applied voltages that would otherwise require no adjustment.
From the outer retina model, discussed in outer retina section, how the silicon
model’s cone activity depends on contrast was derived. The analytical result is fitted to
the measured luminance adaptation curves (Fig. 6C), allowing r to increase with
decreasing intensities as that data were obtained by exploiting the dependence of contrast sensitivity on horizontal-cell coupling (controlled globally in the circuit by Vhh),
thereby the effect of stray photocurrents was being compensated. These photocurrents,
which set an upper limit for the membrane time-constants that can be realized, reduce
the silicon retina’s sensitivity by speeding up ganglion-cell spike-frequency adaptation
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Fig. 6. Luminance adaptation: (A) Varying intensity: OnT and OnS responses to a sinusoidal
grating (0.22 cpd) whose mean intensity was attenuated by amounts listed, using neutral density
filters. Because of increases in sensitivity, the response amplitude hardly changes. The noisier
responses at high intensity are due increased background activity, which tends to invoke synchronous firing because of cross-talk (i.e., ephatic interactions) in the silicon chip. (B) Cat ON-center
Y-cell intensity curves: the sinusoidal grating’s (0.2 cpd) contrast varied from 1 to 50% and
reversed at 2 Hz, for five mean luminances (39). Here, and in C, response vs contrast (small
x-axis) curves are shifted to align the 50% contrast response with that particular mean luminance
(large x-axis). Mean luminance is converted from trolands to cd per m2 based on a 5 mm diameter
pupil (adapted from ref. 39). (C) OnT intensity curves: the sinusoidal grating’s (0.22 cpd) contrast varied from 3.25 to 50% and reversed at 3 Hz, for four different mean luminances. Solid
lines represent the best fit of the equation given in the text for cone terminal activity; the fit indicates that the ratio of the horizontal cell and cone terminal space constants increased from 0.46 to
0.69, with a corresponding drop in peak spatial frequency from 0.22 to 0.16 cpd (30).
and narrow-field amacrine-cell presynaptic inhibition as intensity increases. The latter
effect was compensated by adjusting a second externally applied voltage that sets the
narrow-field amacrine-cell’s (baseline) membrane leakage.
The analytical fits to the measured luminance adaptation curves support the conclusion that the silicon retina’s local modulation of synaptic strengths was largely responsible for adaptation. As mean luminance increased from 6 to 192 cd/m2, the value
assigned to the ratio between the HC and cone space constants, r, in the fitted equation
decreased monotonically from 0.69 to 0.46 (unexpectedly, the best fits were found with
r less than one; the corresponding reduction in peak spatial frequency response was
from 0.22 to 0.16 cpd). Thus, even though we intervened by manually adjusting Vhh,
the resulting change in r, a drop of only 36%, fell far short of what is required to reduce
the sensitivity by a decade and a half. Overall, the silicon retina’s ganglion-cell activity
remained weakly correlated with absolute light intensity because of the residual effect
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Fig. 7. Contrast gain control: (A) Varying contrast: responses to a 1 Hz square-wave contrast
reversal of a sinusoidal grating (0.22 cpd) at four different peak stimulus contrasts. Bin width is
4 ms. Responses increase sublinearly and change more rapidly with increasing contrast; these
effects are more pronounced in the transient cells. Their responses decayed with a time-constant
that decreased from 28 to 22 ms as contrast increased from 6.25 to 50%. Inset: Response of
ON-center cat X cell to half a cycle of the same stimulus (29). (B) ON-center cat Y cell contrastdependent temporal filtering: a stationary sinusoidal grating (0.25 cpd) whose contrast was
determined by the sum of eight sinusoids was used. All eight sinusoids had the same amplitude
whose value relative to the background is stated. The amplitude of the fundamental Fourier
component at these eight frequencies was plotted for two different amplitudes (reproduced from
ref. 28). The peak sensitivity shifted from 3.9 to 7.8 Hz as the contrast increased from 1.25 to
10%. (C) OffT contrast-dependent temporal filtering: the stimulus was the same except that the
spatial frequencywas reduced to 0.14 cpd and four different contrasts were tested. The peak sensitivity shifted from 3.9 to 7.8 Hz as the contrast increased from 1.25 to 10%. Solid lines are the
best fit of an analytical model, which indicated that an increase in the strength of narrow-field
amacrine-cell feedback inhibition from w = 1.07 to w = 3.76 could account for this change in
temporal dynamics (30).
of the stray photocurrents. Thus, as found in mammalian ganglion cell behavior (39),
responses at low contrasts are weaker at lower light intensities.
The silicon retina’s GCs also adapt to temporal contrast. When presented with contrast-reversing gratings, the transient GCs respond more quickly, but more transiently
with increasing contrast (Fig. 7A). And as the responses became even more transient,
the peak-firing rate tended to saturate at the highest contrast levels. This adaptation is
similar to the contrast gain control observed in mammalian narrow-field sustained (29)
and wide-field transient GCs. However, it was not as dramatic in the silicon retina’s
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sustained cells, whose responses did not decay nor saturate as much; they did, however,
display a more rapid onset with increasing contrast. This difference between the silicon
retina’s sustained and transient GCs suggests that narrow-field amacrine cell feed-forward inhibition enhances contrast gain control by making the response more transient.
To better quantify the effect of contrast gain control (28), the silicon retina’s temporal frequency was measured, tuning at different contrasts, using a mixture of sinusoids
with a flat spectrum. The OFF-Transient cells’ peak response shifted to higher frequencies with increasing contrast, moving by an amount similar to that observed in the
mammalian retina (Fig. 7B,C). But while this shift in tuning was accompanied by an
overall strengthening of responses at all frequencies in the data, it was accompanied by
preferential strengthening of high frequency responses in the cat data.
From the inner retina model, discussed in inner retina section, how the silicon
model’s ganglion cell responses depend on input contrast for a flat spectrum (i.e., white
noise) was derived (21). This stimulus was characterized by contrast per unit frequency
d. The transient ganglion cell response, iGt, in spikes per second, is given by
 
 j τ ω + ε(1 − g )  

1
1
iGt = S  d A
 
 

j τ Aω +1   j τ oω + 1   j τ P ω + 1 

2
where τA = ετna, ε = 1/1(1 + wg). τna is the narrow-field amacrine cell’s time constant,
g is the gain from the bipolar terminal to the narrow-field amacrine cell, w is the widefield amacrine cell-modulated strength of narrow-field amacrine cell inhibition onto the
bipolar terminal, and S is a gain constant. The sustained ganglion cell response can be
obtained by setting g to zero. The outer retina was approximated, using a lowpass temporal filter with time constant τo. The lowpass filtering behavior of the chip’s photoreceptors was also included whose time-constant is τp. The four data sets are fitted (Fig. 7C)
by allowing the system gain term, S, and the inhibition modulation (w) to vary across
different stimulus contrasts, and fixed the remaining parameters.
The best fits of this model to the four input contrast densities (solid lines in Fig. 7C)
support the conclusion that the silicon retina’s wide-field-amacrine-mediated modulation
of presynaptic inhibition was responsible for contrast gain control. The parameter values
for these fits were τp = 33 ms, τo = 77 ms, τna = 1.0382 s, and g = 1.07. The system gain,
S, saturated over the four contrasts (352–1358 to 1711–1929), whereas the inhibition
strength (w) increased exponentially (1.07–1.51 to 2.38–3.76). Thus, the inhibition strength
increased with contrast as it was expected, but the system gain was not constant because of
a static nonlinearity (40), canceling part of the expected decrease in sensitivity.
CONCLUSIONS
By autonomously extracting the same visual information encoded by the mammalian
retina at a similar physical scale and energy efficiency, the silicon retina satisfies the
criteria for a fully implantable ocular prosthesis. The device approximates the behavior
of the mammalian retina in both linear response and nonlinear adaptation. This success
validates the neuromorphic modeling approach for advanced prosthetic applications. In
addition, this real-time silicon model may be useful in both further testing specific
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hypotheses about the retina and in serving as a realistic retinal front-end to other downstream processes like cortical models, other artificial neural systems, or robots.
The approach in constructing this silicon retina was to model synaptic connections
found in the mammalian retina and to implement them using transistor primitives. For
example, reciprocal inhibition between bipolar and amacrine cells in complementary
ON and OFF channels in the model mimics vertical inhibition between ON and OFF laminae (24) and serial inhibition found between amacrine cells (41) in the mammalian
retina. Furthermore, the model proposes an anatomical substrate for computing Victor
and Shapley’s “neural measure of contrast” (28,29), suggesting that wide-field amacrine
cells play this role in the mammalian retina. Whereas this hypothesis remains to be
tested experimentally, there are instances in which the model oversimplifies the functional architecture of the mammalian retina. For instance, dopaminergic amacrine cells
(42), and light sensing GCs (43), are likely important in modulating mammalian retinal
cone and horizontal gap-junction conductance. These dopaminergic cells are not
included in the model, and instead the local horizontal-cell signal is relied on to modulate cone coupling.
Capturing the mammalian retina’s synaptic organization proved sufficient to recreate
its computations in the silicon retina, although there were some specific quantitative
differences of note, which arose from technological limitations. The device’s sensitivity
dropped when luminance was high and its background firing rates increased. These
deficiencies can be addressed by reducing photo-induced leakage currents, which tend
to speed up inhibition and firing rates in the silicon retina GCs, and by reducing crosstalk between silicon GCs, which produced high background activity when bright or
large stimuli were presented. The device’s sustained GCs also displayed little or no
contrast gain control. A faster photodetector should rectify this situation, which appears
to be related to the absence of any significant transient component in the sustained
GCs’ responses. This speed-up will lead to a transient component at the bipolar terminal, and hence in the sustained GCs.
The goal of designing and fabricating a silicon retina was realized that can operate
and adapt independent of external control to a large extent, but there remains some
degree of manual intervention necessary to make the device work properly. Whereas
the voltages applied to the biases that set mean cone terminal activity, mean bipolar
terminal activity, mean ganglion cell activity, and coupling strength in wide-field
amacrine cells remained fixed, the voltages applied to the biases had to be manually
adjusted that set the coupling strength between HCs and the bias that sets the narrowfield amacrine cell leakage current to compensate for light-dependent leakage currents,
a shortcoming of silicon microtechnology at these small length scales. However, this
fine tuning was only required for light adaptation. Any bias voltages was not adjusted
whatsoever during any of the other experiments. Hence, addressing the leakage issue
will make it possible to hard-wire all of the silicon retina’s external biases to specific
voltages, as required by a final prosthetic application.
The artificial retina satisfies the requirements of a neural prosthesis by matching the
biological retina in size and weight and using under a tenth of a watt. Rabbit retina uses
16.2 nW per ganglion cell (82 µmoles of ATP g per min [44], or 88 mW g/min, times
70 mg average weight, divided by 380,000 GCs [12]). In contrast, the chip consumes
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17 µW per ganglion cell (62.7 mW for the entire chip) at an average spike rate of 45 spikes
s per ganglion cell. Although, this energy consumption is one thousand times less efficient
than the mammalian retina, it still represents a 100-fold improvement over conventional
microprocessors. A 1 GHz Pentium® processor operating at 10 W would dissipate
2.2 mW per ganglion cell to compute the response of a13 × 13 × 13 kernel (X × Y × T)
updated at 100 times/s. With an upper limit on a proposed intraocular implant’s power dissipation of 100 mW, the Pentium® could thus only compute the responses of under 40
GCs, or a 6 by 6 array, which is too small for functional vision (5). However, with the
same 100 mW limit, our neuromophic chip’s energy efficiency allows it to compute the
responses of 4000 GCs, roughly a 60 × 60 array. This energy efficiency is expected to
improve further, together with spatial resolution and dynamic range, as microfabrication
technology advances.
In conclusion, based on detailed knowledge of the retina’s neuronal specializations,
synaptic organization, and functional architecture (45), thirteen neuronal types have
been constructed in silicon and linked them together in two synaptic layers on a physical scale comparable with the human retina. Furthermore, a silicon retina has been created that modulates its synaptic strengths locally. The silicon retina realizes luminance
adaptation, without using logarithmic compression, and contrast gain control independent of external control, thus, capturing properties of retinal neural adaptation for the
first time. The success modeling neural adaptation using single-transistor primitives
suggests that a similar approach could be used to morph other neural systems into silicon as well; this may eventually lead to fully implantable neural prostheses (46,47) that
do not require external interfaces.
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