A silicon retina that reproduces signals in the optic nerve

A silicon retina that reproduces signals in the optic nerve
INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF NEURAL ENGINEERING
doi:10.1088/1741-2560/3/4/002
J. Neural Eng. 3 (2006) 257–267
A silicon retina that reproduces signals in
the optic nerve
Kareem A Zaghloul1 and Kwabena Boahen2,3
1
2
Department of Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, USA
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
E-mail: [email protected]
Received 4 April 2006
Accepted for publication 18 August 2006
Published 5 September 2006
Online at stacks.iop.org/JNE/3/257
Abstract
Prosthetic devices may someday be used to treat lesions of the central nervous system. Similar
to neural circuits, these prosthetic devices should adapt their properties over time, independent
of external control. Here we describe an artificial retina, constructed in silicon using
single-transistor synaptic primitives, with two forms of locally controlled adaptation:
luminance adaptation and contrast gain control. Both forms of adaptation rely on local
modulation of synaptic strength, thus meeting the criteria of internal control. Our device is the
first to reproduce the responses of the four major ganglion cell types that drive visual cortex,
producing 3600 spiking outputs in total. We demonstrate how the responses of our device’s
ganglion cells compare to those measured from the mammalian retina. Replicating the retina’s
synaptic organization in our chip made it possible to perform these computations using a
hundred times less energy than a microprocessor—and to match the mammalian retina in size
and weight. With this level of efficiency and autonomy, it is now possible to develop fully
implantable intraocular prostheses.
1. Introduction
One goal of understanding neural systems is to develop
prosthetic devices that can someday be used to replace
lesioned neural tissue. Designing a successful prosthesis
that faithfully replicates the computations performed by a
neural circuit requires a detailed understanding of that circuit’s
anatomic connections and functional computations. For
such a prosthesis to be practical, the device must perform
these computations as efficiently as, and at a physical scale
comparable to, the lesioned network and must be independent
of external control. Development of a retinal prosthesis is a
logical first step in attaining this goal since the retina’s circuits
and computations are well understood.
Present attempts to engineer a viable retinal prosthesis
have focused on the significant problem of efficient electrical
stimulation of neurons along the visual pathway [1, 2].
Microelectrode arrays implanted epiretinally or subretinally
evoke phosphenes in patients with visual loss (due to outer
3
Address for correspondence: Bioengineering Department, Stanford
University, W082 Clark Center, 318 Campus Drive West, Stanford, CA 943055439, USA.
1741-2560/06/040257+11$30.00
retinal degeneration) by relying on electrical stimulation of
the remaining retinal cells to dictate firing patterns [3, 4].
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 [5, 6]. 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.
While 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 to biology by morphing neural
circuits into electronic circuits [7]. Micron-sized transistors
function as excitatory or inhibitory synapses or as gap
junctions, thereby recreating the synaptic organization of
© 2006 IOP Publishing Ltd Printed in the UK
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K A Zaghloul and K Boahen
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. As millions of transistors can be
fabricated on a thumb-nail-sized piece of silicon using VLSI
(very large scale integration) technology, this neuromorphic
approach offers a fully implantable solution for neural
prostheses.
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 and bipolar cells [8]. Second, a logarithmic photoreceptor
(cf cone) was used to capture a wide intensity range, but
this degraded the signal-to-noise ratio by attenuating large
amplitudes (i.e., signal) while leaving small amplitudes (i.e.,
noise) unchanged. Third, the local spatiotemporal average (cf
horizontal cell) 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 [9] 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 [10].
Here, we present a silicon retina modelled on neural
circuitry in both the outer and the inner retina. It is constructed
at a scale comparable to the human retina and uses under
a tenth of a watt, thereby satisfying the requirements of a
fully implantable prosthesis. By capturing both outer and
inner retina circuitry using single-transistor synapses, the
silicon retina we 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 singletransistor 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 silicon retina outputs
spike trains that capture the behaviour of ON- and OFF-centre
[11] versions of wide-field transient and narrow-field sustained
ganglion cells [12], which provide 90% of the primate retina’s
optic nerve fibres [13]. And, more significant for a prosthetic
application, these are the four major types that project, via
thalamus, to primary visual cortex.
In the remainder of this paper, we describe our model
for the retinal circuitry, which includes a total of 13 neuronal
types. We briefly outline our procedure for morphing neural
circuits into electronic ones. And we compare the responses
of our silicon retina’s four output cell types to the mammalian
retina.
2. Methodology
We implemented modulation 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
258
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 = I0 eκVg (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 n-type device; voltage and current
signs are reversed for a p-type [14]). Hence, the transistor
converts voltage to current exponentially and converts current
back to voltage logarithmically. Modulation occurs by
changing the source voltage, which changes the transistor’s
transconductance. Current mirrors are added to reverse the
direction of current when necessary.
Spike responses from silicon neurons on the chip are
read out of the array by a digital arbiter [15], generating
a sequence of ganglion cell addresses that are relayed off
chip. The arbiter, which outputs the physical address and
cell type of one ganglion cell at a time, is capable of relaying
a new spiking address off chip every 35 ns. We display the
colour-coded activity of the chip’s four ganglion cell types
on a monitor, which enables us to observe the entire array
in real time. This video signal is generated by a chip with
an array of leaky integrators, which convert spikes back into
graded signals. We used a logic analyser (Tektronix TLA715,
v 4.1.108, Beaverton, OR) to capture spike activity in response
to visual stimuli projected onto a screen 136.5 cm in front
of the chip (InFocus LP425, Wilsonville, OR). A CS mount
video lens with a focal length of 8.5 mm (Edmund Scientific,
Tonawanda, NY) was placed in front of the chip to focus
images onto the chip surface. Spike activity from a particular
column was analysed by restricting captured addresses to that
column. Visual stimuli were programmed using Microsoft
R
DirectDraw
. Periodic stimuli were defined by per cent
Michelson contrast: 100 × (Imax − Imin)/(Imax + Imin), where
Imax and Imin are the peak and trough intensities (range =
0–100%).
Spatial frequency responses of ganglion cell activity
(figure 4(b)) were fit with a balanced difference-of-Gaussian
model. Briefly, we computed the frequency profile of a
one-dimensional zero-mean inhibitory Gaussian with standard
deviation, σ Inh, and unit area subtracted from a onedimensional zero-mean excitatory Gaussian with standard
deviation, σ Exc, and unit area. We compared this frequency
response to our data and optimized σ Exc and σ Inh to give the
best fit.
We reconstructed the visual image from the spikes
(figure 6) 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 (σ Exc and σ Inh, figure 4(b)). We passed the outputs
of this convolution through a temporal low-pass filter with
a time constant of 22.7 ms, computing a new frame every
20 ms. We took the difference between images obtained from
ON and OFF spikes and displayed it on a grey scale, with
ON and OFF activity corresponding to bright and dark pixels,
respectively. Activity from transient ganglion cells did not
enhance the resolution of the reconstructed image and was not
included.
A silicon retina
We derived how our silicon model’s cone activity depends
on its cone and horizontal space constants and on contrast [16]:
2r
c,
ICT =
r + 2 − 1/r + 2c
where ICT represents cone terminal activity and c represents
stimulus contrast. r represents the ratio of the horizontal
space constant to the cone space constant and is related to
horizontal cell coupling, controlled globally in the circuit
We fit the luminance adaptation curves
through Vhh.
(figure 7(c)) using this equation. We allowed r to increase
with decreasing intensities since we obtained that data by
exploiting the dependence of contrast sensitivity on horizontal
cell coupling, thereby compensating for the effect of stray
photocurrents. 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 and narrow-field amacrine
cell pre-synaptic inhibition. We compensated for the latter
effect by adjusting a second externally applied voltage that
sets the narrow-field amacrine cell’s (baseline) membrane
leakage.
We derived how our silicon model’s ganglion cell
responses depend on input contrast for a flat spectrum (i.e.,
white noise) [17]. This stimulus was characterized by contrast
per unit frequency d. The transient ganglion cell response, IGt,
in spikes per second, is given by
2 jτ ω + ε(1 − g) 1
1
A
IGt = S d
,
jτA ω + 1
jτ0 ω + 1
jτp ω + 1 where τA ≡ ετna , ε ≡ 1/(1 + wg), τna is the narrow-field
amacrine cell’s time constant, g is the gain from the narrowfield amacrine cell to the transient ganglion cell and w is
the wide-field amacrine cell modulated strength of narrowfield amacrine cell inhibition onto the bipolar terminal. The
sustained ganglion cell response can be obtained by setting
g to zero. We approximated the outer retina using a lowpass temporal filter with time constant τ 0. We also included
the low-pass filtering behaviour of the chip’s photoreceptors
whose time constant is τp . We fit the four data sets (figure 8(c))
by allowing the system gain term, S, and the inhibition strength,
w, to vary across different stimulus contrasts and fixed the
remaining parameters. The best fits of this model to the four
input contrast densities are shown as solid lines in figure 8(c).
We found that the parameter values that fit these curves
best were τp = 33 ms, τ0 = 77 ms, τna = 1.0382 s and
g = 1.07. The increase in system gain, S, saturated over
the four contrasts (352 to 1358 to 1711 to 1929), while the
inhibition strength, w, increased exponentially (1.07 to 1.51
to 2.38 to 3.76).
3. Results
3.1. Modelling the mammalian retina
Our model for retinal circuitry (figure 1(a)) is based
on identified synaptic interactions and local microcircuits
previously described in the literature, obtained using
histological and physiological techniques. After constructing
(a)
CO
(b)
CT
Inhibition
HC
BC
NA
Excitation
WA
OnS
OnT OffT
OffS
Conduction
Figure 1. Modelling the retina. (a) Synaptic organization: cone
outer segments (CO) supply photocurrent to cone terminals (CT),
which excite horizontal cells (HC). Horizontal cells reciprocate with
shunting inhibition. Both cones and horizontal cells are electrically
coupled to their neighbours by gap junctions. Horizontal cells
modulate cone to horizontal cell excitation and cone gap junctions
(see the text). ON and OFF bipolar cells (BC) relay cone signals to
ganglion cells (outputs) and excite narrow- and wide-field amacrine
cells (NA, WA). They also excite amacrine cells that inhibit
complementary bipolars and amacrines. Narrow-field amacrine
cells inhibit bipolar terminals and wide-field amacrine cells; their
inhibition onto wide-field amacrine cells is shunting. They also
inhibit transient ganglion cells (OnT, OffT)—but not sustained
ganglion cells (OnS, OffS). Wide-field amacrine cells modulate
narrow-field amacrine cell pre-synaptic inhibition and spread their
signals laterally through gap junctions. (b) Single-transistor
synapses: electrical nodes represent neurons; we assume that they
are electrotonically compact. Inhibition (bubble): increased voltage
on the pre-synaptic node (purple) turns on the transistor and sinks
more current (red) from the post-synaptic node (green), decreasing
its voltage. The voltage applied to the third terminal (blue)
modulates the transconductance (i.e., dIpost/dVpre). A short line
represents modulation. Excitation (arrowhead): current is sourced
onto the post-synaptic node, increasing its voltage. In this case, the
post-synaptic voltage modulates the conductance itself, shunting the
current. We can change shunting excitation to shunting inhibition or
modulated inhibition to modulated excitation by reversing the sign
of either the pre- or post-synaptic voltage (using a p-type transistor
instead of an n-type) or the sign of the current (using a current
mirror). Conduction (bi-directional arrow): a bi-directional current
flows between the two nodes (brown), whose voltages determine its
forward and reverse components. Voltage on the third terminal
modulates both (trans)conductances.
this model of the retina’s synaptic connections, we use this
model as a blueprint with which we assemble our silicon
retina.
Our model for the outer retina is designed to realize
luminance adaptation by adjusting synaptic strengths locally.
Photocurrents from the cone outer segments in our model
drive a network of cone terminals, which subsequently excite
a network of horizontal cells. Because they are coupled
through gap junctions, these horizontal cells compute the
local average intensity in our model. We use this signal
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 while preventing the changes in spatial frequency
tuning that plagued previous attempts at light adaptation [9].
To compensate for the resulting signal attenuation at the cone
terminal, we also use our horizontal cell’s local intensity signal
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K A Zaghloul and K Boahen
to modulate the cone to horizontal cell synaptic strength.
This auto-feedback mechanism, whereby our horizontal cell
regulates its own input, is similar to that found in the retina
[18, 19].
Cone terminals in our model drive two types of bipolar
cells that rectify the cone signal into ON and OFF channels,
thus reproducing the complementary signalling scheme found
in the mammalian retina [11]. Bipolar cells subsequently
excite amacrine cells with either narrow or wide fields. To
ensure that the ON or OFF channels decorrelate their activity
such that one channel is not fully active when the other
channel is, bipolar and amacrine cells receive inhibition from
the complementary channel in our model, similar to vertical
inhibition found between the inner plexiform layer’s ON or
OFF laminae [20]. We make the signal at the bipolar cell’s
terminal more transient (high-pass filtered) than its cone input
by applying sustained (low-pass filtered) inhibition from the
narrow-field amacrine cell [21]. The bipolar cell terminal
in our model also excites two types of ganglion cells, which
we call transient and sustained. In transient ganglion cells,
feed-forward inhibition from the narrow-field amacrine cells
cancels residual sustained excitation from the bipolar terminal,
similar to the synaptic complex found in mammalian retina
[22].
Our model of the inner retina realizes contrast gain
control, the control of sensitivity to temporal contrast, through
modulatory effects of wide-field amacrine cell activity. These
cells are excited by both ON and OFF bipolar cells and
inhibited by both ON and OFF narrow-field amacrine cells
in our model, similar to ON–OFF amacrine cells found in the
retina [23]. By modulating their own inhibitory inputs as well
as narrow-field amacrine cell inhibition at bipolar terminals,
our wide-field amacrine cells compute temporal contrast. That
is, their activity reflects the ratio between contrast fluctuations
(high-pass signal) and average contrast (low-pass signal). As
this temporal contrast increases, their modulatory activity
increases, the net effect of which is to make our ganglion
cells respond more quickly and more transiently. There is
also an overall decrease in sensitivity due to the less sustained
nature of the response. This adaptation captures properties of
contrast gain control in the mammalian retina [17, 24].
3.2. Morphing the retina into silicon
We morphed our retinal model into a silicon chip by replacing
each synapse or gap junction in our model with a transistor.
One of its terminals is connected to the pre-synaptic node,
another to the post-synaptic node and a third to the modulatory
node. By permuting these assignments, we realize excitation,
inhibition and conduction, all of which are under modulatory
control (figure 1(b), see section 2). Their strengths are
modulated locally, within the chip, except for a small number
of biases globally controlled by the user (such as coupling
between horizontal cells and between wide-field amacrine
cells).
Morphing our model for the outer retina yielded the
electronic circuit shown in figure 2(a). Omitting adaptation
in the phototransduction cascade, photocurrents linearly
260
proportional to luminance discharge the cone terminal node,
Vc, which we define as an increase in cone terminal activity.
This drop in Vc produces a current that excites the horizontal
cell network through an nMOS transistor followed by a pMOS
current mirror. This excitatory current is modulated by
horizontal cell activity, represented by Vh, and increases as
Vh increases to realize auto-feedback. But this increased
current also releases more charge onto Vc, thereby realizing
horizontal cell inhibition of cone terminal activity. Thus, a
single transistor implements two distinct synaptic interactions,
one excitatory and the other inhibitory. Cone nodes are
electrically coupled to their six nearest neighbours through
nMOS transistors whose gates are controlled locally by
horizontal cells, implementing our model of cone gap-junction
modulation. Horizontal cells also communicate with one
another, through pMOS transistors, but this coupling is
controlled in this device by an externally applied voltage (Vhh).
Morphing our model for the inner retina yielded the
electronic circuit shown in figure 2(b). Wide-field amacrine
cell modulation of narrow-field amacrine cell inhibition is
realized by applying voltages representing wide- and narrowfield amacrine activity to a transistor’s source and gate
terminals, respectively. This transistor drains current from the
node that represents bipolar terminal activity, implementing
pre-synaptic inhibition. It also sources current onto the node
that represents wide-field amacrine activity, charging up that
voltage, Vwa. This increase corresponds to inhibition of widefield 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
p-type transistor and a current mirror realize excitation of the
wide-field amacrine by the bipolar terminal. Additional details
of this circuit, and the complete circuit schematics for our
silicon retina, may be found elsewhere [25].
Morphing our model for the ganglion cell spiking neuron
yielded the electronic circuit shown in figure 2(c). Details
of this circuit are described elsewhere [26]. Briefly, input
current charges up a ganglion cell membrane capacitor. As the
membrane voltage approaches threshold, a positive feedback
loop, modulated by Vfb, accelerates the voltage’s rate of
change. Once threshold is passed, the circuit generates a
pulse (or spike) that is relayed to digital circuitry. The digital
circuitry acknowledges receipt of the spike by sending a reset
pulse which discharges the membrane. The reset pulse also
dumps a quanta of charge onto a current mirror integrator
through a pMOS transistor gated by Vw. Charge accumulating
on the integrator models the build-up of Ca2+ within the cell
after it spikes. This charge, which leaks away with a time
constant determined by Vtn, draws current away from the
membrane capacitor, modelling Ca2+-mediated K+ channels.
Our 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 (figure 2(d)). 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 [27]. The phototransistors are only 10 µm
on a side, leaving ample space for post-synaptic circuitry,
which is interspersed between them. Unlike neural tissue,
A silicon retina
(a)
(b)
(d)
(c)
(e)
Figure 2. Morphing the retina. (a) Outer retina circuitry: a phototransistor draws current through an nMOS transistor whose source is tied
to Vc, which represents cone terminal (CT) activity, and whose gate is tied to Vh, which represents horizontal cell (HC) activity. This
transistor passes a current proportional to the product of cone terminal and horizontal cell activities, thus modelling shunting inhibition from
horizontal cells to cones. In addition, this current, mirrored through pMOS transistors, dumps charge on the horizontal cell node, Vh,
modelling cone terminal excitation of the horizontal cells. VL, a global bias set externally, sets the mean level of Vc. (b) 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 onto the bipolar terminal, subtracting a current wI na 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. (c) Ganglion cell spiking circuitry: current Iin from the inner retina charges up a ganglion cell (GC) membrane
capacitor. When the membrane voltage crosses threshold, the circuit produces a spike (Sp) that is relayed off chip by digital circuitry. This
circuitry acknowledges receipt of the spike by sending a reset pulse (Rst) that discharges the membrane and dumps charge on a current
mirror integrator that implements Ca2+-dependent spike rate adaptation. (d) Chip design and human photoreceptor mosaic: each pixel, with
38 transistors on average, has a phototransistor (P), outer plexiform (synaptic) layer (OPL) circuitry, bipolar cells (BC) and inner plexiform
layer (IPL) circuitry. Spike-generating ganglion cells (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 [27]). (e) Functional architecture: signals from a central photoreceptor (not shown) and its six
neighbours (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 IPL circuit. Sustained ganglion cells, which have a dendritic field diameter of 80 µm, receive input from a single
local IPL circuit. Transient ganglion cells, however, receive signals from a central IPL circuit (not shown) and its six neighbours, and hence
their dendritic field is 240 µm wide.
silicon microfabrication technology cannot produce threedimensional structures. Finally, to preserve the mammalian
retina’s functional architecture, the chip includes convergence
from cones to bipolar cells and from bipolar cells to transient
ganglion cells (figure 2(e)) [28]. The 3.5 × 3.3 mm2 silicon
die has 5760 phototransistors at a density of 722 per mm2 and
3600 ganglion cells at a density of 461 per mm2—tiled in 2 ×
48 × 30 and 2 × 24 × 15 mosaics of sustained and transient
ON and OFF ganglion cells.
3.3. Spatiotemporal filtering
Our silicon retina’s ganglion cells 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 active ganglion cells of the
same type differ significantly due to the cumulative effect of
variability between transistors (CV = 20–25% for currents
in identically sized and biased transistors) (figure 3(a)).
In the entire array, 151 out of 360 ON-transient, 202/360
OFF-transient, 890/1440 ON-sustained and 792/1440 OFFsustained ganglion cells exhibited no activity. Many of these
ganglion cells were located near the edge of the chip, and as
such, we did not investigate responses of ganglion cells there.
Despite this heterogeneity, we were able to obtain results that
match physiological data by averaging responses from all cells
in a given column (figure 3(b)), much as physiologists average
several trials from the same cell.
Our results reveal that both low and high spatial
frequencies are attenuated. Sustained cells respond to a higher
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K A Zaghloul and K Boahen
cells
spikes s-1
30
0.05 cpd
200
100
0.33 cpd
200
100
0.66 cpd
200
100
0
0.2
0.4
time (s)
(b)
spikes s-1
1000
spikes
s -1
1
200
100
OffT
OffS
10
0.4
0.8
time (s)
Figure 3. Quadrature representation. (a) A single false-colour
frame rendered from spike activity in the entire 48 × 30 ganglion
cell array, captured in response to a 3 Hz 50% contrast drifting
sinusoidal grating (0.14 cpd) whose luminance varied horizontally
across the screen and was constant in the vertical direction. We use
a 50% contrast stimulus in all responses presented here unless
otherwise noted. Ganglion cell outputs are colour coded as shown in
figure 1(a). Where sustained and transient ganglion cells fire at the
same spatial location, the colours overlap. Note that transient
ganglion cells are tiled at half the resolution of sustained ganglion
cells, and hence only appear in every other row and every other
column, in a checkerboard-like pattern. (b) Spike raster (top)
recorded from all cells in a single column (arrow in (a)) and
histogram (bottom, bin width = 20 ms) of all ganglion cell
responses for that column. Sustained cells (green and red) occur in
every row (some are unresponsive) while transient cells (blue and
yellow) occur in every other row, overlaid on the sustained ones.
Spike-rate CVs (coefficient of variation) within this column,
computed for all 30 sustained and 15 transient ganglion cells in this
column regardless of activity, were 57% (OnT) and 162% (OnS).
Complementary ON and OFF channels respond out of phase while
transient cells lead sustained cells, exhibiting both earlier onset and
shorter duration of firing. We computed the amplitude of the
fundamental Fourier component of these histograms, which is
plotted in all frequency responses presented, unless otherwise noted.
The same applies to physiological data reproduced for comparison.
range of frequencies, as expected from their smaller receptive
fields (figures 4(a) and (b)). When we varied the phase of a
contrast-reversing sinusoidal grating, we observed frequency
doubling in transient cells (figures 4(c) and (d)). This nonlinear
summation is the fundamental distinction between narrowand wide-field mammalian ganglion cells [29–31] and arises
because the bipolar cell signals are rectified before they are
summed [30].
Sustained cells in the silicon retina retain bandpass spatial
filtering at all temporal frequencies (figures 5(a) and (b)). This
pattern of spatiotemporal filtering matches the mammalian
retina, except for a resonance found at very high temporal
frequencies [32]. In the silicon retina, fast wide-field amacrine
262
100
0.1
cpd
1
15o
200
100
105o
200
100
195o
200
100
285o
200
100
0
(d)
F2 spikes s-1
spikes s-1 spikes s-1
(b)
spikes s-1 spikes s-1 spikes s-1 spikes s-1
(c)
(a)
(a)
OffT
OffS
300
0.2
0.4
time (s)
200
100
0
0
100
200
300
phase (degrees)
Figure 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
strongest at an intermediate frequency, except for OnT cells,
which showed an anomalous preference for low frequencies. (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: σ Exc/σ Inh =
0.20; OffS: σ Exc/σ Inh = 0.15; see section 2) [48]. (c) Varying spatial
phase: responses to a 5 Hz 0.33 cpd contrast-reversing grating at
four different spatial phases. Transient cells 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.
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.
On the other hand, the silicon retina’s transient cells
retain bandpass temporal filtering at all spatial frequencies
(figures 5(a) and (c)).
This pattern also matches the
mammalian retina, except for the high-frequency resonance
[32]. In the silicon retina, focused 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 best
illustrated by natural stimuli (figure 6). Edges are enhanced
A silicon retina
OffS
(b)
spikes s-1
200
spikes s-1
100
200
200
Cat X
1000
1000
2 Hz
spikes s-1
100
100
7.5 Hz
(c)
100
Cat Y
OffT
12 Hz
0.03 cpd
0.22 cpd
0.33 cpd
100
100
0
0.2
0.4
time (s)
0.01 cpd
0.20 cpd
0.42 cpd
1000
1000
spikes s-1
spikes s-1
(a)
1
10
Hz
100
100
1
10
100
Hz
Figure 5. Temporal filtering. (a) Varying temporal frequency: responses to 0.22 cpd horizontally drifting sinusoids at three different
temporal frequencies. The response is strongest at an intermediate frequency for transient cells, whereas sustained cell responses decline
monotonically. (b) Sustained-cell temporal frequency tuning: responses of OffS and cat ON-centre X cells to low, medium and high
spatial-frequency sinusoidal gratings drifting horizontally at different temporal frequencies (see the legend in (c)). Both pass all temporal
frequencies below 10 Hz, except at low spatial frequencies. However, the cat data display a high-frequency resonance (cat data are
reproduced from [32]). 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-centre Y cells.
Both pass a restricted band of temporal frequencies at all spatial frequencies below 0.33 cpd. Both (b) and (c) contain previously published
data [25], reprinted here for comparison to mammalian data.
3.4. Light and contrast adaptation
Figure 6. Response to a face. In the static image (top), only
sustained ganglion cells respond. Reconstruction of the image from
their activity (middle, see section 2) demonstrates fidelity of retinal
encoding. In the moving image (bottom), transient ganglion cells
respond as well, highlighting moving edges. The velocity of the
image was approximately 26.96 deg s−1. The mean spike rate was
19 spikes/cell/s. A similar version of this figure was published
earlier [25], but did not include the response of the array to stimulus
motion.
by sustained ganglion cell activity in the static image. During
rapid motion, transient ganglion cells capture this information
with surprisingly little blurring. To confirm that the chip
captures visual information, we reconstructed the natural
stimulus from the sustained ganglion cell spike activity.
Passing spike output through a spatiotemporal filter (see
section 2) 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.
The silicon retina’s ganglion cells adapt to mean luminance and
encode stimulus contrast (figure 7). They maintain contrast
sensitivity over at least one and a half decades of mean
luminance. This intensity range was limited on the low end
by leakage currents; these transistors pass a few picoamperes
even when their gate voltage is zero. And it was limited on
the high end by the projector in our experimental set-up (could
not exceed 200 cd m–2) and by stray photocurrents (lightinduced leakage currents) in the silicon chip. To obtain the
results presented here, we compensated for the effect of these
photocurrents by changing two externally applied voltages
that would otherwise require no adjustment (see section 2).
Overall, the silicon retina’s ganglion cell activity remained
weakly correlated with absolute light intensity due to the
residual effect of the stray photocurrents. Thus, as found
in mammalian ganglion cell behaviour [33], responses at low
contrasts are weaker at lower light intensities
The silicon retina’s ganglion cells also adapt to temporal
contrast. When presented with contrast-reversing gratings,
the transient ganglion cells respond more quickly but more
transiently with increasing contrast (figure 8(a)). And the
peak firing rate tends to saturate at the highest contrast levels,
as the responses became even more transient. This adaptation
is similar to the contrast gain control observed in mammalian
narrow-field sustained [34] and wide-field transient ganglion
cells [49]. However, it was not as dramatic in the silicon
retina’s 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 ganglion cells suggests that
narrow-field amacrine cell feed-forward inhibition enhances
contrast gain control by making the response more transient
(see section 4).
263
K A Zaghloul and K Boahen
400
1
200
0
400
1
3
200
Cat Y
100
spikes s-1
400
cd m-2
10
1
10
50
% contrast
5
321
128
51
20
6.4
0
1
(c)
OnT
10
200
1000
0
400
1
30
200
spikes s -1
spikes s-1
spikes s-1 spikes s -1
(b)
spikes s-1
(a)
100
50
0
0.4
0.8
time (s)
cd m-2
1
10
50
% contrast
192
65
19
6
1
10
100
mean illumination (cd/m2 )
Figure 7. 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. Due to increases in sensitivity, the response amplitude hardly changes. The
noisier responses at high intensity are due to increased background activity, which tends to invoke synchronous firing due to cross-talk (i.e.,
ephatic interactions) in the silicon chip. (b) Cat ON-centre 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 [33]. Here, and in (c), response versus 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 m–2
based on a 5 mm diameter pupil (adapted from [33]). (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 an equation governing cone terminal
activity (see section 2). As mean luminance decreased from 192 to 6 cd m–2, the value assigned to the ratio of the horizontal space constant
to the cone space constant, r, in this equation increased monotonically from 0.46 to 0.69, reflecting a reduction in peak spatial frequency
response from 0.22 to 0.16 cpd (see section 2). This figure is similar to previously published data [25], but is replotted on a different scale
for comparison to mammalian data.
To better quantify the effect of contrast gain control [24],
we measured the silicon retina’s temporal frequency tuning at
different contrasts. Our OFF-transient cells’ peak response
shifted to higher frequencies with increasing contrast, moving
by an amount similar to that observed in the mammalian retina
(figures 8(b) and (c)). But while this shift in tuning was
accompanied by an overall strengthening of responses at all
frequencies in our data, it was accompanied by preferential
strengthening of high-frequency responses in the cat data.
4. Discussion
A fully implantable prosthesis requires a device that can
independently extract the same visual information encoded by
the mammalian retina at a similar physical scale and energy
efficiency. Our silicon retina approximates the behaviour of
the mammalian retina, in both linear response and nonlinear
adaptations, validating this neuromorphic modelling approach
for such applications. In addition, this real-time silicon model
may be useful both in further testing specific hypotheses
about the retina and in serving as a realistic retinal input
to other downstream applications like cortical models, other
artificial neural systems or robots. Yet although our silicon
retina qualitatively recreates the computations performed by
the mammalian retina, there are some specific quantitative
differences of note as well as some simplifications of retinal
circuitry.
Our approach in constructing this silicon retina was to
model synaptic connections found in the mammalian retina
264
and to implement that model using transistor primitives. For
example, reciprocal inhibition between bipolar and amacrine
cells in complementary ON and OFF channels in our model
mimics vertical inhibition between ON and OFF laminae
[20] and serial inhibition found between amacrine cells [35]
in the mammalian retina. Furthermore, our model extends
that proposed by Victor and Shapley [24, 34] to include an
anatomical substrate for computing the ‘neural measure of
contrast’, suggesting that wide-field amacrine cells play this
role in mammalian retina. However, there still remain some
differences between our model and the functional architecture
of the mammalian retina. Dopaminergic amacrine cells [36],
and light sensing ganglion cells [37], are likely important
in modulating mammalian retinal cone and horizontal gapjunction conductance, for example. These dopaminergic cells
are not included in our model, and we instead rely on the local
horizontal cell signal to modulate cone coupling.
We realized our goal of designing and fabricating a
silicon retina that can operate and adapt independent of
external control to a large extent, but there remains some
degree of manual intervention necessary to make our chip
work properly. To achieve autonomous operation in a final
prosthetic application, all of the silicon retina’s external
biases were designed to be hard-wired to specific voltages.
However, 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 widefield amacrine cells remained fixed, we had to manually
adjust the voltages applied to the biases that set the coupling
strength between horizontal cells and the bias that sets the
A silicon retina
(b)
1000
6.25%
6.25%
32
500
spikes s-1
0
1000
12.5%
12.5%
3.2
1
500
0.32
1000
25%
25%
500
10%
1.25%
.32
3.2
1
10
32
Hz
(c)
OffT
100
0
50%
50%
spikes s-1
spikes s-1
spikes s-1
0
1000
Cat Y
10
spikes s-1
spikes s-1
(a)
10%
5%
2.5%
1.25%
10
500
1
0
0
0.5
time (s)
1
0
0.5
time (s)
1
10
1
Hz
Figure 8. 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-centre cat X cell to half a cycle of the same stimulus [34]. (b) ON-centre cat
Y-cell contrast-dependent 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 [24]). The peak
sensitivity shifted from 3.9 Hz 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 we reduced the spatial frequency to 0.14 cpd and tested four different contrasts. The peak sensitivity
shifted from 3.9 Hz to 7.8 Hz as the contrast increased from 1.25% to 10%. Solid lines are the best fit of an analytical model (see section 2),
which indicated that an increase in the strength of narrow-field amacrine cell feedback inhibition from w = 1 to w = 3.5 could account for
this change in temporal dynamics.
narrow-field amacrine cell leakage current to compensate for
light-dependent leakage currents, a shortcoming of silicon
microtechnology at these small length scales. This fine tuning
was only required for light adaptation. We did not adjust any
bias voltages during any of the other experiments.
Leakage currents in the silicon substrate caused another
discrepancy between our device and the mammalian retina.
We had to set up the silicon retina’s ganglion cells to have
higher firing rates than their mammalian counterparts because
a higher firing rate proves useful in limiting the effects of
leakage currents in our circuit. Nevertheless, the baseline
firing rate still tends to increase with light intensity due to
stray photocurrents. The increase in background activity
causes the silicon retina’s temporal responses to become less
sharp with increasing light intensity (figures 7(a) and (c)).
Furthermore, cross-talk between the silicon neurons causes
them to synchronize their firing (see figures 7(a) and 8(a)),
especially in the presence of the high background activity
induced by bright or large stimuli, distorting the response
further. We expect to reduce these leakage currents in future
designs so as to improve the silicon retina’s operation.
Unlike mammalian retina, the silicon retina’s ganglion
cells fail to respond to temporal frequencies above 10 Hz
(figure 5(a)). We had expected that because of our model’s
ability to temporally adapt, responses to higher temporal
frequencies should be preserved. We find instead that highfrequency responses are eliminated in our device, which may
explain why chip ganglion cells fail to exhibit the resonance
seen at high frequencies in cat ganglion cells. We suspect
that this discrepancy may be a result of slow time constants in
our phototransistors and outer retina circuit. When fitting our
model to the data (figure 8(c), see section 2), we found that
the time constants of the low-pass filters associated with the
photoreceptors and outer retina were relatively long. This
suggests that these sluggish responses in the feed-forward
pathway impose a low-pass filter effect on the silicon retina’s
ganglion cell responses that is greater than in mammalian
retina.
We also failed to observe contrast gain control in
the silicon retina’s sustained ganglion cells, unlike in the
mammalian retina. This failure is likely related to the
absence of any significant transient component in our sustained
ganglion cells’ responses. The mammalian retina’s narrowfield sustained cells, on the other hand, do have a transient
component, albeit less than that in their transient counterparts.
In our model, we expected pre-synaptic inhibition to introduce
a transient component at the bipolar terminal by sharpening
the sluggish outer retina response, as it is thought to do in the
retina. However, the sharpening was apparently insufficient
to compensate for the long time constants associated with the
silicon retina’s phototransistors and outer retina circuits. We
believe that speeding up the outer retina will result in a transient
component at the bipolar terminal, and hence produce contrast
gain control in the sustained cells. Implementing feed-forward
265
K A Zaghloul and K Boahen
inhibition to a lesser degree in sustained cells in our silicon
retina, like in the mammalian retina [22, 38], will also likely
help in restoring the transient component and therefore contrast
gain control in these sustained cells.
Transient ganglion cells overcome the sluggish outer
retina response because feed-forward inhibition suppresses
the residual sustained component in the bipolar terminal,
leaving a mostly transient response. There remains a sustained
component in these cells which is not fully compensated for
by feed-forward inhibition, however, as demonstrated in their
response to a drifting grating in figure 8(a). The overall
decrease in transient behaviour in both sustained and transient
cells due to the sluggish outer retina response, together with
the ineffectiveness of spike frequency adaptation at the high
firing rates we used [26, 39], makes our transient ganglion
cells more similar to sustained mammalian ganglion cells than
to their transient counterparts (see figure 8(a)).
We have used the same axon-hillock model to generate
spikes in our transient and sustained ganglion cells
(figure 2(c)). In the mammalian retina, however, physiological
studies have demonstrated different membrane properties in
different types of ganglion cells [40, 41]. These differences in
membrane properties may account for some of the differences
seen in behaviour. Taking these differences in the spike
generation into account may produce responses that better
replicate those seen in mammalian ganglion cells.
We also find that, although transient ganglion cells in the
silicon retina and in the mammalian retina both shift their
peak responses to higher frequencies as we increase stimulus
contrast (figure 8(c)), mammalian transient ganglion cells
demonstrate a preferential strengthening of high-frequency
responses as well (figure 8(b)). Analysis of our model
indicates that modulation of pre-synaptic inhibition, as
proposed by Victor and Shapley [24, 34], cannot alone account
for such differential effects [17]. Thus, the discrepancy
between our model and the mammalian retina indicates that
there may be additional mechanisms for contrast gain control
in the mammalian retina that account for the differential
change in sensitivity at low and high temporal frequencies
with increasing contrast (see [42–44]). Elucidating these
mechanisms and implementing them in our model will
help in generating ganglion cell responses that better match
mammalian data.
Our 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. A rabbit retina uses 16.2 nW
per ganglion cell (82 µmoles of ATP g−1 min−1 [45], or
88 mW g−1 min−1, times 70 mg average weight, divided by
380 000 ganglion cells [10]). In contrast, our chip consumes
17 µW per ganglion cell (62.7 mW for the entire chip) at an
average spike rate of 45 spikes s−1 per ganglion cell. Although
this energy consumption is 1000 times less efficient than the
mammalian retina, it still represents a 100-fold improvement
R
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 a 13 × 13 ×
13 kernel (X × Y × T) updated at 100 times per second.
With an upper limit on a proposed intraocular implant’s power
266
R
similar
dissipation of 100 mW, a chip with the Pentium’s
computing power could thus only compute the responses of
under 40 ganglion cells, or a 6 × 6 array, which is too small for
functional vision [3]. However, with the same 100 mW limit,
our neuromorphic chip’s energy efficiency allows it to compute
the responses of 4000 ganglion cells, roughly a 60 × 60 array.
We expect this energy efficiency to improve further, together
with spatial resolution and dynamic range, as microfabrication
technology advances.
5. Conclusion
Based on detailed knowledge of the retina’s neuronal
specializations, synaptic organization and functional
architecture [28], we have constructed 13 neuronal types in
silicon and linked them together in two synaptic layers on a
physical scale comparable to the human retina. Furthermore,
we have created a silicon retina that modulates its synaptic
strengths locally. Our 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. Our success modelling neural adaptation using singletransistor 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.
Acknowledgments
We thank the support of the Whitaker Foundation, the NIH
Vision Training Grant and the University of Pennsylvania. We
are grateful to P Sterling and J Demb for discussions about the
retinal microcircuits. We are also grateful to P Sterling and
J Demb for assistance in preparation of this document.
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