08-11-2012, 11:43 AM
Real-Time Simulation of Biologically Realistic Stochastic Neurons in VLSI
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Abstract
Neuronal variability has been thought to play an
important role in the brain. As the variability mainly comes from
the uncertainty in biophysical mechanisms, stochastic neuron
models have been proposed for studying how neurons compute
with noise. However, most papers are limited to simulating
stochastic neurons in a digital computer. The speed and the
efficiency are thus limited especially when a large neuronal
network is of concern. This brief explores the feasibility of
simulating the stochastic behavior of biological neurons in a very
large scale integrated (VLSI) system, which implements a programmable
and configurable Hodgkin-Huxley model. By simply
injecting noise to the VLSI neuron, various stochastic behaviors
observed in biological neurons are reproduced realistically in
VLSI. The noise-induced variability is further shown to enhance
the signal modulation of a neuron. These results point toward the
development of analog VLSI systems for exploring the stochastic
behaviors of biological neuronal networks in large scale.
Introduction
Biological neurons have been found noisy both in the generation
of spikes and in the transmission of synaptic signals.
The noise comes from the random openings of ion channels,
the quantal releases of neural transmitters, the coupling of
background neural activity, etc. [19], [25]. As the noise affects
neural computation directly, it has been of great interest to
study how neurons compute with noise reliably [24]. Interestingly,
many studies have indicated that noise plays a beneficial
role at least by:
1) inducing neuronal variability [7];
2) enhancing the sensitivity of neurons to environmental
stimuli [26];
3) inducing synchronization between neurons [1];
4) facilitating probabilistic inference according to the
Bayes’ rule in the brain [16].
Mapping Biological Models Into VLSI
The minimal HH model proposed in [18] is of our particular
interests, as different classes of cortical and thalamic neurons
have been modeled satisfactorily with a minimal number of
ionic conductances. In addition, the conductance models in
[18] are similar to those implemented in the Pamina chip,
allowing most parameters to be adopted directly for VLSI
simulation according to the mappings described as follows.
All voltage levels in the VLSI neuron are designed to be
five times greater than their corresponding values in biological
neurons, i.e., VVLSI = 5∗VBIO, while the time scale is identical
for both VLSI and biological neurons. Let CVLSI and CBIO
represent the membrane capacitances of VLSI and biological
neurons, respectively. The conductance mapping is proportional
to the capacitance ratio as gVLSI/gBIO = CVLSI/CBIO.
Regular-Spiking Neurons
The RS neuron has been the largest class of neurons in
the neocortex. The slow potassium current (IM) is activated
by the depolarization of neuronal membranes. Once activated,
IM functions as an extra polarizing current, causing the spiking
frequency to adapt toward a minimum.
With VS stepping from 1.3-V (inhibition) to 2.4-V (above
threshold) at t = 0.2s and Vn = 300mVpp, the measured responses
of the stochastic RS neuron in the Pamina chip
are shown in Fig. 4(a). The frequency adaptation is clearly
shown, and the noise distorts the spiking frequency during
adaptation. Let the inverse of the inter-spike-interval (ISI)
between consecutive spikes approximate the instantaneous
spiking frequency. Fig. 4(b) plots the spiking frequency of the
RS neuron during 1600 ms of the above-threshold stimulation
(VS = 2.4-V). Without noise, the spiking frequency adapts
from 137 Hz to 25 Hz gradually. The variability around 25 Hz
is attributed to the clockfeedthroughs in the PCI system. As the
noise is increased, the adaptation process becomes distorted.
The initial firing frequency further reduces when Vn is greater
than 300 mVpp, owing to the serious threshold variations
induced by the noise. On the contrary, the adaptation rate is
nearly constant for different Vn. This is because IM with a
large τs (200 ms) is less affected by noise.
Conclusion
This brief demonstrated the feasibility of simulating various
stochastic neurons in VLSI by simply injecting noise into
the membrane capacitor of a HH model in VLSI. Various
stochastic behaviors observed in biological neurons have been
reproduced in VLSI realistically. The effect of noise on
different neurons has thus been studied efficiently. These
promising results point toward the development of analog
VLSI systems able to simulate stochastic neuronal networks
in real or accelerated time. The influence of noise on synaptic
connections and network behaviors will then be explored. In
addition, hybrid silicon-neuron networks could be built to ease
the investigation on how individual parameters affect stochastic
neural computation.