Biomedical Engineering Reference
In-Depth Information
most of the information is conveyed during the
first 20-50 ms
[17, 18]
. However, time-to-first-
spike encoding is susceptible to channel noise and
spike loss; therefore, this type of encoding is typi-
cally observed in the cortex, where the spiking
rate could be as low as one spike per second.
An extension of the time-to-spike code is the
phase code that is applicable for a periodic stim-
ulus. An example of phase encoding is shown in
Figure 2.4
e, where the spiking rate is shown to
vary with the phase of the input stimulus. Yet
another kind of neural code that has attracted
significant interest from the neuroscience com-
munity uses the information encoded by corre-
lated and synchronous firings between groups
of neurons
[13]
. The response is referred to as
synchrony
and is illustrated in
Figure 2.4
f, where
a sequence of spikes generated by neuron 1, fol-
lowed by neuron 2 and neuron 3, encodes a
specific feature of the input stimulus. Thus
information is encoded in the trajectory of the
spike pattern and so can provide a more elabo-
rate mechanism of encoding different stimuli
and its properties
[19]
.
of these limitations, networks of spiking neurons
are remarkably accurate and are able to process
large-bandwidth (much higher than 500 Hz)
analog sensory signals with very high precision
(greater than 120 dB)
[28]
. Through evolution,
neurobiological systems have evolved to exploit
noise as a computational resource rather than a
hindrance. A study reported in Ref.
29
demon-
strated the increase in the reliability of neuronal
firings with the addition of noise. In yet another
study
[30]
, it was shown that noise facilitates
reliable synchronization of the firing patterns in
a population of neurons.
In this section, we describe two types of noise
exploitation techniques commonly observed in
neurobiology: (a) stochastic resonance (SR) and
(b) noise shaping. In stochastic resonance, the
addition of random noise enhances the detec-
tion of a weak, periodic signal, the amplitude of
which is smaller than the firing threshold of the
neuron. Noise-shaping principles apply to a
population of neurons where the SNR of the
network is enhanced by shifting the intrinsic
noise out of the frequency bands where the sig-
nals of interest are present.
2.3 NOISE EXPLOITATION IN
NEUROBIOLOGY
2.3.1 Stochastic Resonance
Figure 2.5
shows the basic principle of signal
enhancement using stochastic resonance. The
threshold of an integrate-and-fire neuron is
denoted by
V
th
, whereas
v
(
t
) is the membrane
potential driven by a periodic stimulus. When
noise
or random perturbation is absent, as
shown in
Figure 2.5
a, the neuron does not fire
because the amplitude of the membrane poten-
tial
v
(
t
) is below the threshold
V
th
.
When noise
(extrinsic or intrinsic) is added to the system,
as shown in
Figure 2.5
b, there exists a finite
probability that the membrane potential
v
(
t
)
will cross the threshold
V
th
, which would result
in the generation of spikes. The rate of spikes
would therefore be proportional to the level of
the noise and to the amplitude of the membrane
potential or input stimulus. However, when the
As mentioned in Section
2.1
, noise plays a con-
structive role in neurobiology. A single neuron,
by its very nature, acts as a noisy and crude (less
than 3 bits accurate) computational unit
[20-23]
.
It is not only affected by intrinsic
noise
(e.g., ther-
mal noise in the ion channels) and extrinsic
noise
(e.g., noise due to the neurotransmitters present
in the synaptic junctions), but it is also affected
by noise in the sensor
[24-27]
. For example, the
photoreceptor cells in the retina generate thermal
and quantum noise due to the photons imping-
ing on the retinal membrane. Thus, the spike train
generated by a neuron not only exhibits a signifi-
cant amount of jitter and drift but is also severely
limited in its dynamic range and bandwidth (less
than 500 Hz) due to its refractory period. In spite
