Biomedical Engineering Reference
In-Depth Information
about 30 ms. Similarly, primate pattern recognition can be so rapid (
200ms) that
the processing at each of the many stages that intervene between photoreceptors and
motor neurons can take probably only
∼
10 ms, before the results must be passed
on to the next stage [37]. Since neurons rarely fire more than a single spike in such
short periods of time, it seems that neuronal computation is capable of operating on
the basis of very small numbers of action potentials.
In these situations, each stimulus must be encoded by few spikes per neuron. This
observation is important because it strongly limits the complexity of the neuronal
response and encourages us that it might be possible to get a thorough understanding
of the neural code.
Cracking the neural code for a given stimulus set means understanding the manner
in which the space of spike trains is divided into clusters representing the different
stimuli. We would like to answer two basic questions: (1) Does this clustering de-
pend on the precise timing of spikes, or only on the number of spikes that each
neuron emits? (2) Does the clustering depend on correlations across multiple spikes,
or only on individual spikes? To address these questions, it is necessary to quantify
and compare the stimulus discriminability that the different candidate codes afford -
the natural framework for which is Shannon's information theory.
Recently, the
series expansion
method of estimating mutual information has been
developed, which is specifically tailored to the case of sparsely responding neurons
[21, 22]. We have applied it to a popular model system - the somatosensory cortex
of the rat - where the number of evoked spikes per stimulus is also small, and have
thereby been able to study issues of spike timing and population coding in a rigorous
manner [18, 25, 26]. These developments are reviewed in the following sections.
∼
13.2
Series expansion method
13.2.1
Quantifying neuronal responses and stimuli
To measure the stimulus discriminability of a given neural code, the first step is to
categorise the neuronal response in a manner that reflects the code.
We consider
spike times in the interval
ms relative to the onset of the stimulus. For a
spike
count
code, the response of a neuron on a given trial is simply the number of spikes
emitted in the interval. To evaluate spike timing, the interval is subdivided into a
sequence of
L
bins of width
dt
ms (
dt
[
0
,
T
]
L
). If each bin contains at most 1 spike,
then the response on a given trial is the one of the 2
L
possible sequences that occurs.
It is not, however, necessary for the analyses described below that the sequence to
be binary [28]. If a population of
C
neurons is being considered, the response on a
given trial is the set of
C
simultaneously recorded spike counts or spike sequences.
Having quantified the response, we can ask how well it discriminates between the
different stimuli.
=
T
/
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