Biomedical Engineering Reference
In-Depth Information
2.7.1 Rate Coding
To understand the neuronal firing representations, neuroscientists have correlated the firing rate
(
2.3
) with a wide variety of behaviors. The most celebrated leader of the rate coding hypothesis is
English physiologist Edgar Adrian, who determined that neurons tended to modulate their firing
rate in response to a stimulus (stretch receptor in the frog leg)
11
[
39
]. Most microelectrode-based
BMIs have also utilized rate coding to map motor parameters. To represent the neural activity, most
of experimental designs utilize the local mean firing rate of neurons as the input. The mean firing
rate has been estimated by “binning” neural spikes with sliding rectangular time windows of length
ranging from 50 up to 100 msec. This method greatly reduces the number of zeros in the spike
train point process and also provides a time to amplitude conversion of the firing events. The spike
rate response of cells in muscles, visual cortex, and motor cortex have lead to the development of
receptive fields and tuning curves that describe the reliability of firing of a neuron as a function of
the variation in an experimental condition (i.e., muscle stretch, visual orientation, movement veloc-
ity). The search for more complete mappings of receptive fields and tuning curves to the external
environment has lead to the need for massively parallel neuronal recordings. These techniques yield
the activity of neural ensembles or large groups of neurons from spatially disparate parts of the
brain. The known concepts of the computational structure and basis of neuronal representations
have been the driving force for deriving models for BMIs [
14
,
52-57
], which will be described in
the next chapter.
s(t) = number of spikes in
Δ
t
(2.3)
2.7.2 Effect of Resolution on Rate Coding
Because the local firing rate may represent the local frequency of a neural spike train, the fea-
tures can be extracted based on local frequency. One of the methods for the representation of local
frequency information is multiresolution analysis [
58
], usually realized by the wavelet transform.
Through multiresolution analysis, it is possible to represent the time-frequency characteristics of
a signal. Basically, we can obtain as many local frequency components as we want at a given time
instance. Hence, multiresolution analysis of neural spikes may provide richer information about
neuronal behavior compared with to the binning using a fixed-width time window as is traditionally
performed in the literature.
If we consider multiresolution spike train analysis, it is straightforward to see that the
binning process is nothing but a discrete wavelet transform (DWT) with a Haar wavelet [
59
].
11
Firing rate increased with increasing load on the leg.
