Biomedical Engineering Reference
In-Depth Information
The most common time-domain method to char-
acterize association between two spike trains was
and is still the cross-correlation histogram (Perkel
et al., 1967), called peristimulus time histogram
(PSTH) when neural response to stimulus events
is studied. A waste amount of electrophysiological
data show that neuronal spike trains may exhibit
correlation; the occurrence of a spike at one time
is not independent on the occurrence of spikes at
other times, both within spike trains from single
neurons and across spike trains from multiple
neurons. The well extended opinion is that the
presence of these correlations is a key element
of the neural code. However, the absence of an
event may be also considered as information bit.
Such “negative logic” is less accepted by the
neural community, in part due to difficulties of
experimental and theoretical investigation. How
to measure the absence of something? A possible
solution is to use frequency domain methods.
In frequency domain, the Fourier transform
estimates the power spectrum of the process
providing a measure of the frequency content of
the spike train. However, such transformation is
known to have difficulties when dealing with point
processes (Brillinger, 1978). To overcome some
of them in the literature the use of multi-taper
Fourier transform has been advocated (Jarvis &
Mitra, 2001). Although the multi-taper Fourier
transform usually provides a good estimate of
the power spectrum, in the case of highly peri-
odic spike trains (e.g. in experimental conditions
of periodic sensory stimulation) it may fail to
consistently represent the spectral density. A
frequency domain analysis of a neural ensemble
from spiking activity can be conducted by taking
Fourier transforms of spike trains, and using these
to compute the spectrum of individual trains and
the cross-spectrum or coherence between pairs
of spike trains. The spectral coherence is then
a frequency-dependent measure of functional
association (coupling) between two processes.
It has two important advantages over its time
domain counterpart: the normalization is not
bin-size dependent, and it can be pooled across
neuron pairs.
Although being useful, this method suffers
from the fundamental assumption that the spike
trains under study are generated by stationary
stochastic processes. On the other hand, our
understanding of the complicated interplay, com-
munication, information exchange between cells
and cell groups, and of the role of the intriguing
dynamic phenomena they produce may stack in
the framework of this hypothesis. To overcome
this lack of balance between theory and experi-
ment, first of all one requires a stronger emphasis
on a systems oriented approach where mecha-
nism-based modeling is used to establish a more
complete and coherent picture. It also requires
the use of concepts and methods from the rapidly
growing fields of nonlinear dynamics and complex
systems theory, and it requires the continuous
development and improvement of tools that can
help us interpret the information embedded in
complex biological time series.
Relatively recently a new method of time
series analysis that can, and has been designed
to, cope with complex non-stationary signals
has been introduced. The approach is based on
the wavelet transform, technique providing high
temporal resolution with a reasonably good bal-
ance in frequency resolution. Wavelet analysis
is presumably one of the most powerful tools
to investigate the features of a complex signal.
The wavelet approach has shown its strength
in connection with a broad range of application
such as noise reduction, information compres-
sion, image processing, synthesis of signals, etc.
The majority of its applications in neuroscience
are in electroencephalographic recordings (see
e.g. Alegre et al., 2003; Castellanos & Makarov,
2006; Goelz et al., 2000; Murata, 2005; Quiroga &
Garcia, 2003; Schiff et al., 1994). However, there
are few studies on synchronization between pair
of spike trains (e.g. stimulus-neural response). In
this direction the wavelet cross-spectrum has been
used to analyze the phase-locked oscillations in
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