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estimation of the respiratory motor output. By classifying each pixel into five types
based on our model parameter values and the estimation error ratio, we obtained
detailed classification of neuronal activities. The parametric modeling approach can
be effectively employed for the evaluation of voltage-imaging data and thus for the
analysis of the brain function.
12.1 Introduction
Electrical neuronal activity in the brain, on the scale of tissue or multiple cellular
levels, has been investigated classically with a multielectrode technique. Although
this technique enables us to analyze spatiotemporal profiles of neuronal activities
as multiple spike trains [25, 16, 2], the spatial resolution is generally low (e.g., 20
recording points/200 mm
2
) due to the limited number and density of microelec-
trodes. Further, because a multielectrode technique requires insertion of multiple
microelectrodes into brain tissue, it could cause mechanical tissue damage espe-
cially in the brain of small animals.
On the contrary, optical recording techniques do not have such drawbacks.
Optical recording techniques were first reported in 1968 [3, 28], have been steadily
improved, and have now become more popular than a multielectrode technique in
the analysis of neuronal activity of the brain. Among various optical recording meth-
ods, a technique using a voltage-sensitive dye (voltage imaging) enables us to non-
invasively analyze membrane potential changes of multiple neurons in a region of
interest (ROI) [29, 17, 23, 11, 10, 18, 19, 22, 21]. Although the temporal resolution of
voltage imaging is generally lower than that of a multielectrode technique, voltage
imaging provides much higher spatial resolution than a multielectrode technique
(e.g., 10,000 recording points/10 mm
2
).
Optical imaging data give us copious information especially in the spatial do-
main. However, the data obtained with this technique must be cautiously evaluated.
This is because optical signals are small and thus usually require cycle triggered sig-
nal averaging (e.g., 50 times) and noise cutting near the baseline using an arbitrarily
set threshold in order to improve the apparent signal-to-noise ratio. Further, opti-
cal signals can be affected by photobleaching and thus may need correction of the
deviated baseline. Through such preprocessing, the timing of activity occurrence in
different regions cannot be directly compared, as an example indicates in Fig. 12.1.
Several researchers have developed more sophisticated analytical methods, which
have fled from such threshold problems. Fukunish and Murai [12] were pioneers of
statistical analysis of voltage-imaging data. They analyzed the spatiotemporal pat-
terns of neuronal activities and oscillatory neural activity transfer by applying a
multivariable autoregressive model to the voltage-imaging signals of the guinea pig
primary auditory cortex. Fisher et al. [9] conducted voltage-imaging experiments
in the intra-arterially perfused in situ rat preparation and applied a correlation co-
efficient imaging technique to extract and classify respiratory related signals from
optical images. They calculated the correlation for each pixel with a given corre-
lation function; they used five different functions that approximated activities of
