  Multi-electrode arrays (MEA) are increasingly used to investigate spontaneous
neuronal network activity. The recorded signals comprise several distinct
components: Apart from artefacts without biological significance, one can
distinguish between spikes (action potentials) and subthreshold fluctuations
(local fields potentials). Here we aim to develop a theoretical model that
allows for a compact and robust characterization of subthreshold fluctuations
in terms of a Gaussian statistical field theory in two spatial and one temporal
dimension. What is usually referred to as the driving noise in the context of
statistical physics is here interpreted as a representation of the neural
activity. Spatial and temporal correlations of this activity give valuable
information about the connectivity in the neural tissue. We apply our methods
on a dataset obtained from MEA-measurements in an acute hippocampal brain slice
from a rat. Our main finding is that the empirical correlation functions indeed
obey the logarithmic behaviour that is a general feature of theoretical models
of this kind. We also find a clear correlation between the activity and the
occurence of spikes. Another important insight is the importance of correcly
separating out certain artefacts from the data before proceeding with the
analysis.
