  Models of neural networks have proven their utility in the development of
learning algorithms in computer science and in the theoretical study of brain
dynamics in computational neuroscience. We propose in this paper a spatial
neural network model to analyze the important class of functional networks,
which are commonly employed in computational studies of clinical brain imaging
time series. We developed a simulation framework inspired by multichannel brain
surface recordings (more specifically, EEG -- electroencephalogram) in order to
link the mesoscopic network dynamics (represented by sampled functional
networks) and the microscopic network structure (represented by an
integrate-and-fire neural network located in a 3D space -- hence the term
spatial neural network). Functional networks are obtained by computing pairwise
correlations between time-series of mesoscopic electric potential dynamics,
which allows the construction of a graph where each node represents one
time-series. The spatial neural network model is central in this study in the
sense that it allowed us to characterize sampled functional networks in terms
of what features they are able to reproduce from the underlying spatial
network. Our modeling approach shows that, in specific conditions of sample
size and edge density, it is possible to precisely estimate several network
measurements of spatial networks by just observing functional samples.
