  Multi-electrode arrays covering several square millimeters of neural tissue
provide simultaneous access to population signals such as extracellular
potentials and spiking activity of one hundred or more individual neurons. The
interpretation of the recorded data calls for multiscale computational models
with corresponding spatial dimensions and signal predictions. Such models
facilitate identifying candidate mechanisms underlying experimentally observed
spatiotemporal activity patterns in the cortex. Multi-layer spiking neuron
network models of local cortical circuits covering about 1 mm$^2$ have been
developed, integrating experimentally obtained neuron-type-specific
connectivity data and reproducing features of observed in-vivo spiking
statistics. Local field potentials (LFPs) can be computed from the simulated
spiking activity. We here extend a local network and LFP model to an area of
4$\times$4 mm$^2$. The upscaling preserves the densities of neurons while
capturing a larger proportion of the local synapses within the model. The
procedure further introduces distance-dependent connection probabilities and
conduction delays. Based on model predictions of spiking activity and LFPs, we
find that the upscaling procedure preserves the overall spiking statistics of
the original model and reproduces asynchronous irregular spiking across
populations and weak pairwise spike-train correlations in agreement with
experimental data recorded in the sensory cortex. In contrast with the weak
spike-train correlations, the correlation of LFP signals is strong and decays
over a distance of several hundred micrometers, compatible with experimental
observations. Enhanced spatial coherence in the low-gamma band around 50 Hz may
explain the recent experimental report of an apparent band-pass filter effect
in the spatial reach of the LFP.
