Rhythmic local field potential (LFP) oscillations observed during deep sleep are the result of synchronized electrical activities of large neuronal ensembles, which consist of alternating periods of activity and silence, termed 'up' and 'down' states, respectively. Current-source density (CSD) analysis indicates that the up states of these slow oscillations are associated with current sources in superficial cortical layers and sinks in deep layers, while the down states display the opposite pattern of source-sink distribution. We show here that a network model of up and down states displays this CSD profile only if a frequency-filtering extracellular medium is assumed. When frequency filtering was modelled as inhomogeneous conductivity, this simple model had considerably more power in slow frequencies, resulting in significant differences in LFP and CSD profiles compared with the constant-resistivity model. These results suggest that the frequency-filtering properties of extracellular media may have important consequences for the interpretation of the results of CSD analysis.