Non-threatening familiar sounds can go unnoticed during sleep despite the fact that they enter our brain by exciting the auditory nerves. Extracellular cortical recordings in the primary auditory cortex of rodents show that an increase in firing rate in response to pure tones during deep phases of sleep is comparable to those evoked during wakefulness. This result challenges the hypothesis that during sleep cortical responses are weakened through thalamic gating. An alternative explanation comes from the observation that the spatiotemporal spread of the evoked activity by transcranial magnetic stimulation in humans is reduced during non-rapid eye movement (NREM) sleep as compared to the wider propagation to other cortical regions during wakefulness. Thus, cortical responses during NREM sleep remain local and the stimulus only reaches nearby neuronal populations. We aim at understanding how this behavior emerges in the brain as it spontaneously shifts between NREM sleep and wakefulness. To do so, we have used a computational neural-mass model to reproduce the dynamics of the sensory auditory cortex and corresponding local field potentials in these two brain states. Following the synaptic homeostasis hypothesis, an increase in a single parameter, namely the excitatory conductance g¯AMPA, allows us to place the model from NREM sleep into wakefulness. In agreement with the experimental results, the endogenous dynamics during NREM sleep produces a comparable, even higher, response to excitatory inputs to the ones during wakefulness. We have extended the model to two bidirectionally connected cortical columns and have quantified the propagation of an excitatory input as a function of their coupling. We have found that the general increase in all conductances of the cortical excitatory synapses that drive the system from NREM sleep to wakefulness does not boost the effective connectivity between cortical columns. Instead, it is the inter-/intra-conductance ratio of cortical excitatory synapses that should raise to facilitate information propagation across the brain.