During NREM sleep and anesthesia, the cerebral cortex generates low-frequency synchronized activity, known as Slow Wave Oscillation (SWO). In this brain state, cortical neurons alternate between hyperpolarized Down states and depolarized Up states, which will travel from their source through cortico-cortical connections along the whole cortex. This makes the SWO an ideal model to understand cortico-cortical communication and disentangle local properties from those that are controlled by the network state.In this project, we built a computational model of coupled cortical populations under the SWO regime, which includes pyramidal and inhibitory neurons, expanding previous conductance based neuronal models. We have generated our model to study how intrinsic properties of a population can shape their SWO and their neighbors, and which parameters of this oscillation remain local and thus can be used to understand the physiology of the recorded circuit. We first show how sparse long range connections are sufficient to synchronize populations that are able to otherwise sustain autonomous SWO. We have also studied how this wave which travels along the preferred axis of propagation can impose a single frequency of oscillation along distal areas, together with distinct properties of the Up states, such as their length or the speed of the transitions from and to the Down states. Conversely, other attributes that describe the internal structure of the Up state remain mostly modulated by local properties of each population. With this, our work bridges the intrinsic properties of a circuit with the macroscopic synchronized dynamics of the embedding network.