Biophysically-grounded whole-brain models were built recently using tractography data to interconnect multiple mesoscopic models, which can simulate the dynamics of neuronal populations with only a few equations. Mean-field models of neural populations, specifically the Adapting AdEx meanfield, was used for this purpose because it can integrate key biophysical mechanisms such as spike-frequency adaptation and its regulation at cellular scales, to the emergence of brain-scale dynamics. Using this approach, with the Virtual Brain (TVB) environment, it has been possible to model the macroscopic transitions between brain states, described by variation in brain-scale dynamics between asynchronous and rapid dynamics during conscious brain states, and synchronized slow-waves, with Up-and-Down state dynamics during unconscious brain states, emerging from mechanisms at the cellular level. Transitions between brain states are driven by changes in neuromodulation that can be due to intrinsic regulation during sleep-wake cycles or extrinsic factors such as anesthetics, which, in turn, affect spike-frequency adaptation. Here, we perform a dense grid parameter exploration of the TVB-AdEx model, making use of High Performance Computing, to thoroughly explore the properties of this model. We find that there is a remarkable robustness of the effect of adaptation to induce synchronized slow-wave activity. Moreover, the occurrence of slow waves is often paralleled with a closer relation between functional and structural connectivity.We find that hyperpolarization can also generate unconscious-like synchronized Up and Down states, which may be a mechanism underlying the action of anesthetics. We conclude that the parameter space of the TVB-AdEx model reveals features identified experimentally in sleep and anesthesia.