Global Neuronal Workspace
Integrated Information Theory
Global Neuronal Workspace (GNW)
This theory effectively is a biologically-plausible computational model for human consciousness. It conjectures that signals flow from several perceptual, memory, and attentional regions to a central broadcast medium where certain signals cause a cascade that enters conscious awareness.
Integrated Information Theory (IIT)
Also considering the nature by which brain regions are coordinated, the IIT model proposes that there exists a multivariate information measure that generalizes Shannon’s mutual information which captures the interactivity among various brain regions and therefore measures consciousness. There are many candidate information measures.
I believe that work studying individuals coming out of anesthesia is a very intriguing means for understanding quantitatively when consciousness comes about. By analyzing the brain during the transition into an unconscious state, these quantitative measures may be elucidated.