Just some thoughts about the modeling of anaesthesia and sleep. Both are rather global phenomena with (probably) microscopic neural origins. Hence there is a vast bridge between origin and phenomenon.
For instance, anaesthestics act on synaptic receptors and ion channels on a scale of tens of micrometers. The spatial distribution of these receptors is rather unknown. E.g. GABAergic receptors are major targets of anaesthetics and they are almost omnipresent in the brain. Since they occur in almost all brain areas, some studies argue that it is sufficient to model the brain areas as effective entities and then study the interaction between the brain areas. Then the question still arises, how the network of brain areas generate the phenomenon, let us say, the loss of awareness/consciousness in anaesthesia and sleep. Hence, it is important to study the interaction between the brain areas in some more physiological detail. At the end, the problem is how to work on a network of brain areas, in which the detailed physiology plays an important role. Level of description ? Does mathematics help ? Or just focus on numerical simulations ?
What do you think ?