There is considerable room for PhD level research on using neural networks to simulate theories of consciousness. One direction would be to develop models of how masking works in psychological studies of perception. It is well known that following a stimulus by a mask prevents conscious experience of the stimulus (in fact, related effects arise if the mask is presented at the same time as the stimulus). However, even though we have no awareness of the stimulus, our motor system still responds to it. Notice that such masking underlies the subliminal presentation of frames during films.
Despite the fact that such masking has empirically been investigated very extensively and indeed many theories of its functioning exist, there is currently no comprehensive computational model of the phenomenon. Thus, a possible avenue for a PhD in this area would be to construct neural network models of the competing theories of masking in order to verify their validity.