What kind of research has been done on this?

In a 2014 case study (University of Ottawa's School of Psychology),a woman who said she could astral project was put under a fMRI machine. The patient was physically stationary for an hour but guided in and out of astral projections in which she was prompted to move her nonphysical body in different ways. Researchers monitored the activity in different regions of her brain throughout the exercise and found that they did show activity that correlated with motion during the times she claimed to be astral projecting.