Do brain cells shrink during REM sleep or a lucid dream?
For those who have access, here's the full text.

Having read the paper, I can't give you a good answer.  This study was performed in mice, not humans, and "sleep" was achieved in a few ways.  Mice normally sleep most of the day, so it was easy to get mice sleeping normally.  They also induced "sleep" through anesthesia (incidentally, they saw these same results in anesthetized mice, which I think is quite interesting).  The state of "sleep" was confirmed mainly through the measurement of brain waves, in particular the delta wave.  Delta waves correlate to deep sleep, and that's what they measured.  Panels D and G from figure 1 (below) basically confirm just that - the mice were asleep - and that's all we know so far.  More exciting research to be done!