They used MRIs with contrast to image the brain's glymphatic pathway--a complex system than clears wastes from the brain. Sleeping on one's side made this system work the most efficiently. (J of Neuroscience)
Of course, this was in ...rats..anesthetized rats.
This sort of makes sense to me--even for humans. The scientists say sleeping on one's side is the most popular position for humans and animals. And--many dementias do seem linked to sleep disturbances.
What do you think? They are turning now to checking this out in humans.
For now, it's an intriguing theory.