Is there any research on physiology of deep and long meditative states (i.e. days and weeks of sitting)? I keep hearing about Theravada monks who are able to stay in deep meditative states for days and weeks on end. While I do not [yet] question ability to stay in meditation for that long, what interests me is the physiological side of things: how human beings are able to spend that much time meditating without dying of dehydration or having some issues due to blocked blood flow etc. 

Has anyone seen any research on topic or can offer a proper search query for Google scholar?
Check out this article: Meditation as a Voluntary Hypometabolic
State of Biological Estivation by John Ding-E Young and Eugene Taylor.

It's a really interesting, brief read. Basically, it is a review of several studies on the physiology of meditators. It provides evidence for the case that aspects of meditation may be similar to hibernation, or "hypometabolism". For example, like some bear species are able to not eat or drink for months on end (as far as I know) and come out fine, maybe meditators are able to lower their metabolism and thus meditate indefinitely without physiological upset. Some really cool examples of people meditating underground for days, or in airtight boxes for multiple hours with no ill effects.