How much additional sleep is required to recover from a given number of hours of sleep deprivation? A previous question dealt with whether it is possible to catch up on lost sleep.
This question is a little different.

Assume that a healthy adult has been deprived of sleep for "x" hours.
How much sleep is required to restore healthy brain function, compared to sleep lost?   

I wouldn't think the hours needed could be predicted by a linear scale.
Is there some predictable relationship between the two and what type of relationship is it?
It is funny that you ask this question. The answer is you can't. When you dont get enough sleep and you feel tired and your brain activity is lower (for example, trouble remembering what you were doing or where you left your keys) you cant catch up to it. You might take a powernap (not longer than 90 minutes) to give you a sensation of feeling awake, but the brain doesnt become more active. I dont know exactly why you cant catch up to lost hours of sleep, but you just cant. That also the reason, besides a messed up biogical clock according to light, why people working night shift experience more mental and health issues.