A common sight in science fiction that features mad scientists is a brain in a jar. The mad scientist has extracted some poor sap's brain in order to do some demented experiment on a person who now cannot move or communicate in any possible fashion. But what would it take to actually extract a person's brain from their head and keep it alive?
Well, in the immediate physiological category, the brain needs glucose and oxygen from a blood supply, or it quickly will die. It also needs support -- a live human brain has about the tensile strength of a raw egg yolk. Hence the jar, it provides a supporting saline environment. The arteries and veins of the lower brainstem would be connected to an extracorporeal circulatory machine, to keep the blood oxygenated and circulating, and another machine would drip glucose into the blood. Not too fast, or we'll be giving our brain diabetes. Not too slow, or we'll starve it.
We will also, within a week or so of connecting the brain, also need to provide a dialysis machine to remove the metabolic waste. It'll be an easy duty-cycle for it, as it only must support the brain alone, which accounts for about a quarter of the body's entire metabolic activity.
We'll inevitably need some sort of electrical-communication system to keep the brain stimulated. Experiments show that sensory deprevation makes everyone eventually go totally insane, and lowers the person's IQ to boot. This will be connected to the brain-stem at the place where the spinal cord was formerly connected, and a computer can provide a virtual-reality of our choosing to the brain. This would probably form the bulk of useful experiments, too, as you expose your subject to all kinds of scenarios of varying degrees of plausibility.
We'll need blood-cell generation within 120 days, and some sort of dead-blood-cell removal system to go with it. The dialysis machine may be able to help with this. Possibly.
The brain will have to sleep between 7 and 9 hours every 24, and prefers to do this regularly. This will have to be factored into our brainstem-tap-device, because if it wakes up the brain frequently, that will be bad for its health.
All of these machines together will be considerably larger than the original human being was, and will consume far more energy. Putting the brain back into its original body will be impossible, plus the ethics of this situation are horrible, so I can't see sane science doing this anytime soon. Or, for that matter, ever.