I'm no expert on any of this, but I did a little hunting around.
The experiment that involved keeping a severed dog head alive was purportedly performed by a Soviet-era surgeon and inventor called Sergey Sergeyevich Bryukhonenko (1890-1960), not by Demikhov. Supposedly a machine called an autojektor, which Wikipedia describes as a "primitive heart-lung machine", was used to circulate oxygenated blood through the head.
The film of this exploit, narrated amazingly enough by the great English biologist J.B.S. Haldane (who was quite sympathetic to communism and the Soviet Union), was made in 1940 and is called Experiments in the Revival of Organisms. It's supposedly available here:
http://www.archive.org/details/Experime1940
Unfortunately, the link seems to be blocked in China, where I'm based. The authenticity of the film is indeed controversial, but I don't see why it would be impossible in principle to keep a detached head alive by maintaining a circulation of blood suitably enriched with oxygen and nutrients. Whether the autojektor was up to the job is another matter.
Again according to Wikipedia (http://en.wikipedia.org/wiki/Experiment
_Organisms), the film also contains footage of another feat that to me sounds a lot less likely than the severed head bit:
Finally, a dog is brought to clinical death (mostly via a graphical plot
of lung and heart activity) by draining all blood from it, left for ten
minutes, then connected to the heart-lung machine described earlier.
After several minutes, the heart fibrillates, then restarts a normal
rhythm. Respiration likewise resumes, the machine is removed and the dog
is shown to continue living a healthy life.
Then again, I'm not a physiologist. Perhaps one of my colleagues would care to comment.