I’d say that a “brain transplant” is perhaps better regarded as a “body transplant” seeing as the self-identify of the combination comes from the brain.
Anyways … there have been “head transplant” and even “head addition” (extra head) experiments done on monkeys … I used to have photos of these in my scrapbook as a kid, so we’re talking 1960’s or 1970’s. Perhaps there have been more recent ones too.
The “head transplant” is exactly as you imagine it, and the “head addition” was adding an extra head on the side of a monkey’s neck (presumably without attempting to connect the spinal cord?). I’m not sure whether in the “head transplant” they did connect the spinal cord, or just the blood vessels, but it was successful enough that the head regained consciousness and was alive for (if I recall correctly) a few days.
Given the modern success of reattaching severed arms etc, I don’t suppose there is necessarily any reason why reattaching the spinal cord might not work, although not sure how that would work in terms of life support functions like breathing while connections grew back.
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