CABG can be performed on-pump (bypass machine) or off pump on a beating heart. Depends on the cardiothoracic surgeon's choice and the patient's health status and needs.
The heart is not "disconnected" from the body, ever, unless it is removed for a transplant, or during an autopsy(or if you happen to be a vampire). During CABG, veins are "harvested" from usually the thighs and used as bypass funnels...attached just before the blockage and just after, so blood can bypass the blockage and still get to the heart muscle with oxygen-rich blood.
It's actually pretty cool to watch and especially cool to see the patient feel so much better afterward.
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