There is some risk for cardiac arrhythmias during general anaesthesia and the finding for the most commonest arrhythmia to be ventricular bigeminy. Your doctor would be the best source for the risk you may have based on your general health, etc.
I don't know about bigeminy, that's not one of my heart problems, yet. But I have had anesthesia many times, including for several hours for open heart surgery. I don't remember any concern by my doctors about my atrial fibrillation and being under an anesthesia.
I agree, and assume your doctor/surgeon knows all your heath issues/concerns and medications. That's were your best answer is.
I just read you detail post on the question and it seems the anesthesiologist see a specific risk. It is news to me to learn they have the authority to stop an operation/surgery when the surgeon and consulting cardiologist say go ahead.
I understand your dilemma, and assume the anesthesiologist is "the expert" in this case. It may be that a full hospital environment would remove the concerns, that is you still have to get an anesthesiologist to administer for your surgery. I'd be sure the anesthesiologist explicitly knows about your bigeminy and does not see it as a stop.
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