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I have had 3 open surgeries over the years and will have a 4th soon. All have been open, so I can't speak to the lap procedure. I have had some damage to the Vagus nerve over the years. There are a lot of things that "could" be damaged in any surgery. My surgeries, for example, could easily damage liver and spleen...but that has never happened. Friday, my surgeons and I will discuss the vagus issue. I will see if I get their perspective (vagus open VS lap). If I learn anything (2 doctors opinions, only) I'll post it.
Good Luck (with a skilled and very experienced surgeon, the surgery can be life changing).