Hi Taly,
I think you're getting some good advice here.
Here is a link I found to an article about Dural Inversion that was published in 1997. I don't know anything about it, but thought it might helpful. Found quite a bit when I did a google search. Maybe you can find some more recent information.
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I especially like the advice given by Dr. Scott at Boston's Children's Hospital about this and other surgeries recommended for children with Moyamoya. Here's that link
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Don't agree to any surgery until you understand exactly:
1. what the doctor is proposing to do
2. why this procedure and not another
3. what problems could possibly occur
4. how likely it is that those will be encountered
5. how many times has the surgeon performed the procedure (they aren't considered proficient until they have at least 100 of a given procedure under their belt)
6. how many of those patients have had successful outcomes and
7. what is his definition of successful
If you're not satisfied with the answers received, you may be able to use his answers to convince your insurance carrier that only a moyamoya specialist can successfully treat you child. To do that you'll need to ask the same questions of a Moyamoya specialist like Dr. Scott or Dr. Steinberg for comparison.
Another thought, have you sent your child's diagnostic scans to Dr. Steinberg? If he's familiar with the case, you might talk to Bob, in Dr. Steinberg's office about his possibly speaking to your insurance company for you, that's what he does. I know he's been able to negotiate with them for other patients so that they were able to have the surgery there. Sometimes Stanford will agree to do the surgery for the same cost as the insurance company would pay to your in-network hospital and surgeon. It might be worth a try.
Best of luck,
Kim