I think it takes a mod to combine threads but it's actually two very different concepts. What Dr. Arata is talking about with the vagus nerve is not a matter of relieving compression. He is saying
The vagus nerve is the conduit for autonomic signals and it travels alongside the jugular vein. Renal denervation therapy has shown us that autonomic fibers can be manipulated via a transvascular approach. If the balloon mechanically stimulated the vagus nerve and it was what lead to the response to treatment it would solve the mystery of how a patient with a normal jugular vein could respond to jugular ballooning. http://blog.synergyhealthconcepts.com/d ... -magazine/
I interpret this as saying the ballooning squeezes the vagus nerve and that mechanical stimulation is supposed to be enough to cause the improvements seen after CCSVI treatment. Changes in blood flow are not what's causing the improvements, according to this. The compression of the vagus nerve occurs temporarily during the procedure; it was not compressed prior nor afterwards.
The brainstem compression theory is saying that changes in blood flow are important, so much so that it also leads to changes in cerebrospinal fluid flow since CSF drains into the sinuses which drain into the jugulars, and those changes in cerebrospinal fluid flow potentially in some patients relieve brainstem compression. The brainstem was compressed prior to the procedure, and afterwards is not.
There is research on brainstem compression in conditions such as Chiari malformation.