That's a great thread, glad it's been reposted. It's actually about the internal jugular veins (IJVs) being resectioned...not the external jugular veins. The "external" reference in the paper refers to outside of the brain. The external jugulars are much smaller and drain the exterior of the brain and face, not as essential to the brain, and not related to where we see lesions in MS.
Authors of previous studies have suggested that the vertebral venous system should be adept at tolerating increased venous drainage when internal jugular venous flow is compromised, thereby raising the question as to if there were physiological consequences associated with bi-lateral IJV resection including facial cyanosis and edema.5
Many docs think the collateral circulation formed if the IJVs are not working should be sufficient for drainage. This paper says otherwise.