This is the only abstract from the largest medical library in the U.S. This procedure is very far from being used as a proven treatment.
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J Oral Maxillofac Surg. 2013 Apr;71(4):677-81.
A new minimally invasive technique for cauterizing the maxillary artery and its application in the treatment of cluster headache.
Shevel E.
SourceThe Headache Clinic, Johannesburg, South Africa. drshevel@headclin.com
Abstract
PURPOSE: To describe a new, relatively atraumatic method of cauterizing the maxillary artery and its effectiveness in treating cluster headache.
MATERIALS AND METHODS: Five patients with cluster headache were treated with arterial ligation of certain terminal branches of the external carotid artery. A new, atraumatic method of cauterizing the maxillary artery is described.
RESULTS: The success rate and postoperative morbidity are presented. In four out of five patients the cluster attacks ceased immediately following surgery.
CONCLUSION: A new intraoral technique for maxillary artery cauterization and the effectiveness of cauterization of the terminal branches of the external carotid artery in the treatment of cluster headache are described. Although the sample is small, the results are encouraging, and may offer permanent relief of cluster headache pain.
PMID:23507321[PubMed]
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Given your uneven response to the usual treatments, it would be wise to find a headache specialist to get a fresh look at your options are.
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LOCATING HEADACHE SPECIALIST
1. Yellow Pages phone book: look for "Headache Clinics" in the M.D. section and look under "neurologist" where some docs will list speciality areas of practice.
2. Call your hospital/medical center. They often have an office to assist in finding a physician. You may have to ask for the social worker/patient advocate.
3. Multimedia File Viewing and Clickable Links are available for Registered Members only!! You need to

or

On-line screen to find a physician.
4. Multimedia File Viewing and Clickable Links are available for Registered Members only!! You need to

or

Look for "Physician Finder" search box. They will send a list of M.D.s for your state.I suggest using this source for several reasons: first, we have read several messages from people who, even seeing neurologists, are unhappy with the quality of care and ATTITUDES they have encountered; second, the clinical director of the Jefferson (Philadelphia) Headache Clinic said, in late 1999, that upwards of 40%+ of U.S. doctors have poor training in treating headache and/or hold attitudes about headache ("hysterical female disorder") which block them from sympathetic and effective work with the patient; third, it's necessary to find a doctor who has experience, skill, and a set of attitudes which give hope of success. This is the best method I know of to find such a physician.
5. Multimedia File Viewing and Clickable Links are available for Registered Members only!! You need to

or

NEW certification program for "Headache Medicine" by the United Council for Neurologic Subspecialties, an independent, non-profit, professional medical organization.
Since this is a new program, the initial listing is limited and so it should be checked each time you have an interest in locating a headache doctor.