The Essential Health Clinic, which set up its city practice at The Edinburgh Clinic in Colinton two weeks ago, has more than 1000 people with MS who have been screened or are waiting to be screened for chronic cerebrospinal venous insufficiency, with a further 4000 signing up for more information.
The condition has been linked to MS but the NHS and the MS Society say there is not enough evidence to determine what effect CCSVI has on MS.
MS itself is caused by the auto-immune system destroying myelin, the fatty sheath which surrounds nerves. Essential Health Clinic's medical director Dr Tom Gilhooly, a former government advisor on drug abuse who has worked with those affected by MS for six years, opened the clinic a fortnight ago to coincide with a CCSVI conference in Glasgow.
Dr Gilhooly admitted that he was initially cautious about the new procedure, which costs around 6000, but changed his mind.
He said: "There's new 'miracles' all the time in MS so I thought here we go again.
"I started reading some of the papers and thought there's an actual biological hypothesis here that holds weight and makes sense."
Dr Gilhooly studied the theory of Italian Dr Paolo Zamboni, of the University of Ferrara in Italy, who was researching treatment for his wife, who has MS.
Using ultrasound scans he concluded that some symptoms associated with MS are caused by veins leading from the brain becoming narrowed, twisted or blocked.
He saw that blockages were allowing iron from the blood to leak into the brain tissue, where it caused damage.
It can be relieved by inserting a tiny balloon device into the blocked vein and then blowing it up to open the blood vessel.
Dr Gilhooly, whose team has treated 16 people since early November, said: "It's very early days but the experience has been pretty positive.
"It varies in person to person but there's a clear pattern of some symptoms that do improve and some that don't.
"I don't think there's a cure but I think there's a tremendous development."
The Evening News told yesterday how city joiner Kenny Meldrum, 44, had the treatment at a clinic in Belgium three weeks ago.
The father-of-one, who had an MS attack four years ago, was left with numbness, balance difficulties and fatigue, but says he felt an "incredible" change within hours.
He said: "I knew they'd come up with something but I didn't think it would be in my lifetime."
Dr Doug Brown, head of biomedical research at the MS Society, said: "We welcome further research. At this stage there is not enough evidence to state whether CCSVI plays a part in the development of MS, nor whether treating CCSVI would have an effect on MS."