Maybe this is obvious, but as someone with a ton of celiacs in the family, who has been living with this diet for almost tenty years and has seen major advances in celiac knowledge . . . remember the misdiagnosis rate for MS is 5 to 10 percent. I think many people who have amazing recoveries from many illnesses from various diets do so because the diets include a gluten-free component. I think many, many people are undiagnosed celiacs.
I think many people who have been told theey have MS but then improve on a GF diet may in fact have celiac disease and not have MS at all. Celiac disease can cause many of the same symptoms as MS. It can cause lesions on the MRI. It can cause multiple nutritional abnormailities that produce neurolgical symptoms that mimic MS symptoms.
Testing for celiac disease is only accurate BEFORE you go on an alternative diet. I urge peopple to get tested before they try alternative diets. Of course you could go ahead and change your diet anyway, but if you do, you will never know if you have gluten intolerance, and then you will be more likely to stop complying with the diet after a number of years.

This will open you to the possibility of lymphoma, renewed silent damage, etc.
The target of damage in gluten intolerance can be any organ -- the intestines, the brain, the skin, the immune system, etc. Most awareness has been focused on the intestines.
I am an example of someone who has celiac in the family but does not have celiac disease but DOES have MS. I have been tested so many times for celiac, and I have followed a GF diet for many years, and I still have a big case of MS. So there is still a co-genetic issue, and gluten is not the only answer, but definitely the gluten factor can be huge for many people.
Thanks for the post, squiffy.
