I'm really surprised reading this, that so many people have thryoid disease. I just found out this spring that I have Hashimoto's, which is HYPO and the opposite of Hyper, which means your thyroid slows down. Howeve, it only requires medication and not surgery, fortunately. It's a different disease.
ALl I can say is that during the winter, I went through a period where I felt horrible, and that's what promted me to see a doctor and get tested, because I had begun to suspect it was thryroid. The condition runs in my family and I'd been having symptoms for a while which weren't all that serious but odd for me to have. One of them, I should mention was dizzy spells and feelings of vertigo which I thought were from low blood pressure. But during the wintr, something triggered off a spell where I could barely move for about a week- perhaps it was a cold I'd had. I also felt so tired all the time it was like being stoned.
I was sure I'd never be able to do anything again, let alone cycling, but here I am in the summer and I've been cycling nearly every day. I have to, because I put on weight from hypo and am not medicated yet, and it's essential for me to keep that weight off. In fact, it's made me feel better. I think that your wife, once she's on medication, should have no trouble. I look at it this way- if Lance Armstrong or Greg Lemond could get back on a bike after their troubles, then anyone can (unless they're quadriplegic or something).
However, having a condition like this has made me realize how little info there is for people like us who are serious about a sport and who want to know what we can do. I remember looking up a page about "how to keep fit with hypothyroid" and there was a page of exercises- some chubby guy doing situps and deep knee bends. I'm a bit beyond that! I want to know about how things like long distance cycling can affect you, with things like heart rate, etc. A friend of mine is type 2 diabetes and has the same problem- he has to worry about things like dehydration. But when you aska doctor they think of cyclings as riding your bike to the store or around the block! There isn't much info for people like us!
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You can catch more flies with honey than with vinegar. That's great...if you want to attract vermin.