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considering it costs nothing, there are no possible side effects its within every ones capabilities and takes no realy effort its not really something to ignore and in all likleyhood avoliding these products would give you a healthier diet there is no reason not to try.... you also know within a few days weather it is going to make any difference..
also loads of people are intolerant to the those products and would benefit from avoiding them...
I don't now weather there is a direct link but loads of poeple write about it, I know two brothers who if they eat too much of the wrong products say if 'boggles their minds' (they are both on the spectrum) and our lad used to go very odd if he had too much...
no risk / no effort / no cost + possible benefit = give it a try...
I'm not saying it does or doesn't work, but, a GP/Consultant is not going to put false hope into someone mind, especially with no conclusive evidence to support.
There is no medical treatment for Autism/Asperges, the only thing that can be done is to understand the condition and help those affected by it learn how to deal with it and support them through life. Much like you would anyone else if they're having troubles.