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There is no currently known supplement that actively treats Galactosemia (G) . The standard treatment is completely eliminating dairy and not eating foods high in galactose, which can work in the near term, but significant health issues can occur over the longer term even with strict adherence to avoidance of dairy.
Two mechanisms of action with G are elevated oxidative stress levels and inflammation which can both cause long term damage to the brain, liver eyes and kidneys. I think using supplements that are protective of these organs while reducing oxidative stress and increased inflammation levels and have a good safety profile is probably a good idea over the long term in terms of what you can do to try and prevent these longer term effects of G on the body.
So such a supplement would also need to cross the blood brain barrier while specifically being able to target the other affected organs as a protective agent.
One supplement that has shown these abilities is melatonin, but some people don't tolerate melatonin supplementation well, in which case, you can get melatonin naturally which everyone seems to tolerate as melatonin is naturally produced in the body and there are no reported cases of people not tolerating melatonin produced in the body. I wrote about how to do this for people who don't tolerate melatonin supplements here :
https://www.earthclinic.com/supplements/how-to-increase-melatonin-naturally.html
I would also like to add that a new systematic review showed that the Mediterranean diet also increases melatonin levels as described here :
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9951922/
Here is a relevant quote from the study :
' MD-related foods, such as tomatoes, olive oil, red wine, beer, nuts, and vegetables, showed high melatonin contents. The consumption of specific MD foods increases melatonin levels and improves the antioxidant status in plasma. '
While melatonin is very good for the purposes at hand, it would be helpful to take at least two such supplements for an additive protective effect and possibly even three.
Another supplement that meets the above criteria is Astaxanthin and like melatonin it has a very good safety profile. Maximum study dosages have been 24 mg per day and this dose is readily available from online suppliers.
A third supplement that also meets these criteria and has a very good safety profile is Grape Seed Proanthocyanidin Extract (GSPE). This is one I have used to good effect :
This is a link to what I wrote about the benefit that I found from my use of Astaxanthin, but not the only reason I take it :
https://www.earthclinic.com/supplements/astaxanthin-for-endurance.html
I have written a very significant amount about melatonin on EC for many more issues than you would be considering it for.
Good luck!
Art