Your TgAb and TPO antibodies are thyroid antibodies and your results are not elevated. As you can see, they are well below the top of the lab range which means your hypothyroid condition is not caused by autoimmune thyroid disease.
I don't know for sure if there is a connection. Many people with autoimmune thyroid disease finds it helps to go gluten free. I don't have thyroid antibodies but I've found I feel a lot better on a gluten free diet so I've stayed on it.
If you have gluten sensitivity then it's likely your gut absorption is affected. Taking levothyroxine, although necessary with hypothyroidism may cause some small intestinal bacterial imbalance according to some recent scientific reports so there may be some connection that is as yet not fully understood.
My own opinion is that if we have any kind of thyroid disease the best thing we can do is support our own nutrition by making sure our diet is nutrient rich.
If gluten sensitive it makes sense to cut out gluten. If you don't buy gluten free manufactured products but instead eat whole and home prepared vegetables, fruit, meat and dairy then you may find it improves your health and thyroid function due to better nutrition helping your thyroid hormone levels. You may also enjoy a low carb high (good) fats diet which seems to be good for many people.
What are your vitamin D levels now and are you taking enough vitamin D3 supplement?
Have you also had ferritin, folate and Vitamin B12 tested? If not then ask GP to do them.
Read up on SlowDragon 's responses to other people regarding gut function. Although you do not have Hashimotos, you have antibodies to gluten by the sounds of it so the advice is relevant.
I have not heard that vitamin D helps convert T4 into T3 although I'm sure good vitamin D levels help your body to function better as it's a hormone and you need a good level for bone health and various other functions. All the vital nutrients work together to produce better hormone function in general. I don't have a medical or scientific background so I don't know the details. We see a lot of people on this forum who improve when vitamin levels are improved though. T4 to T3 conversion is selenium dependent so making sure you have good levels of selenium might help.
If you're taking vitamin D supplement then consider taking the co-factors K2-MK7 and magnesium. Magnesium improves absorption and K2 helps to ensure the vitamin D goes to bone and not arteries, as I understand it.
Were you tested for B12 and folate deficiency? They are important for nervous system function. According to the pernicious anaemia society levels over 500 or near to the top of the lab range are best to ensure sufficiency of B12. If you have results you could check with Healthunlocked Pernicious Anaemia forum.
You can also take 1000mg of vitamin C a day. Some people say it's best in 2 split doses. This may help support adrenal function and helps absorption of other nutrients.
Do you know what your folate level is? B12 and folate work together for good function. Do you have symptoms of B12 deficiency? If so then worth another check for both B12 and folate.
If you take a B vitamin supplement make sure it does not have biotin in or stop taking a week before any thyroid blood test as it can falsly alter the results.
Not sure what the upper reference range for folate is in your lab as it's not given but 6.8 is usually quite low. In the UK, I've noticed that the range can be somewhere between 2.6 and 20 or thereabouts but labs vary. If it is low in range then you could supplement with a good B complex and retest to see if that raises both B12 and folate nearer to the top of the range. Try to find a B complex with all the methylated forms of B's for best absorption. I've taken Thorne Basic B to improve mine.
You might also want to get full evaluation for Coeliac disease. If you want to do this it's important to keep eating gluten for the test to be acccurate apparently. Something you might not want to do if it makes you ill.
Most people should be able to improve their vitamin levels with nutrition but people with thyroid conditions or antibodies cannot always do so. Older people may also experience problems due to less effective absorption as we age. Thyroid imbalance causes an imbalance in stomach acid. Usually low stomach acid. The stomach needs to be the right acidity level to extract nutrients efficiently. Thyroid conditions are as much about the gut as they are about the thyroid. A very great proportion of our immune system resides in our gut. When the gut is adversely affected then it makes it very difficult to absorb nutrients effectively and can affect our immune responses.
Our ability to absorb nutrients is compromised by the thyroid disease or due to thyroxine. Probably because for many people just T4 (Levo) does not fully alleviate hypothyroidism.
Gut malabsorption may be due to lower stomach acid a common issue for many hypothyroid patients.
Lower stomach acid is also much more common as we age too
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