Brief Answer:
Thyroid

Detailed Answer:
I understand your question.

The TSH has now come down towards normal.

The target in the first 3 months is to keep it in the range of 0.1 to 2.5

The target in the second 3 months is to keep it in the range of 0.2 to 3

The target in the last 3 months is to keep it in the range of 0.3 to 3 (to 3.5)

So although it may seem logical to you that your wife's TSH has come down from 12 to about 2, the medication should be either stopped or lowered in dose. Because, doing so will result in the TSH rising back up again into the abnormal range. This is not at all desirable.

I am asked this question everyday by concerned patients.

The reason is that it is quite possible that your wife has a form of permanently under-active thyroid condition called Hypothyroidism. The most common cause of this is an 'auto-immune' problem ie the body's own defences target the thyroid and make it non-functional.
The best way to test for this is a simple blood test called

Thyroid auto antibodies (anti TPO and anti Thyroglobulin)

There is no need to fast for this test and it can be done at anytime of the day or night.

TPO stands for Thyroid PerOxidase.

You can request your doctor to consider ordering this test with her next set of TSH.

Furthermore it is preferable to test for Total T and Total T3, during pregnancy along with TSH. If your laboratory does not define the upper limit of normal for Total T3 and Total T4 DURING PREGNANCY, the it is safe to take 150% of the upper limit of normal for the non-pregnant range as the upper limit of normal for pregnancy.
The reason for not going by the Free T4 during pregnancy is that most lab methods have not studied the normal range for Free T4 in pregnancy. However, if your lab's Free T4 reports normal ranges for Free T4 in pregnancy then one can use that as a guide to determine the right eltroxin dose, in addition to the TSH values.

Otherwise, outside of pregnancy situations, Free T4 is a useful test and I hardly order Total T3/T4 in non-pregnant patients.

All this may seem complex to you but thyroid can be challenging for the non-expert and that is why I strongly recommend you follow up with an Endocrinologist in person to ensure your wife's thyroid is managed well.

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Brief Answer:
Follow up

Detailed Answer:
I see. It is good you are following up regularly with a qualified Endocrinologist. This is very important.

I generally recommend my patients to take their Eltroxin with water 30 to 60 minutes before breakfast, although I would prefer if they took it 60 minutes prior.
So the 45 minute gap that you have been recommended is also fine.

Keeping the TSH in target range is the important thing, which it is now.

So checking at regular intervals as guided by your endocrinologist will ensure it stays in the goal range.

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