The more carbs we eat, the more Iodine depleted we are, thus, the higher the requirement for Iodine (due to increased T3 levels).
An increased iodine requirement as a result of significant changes in human nutrition rather than a decreased environmental iodine supply is suggested to represent the main cause of the iodine deficiency disorders (IDD). The pathomechanism proposed is based on the fact that serum concentrations of thyroid hormones, especially of trijodothyronine (T3), are dependent on the amount of dietary carbohydrate. High-carbohydrate diets are associated with significantly higher serum T3 concentrations, compared with very low-carbohydrate diets. While our Paleolithic ancestors subsisted on a very low carbohydrate/high protein diet, the agricultural revolution about 10,000 years ago brought about a significant increase in dietary carbohydrate. These nutritional changes have increased T3 levels significantly. Higher T3 levels are associated with an enhanced T3 production and an increased iodine requirement. The higher iodine requirement exceeds the availability of iodine from environmental sources in many regions of the world, resulting in the development of IDD.
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http://www.sciencedirect.com/science/article/pii/S0306987704001690