How can doctors tell if a patient's thyroid is not working by using iodine tracers?

The thyroid gland uses iodine in producing thyroxine (T4) and triiodothyronine (T3). By using iodine tracers we can see where the iodine is going in the body. A normally functioning thyroid gland will have a high concentration of the labeled iodine, since it will take it up to produce new T4 and T3. A nonfunctioning thyroid will not. (That's my understanding of the process anyway, but keep in mind I'm a pharmacist, so I'm not as well-versed as physicians in the diagnosis of illness.)