A 30 year old Caucasian female is admitted to the ER with profound weight loss.
After radiology studies it is determined that she has a fast growing spherical lesion on her
thyroid gland approximate 2 cm in diameter and volume of 4.19 cc.

The biological half-life of iodine is different in the various organs of the body,
from 100 days in the thyroid, to 14 days in the kidneys and spleen,
to 7 days in the reproductive organs.

The thyroid weighs 18-60 grams in adults, with a mean of 39 grams.

15-20 mg of iodine is concentrated in the thyroid.
30% of the bodies iodine is concentrated in the thyroid with
70% of the body's iodine is distributed in other tissues, including mammary glands, eyes, gastric mucosa, the cervix, and salivary glands. 

Thyroid cancer is quite deadly when left to grow,
Fortunately it responds very well to treatment with Iodine 131
However, if too little I-131 is given, it will produce thyroid cancer, so in a bizarre way, too much I-131 is better than too little.

Patients whose thyroids are completely ablated (destroyed) after I-131 therapy must take oral thyroid hormone supplements for the rest of their life.

Iodine 131 has a half-life of 8.0197 days.
It is prepared by neutron bombardment of tellurium.
Pure I=131 has an atomic mass of 130.906 g/mole
But it is administered as sodium iodide. Sodium has an atomic mass of 22.990 g/mole
NaI-131 has a molecular weight of 130.906 + 22.990 = 153.896 g/mole

The typical treatment dose for papillary thyroid cancer (86% of thyroid cancer cases) is 100 mCi

1 Curie (Ci) is 3.7 x 10^10 disintegration per second.

So the first thing we want to compute is the number of undecayed I-131 molecules in a given sample.

let n be the number of cancerous thyroid cells

let r be the number of radioactive Iodine 131 atoms

as r increases n decreases