Hyperthyroidism is caused by growth of tumor-like cells that secrete thyroid hor
ID: 1720947 • Letter: H
Question
Hyperthyroidism is caused by growth of tumor-like cells that secrete thyroid hormones in excess of normal amounts. If untreated, an individual with hyperthyroidism may experience extreme weight loss, anorexia, muscle weakness, heart disease, and intolerance to stress and eventually may die. The most successful and least invasive treatment option is generally considered to be radioactive iodine-131 therapy. This involves the injection of a small amount of radioactive iodine into the body. For the type of hyperthyroidism called Graves' disease, it is usual for about 40% to 80% of the administered radioactive iodine to concentrate in the thyroid gland. For functioning adenomas ("hot nodules"), the uptake is closer to 20% to 30%. Excess iodine-131 is excreted rapidly by the kidneys. The quantity of radioiodine used to treat hyperthyroidism is not enough to injure any tissue except the thyroid, which slowly shrinks over a matter of weeks to months. Radioactive iodine is either swallowed in a capsule or sipped in solution through a straw. A typical dose is 5 to 15 millicuries. The half-life of iodine-131 is eight days. Suppose that it takes forty-eight hours for a shipment of iodine-131 to reach a hospital. How much of the initial amount shipped is left once it arrives at the hospital? Suppose a patient is given a dose of 10 millicuries, of which 30% concentrates in the thyroid gland. How much is left one week later? Suppose a patient is given a dose of 10 millicuries, of which 30% concentrates in the thyroid gland. How much is left thirty days later?Explanation / Answer
a) Using the differential equation
ln(Qo/Qt) = kt
Half-life = ln2/k or k = ln2/8 days^(-1)
ln(Qo/Qt) = ln2/8 * (48/24)
since 48 hours = 2 days
ln(Qo/Qt) = ln 2^(0.25)
ln(Qo/Qt) = ln(1.189)
Qt = Qo/1.189 = 0.8408Qo
b) Dose in the thyroid gland = 30% of the complete dost = 30/100 * 10 millicuries = 3 millicuries
ln(Qo/Qt) = ln2/8 * 7
ln(Qo/Qt) = ln 2^(0.875)
ln(Qo/Qt) = ln(1.834)
Qt = Qo/1.834 = 1.635 millicuries
b) Dose in the thyroid gland = 30% of the complete dost = 30/100 * 10 millicuries = 3 millicuries
ln(Qo/Qt) = ln2/8 * 30
ln(Qo/Qt) = ln 2^(3.75)
ln(Qo/Qt) = ln(13.4543)
Qt = Qo/13.4543 = 0.2229 millicuries
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.