Fun With Nuclear Medicine!

Suppose that you're given 150 mCi of radioactive iodine (I-131) for treatment of your thyca. What's an mCi?? And just how much iodine are you gulping in that mouthful of stale tap water or that little capsule?

(If you have no patience with my derivation, which does get rather mathematical, you can skip down to the answer.)

OK, you know that radioactivity happens because atoms burst apart, spewing subatomic particles and changing into different atoms. Well, the Curie (named after the Polish scientist Marie Curie) is just a measure of how many of these tiny explosions are happening per second.

One Curie is equal to the amount of matter you need in order to have 3.7 × 10E10 disintegrations per second (page F-99 of the CRC Handbook of Chemistry and Physics, 60th Edition [1979-1980] - all other citations on this page also refer to this book). (Another standard way to measure activity is the Bequel, abbreviated Bq, which is one disintegration per second, so a Curie equals 3.7 × 10E10 Bq, or 0.037 gigaBequel.)

The Curie is abbreviated Ci. One one-thousandth of a Curie is a milliCurie, abbreviated mCi. So one mCi is equal to 3.7 × 10E7 disintegrations per second. Therefore, a 150 mCi dose of I-131 is 150 milliCuries or 5.50 × 10E9 disintegrations per second. That's a lot of little atoms popping away!

(By the way, the NCRP permissible quarterly intake for occupational exposure to I-131 is 4.0 microCuries, or 0.004 mCi [page B-381], which is why your nuclear medicine doc is very careful when he or she hands you your dose.)

Now we look at the half-life of I-131, which is 8.070 days (page B-270). By my calculations, this is 697,248 seconds. Now we can use the equation on page F-100 to calculate Lambda, the decay constant, for I-131 (trust me, we need the decay constant):

decay constant Lambda = (ln 2)÷(697248 seconds) = 9.94 × 10E-7 /seconds

Now, the rate of decay is given by the equation

-delta N÷delta t = Lambda × N
(so if N₀ atoms are present at time 0, then at an arbitrary time t there are N_t = N₀e^{(-Lambda t)} atoms present at time t)
5.50 × 10E9 /sec = Lambda × N₀ then N₀ = (5.50 × 10E9 /sec)÷(9.94 × 10E-7 /sec) = 5.53 × 10E15 atoms

OK, now we know it takes 5.53 × 10E15 atoms (553,000,000,000,000 atoms!) of I-131 to make up 150 mCi. Wow, that sounds like a lot! But how much is it really? Not a handful, obviously, or it wouldn't fit in that little pill. Chemists generally count atoms using a unit called a "mole" to avoid dealing with such huge numbers. A mole is 6.02 × 10E23 atoms, (602,000,000,000,000,000,000,000 atoms), so what we are dealing with is just 0.000000009 moles. (Sounds like a lot less when I write it like that, doesn't it?)

The neat thing about moles is that if you multiply the number of moles by the atomic weight of the atom, you get the number of grams. There is no atomic weight given for I-131 (no one cares about I-131 except thyroid patients and their doctors) but I figure that 131.0 is probably within one percent of the correct value.

So, multiplying the number of moles by the atomic weight,

(0.000000009 M)(131 gram/M) = 0.0000012 gram I-131

which can also be written as 0.0012 milligram (mg) or 1.2 microgram (mcg or ug) of I-131 in 150 mCi.

So, there are 1.2 micrograms (mcg, also abbreviated as µg or ug) of I-131 in 150 mCi.

Now, that is NOT very much! For comparison:

The Recommended Daily Allowance for iodine, set by the US FDA, is 150 mcg a day
When on the Low-Iodine Diet, you are attempting to consume less than 50 mcg per day
The largest cell of the human body, the egg cell, has a mass of about 1.5 mcg and is therefore heavier than my 150 mCi dose!
If my 150 mCi dose of radioactive iodine were formed into a little ball, the ball would be about 15 micrometers in diameter. That's about the size of an average-sized cell in the human body, such as a liver cell at 12 micrometers across. (Iodine is denser the stuff that our cells are made of, so a given mass of it takes less space than human tissue.)

Note that the mathematical path from 150 mCi to 1.2 mcg I-131 was all straight multiplication and division. (The logarithm stuff was just to get Lambda, which is a constant.) That means we can continue to use multiplication and division to get other values in a straightforward way, for example:

(1.2 mcg I-131/150 mCi)÷150 = 0.008 mcg I-131 in 1 mCi (or 8 nanograms!)

(Wow, 8 nanograms per mCi. For comparison: An average-sized cell in the human body, such as a liver cell, has a mass of 8 nanograms. If you made 8 nanograms of iodine into a little ball, the ball would be about 0.4 micrometers across, or smaller than the smallest cell of the human body, a sperm cell - the head of a sperm cell is about 2 micrometers long. In fact, this little iodine ball would be about the size of a wavelength of violet light!)

So, a 5 mCi scan dose would be:

(5 mCi)(0.008 mcg/mCi) = 0.04 mcg I-131
In other words, to find out how much iodine you're getting in micrograms, multiply your mCi dose by 0.008.

You also sometimes see doses given in GBq (gigaBequel) instead of mCi. The conversion factor there is 0.216 mcg I-131 in 1 GBq. So, for example, a 9.04 GBq dose contains

(9.04 GBq)(0.216 mcg/GBq) = 1.95 mcg I-131

The GBq measurement is used more often in Europe than in the US. The above dose was given to a British member of the thyca mailing list. To get mCi from GBq, multiply by 27. Thus, the 9.04 GBq dose is about

(9.04 GBq)(27 mCi/GBq) = 244 mCi

Nice stiff dose there.

I told you that I did the above calculations at 2:00 in the morning. Also, it had been 13 years since I took that P-chem class. So I didn't trust my results 100% until I posted them to the thyca mailing list and was pleased to get the following response:

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Rex and Linda Tam wrote:
> 
> Hypo insomnia amusements at 2:00 AM last week-- I took down the old CRC
> Handbook of Chemistry and Physics and tried to figure out how much I-131
> makes 150 mCi. Now it's been 13 years since I took P-chem so I am totally
> rusty (and I ended up being a Math major instead) so I may be wrong, but I
> came up with 150 mCi of I-131 = 1.2 ug (micrograms) of I-131.
> 
> (And the calculations were all straightforward multiplication/division, so
> you can get numbers for any dose from the above-- for example 1 mCi =
> 1.2/150 = 0.008 ug.)
> 

I checked your calculations. You are right.

I go through those calculation during an 8 day physics course I teach to
the radiology residents every year. I have yet to find one resident who
can do those calculations on their own at the end of their fourth year.
I you go to medical school, I'll hold a spot in our radiology program
for you.

Jeff Cooper

-- 
Jeffrey A. Cooper, MD		(518) 262-3372
Nuclear Medicine, A-72		(518) 262-3394 (Fax)
Albany Medical CENTER		(518) 422-4655 (Beeper)
Albany, NY 12203		cooper@rad.amc.edu

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Last updated on October 10, 2002.