Question

Fentanyl is a synthetic opioid used as a pain medication, and lately heavily abused as the cheap alternative to other illicit drugs. It is 50 times more potent than heroin and 100 times more potent than morphine. The lethal dosage is 3 mg on an average sized person. There are many sources where fentanyl may be obtained, legally and illegally. One of legal sources is in the slow release transdermal fentanyl patches for longer term pain relief. One of the highest concentration is called Fentanyl Sandoz 100: Each patch contains 16.8 mg fentanyl in a patch size 42cm^2 , releasing at 100 µg/hour. Analyze what could be the maximum number of patches an average person can have without dying. How many milligrams of fentanyl left on the patch after 24 hours usage?

Answer 1

First, the max amount of patches an average person can have without dying. We are going to assume that the body takes 1 hour to start eliminatin fentanyl, se we will calculate the amount of patches that would release the lethal 3 mg of drug in 1 hour.

If each patch releases 100 micrograms per hour, to get a 3 mg dose in one hour the person should have (we will use the fact that 1000 micrograms equal 1 milligram):

So, a person wearing 30 patches would get a 3mg dose in 1 hour.

Now, to calculate the amount left in a patch after 24 hours use, we substract the released amount in 24 hours to the initial amount of fentanyl: