Pharmaceutical companies take the motto "no pain, no gain" quite literally; without pain to medicate, they'd lose out on billions of dollars in the United States alone. But how does your body to respond to this sort of medication...and how much can you safely take?
For simplicity, let's consider one of the most popular over-the-counter pain relievers: Tylenol. When you take a couple of Tylenol tablets, the active ingredient (acetaminophen) is absorbed into your system and then gradually dissipates. Though individual responses may vary, typically acetaminophen has a half-life of around 3 hours once it's working its magic: this means that if you take two regular strength tablets (650 mg acetaminophen), you'll have 325 mg in your system after 3 hours, 162.5 mg after 6 hours, and so on. In other words, if you take an initial amount A0, the amount of acetaminophen in your system after t hours will be A0 × (1/2)t/3.
Here's an interactive that lets you play around with these parameters to see how much acetaminophen will be in your system over time. The red line lets you model the point after which the acetaminophen stops having a therapeutic effect, because there isn't enough in your system. You can use the graph to confirm recommendations on Tylenol bottles; for instance, with a half life of 3 hours, two regular strength Tylenol tablets (650 mg acetaminophen) will dip below a 200 mg threshold after about 5 hours, while it's recommended that you take two tablets every 4-6 hours.
But if a little bit of Tylenol is therapeutic, a lot must be even more so, right? Well, not quite. While your pounding head may love a dose of acetaminophen, your liver is less of a fan, and too much acetaminophen can cause it to shut down. Also, unlike other pain relief drugs, the difference between a healthy dose of acetaminophen and a dangerous dose can be as small as two extra-strength Tylenol tablets (1000 mg acetaminophen).
Suppose you've got a killer headache, and take two extra-strength Tylenol tablets every 6 hours for an entire day. Whether or not this is dangerous depends on your individual tolerance, as well as whether or not you're taking any other drugs containing acetaminophen. A conservative estimate for the danger zone is 4000 mg; above that, your liver may not be able to handle everything you've given it. Using the model above, it may seem like taking two tablets every 6 hours is fine: as the graph below shows, the total amount of acetaminophen in your body never exceeds around 1331 mg during that 24-hour period:
However, it's not the amount at any one point in time that matters; it's the cumulative effect that can be damaging. And in fact, it can be damaging in ways that, until recently, weren't very well known. (This American Life did a great story on Tylenol and acetaminophen last year.) As a matter of fact, a few years ago the makers of Tylenol dropped the maximum daily recommended dose from 4000 mg of acetaminophen to 3000 mg; that's 6 extra strength tablets per day. So taking two tablets every 6 hours means taking just two tablets over the recommended dose. For some people, that's fine. But it's probably not worth pushing your luck.
Teachers: want to have this conversation with your students? Then check out our latest lesson, Pounding Headache.