If a drug has a half life of, let say 72 hours, and you take it every day, how do the levels not continuously climb?
In: Biology
This is a good question. Let’s look at a basic case. You take 10 mg of a drug every 24 hours. Just for easy math, let’s say this drug has a 24 hour half – life.
Think of taking a drug as having peaks and valleys. When you take the drug, the amount of drug in your body is at a high point, or “peak,” and slowly declines until you take the next dose. The drug concentration right before you take your next dose is at a relative low point, or “trough.”
Going back to our example, let’s say you take your first dose on day 1. The peak is 10 mg, and then the amount of drug in your body will start to decline. After 24 hours, there will be 5 mg left (since the half-life is 24 hours and 5 is 50% of 10).
Now it’s day 2 and you still have 5 mg left from day 1. You take the 10 mg so your peak for day 2 is 15 mg. After 24 hours, you have 7.5 mg left in your body.
Let’s see how this pattern progresses over the next couple days.
Day 3: Peak = 17.5, trough = 8.75
Day 4: Peak = 18.75, trough ~ 9.4
Day 5: Peak = 19.4, trough = 9.7
Day 6: Peak = 19.7, trough = 9.85
Day 7: Peak = 19.85, trough ~9.9
Day 8: Peak = 19.9, trough ~10
Day 9: Peak = 20, trough = 10
Day 10: Peak = 20, trough = 10
Do you see how after awhile, the peaks and troughs stay the same day after day? This is known as “steady state” since the peaks and troughs don’t change over time.
If we look at the values, the steady state peak concentration is 20 and the steady state trough is 10. Let’s look at each day’s concentration as a percentage of steady state (we will just use peaks here).
Day 1: 10/20 = 50%
Day 2: 15/20 = 75%
Day 3: 17.5/20 = 87.5%
Day 4: 18.75/20 = 93.75%
Day 5: 19.4/20 = 97%
Day 6: 19.7/20 = 98.5%
And so on and so forth.
What we see is that after about 5 days, we’re at greater than 95% of steady state concentration. In this case, since one day is also one half – life, we can say that we’re at greater than 95% steady state after 5 half-lives. And this turns out to be the case for many, many drugs. You can approximate the time at which a person will reach steady state by multiplying the half-life by 5. So in your example, if a drug has a half – life of 72 hours, steady state will be reached in 72 hours x 5 = 360 hours, or 15 days.
This type of question falls into a field called pharmacokinetics, and there are many other variables that can affect drug disposition (and then equations can get fairly complex). However, if you need to come up with how long it takes for someone to reach steady state, 5 times the half-life is a good rule of thumb.
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