A 16-year-old male high school football player takes 800 mg of ibuprofen after morning practice for a sore knee. Ibuprofen has a half-life of about 2 h. What percentage of the original plasma load of ibuprofen will remain in his blood when afternoon practice starts in 4 h? (A) 0% (B) 12.5% (C) 25% (D) 50% (E) 75%
The Correct Answer and Explanation is:
The correct answer is (C) 25%.
Explanation:
Ibuprofen is a drug that follows first-order kinetics, meaning that the rate at which it is eliminated from the body is proportional to the concentration remaining. The key concept here is the half-life of the drug, which is the time it takes for the plasma concentration of the drug to reduce to half of its original amount.
- Given:
- Half-life (t₁/₂) of ibuprofen = 2 hours
- Time elapsed since ingestion = 4 hours
Because the half-life is 2 hours, every 2 hours, the plasma concentration of ibuprofen will reduce by 50%.
- After the first 2 hours:
The plasma level decreases from 100% to 50%. - After the next 2 hours (total 4 hours):
The plasma level again reduces by half, from 50% to 25%.
Thus, after 4 hours (two half-lives), only 25% of the original ibuprofen remains in the bloodstream.
Why this matters:
Understanding drug half-life is important for several reasons:
- Dosage timing: Knowing how long a drug stays active helps in determining how often a drug should be administered to maintain therapeutic levels without toxicity or subtherapeutic effects.
- Effectiveness and safety: If a drug is taken too frequently, it may accumulate and cause side effects; if taken too infrequently, the therapeutic effect may be lost.
- Drug clearance: Half-life is influenced by how quickly the liver metabolizes the drug and the kidneys excrete it.
Additional points:
- This calculation assumes normal metabolism and excretion in a healthy 16-year-old.
- If the half-life were different, the remaining percentage after 4 hours would change accordingly.
- After 3 half-lives (6 hours), only 12.5% would remain; after 4 half-lives (8 hours), 6.25% would remain, and so forth.
Summary:
After 4 hours (two half-lives) since taking ibuprofen, the plasma concentration will be halved twice, resulting in 25% of the original dose remaining. Therefore, the correct choice is (C) 25%.
