Predicting drug concentrations

What is this for?

In first-order elimination a constant fraction of drug is removed per unit time, so concentration decays exponentially. Three questions follow from the same relationship: what will the concentration be later, how fast is this patient eliminating the drug, and how long until it is safe to redose.

How to use it

1. Choose what you want to find: a future concentration, the elimination rate constant, or the time to a target.
2. Fill in the fields that mode requires — the blocked message tells you exactly which are missing.
3. You can supply either ke or the half-life; PharmCalc converts between them.

Worked example

A vancomycin concentration is 20 mg/L. The patient's elimination rate constant is 0.1 h⁻¹. What will the concentration be 8 hours later?

Answer: C₂ = 20 × e^(−0.1 × 8) = 20 × 0.449 = 8.99 mg/L. That is 1.15 half-lives, so a little more than half has been eliminated.

Clinical pearls & pitfalls

• The elimination rate constant is a fraction per unit time, not an amount per unit time. A ke of 0.1 h⁻¹ means about 9.5% of what is present is removed each hour — not 10%, because the fraction applies continuously.
• This is the calculation behind deciding when a supratherapeutic level has fallen far enough to redose safely, and it is used routinely in aminoglycoside and vancomycin monitoring.
• The two-concentration method gives the patient's own elimination rate rather than a population estimate, which is why paired levels are drawn. Both samples must be in the elimination phase, after distribution is complete.
• A common trap is entering the second concentration as the higher of the two. The equation describes decay, so C₂ must be smaller than C₁.

Assumptions & limitations

• First-order elimination only. Phenytoin at therapeutic concentrations follows saturable kinetics, where a small dose increase produces a disproportionate concentration rise.
• Assumes both samples are drawn in the terminal elimination phase. A level drawn during distribution gives a falsely rapid apparent elimination.
• Assumes no further doses are given during the interval. Any dose administered invalidates the prediction.
• Assumes clearance is stable. In evolving renal impairment or during dialysis it is not.

References

• Rybak MJ, et al. Therapeutic monitoring of vancomycin for serious MRSA infections: a revised consensus guideline of ASHP, IDSA, PIDS, and SIDP. Am J Health Syst Pharm. 2020;77(11):835-864.
• Bauer LA. Applied Clinical Pharmacokinetics. 3rd ed. McGraw-Hill.
• Winter ME. Basic Clinical Pharmacokinetics. 5th ed. Lippincott Williams & Wilkins.

Related calculators