Pharmacokinetic workspace (linked solver)
Enter any sufficient subset of pharmacokinetic parameters and derive the rest, with each result labelled by the relation used to obtain it.
What is this for?
The core one-compartment parameters are interlocked: clearance is the product of the elimination rate constant and the volume of distribution, half-life is fixed by the rate constant, and clearance also follows from dose and area under the curve. Supply any two or three and the rest follow. This workspace resolves them iteratively and shows the derivation chain.
How to use it
- Enter whichever parameters you know and leave the rest blank. Two is usually enough, three if you are using the dose/AUC route to clearance.
- Keep units consistent: dose in mg, volumes in L, concentrations in mg/L, time in hours.
- Read the derived values in the result panel. Each is labelled with the relation used, so you can audit the chain.
Worked example
A drug has a volume of distribution of 50 L and a clearance of 5 L/h. Derive the elimination rate constant and half-life.
Answer: ke = Cl ÷ Vd = 5 ÷ 50 = 0.1 h⁻¹. t½ = 0.693 ÷ 0.1 = 6.93 hours. Steady state is reached after about 5 half-lives, roughly 35 hours.
Clinical pearls & pitfalls
- Clearance and volume of distribution are the two independent parameters. Half-life is derived from them — it is not a property in its own right, which is why a change in either alters the half-life.
- Because half-life is derived, a drug can have a prolonged half-life from reduced clearance (renal impairment) or from an expanded volume of distribution (fluid overload, ascites). The management differs.
- Steady state is reached after about 5 half-lives regardless of dose or interval. Increasing the dose raises the plateau but does not reach it any sooner — that is what a loading dose is for.
- The 0.693 constant is the natural logarithm of 2, rounded. Using ln(2) exactly gives 0.6931; the difference is immaterial clinically but may cause a small mismatch against an exam answer key.
Assumptions & limitations
- One-compartment, first-order kinetics only. Phenytoin, ethanol, and high-dose salicylate follow saturable kinetics where these relations fail.
- Assumes linear pharmacokinetics — that clearance and volume of distribution do not change with concentration.
- Does not model absorption. Extravascular administration has an absorption phase that this workspace ignores.
- Population parameters carry substantial interindividual variability. Where therapeutic drug monitoring is available, measured concentrations should override calculated predictions.
References
- Rowland M, Tozer TN. Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 4th ed. Lippincott Williams & Wilkins.
- Bauer LA. Applied Clinical Pharmacokinetics. 3rd ed. McGraw-Hill.
- Winter ME. Basic Clinical Pharmacokinetics. 5th ed. Lippincott Williams & Wilkins.