Pharmacokinetics · Short notes

Clearance and Half Life: Short Notes & Cheat Sheet

Clearance, half-life and the elimination constant, first- and zero-order kinetics, steady state, and hepatic and renal clearance.

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Short notes

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Approaching steady state

Whatever the dose, a drug reaches about 97% of steady state after 5 half-lives, and the same rule applies to washout.

Key relationships

Clearance (CL) is the volume of plasma cleared of drug per unit time: CL = rate of elimination ÷ plasma concentration.
Total clearance is the sum of renal, hepatic and other clearances. CL = F × dose ÷ AUC.
Half-life depends on both volume and clearance: t½ = 0.693 × Vd ÷ CL. The elimination rate constant k = CL ÷ Vd = 0.693 ÷ t½.
About 4–5 half-lives are needed to reach steady state after starting a drug, and to eliminate it after stopping.

Order of kinetics

First-order: a constant fraction is eliminated per unit time, and half-life is constant. This applies to most drugs.
Zero-order: a constant amount is eliminated per unit time, because elimination is saturated. Half-life changes with concentration.
Zero-order examples: ethanol, high-dose phenytoin and high-dose aspirin. Small dose increases can cause large rises in level.

Liver and kidney

High-extraction drugs (lidocaine, propranolol, morphine) depend mainly on liver blood flow (flow-limited).
Low-extraction drugs (warfarin, phenytoin, theophylline, diazepam) depend on enzyme activity and protein binding (capacity-limited).
Renal clearance = filtration + tubular secretion − reabsorption. Normal GFR is about 120–125 mL/min; inulin measures GFR and PAH measures renal plasma flow.
If renal clearance is greater than GFR the drug is secreted; if it is less, the drug is reabsorbed.
Alkalinising the urine traps weak acids (aspirin, phenobarbital) and speeds their excretion.
Drugs that need dose reduction in renal impairment include aminoglycosides, vancomycin, digoxin, lithium, metformin, gabapentin and enoxaparin.

Cheat sheet

High-yield facts in one place. Cover the right-hand column and test yourself.

Formulas

Quantity	Formula
Half-life	t½ = 0.693 × Vd ÷ CL = 0.693 ÷ k
Elimination constant	k = CL ÷ Vd
Clearance	CL = F × dose ÷ AUC
Renal clearance	(Urine conc × urine flow) ÷ plasma conc
Steady state	≈ 4–5 × t½

First- vs zero-order

Feature	First-order · zero-order
Eliminated per hour	Constant fraction · constant amount
Half-life	Constant · changes with dose
Log C vs time plot	Straight line · curved
Examples	Most drugs · ethanol, high-dose phenytoin

Memory aids

50, 75, 87.5, 94, 97: Percentage of steady state reached after 1, 2, 3, 4 and 5 half-lives.

Exam traps

Half-life depends on both Vd and clearance; a drug can have a long half-life simply because its Vd is large.
Time to steady state depends only on half-life, not on dose or dosing interval.
In zero-order kinetics, half-life is not constant.
Renal clearance higher than GFR means the drug is actively secreted.

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