Half-life depends on both clearance and volume of distribution
Mnemonic
Three equations that connect:
- Half life = 0.693 x Vd / clearance
- Loading dose = Vd x target concentration
- Maintenance dose = clearance x target concentration
“Loading depends on volume, maintenance depends on clearance.” That single distinction explains why a loading dose is unchanged in renal failure while the maintenance dose must be reduced.
Steady state takes 4 to 5 half lives, whatever the dose, which is why a loading dose is used when the effect is needed sooner, as with digoxin, amiodarone and phenytoin.
First order kinetics means a constant proportion is cleared per unit time, so half life is constant. Zero order means a constant amount, because the enzymes are saturated, so small dose increases cause large concentration rises. The classic zero order drugs are phenytoin, ethanol, aspirin in overdose and theophylline.
Expansion
Half-life = (0.693 x volume of distribution) / clearance
So a long half-life can result from either low clearance or a large volume of distribution, which is why amiodarone has a half-life of about 50 days despite normal hepatic function.
Clearance determines the maintenance dose; volume of distribution determines the loading dose.
Time course
- Steady state after about 5 half-lives, whatever the dose
- 95 per cent eliminated after 5 half-lives from stopping
- A loading dose shortcuts the wait, which is why it is used for amiodarone, digoxin and phenytoin when a rapid effect is needed
Clinical consequences
- Changing a dose requires 5 half-lives before the new steady state can be judged, which is why thyroxine is rechecked at 6 weeks and warfarin more frequently only because its effect is monitored directly
- Renal or hepatic impairment reduces clearance, prolonging half-life and requiring dose or interval adjustment
- Drugs with short half-lives need frequent dosing or modified release formulations