STEPTRACKERPHARMACOLOGY | PHARMACOKINETICS | HIGH-YIELD REVIEW

Clearance, Half-Life & Dosing

Four equations explain almost every dosing question: clearance, half-life, loading dose and maintenance dose — plus the difference between first- and zero-order elimination.

FOCUS ON
Clearance: CL = rate of elimination ÷ plasma concentration = 0.693 × Vd ÷ t½. Half-life: t½ = 0.693 × Vd ÷ CL. Steady state is reached after 4–5 half-lives (94–97%), whatever the dose — the same rule for washout. Loading dose = Cp × Vd ÷ F; maintenance dose = Cp × CL × τ ÷ F. In renal or hepatic impairment the maintenance dose falls; the loading dose usually doesn't. First-order elimination: constant fraction per unit time (most drugs; exponential curve). Zero-order: constant amount per unit time (saturated enzymes; linear fall): phenytoin, ethanol, aspirin at high doses — small dose increases cause large level jumps.
PARAMETER
FORMULA
MEANING
CLINICAL USE
Clearance (CL)
CL = rate of elimination ÷ Cp = 0.693 × Vd ÷ t½
Volume of plasma cleared of drug per unit time
Sets the maintenance dose
Half-life (t½)
t½ = 0.693 × Vd ÷ CL
Time for plasma level to fall by half (first-order)
↑ with ↑ Vd or ↓ CL (renal failure, elderly)
Time to steady state
≈ 4–5 half-lives
Input = output at a constant infusion or regular dosing
Independent of dose or loading dose
Fraction remaining
1 t½ = 50% · 2 = 25% · 3 = 12.5% · 4 = 6.25%
Same pattern for accumulation (50, 75, 87.5, 94%)
Washout before switching drugs
Loading dose
LD = Cp × Vd ÷ F
Reach target level quickly
Digoxin, amiodarone, phenytoin, vancomycin
Maintenance dose
MD = Cp × CL × τ ÷ F (τ = dosing interval)
Replace what is eliminated
↓ in renal or hepatic failure
First-order kinetics
Rate ∝ concentration; constant fraction per hour
Exponential decline; constant t½
Most drugs at therapeutic doses
Zero-order kinetics
Rate constant (enzymes saturated); constant amount per hour
Linear decline; t½ not constant
Phenytoin, ethanol, high-dose aspirin
Renal elimination
Filtration + secretion − reabsorption
Free drug filtered; organic acid/base transporters secrete
Probenecid ↓ secretion of penicillin, methotrexate · dose by creatinine clearance
Therapeutic drug monitoring
Measure trough or peak levels
Narrow therapeutic index drugs
Digoxin, lithium, aminoglycosides, vancomycin, phenytoin, tacrolimus, theophylline
Elderly
↓ renal clearance, ↓ hepatic metabolism, ↑ fat (↑ Vd lipophilic)
Longer half-lives
Start low, go slow

Picture it — elimination and accumulation

timeplasma level50%25%12.5%constant FRACTION losteach half-life
First-order eliminationMost drugs: the same fraction is cleared each half-life, so the level halves at a fixed interval and the curve flattens.
timeplasma levelconstant AMOUNT lostper hour (enzyme saturated)phenytoin · ethanolhigh-dose aspirin
Zero-order eliminationEnzymes saturated: the same amount is cleared every hour, so the level falls in a straight line and half-life is not constant.
% of steady statenumber of half-lives150275388494597plateau ≈ 4–5 half-lives
Approach to steady stateWith regular dosing the level climbs 50, 75, 88, 94, 97% of steady state at successive half-lives — dose size doesn't change the timing.

Schematic diagrams, not to scale.

Mechanism — why phenytoin levels jump

Low doseEnzyme not saturated → first-order
→
Dose ↑ past capacityEnzyme saturated → zero-order
→
Elimination fixed, intake rising
→
Level rises out of proportionNystagmus, ataxia

First vs zero order

FEATURE
FIRST ORDER
ZERO ORDER
Amount eliminated
Constant fraction
Constant amount
Half-life
Constant
Varies with level
Curve (linear axes)
Exponential
Straight line
Examples
Most drugs
Phenytoin, ethanol, aspirin (high)

How it's tested

COMMON CONFUSIONDoubling the dose doubles the steady-state level (first order) but doesn't change how long it takes to get there — only half-life does.
THE TRAPIn renal failure, keep the loading dose and cut the maintenance dose (or lengthen the interval) for renally cleared drugs.
YOUR APPROACHPick the formula: rate question → CL; time question → t½; first dose → Vd; repeat dose → CL. Then check order of kinetics.

If you see… think…

Time to reach steady state → 4–5 half-lives
Plasma level after 3 half-lives → 12.5% of starting
Constant amount eliminated per hour → zero-order kinetics
Small dose increase → toxic level → phenytoin (saturable)
Half-life formula → 0.693 × Vd ÷ CL
Maintenance dose in renal failure → reduce it
Loading dose in renal failure → usually unchanged
Probenecid prolongs penicillin → blocks tubular secretion
Drugs needing level monitoring → narrow therapeutic index
Ethanol elimination → zero order (~1 drink/h)