3 Clinical psychopharmacology3.2 Pharmacokinetics

3.2.1.5 Kinetic modelling linear versus zero order

Creator: Resident Doctor Committee
Published: 2026-10-14T21:05:16.259Z

1 min read1 figure

Written by Resident Doctor Committee · Published 14 October 2026

First-order (linear) elimination

First-order elimination removes a constant fraction of the drug present per unit time, so the elimination rate is proportional to plasma concentration.
At 10% per hour, 100 units loses 10 units in an hour, whereas 10 units loses 1.
The half-life is constant whatever the plasma level.
Clearance is constant, so steady-state concentration (dose rate divided by clearance) is directly proportional to dose rate.
Most drugs are eliminated by first-order kinetics, including lithium at a standard maintenance dose.

Zero-order (saturable) elimination

Zero-order elimination, also called saturable or non-linear elimination, removes a fixed amount of drug per unit time, independent of plasma concentration, once the eliminating enzyme is saturated.
Plasma level therefore rises out of proportion to dose.
Half-life is not fixed: it lengthens as concentration rises and shortens as the level falls.
At 10 units removed per hour, falling from 100 to 50 takes 5 hours, but falling from 50 to 25 takes 2.5 hours.

Two side by side graphs of plasma concentration against time in hours, both starting at 200. On the left an orange straight line falls to zero, with arrows marking halving intervals of 5, 2.5 and 1.25 hours. On the right a blue curve falls exponentially, with three equal halving intervals of 3 hours. — Compare the halving arrows: zero-order elimination removes a constant amount per hour, so the level falls in a straight line and each halving is quicker (5, 2.5 and 1.25 hours), while first-order elimination removes a constant fraction, so every half-life takes the same 3 hours. Drawn for MRCPsychiatrist

Capacity-limited metabolism

The two orders are ends of one relationship: elimination rate = Vmax x concentration / (Km + concentration). Vmax is the enzyme's maximum rate and Km is the concentration that gives half of it.

Concentration	Elimination
Far below Km	First order
Around Km	Mixed, shifting continuously with no sudden switch
Far above Km	Zero order, at a rate approaching Vmax

Which drugs are zero-order

Drug	Why elimination is zero-order
Phenytoin	Its hepatic enzymes saturate at therapeutic concentrations, so small increments can cause nystagmus, ataxia or confusion
Ethanol	Alcohol dehydrogenase, the rate-limiting first oxidation step, is saturated at ordinary drinking concentrations

Zero-order behaviour needs either a saturable enzyme or a formulation built to release drug at a constant rate.
Autoinduction, a narrow therapeutic index, a long half-life or absence of metabolism do not make elimination zero-order.

Revision material for the MRCPsych examinations. Not clinical guidance, and not for use in patient care.