Pharmacokinetic Models
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Direct answer
Compartment models are mathematical shorthand for how a drug distributes and disappears: a one-compartment model treats the body as a single well-stirred bucket in which concentration falls exponentially with one elimination rate constant, while the two-compartment model adds a peripheral (tissue) compartment so that plasma curves bend through a steep alpha distribution phase and a slower beta elimination phase. Three-compartment models describe fat-soluble drugs such as propofol and thiopentone with slow redistribution returns. Superimposed on this geometry is the order of kinetics — first-order (a constant fraction eliminated per unit time) versus zero-order (a constant amount, seen with saturated metabolism such as ethanol) — and model-independent parameters such as area under the curve, clearance and half-life.
What you must remember
- One-compartment model: drug equilibrates instantly throughout its apparent volume of distribution (Vd); single exponential decay, C = C0 × e^(-kt); fits aminoglycosides reasonably after distribution completes.
- Two-compartment model: central (plasma, well-perfused organs) plus peripheral (muscle, fat) compartments linked by intercompartmental rate constants; plasma curve shows the rapid alpha phase (distribution into tissues) then the log-linear beta phase (elimination), and the intercepts yield A and B with rate constants alpha and beta.
- Three-compartment model: thiopentone and propofol — a deep fat compartment explains the prolonged terminal elimination and context-sensitive half-time with long infusions.
- First-order kinetics: rate proportional to concentration; constant half-life t½ = 0.693/k; doubling the dose doubles the concentration, not the duration of effect.
- Zero-order kinetics: enzymes saturated, a constant amount cleared per hour (ethanol about 7-10 g per hour); half-life lengthens with dose; concentration-time plot is linear until levels fall into first-order range.
- Key parameters: AUC (total exposure, proportional to dose/clearance), Cmax and Tmax (rate of absorption), Vd (dose divided by plasma concentration at time zero — a proportionality constant, not an anatomical space), clearance (volume of plasma cleared per unit time).
- Flip-flop kinetics: when absorption is slower than elimination (modified-release formulations, poorly soluble drugs), the terminal slope tracks absorption — an examiner favourite.
- Loading vs maintenance link: in multicompartment drugs the loading dose targets initial Vd, while maintenance depends on total clearance — amiodarone's huge Vd is why it loads at grams and maintains at 200 mg.
Reading a plasma concentration curve
A volunteer receives a single intravenous bolus of a new lipophilic sedative, and concentrations are plotted on a semilog scale. The curve is not a straight line — it plunges for the first 30 minutes (alpha, the drug leaving plasma for muscle and fat), then settles into a steady single-slope decline (beta, elimination by liver and kidney). Back-extrapolating the beta slope to time zero gives B; subtracting early points gives a second line with intercept A. The central lesson follows: the half-life you quote for such a drug is the beta half-life, and a level drawn during the alpha phase overestimates exposure — the aminoglycoside peak drawn too early. Now stop an 8-hour infusion: the time for concentration to halve is no longer the beta half-life but the context-sensitive half-time, which grows the longer the infusion ran, because tissue keeps returning drug. This is why remifentanil's tiny distribution and rapid ester hydrolysis keep its context-sensitive half-time near 3-4 minutes whatever the duration, while thiopentone by infusion would sleep patients into next week.
Where students slip
The first slip is treating Vd as a real volume: a Vd of 400 litres for amiodarone means the drug hides in tissue at high affinity, not that the patient contains 400 litres of water. The second is assuming a constant half-life always: phenytoin, ethanol and high-dose salicylate leave zero-order territory as they fall, so a "half-life" quoted at toxic levels misleads at therapeutic ones. The third is confusing the slopes — alpha is distribution between compartments, not loss from the body; beta is elimination. Shown a curve, the early steep drop is redistribution, not excretion. Finally, compartment number is a modelling choice — the simplest model that fits and predicts dosing wins, which is why most therapeutic drug monitoring uses one-compartment logic.
Frequently asked questions
What are the alpha and beta phases of a two-compartment model?
Alpha is the rapid distribution phase as drug leaves plasma for tissues; beta is the slower elimination phase once distribution equilibrates — the clinically quoted half-life.
How does first-order kinetics differ from zero-order?
First order eliminates a constant fraction per unit time with a fixed half-life; zero order eliminates a constant amount because metabolism is saturated, so half-life lengthens with dose.
What is volume of distribution conceptually?
A proportionality constant (dose ÷ plasma concentration) relating amount in body to plasma concentration — large values indicate tissue sequestration, not anatomical volume.
What is flip-flop kinetics?
When absorption is slower than elimination, the terminal plasma slope reflects absorption rather than elimination — common with sustained-release products.
What is context-sensitive half-time?
The time for plasma concentration to halve after stopping an infusion of a given duration; it lengthens with infusion length for fat-soluble anaesthetics but stays short for remifentanil.