Pharmacokinetic three-compartment model

Pharmacokinetics refers to the rate and extent of distribution of a drug to different tissues, and the rate of elimination of the drug. Pharmacokinetics can be reduced to mathematical equations, which describe the transit of the drug throughout the body, a net balance sheet from absorption and distribution to metabolism and excretion.

Pharmacokinetic three-compartment model divided the body into central compartment and two peripheral compartments. The central compartment (compartment 1) consists of the plasma and tissues where the distribution of the drug is practically instantaneous. The peripheral compartments (compartments 2 and 3) consist of tissues where the distribution of the drug is slower compared to compartment 1.

Pharmacokinetic three-compartment model
Figure 1. Three-compartment model with first-order elimination. C1, C2, and C3 are the concentrations of drug in the central compartment (including plasma), and the two peripheral compartment, respectively. k12, k21, k13, k31, and k10 represent the first-order fractional rate constants for distribution, redistribution, and elimination.

Compartments could represent drug amounts instead of concentrations. Drug amounts in the compartments equal to the concentrations multiplied by volumes: A1=C1×V1 and A2=C2×V2. A3=C3×V3. Drug concentration in the central compartment is equal to the concentration in the plasma (or blood): CP=C1. Clearance (in units L/h) is often used instead of the fractional rate constants (in units h-1); in pharmacokinetics the distribution volume is given in volume units (L), and rate constants can be represented as the ratio of clearance and distribution volume, k=CL/V.

In case of intravenous bolus infusion or oral administration of the drug, at time t=0 all concentrations are zero. Drug concentrations in the central and peripheral compartments can be calculated with differential equations:

In case of bolus injection of the drug, at time t=0 the central compartment is assumed to contain all of the injected drug, and I(t)=0.

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Created at: 2019-01-06
Updated at: 2019-01-06
Written by: Vesa Oikonen