singlecompartment

Single-compartment model, also written as one-compartment model, is a basic pharmacokinetic framework in which the body is represented as a single, homogeneous compartment. After drug administration, the agent is assumed to distribute rapidly and uniformly within this compartment, and elimination occurs from the same space. This simplification yields a monoexponential decline in plasma concentration for many drugs after an intravenous dose.

Mathematically, for an IV bolus dose D, the plasma concentration is C(t) = (D / Vd) e^{-k t}, where Vd is the apparent volume of distribution and k is the elimination rate constant (k = CL / Vd). The half-life is t1/2 = ln 2 / k. For a constant-rate intravenous infusion with rate R0 over a period T, during infusion C(t) = (R0 / (Vd k)) (1 - e^{-k t}) for 0 <= t <= T; after the infusion ends, C(t) = C(T) e^{-k (t - T)}.

Assumptions include instantaneous and uniform mixing within the body and linear pharmacokinetics, meaning clearance is proportional to concentration. The model is most suitable for drugs that rapidly equilibrate and do not show complex tissue distribution or saturable processes.

Limitations arise when distribution is slower or more complex, when non-linear kinetics are present, or when absorption and tissue binding significantly affect concentration-time profiles. In such cases, multi-compartment models or noncompartmental analyses may provide more accurate descriptions.

Relation to other models: the single-compartment model is the simplest compartmental approach, often contrasted with two- or multi-compartment models that distinguish central and peripheral spaces. It remains a foundational tool in pharmacokinetics and introductory pharmacology.