Two-Compartment vs. One-Compartment IV Bolus Pharmacokinetics

Two-Compartment IV Bolus Model

The two-compartment intravenous (IV) bolus model describes the kinetics of drugs that do not distribute instantaneously throughout the body. Following rapid IV injection, drugs distribute quickly into a central compartment (blood/well-perfused tissues) and slowly into a peripheral compartment (tissues), displaying a biexponential plasma concentration decline over time.

Compartment Definitions

• Central Compartment (V_c): Blood and highly perfused tissues (liver, kidneys, heart). Elimination mainly occurs here.
• Peripheral Compartment (V_p): Poorly perfused or slowly equilibrated tissues (muscles, adipose, skin).

Biexponential Decline

The plasma level-time plot is not a straight line on a semi-log scale; it shows a rapid distributive phase (initial) followed by a slower elimination phase.

Kinetic Parameters and Equations

Plasma Concentration Formula: C = Ae^-αt + Be^-βt

• C: Drug concentration at time t
• α: Hybrid constant for rapid distribution phase
• β: Hybrid constant for slow elimination phase
• A, B: Intercepts of the two phases
• Micro-constants: k₁₂ (transfer from 1 to 2), k₂₁ (transfer from 2 to 1), k_e (elimination).
• Volume of Distribution (V): Apparent volume changes over time, with V_c and V_ss (total) being standard measures.

Phases of Drug Disposition

• Distributive Phase (α-phase): Rapid decline in concentration due to redistribution from blood into tissue compartments.
• Post-distributive Phase (β-phase): Slower decline in concentration, representing elimination, once pseudo-equilibrium is reached.

Method of Residuals

To calculate parameters, the method of residuals (or feathering) is used to separate the two exponential terms (Ae^-αt and Be^-βt) from the plasma concentration-time curve.

Applications

This model is used for drugs that show rapid distribution initially (e.g., thiopental) and helps calculate V_c, V_p, V_ss, and clearance (Cl) to determine proper dosing regimens.

One-Compartment IV Bolus Model

The one-compartment IV bolus model is the simplest pharmacokinetic model, treating the body as a single, uniform compartment where a drug distributes instantaneously and is eliminated via first-order kinetics. It is used for rapid intravenous injections, assuming no absorption phase and uniform concentration throughout blood and tissues.

Key Concepts and Parameters

Definition: "One-compartment" implies rapid, homogeneous distribution; "Open" means the drug is eliminated; "IV bolus" means rapid administration.

• Volume of Distribution (V_d): Relates the amount of drug in the body (X) to plasma concentration (C): V_d = X / C
• Elimination Rate Constant (K): Characterizes the speed of elimination; it represents the fraction of drug removed per unit of time.
• Elimination Half-life (t_1/2): Time taken to reduce plasma concentration by 50%.
• Clearance (Cl): Volume of blood cleared of drug per unit time (Cl = K × V_d).