Two Compartment Model

Adapted from Physics, Pharmacology and Physiology for Anaesthetists

• Where:
• C₀ = 'outside compartment'
• C₁ = central compartment
• C₂ = peripheral compartment [representing less vascular tissues of the body]
• K₀₁ = rate constant for a drug moving from C₀ to C₁ i.e. rate of administration of the drug
• K₁₀ = rate constant of elimination from the central compartment
• K₁₂ = rate constant for a drug moving from C₁ to C₂
• K₂₁ = rate constant for a drug moving from C₂ to C₁


• The volume of distribution is the sum of the volumes of the two compartments (V_D = V₁ + V₂)
• Elimination (removal of drug from plasma) only occurs from C₁, and occurs either via:
• Removal of the central compartment
• Redistribution to C₂

• A semi-logarithmic graph of ln(concentration) vs. time is no longer linear - it is a bi-phasic exponential decay curve

Adapted from Physics, Pharmacology and Physiology for Anaesthetists

• Phase 1 represents distribution of drug from C₁ to C₂
• The rate of this depends on the different concentration gradients and the rate constant for the transfer (K₁₂)


• Phase 2 represents terminal elimination of the drug from C₁
• The tangent to phase 2 (line b) intercepts the y-axis at point B
• (NB as a convention, line b always represents elimination from the body)
• Subtracting line b from the exponential curve gives line a
• Line a intercepts the y-axis at point A


• The initial drug plasma concentration (C₀) = A + B
• As the y-axis is logarithmic, A is much larger than B, so A is close to C₀

• The equation for a one compartment model was:

C = C₀.e^-kt



• For a two compartment model, there are two terms on the right hand side of the equation instead:

C_t = A.e^-ɑt + B.e^-βt

• Where:
• C_t = concentration at time t
• A = concentration A from the ln(concentration) vs. time curve
• ɑ = gradient of line a (i.e. the rate constant)
• This is dependent on the ratio of K₁₂ to K₂₁
• Determines the rate of fall of plasma concentration following initial bolus - if the ratio is high then the plasma concentration falls quickly
• B = concentration B from ln(concentration) vs. time curve
• β = gradient of line b

Terminal elimination

• The term B.e^-βt represents the terminal elimination phase
• Its rate constant is β
• Its time constant (τ_β) is the inverse of the rate constant (i.e. τ_β = 1/β
• Its half life is related to the time constant by a factor of ln(2) i.e. 0.693 and is the terminal elimination half-life


• As the terminal elimination half-life reflects both elimination from the body and re-distribution from the peripheral compartments, it is not the reciprocal of the rate constant for elimination (K₁₀)
• Clearance, however, is still a produce of rate constant for elimination and volume of central compartment