Multi-Compartment Models
In multi-compartment models, the body is treated as more than one compartment (usually
two or three), which allows for a more complex and accurate representation of drug
distribution and elimination. These models are used to describe drugs that do not distribute
uniformly throughout the body, as is assumed in the one-compartment model.
Pharmacokinetic Formula and Equations
Plasma Drug Concentration (Two-Compartment Model):
C(t) = A e^{-\alpha t} + B e^{-\beta t}
Volume of Distribution (Central Compartment):
V_d = \frac{Dose}{C_0}
Clearance (Cl):
Cl = V_d \times k_e
Elimination Rate Constant (k_e):
k_e = \frac{Cl}{V_d}
Half-Life (t_{1/2}):
t_{1/2} = \frac{0.693}{k_e}
Steady-State Concentration (C_{ss}):
C_{ss} = \frac{Rate_{infusion}}{Cl}
Graphical Representation
IV Bolus (Two-Compartment Model):
Biphasic curve: Sharp initial decline (distribution) followed by slower decline (elimination).
IV Infusion (Two-Compartment Model):
Gradual increase to steady state, with a decline post-infusion.
Oral Administration (Two-Compartment Model):
Gradual rise to peak concentration, followed by elimination phase.