2.5 Pharmacokinetic Models
PK models mathematically describe drug concentration-time profiles. They enable prediction of drug levels, dosing optimization, and understanding ADME processes.
One-Compartment Model
\( C(t) = C_0 \cdot e^{-kt} \)
First-order elimination, single compartment
Assumes drug distributes instantaneously and uniformly. Body acts as single homogeneous compartment. Good for water-soluble drugs with rapid distribution.
k = elimination rate constant = CL/Vd = 0.693/t½
Two-Compartment Model
\( C(t) = Ae^{-\alpha t} + Be^{-\beta t} \)
Distribution (α) and elimination (β) phases
Central Compartment
Plasma, highly perfused organs. Rapid equilibration.
Peripheral Compartment
Poorly perfused tissues, fat. Slower distribution.
Key PK Parameters
| Parameter | Symbol | Typical Units | Significance |
|---|---|---|---|
| Area Under Curve | AUC | mg·h/L | Total drug exposure |
| Peak Concentration | Cmax | mg/L | Maximum exposure |
| Time to Peak | Tmax | hours | Absorption rate |
| Clearance | CL | L/h | Elimination capacity |
| Volume of Distribution | Vd | L | Tissue distribution |
Multiple Dosing
Steady State
Rate of input = Rate of elimination. Reached after 4-5 half-lives. Css,avg = F×Dose/(CL×τ)
Accumulation Factor
R = 1/(1 - e^(-kτ)). Predicts accumulation with repeated dosing.
Loading Dose
LD = Css × Vd. Achieves target concentration immediately. Important for long t½ drugs.
Non-Linear Kinetics
Saturation Kinetics
Michaelis-Menten. Phenytoin, ethanol. Small dose changes → large concentration changes.
Capacity-Limited Binding
Protein binding saturation. Free fraction increases with dose.