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 = $CL/V_d = 0.693/t_{1/2}$
Two-Compartment Model
\( C(t) = Ae^{-\alpha t} + Be^{-\beta t} \)
Distribution (ฮฑ) and elimination (ฮฒ) 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 | mgยทh/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. $C_{ss,avg} = F \times Dose/(CL \times \tau)$
Accumulation Factor
$R = 1/(1 - e^{-k\tau})$. Predicts accumulation with repeated dosing.
Loading Dose
$LD = C_{ss} \times V_d$. Achieves target concentration immediately. Important for long tยฝ drugs.
Non-Linear Kinetics
Saturation Kinetics
Michaelis-Menten. Phenytoin, ethanol. Small dose changes โ large concentration changes.
Capacity-Limited Binding
Protein binding saturation. Free fraction increases with dose.