Pharmacokinetic Modeling
The mathematical frameworks used to describe drug concentration-time profiles, from simple compartmental models to physiologically based models.
Why Model Pharmacokinetics?
PK modeling translates observed drug concentration data into mathematical descriptions that predict drug behavior under different conditions — new doses, different populations, drug combinations. Models are essential for dose selection in drug development, regulatory submissions, and clinical decision-making.
Non-Compartmental Analysis (NCA)
The simplest approach does not assume any model structure. NCA calculates PK parameters directly from observed concentration-time data using the trapezoidal rule:
- AUC: area under the curve (trapezoidal integration)
- Cmax and Tmax: read directly from data
- Terminal half-life: from the log-linear slope of the elimination phase
- CL = Dose / AUC and Vd = CL / kel
NCA is widely used in bioequivalence studies and early drug development because it makes minimal assumptions. However, it cannot predict concentrations at unmeasured time points or under different dosing scenarios.
Compartmental Models
One-Compartment Model
The body is treated as a single, well-mixed compartment. Drug enters (absorption) and leaves (elimination) from this compartment following first-order kinetics.
After IV bolus: C(t) = (Dose/Vd) x e^(-kel x t)
Best for drugs that distribute rapidly and equilibrate quickly (aminoglycosides, theophylline).
Two-Compartment Model
Adds a peripheral (tissue) compartment connected to the central (plasma) compartment by distribution rate constants. The concentration-time curve shows two phases:
- Alpha (distribution) phase: rapid initial decline as drug distributes into tissues
- Beta (elimination) phase: slower decline governed by terminal elimination
C(t) = A x e^(-alpha x t) + B x e^(-beta x t)
Most drugs are adequately described by one- or two-compartment models. Examples: vancomycin, digoxin, thiopental.
Three-Compartment Model
Adds a deep tissue compartment with very slow equilibration. Used for drugs like amiodarone and thiopental with prolonged redistribution phases.
Physiologically Based PK (PBPK)
PBPK models replace abstract compartments with anatomically and physiologically defined organs and tissues. Each tissue compartment has:
- Physiological blood flow rate
- Tissue volume
- Tissue-to-plasma partition coefficient
- Metabolic enzyme expression levels
PBPK models can predict drug behavior in situations never directly studied:
- Drug-drug interactions based on CYP expression and inhibition kinetics
- PK in special populations by adjusting organ volumes, blood flows, and enzyme ontogeny
- First-in-human dose selection from animal data using interspecies scaling
- Effect of genetic polymorphisms by modifying enzyme activity
The FDA increasingly accepts PBPK modeling as supporting evidence for labeling decisions, particularly for CYP-mediated drug interaction predictions.
Model Selection
| Approach | Complexity | Best For |
|---|---|---|
| NCA | Low | Bioequivalence, early development |
| 1-compartment | Low | Rapid distribution drugs |
| 2-compartment | Moderate | Most drugs |
| PopPK | Moderate-High | Clinical variability, sparse data |
| PBPK | High | Mechanistic prediction, DDI, special populations |
Key Takeaways
- NCA is assumption-free but cannot predict beyond observed data
- Compartmental models balance simplicity with predictive power
- Two-compartment models fit most drugs with distinct distribution and elimination phases
- PBPK models use physiological parameters to predict drug behavior mechanistically
- Regulatory agencies increasingly rely on modeling for dose selection and labeling decisions