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