Non-Linear Pharmacokinetics
When pharmacokinetics deviate from first-order behavior — saturable metabolism, dose-dependent kinetics, and Michaelis-Menten elimination.
## When Linearity Breaks Down
Most drugs follow linear (first-order) pharmacokinetics at therapeutic doses: doubling the dose doubles the AUC and steady-state concentration. Non-linear pharmacokinetics occurs when one or more ADME processes become saturated, causing disproportionate changes in drug exposure with dose adjustments.
## Michaelis-Menten Kinetics
When metabolic enzymes approach saturation, elimination transitions from first-order to zero-order. The Michaelis-Menten equation describes this:
**Rate = Vmax x C / (Km + C)**
- When C << Km: rate is proportional to concentration (first-order)
- When C >> Km: rate equals Vmax (zero-order, saturated)
- When C = Km: rate is exactly Vmax/2
## Classic Examples
### Phenytoin
The most clinically important example of non-linear PK. CYP2C9, which metabolizes phenytoin, saturates within the therapeutic range (10-20 mcg/mL). Consequences:
- Small dose increases (e.g., 300 to 330 mg/day) can cause disproportionately large concentration increases
- Half-life is not constant — it increases as concentration rises
- Steady state takes unpredictably long to achieve
- Therapeutic drug monitoring is essential
### Ethanol
Alcohol dehydrogenase saturates at typical drinking levels. Ethanol is eliminated at a fixed rate (~7-10 g/hour in adults) regardless of blood concentration. This is why BAC declines linearly rather than exponentially.
### Aspirin (High Dose)
At anti-inflammatory doses (> 4 g/day), salicylate metabolism saturates. The apparent half-life extends from 2-3 hours to 15-30 hours, risking accumulation and toxicity.
## Types of Non-Linearity
| Process | Mechanism | Effect |
|---------|-----------|--------|
| Saturable metabolism | Enzyme capacity exceeded | Disproportionate AUC increase |
| Saturable absorption | Carrier-mediated transport limited | AUC increases less than dose |
| Saturable protein binding | Binding sites filled | Free fraction increases with dose |
| Saturable renal secretion | Transporter capacity exceeded | Renal clearance decreases |
| Autoinduction | Drug induces its own metabolism | Clearance increases over time |
## Autoinduction
Carbamazepine induces its own metabolism via CYP3A4. During the first weeks of therapy, clearance progressively increases, and plasma levels fall. Doses must be titrated upward to maintain therapeutic concentrations. This is the opposite of saturation — the system becomes more efficient over time.
## Clinical Management
- **Frequent monitoring**: phenytoin, theophylline at high doses
- **Cautious titration**: small dose increments with level checks
- **Dosing nomograms**: specialized charts for phenytoin dosing based on Km and Vmax
- **Time-dependent dosing**: carbamazepine autoinduction requires planned dose escalation
## Key Takeaways
- Non-linear PK occurs when ADME processes saturate
- Phenytoin is the classic example — small dose changes cause large concentration shifts
- Michaelis-Menten kinetics describe the transition from first-order to zero-order
- Autoinduction (carbamazepine) increases clearance over time
- Drugs with non-linear PK require more frequent therapeutic drug monitoring