Michaelis-Menten Elimination Model

One-compartment model with saturable (nonlinear) elimination kinetics.

Model Schematic

IV Bolus
    │
    ▼
┌─────────────┐
│   Central   │
│      V      │──── Vmax/(Km + C) ────▶ Saturable Elimination
└─────────────┘

Differential Equation

dA_central/dt = -Vmax × A_central / (Km × V + A_central)

Or in terms of concentration:

dC/dt = -Vmax × C / (Km + C) / V

Parameters

Parameter	Description	Typical Range	Units
Vmax	Maximum elimination rate	10-1000	mg/h
Km	Michaelis constant	1-100	mg/L
V	Volume of distribution	10-500	L

Example Values

Parameter	Value	Rationale
Vmax	50.0 mg/h	Maximum enzyme capacity
Km	10.0 mg/L	Half-saturation concentration
V	50.0 L	Total body water
Dose	500 mg	High dose to show saturation

Key Features

• At low C (C << Km): First-order kinetics, CL ≈ Vmax/Km
• At high C (C >> Km): Zero-order kinetics, rate ≈ Vmax
• Nonlinear PK: AUC not proportional to dose
• Examples: phenytoin, ethanol, aspirin (high dose)

Derived Parameters

Parameter	Formula	Description
CLint	Vmax/Km	Intrinsic clearance (at low C)
t½ (low C)	0.693 × V × Km / Vmax	Half-life at low concentrations

Use Cases

• Drugs with capacity-limited metabolism
• High-dose regimens
• Therapeutic drug monitoring
• Phenytoin dosing optimization

Clinical Implications

1. Dose escalation: Small dose increases can cause large concentration changes
2. Steady-state: Takes longer to reach at higher doses
3. Drug interactions: Enzyme inhibitors have greater effect when near saturation

Files

File	Description
julia.jl	Julia implementation
python.py	Python implementation
cli.json	CLI specification