Three-Compartment IV Bolus Model¶

Three-compartment model for drugs with complex tissue distribution.

Model Schematic¶

                  IV Bolus
                      │
                      ▼
┌─────────────┐  Q2  ┌─────────────┐  Q3  ┌─────────────┐
│ Peripheral  │◄────▶│   Central   │◄────▶│ Peripheral  │
│   Shallow   │      │     V1      │      │    Deep     │
│     V2      │      └──────┬──────┘      │     V3      │
└─────────────┘             │             └─────────────┘
                            │ CL
                            ▼
                       Elimination

Differential Equations¶

dA_central/dt = Q2/V2 × A_shallow - Q2/V1 × A_central
              + Q3/V3 × A_deep - Q3/V1 × A_central
              - CL/V1 × A_central

dA_shallow/dt = Q2/V1 × A_central - Q2/V2 × A_shallow

dA_deep/dt = Q3/V1 × A_central - Q3/V3 × A_deep

Parameters¶

Parameter	Description	Typical Range	Units
CL	Clearance	1-50	L/h
V1	Central volume	5-50	L
Q2	Shallow distribution clearance	5-100	L/h
V2	Shallow peripheral volume	10-200	L
Q3	Deep distribution clearance	0.1-10	L/h
V3	Deep peripheral volume	50-1000	L

Example Values¶

Parameter	Value	Rationale
CL	5.0 L/h	Moderate clearance
V1	10.0 L	Plasma volume
Q2	20.0 L/h	Rapid shallow distribution
V2	20.0 L	Well-perfused tissues
Q3	2.0 L/h	Slow deep distribution
V3	100.0 L	Poorly perfused tissues/fat
Dose	100 mg	IV bolus

Key Features¶

Tri-exponential decline (α, β, γ phases)
α phase: rapid distribution
β phase: slow distribution
γ phase: terminal elimination
Vss = V1 + V2 + V3

Files¶

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