One-Compartment Oral First-Order Absorption Model

One-compartment model with first-order absorption from an oral dose.

Model Schematic

Oral Dose
    │
    ▼
┌─────────┐     Ka      ┌─────────────┐
│   Gut   │ ─────────▶  │   Central   │
│  (A_d)  │             │      V      │──── CL ────▶ Elimination
└─────────┘             └─────────────┘

Differential Equations

dA_depot/dt = -Ka × A_depot
dA_central/dt = Ka × A_depot - CL/V × A_central

With initial conditions: A_depot(0) = Dose × F, A_central(0) = 0

Parameters

Parameter	Description	Typical Range	Units
Ka	Absorption rate constant	0.1-5.0	1/h
CL	Clearance	1-50	L/h
V	Volume of distribution	10-500	L
F	Bioavailability	0.1-1.0	-

Example Values

Parameter	Value	Rationale
Ka	1.5 1/h	Moderate absorption
CL	5.0 L/h	Moderate clearance
V	50.0 L	Total body water
Dose	100 mg	Oral tablet
F	1.0	Assumed 100%

Key Features

• Absorption phase followed by elimination phase
• Tmax occurs when absorption rate = elimination rate
• "Flip-flop" kinetics possible when Ka < k

Derived Parameters

Parameter	Formula	Example Value
k	CL/V	0.1 h⁻¹
Tmax	ln(Ka/k)/(Ka-k)	1.79 h
Cmax	(F×Dose/V)×(Ka/(Ka-k))×[exp(-k×Tmax)-exp(-Ka×Tmax)]	1.43 mg/L
t½	ln(2)/k	6.93 h

Files

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