Biophase Equilibration (Effect Compartment) Model¶

PK/PD model with delayed effect due to distribution to an effect site.

Model Schematic¶

IV Bolus
    │
    ▼
┌─────────────┐     Ke0      ┌─────────────┐
│   Central   │ ───────────▶ │   Effect    │
│      V      │              │ Compartment │
└──────┬──────┘              │    (Ce)     │
       │                     └──────┬──────┘
       │ CL                         │
       ▼                            ▼
   Elimination              ┌─────────────────┐
                            │ E = E0 + Emax×Ce│
                            │     ───────────  │
                            │     EC50 + Ce   │
                            └─────────────────┘

Differential Equations¶

PK:

dA_central/dt = -CL/V × A_central

Effect Compartment:

dCe/dt = Ke0 × (Cp - Ce)

PD:

Effect = E0 + Emax × Ce / (EC50 + Ce)

Parameters¶

Parameter	Description	Typical Range	Units
Ke0	Effect site equilibration rate	0.1-5	1/h
E0	Baseline effect	0-100	varies
Emax	Maximum effect	0-100	varies
EC50	Effect site EC50	0.1-100	mg/L

Example Values¶

Parameter	Value	Rationale
CL	5.0 L/h	Moderate clearance
V	50.0 L	Central volume
Ke0	0.5 1/h	1.4h equilibration half-life
E0	0	No baseline
Emax	100	Maximum response
EC50	1.0 mg/L	Effect site potency

Key Features¶

Counter-clockwise hysteresis: Effect lags behind concentration
t½ke0 = ln(2)/Ke0: Time for effect compartment to equilibrate
Peak effect occurs after peak concentration
Effect persists longer than plasma concentration

Use Cases¶

CNS-active drugs (BBB penetration delay)
Anesthetics (propofol, remifentanil)
Sedatives/hypnotics
Analgesics

Hysteresis Interpretation¶

When plotting Effect vs Concentration: - Counter-clockwise loop: Effect delayed (biophase model) - Clockwise loop: Tolerance development

Files¶

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