Direct Emax PD Model¶

PK/PD model with direct, hyperbolic concentration-effect relationship.

Model Schematic¶

┌─────────────┐
│     PK      │──── Conc ────┐
│ OneCompIVBolus             │
└─────────────┘              ▼
                      ┌─────────────────────┐
                      │   Direct Effect     │
                      │                     │
                      │ E = E0 + Emax × C   │
                      │       ──────────    │
                      │        EC50 + C     │
                      └─────────────────────┘

PD Equation¶

Effect = E0 + (Emax × C) / (EC50 + C)

Where: - E0 = baseline effect - Emax = maximum effect above baseline - EC50 = concentration producing 50% of Emax - C = drug concentration

Parameters¶

Parameter	Description	Typical Range	Units
E0	Baseline effect	0-100	varies
Emax	Maximum effect	0-100	varies
EC50	Potency (C for 50% Emax)	0.1-100	mg/L

PK Parameters¶

Parameter	Description	Units
CL	Clearance	L/h
V	Volume	L

Example Values¶

Parameter	Value	Rationale
E0	0	No baseline effect
Emax	100	Maximum response = 100 units
EC50	1.0 mg/L	Moderate potency
CL	5.0 L/h	Moderate clearance
V	50.0 L	Total body water

Key Features¶

Immediate response (no hysteresis)
Hyperbolic saturation curve
Effect at C = EC50 is E0 + Emax/2
Effect at C >> EC50 approaches E0 + Emax

Use Cases¶

Receptor binding studies
Enzyme inhibition
Blood pressure lowering
Biomarkers with rapid equilibration

Files¶

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