Sigmoid Emax (Hill) PD Model

PK/PD model with sigmoidal concentration-effect relationship.

Model Schematic

┌─────────────┐
│     PK      │──── Conc ────┐
│ OneCompIVBolus             │
└─────────────┘              ▼
                      ┌───────────────────────────┐
                      │   Sigmoid Effect (Hill)   │
                      │                           │
                      │ E = E0 + Emax × C^γ       │
                      │       ─────────────       │
                      │       EC50^γ + C^γ        │
                      └───────────────────────────┘

PD Equation

Effect = E0 + (Emax × C^γ) / (EC50^γ + C^γ)

Where: - E0 = baseline effect - Emax = maximum effect - EC50 = concentration at 50% effect - γ (gamma) = Hill coefficient (sigmoidicity factor)

Parameters

Parameter	Description	Typical Range	Units
E0	Baseline effect	0-100	varies
Emax	Maximum effect	0-100	varies
EC50	Potency	0.1-100	mg/L
gamma	Hill coefficient	0.5-5	-

Hill Coefficient Interpretation

γ Value	Curve Shape	Interpretation
< 1	Shallow	Negative cooperativity
= 1	Hyperbolic	No cooperativity (= Emax)
> 1	Steep	Positive cooperativity
>> 1	Switch-like	Threshold effect

Example Values

Parameter	Value	Rationale
E0	0	No baseline
Emax	100	100% max effect
EC50	1.0 mg/L	Moderate potency
gamma	2.0	Positive cooperativity

Key Features

• Steeper dose-response than simple Emax
• Common for drugs with cooperative binding
• Can model all-or-none responses (high γ)

Files

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