Indirect Response (Turnover) Model¶

PK/PD model for drugs that affect the synthesis or degradation of a response variable.

Model Schematic¶

┌─────────────┐
│     PK      │──── Conc ────┐
│ OneCompIVBolus             │
└─────────────┘              │
                             ▼
                      ┌─────────────────────────┐
                      │ Inhibition/Stimulation  │
                      │  of Kin or Kout         │
                      └───────────┬─────────────┘
                                  │
                                  ▼
                      ┌─────────────────────────┐
                      │   Response Variable     │
                      │   dR/dt = Kin - Kout×R  │
                      └─────────────────────────┘

Four Types of Indirect Response Models¶

Type	Drug Effect	Example
IRM-I	Inhibition of Kin	Corticosteroids on cortisol
IRM-II	Inhibition of Kout	Warfarin on clotting factors
IRM-III	Stimulation of Kin	EPO on RBC production
IRM-IV	Stimulation of Kout	Diuretics on sodium excretion

Differential Equations¶

Response:

dR/dt = Kin × (1 - I(C)) - Kout × R    (IRM-I: inhibit production)
dR/dt = Kin - Kout × (1 - I(C)) × R    (IRM-II: inhibit loss)
dR/dt = Kin × (1 + S(C)) - Kout × R    (IRM-III: stimulate production)
dR/dt = Kin - Kout × (1 + S(C)) × R    (IRM-IV: stimulate loss)

Where: - I(C) = Imax × C / (IC50 + C) (inhibition function) - S(C) = Smax × C / (SC50 + C) (stimulation function)

Parameters¶

Parameter	Description	Typical Range	Units
Kin	Zero-order production rate	0.1-100	units/h
Kout	First-order loss rate	0.01-1	1/h
Imax/Smax	Maximum inhibition/stimulation	0.1-1	-
IC50/SC50	Potency for effect	0.1-100	mg/L

Example Values (IRM-I)¶

Parameter	Value	Rationale
CL	5.0 L/h	Drug clearance
V	50.0 L	Drug volume
Kin	10 units/h	Production rate
Kout	0.1 1/h	Loss rate (t½ = 6.9h)
Imax	0.9	90% max inhibition
IC50	1.0 mg/L	Potency

Key Features¶

Baseline: R₀ = Kin/Kout
Response half-life: t½_R = ln(2)/Kout
Delayed response (not immediate)
Rebound possible after drug washout

Files¶

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