Transit Compartment PD Model¶

PD model with a chain of transit compartments to model delayed drug effects and signal transduction cascades.

Usage¶

using NeoPKPD

# Create PK model
pk_model = OneCompIVBolus()
pk_params = OneCompIVBolusParams(5.0, 50.0)  # CL, V
doses = [DoseEvent(0.0, 500.0)]
pk_spec = ModelSpec(pk_model, "pk", pk_params, doses)

# Create Transit Compartment PD
pd_model = TransitCompartmentPD()
pd_params = TransitCompartmentPDParams(
    5,        # n_transit
    0.5,      # ktr
    100.0,    # e0
    -50.0,    # emax
    5.0,      # ec50
    1.0       # gamma
)

pd_spec = PDSpec(pd_model, "pd", pd_params, :conc, :effect)

grid = SimGrid(0.0, 168.0, 0:1:168)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate_pkpd_coupled(pk_spec, pd_spec, grid, solver)

Parameters¶

Parameter	Type	Description
`n_transit`	Int	Number of transit compartments (1-20)
`ktr`	Float64	Transit rate constant (1/h)
`e0`	Float64	Baseline effect
`emax`	Float64	Maximum effect change
`ec50`	Float64	EC50 for effect
`gamma`	Float64	Hill coefficient

Key Derived Parameter¶

Mean Transit Time (MTT): $$MTT = \frac{N + 1}{K_{tr}}$$

Model Equations¶

Drug-induced signal: $$Signal(C) = E_0 + \frac{E_{max} \cdot C^\gamma}{EC_{50}^\gamma + C^\gamma}$$

Transit compartment chain: $$\frac{dA_1}{dt} = K_{tr} \cdot (Signal(C) - A_1)$$

\[\frac{dA_i}{dt} = K_{tr} \cdot (A_{i-1} - A_i) \quad \text{for } i = 2..N\]

Final effect: $$Effect = A_N$$

Basic Example¶

using NeoPKPD

# PK setup
pk_model = OneCompIVBolus()
pk_params = OneCompIVBolusParams(5.0, 50.0)
doses = [DoseEvent(0.0, 500.0)]
pk_spec = ModelSpec(pk_model, "pk", pk_params, doses)

# PD setup: 5 transit compartments
pd_model = TransitCompartmentPD()
pd_params = TransitCompartmentPDParams(5, 0.5, 100.0, -50.0, 5.0, 1.0)
pd_spec = PDSpec(pd_model, "pd", pd_params, :conc, :effect)

grid = SimGrid(0.0, 168.0, 0:1:168)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate_pkpd_coupled(pk_spec, pd_spec, grid, solver)

effect = result.observations[:effect]
t = result.t

# MTT = (5+1) / 0.5 = 12 hours
mtt = (5 + 1) / 0.5
println("MTT: $mtt h")

nadir, idx = findmin(effect)
println("Nadir: $nadir at t = $(t[idx]) h")

Clinical Example: Myelosuppression¶

using NeoPKPD

# Neutropenia model (MTT ~5 days)
mtt_days = 5.0
n_transit = 5
ktr = (n_transit + 1) / (mtt_days * 24)

pk_model = OneCompIVBolus()
pk_params = OneCompIVBolusParams(3.0, 30.0)
doses = [DoseEvent(0.0, 100.0)]
pk_spec = ModelSpec(pk_model, "chemo", pk_params, doses)

pd_model = TransitCompartmentPD()
pd_params = TransitCompartmentPDParams(n_transit, ktr, 5.0, -4.5, 1.0, 1.5)
pd_spec = PDSpec(pd_model, "neutro", pd_params, :conc, :effect)

grid = SimGrid(0.0, 504.0, 0:2:504)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate_pkpd_coupled(pk_spec, pd_spec, grid, solver)

effect = result.observations[:effect]
t = result.t

nadir, idx = findmin(effect)
println("Baseline ANC: 5.0 x10^9/L")
println("Nadir ANC: $nadir x10^9/L at day $(t[idx]/24)")

Clinical Applications¶

Chemotherapy-induced neutropenia
Thrombocytopenia
Delayed biomarker responses
Signal transduction cascades

Equations Summary¶

Quantity	Formula
MTT	$(N+1) / K_{tr}$
Signal	$E_0 + E_{max} \cdot C^\gamma / (EC_{50}^\gamma + C^\gamma)$
Transit rate	$K_{tr} \cdot (A_{i-1} - A_i)$
CV of delay	$1 / \sqrt{N+1}$

Quantity	Formula
MTT	\((N+1) / K_{tr}\)
Signal	\(E_0 + E_{max} \cdot C^\gamma / (EC_{50}^\gamma + C^\gamma)\)
Transit rate	\(K_{tr} \cdot (A_{i-1} - A_i)\)
CV of delay	\(1 / \sqrt{N+1}\)