Parallel First-Order Absorption¶

PK model for drugs with multiple absorption sites or mechanisms, each with distinct absorption rate constants.

Usage¶

using NeoPKPD

# Create parallel absorption model
model = parallel_first_order_absorption()
params = CustomODEParams(
    Ka1 = 2.0,    # Fast absorption (1/h)
    Ka2 = 0.5,    # Slow absorption (1/h)
    F1 = 0.6,     # Fraction to fast pathway
    CL = 10.0,    # Clearance (L/h)
    V = 50.0      # Volume (L)
)

doses = [DoseEvent(0.0, 500.0)]
spec = ModelSpec(model, "parallel_abs", params, doses)
grid = SimGrid(0.0, 24.0, 0:0.25:24)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate(spec, grid, solver)

Parameters¶

Parameter	Type	Description
`Ka1`	Float64	First absorption rate constant (1/h)
`Ka2`	Float64	Second absorption rate constant (1/h)
`F1`	Float64	Fraction to first depot (0-1)
`CL`	Float64	Clearance (L/h)
`V`	Float64	Volume of distribution (L)

Model Equations¶

Three-compartment system (two depots, one central):

\[\frac{dA_1}{dt} = -K_{a1} \cdot A_1\]

\[\frac{dA_2}{dt} = -K_{a2} \cdot A_2\]

\[\frac{dA_c}{dt} = K_{a1} \cdot A_1 + K_{a2} \cdot A_2 - \frac{CL}{V} \cdot A_c\]

Initial conditions after dose D: - \(A_1(0) = F_1 \cdot D\) - \(A_2(0) = (1-F_1) \cdot D\)

Basic Example¶

using NeoPKPD

model = parallel_first_order_absorption()
params = CustomODEParams(
    Ka1 = 2.0,
    Ka2 = 0.5,
    F1 = 0.6,
    CL = 10.0,
    V = 50.0
)

doses = [DoseEvent(0.0, 500.0)]
spec = ModelSpec(model, "parallel", params, doses)
grid = SimGrid(0.0, 24.0, 0:0.25:24)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate(spec, grid, solver)

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

# Find Tmax and Cmax
cmax, idx = findmax(conc)
tmax = t[idx]
println("Tmax: $tmax h")
println("Cmax: $cmax mg/L")

Effect of Fraction Split¶

using NeoPKPD

model = parallel_first_order_absorption()
f1_values = [0.2, 0.4, 0.6, 0.8]

println("F1 (fast) | Cmax (mg/L) | Tmax (h)")
println("-" ^ 40)

for f1 in f1_values
    params = CustomODEParams(
        Ka1 = 3.0, Ka2 = 0.3, F1 = f1, CL = 10.0, V = 50.0
    )

    doses = [DoseEvent(0.0, 500.0)]
    spec = ModelSpec(model, "parallel", params, doses)
    grid = SimGrid(0.0, 24.0, 0:0.1:24)
    solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

    result = simulate(spec, grid, solver)
    conc = result.observations[:conc]
    t = result.t

    cmax, idx = findmax(conc)
    tmax = t[idx]

    println("$f1 | $cmax | $tmax")
end

Clinical Applications¶

Extended-release formulations with immediate release coating
Drugs with multiple absorption sites in GI tract
Food effects changing absorption pathways
Modified-release dosage forms

Equations Summary¶

Quantity	Formula
Depot 1 initial	\(A_1(0) = F_1 \cdot Dose\)
Depot 2 initial	\(A_2(0) = (1-F_1) \cdot Dose\)
Total absorption	\(K_{a1} \cdot A_1 + K_{a2} \cdot A_2\)
Concentration	\(C = A_c / V\)