Structural model - One compartment linear elimination with first order absorption.

Route of administration - Oral, Multiple dosing

Dosage Regimen - 352.3 μg

Number of Subjects - 1

This is a one compartment multiple oral dosing model. In the exercise pk04, four models are compared.

Model 1 - One compartment model without lag-time,

**distinct parameters Ka and K**Model 2 - One compartment model with lag time,

**distinct parameters Ka and K**Model 3 - One compartment model without lag time,

**Ka = K = K¹**Model 4 - One compartment model with lag time,

**Ka = K = K¹**

In this tutorial, you will learn how to build one compartment model for multiple oral dosing and to simulate the model for a single subject.

call the "necessary" libraries to get start.

using Random using Pumas using PumasUtilities using CairoMakie

In this one compartment model, we administer multiple doses orally.

pk_04_3_4 = @model begin @metadata begin desc = "One Compartment Model" timeu = u"hr" end @param begin "Absoprtion & Elimination Rate Constant (1/hr)" tvk¹ ∈ RealDomain(lower=0) "Volume of Distribution (L)" tvvc ∈ RealDomain(lower=0) "Lag-time (hr)" tvlag ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(2) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin K¹ = tvk¹ * exp(η[1]) Vc = tvvc * exp(η[2]) lags = (Depot = tvlag,) end @dynamics begin Depot' = -K¹*Depot Central' = K¹*Depot - K¹*Central end @derived begin """ PK04 Concentration (ug/L) """ cp = @. Central/Vc """ PK04 Concentration (ug/L) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

PumasModel Parameters: tvk¹, tvvc, tvlag, Ω, σ²_prop Random effects: η Covariates: Dynamical variables: Depot, Central Derived: cp, dv Observed: cp, dv

The parameters are as given below. `tv`

represents the typical value for parameters.

$K¹$ - Absorption and Elimination Rate Constant (hr⁻¹)

$Vc$ - Volume of Central Compartment(L)

$Ω$ - Between Subject Variability

$σ$ - Residual error

param = [ (tvk¹ = 0.14, tvvc = 56.3, tvlag = 0, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.015), (tvk¹ = 0.15, tvvc = 52.3, tvlag = 0.68, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.01) ]

2-element Vector{NamedTuple{(:tvk¹, :tvvc, :tvlag, :Ω, :σ²_prop), T} where T<:Tuple}: (tvk¹ = 0.14, tvvc = 56.3, tvlag = 0, Ω = [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0 .0 0.0], σ²_prop = 0.015) (tvk¹ = 0.15, tvvc = 52.3, tvlag = 0.68, Ω = [0.0 0.0 0.0; 0.0 0.0 0.0; 0. 0 0.0 0.0], σ²_prop = 0.01)

Subject received 352.3 μg of oral dose once a day for 10 days.

ev1 = DosageRegimen(352.3, time = 0, ii = 24, addl = 9, cmt = 1) pop = map(i -> Subject(id = i, events = ev1, observations = (cp = nothing,)), ["1: No Lag", "1: With Lag"])

Simulation the plasma concentration of the drug after multiple oral dosing

Random.seed!(123) sim = map(zip(pop, param)) do (subj, p) return simobs(pk_04_3_4, subj, p, obstimes = 0:0.1:240) end

f, a, p = sim_plot(pk_04_3_4, sim, observations=:cp, linewidth = 4, color = :redsblues, axis = (xlabel = "Time (hours)", ylabel = "PK04 Concentrations (ug/L)", xticks = 0:24:240,)) axislegend(a) f