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 Pumas using Plots using CSV using StatsPlots using Random
In this one compartment model, we administer multiple doses orally.
pk_04_1_2 = @model begin @param begin tvka ∈ RealDomain(lower=0) tvk ∈ RealDomain(lower=0) tvvc ∈ RealDomain(lower=0) tvlag ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(3) σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Ka = tvka * exp(η) K = tvk * exp(η) Vc = tvvc * exp(η) lags = (Depot = tvlag,) end @dynamics begin Depot' = -Ka*Depot Central' = Ka*Depot - K*Central end @derived begin cp = @. Central/Vc dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end
PumasModel Parameters: tvka, tvk, 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.
Ka - Absorption Rate Constant (hr⁻¹),
K - Elimination Rate Constant (hr⁻¹),
Vc - Volume of Central Compartment(L),
Ω - Between Subject Variability,
σ - Residual error
param1 = (tvka = 0.14, tvk = 0.14, tvvc = 56.6, tvlag = 0, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.015)
(tvka = 0.14, tvk = 0.14, tvvc = 56.6, 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)
param2 = (tvka = 0.20, tvk = 0.12, tvvc = 64.9, tvlag = 0.70, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.01)
(tvka = 0.2, tvk = 0.12, tvvc = 64.9, tvlag = 0.7, 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) sub1 = Subject(id=1, events=ev1) sub2 = Subject(id=2, events=ev1)
Simulation the plasma concentration of the drug after multiple oral dosing
## Model 1 - without lag time Random.seed!(123) sim_sub1 = simobs(pk_04_1_2,sub1,param1,obstimes= 0:0.1:240) df1 = DataFrame(sim_sub1) ## Model 2 - with lag time Random.seed!(123) sim_sub2 = simobs(pk_04_1_2,sub2,param2,obstimes= 0:0.1:240) df2 = DataFrame(sim_sub2)
df2_dv = filter(x -> x.time in [1,2,3,4,5,6,7,8,10,12,14,24,216,216.5,217,218,219,220,221,222,223,224,226,228,230,240], df2) @df df1 plot(:time, :cp, xlabel = "Time (hr)", ylabel = "Concentration (ug/L)", label = "Pred-Without lag-time", title = "Plasma Concentration vs Time", linewidth = 3, legend=:outerright, xticks = [0,24,48,72,96,120,144,168,192,216,240], ylims=(0,3.0)) @df df2 plot!(:time, :cp, label = "Pred-With lag-time", linewidth=3) @df df2_dv scatter!(:time, :dv, label="Obs-Conc")