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_3_4 = @model begin @param begin tvk¹ ∈ RealDomain(lower=0) tvvc ∈ RealDomain(lower=0) tvlag ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(2) 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 cp = @. Central/Vc 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

param3 = (tvk¹ = 0.14, tvvc = 56.3, tvlag = 0, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.015)

(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)

param4 = (tvk¹ = 0.15, tvvc = 52.3, tvlag = 0.68, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.01)

(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) sub3 = Subject(id=3, events=ev1) sub4 = Subject(id=4, events=ev1)

Simulation the plasma concentration of the drug after multiple oral dosing

## Model 3 - without lag time Random.seed!(123) sim_sub3 = simobs(pk_04_3_4,sub3,param3,obstimes= 0:0.1:240) df3 = DataFrame(sim_sub3) ## Model 4 - with lag time Random.seed!(123) sim_sub4 = simobs(pk_04_3_4,sub4,param4,obstimes= 0:0.1:240) df4 = DataFrame(sim_sub4)

df4_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], df3) @df df3 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 df4 plot!(:time, :cp, label = "Pred-With lag-time", linewidth=3) @df df4_dv scatter!(:time, :dv, label="Obs-Conc")