# Exercise 46 - Long Infusion Short Half Life

##### 2021-09-06

### Background

Structural model - Long infusion short half life one compartment model

Route of administration - IV infusion

Dosage Regimen - 500000 ug

Number of Subjects - 1

### Learning Outcome

This exercise deals with the drug having short half life.

### Objectives

To build a model for drug having short half life given as a very long infusion up to 3 months.

### Libraries

Call the "necessary" libraries to get started.

using Random
using Pumas
using PumasUtilities
using CairoMakie

### Model

To build a one compartment model for a drug having short half life given a long infusion for 3 months.

pk_46 = @model begin
@metadata begin
desc = "One Compartment Model"
timeu = u"hr"
end
@param begin
"Volume at Steady State (L)"
tvvss ∈ RealDomain(lower=0)
"Clearance (L/hr)"
tvcl ∈ RealDomain(lower=0)
Ω ∈ PDiagDomain(2)
"Additive Error"
σ_add ∈ RealDomain(lower=0)
end
@random begin
η ~ MvNormal(Ω)
end
@pre begin
Vss = tvvss*exp(η[1])
Cl = tvcl*exp(η[2])
end
@dynamics begin
Central' = - (Cl/Vss)*Central
end
@derived begin
cp = @. Central/Vss
"""
Observed Concentration (ug/L)
"""
dv ~ @. Normal(cp, σ_add)
end
end

PumasModel
Parameters: tvvss, tvcl, Ω, σ_add
Random effects: η
Covariates:
Dynamical variables: Central
Derived: cp, dv
Observed: cp, dv

### Parameters

Parameters provided for simulation are as below. `tv`

represents the typical value for parameters.

param = ( tvvss = 35.6,
tvcl = 61,
Ω = Diagonal([0.0,0.0]),
σ_add = 0.196337)

(tvvss = 35.6, tvcl = 61, Ω = [0.0 0.0; 0.0 0.0], σ_add = 0.196337)

### DosageRegimen

A dose of **500000 ug** was given as an Intravenous Infusion to a single subject for over 3 months.

ev1 = DosageRegimen(500000, time = 0, cmt = 1, duration = 2016)
sub1 = Subject(id = 1, events = ev1)

Subject
ID: 1
Events: 2

### Simulation

Simulate the data after the administration of Infusion

Random.seed!(123)
sim_sub1 = simobs(pk_46, sub1, param, obstimes = 0.5:0.1:2100)

### Visualization

f, a, p = sim_plot(pk_46, [sim_sub1],
observations = :cp,
color = :redsblues,
linewidth = 4,
axis = (xlabel = "Time (hrs)",
ylabel = "PK46 Concentrations (μg/L)",
xticks = 0:500:2000))
axislegend(a)
f