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

Graphical representation of the model

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.

  • $Vss$ - Steady state volume (L)

  • $CL$ - Clearance (L/hr)

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