Exercise PK49 - Turnover IV - Factor II data in healthy volunteers

2021-09-06

Background

  • Structural model - One compartment turnover model

  • Route of administration - Intravenous infusion

  • Dosage Regimen - 400 mg dose given as 19 minute constant intravenous infusion

  • Number of Subjects - 1 ( Healthy Volunteer )

PK49

Objectives

In this tutorial, you will learn how to build One compartment turnover model with constant intravenous infusion and simulate the model for one single subject and single dosage regimen.

Libraries

call the "necessary" libraries to get started.

using Random
using Pumas
using PumasUtilities
using CairoMakie

Model

pk_49            = @model begin
  @metadata begin
    desc         = "One Compartment Model"
    timeu        = u"hr"
  end

  @param begin
    "Clearance (L/hr)"
    tvcl          RealDomain(lower=0)
    "Volume of Central Compartment (L)"
    tvvc          RealDomain(lower=0)
    "Synthesis of endogenous coagulation Factor II (mg/hr)"
    tvsynthesis   RealDomain(lower=0)
    Ω             PDiagDomain(3)
    "Additive RUV"
    σ_add         RealDomain(lower=0)
  end

  @random begin
    η            ~ MvNormal(Ω)
  end

  @pre begin
    CL           = tvcl * exp(η[1])
    Vc           = tvvc * exp(η[2])
    Synthesis    = tvsynthesis * exp(η[3])
  end

  @init begin
    Central      = Synthesis/(CL/Vc) #we add Vc here because we want it in "amount". not conc.
  end

   @dynamics begin
     Central'    = Synthesis - (CL/Vc)*Central
   end

   @derived begin
     cp          = @. Central/Vc
     """
     Observed Concentration (ug/L)
     """
     dv          ~ @. Normal(cp, σ_add)
   end
end
PumasModel
  Parameters: tvcl, tvvc, tvsynthesis, Ω, σ_add
  Random effects: η
  Covariates: 
  Dynamical variables: Central
  Derived: cp, dv
  Observed: cp, dv

Parameters

The parameters are as given below. tv represents the typical value for parameters.

  • $Cl$ - Clearance (L/hr)

  • $Vc$ - Volume of Central Compartment (L)

  • $Synthesis$ - Synthesis of endogenous coagulation Factor II (mg/hr)

  • $Ω$ - Between Subject Variability

  • $σ$ - Residual error

param = ( tvcl        = 0.14204,
          tvvc        = 3.59259,
          tvsynthesis = 16.2272,
          Ω           = Diagonal([0.0,0.0,0.0]),
          σ_add       = 2.96)
(tvcl = 0.14204, tvvc = 3.59259, tvsynthesis = 16.2272, Ω = [0.0 0.0 0.0; 0
.0 0.0 0.0; 0.0 0.0 0.0], σ_add = 2.96)

Dosage Regimen

A single dose of 400 mg is given as an IV-Infusion over a period of 19 minutes in a healthy individual.

ev1  = DosageRegimen(400, cmt=1, duration=0.3166)
sub1 = Subject(id=1, events=ev1)
Subject
  ID: 1
  Events: 2

Simulation

Lets simulate for plasma concentration with the specific observation time points after Intravenous administration.

Random.seed!(123)
sim_sub1 = simobs(pk_49, sub1, param, 
                obstimes=[0.01,0.05,0.08,0.16,0.25,0.5,1,2,3,4,5,6,7,8,9,12,15,18,24,32,48,72,96,144])

Visualization

f, a, p = sim_plot(pk_49, [sim_sub1], 
        observations = :cp, 
        color = :redsblues,
        linewidth = 4,
        axis = (xlabel = "Time (hrs)", 
                ylabel = "PK49 Concentrations (μg/L)",
                xticks = 0:20:160, yticks = 80:20:240))
axislegend(a) 
f