Exercise PK39 - Two Compartment data-Experimental design issues

2021-09-06

Background

  • Structural model - Two compartment linear elimination with zero order absorption

  • Route of administration - Three consecutive constant rate IV infusion

  • Dosage Regimen - 1st dose:- 26.9 mcg/kg over 15min, 2nd dose:- 139 mcg/kg from 15min to 8hr, 3rd dose:- 138.95 mcg/kg between 8hr to 24hr

  • Number of Subjects - 1

pk39

Objectives

In this model you will learn how to build a two compartment model and simulate for a single subject.

Libraries

Call the "necessary" libraries to get start.

using Random
using Pumas
using PumasUtilities
using CairoMakie

Model

In this two compartment model we administer three consecutive IV infusion for a single subject and we assess the disposition of drug and fitting the model to the observed data.

pk_39           = @model begin
  @metadata begin
    desc        = "Two Compartment Model"
    timeu       = u"hr"
  end

  @param begin
    "Clearance (L/kg/hr)"
    tvcl         RealDomain(lower=0)
    "Volume of Central Compartment (L/kg)"
    tvvc         RealDomain(lower=0)
    "Volume of Peripheral Compartment (L/kg)"
    tvvp         RealDomain(lower=0)
    "Intercompartmental clearance (L/kg/hr)"
    tvq          RealDomain(lower=0)
    Ω            PDiagDomain(4)
    "Proportional RUV"
    σ²_prop      RealDomain(lower=0)
  end

  @random begin
    η           ~ MvNormal(Ω)
  end

  @pre begin
    CL          = tvcl * exp(η[1])
    Vc          = tvvc * exp(η[2])
    Vp          = tvvp * exp(η[3])
    Q           = tvq * exp(η[4])
  end

  @dynamics begin
    Central'    =  (Q/Vp)*Peripheral - (Q/Vc)*Central -(CL/Vc)*Central
    Peripheral' = -(Q/Vp)*Peripheral + (Q/Vc)*Central
  end

  @derived begin
    cp          = @. Central/Vc
    """
    Observed Concentration (ug/L)
    """
    dv          ~ @. Normal(cp, sqrt(cp^2*σ²_prop))
  end
end
PumasModel
  Parameters: tvcl, tvvc, tvvp, tvq, Ω, σ²_prop
  Random effects: η
  Covariates: 
  Dynamical variables: Central, Peripheral
  Derived: cp, dv
  Observed: cp, dv

Parameters

Parameters provided for simulation. tv represents the typical value for parameters.

  • $Cl$ - Clearance (L/kg/hr)

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

  • $Vp$ - Volume of Peripheral Compartment (L/kg)

  • $Q$ - Intercompartmental clearance (L/kg/hr)

  • $Ω$ - Between Subject Variability

  • $σ$ - Residual error

param = (tvcl    = 0.417793,
         tvvc    = 0.320672,
         tvvp    = 2.12265,
         tvq     = 0.903188,
         Ω       = Diagonal([0.0,0.0,0.0,0.0]),
         σ²_prop = 0.005)
(tvcl = 0.417793, tvvc = 0.320672, tvvp = 2.12265, tvq = 0.903188, Ω = [0.0
 0.0 0.0 0.0; 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0], σ²_prop =
 0.005)

Dosage Regimen

Single subject receiving three consecutive IV infusion

  • 1st dose: 26.9 mcg/kg over 15min

  • 2nd dose: 139 mcg/kg from 15min to 8hr

  • 3rd dose: 138.95 mcg/kg between 8hr to 24hr

ev1  = DosageRegimen([26.9,139,138.95], time=[0,0.25,8], cmt=1, duration=[0.25,7.85,16])
sub1 = Subject(id=1, events=ev1)
Subject
  ID: 1
  Events: 6

Simulation

Lets simulate for plasma concentration with the specific observation time points after IV infusion.

Random.seed!(123)
sim_sub1 = simobs(pk_39, sub1, param, obstimes=0:0.01:60)

Visualization

f1, a1, p1 = sim_plot(pk_39, [sim_sub1], 
        observations = :cp, 
        color = :redsblues,
        linewidth = 4,
        axis = (
                xlabel = "Time (hr)", 
                ylabel = "PK39 Concentrations (μg/L)",
                xticks = 0:10:60))
f1