Exercise PK43 - Multiple absorption routes

2021-09-06

Background

  • Structural model - 1 compartment linear elimination with first order absorption

  • Route of administration - Sublingual

  • Dosage Regimen - 2mg Sublingual dose

  • Number of Subjects - 1

pk43

Learning Outcome

In this model, Multiple absorption routes helps in understanding absorption of sublingually administered dose partly from buccal cavity and partly from gastrointestinal tract

Objectives

In this model you will learn how to write differential equation model for a drug that is partly absorbed from buccal and partly from GI 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 one compartment model, we administer dose Sublingually.

pk_43        = @model begin
  @metadata begin
    desc     = "Multiple Absorption Model"
    timeu    = u"hr"
  end

  @param begin
    "Absorption rate constant(rapid from buccal) (hr⁻⅟)"
    tvkar     RealDomain(lower=0)
    "Absorption rate constant(delayed from GI) (hr⁻⅟)"
    tvkad     RealDomain(lower=0)
    "Volume of Central Compartment (L)"
    tvv       RealDomain(lower=0)
    "Lagtime (hr)"
    tvlag     RealDomain(lower=0)
    "Fraction of drug absorbed"
    tvfa      RealDomain(lower=0)
    "Elimination rate constant (hr⁻⅟)"
    tvk       RealDomain(lower=0)
    Ω         PDiagDomain(4)
    "Additive RUV"
    σ_add     RealDomain(lower=0)
  end

  @random begin
    η        ~ MvNormal(Ω)
  end

  @pre begin
    KaR      = tvkar * exp(η[1])
    KaD      = tvkad * exp(η[2])
    V        = tvv * exp(η[3])
    K        = tvk * exp(η[4])
  end

  @dosecontrol begin
    bioav    = (Buccal=tvfa, Gi= 1-tvfa)
    lags     = (Gi=tvlag,)
  end

  @dynamics begin
    Buccal'  = -KaR*Buccal
    Gi'      = -KaD*Gi
    Central' =  KaR*Buccal + KaD*Gi - K*Central
  end

  @derived begin
    cp       = @. Central/V
    """
    Observed Concentration (mcg/L)
    """
    dv       ~ @. Normal(cp, σ_add)
  end
end
PumasModel
  Parameters: tvkar, tvkad, tvv, tvlag, tvfa, tvk, Ω, σ_add
  Random effects: η
  Covariates: 
  Dynamical variables: Buccal, Gi, Central
  Derived: cp, dv
  Observed: cp, dv

Parameters

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

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

  • $K$ - Elimination rate constant (hr⁻⅟)

  • $Kar$ - Absorption rate constant(rapid from buccal) (hr⁻⅟)

  • $Kad$ - Absorption rate constant(delayed from GI) (hr⁻⅟)

  • $Fa$ - Fraction of drug absorbed

  • $lags$ - Lagtime (hr)

  • $Ω$ - Between Subject Variability

  • $σ$ - Residual error

param = (tvkar  = 7.62369,
         tvkad  = 1.0751,
         tvv    = 20.6274,
         tvk    = 0.0886931,
         tvfa   = 0.515023,
         tvlag  = 2.29614,
         Ω      = Diagonal([0.0,0.0,0.0,0.0]),
         σ_add  = 0.86145)
(tvkar = 7.62369, tvkad = 1.0751, tvv = 20.6274, tvk = 0.0886931, tvfa = 0.
515023, tvlag = 2.29614, 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], σ_add = 0.86145)

DosageRegimen

Single subject receiving 2mg dose given orally (absorbed - Sublingually and remaining from the Gut).

ev1  = DosageRegimen(2000, time = 0, cmt = [1,2])
sub1 = Subject(id = 1, events = ev1)
Subject
  ID: 1
  Events: 2

Simulation

Lets simulate plasma concentration with specific observation times after Sublingual dose considering multiple absorption routes.

Random.seed!(123)
sim_sub1 = simobs(pk_43, sub1, param, obstimes=0.00:0.01:24)

Visualization

f1, a1, p1 = sim_plot(pk_43, [sim_sub1], 
        observations = :cp, 
        color = :redsblues,
        linewidth = 4,
        axis = (
                xlabel = "Time (min)", 
                ylabel = "PK43 Concentrations (μg/L)",
                xticks = 0:5:25))
axislegend(a1) 
f1