Structural model - 1 compartment linear elimination with first order absorption

Route of administration - Sublingual

Dosage Regimen - 2mg Sublingual dose

Number of Subjects - 1

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

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.

Call the "necessary" libraries to get start.

using Random using Pumas using PumasUtilities using CairoMakie

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 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)

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

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)

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