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 gatrointestinal 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 Pumas using Plots using StatsPlots using CSV using Random

In this one compartment model, we administer dose Sublingually.

pk_43 = @model begin @param begin tvkar ∈ RealDomain(lower=0) tvkad ∈ RealDomain(lower=0) tvv ∈ RealDomain(lower=0) tvlag ∈ RealDomain(lower=0) tvfa ∈ RealDomain(lower=0) tvk ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(4) 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]) 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 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) df1 = DataFrame(sim_sub1)

Simulated data is saved as dataframe and used for plotting.

df1_dv = filter(x -> x.time in [0.1,0.15,0.25,0.5,0.75,0.8,1,1.25,1.5,2,3,4,5,6,8,12,24], df1) @df df1 plot(:time, :cp, title="Multiple absorption routes",label="Pred - Conc", xlabel="Time(hr)",ylabel="Conc(mcg/l)", linewidth=3, xticks=[0,5,10,15,20,25], xlim=(-0.1,25), yticks=[10,20,30,40,50,60,70,80], ylim=(10,80)) @df df1_dv scatter!(:time, :dv, label="Obs - Conc")