Structural model - Multi compartment model with saturable absorption kinetics

Route of administration - Oral Route

Dosage Regimen - 10 mg, 30 mg, 90 mg oral dose given at different occasions

Number of Subjects - 1

This model gives an understanding of non linear absorption due to saturation of drug transporters at higher doses of drug administered orally.

In this tutorial, you will learn to build a multi compartment model for a drug following saturable absorption kinetics and simulate the data.

Call the "necessary" libraries to get started.

using Random using Pumas using PumasUtilities using CairoMakie

In this multi compartment model,a single subject receives oral doses of a compound X at three different occasions which follows non linear absorption and linear disposition kinetics.

pk_42 = @model begin @metadata begin desc = "Non-linear Absorption Model" timeu = u"minute" end @param begin "Maximum Metabolic Capacity (ug/min)" tvvmax ∈ RealDomain(lower=0) "Michaelis-Menten Constant (ug/L)" tvkm ∈ RealDomain(lower=0) "Volume of Distribution of Central Compartment (L)" tvvc ∈ RealDomain(lower=0) "Volume of Distribution of Peripheral compartment (L)" tvvp ∈ RealDomain(lower=0) "Inter Compartmental Clearance (L/min)" tvq ∈ RealDomain(lower=0) "Clearance (L/min)" tvcl ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(6) "Additive RUV" σ_add ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Vmax = tvvmax*exp(η[1]) Km = tvkm*exp(η[2]) Vc = tvvc*exp(η[3]) Vp = tvvp*exp(η[4]) Q = tvq*exp(η[5]) CL = tvcl*exp(η[6]) end @vars begin VMKM := Vmax/(Km+Depot) end @dynamics begin Depot' = -VMKM*Depot Central' = VMKM*Depot -CL*(Central/Vc) - (Q/Vc)*Central + (Q/Vp)*Peripheral Peripheral' = (Q/Vc)*Central - (Q/Vp)*Peripheral end @derived begin cp = @. Central/Vc """ Observed Concentration (ug/L) """ dv ~ @. Normal(cp,σ_add) end end

PumasModel Parameters: tvvmax, tvkm, tvvc, tvvp, tvq, tvcl, Ω, σ_add Random effects: η Covariates: Dynamical variables: Depot, Central, Peripheral Derived: cp, dv Observed: cp, dv

Parameters provided for simulation as below. `tv`

represents the typical value for parameters.

$Vmax$ - Maximum Metabolic Capacity (ug/min)

$Km$ - Michaelis-Menten Constant (ug/ml)

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

$Vp$ - Volume of Distribution of Peripheral compartment (L)

$Q$ - Inter Compartmental Clearance (L/min)

$CL$ - Clearance (L/min)

$Ω$ - Between Subject Variability

$σ$ - Residual Error

param = (tvvmax = 982.453, tvkm = 9570.63, tvvc = 4.66257, tvvp = 35, tvq = 0.985, tvcl = 2.00525, Ω = Diagonal([0.0, 0.0, 0.0,0.0,0.0,0.0]), σ_add = 0.123)

(tvvmax = 982.453, tvkm = 9570.63, tvvc = 4.66257, tvvp = 35, tvq = 0.985, tvcl = 2.00525, 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 = 0.123)

A single subject received oral dosing of **10,30,90 mg** on three different occasions

dose_ind = [90000,30000,10000] ids = ["10 mg","30 mg", "90 mg"] ev(x) = DosageRegimen(dose_ind[x], time=0, cmt=1) pop = map(i -> Subject(id=ids[i], events=ev(i)), 1:length(ids))

Population Subjects: 3 Observations:

Simulate the plasma concentration for single subject after an oral dose given at three different occasions.

Random.seed!(123) sim_pop3_sub = simobs(pk_42, pop, param, obstimes=0.1:0.1:360)

f1, a1, p1 = sim_plot(pk_42, sim_pop3_sub, observations = :cp, color = :redsblues, linewidth = 4, axis = ( xlabel = "Time (min)", ylabel = "PK42 Concentrations (μg/L)", xticks = 0:50:400, yscale = log10)) axislegend(a1) f1