Structural model - Two compartment disposition model with nonlinear elimination

Route of administration - IV infusion

Dosage Regimen - 0.4g/Kg (i.e.,28g for a 70Kg healthy individual), infused over a time span of 30 minutes

Number of Subjects - 1

In this model, you will learn -

To build a two compartment disposition model, the drug is given as an

`Intravenous Infusion`

which follows Michaelis-Menten Kinetics.To apply

*differential equation*in the model as per the compartment model.To design the dosage regimen for the subjects and simulate the plot.

In this tutorial, you will learn how to build a two Compartment disposition model with Non-linear elimination following *Intravenous infusion* and simulate the model for *single subject* and *single dosage regimen*.

Call the "necessary" libraries to get started

using Random using Pumas using PumasUtilities using CairoMakie

In this two compartment model, we administer dose on Central compartment.

pk_18 = @model begin @metadata begin desc = "Two Compartment Model - Nonlinear Elimination" timeu = u"hr" end @param begin "Maximum rate of elimination (mg/hr)" tvvmax ∈ RealDomain(lower=0) "Michaelis-Menten rate constant (mg/L)" tvkm ∈ RealDomain(lower=0) "Intercompartmental Clearance (L/hr)" tvQ ∈ RealDomain(lower=0) "Volume of Central Compartment (L)" tvvc ∈ RealDomain(lower=0) "Volume of Peripheral Compartment (L)" tvvp ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(5) "Proportional RUV" σ_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Vmax = tvvmax * exp(η[1]) Km = tvkm * exp(η[2]) Q = tvQ * exp(η[3]) Vc = tvvc * exp(η[4]) Vp = tvvp * exp(η[5]) end @dynamics begin Central' = - (Vmax/(Km+(Central/Vc))) * Central/Vc + (Q/Vp) * Peripheral - (Q/Vc) * Central Peripheral' = - (Q/Vp) * Peripheral + (Q/Vc) * Central end @derived begin cp = @. Central/Vc """ Observed Concentration (g/L) """ dv ~ @. Normal(cp, cp^2*σ_prop) end end

PumasModel Parameters: tvvmax, tvkm, tvQ, tvvc, tvvp, Ω, σ_prop Random effects: η Covariates: Dynamical variables: Central, Peripheral Derived: cp, dv Observed: cp, dv

The parameters are as given below. `tv`

represents the typical value for parameters.

$Vmax$ - Maximum rate of elimination (mg/hr)

$Km$ - Michaelis-Menten rate constant (mg/L)

$Q$ - Intercompartmental Clearance (L/hr)

$Vc$ - Volume of Central Compartment (L)

$Vp$ - Volume of Peripheral Compartment (L)

$Ω$ - Between Subject Variability

$σ$ - Residual error

param = (tvvmax = 0.0812189, tvkm = 0.0125445, tvQ = 1.29034, tvvc = 8.93016, tvvp = 31.1174, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0]), σ_prop = 0.005)

(tvvmax = 0.0812189, tvkm = 0.0125445, tvQ = 1.29034, tvvc = 8.93016, tvvp = 31.1174, 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_prop = 0.005)

**0.4g/Kg** (i.e.,**28g** for a 70Kg healthy individual), infused over a `time span of 30 minutes`

, given to a single subject.

ev1 = DosageRegimen(28, time = 0, cmt = 1, duration = 30) sub1 = Subject(id = 1, events = ev1, observations = (cp = nothing,))

Subject ID: 1 Events: 2 Observations: cp: (nothing)

Lets simulate for plasma concentration with the specific observation time points after Intravenous administration.

Random.seed!(1234) sim_sub = simobs(pk_18,sub1, param, obstimes = 0.1:1:360)

f, a, p = sim_plot(pk_18, [sim_sub], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (minute)", ylabel = "PK18 Concentrations (g/L)", xticks = 0:50:400, yscale = log10)) axislegend(a) f