Structural model - One compartment linear elimination

Route of administration - IV bolus

Dosage Regimen - 10 mg IV

Number of Subjects - 4

In this model, you will learn -

To build One compartment model for four subjects given

`Intravenous Bolus`

dosage.To estimate the fundamental parameters involved in building the model.

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 one compartment model and to simulate the model for four subjects with different values of Parameter estimates.

call the "necessary" libraries to get started.

using Pumas using PumasUtilities using Random using CairoMakie

In this One compartment model, intravenous dose is administered into the central compartment. We account for rate of change of concentration of drug in plasma (Central Compartment) for the time duration upto 150 min.

pk_01 = @model begin @metadata begin desc = "One Compartment Model" timeu = u"minute" end @param begin "Clearance (L/hr)" tvcl ∈ RealDomain(lower=0) "Volume (L)" tvvc ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(2) "Additive RUV" σ ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Cl = tvcl * exp(η[1]) Vc = tvvc * exp(η[2]) end @dynamics begin Central' = -(Cl/Vc)*Central end @derived begin """ PK01 Concentrations (ug/L) """ cp = @. 1000*(Central/Vc) """ PK01 Concentrations (ug/L) """ dv ~ @. Normal(cp, σ) end end

PumasModel Parameters: tvcl, tvvc, Ω, σ Random effects: η Covariates: Dynamical variables: Central Derived: cp, dv Observed: cp, dv

In this exercise, parameter estimate values for each subject are different. For each subject, parameters are defined individually wherein tv represents the typical value for parameters. Parameters provided for simulation are:-

$Cl$ - Clearance(L/hr),

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

$Ω$ - Between Subject Variability,

$σ$ - Residual error

param = [ (tvcl = 0.10, tvvc = 9.98, Ω = Diagonal([0.00,0.00]), σ = 20.80), (tvcl = 0.20, tvvc = 9.82, Ω = Diagonal([0.00,0.00]), σ = 27.46), (tvcl = 0.20, tvvc = 10.22, Ω = Diagonal([0.00,0.00]), σ = 8.78), (tvcl = 0.20, tvvc = 19.95, Ω = Diagonal([0.00,0.00]), σ = 8.50) ]

4-element Vector{NamedTuple{(:tvcl, :tvvc, :Ω, :σ), Tuple{Float64, Float64, Diagonal{Float64, Vector{Float64}}, Float64}}}: (tvcl = 0.1, tvvc = 9.98, Ω = [0.0 0.0; 0.0 0.0], σ = 20.8) (tvcl = 0.2, tvvc = 9.82, Ω = [0.0 0.0; 0.0 0.0], σ = 27.46) (tvcl = 0.2, tvvc = 10.22, Ω = [0.0 0.0; 0.0 0.0], σ = 8.78) (tvcl = 0.2, tvvc = 19.95, Ω = [0.0 0.0; 0.0 0.0], σ = 8.5)

**10 mg** IV bolus dosage administered to four subjects at time `zero`

.

**Note:-** The concentrations are in `μg/L`

and dose is in **mg**, thus the final conc is *multiplied by 1000* in the model

ev1 = DosageRegimen(10,time=0,cmt=1) ids = ["1: CL = 0.10, V = 9.98", "2: CL = 0.20, V = 9.82", "3: CL = 0.20, V = 10.22", "4: CL = 0.20, V = 19.95"] pop = map(i -> Subject(id = ids[i], events = ev1, observations = (cp = nothing,)), 1:length(ids))

Lets simulate for plasma concentration for four subjects for specific observation time points after IV bolus dose.

Random.seed!(123) sim = map(zip(pop, param)) do (subj, p) return simobs(pk_01, subj, p, obstimes = [10,20,30,40,50,60,70,90,110,150]) end

Simulated population (Vector{<:Subject}) Simulated subjects: 4 Simulated variables: cp, dv

f, a, p = sim_plot(pk_01, sim, observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (minute)", ylabel = "PK01 Concentrations (ug/L)", xticks = 0:20:160)) axislegend(a) f