Structural model - Two compartment with additional input for basal hormone synthesis in the central compartment

Route of administration - IV infusion (1 minute)

Dosage Regimen - 36,630 pmol

Number of Subjects - 1

In this model, you will learn how to build a two compartment with additional input for basal hormone level. This model will help to simulate the plasma concentration profile after IV administration considering basal hormone input.

To analyze the intravenous datasets with parallel turnover

To write multi-compartment model in terms of differential equations

Call the "necessary" libraries to get start.

using Random using Pumas using PumasUtilities using CairoMakie

In this one compartment model PK31, we administer IV infusion dose to central compartment.

pk_31 = @model begin @metadata begin desc = "Two Compartment Model" timeu = u"hr" end @param begin "Basal hormonal input (pmol/hr)" tvkin ∈ RealDomain(lower=0) "Central Volume of Distribution (L)" tvvc ∈ RealDomain(lower=0) "Clearance (L/hr)" tvcl ∈ RealDomain(lower=0) "Intercompartmental Clearance (L/hr)" tvq ∈ RealDomain(lower=0) "Peripheral Volume of Distribution (L)" tvvp ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(5) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Kin = tvkin * exp(η[1]) Vc = tvvc* exp(η[2]) Cl = tvcl * exp(η[3]) Q = tvq * exp(η[4]) Vp = tvvp * exp(η[5]) end @dynamics begin Central' = Kin - (Cl/Vc)*Central - (Q/Vc)*Central + (Q/Vp)*Peripheral Peripheral' = (Q/Vc)*Central - (Q/Vp)*Peripheral end @derived begin cp = @. Central/Vc """ Observed Concentration ((pmol/L) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

PumasModel Parameters: tvkin, tvvc, tvcl, tvq, tvvp, Ω, σ²_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.

$Kin$ - Basal hormonal input (pmol/hr)

$Vc$ - Central Volume of Distribution (L)

$Cl$ - Clearance (L/hr)

$Q$ - Intercompartmental Clearance (L/hr)

$Vp$ - Peripheral Volume of Distribution (L)

$Ω$ - Between Subject Variability,

$σ$ - Residual error

param = ( tvkin = 1531.87, tvvc = 8.8455, tvcl = 76.5987, tvq = 56.8775, tvvp = 58.8033, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0]), σ²_prop = 0.015)

(tvkin = 1531.87, tvvc = 8.8455, tvcl = 76.5987, tvq = 56.8775, tvvp = 58.8 033, 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], σ²_prop = 0.015)

A single dose of 36630 pmol is given as an IV Infusion

ev1 = DosageRegimen(36630, time = 0, cmt = 1, duration = 0.0166) sub1 = Subject(id = 1, events = ev1, observations = (cp = nothing,))

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

Simulate the plasma concentration profile

Random.seed!(123) sim_sub1 = simobs(pk_31, sub1, param , obstimes = 0.01:0.0001:32)

f, a, p = sim_plot(pk_31, [sim_sub1], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hrs)", ylabel = "PK31 Concentrations (pmol/L)", xticks = 0:5:35, yscale = log10)) axislegend(a) f