Structural model - Two compartment model with first order elimination

Route of administration - IV-Bolus and IV-Infusion given simultaneously

Dosage Regimen - 400 μg/kg IV-Bolus and 800 μg/kg IV-Infusion for 26 mins at

*time=0*Number of Subjects - 1

Write the differential equation for a

*two-compartment model*in terms of Clearance and VolumeSimulate data for both a bolus dose followed by a constant rate infusion regimen

Administration of

*loading dose*helps to achieve*therapeutic concentrations*faster

The objective of this exercise is to simulate data from a bolus followed by a constant rate infusion using differential equation model.

Call the "necessary" libraries to get started

using Random using Pumas using PumasUtilities using CairoMakie

The given data follows a two compartment model in which the IV Bolus and IV-Infusion are administered at `time=0`

pk_13 = @model begin @metadata begin desc = "Two Compartment Model" timeu = u"minute" end @param begin "Clearance (L/min/kg)" tvcl ∈ RealDomain(lower=0) "Volume of Central Compartment (L/kg)" tvvc ∈ RealDomain(lower=0) "Inter-compartmental Clearance (L/min/kg)" tvq ∈ RealDomain(lower=0) "Volume of Peripheral Compartment (L/kg)" tvvp ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(4) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) "Additive RUV" σ²_add ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Cl = tvcl * exp(η[1]) Vc = tvvc * exp(η[2]) Q = tvq * exp(η[3]) Vp = tvvp * exp(η[4]) end @dynamics begin Central' = -(Cl/Vc)*Central -(Q/Vc)*Central +(Q/Vp)*Peripheral Peripheral' = (Q/Vc)*Central -(Q/Vp)*Peripheral end @derived begin cp = @. Central/Vc """ Observed Concentrations (ug/L) """ dv ~ @. Normal(cp, sqrt((cp*σ²_prop)^2 + σ²_add^2)) end end

PumasModel Parameters: tvcl, tvvc, tvq, tvvp, Ω, σ²_prop, σ²_add Random effects: η Covariates: Dynamical variables: Central, Peripheral Derived: cp, dv Observed: cp, dv

$Cl$ - Clearance of central compartment (L/min/kg)

$Vc$ - Volume of central compartment (L/kg)

$Q$ - Inter-compartmental clearance (L/min/kg)

$Vp$ - Volume of peripheral compartment (L/kg)

$Ω$ - Between Subject Variability

$σ$ - Residual Unexplained Variability

param = ( tvcl = 0.344708, tvvc = 2.8946, tvq = 0.178392, tvvp = 2.18368, Ω = Diagonal([0.0, 0.0, 0.0, 0.0]), σ²_prop = 0.0571079, σ²_add = 0.1)

(tvcl = 0.344708, tvvc = 2.8946, tvq = 0.178392, tvvp = 2.18368, 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 .0571079, σ²_add = 0.1)

Single dose of 400 μg/kg given as IV-Bolus at

`time=0`

Single dose of 800 μg/kg given as an IV-Infusion for

*26 mins*at`time=0`

ev1 = DosageRegimen(400, time = 0, cmt = 1) ev2 = DosageRegimen(800, time = 0, cmt = 1, rate = 30.769) ev3 = DosageRegimen(ev1, ev2) sub1 = Subject(id = 1, events = ev3)

Subject ID: 1 Events: 3

We will simulate the plasma concentration at the pre specified time points.

Random.seed!(123) sim_sub1 = simobs(pk_13, sub1, param, obstimes=[2,5,10,15,20,25,30,33,35,37,40,45,50,60,70,90,110,120,150])

sim_plot(pk_13, [sim_sub1], observations = :cp, linewidth = 4, color = :maroon, axis = (xlabel = "Time (min)", ylabel="Concentration (ug/L)", yscale = log10, xticks = 0:20:160))