Structural model - Two compartment linear elimination with first order elimination

Route of administration - IV bolus,

Dosage Regimen - 100 μg IV or 0.1 mg IV

Number of Subjects - 1

This exercise explains simulating single IV bolus dose kinetics from a two compartment model.

To build a two compartment model and to simulate the model for a single subject given a single IV bolus dose.

call the "necessary" libraries to get started.

using Random using Pumas using PumasUtilities using CairoMakie

pk_08_05 = @model begin @metadata begin desc = "Two Compartment Model" timeu = u"hr" end @param begin "Clearance (L/hr)" tvcl ∈ RealDomain(lower=0) "Volume of Distribution (L)" tvvc ∈ RealDomain(lower=0) "Intercompartmental Clearance (L/hr)" tvq ∈ RealDomain(lower=0) "Peripheral Volume of Distribution (L)" tvvp ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(4) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Cl = tvcl * exp(η[1]) Vc = tvvc * exp(η[2]) Vp = tvvp * exp(η[3]) Q = tvq * 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 """ PK08 Concentration (ug/L) """ cp = @. Central/Vc """ PK08 Concentration (ug/L) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

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

$C$L - Clearance(L/hr),

$V$c - Volume of Central Compartment(L),

$V$p - Volume of Peripheral Compartment(L),

$Q$ - Inter-departmental clearance(L/hr),

$Ω$ - Between Subject Variability,

$σ$ - Residual error

param = (tvcl = 6.6, tvvc = 53.09, tvvp = 57.22, tvq = 51.5, Ω = Diagonal([0.0,0.0,0.0,0.0]), σ²_prop = 0.047)

(tvcl = 6.6, tvvc = 53.09, tvvp = 57.22, tvq = 51.5, 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 = 0.047)

Dosage Regimen - 100 μg or 0.1mg of IV bolus was given to the single subject.

ev1 = DosageRegimen(100, time = 0, cmt = 1, evid = 1, addl = 0, ii = 0) sub1 = Subject(id = 1, events = ev1)

Subject ID: 1 Events: 1

To simulate the plasma concentration with given observation time-points for single subject.

Random.seed!(123) sim_s1 = simobs(pk_08_05,sub1,param, obstimes=[0.08,0.25,0.5,0.75,1,1.33,1.67,2,2.5,3.07,3.5,4.03,5,7,11,23,29,35,47.25]);

f, a, p = sim_plot(pk_08_05, [sim_s1], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hours)", ylabel = "PK08 Concentrations (ug/L)", xticks = 0:5:50, yscale = log10)) axislegend(a) f