Structural Model - Two Compartment model with first order elimination

Route of Administration - Intravenous infusion (Multiple-dose)

Dosage Regimen - 538 µmol/kg followed by 3390 µmol/kg

Number of Subjects - 1

This exercise explains simultaneous analysis of plasma and urine data using Two-compartment model with additional Urinary compartment accounting for amount of drug excreted in Urine.

In this exercise, you will learn how to build a two compartment model and to simulate the data for a single subject based on the given dosage regimen.

call the "necessary" libraries to get started.

using Pumas using Plots using CSV using StatsPlots using Random

Two-compartment model with one Central and one Peripheral compartment will help in understanding the plasma concentration. A separate Urine compartment accounts for the fraction (amount) of drug excreted in Urine.

pk_16 = @model begin @param begin tvclr ∈ RealDomain(lower=0) tvclm ∈ RealDomain(lower=0) tvvc ∈ RealDomain(lower=0) tvvp ∈ RealDomain(lower=0) tvq ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(5) σ²₁_prop ∈ RealDomain(lower=0) σ²₂_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin CLr = tvclr*exp(η[1]) CLm = tvclm*exp(η[2]) Vc = tvvc*exp(η[3]) Vp = tvvp*exp(η[4]) Q = tvq*exp(η[5]) CL = CLr+CLm Vss = Vc+Vp t12 = 0.693*Vss/CL end @dynamics begin Central' = - (CLr/Vc)*Central - (CLm/Vc)*Central + (Q/Vp)*Peripheral - (Q/Vc)*Central Peripheral' = (Q/Vc)*Central - (Q/Vp)*Peripheral Urine' = (CLr/Vc)*Central end @derived begin cp_plasma = @. Central/Vc dv_plasma ~ @. Normal(cp_plasma, sqrt(cp_plasma^2*σ²₁_prop)) cp_urine = @. Urine dv_urine ~ @. Normal(cp_urine, sqrt(cp_urine^2*σ²₂_prop)) end end

PumasModel Parameters: tvclr, tvclm, tvvc, tvvp, tvq, Ω, σ²₁_prop, σ²₂_prop Random effects: η Covariates: Dynamical variables: Central, Peripheral, Urine Derived: cp_plasma, dv_plasma, cp_urine, dv_urine Observed: cp_plasma, dv_plasma, cp_urine, dv_urine

CLr - Renal Clearance (L/hr/kg)

CLm - Non-renal Clearance (L/hr/kg)

Vc - Volume of Central Compartment (L/kg)

Vp - Volume of Peripheral Compartment (L/kg)

Q - Inter-compartmental Clearance (L/hr/kg)

Ω - Between Subject Variability

σ²₁ - Residual error 1 (for plasma conc)

σ²₂ - Residual error 2 (for amount excreted in urine)

**Derived Parameters:**

CL - Total Clearance (L/hr/kg)

Vss - Volume of distribution at steady state (L/kg)

t1/2 - Half life (hr)

Typical value (tv) estimates for individual parameters

param = ( tvclm = 0.05, tvclr = 0.31, tvvc = 1.6, tvvp = 0.16, tvq = 0.03, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0]), σ²₁_prop = 0.01, σ²₂_prop = 0.01)

(tvclm = 0.05, tvclr = 0.31, tvvc = 1.6, tvvp = 0.16, tvq = 0.03, 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] , σ²₁_prop = 0.01, σ²₂_prop = 0.01)

The subject (male dog) received two consecutive intravenous infusions of a drug.

The subject received initial dose of 538 µmol/kg as from

*time 0 to 0.983 hr (rate= 547.304)*followed by 3390 µmol/kg from*time 0.983 to 23.95 hr (rate=147.603)*.Total infused dose: 3928 µmol/kg.

ev1 = DosageRegimen([538,3390], time = [0,0.983], cmt = [1,1], rate = [547.304,147.603]) sub1 = Subject(id=1, events=ev1)

Subject ID: 1 Events: 4

To simulate the following for the above subject with specific observation time points.

Plasma concentration.

Amount excreted unchanged in Urine.

Random.seed!(123) sim_sub1 = simobs(pk_16,sub1,param,obstimes = [0.5,1,2,4,6.1,7.6,8.02,12.05,12.15,15.95,22.13,23.89,24.05,24.46,24.94,25.94,26.96,27.95,29.97,31.94,35.96,36.2,48,48.2,54,60,60.2,72,72.2])

Create a dataframe of the simulated data.

df1 = DataFrame(sim_sub1) df_plasma = filter(x -> x.time in [0.5,1,2,4,7.6,8.02,12.05,15.95,22.13,23.89,24.46,24.94,25.94,26.96,27.95,29.97,31.94,35.96,48,54,60,72], df1) df_urine = filter(x -> x.time in [6.1, 12.15, 24.05, 36.2, 48.2, 60.2, 72.2], df1)

To plot the simulated plasma concentration data and amount of drug excreted in urine in a single plot.

@df df_plasma plot(:time, :cp_plasma, yaxis=:log, label="Pred Plasma Conc", xlabel="Time (hr)", ylabel= "Concentration (uM) & Amount (umol)", title= "Plasma Drug Conc & Amt Excreted in Urine Vs Time", color = "blue", linewidth=3, legend=:bottomleft, xticks=[0,10,20,30,40,50,60,70,80], yticks=[0.1,0,1,10,100,1000,10000], ylims=(0.1,10000), xlims=(0,80)) @df df_urine plot!(:time, :cp_urine, yaxis=:log, label="Pred Amount in urine", color= "black", linewidth=3) @df df_plasma scatter!(:time, :dv_plasma, yaxis=:log, label="Obs Plasma Conc", color= "red", markershape=:circle) @df df_urine scatter!(:time, :dv_urine, yaxis=:log, label="Obs Amount in urine", color= "blue", markershape=:square)