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 about the two compartment modelling with analyzing the parameters to be taken and simulate it for single subject given single IV bolus dose.

To build 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 Pumas using Plots using CSV using StatsPlots using Random

To build the two compartment model for a single subject given IV dose of 100micrograms and concentration-time graph was plotted for 50 hours specified in terms of differentiall equations considering plasma clearance(CL), the volume of central compartment(Vc),inter-compartmental distribution(Q) and volume of peripheral compartment(Vp) as initial parameters for simulation of plot.

pk_08_05 = @model begin @param begin tvcl ∈ RealDomain(lower=0) tvvc ∈ RealDomain(lower=0) tvq ∈ RealDomain(lower=0) tvvp ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(4) 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 cp = @. Central/Vc 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

CL - Clearance(L/hr),

Vc - Volume of Central Compartment(L),

Vp - 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 simultate 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]);

Generate a dataframe from the simulation and use it for plotting.

df1 = DataFrame(sim_s1) # Plot the Plasma Concentration vs Time @df df1 plot(:time,:cp, yaxis=:log, label="Pred Conc - cp", xlabel= "Time (hr)", ylabel="Concentration (ug/L)", title="Plot of Concentration Vs Time", xticks=[0,5,10,15,20,25,30,35,40,45,50],xlims=(0,50), ylims=(0.03,3), color=[:blue], linestyle=[:solid], linewidth=3) @df df1 scatter!(:time,:dv, label="Obs Conc - dv", color=[:red], markershape=[:circle])