Structural model - 1 compartment with first order absorption (without/with Lag time)
Route of administration - Oral
Dosage Regimen - 100 μg Oral
Number of Subjects - 1
By the application of the present model, we will learn how to simulate model for first order input model with and without lag-time.
In this exercise you will learn how to
Simulate an Oral One Compartment (without/ with lag-time). Assuming oral bioavailability of 100%. The interpretation V includes bioavailability (i.e., it is really estimating V/F).
Write a differential equation for a one-compartment model
call the "necessary" libraries to get start.
using Pumas using Plots using CSV using StatsPlots using Random
In this one compartment model, we administer dose in Depot compartment at
pk_02 = @model begin @param begin tvka ∈ RealDomain(lower=0) tvkel ∈ RealDomain(lower=0) tvvc ∈ RealDomain(lower=0) tvlag ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(4) σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Ka = tvka * exp(η) Kel = tvkel * exp(η) Vc = tvvc * exp(η) lags = (Depot=tvlag * exp(η),) end @dynamics begin Depot' = -Ka*Depot Central' = Ka*Depot - Kel*Central end @derived begin cp = @. Central/Vc dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end
PumasModel Parameters: tvka, tvkel, tvvc, tvlag, Ω, σ²_prop Random effects: η Covariates: Dynamical variables: Depot, Central Derived: cp, dv Observed: cp, dv
The compound follows a one compartment model, in which the various parameters are as mentioned below:
Ka - Absorption Rate Constant (min⁻¹)
Kel - Elimination Rate Constant(min⁻¹)
Vc - Central Volume of distribution (L)
tlag - Lag-time (min)
Ω - Between Subject Variability
σ - Residual error
param1 = (tvka = 0.013, tvkel = 0.013, tvvc = 32, tvlag = 0, Ω = Diagonal([0.0,0.0,0.0,0.0]), σ²_prop = 0.015)
(tvka = 0.013, tvkel = 0.013, tvvc = 32, tvlag = 0, 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)
param2 = (tvka = 0.043, tvkel = 0.0088, tvvc = 32, tvlag = 16, Ω = Diagonal([0.0,0.0,0.0,0.0]), σ²_prop = 0.015)
(tvka = 0.043, tvkel = 0.0088, tvvc = 32, tvlag = 16, 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)
In this section the Dosage regimen is mentioned:
Oral dosing of 100 μg at
time=0 for a single subject
ev1 = DosageRegimen(100,time=0,cmt=1) sub1 = Subject(id=1,events=ev1)
Subject ID: 1 Events: 1
Let's simulate for plasma concentration after oral administration, without lag-time.
Random.seed!(123) sim_sub1 = simobs(pk_02,sub1,param1,obstimes=0:1:400) df1 = DataFrame(sim_sub1);
Let's simulate for plasma concentration after oral administration, with lag-time.
Random.seed!(123) sim_sub2 = simobs(pk_02,sub1,param2,obstimes=0:1:400) df2 = DataFrame(sim_sub2);
df_lag = filter(x -> x.time in [0,10,15,20,30,40,60,90,120,180,210,240,300,360], df2) @df df1 plot(:time, :cp, label="Predicted Data - Without lag-time", xlabel="Time (min)", ylabel="Concentration (ug/L)", title="Concentration vs Time", color=[:aqua], linestyle=[:dash], linewidth=3, xticks=[0,50,100,150,200,250,300,350,400], yticks=[0.0,0.5,1.0,1.5,2.0,2.5], xlims=(-5,400), ylims=(-0.05,2.5)) @df df2 plot!(:time, :cp, label="Pred Conc - With lag-time", color=[:darkblue], linewidth=3) @df df_lag scatter!(:time,:dv, label="Observed Conc", color=[:red])