To determine (oral) bioavailability, the drug is administered by both oral and intravenous route. The adminstration generaly is done in crossover manner at diffrent times separated by a washout period. But if the drug follows a time-dependant clearance (and if the washout period is long), then it may affect the results. To avoid this situation, the doses can be administered semi-simultaneously separated by a small time upto 1 hour.

In the current study, the test drug was administered oraly followed a constant rate infusion (reference) for 15 mins at 60 mins .

Structural model - Two compartment model with first order absorption and elimination

Route of administration - Oral and IV given simulataneously

Dosage Regimen - 2.5 mg Oral and 0.5mg IV infusion of 15 mins

Number of Subjects - 1

This exercise will help to determine bioavailability of a compound administered semi-simultaneously by oral and intravenous route

To bulid a two compartment model for semi-simultaneous oral and intravenous administeration

To use final parameter estimates

To design semi-simultaneous dosage regimen

To simulate and plot a single subject with predefined time points.

call the "necessary" libraries to get started.

using Pumas using Plots using CSV using StatsPlots using Random

A two compartment model with oral absorption is build for a semi-simultaneous administration of oral dose followed by intravenous infusion.

pk_12 = @model begin @param begin tvka ∈ RealDomain(lower=0) tvcl ∈ RealDomain(lower=0) tvq ∈ RealDomain(lower=0) tvvc ∈ RealDomain(lower=0) tvvp ∈ RealDomain(lower=0) tvlag ∈ RealDomain(lower=0) tvF ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(7) σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Cl = tvcl * exp(η[1]) Q = tvq * exp(η[2]) Vc = tvvc * exp(η[3]) Vp = tvvp * exp(η[4]) Ka = tvka * exp(η[5]) lags = (Depot = tvlag * exp(η[6]),) bioav = (Depot = tvF * exp(η[7]),) end @dynamics begin Depot' = -Ka*Depot Central' = Ka*Depot - (Cl/Vc)*Central - (Q/Vc)*Central + (Q/Vp)*Peripheral Peripheral' = (Q/Vc)*Central - (Q/Vp)*Peripheral end @derived begin cp = @. 1000*(Central/Vc) dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

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

Ka - Absorption Rate Constant (min⁻¹)

Cl - Clearance (L/min/kg)

Q - Inter-compartmental distribution (L/kg)

Vc - Volume of Central Compartment (L/kg)

Vp - Volume of Peripheral Compartment (L/kg)

lag - Lag time (min)

F - Bioavailability

σ - Residual Error

param = (tvka = 0.103, tvcl = 0.015, tvq = 0.021, tvvc = 0.121, tvvp = 0.276, tvlag = 4.68, tvF = 0.046, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0,0.0,0.0]), σ²_prop = 0.04)

(tvka = 0.103, tvcl = 0.015, tvq = 0.021, tvvc = 0.121, tvvp = 0.276, tvlag = 4.68, tvF = 0.046, 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 = 0.04)

Dosage Regimen = 2.5 mg/kg oraly followed by 15 min intravenous infusion of 0.5 mg/kg starting from 60 mins after oral dosing administered to a single subject (sub1)

ev_oral = DosageRegimen(2.5, time=0, cmt=1) ev_inf = DosageRegimen(0.5, time=60, cmt=2, duration=15) ev1 = DosageRegimen(ev_oral,ev_inf) sub1 = Subject(id=1, events=ev1)

Subject ID: 1 Events: 3

To simulate plasma concentration with the specific observation time points for a given dosage regimen 'DR'

Random.seed!(123) sim_s1 = simobs(pk_12, sub1, param, obstimes = [6,10,15,20,30,45,60,63,66,75,80,90,107,119,134,150]);

df1 = DataFrame(sim_s1) dropmissing!(df1, :cp) @df df1 plot(:time, :cp, yaxis=:log, label= "Pred - cp", xlabel="Time (min)", ylabel="Concentration (ug/L)", title= "Time Vs Plasma concentration", color=[:blue], linewidth=4, xticks=[0,20,40,60,80,100,120,140,160], xlims=(0,160), ylims=(10,2000)) @df df1 scatter!(:time, :dv, yaxis=:log, label="Obs - dv", color=[:red], markershape=[:circle])