To determine (oral) bioavailability, the drug is administered by both oral and intravenous route. The adminstration generally is done in crossover manner at different 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 up to 1 hour.

In the current study, the test drug was administered orally 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 simultaneously

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 build a two compartment model for semi-simultaneous oral and intravenous administration

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 Random using Pumas using PumasUtilities using CairoMakie

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 @metadata begin desc = "Two Compartment Model" timeu = u"minute" end @param begin "Absorption Rate Constant (min⁻¹)" tvka ∈ RealDomain(lower=0) "Clearance (L/min/kg)" tvcl ∈ RealDomain(lower=0) "Inter-compartmental distribution (L/kg)" tvq ∈ RealDomain(lower=0) "Volume of Central Compartment (L/kg)" tvvc ∈ RealDomain(lower=0) "Volume of Peripheral Compartment (L/kg)" tvvp ∈ RealDomain(lower=0) "Lag time (min)" tvlag ∈ RealDomain(lower=0) "Bioavailability" tvF ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(7) "Proportional RUV" 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]) end @dosecontrol begin lags = (Depot = tvlag * exp(η[6]),) bioav = (Depot = tvF * exp(η[7]),) end @dynamics Depots1Central1Periph1 @derived begin cp = @. 1000*(Central/Vc) """ Observed Concentrations (ug/L) """ 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, observations= (cp = nothing,))

Subject ID: 1 Events: 3 Observations: cp: (nothing)

To simulate plasma concentrations with specific observation time points

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])

sim_plot(pk_12, [sim_s1], observations = :cp, linewidth = 4, color = :maroon, axis = (xlabel = "Time (min)", ylabel="Concentration (ug/L)", yscale = log10, xticks = 0:20:160))