Structural model - One compartment Oral administration consists of time dependent change in the elimination rate constant.

Route of administration - Oral

Dosage Regimen - Nortriptyline (NT) 10 mg (or 10000 μg) Oral, three times daily for 29 days (i.e. 696 hours), after 216 hours treatment with an enzyme inducer i.e. Pentobarbital (PB) for a period of 300 hours i.e up till 516 hours of treatment with NT.

Number of Subjects - 1

We will learn how to simulate from a heteroinduction model after repeated oral dose data on treatment with an enzyme inducer for a limited duration.

In this exercise you will learn how to simulate from an Oral One Compartment model with enzyme induction where clearance is time dependent.

Certain assumptions to be considered:

The fractional turnover rate i.e. $Kout$ of the enzyme has a longer half-life than the drug or the inducer

The duration from one level of enzyme activity to other will be influenced by $Kout$ of the enzyme

The $Kout$ is not regulated by the Pentobarbital. The interpretation $V$ includes bioavailability (i.e., it is really $V/F$).

Call the "necessary" libraries to get start.

using Random using Pumas using PumasUtilities using CairoMakie

In this one compartment model, we administer dose in Depot compartment at *'time= 0'* that is given every *'8 hours'* for *'87 additional doses'*. A second drug which is an enzyme inducer (Pentobarbital) is added at 216 hrs for 300 hrs up to 516 hours of treatment with Nortriptyline.

**Note:-** We do not have concentrations of Pentobarbital and hence it is not included in the model.

pk_21 = @model begin @metadata begin desc = "Heteroinduction Model" timeu = u"hr" end @param begin "Absorption Rate Constant (1/hr)" tvka ∈ RealDomain(lower=0) "Intrinsic Clearance post-treatment (L/hr)" tvclss ∈ RealDomain(lower=0) "Lag-time (hrs)" tvlag ∈ RealDomain(lower=0) "Intrinsic Clearance pre-treatment (L/hr)" tvclpre ∈ RealDomain(lower=0) "Fractional turnover rate (1/hr)" tvkout ∈ RealDomain(lower=0) "Volume of distribution (L)" tvv ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(3) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @covariates TBP TBP2 @pre begin Ka = tvka * exp(η[1]) Clpre = tvclpre * exp(η[3]) Clss = tvclss * exp(η[2]) Vc = tvv Kout = tvkout Kpre = Clpre/Vc Kss = Clss/Vc Kperi = Kss-(Kss-Kpre)*exp(-Kout*(t-TBP)) A = Kss - (Kss-Kpre)*exp(-Kout*(TBP2-TBP)) Kpost = Kpre - (Kpre-A)*exp(-Kout*(t-TBP2)) K10 = (t<TBP) * Kpre + (t>=TBP && t<TBP2) * Kperi + (t>=TBP2) * Kpost end @dosecontrol begin lags = (Depot=tvlag,) end @dynamics begin Depot' = -Ka*Depot Central' = Ka*Depot - K10*Central end @derived begin cp = @. (1000/263.384)*Central/Vc """ Observed Concentration (nM) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

PumasModel Parameters: tvka, tvclss, tvlag, tvclpre, tvkout, tvv, Ω, σ²_prop Random effects: η Covariates: TBP, TBP2 Dynamical variables: Depot, Central Derived: cp, dv Observed: cp, dv

The parameters are as given below. `tv`

represents the typical value for parameters.

Ka - Absorption Rate Constant (1/hr)

CLss - Intrinsic Clearance post-treatment (L/hr),

tlag - Lag-time (hrs),

CLpre - Intrinsic Clearance pre-treatment (L/hr),

Kout - Fractional turnover rate (1/hr),

V - Volume of distribution (L),

Ω - Between Subject Variability,

σ - Residual error.

param = ( tvka = 1.8406, tvclss = 114.344, tvlag = 0.814121, tvclpre = 46.296, tvkout = 0.00547243, tvv = 1679.4, Ω = Diagonal([0.0,0.0,0.0]), σ²_prop = 0.015)

(tvka = 1.8406, tvclss = 114.344, tvlag = 0.814121, tvclpre = 46.296, tvkou t = 0.00547243, tvv = 1679.4, Ω = [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 for:

Oral dosing of

**10 mg or 10000 μg**at`time=0`

that is given every`8 hours`

for`87 additional doses`

for a single subject.

ev1 = DosageRegimen(10000, cmt = 1, time = 0, ii = 8, addl = 87) sub1 = Subject(id = 1, events = ev1, covariates =(TBP = 216, TBP2 = 516), observations = (cp = nothing,))

Subject ID: 1 Events: 88 Observations: cp: (nothing) Covariates: TBP, TBP2

Let's simulate for plasma concentration with the specific observation time points after Oral administration of NT before, during and after treatment with PB.

Random.seed!(123) sim_sub1 = simobs(pk_21, sub1, param, obstimes = 0:1:800)

f, a, p = sim_plot(pk_21, [sim_sub1], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hr)", ylabel = "PK21 Concentrations (nM)", xticks = 0:100:800)) axislegend(a) f