Structural model - One compartment linear elimination with zero-order input

Route of administration - Transdermal

Dosage Regimen - 15,890 μg per patch. The patch was applied for 16 hours for 5 consecutive days

Number of Subjects - 1

To understand the kinetics of a given drug using Transdermal input following 2 different input rates

To build one compartment model with zero-order input and to understand its function using transdermal delivery system.

Call the "necessary" libraries to get started.

using Random using Pumas using PumasUtilities using CairoMakie

To build one compartment model with zero-order input following transdermal drug administration

pk_33 = @model begin @metadata begin desc = "One Compartment Model" timeu = u"hr" end @param begin "Clearance (L/hr)" tvcl ∈ RealDomain(lower=0) "Volume of Central Compartment (L)" tvvc ∈ RealDomain(lower=0) "Dose of slow infusion (μg)" tvdslow ∈ RealDomain(lower=0) "Duration of fast release (hr)" tvtfast ∈ RealDomain(lower=0) "Duration of slow release (hr)" tvtslow ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(5) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) "Additional RUV" σ_add ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Cl = tvcl * exp(η[1]) Vc = tvvc * exp(η[2]) Dose_slow = tvdslow * exp(η[3]) Tfast = tvtfast * exp(η[4]) Tslow = tvtslow * exp(η[5]) Ffast = (t<=Tfast) * (15890-Dose_slow)/Tfast Fslow = (t<=Tslow) * Dose_slow/Tslow end @init begin Central = 2*Vc end @dynamics begin Central' = Ffast + Fslow -(Cl/Vc)*Central end @derived begin cp = @. Central/Vc """ Observed Concentration (ug/L) """ dv ~ @. Normal(cp, sqrt((cp^2*σ²_prop) + σ_add^2)) end end

PumasModel Parameters: tvcl, tvvc, tvdslow, tvtfast, tvtslow, Ω, σ²_prop, σ_add Random effects: η Covariates: Dynamical variables: Central Derived: cp, dv Observed: cp, dv

Parameters provided for simulation are as below. `tv`

represents the typical value for parameters.

$CL$ - Clearance (L/hr),

$Vc$ - Volume of Central Compartment (L)

$Dslow$ - Dose of slow infusion (μg)

$Tfast$ - Duration of fast release (hr)

$Tslow$ - Duration of slow release (hr)

$Ω$ - Between Subject Variability

$σ$ - Residual error

param = ( tvcl = 79.8725, tvvc = 239.94, tvdslow = 11184.3, tvtfast = 7.54449, tvtslow = 19.3211, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0]), σ²_prop = 0.005, σ_add = 0.01)

(tvcl = 79.8725, tvvc = 239.94, tvdslow = 11184.3, tvtfast = 7.54449, tvtsl ow = 19.3211, 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 = 0.005, σ_add = 0.01)

15,890 μg per patch.

The patch is applied for 16 hours, for 5 consecutive days

The patch releases the drug at two different rate processes, fast and slow simultaneously over a period of 6 and 18 hours respectively.

sub1 = Subject(id = 1, time = 0:0.1:24, observations = (cp = nothing, ))

Subject ID: 1 Observations: cp: (nothing)

Simulate the plasma concentration

Random.seed!(123) sim_sub1 = simobs(pk_33, sub1, param, obstimes = 0:0.1:24)

f, a, p = sim_plot(pk_33, [sim_sub1], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hr)", ylabel = "PK33 Concentrations (μg/L)", xticks = 0:5:25, )) axislegend(a) f