Structural model - Two compartment model

Route of administration - IV-infusion (with an infusion pump)

Dosage Regimen - 100 mg/m² of Cisplatin for 1-h at

*time=0*considering a patient with 1.7m²Number of Subjects - 1

We will learn how to simulate kinetics of drug that exhibits reversible metabolism.

Simulate data for two IV-Infusion with two different rates of infusion regimen.

In this exercise you will learn how to

Simulate an IV-infusion two compartment model and kinetic of reversible metabolism.

Certain assumptions to be considered:

A fraction of the dose (2.3%) is present as the monohydrated complex in the infusion solution,

That there is a reversible reactions between cisplatin (p) and its monohydrated complex (m),

The input rate can be split into cisplatin infusion rate (Inp) and monohydrate infusion rate (Inm).

Call the "necessary" libraries to get start.

using Random using Pumas using PumasUtilities using CairoMakie

In this two compartment model, we administer the mentioned dose in the `Central`

compartment as well as in the `Metabolite`

compartment at *'time= 0'*. Also, $K12$ and $K21$ are the rate constants for the conversion of cisplatin into monohydrated complex and the monohydrated complex into cisplatin, respectively.

pk_34 = @model begin @metadata begin desc = "Microconstant Model" timeu = u"minute" end @param begin "Volume of Central Compartment (L)" tvvc ∈ RealDomain(lower=0) "Clearance of metabolite (L/min)" tvclm ∈ RealDomain(lower=0) "Volume of Metabolite Compartment (μg/L)" tvvm ∈ RealDomain(lower=0) "Clearance of parent (L/min)" tvclp ∈ RealDomain(lower=0) tvk12 ∈ RealDomain(lower=0) tvk21 ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(6) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Vc = tvvc * exp(η[1]) CLm = tvclm * exp(η[2]) Vm = tvvm * exp(η[3]) CLp = tvclp * exp(η[4]) K12 = tvk12 * exp(η[5]) K21 = tvk21 * exp(η[6]) end @dynamics begin Central' = -(CLp/Vc)*Central - K12*Central + K21*Metabolite*Vc/Vm Metabolite' = -(CLm/Vm)*Metabolite - K21*Metabolite + K12*Central*Vm/Vc end @derived begin cp = @. Central/Vc """ Observed Concentration - Cisplatin (ug/ml) """ dv_cp ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) met = @. Metabolite/Vm """ Observed Concentration - Metabolite (ug/ml) """ dv_met ~ @. Normal(met, sqrt(cp^2*σ²_prop)) end end

PumasModel Parameters: tvvc, tvclm, tvvm, tvclp, tvk12, tvk21, Ω, σ²_prop Random effects: η Covariates: Dynamical variables: Central, Metabolite Derived: cp, dv_cp, met, dv_met Observed: cp, dv_cp, met, dv_met

Parameters provided for simulation are as below. `tv`

represents the typical value for parameters.

$Vc$ - Volume of central compartment (L)

$CLm$ - Clearance of metabolite (L/min)

$Vm$ - Volume of metabolite compartment (μg/L)

$CLp$ - Clearance of parent (L/min)

$K12$ - Rate constant for the conversion of cisplatin into monohydrated complex (min⁻¹)

$K21$ - Rate constant for the conversion of monohydrated complex into cisplatin (min⁻¹)

$Ω$ - Between Subject Variability

$σ$ - Residual error

param = ( tvvc = 14.1175, tvclm = 0.00832616, tvvm = 2.96699, tvclp = 0.445716, tvk12 = 0.00021865, tvk21 = 0.021313, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0,0.0]), σ²_prop = 0.001)

(tvvc = 14.1175, tvclm = 0.00832616, tvvm = 2.96699, tvclp = 0.445716, tvk1 2 = 0.00021865, tvk21 = 0.021313, 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 = 0.001)

In this section the Dosage regimen is mentioned for:

Cisplatin Infusion - A total dose of

**170mg**(100mg/m² * 1.7m²) split as Cisplatin 166.09 and Monohydrate 3.91.Monohydrate Infusion - A total dose of

**10 mg/L**is given as Monohydrate

ev1 = DosageRegimen([166.09,3.91], time = 0, cmt = [1,2], duration = [60,60]) sub1 = Subject(id = "Cisplatin (Inf-Cisplatin)", events = ev1, time = 20:0.1:180) ev2 = DosageRegimen(10, time = 0, cmt = 2, duration = 2) sub2 = Subject(id = "Monohydrate (Inf-Cisplatin)", events = ev2, time = 5:0.1:180) pop2_sub = [sub1, sub2]

Population Subjects: 2 Observations:

We will simulate the plasma concentration at the pre specified time points.

Random.seed!(123) sim_sub1 = simobs(pk_34, pop2_sub, param)

f1, a1, p1 = sim_plot(pk_34, sim_sub1, observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hr)", ylabel = "PK34 Parent Concentrations (μg/mL)", xticks = 0:20:180, )) axislegend(a1) f1

f2, a2, p2 = sim_plot(pk_34, sim_sub1, observations = :met, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hr)", ylabel = "PK34 Metabolite Concentrations (μg/mL)", xticks = 0:20:180, )) axislegend(a2) f2