Following info:

Structural model - Two compartment model

Route of administration - Intravenous infusion

Dosage Regimen - 0.77,7.7,77,257,771, μmol/Kg dose given as intravenous infusion

Number of Subjects - 1 (Monkey)

In this tutorial, you will learn how to build two compartment turnover model to characterize linear antibody kinetics and simulate the model for one single subject and different dosage regimen.

Call the "necessary" libraries to get started

using Random using Pumas using PumasUtilities using CairoMakie

In this model, we administer dose in central compartment.

pk_53 = @model begin @metadata begin desc = "Two Compartment Model" timeu = u"hr" end @param begin "Volume of Central Compartment (L/kg)" tvvc ∈ RealDomain(lower=0) "Volume of Peripheral Compartment (L/kg)" tvvp ∈ RealDomain(lower=0) "Clearance (L/hr/kg)" tvcl ∈ RealDomain(lower=0) "Intercompartmental CLearance (L/hr/kg)" tvq ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(4) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Vc = tvvc * exp(η[1]) Vp = tvvp * exp(η[2]) CL = tvcl * exp(η[3]) Q = tvq * exp(η[4]) end @dynamics begin Central' = -(Q/Vc)*Central +(Q/Vp)*Peripheral -(CL/Vc)*Central Peripheral'= (Q/Vc)*Central -(Q/Vp)*Peripheral end @derived begin cp = @. Central/Vc """ Observed Concentration (uM) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

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

The parameters are as given below. `tv`

represents the typical value for parameters.

$Cl$ - Clearance (L/hr/kg)

$Vc$ - Volume of Central Compartment (L/kg)

$Vp$ - Volume of Peripheral Compartment (L/kg)

$Q$ - Intercompartmental CLearance (L/hr/kg)

$Ω$ - Between Subject Variability

$σ$ - Residual error

param = (tvvc = 2.139, tvvp = 1.5858, tvcl = 0.00541, tvq = 0.01640, Ω = Diagonal([0.00,0.00,0.00,0.00]), σ²_prop = 0.04)

(tvvc = 2.139, tvvp = 1.5858, tvcl = 0.00541, tvq = 0.0164, 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)

Dose 1:- 0.77 μmol/kg given as an IV-infusion at

`time=0`

Dose 2:- 7.7 μmol/kg given as an IV-infusion at

`time=72.17`

Dose 3:- 77 μmol/kg given as an IV-infusion at

`time=144.17`

Dose 4:- 257 μmol/kg given as an IV-infusion at

`time=216.6`

Dose 5:- 771 μmol/kg given as an IV-infusion at

`time=288.52`

ev1 = DosageRegimen(0.77, time = 0, cmt = 1, duration = 0.416667) ev2 = DosageRegimen(7.7, time = 72.17, cmt = 1, duration = 0.5) ev3 = DosageRegimen(77, time = 144.17, cmt = 1, duration = 0.5) ev4 = DosageRegimen(257, time = 216.6, cmt = 1, duration = 0.4) ev5 = DosageRegimen(771, time = 288.52, cmt = 1, duration = 0.5) ev = DosageRegimen(ev1,ev2,ev3,ev4,ev5) sub1 = Subject(id = 1, events = ev)

Subject ID: 1 Events: 10

Lets simulate for plasma concentration with the specific observation time points after Intravenous administration.

Random.seed!(123) sim_sub1 = simobs(pk_53, sub1, param, obstimes = 0.01:0.01:2000) df1 = DataFrame(sim_sub1)

f, a, p = sim_plot(pk_53, [sim_sub1], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (hrs)", ylabel = "PK53 Concentrations (μM)", xticks = 0:200:2000, yscale = log10)) axislegend(a) f