Following info:

Structural model - Two compartment model with parallel linear and Non-linear elimination

Route of administration - IV bolus (Single dose)

Dosage Regimen - 0.1mg/kg, 0.3mg/kg, 1mg/kg, 3mg/kg, and 10 mg/kg

Number of Subjects - 5

To understand the antibody kinetics with linear and nonlinear elimination after IV bolus dose in man.

To build a two compartment model with parallel linear and non-linear elimination to understand the antibody kinetics.

To simulate 5 subjects after single dose IV bolus administration

Call the "necessary" libraries to get started.

using Random using Pumas using PumasUtilities using CairoMakie

Two compartment model with parallel linear and Non- linear elimination

pk_26 = @model begin @metadata begin desc = "Parallel Linear and Non-linear Elimination Model" timeu = u"hr" end @param begin "Maximum rate of Metabolism(mg/hr/kg)" tvvmax ∈ RealDomain(lower=0) "Michaelis constant (mg/L/kg)" tvkm ∈ RealDomain(lower=0) "Volume of Peripheral Compartment(L/kg)" tvvp ∈ RealDomain(lower=0) "Volume of Central Compartment(L/kg)" tvvc ∈ RealDomain(lower=0) "Inter-compartmental Clearance(L/hr/kg)" tvq ∈ RealDomain(lower=0) "Linear Clearance(L/hr/kg)" tvcll ∈ RealDomain(lower=0) Ω ∈ PDiagDomain(6) "Proportional RUV" σ²_prop ∈ RealDomain(lower=0) end @random begin η ~ MvNormal(Ω) end @pre begin Vmax = tvvmax*exp(η[1]) Km = tvkm*exp(η[2]) Vp = tvvp*exp(η[3]) Vc = tvvc*exp(η[4]) Q = tvq*exp(η[5]) CLl = tvcll*exp(η[6]) # Linear clearance # CLmm = Vmax/(Km+C) Non-linear clearance end @dynamics begin Central' = -(Vmax/(Km+(Central/Vc)))*(Central/Vc) - CLl*(Central/Vc)-(Q/Vc)*Central +(Q/Vp)*Peripheral Peripheral' = (Q/Vc)*Central -(Q/Vp)*Peripheral end @derived begin cp = @. Central/Vc """ Observed Concentration (mg/L) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

PumasModel Parameters: tvvmax, tvkm, tvvp, tvvc, tvq, tvcll, 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.

$Vmax$ - Maximum rate of Metabolism(mg/hr/kg)

$Km$ - Michaelis constant (mg/L/kg)

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

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

$Q$ - Inter-compartmental Clearance(L/hr/kg)

$CLl$ - Linear Clearance(L/hr/kg)

$Ω$ - Between Subject Variability

$σ²_prop$ - Residual error

param = ( tvvmax = 0.0338, tvkm = 0.0760, tvvp = 0.0293, tvvc = 0.0729, tvq = 0.0070, tvcll = 0.0069, Ω = Diagonal([0.0,0.0,0.0,0.0,0.0,0.0]), σ²_prop = 0.04)

(tvvmax = 0.0338, tvkm = 0.076, tvvp = 0.0293, tvvc = 0.0729, tvq = 0.007, tvcll = 0.0069, 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)

5 subjects received an IV bolus dose of 0.1, 0.3, 1, 3 and 10 mg/kg respectively at *time=0*

DR1 = DosageRegimen(0.1, time = 0) s1 = Subject(id = "0.1 mg/kg", events = DR1, time = 0.1:0.01: 1.5) DR2 = DosageRegimen(0.3, time = 0) s2 = Subject(id = "0.3 mg/kg", events = DR2, time = 0.1:0.01:7) DR3 = DosageRegimen(1, time = 0) s3 = Subject(id = "1 mg/kg", events = DR3, time = 0.1:0.1:21) DR4 = DosageRegimen(3, time = 0) s4 = Subject(id = "3 mg/kg", events = DR4, time = 0.1:0.1:30) DR5 = DosageRegimen(10, time = 0) s5 = Subject(id = "10 mg/kg", events = DR5, time = 0.1: 0.1:43) pop = [s1,s2,s3,s4,s5]

Population Subjects: 5 Observations:

To simulate plasma concentration data for 5 subjects with specific obstimes.

Random.seed!(123) sim = simobs(pk_26, pop, param)

f, a, p = sim_plot(pk_26, sim, observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (days)", ylabel = "PK26 Concentrations (mg/L)", xticks = 0:10:40, yscale = log10)) axislegend(a) f