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

Route of administration - IV infusion

Dosage Regimen - Multiple intravenous infusions (Three sets of Rapid iv infusion followed by slow iv infusion)

Number of Subjects - 1

We will learn to simulate data for Multiple infusions of an endogenous compound with non-linear disposition

To build a one compartment model for an endogenous compound with non-linear disposition

To use final parameter estimates and design a multiple infusion dosage regimen

To simulate and plot a single subject with predefined time points.

Call the "necessary" libraries to get started.

using Random using Pumas using PumasUtilities using CairoMakie

One compartment model for an endogenous compound with non-linear disposition

pk_32 = @model begin @metadata begin desc = "Non-linear Elimination Model" timeu = u"minute" end @param begin "Volume of Central Compartment (L)" tvvc ∈ RealDomain(lower=0) "Maximum metabolic capacity (μg/min)" tvvmax ∈ RealDomain(lower=0) "Michaelis-Menten constant (μg/L)" tvkm ∈ RealDomain(lower=0) "Rate of synthesis (μg/min)" tvkin ∈ 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]) Vmax = tvvmax*exp(η[2]) Km = tvkm*exp(η[3]) Kin = tvkin*exp(η[4]) #CL = Vmax/(Km+(Central/Vc)) end @init begin Central = Kin/((Vmax/Km)/Vc) end @dynamics begin Central' = Kin - (Vmax/(Km+Central/Vc))*(Central/Vc) end @derived begin cp = @. Central/Vc """ Observed Concentration (ug/L) """ dv ~ @. Normal(cp, sqrt(cp^2*σ²_prop)) end end

PumasModel Parameters: tvvc, tvvmax, tvkm, tvkin, Ω, σ²_prop Random effects: η Covariates: Dynamical variables: Central Derived: cp, dv Observed: cp, dv

The parameters are as given below. `tv`

represents the typical value for parameters.

$Vc$ - Volume of Central Compartment (L)

$Vmax$- Maximum metabolic capacity (μg/min)

$Km$ - Michaelis- menten constant (μg/L)

$Kin$ - Rate of synthesis,Turnover rate (μg/min)

$Ω$ - Between Subject Variability

$σ$ - Residual error

param = (tvvc = 5.94952, tvvmax = 361.502, tvkm = 507.873 , tvkin = 14.9684, Ω = Diagonal([0.00,0.00,0.00,0.00]), σ²_prop = 0.05)

(tvvc = 5.94952, tvvmax = 361.502, tvkm = 507.873, tvkin = 14.9684, 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 = 0.05)

DosageRegimen (DR) = Three sets of rapid intravenous infusion followed by slow intravenous infusion as followed

IV bolus of 1669 μg (Time=0 min) followed by IV infusion of 1131.8 μg (Time= 0-30.1 min)

IV infusion of 1701 μg (Time= 0-30.1 min) followed by IV infusion of 1884.4 μg (Time= 125.2-154.3 min)

IV infusion of 1773 μg (Time= 260-261 min) followed by IV infusion of 6300 μg (Time= 260.1-290.1 min)

IVinfRapid = DosageRegimen([1669,1701,1733], time = [0,125,260], cmt = [1,1,1], duration = [0,1,1]) IVinfSlow = DosageRegimen([1131.8,1884.4,6300], time = [0,125.2,260.1], cmt = [1,1,1], duration = [30.1,29.1,30]) DR = DosageRegimen(IVinfRapid,IVinfSlow) sub1 = Subject(id = 1, events = DR)

Subject ID: 1 Events: 11

To simulate plasma concentration for single subject with the specific observation time points for a given dosage regimen 'DR'

Random.seed!(123) sim = simobs(pk_32, sub1, param, obstimes=0:0.01:450)

f, a, p = sim_plot(pk_32, [sim], observations = :cp, color = :redsblues, linewidth = 4, axis = (xlabel = "Time (min)", ylabel = "PK32 Concentrations (μg/L)", xticks = 0:50:450, )) axislegend(a) f