# PK model with inter individual variability

[LONGITUDINAL]
input = {V, k}

PK:
depot(target=Ac)

EQUATION:
ddt_Ac = -k*Ac
Cc=Ac/V

;-----------------------
[INDIVIDUAL]
input = {V_pop, k_pop, omega_V, omega_k}

DEFINITION:
V = {distribution=lognormal, reference=V_pop, sd=omega_V}
k = {distribution=lognormal, reference=k_pop, sd=omega_k}
source('prctilemlx.R')

adm <- list(time=1, amount=40)
Cc  <- list(name='Cc',time=seq(from=0, to=20, by=1))
p   <- list(name=c('V_pop','k_pop','omega_V','omega_k'), value=c(10,0.2,0.3,0.2))
g <- list(size=1000,level='individual')
res <- simulx(model='pk1b_model.txt', parameter=p, output=Cc, treatment=adm, group=g)

band.level=80
band.nb=8

qr <- prctilemlx(res\$Cc,band.level,band.nb)

#----------------------------------

#### PK model with inter individual variability (IIV)

The amount $$A_c$$ in the central compartment is solution of the ODE $$\ \ \dot{A_c}(t) = - k \, A_c(t)$$

The concentration $$C_c$$ in the central compartment is defined by $$\ \ C_c(t) = A_c(t)/V$$

$$V$$ and $$k$$ are both log-normally distributed: \begin{aligned} \log(V) & \sim {\cal N}(\log(V_{\rm pop}), \omega^2_V) \\ \log(k) & \sim {\cal N}(\log(k_{\rm pop}), \omega^2_k) \end{aligned}

• Define the dosage regimen in the tab iv: time of first dose, number of doses, interdose interval, infusion time, amount.

• select the PK parameters in the tab parameters:
• $$k_{\rm pop}$$, the population value of the elimination rate constant $$k$$,
• $$V_{\rm pop}$$, the population value of the volume $$V$$,
• $$\omega_k$$, the standard deviation of $$\log(k)$$,
• $$\omega_V$$, the standard deviation of $$\log(V)$$.

• define the outputs in the tab outputs :
• select the output to display: the amount $$A_c$$ or the concentration $$C_c$$,
• select the time range where the prediction is computed,
• select the number of time points of the grid where the prediction is computed.

• define the prediction distribution to display in the tab settings:
• select the level of the prediction interval (between 5% and 95%),
• select the number of bands which form this prediction interval
• the number of simulations used for estimating this prediction distribution.

By default a 80% prediction interval decomposed in 8 bands is used. Then, the 10th, 20th, 30th, …, 70th and 90th percentiles are displayed.