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) #----------------------------------
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: \[ \begin{aligned} \log(V) & \sim {\cal N}(\log(V_{\rm pop}), \omega^2_V) \\ \log(k) & \sim {\cal N}(\log(k_{\rm pop}), \omega^2_k) \end{aligned} \]
By default a 80% prediction interval decomposed in 8 bands is used. Then, the 10th, 20th, 30th, …, 70th and 90th percentiles are displayed.