Combination of oral and iv administrations
[LONGITUDINAL]
input = {F, ka, V, Cl}
PK:
depot(type=1, target=Ad, p=F)
depot(type=2, target=Ac)
EQUATION:
k = Cl/V
ddt_Ad = -ka*Ad
ddt_Ac = ka*Ad - k*Ac
Cc = Ac/V
shinyUI(fluidPage(
titlePanel(
list(HTML('<p style="color:#4C0B5F; font-size:24px" fontsize=14>Combination of oral and iv administrations</p>' )),
windowTitle="oral and iv"),
tabsetPanel(
tabPanel("Plot",
fluidRow(
column(3,
tabsetPanel(
tabPanel("oral",
sliderInput("tfd1", "time of first dose:", value=18, min=0, max = 20, step=1),
sliderInput("nd1", "number of doses:", value=5, min=0, max = 20, step=1),
sliderInput("ii1", "interdose interval:", value = 9, min = 0.5, max = 15, step=0.5),
sliderInput("amt1", "amount:", value = 5, min = 0, max = 20, step=1),
br(),
br()
),
tabPanel("iv",
sliderInput("tfd2", "time of first dose:", value=0, min=0, max = 20, step=1),
sliderInput("nd2", "number of doses:", value=3, min=0, max = 10, step=1),
sliderInput("ii2", "interdose interval:", value = 12, min = 0.5, max = 15, step=0.5),
sliderInput("tinf2", "infusion time:", value = 1, min = 0, max = 10, step=0.5),
sliderInput("amt2", "amount:", value = 3, min = 0, max = 20, step=1),
br(),
br()
),
tabPanel("parameters",
sliderInput("F", "bioavailability F:", value = 0.7, min = 0, max = 1, step=0.05),
br(),
sliderInput("ka", "absorption rate constant ka:", value = 0.5, min = 0, max = 4, step=0.1),
br(),
sliderInput("V", "volume V:", value = 10, min = 1, max = 20, step=1),
br(),
sliderInput("Cl", "clearance Cl:", value = 2, min = 0, max = 4, step=0.1),
br(),
br()
),
tabPanel("outputs",
selectInput("output","",c("concentration (central)" = "Cc",
"amount (central)" = "Ac", "amount (depot)" = "Ad")),
br(),
sliderInput("range", "time range", min = -10, max = 200, value = c(-5,100), step=5),
br(),
sliderInput("ngp", "grid size", min = 10, max = 1000, value = 300, step=10),
br(),
sliderInput("lsize", "line width", min = 0, max = 2, value = 0.75, step=0.25),
br()
)
)),
column(9,
plotOutput("plot", height="500px"),
column(1),
column(5,
radioButtons("log", "", c("linear scale" = FALSE,"log scale" = TRUE), inline=TRUE))
)
)),
tabPanel("Table", tableOutput("table")),
tabPanel("Mlxtran", pre(includeText("pk2_model.txt"))),
tabPanel("Simulx", verbatimTextOutput("RFile")),
tabPanel("ui.R", pre(includeText("ui.R"))),
tabPanel("server.R", pre(includeText("server.R"))),
tabPanel("ReadMe", withMathJax(), includeMarkdown("ReadMe.Rmd"))
)
))
# source("../../initMlxR.R")
library(mlxR)
simulx.text <- ("
parameter = p,
output = Cc)
print(ggplot(data=res$Cc, aes(x=time, y=Cc)) + geom_line() +
xlab('time (h)') + ylab('concentration (mg/L)'))
")
shinyServer(function(input, output) {
ggplotmlx <- function(...) {
ggplot(...) + theme_bw() + theme(plot.background=element_rect(fill=rgb(1,1,1)))}
r <- reactive({
if (input$tinf2>input$ii2)
stop("The infusion time should not exceed the interdose interval")
param.value=c(input$F,input$ka,input$V,input$Cl)
t.value=seq(input$range[1],input$range[2],length.out=input$ngp)
t11=input$tfd1
t12=input$ii1*(input$nd1-1)+t11
if (t12>=t11){
t1.dose=seq(t11,t12,by=input$ii1)
adm1 <- list(time=t1.dose, amount=input$amt1, type=1)
}else{
adm1 <- list(time=t11, amount=0, type=1)
}
t21=input$tfd2
t22=input$ii2*(input$nd2-1)+t21
if (t22>=t21){
t2.dose=seq(t21,t22,by=input$ii2)
adm2 <- list(time=t2.dose, amount=input$amt2, rate=input$amt2/input$tinf2, type=2)
}else{
adm2 <- list(time=t21, amount=0, type=2)
}
f <- list(name=c('Ac','Ad','Cc'),time=t.value)
p <- list(name=c('F','ka','V','Cl'), value=param.value)
res <- simulx( model = 'pk2_model.txt',
treatment = list(adm1,adm2),
parameter = p,
output = f)
if (input$nd1==0){
a1.text <- ''
} else if(input$nd1==1){
a1.text <- paste0('adm1 <- list(type=1, amount=',input$amt1,', time=',input$tfd1,')\n')
} else{
t1=input$tfd1
t2=input$ii1*(input$nd1-1)+t1
a1.text <- paste0('adm1 <- list(type=1, amount=',input$amt1,
', time=seq(',t1,', ',t2,', by=',input$ii1,'))\n')
}
if (input$nd2==0){
a2.text <- ''
}else{
if(input$nd2==1){
a2.text <- paste0('adm2 <- list(type=2, amount=',input$amt2,', time=',input$tfd2)
} else{
t1=input$tfd2
t2=input$ii2*(input$nd2-1)+t1
a2.text <- paste0('adm2 <- list(type=2, amount=',input$amt2,
', time=seq(',t1,', ',t2,', by=',input$ii2,')')
}
if (input$tinf2>0){
a2.text <- paste0(a2.text,', tinf=',input$tinf2,')\n')
}else{
a2.text <- paste0(a2.text,')\n')
}
}
a.text <- paste0(a1.text,a2.text)
m.text <- "res <- simulx(model = 'pk2_model.txt',\n "
if (input$nd1>0){
if (input$nd2>0){
m.text <- paste0(m.text,'treatment = list(adm1, adm2),')
}else{
m.text <- paste0(m.text,'treatment = adm1,')
}
}else{
if (input$nd2>0){
m.text <- paste0(m.text,'treatment = adm2,')
}
}
p.text <- paste0('p <- c(F=',input$F,', ka=',input$ka,', V=',input$V,', Cl=',input$Cl,')')
t.text <- paste0('t <- seq(',input$range[1],', ',input$range[2],
', length=',length.out=input$ngp,')')
simulx.text <- paste0(a.text,p.text,'\n',t.text,'\n',m.text,simulx.text)
out <- list(res,simulx.text)
return(out)
})
output$plot <- renderPlot({
r=r()[[1]]
r <- r[[input$output]]
j<-which(names(r)==input$output)
names(r)[j] <- "f"
pl <- ggplotmlx(data=r, aes(x=time, y=f)) + geom_line(size=input$lsize) +
ylab(input$output)
if (input$log==TRUE)
pl <- pl + scale_y_log10()
print(pl)
})
output$table <- renderTable({r()[[1]]$Cc})
output$RFile <- renderText(r()[[2]])
})
Combination of repeated oral and intravenous administrations
Let \(A_d\) and \(A_c\) be, respectively, the amounts in the depot compartment (gut) and the central compartment (bloodtsream). Kinetics of \(A_d\) and \(A_c\) are described by the following system of ODEs \[ \begin{aligned} \dot{A_d}(t) & = - ka \, A_d(t) \\ \dot{A_c}(t) & = ka \, A_d(t) - k \, A_c(t) \end{aligned} \]
The concentration \(C_c\) in the central compartment is defined by \(\ \ C_c(t) = A_c(t)/V\)
- Define the dosage regimen for the intravenous (iv) administration in the tab iv:
time of first dose,
number of doses,
interdose interval,
infusion time,
amount.
- Define the dosage regimen for the oral administration in the tab oral:
time of first dose,
number of doses,
interdose interval,
amount.
- select the PK parameters in the tab parameters:
- \(F\), the bioavalabililty (a fraction between 0 and 1) ,
- \(ka\), the absorption rate constant,
- \(V\), the volume of the central compartment.
- \(k\), the elimination rate constant,
- define the outputs in the tab outputs :
- select the output to display: the amount \(A_d\) or \(A_c\), 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.
- set some settings in the tab settings: line width, linear or semi-log scale.