A one-compartment model for oral administration with linear elimination is used in this application.
Let \(A_d(t)\) and \(A_c(t)\) be, respectively, the amounts in the depot and central compartments.
We display the concentration in the central compartment \(C_c(t) = A_c(t)/V\), where \(V=1\) in this example.
Several absorption processes can be selected:
1. first order
\[ \begin{aligned} \dot{A_d}(t) & = -ka \, A_d(t) \\ \dot{A_c}(t) & = ka \, A_d(t) - k \, A_c(t) \end{aligned} \]
2. zero order
\[ \begin{aligned} \dot{A_d}(t) & = - R_0 \\ \dot{A_c}(t) & = R_0 - k \, A_c(t) \end{aligned} \] where \(R_0 = D/Tk0\) if \(A_d(t)>0\) and \(R_0 = 0\) otherwise.
3. alpha order
\[ \begin{aligned} \dot{A_d}(t) & = - R_\alpha \\ \dot{A_c}(t) & = R_\alpha - k \, A_c(t) \end{aligned} \] where \(R_\alpha = ka \, A_d(t)^\alpha\) if \(A_d(t)>0\) and \(R_\alpha = 0\) otherwise.
You can check that an \(\alpha\) order absorption process is
- a zero order absorption process if \(\alpha=0\)
- a first order absorption process if \(\alpha=1\)
4. sequential zero order - first order
A fraction \(F_0\) of the dose \(D\) is first absorbed with a zero-order absorption process during a time \(Tk0\), then, the remaining fraction \(1-F_0\) is absorbed with a first order absorption order process with rate constant \(\alpha\).
5. simultaneous zero order - first order
A fraction \(F_0\) of the dose \(D\) is absorbed with a zero-order absorption process during a time \(Tk0\). The remaining fraction \(1-F_0\) is simultaneously absorbed with a first order absorption order process with rate constant \(\alpha\).
6. saturated (Michaelis Menten)
\[ \begin{aligned} \dot{A_d}(t) & = - R_m \\ \dot{A_c}(t) & = R_m - k \, A_c(t) \end{aligned} \] where \(R_m(t) = V_m \, A_d(t)/(K_m + A_d(t))\).
Use the menu
Plotto plot the PK profiles and modify either the PK parameters or the dosage regimen (default is a single dose at time 0)Use the menu
Tableto create and save a table with the concentration values.Use the menu
Codesto display and download the Mlxtran code, the ui.R and server.R files used for this application
Plot
Table
absorptionModel.txt
[LONGITUDINAL]
input = {ka, Tk0, alpha, F0, Vm, Km, V, k}
PK:
; first order
compartment(cmt=1, amount=A1)
oral(cmt=1, ka)
elimination(cmt=1, k)
; zero order
tk0 = max(Tk0, 0.0001)
compartment(cmt=2, amount=A2)
oral(cmt=2, Tk0=tk0)
elimination(cmt=2, k)
; alpha order (ODE)
depot(target=Ad3)
; sequential zero order - first order
compartment(cmt=4, amount=A4)
oral(cmt=4, Tk0=tk0, p=F0)
oral(cmt=4, ka, Tlag=tk0, p=1-F0)
elimination(cmt=4, k)
; mixed zero order - first order
compartment(cmt=5, amount=A5)
oral(cmt=5, Tk0=tk0, p=F0)
oral(cmt=5, ka, p=1-F0)
elimination(cmt=5, k)
; saturated absorption (ODE)
depot(target=Ad6)
EQUATION:
if Ad3>0
R3 = ka*(Ad3^alpha)
else
R3 = 0
end
ddt_Ad3 = -R3
ddt_A3 = R3 - k*A3
R6 = Vm*Ad6/(Km+Ad6)
ddt_Ad6 = -R6
ddt_A6 = R6 - k*A6
C1=A1/V
C2=A2/V
C3=A3/V
C4=A4/V
C5=A5/V
C6=A6/V
ui.R
#-------------------------------------------------------------------------
# This application is governed by the CeCILL-B license.
# You can use, modify and/ or redistribute this code under the terms
# of the CeCILL license: http://www.cecill.info/index.en.html
#
# Marc Lavielle, Inria Saclay
# April 29th, 2015
#-------------------------------------------------------------------------
library(shinydashboard)
sidebar <- dashboardSidebar(
hr(),
sidebarMenu(id="tabs",
menuItem("Plot", tabName="plot", icon=icon("line-chart"), selected=TRUE),
menuItem("Table", tabName = "table", icon=icon("table")),
menuItem("Codes", icon = icon("file-text-o"),
menuSubItem("Mlxtran", tabName = "pkmodel", icon = icon("angle-right")),
menuSubItem("ui.R", tabName = "ui", icon = icon("angle-right")),
menuSubItem("server.R", tabName = "server", icon = icon("angle-right"))
),
menuItem("ReadMe", tabName = "readme", icon=icon("mortar-board")),
menuItem("About", tabName = "about", icon = icon("question"))
),
hr(),
conditionalPanel("input.tabs=='plot'",
fluidRow(
column(1),
column(10,
checkboxInput("first", "First order", TRUE),
checkboxInput("zero", "Zero order", TRUE),
checkboxInput("al", "alpha order", FALSE),
checkboxInput("sequential", "Sequential (0-1)", FALSE),
checkboxInput("mixed", "Simultaneous (0-1)", FALSE),
checkboxInput("saturated", "Saturated", FALSE),
checkboxInput("legend", "Legend", TRUE)
)
)
)
)
body <- dashboardBody(
tabItems(
tabItem(tabName = "readme",
withMathJax(),
includeMarkdown("readMe.Rmd")
),
tabItem(tabName = "plot",
fluidRow(
column(width = 4,
tabBox( width = NULL,
tabPanel(h5("parameters"),
conditionalPanel(condition="input.sequential=='1' | input.mixed=='1' | input.first=='1' | input.alpha=='1' ",
sliderInput("ka", "ka:", value = 0.5, min = 0.1, max = 3, step=0.1)
),
conditionalPanel(condition="input.sequential=='1' | input.mixed=='1' | input.zero=='1' ",
sliderInput("Tk0", "Tk0:", value = 5, min = 0, max = 10, step=0.5)
),
conditionalPanel(condition="input.al=='1'",
sliderInput("alpha", "alpha:", value = 0.5, min = 0, max = 2, step=0.1)
),
conditionalPanel(condition="input.sequential=='1' | input.mixed=='1' ",
sliderInput("F0", "F0:", value = 0.5, min = 0, max = 1, step=0.1)
),
conditionalPanel(condition="input.saturated=='1'",
sliderInput("Vm", "Vm:", value = 0.9, min = 0, max = 2, step=0.1),
sliderInput("Km", "Km:", value = 0.2, min = 0, max = 1, step=0.1)
),
sliderInput("k", "k:", value = 0.1, min = 0, max = 2, step=0.05)
),
tabPanel(h5("dosage"),
sliderInput("tfd", "Time of first dose:", value=0, min=0, max = 20, step=1),
sliderInput("nd", "Number of doses:", value=1, min=0, max = 10, step=1),
sliderInput("ii", "Interdose interval:", value = 9, min = 0.5, max = 15, step=0.5),
sliderInput("amt", "Amount:", value = 5, min = 0, max = 20, step=1)
)
)),
column(width = 8,
box( width = NULL, plotOutput("plot",height="500px"), collapsible = TRUE,
title = "Plot", status = "primary", solidHeader = TRUE)
))
),
tabItem(tabName = "table",
box( width = NULL, status = "primary", solidHeader = TRUE, title="Table",
downloadButton('downloadTable', 'Download'),
br(),br(),
tableOutput("table")
)
),
tabItem(tabName = "pkmodel",
box( width = NULL, status = "primary", solidHeader = TRUE, title="absorptionModel.txt",
downloadButton('downloadData1', 'Download'),
br(),br(),
pre(includeText("absorptionModel.txt"))
)
),
tabItem(tabName = "ui",
box( width = NULL, status = "primary", solidHeader = TRUE, title="ui.R",
downloadButton('downloadData2', 'Download'),
br(),br(),
pre(includeText("ui.R"))
)
),
tabItem(tabName = "server",
box( width = NULL, status = "primary", solidHeader = TRUE, title="server.R",
downloadButton('downloadData3', 'Download'),
br(),br(),
pre(includeText("server.R"))
)
),
tabItem(tabName = "about",
includeMarkdown("../../about/about.Rmd")
)
)
)
dashboardPage(
dashboardHeader(title = "Absorption processes"),
sidebar,
body
)
server.R
#-------------------------------------------------------------------------
# This application is governed by the CeCILL-B license.
# You can use, modify and/ or redistribute this code under the terms
# of the CeCILL license: http://www.cecill.info/index.en.html
#
# Marc Lavielle, Inria Saclay
# April 29th, 2015
#-------------------------------------------------------------------------
library(shinydashboard)
library(mlxR)
shinyServer(function(input, output){
r <- reactive({
p <- c(ka=input$ka, Tk0=input$Tk0, alpha=input$alpha,
F0=input$F0, Vm=input$Vm, Km=input$Km, V=1, k=input$k)
t.value=seq(0,24,length.out=241)
out <- list(name=c("C1", "C2", "C3", "C4", "C5", "C6"), time=t.value)
t1=input$tfd
t2=input$ii*(input$nd-1)+t1
if (t2>=t1){
t.dose=seq(t1,t2,by=input$ii)
adm <- list(time=t.dose, amount=input$amt)
}else{
adm <- list(time=t1, amount=0)
}
#----------------------------------------------------
res <- simulx(model = "absorptionModel.txt",
parameter = p,
output = out,
treatment = adm)
#----------------------------------------------------
return(res)
})
gg_color_hue <- function(n) {
hues = seq(15, 375, length=n+1)
hcl(h=hues, l=65, c=100)[1:n]}
vc=gg_color_hue(6)[c(1,4,2,3,6,5)]
names(vc)=letters[1:6]
lc <- c("first order", "zero order", "alpha order",
"sequential 0-1", "simultaneous 0-1", "saturated")
names(vc)=letters[1:6]
output$plot <- renderPlot({
r <- r()
npl <- 0
vdisp <- rep(FALSE,6)
pl=ggplotmlx()
if (input$first==TRUE){
pl=pl + geom_line(data=r$C1, aes(x=time, y=C1, colour="a"), size=1)
vdisp[1] <- TRUE}
if (input$zero==TRUE){
pl=pl + geom_line(data=r$C2, aes(x=time, y=C2, colour="b"), size=1)
vdisp[2] <- TRUE}
if (input$al==TRUE){
pl=pl + geom_line(data=r$C3, aes(x=time, y=C3, colour="c"), size=1)
vdisp[3] <- TRUE}
if (input$sequential==TRUE){
pl=pl + geom_line(data=r$C4, aes(x=time, y=C4, colour="d"), size=1)
vdisp[4] <- TRUE}
if (input$mixed==TRUE){
pl=pl + geom_line(data=r$C5, aes(x=time, y=C5, colour="e"), size=1)
vdisp[5] <- TRUE}
if (input$saturated==TRUE){
pl=pl + geom_line(data=r$C6, aes(x=time, y=C6, colour="f"), size=1)
vdisp[6] <- TRUE}
pl <- pl + ylab("Amount = Concentration (V=1)")
pl <- pl + scale_colour_manual(values=vc[vdisp], labels=lc[vdisp])
if (input$legend==TRUE){
pl <- pl + theme(legend.position=c(.65, 0.95), legend.justification=c(0,1), legend.title=element_blank())
}else{
pl <- pl + theme(legend.position="none")
}
if (input$nd==1)
pl <- pl +ylim(c(0,input$amt))
print(pl)
})
rr <- reactive({
r <- r()
rr <- r[[1]]
for (k in (2:6))
rr <- merge(rr, r[[k]])
return(rr)
})
output$table <- renderTable({
rr()
})
output$downloadTable <- downloadHandler(
filename = "table.csv",
content = function(file) {
write.csv(rr(), file)
}
)
})
This application is governed by the CeCILL-B license.
You can use, modify and/or redistribute these codes under the terms of the
CeCILL license.
This Shiny application requires the mlxR package.
Marc Lavielle
Inria Saclay, Popix team
April 29th, 2015