Tumor growth inhibition model
Exploring the model
[LONGITUDINAL]
input={K, KDE, KPQ, KQPP, LAMBDAP, GAMMA, DELTAQP}
PK:
depot(target=C)
EQUATION:
PT_0=5
Q_0 = 40
PSTAR = PT+Q+QP
ddt_C = -KDE*C
ddt_PT = LAMBDAP*PT*(1-PSTAR/K) + KQPP*QP - KPQ*PT - GAMMA*KDE*PT*C
ddt_Q = KPQ*PT - GAMMA*KDE*Q*C
ddt_QP = GAMMA*KDE*Q*C - KQPP*QP - DELTAQP*QP
#-------------------------------------------------------------------------
# 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
#-------------------------------------------------------------------------
shinyUI(fluidPage(
titlePanel(
list(HTML('<p style="color:#4C0B5F; font-size:24px">Tumor growth inhibition model</p>
<p style="color:#4C0B5F; font-size:18px">Exploring the model</p>' )),
windowTitle="tumor growth I"),
navbarPage("", selected="Plot", id="nav", inverse="FALSE",
title="",
tabPanel("Plot",
tabsetPanel( id="tabs", type="pills",
tabPanel("dosage"),
tabPanel("parameters"),
tabPanel("output")
),
fluidRow(
column(3,
br(), br(),
conditionalPanel(condition="input.tabs=='dosage'",
sliderInput("tfd", "time of first dose:", value=0, min=-50, max = 50, step=5),
sliderInput("nd", "number of doses:", value=6, min=0, max = 20, step=1, animate=TRUE),
sliderInput("ii", "interdose interval:", value = 15, min = 1, max = 20, step=1),
sliderInput("amt", "amount:", value = 1, min = 0, max = 5, step=0.2),
br()
),
conditionalPanel(condition="input.tabs=='parameters'",
sliderInput("GAMMA", "GAMMA:", value = 1, min = 0, max = 4, step=0.1),
sliderInput("K", "K:", value = 100, min = 0, max = 200, step=5),
sliderInput("KDE", "KDE:", value = 0.3, min = 0, max = 1, step=0.05),
sliderInput("LAMBDAP", "LAMBDAP:", value = 0.12, min = 0, max = 0.5, step=0.025) ,
sliderInput("DELTAQP", "DELTAQP:", value = 0.01, min = 0, max = 0.05, step=0.0025),
sliderInput("KPQ", "KPQ:", value = 0.025, min = 0, max = 0.1, step=0.005),
sliderInput("KQPP", "KQPP:", value = 0.004, min = 0, max = 0.01, step=0.0005),
br()
),
conditionalPanel(condition="input.tabs=='output'",
checkboxInput("PSTAR", "PSTAR", TRUE),
checkboxInput("PT", "PT", FALSE),
checkboxInput("Q", "Q", FALSE),
checkboxInput("QP", "QP", FALSE),
checkboxInput("legend", "legend", TRUE),
br(),
sliderInput("range", "time range", min = -100, max = 500, value = c(-50,200), step=10),
sliderInput("ngp", "grid size", min = 101, max = 1001, value = 501, step=100),
br()
)
),
column(9,
plotOutput("plot", height="500px"))
)),
tabPanel("Table", tableOutput("table")),
navbarMenu("Codes",
tabPanel("Mlxtran", pre(includeText("tgi_model.txt"))),
tabPanel("ui.R", pre(includeText("ui.R"))),
tabPanel("server.R", pre(includeText("server.R"))
)
),
tabPanel("ReadMe", withMathJax(), includeMarkdown("readMe.Rmd")),
tabPanel("About", includeMarkdown("../../about/about.Rmd"))
)
))
#-------------------------------------------------------------------------
# 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 30th, 2015
#-------------------------------------------------------------------------
library(mlxR)
shinyServer(function(input, output) {
r <- reactive({
param.value=c(input$K,input$KDE,input$KPQ,input$KQPP,input$LAMBDAP,input$GAMMA,input$DELTAQP)
t.value=seq(input$range[1],input$range[2],length.out=input$ngp)
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$amt)
}else{
adm <- list(time=t1, amount=0)
}
f <- list(name=c('PSTAR','PT','Q','QP'),time=t.value)
p <- list(name=c('K','KDE','KPQ','KQPP','LAMBDAP','GAMMA','DELTAQP'),
value=param.value)
res <- simulx( model = 'tgi_model.txt',
treatment = adm,
parameter = p,
output = f)
return(res)
})
txt <- reactive({
ttt <- paste0("
library(mlxR)
param.value=c(",input$K,",",input$KDE,",",input$KPQ,",",input$KQPP,",",input$LAMBDAP,",",input$GAMMA,",",input$DELTAQP,")
t.value=seq(",input$range[1],",",input$range[2],",length.out=",input$ngp,")
t1=",input$tfd,"
t2=",input$ii*(input$nd-1)+input$tfd,"
if (t2>=t1){
t.dose=seq(t1,t2,by=input$ii)
adm <- list(time=t.dose, amount=input$amt)
}else{
adm <- list(time=t1, amount=0)
}
f <- list(name=c('PSTAR','PT','Q','QP'),time=t.value)
p <- list(name=c('K','KDE','KPQ','KQPP','LAMBDAP','GAMMA','DELTAQP'),
value=param.value)
res <- simulx( model = 'tgi_model.txt',
treatment = adm,
parameter = p,
output = f)
")
return(ttt)
})
output$plot <- renderPlot({
r=r()
# r <- r[[input$output]]
# j<-which(names(r)==input$output)
# names(r)[j] <- "f"
sz <- 0.75
pl=ggplotmlx()
if (input$PSTAR==TRUE)
pl=pl + geom_line(data=r$PSTAR, aes(x=time, y=PSTAR, colour="a"), size=sz)
if (input$PT==TRUE)
pl=pl + geom_line(data=r$PT, aes(x=time, y=PT, colour="b"), size=sz)
if (input$Q==TRUE)
pl=pl + geom_line(data=r$Q, aes(x=time, y=Q, colour="c"), size=sz)
if (input$QP==TRUE)
pl=pl + geom_line(data=r$QP, aes(x=time, y=QP, colour="d"), size=sz)
pl <- pl + scale_colour_manual(
values=c("a"="#F8766D", "b"="#00BFC4", "c"="#B79F00",
"d"="#F564E3"),
labels=c("a"="PSTAR", "b"="PT", "c"="Q",
"d"="QP"))
if (input$legend==TRUE){
pl <- pl + theme(legend.position=c(.05, 0.95), legend.justification=c(0,1), legend.title=element_blank())
}else{
pl <- pl + theme(legend.position="none")
}
print(pl)
})
output$table <- renderTable({
r <- r()
d <- merge(r$PSTAR,r$PT)
d <- merge(d,r$Q)
d <- merge(d,r$QP)
return(d)
})
})
Objective
Visualize and explore the Tumor Growth Inhibition (TGI) model proposed by RIbba et al. by modifying the treatment and the parameters values.
\[ \newcommand{\deriv}[1]{\dot{#1}(t)} \def\iid{\mathop{\sim}_{\rm i.i.d.}} \]
Mathematical model
ODEs:
\[ \begin{aligned} \deriv{C} &= - k_{de} C(t) \\ \deriv{P_T} &= \lambda P_T(t)(1- P^{\star}(t)/K) + k_{QPP}Q_P(t) -k_{PQ} P_T(t) -\gamma \, k_{de} P_T(t)C(t) \\ \deriv{Q} &= k_{PK} P_T(t) -\gamma \, k_{de} Q(t)C(t) \\ \deriv{Q_P} &= \gamma \, k_{de} Q(t)C(t) - k_{QPP} Q_P(t) -\delta_{QP} Q_P(t) \end{aligned} \]
- \(C\): concentration of the compartment that receives the doses.
- \(P_T\): proliferative cells
- \(Q\): quescient cells
- \(Q_P\): damaged quescient cells
- \(P^{\star} = P_T(t) + Q(t) + Q_P(t)\): observed tumor size
Initial conditions:
\[ \begin{aligned} C(0) &= Q_P(0) = 0 \\ P_T(0) &= p_{T0} \\ Q(0) &= q_0 \end{aligned} \]
Playing with the shiny app
1. Define the dosage regimen in the tab input:
- time of first dose,
- number of doses,
- interdose interval,
- amount per dose.
2. select the parameter values in the tab parameters:
3. define the outputs in the tab outputs :
select the output to display,
select the time range where the prediction is computed,
select the number of time points of the grid where the prediction is computed.
Reference
Ribba, B., Kaloshi, G., Peyre, M., Ricard, D., Calvez, V., Tod, M., … & Ducray, F. (2012). A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy. Clinical Cancer Research, 18(18), 5071-5080.
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