Tumor growth inhibition model
Comparing 2 dosage regimens
[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
#-------------------------------------------------------------------------
library(mlxR)
shinyUI(fluidPage(
titlePanel(
list(HTML('<p style="color:#4C0B5F; font-size:24px">Tumor growth inhibition model</p>
<p style="color:#4C0B5F; font-size:18px">Comparing 2 dosage regimens</p>' )),
windowTitle="tumor growth II"),
navbarPage("", selected="Plot", id="nav", inverse="FALSE",
tabPanel("Plot",
tabsetPanel( id="tabs", type="pills",
tabPanel("regimen 1"),
tabPanel("regimen 2"),
tabPanel("parameters"),
tabPanel("output")
),
fluidRow(
column(3,
br(), br(),
conditionalPanel(condition="input.tabs=='regimen 1'",
sliderInput("nd1", "Number of doses:", value=6, min=0, max = 20, step=1),
sliderInput("ii1", "Interdose interval:", value = 12, min = 1, max = 20, step=1),
sliderInput("amt1", "Amount:", value = 1, min = 0, max = 5, step=0.25),
br()
),
conditionalPanel(condition="input.tabs=='regimen 2'",
sliderInput("nd2", "Number of doses:", value=6, min=0, max = 20, step=1),
sliderInput("ii2", "Interdose interval:", value = 4, min = 1, max = 20, step=1),
sliderInput("amt2", "Amount:", value = 1, min = 0, max = 5, step=0.25),
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'",
radioButtons("output","",c("PSTAR" = "PSTAR","PT" = "PT","Q" = "Q","QP" = "QP")),
br(),
sliderInput("range", "time range", min = -100, max = 500, value = c(-50,200), step=10),
br(),
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)
t11=0
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)
}else{
adm1 <- list(time=t11, amount=0, type=1)
}
t21=0
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)
}else{
adm2 <- list(time=t21, amount=0, type=2)
}
g <- list(list(treatment=adm1),list(treatment=adm2))
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',
group = g,
parameter = p,
output = f)
res
})
output$plot <- renderPlot({
r=r()
r <- r[[input$output]]
j<-which(names(r)==input$output)
names(r)[j] <- "f"
pl=ggplotmlx(data=r, aes(x=time, y=f, colour=id)) + geom_line(size=0.75) +
theme(legend.position=c(.1, .9))
print(pl)
})
output$table <- renderTable({
r <- r()
d <- merge(r$PSTAR,r$PT)
d <- merge(d,r$Q)
d <- merge(d,r$QP)
return(d)
})
})
Objective
Compare the effect of two different treatments using the Tumor Growth Inhibition (TGI) model proposed by RIbba et al.
\[ \newcommand{\deriv}[1]{\dot{#1}(t)} \def\iid{\mathop{\sim}_{\rm i.i.d.}} \]
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 two dosage regimens to compare in the tabs regimen 1 and regimen 2:
- 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.
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