How to fit multiple parameters to a differential equation in R?

问题

With a dataset like this

time    C
0.1 2.6
0.25    4.817
0.5 6.596
0.75    6.471
1   6.049
1.5 5.314
2   4.611
2.5 4.5
3   4.392
4   4.013
5   3.698
6   3.505
8   3.382
12  2.844
14  2.383
24  1.287

I want to fit this data to a model, which is defined as below

twocpt <- function(t, Cc, parms){
with(as.list(parms),{
   dC0 <- -k01*C0
   dCc <- k01*C0 + k21*Cp -(k12+ke)*Cc
   dCp <- k12*Cc - k21*Cp
   list(dCc)
   })
   }

I took the reference in this page (http://www.inside-r.org/packages/cran/FME/docs/modCost), and developed the following code:

#two compartment model, oral dosing
require(ggplot2)
require(FME)
require(XLConnect)

#Read Data from xlsx file, draw a scatter plot of the plasma-concentration profile
conc <- readWorksheetFromFile("E:/R/Book1.xlsx", sheet=1, header=TRUE)
pprofile <- ggplot(conc, aes(time, C))
pprofile <- pprofile + scale_x_continuous("Time (hr)")+scale_y_continuous("Concentration (ng/mL)")
(pprofile <- pprofile + geom_point()+geom_line())

#Create a matrix of the data frame.
concm <- as.matrix(conc)

#Define the parameters in the current simulation
k01 <- 1
k12 <- 10
k21 <- 0.5
ke <- 4


# wrap them up in the parms
parms <- c(k01=k01, k12=k12, k21=k21, ke=ke)

#Define the differential function
twocpt <- function(t, Cc, parms){
with(as.list(parms),{
   dC0 <- -k01*C0
   dCc <- k01*C0 + k21*Cp -(k12+ke)*Cc
   dCp <- k12*Cc - k21*Cp
   list(dCc)
   })
   }

#Define Cost function
Cost <- function(P) {
parms["k01"] <- P[1]
parms["k12"] <- P[2]
parms["k21"] <- P[3]
parms["ke"] <- P[4]


time <- conc[,1]
out <- ode(c(C=0), time, twocpt, parms)
return(modCost(out, concm))
}

Fit <- modFit(p=c(k01=10, k12=0.1, k21=0.4, ke=2), f=Cost)

summary(Fit)

However, I got the following warning message:

illegal input detected before taking any integration steps - see written message

Can anybody please tell me where the problem is? Or how to do it quickly? Thanks.

来源：https://stackoverflow.com/questions/15730793/how-to-fit-multiple-parameters-to-a-differential-equation-in-r

标签

curve-fitting

differential-equations

data-fitting

model-fitting