Dear R users:
 I encountered difficulties in michaelis-menten equation. I found
that when I use right model definiens, I got wrong Km vlaue,
and I got right Km value when i use wrong model definiens.
The value of Vd and Vmax are correct in these two models.

#-----right model definiens--------
PKindex<-data.frame(time=c(0,1,2,4,6,8,10,12,16,20,24),
    conc=c(8.57,8.30,8.01,7.44,6.88,6.32,5.76,5.20,4.08,2.98,1.89))
mm.model <- function(time, y, parms) {
    dCpdt <- -(parms["Vm"]/parms["Vd"])*y[1]/(parms["Km"]+y[1])
    list(dCpdt)}
Dose<-300
modfun <- function(time,Vm,Km,Vd) {
    out <- lsoda(Dose/Vd,time,mm.model,parms=c(Vm=Vm,Km=Km,Vd=Vd),
        rtol=1e-8,atol=1e-8)
      out[,2] }
objfun <- function(par) {
 out <- modfun(PKindex$time,par[1],par[2],par[3])
 sum((PKindex$conc-out)^2) }
fit <- optim(c(10,1,80),objfun, method="Nelder-Mead)
print(fit$par)
[1] 10.0390733 0.1341544 34.9891829 #--Km=0.1341544,wrong value--


#-----wrong model definiens--------
#-----Km should not divided by Vd--
PKindex<-data.frame(time=c(0,1,2,4,6,8,10,12,16,20,24),
    conc=c(8.57,8.30,8.01,7.44,6.88,6.32,5.76,5.20,4.08,2.98,1.89))
mm.model <- function(time, y, parms) {
 dCpdt <- -(parms["Vm"]/parms["Vd"])*y[1]/(parms["Km"]/parms["Vd"]+y[1])
 list(dCpdt)}
Dose<-300
modfun <- function(time,Vm,Km,Vd) {
out <- lsoda(Dose/Vd,time,mm.model,parms=c(Vm=Vm,Km=Km,Vd=Vd),
       rtol=1e-8,atol=1e-8)
    out[,2]
}
objfun <- function(par) {
  out <- modfun(PKindex$time,par[1],par[2],par[3])
  sum((PKindex$conc-out)^2)}
fit <- optim(c(10,1,80),objfun, method="Nelder-Mead)
print(fit$par)
[1] 10.038821 4.690267 34.989239 #--Km=4.690267,right value--

What did I do wrong, and how to fix it?
Any suggestions would be greatly appreciated.
Thanks in advance!!

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