Chapter 19 of Rowland and Tozer (Clinical pharmacokinetics and pharmacodynamics, 4th edition) has distribution kinetics. I am examining problem 3. It is fairly easy, especially since essentially all formulas are on the same page under ‘key relationships’. The only difficulty is that the formulas are symmetrical in λ₁, c₁ and λ₂, c₂ and they are exchanged between chains. For this I forced λ₁>λ₂. In addition, I do not really believe concentrations in the 4000 range are as accurately measured as those in the 5 range (in the period 1/2 hour to 1 hour, the decrease is about 80 units per minute). The measurement error is now proportional to concentration.

Data and model

C19SP3 <- data.frame(
    time=c(0.5,1,1.5,2,3,4,5,8,12,16,24,36,48),
    conc=c(4211,1793,808,405,168,122,101,88,67,51,30,13,6))

library(R2jags)
datain <- list(
    time=C19SP3$time,
    lconc=log(C19SP3$conc),
    n=nrow(C19SP3),
    dose=30*1000)

model1 <- function() {
  tau <- 1/pow(sigma,2)
  sigma ~ dunif(0,100)
  llambda1 ~dlnorm(.4,.1)
  cc1 ~ dlnorm(1,.01)
  llambda2 ~dlnorm(.4,.1)
  cc2 ~ dlnorm(1,.01)
  choice <- llambda1>llambda2
  c1 <- choice*cc1+(1-choice)*cc2
  c2 <- choice*cc2+(1-choice)*cc1
  lambda1 <- choice*llambda1+(1-choice)*llambda2
  lambda2 <- choice*llambda2+(1-choice)*llambda1
  
  for (i in 1:n) {
    pred[i] <- log(c1*exp(-lambda1*time[i]) +c2*exp(-lambda2*time[i]))
    lconc[i] ~ dnorm(pred[i],tau)
  }
  V1 <- dose/(c1+c2)
  AUC <- c1/lambda1+c2/lambda2
  CL <- dose/AUC
  V <- CL/lambda2
  Vss <- dose*(c1/pow(lambda1,2)+c2/pow(lambda2,2))/pow(AUC,2)
  }

parameters <- c('c1','c2','lambda1','lambda2' ,
   ‘V1′,’CL’,’Vss’,’AUC’,’V’)
inits <- function() 
  list(
      sigma=rnorm(1,1,.1),
      cc1=9000,
      cc2=150)

jagsfit <- jags(datain, model=model1, 
    inits=inits, 
    parameters=parameters,progress.bar=”gui”,
    n.chains=4,n.iter=14000,n.burnin=5000,n.thin=2)

Results

Plot

Previous posts in this series:

Simple Pharmacokinetics with Jags