1. Population pharmacokinetic analysis of sorafenib in patients with solid tumours
Serge Guzy

2. The PK Model
The final PPK model was a one compartment model with additional components describing the observed absorption delay and underlying enterohepatic circulation(EHC).
The initial delay in quantifiable plasma concentrations was adequately described by the GI transit compartments absorption model. Four transit compartments, each of them receiving drug from the antecedent and releasing drug into the subsequent

3. The PK Model
transit compartment with a first order rate constant ka,accommodated the apparent lag time and a highly variable tmax. EHC was modelled with a semi- mechanistic model, where a fraction of drug from the central compartment (Fent) was hepatobiliary excreted (transferred) into a

4. The PK Model
gall bladder compartment with a first order rate kb, which, in turn, periodically emptied drug into the last GI transit compartment at a first order rate of kEhc. For modelling purposes, Fent was logit transformed, to constrain its value between 0 and 1, and to allow typical parameters to be estimated as a continuous function (–infinity to +infinity). The periodic drug release from the gall bladder compartment was regulated by the on-off switch ‘Ehc

5. The PK Model
associated with use of discontinuous functions such as step functions or lag times. t′ was the time of emptying. At times less than t′, the value of EHC was 0 and the gall bladder did not empty and at times greater than t′ the

6. The PK Model
value of EHC was 1 and the gall bladder emptied. The remaining fraction in the central compartment (1 – Fent), was eliminated with a first order rate constant of ke, reflecting hepatic metabolism and any irreversible loss including the biliary loss which was not recirculated; ke was parameterized in terms of apparent clearance (CL/F) and volume of distribution (V/F).

7. Structural Model

8. PML code for simulation: Structural parameters definition
mtt: The average time spent by sorafenib in travelling from the absorption compartments to the central compartment (i.e.mean absorption transit time
test(){
stparm(ktr=tvktr*exp(nktr))
fixef(tvktr=c(,2.53,))
ranef(diag(nktr)=c(0.1))
mtt = (ntr+1)/ktr
stparm(kehc=tvkehc*exp(nkehc))
fixef(tvkehc=c(,0.857,))
ranef(diag(nkehc)=c(0.1))

9. Fent
Fent is the fraction of dose undergoing enterohepatic recirculation
PML code: We need to constraint Fent between 0 and 1
fent=ilogit(fentlogit)
stparm(fentlogit=tvfent+nfent)
fixef(tvfent=c(,0.0542,))
ranef(diag(nfent)=c(0.1))

10. Number of transit compartments minus 1
ke=Cl/V
stparm(ntr=tvntr*exp(nntr))
fixef(tvntr=c(,4,))
ranef(diag(nntr)=c(0.1))

11. Dose input (the “graph” parameters are used only for initial estimates purposes), differential equations
Aagraph=Aa
ehcgraph=ehc
transit( Aa, mtt, ntr, max = 50, out = -Aa * ktr )
deriv(A4=-ktr*(A4-Aa)+ehc*kehc*agb)
deriv(acc=ktr*A4-fent*ke*acc-(1-fent)*Cl/V*acc)
deriv(agb=fent*ke*acc-ehc*kehc*agb)
agbgraph=agb
a4graph=A4
accgraph=acc

12. EHC on off
fcovariate(dosageinterval)
# we assume that all patient have the same and unique dosage interval
# we are off for tlags then on until next dose
sequence{ while(1)
{ehc=0
sleep(tlags)
ehc=1
sleep(dosageinterval-tlags)
ehc=0 }

13. Dose input dosepoint(Aa) C = acc / V error(CEps = 1)
observe(CObs = C *(1+ CEps))
stparm(V = tvV * exp(nV))
stparm(Cl = tvCl * exp(nCl))
fixef(tvV = c(, 213, ))
fixef(tvCl = c(, 8.13, ))
ranef(diag(nV, nCl) = c(0.1, 0.1)) }

14. Input template data set

15. mapping

16. Output data set