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Dear all,
I wanted to have the wise insight of members of the list interested in
physiological modelling, concerning an assumption used in a
publication by Frederique Fenneteau et al. (Assessing drug
distribution in tissues expressing P-glycoprotein through
physiologically based pharmacokinetic modelling: model structure and
parameters determination, Theoretical Biology and Medical Modelling
2009, 6:2).
In this interesting paper, the authors describe a methodology to
include tissular transport in PBPK models, illustrated with the case
of the P-gp efflux. Including such transport processes in PBPK models
is not an easy task, mainly because of the in vitro in vivo scaling
which is not easy. But another issue is the concentration to be used
when applying the scaled intrinsic clearance (or Vmax/Km). There has
been a recent post reviving the role of the unbound fraction in the
renal filtration and the liver metabolism which could be applied also
in the transport issues, but if we consider the classical assumption
(i.e. only the unbound fraction is transported), we have for the
efflux processes a relationship of this type
rate_efflux = scaled_Clint_efflux * Cunbound_tissue
with Cunbound_tissue = C_tissue * fu_tissue
The problem being to estimate the fu_tissue. Using the mechanistic
equations developed for the Kp, the authors have described a method to
estimate the fu_tissue. The idea is interesting, but I'd like to have
your opinion on an assumption made : during the calculation, it is
assumed that the concentration unbound in the extracellular water
(Cu,ew) is in equilibrium with the concentration unbound in the plasma
(Cu,p) (in their model, the membrane is located between the vascular
and the extravascular space). If this assumption is by definition true
for a well-stirred model, I feel that it is not the case for a
membrane-limited model with transporters. If it was the case, I think
the simplest way to estimate fu_tissue would be to rearrange the
classical relationship Kp = fu_tissue / fu_blood.
So my question is : is the assumption Cu,ew = Cu,p is valid in the
case of a membrane-limited model with the membrane located between the
blood space and the extravascular space (same question with Cu,ew =
Cu,iw if the membrane is the cell membrane)?
I would answer no : taking the theoretical case of a compound with no
passive permeability and both an influx clearance and an efflux
clearance, I would say that the Cu,ew = a * Cu,p with a = CLinflux /
CLefflux, allowing for example an accumulation if the influx is
greater than the efflux).
If someone here has comments on this point, I would be happy to hear
them. I'm also interested if some people have an idea to modify the
mechanistic equations used for the Kp estimation to estimate the
fu_tissue in such case (and also in the case where the membrane
limitation is between the extracellular and the intracellular space).
Best regards
Cedric Vinson
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