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Re: Modelling intracellular and plasma data

From: Leonid Gibiansky <LGibiansky>
Date: Tue, 09 Dec 2008 10:21:17 -0500

I would start by modeling plasma concentrations separately. Then, when
you know the model that gives you good description, you can treat
predicted concentrations in plasma as a driving force of your other
system, that is, intracellular compartment. You can work in $DES terms,
then you do not need to introduce any mass transfer from your main
system to the second one.

There are many ways to model delayed absorption. You may try transit
compartment model, or effect-compartment type model. Once you figured
out how to model is, you can combine two parts together.

DADT(1) = -K*A(1) ; plasma C1=A(1)/V1

DADT(2) = K2*A(1)-K23*A(2) ;"transit"(can be duplicated to increase delay)
DADT(3) = K23*A(3)-K30*A(3) ; intracellular C3=A(3)/V3


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Rob ter Heine wrote:
> Dear all,
> I'm trying to fit concentrations of a drug simultaneously measured in plasma as well as intracellularly (in peripheral blood mononuclear cells). I observe a high accumulation in cells, but with a delayed absorption. I'm trying to fit the intracellular data dependent of the plasma pharmacokinetics. The volume of distribution of the cellular compartment can be considered negligeble compared to the volume of distribution in plasma (no distribution to a second compartment can be observed in the plasma pharmacokinetics. However, cellular accumulation depends on plasma concentrations.
> I'm fitting the data with a first order oral absorption and elimination, basically it can be summarized as:
> $Model (DOSE) (CENTRAL) (CELL)
> I have a rich sampling dataset of 11 individuals with at each timepoint an observation in the cellular and plasma compartment. I have tried several approaches for modelling cellular accumulation. I have tried fixing the cellular volume to a very small volume.
> $PK
> k12=theta(1)
> v1=theta(2)
> cl=theta(3)
> k20=cl/v1
> v3=0.0001
> k23=theta(4)
> k32=theta(5)
> This didn't work. K23 was estimated to be very small and k32 was estimated to be very large, giving the same fit as estimating an accumulation ratio, which is not a good fit, since a delayed absorption in the cellular compartment was observed. There is some mass transport going on between the central and cellular compartments, that I do not want. My cellular pharmacokinetics depend on the plasmapharmacokinetics, but I don't want my cellular pharmacokinetics to influence my plasma pharmacokinetics, since this effect is likely negligible. Does anyone have a smart idea on how to code this?
> Sincerely,
> Rob ter Heine
> _______________________________
> Rob ter Heine, MSc, PharmD
> Department of Pharmacology, Slotervaart Hospital
> Amsterdam, The Netherlands
> E: rob.terheine
> T: +31-20-5124737
Received on Tue Dec 09 2008 - 10:21:17 EST

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