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The following message was posted to: PharmPK Dear colleagues:
As I was looking at my slides for discussing V with students, I realized
that I was not sure about the source of one form.
It can be argued that distribution volume is related to protein binding
(1) V = Vplasma + Vevw * (fu_plasma/ fu_tissue) where Vevw is
extravascular water (from Gillette, 1971)
I understand the result V above to be the steady state distribution
volume. However, I am unable to argue too strongly for this definition,
as I am unable to convince myself that the relationship above can be
shown to be equal to
(2) Vss = Dose* AUMC/(AUC^2) or, more likley, to
(3) Vss = Vc * (1 + k21/k12)
Can anyone point me toward a better identification of Eqn 1 or a means
to show identity with Eqn 3? Or can one just accept that Vss be defined
in separate, but individually satisfying manners?
Paul R. Hutson, Pharm.D.
UW School of Pharmacy
777 Highland Avenue
Madison WI 53705-2222
[Equation 1 is physiologically based, equation 2 is a non-compartmental
version and equation 3 is the compartmental version. It would be
interesting to make a numerical comparison between the three for some
compounds. I don't think a mathematical conversion between these is readily available -
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The following message was posted to: PharmPK
As you know all V terms in PK have no physiologic basis; they are just a
way to convert amount in the body or plasma/blood to a measured
concentration. Gillette and Oie/Tozer, who also published a similar
equation with Vtissue, have no way to measure fu_tissue because they
don't know where the tissue is. As soon as they measure in some tissue
then you must add another tissue to the equation to take account of
other parts of the body in which you are not measuring. You can
determine Vss from Eqs. 2 and 3 because they are defined in terms of the
site where concentrations are measured. You can never determine V by
the Gillette equation. You can only go backwards and determine a
hypothetical fu_tissue once you have the other measured parameters. This
is what was done in the phenytoin examples you see in textbooks, but it
should not be taught because it can't be measured; your always just
looking at the ratio of Vtissue/fu_tissue or a fu_tissue from a
calculated Vss in Gillette's case.
Leslie Z. Benet, Ph.D.
Department of Bioengineering & Therapeutic Sciences
Schools of Pharmacy & Medicine
University of California San Francisco
533 Parnassus Avenue, Room U-68
San Francisco, CA 94143-0912
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Certainly as Les said Volume of distribution in PK have no physiologic basis and should
simply be considered as a scaler. When we discuss this concept in our workshop we start
with the Dominguez's definition then go to its expansion (e.g. Gillette and Sawada) and
move to methods for prediction of partition coefficient values.
One can show Eq 1 leads to Eq2 for the systems with central (plasma) drug elimination;
hence knowing such assumptions for students is very important. I found Berezhkovoskiy's
(2004, 2006) papers very useful where he has discussed many of these issues in detail.
Dominguez R (1934) Studies of renal excretion of clearance: II. Volume of distribution.
Proc Soc Exp Biol Med 31:1146-1150.
Gillette JR (1971) Factors affecting drug metabolism. Ann N Y Acad Sci 179:43-66.
Sawada Y, Hanano M, Sugiyama Y, Harashima H and Iga T (1984) Prediction of the volumes of
distribution of basic drugs in humans based on data from animals. J Pharmacokinet Biopharm
Berezhkovskiy LM (2004) Volume of distribution at steady state for a linear
pharmacokinetic system with peripheral elimination. J Pharm Sci 93:1628-1640.
Berezhkovskiy LM (2006) The connection between the steady state (V(ss)) and terminal
(V(beta)) volumes of distribution in linear pharmacokinetics and the general proof that
V(beta) >/= V(ss). J Pharm Sci.
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This does not apply only to Vss but other PK parameters can have two different type of
equations as well. They can be estimated from observed data i.e. concentration time
profiles and can be also predicted from physiological determinants. For example, clearance
can be related to intrinsic clearance, protein binding and blood flow (CL = Q*fuClint / Q
+ fuClint), but it can also be equated to Dose/AUC, absorption parameters (ka, F) can
also be related to properties such as permeability, solubility and pKa of the drug and can
be estimated from the PK profiles.
The difference between the 2 sets of equations relates to the difference between
estimation and prediction. Pharmacy students are most likely to use equations on
estimating PK parameters from given Pk profiles, the reason why these equations are more
comon in university textbooks. Nevertheless, understanding the physiological components is
also important. The importance in using physiologically based equations for PK parameters
is that they allow prediction of change in PK parameters as a function of physiological
variables e.g. change in fu, metabolic capacity, .... and as function of drug
physicochemical properties when comparing different drug molecules. These changes can not
be inferred from equations e.g. CL = Dose/AUC = ke*V, ....etc.
Kind Regards, Youssef
Youssef Hijazi, PhD. PharmD, member ACCP
Associate Director Pharmacokinetics
81477 Munich, Germany
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