- On 6 Aug 1997 at 11:13:40, "Pardue, Roseline" (Roseline.Pardue.aaa.solvay.com) sent the message

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Recently, I have come across a situation involving nonlinear clearance

of a drug in which the volume of distribution is not well defined. Any

clarification will be greatly appreciated.

The rate of elimination for a drug eliminated by only one

capacity-limited process is given by:

dCp/dt = VmaxCp

Km + Cp

or dXe/dt = Vmax.V

Cp Km + Cp

It is apparent from this relationship that the Cls of a drug is

dependent on V. The question then is: What is the definition of V ? Is

it the volume of distribution in the central compartment, volume of

distribution during the terminal phase or some other combination of

terms especially if multicompartment processess are involved ? - On 11 Aug 1997 at 13:54:48, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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> The rate of elimination for a drug eliminated by only one

> capacity-limited process is given by:

>

> dCp/dt = VmaxCp

> Km + Cp

>

> or dXe/dt = Vmax.V

> Cp Km + Cp

>

> It is apparent from this relationship that the Cls of a drug is

> dependent on V.

If you choose this parameterisation the volume you want is the central

compartment volume. Most people who have used this kind of model in

PK have preferred to define Vmax in units of mass/time rather than

conc/time as you have done.

If you define X as the amt of drug in the central

compartment and Vmax in mass/time units then:

dX Vmax x Cp

--- = (RateIn - ----------- )

dt Km + Cp

then define Cp as X/V you can write:

dCp Vmax x Cp

--- = (RateIn - ----------- )/V

dt Km + Cp

In this case it is obvious that V must refer to the central compartment

volume because the DE is describing the central compartment rates.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html - On 11 Aug 1997 at 13:58:30, "Aldo Rescigno" (resci001.-a-.maroon.tc.umn.edu) sent the message

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Responding to the message of

from PharmPK.at.pharm.cpb.uokhsc.edu:

>

> PharmPK - Discussions about Pharmacokinetics

> Pharmacodynamics and related topics

>

> Recently, I have come across a situation involving nonlinear clearance

> of a drug in which the volume of distribution is not well defined. Any

> clarification will be greatly appreciated.

I have tried to clarify this problem on a recent paper: "Clearance, Turnover

Time, and Volume of Distribution" published by Pharmacological Research,

Volume

35, pages 189-193, 1997. If you want to discuss it further, please write me at

resci001.aaa.maroon.tc.umn.edu. - On 13 Aug 1997 at 10:03:43, "Robert D. Phair, Ph.D." (rphair.-a-.ix.netcom.com) sent the message

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In reply to Roseline Pardue-

Your post reminds me of a productive debate that I had with Nick Holford in

a thread that is still available on the BIS Computational Biology Forum at

http://www.BioInformaticsServices.com/rphair/bis/resources/forum.

The thread is called " Compartmental model parameterisation" and deals

primarily with the relative merits of Clearances and rate constants for

characterization of PK systems. You might find it informative. I know I

learned a lot from Nick in the course of that discussion.

To answer your question, though, appears to require only that you think

about the source of the V in your equation. You start with dCp/dt on the

left hand side, where Cp is the plasma concentration of the drug. You set

this equal to the Michaelis-Menten capacity-limited elimination,

VmCp/(Km+Cp).

You do not give a definition for Xe, and I think you might find a clear

answer to your question by being precise in your definitions. One way to

approach this is to recognize that mass is conserved, so Vp(dCp/dt) elimination flux (units of , say, umole/hour), where Vp is the plasma

volume. The elimination clearance, Cle, is then the ratio of this flux to

the plasma concentration:

Cle = (elimination flux)/Cp

Your post implies that the left hand side of your second equation

represents the Cle, so

(dXe/dt)/Cp = Cle = (elimination flux)/Cp = Vp(dCp/dt)/Cp = VpVm/(Km+Cp)

Consequently, the V in your equations appears to be equal to Vp, the plasma

volume.

Regards,

Bob

----------

Robert D. Phair, Ph.D. rphair.-at-.bioinformaticsservices.com

BioInformatics Services http://www.bioinformaticsservices.com

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