# PharmPK Discussion - Apparent volume of distribution of a drug eliminated only by

PharmPK Discussion List Archive Index page
• On 6 Aug 1997 at 11:13:40, "Pardue, Roseline" (Roseline.Pardue.aaa.solvay.com) sent the message
`Recently, I have come across a situation involving nonlinear clearanceof a drug in which the volume of distribution is not well defined.  Anyclarification will be greatly appreciated.The rate of elimination for a drug eliminated by only onecapacity-limited process is given by:dCp/dt = VmaxCp	  Km + Cpor dXe/dt = Vmax.V       Cp	      Km + CpIt is apparent from this relationship that the Cls of a drug isdependent on V.  The question then is: What is the definition of V ?  Isit the volume of distribution in the central compartment, volume ofdistribution during the terminal phase or some other combination ofterms especially if multicompartment processess are involved ?`
Back to the Top

• On 11 Aug 1997 at 13:54:48, Nick Holford (n.holford.at.auckland.ac.nz) sent the message
`> 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 centralcompartment volume. Most people who have used this kind of model inPK have preferred to define Vmax in units of mass/time rather thanconc/time as you have done.If you define X as the amt of drug in the centralcompartment and Vmax in mass/time units then:dX               Vmax x Cp---  = (RateIn - ----------- )dt                Km  +  Cpthen define Cp as X/V you can write:dCp               Vmax x Cp---  = (RateIn - ----------- )/Vdt                Km  +  CpIn this case it is obvious that V must refer to the central compartmentvolume because the DE is describing the central compartment rates.--Nick Holford, Dept Pharmacology & Clinical PharmacologyUniversity of Auckland, Private Bag 92019, Auckland, New Zealandemail:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html`
Back to the Top

• On 11 Aug 1997 at 13:58:30, "Aldo Rescigno" (resci001.-a-.maroon.tc.umn.edu) sent the message
`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, TurnoverTime, and Volume of Distribution" published by Pharmacological Research,Volume35, pages 189-193, 1997. If you want to discuss it further, please write me atresci001.aaa.maroon.tc.umn.edu.`
Back to the Top

• On 13 Aug 1997 at 10:03:43, "Robert D. Phair, Ph.D." (rphair.-a-.ix.netcom.com) sent the message
`In reply to Roseline Pardue-Your post reminds me of a productive debate that I had with Nick Holford ina thread that is still available on the BIS Computational Biology Forum athttp://www.BioInformaticsServices.com/rphair/bis/resources/forum.The thread is called " Compartmental model parameterisation" and dealsprimarily with the relative merits of Clearances and rate constants forcharacterization of PK systems. You might find it informative. I know Ilearned a lot from Nick in the course of that discussion.To answer your question, though, appears to require only that you thinkabout the source of the V in your equation. You start with dCp/dt on theleft hand side,  where Cp is the plasma concentration of the drug. You setthis 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 clearanswer to your question by being precise in your definitions. One way toapproach this is to recognize that mass is conserved, so Vp(dCp/dt) elimination flux (units of , say, umole/hour), where Vp is the plasmavolume. The elimination clearance, Cle, is then the ratio of this flux tothe plasma concentration:Cle = (elimination flux)/CpYour post implies that the left hand side of your second equationrepresents 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 plasmavolume.Regards,Bob----------Robert D. Phair, Ph.D. rphair.-at-.bioinformaticsservices.comBioInformatics Services  http://www.bioinformaticsservices.comPartnering and Outsourcing for Computational Biology`
Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Apparent volume of distribution of a drug eliminated only by" as the subject

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)