# PharmPK Discussion - Vss clarification

PharmPK Discussion List Archive Index page
• On 19 Sep 2011 at 15:57:27, Paul Hutson (bourne5321.aaa.gmail.com) sent the message
`The following message was posted to: PharmPK Dear colleagues:As I was looking at my slides for discussing V with students, I realizedthat I was not sure about the source of one form.It can be argued that distribution volume is related to protein bindingby:(1) V = Vplasma + Vevw * (fu_plasma/ fu_tissue)   where Vevw isextravascular water (from Gillette, 1971)I understand the result V above to be the steady state distributionvolume.  However, I am unable to argue too strongly for this definition,as I am unable to convince myself that the relationship above can beshown 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 meansto show identity with Eqn 3?  Or can one just accept that Vss be definedin separate, but individually satisfying manners?ThanksPaul--Paul R. Hutson, Pharm.D.Associate ProfessorUW School of Pharmacy777 Highland AvenueMadison WI 53705-2222[Equation 1 is physiologically based, equation 2 is a non-compartmentalversion and equation 3 is the compartmental version. It would beinteresting to make a numerical comparison between the three for somecompounds. I don't think a mathematical conversion between these is readily available -db]`
Back to the Top

• On 20 Sep 2011 at 02:14:56, "Benet, Leslie" (Leslie.Benet.aaa.ucsf.edu) sent the message
`The following message was posted to: PharmPKPaul/DavidAs you know all V terms in PK have no physiologic basis; they are just away to convert amount in the body or plasma/blood to a measuredconcentration.  Gillette and Oie/Tozer, who also published a similarequation with Vtissue, have no way to measure fu_tissue because theydon't know where the tissue is.  As soon as they measure in some tissuethen you must add another tissue to the equation to take account ofother parts of the body in which you are not measuring.  You candetermine Vss from Eqs. 2 and 3 because they are defined in terms of thesite where concentrations are measured.  You can never determine V bythe Gillette equation.  You can only go backwards and determine ahypothetical fu_tissue once you have the other measured parameters. Thisis what was done in the phenytoin examples you see in textbooks, but itshould not be taught because it can't be measured; your always justlooking at the ratio of Vtissue/fu_tissue or a fu_tissue from acalculated Vss in Gillette's case.LesLeslie Z. Benet, Ph.D.ProfessorDepartment of Bioengineering & Therapeutic SciencesSchools of Pharmacy & MedicineUniversity of California San Francisco533 Parnassus Avenue, Room U-68San Francisco, CA 94143-0912`
Back to the Top

• On 20 Sep 2011 at 07:17:27, Masoud Jamei (masoud.jamei.-a-.gmail.com) sent the message
`Hi PaulCertainly as Les said Volume of distribution in PK have no physiologic basis and shouldsimply be considered as a scaler. When we discuss this concept in our workshop we startwith the Dominguez's definition then go to its expansion (e.g. Gillette and Sawada) andmove 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 ofdistribution of basic drugs in humans based on data from animals. J Pharmacokinet Biopharm12:587-596.Berezhkovskiy LM (2004) Volume of distribution at steady state for a linearpharmacokinetic 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 thatV(beta) >/= V(ss). J Pharm Sci.RegardsMasoud`
Back to the Top

• On 23 Sep 2011 at 17:02:09, Youssef Hijazi (youssef.hijazi1.-a-.gmail.com) sent the message
`Dear Paul,This does not apply only to Vss but other PK parameters can have two different type ofequations as well. They can be estimated from observed data i.e. concentration timeprofiles and can be also predicted from physiological determinants. For example, clearancecan 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) canalso be related to properties such as permeability, solubility and pKa of the drug and canbe estimated from the PK profiles.The difference between the 2 sets of equations relates to the difference betweenestimation and prediction. Pharmacy students are most likely to use equations onestimating PK parameters from  given Pk profiles, the reason why these equations are morecomon in university textbooks. Nevertheless, understanding the physiological components isalso important. The importance in using physiologically based equations for PK parametersis that they allow prediction of change in PK parameters as a function of physiologicalvariables e.g. change in fu, metabolic capacity, .... and as function of drugphysicochemical properties when comparing different drug molecules. These changes can notbe inferred from equations e.g. CL = Dose/AUC  =  ke*V, ....etc.Kind Regards, YoussefYoussef Hijazi, PhD. PharmD, member ACCPAssociate Director PharmacokineticsMicromet AG81477 Munich, Germany`
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 "Vss clarification" as the subject Support PharmPK by using thelink to buy books etc.from Amazon.com

Copyright 1995-2011 David W. A. Bourne (david@boomer.org)