# PharmPK Discussion - F equation with same dose and different subjects

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• On 5 Dec 2003 at 09:01:32, chernandez.at.grupovita.com sent the message
`The following message was posted to: PharmPKDear All,As you fully know F (absolute bioavailabity) calculations depend of theuseof different/same doses and participation of the same/differentvolunteers:1. Different subjects and doses:F= [AUCpo/AUCiv]*[Doseiv/(weight*Cliv)/Dosepo/(weight*Clpo)](Spanish reference: Florez Ed. Farmacologia Humana, 1997)2. The same subjects and different doses:F= (AUCpo/AUCiv)*(Doseiv/Dosepo)(Br J Clin Pharmacol 1999; 47: 483-91)3. The same subjects and doses:F= (AUCpo/AUCiv)(Drug Res 1986; 36: 1278-83)   However,  a  scenario  with  different subjects and the same doses isnot   gathered by the equations mentioned above. Could you kindly confirmme if   the next equation would be accceptable for this case?                F= [AUCpo/AUCiv]*[(weight*Clpo)/(weight*Cliv)]Thanks in advanceCándido Hernández-López, M.D.,Ph.D.Clinical Pharmacology SectionLaboratorios VITASant Joan Despí, Barcelona (SPAIN)www.grupovita.com[When did using different subjects become acceptable? - db]`
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• On 6 Dec 2003 at 10:47:35, "Henri Merdjan" (hmerdjan.aaa.wanadoo.fr) sent the message
`The following message was posted to: PharmPKDear Candido,Let me suggest that we go back to the common basis for all theseequations.First of all, there is a direct proportionality between the rate ofchangein the amount of drug present in the body (dA/dt) and the drugconcentrationC(t). The proportionality constant is the drug clearance CL.dA/dt = CL*C(t)Integrating both sides givesAmount = integral (CL*C(t))If, in addition, CL is constant (more specifically: CL is independent oftime andconcentration, i.e. PK is linear), then you can take the CL term out oftheprevious equation and you get the following equation applicable tolinear kinetics, and linear kinetics ONLY:Amount = CL*integral(C(t)) = CL*AUCYou may wish to rewrite it for po administrationF.Dosepo = CLpo*AUCpoand for iv administration as wellDoseiv = CLiv*AUCivRe-arranging the latter 2 equations yieldsF = (AUCpo/AUCiv)*(CLpo/CLiv)*(Doseiv/Dosepo)The dose ratio obviously cancels out when using the same doses iv andpo.However, the rationale for cancelling out the CL ratio is that youassume CLto be the same iv and po. In other words, this is areasonable/acceptableassumption if(and only if) you dose the same subject iv and po.My understanding of using the terms weight*CL is an extra assumptionthat CLis constant on a per kg basis. Nothing to deal with different subjectsofdifferentbody weight.I hope this answers your questions.Kind regards,HenriHenri MerdjanConsultant for the Life Science IndustriesPK and PK/PD specialistNewFreelance sarlParis, France+33 (0)6 23 97 67 34hmerdjan.at.wanadoo.fr`
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• On 9 Dec 2003 at 11:24:37, "vgcasabo" (vicente.casabo.-at-.uv.es) sent the message
`Hi Candido >   However,  a  scenario  with  different subjects and the same dosesis > > not >   gathered by the equations mentioned above. Could you kindly confirmme if >   the next equation would be accceptable for this case? >                F= [AUCpo/AUCiv]*[(weight*Clpo)/(weight*Cliv)]The above equation  is not acceptable because, you can not calculateClpo independently of F in subjects in absence of IV information . For example if you calculate:Clpo= Dpo/AUCpoAndCliv=Div/AUCiv The equation  (the one you mentioned)   always yields  value 1.In the case that  CL changes  for  subjects, and you can assume thatVolume of distribution  does not  change (or remains constant)You can use terminal slope lamdaLamda=Cl/Vd                F= [AUCpo/AUCiv]*[lamdapo*Vd/(lamdaiv*Vd)]Vd cancels, and                              F=(AUCpo/AUCiv)*(lamdapo/lamdaiv)This can be acceptable if variability of Ln(AUC*lamda) is least thanvariability of Ln(AUC), obtained from ANOVA test`
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• On 9 Dec 2003 at 17:22:30, "J.H.Proost" (J.H.Proost.-at-.farm.rug.nl) sent the message
`The following message was posted to: PharmPKDear Dr. Casabo,Your remark with respect to the first equation is correct. On the otherhand, the equation by itself is fully correct. The problem is indeedthat you cannot calculate or estimate CLpo, so the equations is notapplicable.>  For example if you calculate: Clpo= Dpo/AUCpoYes, but one should never calculate CLpo in this way. This is probablydone quite often, but it is definitely incorrect. The correct equationis:CLpo / Fpo = Dpo / AUCpoYou also proposed the following equation:> F=(AUCpo/AUCiv)*(lamdapo/lamdaiv)Since variability in clearance is usually larger than that in volume ofdistribution, this approach may be suited, provided that lambdapo andlambdaiv can be estimated accurately. In many cases the lambda valuesare obtained from the last, say, 4 data points. Such estimates are notaccurate, and the 'lambda correction' may introduce large errors, notunlikely larger than the error introduced by a true difference inclearance between the two administrations.I am not aware that this equation is used in practice. Any furthercomments?Best regards,Johannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.-a-.farm.rug.nl`
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• On 10 Dec 2003 at 09:47:09, chernandez.-a-.grupovita.com sent the message
`The following message was posted to: PharmPKDear David, Henri, Vicente, and Johannes,Many thanks for your useful explanations and clarifications.The scenario described: Different subjects with the same doses testedis acommon situation in initial clinical drug development. The use ofequationsto suggest an hypothetical F value seems also reasonable at this point.Your focus in clear limitations (or nonsense) of F equations use whendifferent subjects are implicated makes me to think that no-solution ispossible in this common context and only the design of clinical trialusingsame subjects, and preferably same doses, can solve the question of F.However, even in this case I find additional questions: At time toselectan intravenous dose regimen to compare, Would be the same approach todecide a bolus dosing or a short-term or long-term constant-rateinfusion?(Please, I remark that usually in an initial clinical drug developmentphase the dose regimen is still to be determined)Having the answer to this question I believe we could have an idea ofthebest procedure to know the F value of a compound.Thanks in advanceCándido Hernández-López, M.D.,Ph.D.Clinical Pharmacology SectionLaboratorios VITASant Joan Despí, Barcelona (SPAIN)www.grupovita.com`
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• On 11 Dec 2003 at 13:26:53, "Durisova Maria" (exfamadu.-a-.savba.sk) sent the message
`The following message was posted to: PharmPKDear All,     For those who are interested in the fundamental theory behingthe equation called in this discussion "the F equation" I wouldrecomend our study: Dedík, L., Durisová , M.: CXT-MAIN:a  software  package  for  determination  of  the analytical  formof  the  pharmacokinetic  system weighting function,Comput. Meth. Programs  Biomed., 51, 1996, 183-192.The full text of this study is available online via Science Direct.On the basis of the equations presented in the Appendix of the givenstudy,the correctformulae can be derived for "the F equation" in the event of:1) equal single drug doses given intravenously and orally;2) nonequal single drug doses given intravenously and orally;3) an intravenous drug dose given in an infusion (at a constant and/ortimevarying rate)and a single oral drug dose.Regards,Maria Durisova PhD, DrSc (Math/Phys)Head of Department of PharmacokineticsInstitute of  Experimental  PharmacologySlovak Academy of Sciences84104 BratislavaSlovakia`
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