PharmPK Discussion - AUCt, AUCinfinity

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• On 7 Apr 1997 at 22:04:00, Bill McNaughton (hossack.at.nbnet.nb.ca) sent the message
`A QUESTION FOR ANYONE WITH THE PATIENCE FOR A NEWCOMER TO PK/PD. IN ASTANDARD STUDY COMPARING BLOOD LEVELS OF A BRAND NAME AND GENERIC DRUG,IS A POSSIBLE TO GET VALUES FOR AUC infinity THAT ARE LESS THAN THEVALUES OBTAINED FOR AUCt?`
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• On 9 Apr 1997 at 12:47:11, "David Nix" (nix.-at-.Pharmacy.Arizona.EDU) sent the message
`No, it is not possible to have values of AUC(0-inf) < AUC(0-t).     AUC(0-inf) = AUC(0-t*) + C*/ke where C* is the last measuredconcentration at time (t*) and ke is the terminal elimination rateconstant.  My guess is that ke was entered as a negative value.  keis determined from the slope of the terminal linear portion of theLN (Conc) vs time curve.  The slope will always be negative sinceconcentrations are declining.  It is sometimes an art in determiningwhich points to use in determining the terminal slope.  The terminalelimination rate constant term implies decreasing concentrations andtherefore the negative is not required (ke is always positve,-(slope))David`
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• On 9 Apr 1997 at 12:47:30, Bob Phair (rphair.aaa.ix.netcom.com) sent the message
`The partial area under the curve (AUCt) is the area from t=0 to t=t.AUCinfinity is the area from t=0 to t=infinity. Since there can be nonegative contributions to the AUC at any time after t (or before t, forthat matter) AUCinfinity is always greater than AUCt.Of course, one might make the mistake of plotting the data on linear,instead of semi-log, paper, and then extrapolating a fast (apparentlyterminal) exponential through the horizontal axis and thus appear tostart accumulating negative contributions to AUCinfinity. It should beclear however that the real blood concentration can never be a negativenumber, so the AUC can only increase as the integration is carried outtoward infinity.Regards,Bob--Robert D. Phair, Ph.D.  rphair.aaa.ix.netcom.comBioInformatics Services  http://www.webcom.com/rphairPartnering and Outsourcing for Computational Biology`
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• On 9 Apr 1997 at 12:47:45, Steve Bramer (STEVEB.aaa.OTSUKA.OAPI.COM) sent the message
`It is possible and is also incorrect.  Check your rules for determining halflife and extrapolation to infinity.`
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• On 9 Apr 1997 at 12:48:37, "Aziz Karim" (AAKARI.at.msn.com) sent the message
`Dear Bill:You have raised a very interesting point. I too have come across occasionswhen AUC(inf) values were lower than AUC(t). We need to clearly define theAUC(t) values. Is this the AUC up to the last validated measurable plasmaconcentration [C(last), I call  the corresponding AUC, AUC(last)] or is it theAUC up to the last point which is below the limit of quantitation [consideredzero in AUC calculation] which I call AUC(all).It would be highly unusual to have AUC(last) larger than AUC(inf). However, itis possible for AUC(all) to be larger than AUC(inf). This occurs when timespan is large between the last validated plasma concentration in thedisposition phase and the next sample with concentration below quantitation.The above is difficult to explain in words. You will get a better appreciationif you draw a figure. I would be happy to fax you one.As a note, I don't particularly like to use AUC(inf) for drugs with short halflives (T1/2 = < 12 hours). The reason for this is one single concentration[C(last)] in the beta phase has a high influence on the AUC(inf) values sinceAUC(inf) = AUC(last) + [C(last)/(0.693/T1/2)]. It is simply better todetermine AUC(last) with most sensitive assay and taking blood samples for atime period exceeding 4*T1/2.AUC(inf) is more appropriate for drugs with long T1/2 (>24 hours) providedthat the ratio of AUC(last)/AUC(inf) exceeds) 0.80.I hope the above will stimulate discussion on AUC determinations since thisparameter is critical in bioavailability assessment.Regards,Aziz Karimaakari.-at-.msn.com`
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• On 10 Apr 1997 at 13:31:57, Allen.E.Cato.-a-.abbott.com sent the message
`Bill,While it is true that the actual AUC(inf) cannot be less than the actualAUC(t), it is possible to calculate an AUC(t) value that is larger than thecalculated AUC(inf) value depending on the sampling scheme relative to thehalf-life, as Dr. Karim discussed.As a follow-up to his note on the potential inaccuracies of the calculation ofAUC(inf) for compounds with short half-lives, if variability of the lowconcentrations is an issue, AUC(inf) could be extrapolated from a predictedC(last) at the time of the last measurable concentration based on the half-life(beta) regression.  With this method, the data used to estimate half-life wouldbe weighted equally in the extrapolation to infinity.  This method assumes thatthere are adequate data to estimate the half-life relatively accurately.Jo Catoallen.cato.-at-.abbott.com`
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• On 10 Apr 1997 at 13:34:03, Brinda Koneru (BRINDAK.-a-.OTSUKA.OAPI.COM) sent the message
`AUCt  cannot exceed AUCinfinity since AUCinf = AUCt + C(t)/?z.However, it is possible to get AUCinfinity < AUC(0-24)  or AUC(0-48),AUCall, etc.If your sampling points in the terminal phase are far apart and your lastsample is BQL (and your program treats BQL samples as zero), then ?zmay be larger than the slope connecting the last 2 points which are C(t)and 0.  This will cause AUCinf to be less than AUC0-24 because in thecalculation of AUCinf, zero is not used.Brinda K TammaraOtsuka America Pharm. Inc.RockvilleMD-20850`
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• On 10 Apr 1997 at 13:34:26, "Faruq H Noormohamed" (f.noormohamed.-at-.s1.cxwms.ac.uk) sent the message
`As indicated by several replies generated from the inquiry as to whetherone can get values of AUC(0-inf) which are less than AUC(0-t), the answeris that in theory NO.  However in practice you may come across data whichsuggests that this is the case.  Apart from the obvious error incalculating AUCs.  I assume you have used the correct formula forcalculating the area of trapezoids, or as David Nix pointed out you mayhave used -ke rather than the absolute value of ke to calculate AUC(t-inf).that is if you have devised you own routine for calculating the parameters. Alternatively the problem may reside in the software package you are usingin that some software may calculate AUC(0-inf) either using the exponentialfitting parameters or alternatively use the expected concentration at time't-last', derived from the terminal rate constant as opposed to observedvalue whilst AUC(0-t) have been calculated using observed values.  Bitcomplicated but I hope it is clear.Faruq H NoormohamedDepartment of TherapeuticsChelsea and Westminster Hospital369 Fulham RoadLONDONSW10 9NHTel +44 (0)181 746 8141Fax +44 (0)181 746 8887email f.noormohamed.at.cxwms.ac.uk`
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